WO2010148411A1 - Method and apparatus for computer modeling hypertension - Google Patents

Method and apparatus for computer modeling hypertension Download PDF

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Publication number
WO2010148411A1
WO2010148411A1 PCT/US2010/039388 US2010039388W WO2010148411A1 WO 2010148411 A1 WO2010148411 A1 WO 2010148411A1 US 2010039388 W US2010039388 W US 2010039388W WO 2010148411 A1 WO2010148411 A1 WO 2010148411A1
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ang
raas
model
computer
representation
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PCT/US2010/039388
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French (fr)
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Jennifer Beh
Hector De Leon
Stuart Friedman
Manoj Rodrigo
Arthur Lo
Serguei Ermako
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Entelos, Inc.
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Publication of WO2010148411A1 publication Critical patent/WO2010148411A1/en

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    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H50/00—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics
    • G16H50/50—ICT specially adapted for medical diagnosis, medical simulation or medical data mining; ICT specially adapted for detecting, monitoring or modelling epidemics or pandemics for simulation or modelling of medical disorders
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16H—HEALTHCARE INFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR THE HANDLING OR PROCESSING OF MEDICAL OR HEALTHCARE DATA
    • G16H10/00—ICT specially adapted for the handling or processing of patient-related medical or healthcare data
    • G16H10/20—ICT specially adapted for the handling or processing of patient-related medical or healthcare data for electronic clinical trials or questionnaires

Definitions

  • the present invention relates generally to the field of computer simulation of hypertension and its associated disease risks, particularly, loss of kidney function, heart failure and stroke.
  • Hypertension the medical condition of elevated blood pressure
  • NHANES National Health and Nutrition Examination Survey
  • Ml myocardial infarction
  • PVD peripheral vascular disease
  • HF renal failure and heart failure
  • Other risk factors contributing to the complex etiology of hypertension include age, weight, race/ethnicity, genetic predisposition, diabetes and dietary sodium intake.
  • vasoconstrictors e.g., Angiotensin Il (Ang II) and endothelin
  • vasoconstrictors e.g., Angiotensin Il (Ang II) and endothelin
  • vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI2).
  • a variety of endogenous vasodilators including Ang (1-7), calcitonin gene-related peptide (CGRP), substance P and adrenomedullin, to name a few, have all been implicated in the development and maintenance of high blood pressure.
  • the hypertensinogenic mechanisms mediated by an increased SNS activity involve perturbed baroreflex and chemoreflex pathways at both central and peripheral levels. Indirect clinical evidence of the contribution of the sympathetic nervous system activity to hypertension is the lowering blood pressure effect of centrally acting sympatholytic agents (alpha-adrenergic antagonists).
  • Peripheral resistance is elevated in hypertension due to structural alterations. Remodeling of small arteries and arterioles contributes to the development and maintenance of high blood pressure and the ensuing organ damage. Elevated resistance in these arterioles is caused by an increased wall-to-lumen ratio. Additional pathophysiological mechanisms have been proposed to explain the increased resistance observed in hypertensive subjects including hyperuricemia, arterial stiffness, increased oxidative stress, vascular inflammation and endothelial dysfunction.
  • the Guyton/Coleman (GC) model does not include vascular remodeling and its effects on vascular geometry and hemodynamics as significant contributors to increased peripheral vascular resistance (Korner and Angus (1997) Vascular remodeling. Hypertension 29:1065-1066; and Korner, et al. (1992) Are cardiac and vascular "amplifiers" both necessary for the development of hypertension? Kidney lnt Suppl 37:S38- S44).
  • the model of hypertension described herein allows one to investigate different hypotheses about the role of angiotensin Il (Ang II) in the physiological function of the kidney, in addition to its recognized role in blood pressure regulation.
  • hypertensive patients receiving therapies that affect renin-angiotensin aldosterone system (RAAS) may experience delay in onset of glomerulosclerosis and interstitial tubulofibrosis.
  • RAAS renin-angiotensin aldosterone system
  • the model is a powerful tool for quickly testing multiple hypotheses about the physiology that can help answer a wide range of drug development questions.
  • it can be used to predict the expected changes in blood pressure for specific therapies in clinical trials, or to identify patient types that are most likely to benefit from anti-hypertensive therapies based on specific characteristics or biomarkers (and thus enrich a clinical trial). It can be used to test mechanistic hypotheses that are infeasible or impractical to test clinically, or to test the impact of known or hypothesized drug characteristics (e.g. localization in the kidney, ability to access specific receptors) on end-organ protection, possibly providing support for drug differentiation claims.
  • drug characteristics e.g. localization in the kidney, ability to access specific receptors
  • the current disclosure provides the first model to integrate systemic RAAS, renal RAAS, renal function and blood pressure regulation into a single system.
  • the present model can be used to confidently test hypotheses underlying the effects of different diseases on renal disease progression.
  • the relative contributions of glucose, MAP and Ang Il on disease progression in the model are realistic assumptions based on clinical measurements, published data and phenomenological observations.
  • One aspect of the invention provides computer models of hypertension comprising a) a RAAS pathway module; b) a renal function module; and c) a blood pressure regulation module.
  • the RAAS pathway module comprises a representation of RAAS in systemic circulation, and a representation of RAAS in the kidney.
  • the RAAS pathway module can also comprise a representation of RAAS in heart tissue.
  • the renal function module can comprise a representation of glomerular filtration rate and/or a representation of renal sodium regulation.
  • the renal function module can additional include a representation of disease effects.
  • the blood pressure regulation module comprises a representation of cardiac output and a representation of vascular resistance.
  • Another aspect of the invention provides systems for simulating hypertension comprising: a) a computer-executable data editor, capable of accepting data describing a subject; b) a computer-executable integrator, capable of executing a computer model of hypertension with the data to generate a set of outputs describing the result of the simulation of hypertension; and c) a computer-executable report generator capable of reporting the set of outputs.
  • the computer model comprises i) a RAAS pathway module; ii) a renal function module; and iii) a blood pressure regulation module.
  • the computer-executable data editor further is capable of accepting a set of parameters describing a virtual patient.
  • the computer- executable integrator further is capable of executing the computer model with the set of parameters describing the subject.
  • the computer-executable data editor further is capable of accepting a virtual protocol and the computer-executable integrator is capable of executing the computer model with the virtual protocol.
  • Yet another aspect of the invention provides systems comprising: a) a processor including computer-readable instructions stored thereon that, upon execution by a processor, cause the processor to simulate atherosclerosis; b) a first user terminal, the first user terminal operable to receive a user input specifying one or more parameters associated with one or more mathematical representations defined by the computer readable instructions; and c) a second user terminal, the second user terminal operable to provide the set of outputs to a second user.
  • the computer readable instructions comprise: i) a RAAS pathway module comprising a mathematical representation of a plurality of biological processes associated with RAAS, wherein the plurality of biological processes comprises RAAS in systemic circulation, RAAS in kidney, and optionally, RAAS in cardiac tissue; ii) a renal function module comprising a mathematical representation of a plurality of biological processes associated with renal function, wherein the plurality of biological processes comprises glomerular filtration rate and albuminuria; iii) a blood pressure regulation module comprising a mathematical representation of a plurality of biological processes associated with blood pressure regulation, wherein the plurality of biological processes comprises cardiac output and vascular resistance; iv) defining a set of mathematical relationships between the representations of biological processes associated with RAAS, renal function and blood pressure regulation; and v) applying a virtual protocol to the set of mathematical relationships to generate a set of outputs.
  • the first user may be the same as or different than the second user.
  • the model of hypertension can be a tool for investigating the effects of a variety of antihypertensive therapies on lower MAP and the progressive loss of renal function.
  • the limited human data on renal enzyme rates, peptide concentrations and the biology underlying the longitudinal progression of disease was a challenge in constructing the model.
  • Development of the model clearly relies on multiple assumptions of the underlying physiology, but these assumptions have been constrained by both data in the literature and clinical observations of renal function.
  • Figure 1 provides a Summary Diagram of the computer model of hypertension.
  • Figure 2 provides an Effect Diagram of the RAAS pathway in systemic circulation.
  • Figure 3 provides an Effect Diagram of the RAAS pathway module in kidney, particularly the glomerulus.
  • Figure 4 provides an Effect Diagram of the RAAS pathway module in kidney, particularly in tubular tissue.
  • Figure 5 provides an Effect Diagram of the RAAS pathway in cardiac (heart) tissue.
  • Figure 6 provides an Effect Diagram of disease representation and progression in the renal function module.
  • Figure 7 provides an Effect Diagram of albumin and creatinine calculations in the renal function module.
  • Figure 8 provides an Effect Diagram of systemic blood circulation, baroreceptor activity, and ADH secretion in the blood pressure regulation module.
  • Figure 9 provides an Effect Diagram of glomerular filtration, sodium filtration, water handling and renal hemodynamics in the blood pressure regulation module.
  • Figure 10 provides an Effect Diagram of calculations relating to RAAS and non- RAAS therapies.
  • Figure 11 provides an Effect Diagram of calculations relating to clinical outputs.
  • Figure 12 provides an Effect Diagram of additional characteristics and conversions for the model.
  • Figure 13 illustrates the effect of various non-RAAS therapies on mean arterial pressure.
  • NT normotensive VP
  • HT-1 hypertensive VP with increased preglomerular resistance
  • HT-2 hypertensive VP with nephropathy
  • HT-3 hypertensive patient with altered Na+ reabsorption
  • HT-4 hypertensive patient with increased TPR.
  • Figure 14 illustrates the effect of different RAAS therapies on mean arterial pressure for normotensive and hypertensive patients. Patient phenotypes as described in Figure 14.
  • the invention encompasses novel computer models of hypertension and systems for predicting development and progression of hypertension and associated risk for developing diseases, such as heart failure, stroke and kidney disease.
  • the computer model of hypertension comprises a RAAS pathway module, a renal function module, and a blood pressure regulation module.
  • a "biological system” can include, for example, a collection of cells such as a cell culture, an organ, a tissue, a multi-cellular organism such as an individual human patient, a subset of cells of a multi-cellular organism, or a population of multi-cellular organisms such as a group of human patients or the general human population as a whole.
  • a biological system can also include, for example, a multi-tissue system such as the nervous system, immune system, or an organ, such as a kidney.
  • biological component refers to a portion of a biological system.
  • a biological component that is part of a biological system can include, for example, an extracellular constituent, a cellular constituent, an intra-cellular constituent, or a combination of them.
  • suitable biological components include, but are not limited to, metabolites, DNA, RNA, proteins, surface and intracellular receptors, enzymes, hormones, cells, organs, tissues, portions of cells, tissues, or organs, subcellular organelles, chemically reactive molecules like H + , superoxides, ATP, as well as combinations or aggregate representations of these types of biological variables.
  • biological components can include therapeutic agents such as an ACE inhibitor or diuretic.
  • biological process is used herein to mean an interaction or series of interactions between biological components.
  • suitable biological processes include, but are not limited to, activation, apoptosis or recruitment of certain cells (such as macrophages), inflammation, cytokine production, and the like.
  • biological process can also include a process comprising one or more therapeutic agents, for example an ACE inhibitor or diuretic.
  • Each biological variable of the biological process can be influenced, for example, by at least one other biological variable in the biological process by some biological mechanism, which need not be specified or even understood.
  • parameter is used herein to mean a value that characterizes the interaction between two or more biological components.
  • parameters include affinity constants, K m , K 0 , /c cat , half life, or net flux of water, sodium or proteins.
  • variable refers to a value that characterizes a biological component.
  • variables include protein concentrations, such as circulating Ang I or plasma renin concentration, physical measures, such as vascular capacity or extracellular fluid volume.
  • phenotype is used herein to mean the result of the occurrence of a series of biological processes. As the biological processes change relative to each other, the phenotype also undergoes changes.
  • One measurement of a phenotype is the level of activity of variables, parameters, and/or biological processes at a specified time and under specified experimental or environmental conditions.
  • a phenotype can include, for example, the state of an individual cell, an organ, a tissue, and/or a multi-cellular organism. Organisms useful in the methods and models disclosed herein include animals. The term "animal" as used herein includes mammals, such as humans. A phenotype can also include, but is not limited to, behavior of the system as a whole, e.g. mean arterial pressure. The conditions defined by a phenotype can be imposed experimentally, or can be conditions present in a patient type. For example a normal phenotype can include a certain amount of circulating Ang Il and sodium and a certain mean arterial pressure. In another example, a disease phenotype can include increased sympathetic nervous activity, increased preglomerular resistance.
  • the phenotype can include the amount of sodium absorption by a nephron or diabetic nephropathy.
  • simulation is used herein to mean the numerical or analytical integration of a mathematical model.
  • biological characteristic is used herein to refer to a trait, quality, or property of a particular phenotype of a biological system.
  • biological characteristics of the biological systems related to hypertension include clinical signs and diagnostic criteria associated with blood pressure and kidney function.
  • the biological characteristics of a biological system can be measurements of biological variables, parameters, and/or processes. Suitable examples of biological characteristics associated with RAAS include, but are not limited to, measurements of glomerular filtration rates (GFR), mean arterial pressure (MAP) and concentration of certain circulating proteins.
  • GFR glomerular filtration rates
  • MAP mean arterial pressure
  • computer-readable medium is used herein to include any medium which is capable of storing or encoding a sequence of instructions for performing the methods described herein and can include, but not limited to, optical and/or magnetic storage devices and/or disks.
  • the present invention provides a mathematical model of hypertension as part of an integrated in s/V/co/experimental approach to the assessment of cardiovascular risk, particularly of heart failure or stroke.
  • the exemplified computer model of hypertension is a large-scale nonlinear ordinary differential equation-based representation of the key biological mechanisms involved in the RAAS pathway, kidney function and blood pressure regulation.
  • a computer model can be designed to model one or more biological processes or functions.
  • the computer model can be built using a "top-down" approach that begins by defining a general set of behaviors indicative of a biological condition, e.g. blood pressure.
  • the behaviors are then used as constraints on the system and a set of nested subsystems are developed to define the next level of underlying detail. For example, given a behavior such mean arterial pressure, the specific mechanisms inducing the behavior can each be modeled in turn, yielding a set of subsystems, which can themselves be deconstructed and modeled in detail.
  • the control and context of these subsystems is, therefore, already defined by the behaviors that characterize the dynamics of the system as a whole.
  • the deconstruction process continues modeling more and more biology, from the top down, until there is enough detail to replicate a given biological behavior.
  • the model is capable of modeling biological processes that can be manipulated by a drug or other therapeutic agent.
  • the methods used to develop computer models of hypertension typically begin by identifying one or more biological processes associated with the RAAS pathway in specific tissues (such as systemic circulation, kidney tissue and/or cardiac tissue), one or more biological processes associated with kidney function and one or more biological processes associated with blood pressure regulation. The identification of these biological processes can be informed by data relating to a metabolic, hormonal or organ system or any portion thereof.
  • the method can also comprise the step of identifying one or biological processes associated with stability of heart tissue and cardiovascular risk, particularly with myocardial tissue damage.
  • the method next comprises the step of mathematically representing each identified biological process.
  • FIG. 1 provides an overview of the modules that can be utilized in designing a computer model of hypertension.
  • identifying a biological process associated with the RAAS pathway comprises identifying one or more biological processes related the RAAS pathway in systemic circulation, identifying one or more biological processes associated with the RAAS pathway in the kidney, and optionally identifying one or more biological processes associated with the RAAS pathway in heart tissue.
  • the RAAS pathway in kidney can be separately represented by glomerular RAAS and tubular RAAS.
  • the biological processes related to the RAAS pathway can comprise one or more of angiotensinogen production, processing of angiotensinogen to Ang I, the action of chymase or ACE to generate Ang II, the production of Ang (1-7), inactivation of Ang Il and binding of AT-1 or AT-2 to Ang Il (see Fig. 2-5).
  • the representation of systemic RAAS pathway in a preferred embodiment, represents the feedback regulation of prorenin synthesis and processing and the equilibrium between prorenin and renin.
  • the biological processes related to the glomerular RAAS pathway comprise Ang I influx and efflux in the kidney, the interaction between changes of Ang I and/or Ang Il in the kidney on blood volume, or the interaction between blood volume on Ang I and Ang Il synthesis and degradation in the kidney (see Fig. 3).
  • identifying a biological process associated with renal function comprise identifying a biological process related to disease progression (see, e.g. Fig. 6) or a biological process related to albumin/creatinine processing (see, e.g. Fig. 7).
  • the biological processes related to disease progression can include, but are not limited to blood pressure effect on filtration, plasma glucose effect on K f and filtration, glomerular Ang Il effect on K f and filtration, glomerular pressure effects on nephron loss and the sieving membrane, the rate of disease damage to sieving, rate of sieving membrane repair, reversible and/or permanent damage to the sieving membrane, Ang Il effect on tubular fibrosis, and excess albumin reabsorption and the effect on tubular fibrosis.
  • the biological processes related to albumin/creatinine processing can relate to a single glomerulus and/or the whole kidney.
  • These processes can include, but are not limited to, SNGFR, glomerular albumin sieving coefficient, glomerular filtrate albumin concentration, reabsorption capacity and fraction, tubular fibrosis level, fibrosis effect on albumin reabsorption, fraction of functional nephrons, albumin excretion rate, creatinine clearance rate, creatinine synthesis rate, serum creatinine concentration, and age effect on GFR.
  • identifying a biological process associated with blood pressure regulation comprises identifying one or more biological processes related to ADH secretion, peripheral resistance, cardiac output, extracellular fluid volume and/or vascular capacity (see, e.g. Fig. 8).
  • identifying a biological process associated with blood pressure regulation comprises identifying one or more biological processes related to water filtration, renal hemodynamics and/or sodium filtration (see, e.g. Fig. 9).
  • the biological processes related to water filtration can include, but are not limited to, urine flow rate, the effect of aldosterone concentration and/or ADH concentration on tubular water reabsorption rate.
  • the biological processes related to sodium filtration can include, but are not limited to, total sodium amount, extracellular fluid volume, filtered sodium load, proximal tubule and LoH reabsorption, macular densa sodium flows, distal sodium reabsorption, distal tubule sodium outflow, macula densa signal accumulation, and sodium excretion via urine.
  • the biological processes related to renal hemodynamics can include, efferent arteriole resistance, afferent arteriole resistance, renal blood flow, renal vascular resistance, renal sympathetic nerve activity, tubule-glomerular feedback effect and glomerular pressure autoregulation
  • each biological process is mathematically represented.
  • the computer model can represent a first biological process using a first mathematical relation and a second biological process using a second mathematical relation.
  • a mathematical relation typically includes one or more variables, the behavior (e.g., time evolution) of which can be simulated by the computer model.
  • mathematical relations of the computer model can define interactions among variables describing levels or activities of various biological components of the biological system as well as levels or activities of combinations or aggregate representations of the various biological components.
  • variables can represent various stimuli that can be applied to the physiological system.
  • the mathematical model(s) of the computer-executable software code represents the dynamic biological processes related to RAAS pathway including kidney function and blood pressure.
  • the form of the mathematical equations employed may include, for example, partial differential equations, stochastic differential equations, differential algebraic equations, difference equations, cellular automata, coupled maps, equations of networks of Boolean or fuzzy logical networks, etc.
  • the parameters are used to represent intrinsic characteristics (e.g., genetic factors) as well as external characteristics (e.g., environmental factors) for a biological system.
  • the phenotype can be mathematically defined by the values of x and p at a given time. Once a phenotype of the model is mathematically specified, numerical integration of the above equation using a computer determines, for example, the time evolution of the biological variables x ⁇ t) and hence the evolution of the phenotype over time.
  • the methods further can comprise methods for validating the computer models described herein.
  • the methods can include generating a simulated biological characteristic associated with development or progression of hypertension, and comparing the simulated biological characteristic with a corresponding reference biological characteristic measured in vivo. The result of this comparison in combination with known dynamic constraints may confirm some part of the model, or may point the user to a change of a mathematical relationship within the model, which improves the overall fidelity of the model.
  • Methods for validating the various models described herein are taught in U.S. Patent Publication 2002-0193979, entitled “Apparatus And Method For Validating A Computer Model," and in U.S. Patent No. 6,862,561 , entitled “Method and Apparatus for Computer Modeling a Joint.”
  • the computer model hypertension provides predictive power to rapidly assess, e.g., the efficacy of novel therapeutics prior to investment in large-scale clinical trials.
  • the model contains three modules: an RAAS pathway module, a renal function module and a blood pressure regulation module.
  • the model can be used to establish a population of virtual patients (representing a variety of clinical phenotypes) to rapidly assess the effects of modulating highly-sensitive target pathways on key clinical endpoints.
  • researchers can assess the efficacy of novel therapeutics, and identify biomarker patterns for predicting long-term clinical efficacy.
  • the goal of a model is to speed up the development process along the drug development pipeline.
  • Novel therapies can be prioritized based on efficacy early in the drug development process, with multiple dosing regimens and protocols tested and results returned prior to recruiting the first patient in a clinical trial.
  • Combination therapies can also be evaluated in the model to look for potential non-additive effects, and to identify the most potent approach in lowering blood pressure in patients with multiple disease etiologies.
  • a set of biomarkers could be determined that can identify the best responders to different therapeutic approaches for treating hypertension.
  • the model is to provide a versatile tool for pharmaceutical research and development to optimize current approaches to drug development, and to provide new insight into the physiology to reduce the time to bring an effective novel therapy to the market.
  • Hypertension is postulated to result from numerous pathophysiological mechanisms including increased peripheral resistance, increased sympathetic nervous system activity, overproduction of sodium-retaining factors and vasoconstrictors (e.g., Ang Il and endothelin), increased sodium reabsorption by the kidneys, deficiencies of vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI 2 ), or from an imbalance in the regulation of glomerular pressure - all of which are difficult to isolate as the cause of hypertension.
  • vasoconstrictors e.g., Ang Il and endothelin
  • vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI 2 )
  • ANP atrial natriuretic peptide
  • NO nitric oxide
  • PKI 2 prostacyclin
  • Ang Il has been the focus of intensive research aimed at elucidating its role in the control of blood pressure, extracellular fluid and electrolyte homeostasis.
  • Ang Il is a peptide with potent vasoconstricting effects. It is part of the RAAS pathway, a cascade of bioactive peptides and regulatory enzymes.
  • the classical systemic RAAS pathway has been described to start with the synthesis and release of angiotensinogen (AGT) into the systemic circulation by the liver.
  • AGT angiotensinogen
  • Renin a proteolytic enzyme synthesized by the juxtaglomerular cells in the kidney, cleaves AGT to form the decapeptide angiotensin I (Ang I).
  • Angiotensin-converting enzyme cleaves Ang I to form Ang II, which is the octapeptide hormone that regulates blood pressure by the modulation of sodium reabsorption in the kidney and by effecting central and peripheral nervous system activity to increase cardiac output and systemic vascular resistance.
  • RAAS-modulating therapies directly manipulate this pathway to alter the levels of Ang Il in the systemic circulation to reduce blood pressure.
  • Three classes of RAAS- modulating pharmacological therapies are currently available on the market.
  • Direct renin inhibitors (DRIs) target renin activity; ACE inhibitors block the conversion from Ang I to Ang II; angiotensin-receptor blockers (ARBs) prevent the binding of Ang Il to the Angiotensin 11-1 receptors (AT1 ). All three reduce the systemic activity of Ang II, which leads to vasodilation, decreased renal sodium reabsorption and reduced secretion of vasopressin (from the brain) and aldosterone (from the adrenal cortex).
  • Figure 10 illustrates various modes of representing therapeutic interventions in the present computer model of hypertension.
  • the model can account for ACE inhibitor effect on systemic and/or renal chymase activity, on systemic and/or glomerular ACE activity, and on Ang(1-7) clearance.
  • the model can account for direct renin inhibitor effects on plasma and glomerular renin activity and the resulting glomerular Ang I production, peritubular ang I synetheis and tubular tissue synthesis of Ang I.
  • the model can account for angiotensin receptor blockers on AT1 receptor binding, renal At1 receptor binding, Ang Il clearance and degradation rate, and Ang III clearance and degradation rate.
  • the computer model accounts for diuretic effects on distal tubule sodium reabsorption, proximal tubule and LoH sodium reabsorption and macula densa signaling.
  • the computer model accounts for the effect of calcium channel blockers on efferent arteriole resistance, preglomerular arteriole resistance and systemic arterial resistance.
  • the computer model accounts for beta blocker effects on renal sympathetic nerve activity.
  • the computer model described herein represents biological processes at multiple levels and then evaluates the effect of the biological processes on biological processes across all levels.
  • the computer model provides a multi-variable view of a biological system.
  • the computer model also, preferably, provides cross-disciplinary observations through synthesis of information from two or more disciplines into a single computer model or through linking a plurality of computer models that represent different disciplines.
  • An exemplary computer model reflects a particular biological system, e.g., the vascular system, and anatomical factors relevant to issues to be explored by the computer model.
  • the level of detail incorporated into the model is often dictated by a particular intended use of the computer model.
  • biological components being evaluated often operate at a subcellular level; therefore, the subcellular level can occupy the lowest level of detail represented in the model.
  • the subcellular level includes, for example, biological components such as DNA, proteins, peptides therapeutic agents, and subcellular organelles.
  • the model can be evaluated at the multicellular level or even at the level of a whole organism. Because an individual biological system, e.g.
  • a single human is a common entity of interest with respect to the ultimate effect of the biological components, the individual biological system (e.g., represented in the form of clinical outcomes) is the highest level represented in the system.
  • Chemical and therapeutic interventions are introduced into the model through changes in parameters at lower levels, with clinical outcomes being changed as a result of those lower level changes, as opposed to representing effects by directly changing the clinical outcome variables.
  • the model represents evolving dynamics of cell populations, rather than the sequence of events for a single cell.
  • This higher level of abstraction can show, for example, major physiological subsystems and their interconnections, but need not report certain detailed elements of the computer model - at least not without the user explicitly deciding to view the detailed elements.
  • This higher level of abstraction can provide a description of the virtual patient's phenotype and underlying physiological characteristics, but need not include certain parametric settings used to create that virtual patient in the computer model.
  • this higher level of abstraction can describe what the therapy does but need not include certain parametric settings used to simulate that exposure in the computer model.
  • a subset of outputs of the computer model that is particularly relevant for subjects and doctors can be made readily accessible.
  • the output can comprise an identification of one or more biological processes that most significantly affect whether hypertension develops or whether a certain patient might respond to a selected therapy.
  • the output may suggest biological assays that can be used to assess the likelihood that a subject may develop high blood pressure.
  • the model of hypertension described herein can be used to generate a model for simulating development and progression of high blood pressure and the associated increased risk of adverse effects, such as heart failure, stroke and kidney damage.
  • the simulation model may include hundreds or even thousands of objects, each of which can include a number of parameters.
  • it is useful to access and observe the input values of certain key parameters prior to performance of a simulation operation, and also possibly to observe output values for these key parameters at the conclusion of such an operation.
  • many parameters are included in the expression of, and are affected by, a relationship between two objects, one may also need to examine certain parameters at either end of such a relationship.
  • the computer model is configured to allow visual representation of mathematical relations as well as interrelationships between variables, parameters, and biological processes.
  • This visual representation includes multiple modules or functional areas that, when grouped together, represent a large complex model of a biological system.
  • simulation modeling software is used to provide a computer model, e.g., as described in U.S. Pat. No. 5,657,255, issued Aug. 12, 1997, titled “Hierarchical Biological Modeling System and Method”; U.S. Pat. No. 5,808,918, issued Sep. 15, 1998, titled “Hierarchical Biological Modeling System and Method”; U.S. Pat. No. 6,051 ,029, issued Apr.
  • FIG. 1 Various Diagrams can be used to illustrate the dynamic relationships among the elements of the model of skin sensitization. Examples of suitable diagrams include Effect and Summary Diagrams.
  • a Summary Diagram can provide an overview of the various pathways modeled in the methods and models described herein.
  • the Summary Diagram illustrated in FIG. 1 provides an overview of modules that can form the present model of hypertension.
  • a Summary Diagram also can provide an overview of pathways modeled in a particular module and/or provide links to individual modules of the model.
  • the models represent the relevant components of the phenotype through the use of "state” and “function” nodes whose relations are defined through the use of diagrammatic arrow symbols.
  • An Effect Diagram can be a visual representation of the model equations and illustrate the dynamic relationships among the elements of the model.
  • FIG. 3 provides an example of an Effect Diagram illustrating the glomerular RAAS Pathway. The Effect
  • Diagram is organized into functional areas, which when grouped together represent the large complex physiology of the phenotype being modeled.
  • State and function nodes show the names of the variables they represent and their location in the model. The arrows and modifiers show the relationship of the state and function nodes to other nodes within the model. State and function nodes also contain the parameters and equations that are used to compute the values of the variables the represent in simulated experiments. In some embodiments, the state and function nodes are represented according to the method described in U.S. Patent No. 6,051 ,029, entitled “Method of Generating a Display for a Dynamic Simulation Model Utilizing Node and Link Representations," incorporated herein by reference. Examples of state and function nodes are further discussed below.
  • State nodes are represented by single-border ovals and represent variables in the system, the values of which are determined by the cumulative effects of inputs over time.
  • “Input” refers to any parameter that can affect the variable being modeled by the state node.
  • input for a state node representing glomerular Ang Il mass can be glomerular Ang Il synthesis and glomerular Ang I mass, regulated by total glomerular ACE activity and chymase activity.
  • State node values are defined by differential equations.
  • the predefined parameters for a state node include its initial value (S 0 ) and its status.
  • state nodes can have a half-life. In these embodiments, a circle containing an "H" is attached to the node that has a half-life.
  • Function nodes are represented by double-border ovals and represent variables in the system, the values of which, at any point in time, are determined by inputs at the same point in time. Function nodes are defined by algebraic functions of their inputs.
  • the predefined parameters for a function node include its initial value (F 0 ) and its status. Setting the status of a node effects how the value of the node is determined.
  • the status of a state or function node can be: 1 ) Computed, i.e., the value is calculated as a result of its inputs; 2) Specified-Locked, i.e., the value is held constant over time; or 3) Specified Data, i.e., the value varies with time according to predefined data points.
  • State and function nodes can appear more than once in the module diagram as alias nodes. Alias nodes are indicated by one or more dots (see, e.g., state node
  • State and Function nodes are also defined by their position, with respect to arrows and other nodes, as being source nodes (S) and/or target nodes (T). Source nodes are located at the tails of arrows and target nodes are located at the heads of arrows. Nodes can be active or inactive.
  • Arrows link source nodes to target nodes and represent the mathematical relationship between the nodes. Arrows can be labeled with circles that indicate the activity of the arrow. A key to the annotations in the circles is located in the upper left corner of each effect Diagram. If an arrowhead is solid, the effect is positive. If the arrowhead is hollow, the effect is negative.
  • the fully-integrated computer model of hypertension preferably is capable of representing a breadth of patient phenotypes in terms of their physiological status, additional risk factors for high blood pressure, and alternate genetic and/or hypothesized mechanistic variants.
  • the resulting virtual patients can be used to predict the effect of therapeutic and/or dietary intervention on hypertension and the risk of adverse endpoints, such as heart failure or stroke.
  • the methods disclosed herein can be used to form a computer model capable of simulating patient phenotypes and further can incorporate the addition of new components, as well as increased detail in components already modeled. For example, computer models predicting changes in filtration capacity in the kidneys of a diabetic or aging patient.
  • the RAAS pathway module incorporates the enzymatic pathways involved in the synthesis and conversion of AGT to Ang I, Ang Il and downstream metabolites, such as Ang(1-7) and Ang IV.
  • the activity of enzymes including renin, ACE, a chymase-like enzyme, and neutral endopeptidase (NEP) were included in the model in addition to the binding rates of Ang Il to the two Ang Il receptors (AT1 and AT2).
  • the inclusion of these peptides and enzymes allows for the investigation antihypertensive therapies that target the RAAS.
  • Figs. 2, 3 and 4 provide a diagrammatic representation of the pathway model, in systemic circulation, glomerulus and tubule, respectively.
  • the Guyton/Coleman (GC) model does not include vascular remodeling and its effects on vascular geometry and hemodynamics as significant contributors to increased peripheral vascular resistance
  • GC Guyton/Coleman
  • Karaaslan et al published a modified version of the GC model that added the influence of the renal sympathetic nervous activity on the synthesis and release of renin and the afferent arteriolar tone.
  • the model that describes the dynamics of the renin-angiotensin system is represented using a system of ordinary differential equations (1 )-(8).
  • Each biochemical reaction has zero th -order components of production (k n ) and first order degradation kinetics expressed through half-life parameters (h n ).
  • Binding or enzymatic reactions can be expressed as first-order reactions with parameters (c n ).
  • a feedback function, f relating plasma renin activity (PRA) to ATI-bound Ang Il is also included in the model.
  • PRA is assumed to be proportional to the concentration of its substrate, AGT, because the concentration of AGT is comparable to the Michaelis-Menten constant (Km).
  • ACE and chymase activity in the vasculature were determined to have V m values of 222 and 154 pmol/ml/hr, respectively, which was considerably greater than rates (-0.3 pmol/ml/hr) measured in humans (Takai, et al. (1997) Characterization of chymase from human vascular tissues. CHn Chim Acta 265:13-20; Meng, et al. (1995) Sensitive method for quantitation of angiotensin-converting enzyme (ACE) activity in tissue. Biochem
  • ACE was assumed to be responsible for >95% of the conversion of Ang I to Ang II.
  • Human and animal data support the hypothesis of ACE being the primary enzyme responsible for Ang I to Ang Il conversion in normotensive humans.
  • ACE expression and systemic conversion of AGT to Ang I take place primarily in the pulmonary circulation.
  • Ang Il binds preferentially to AT1 rather than AT2 receptors.
  • Data from human smooth muscle cells and renal tissue indicate that AT2 receptors are expressed at lower levels compared to AT1 receptors (Haulica, et al. (2005) Angiotensin peptides and their pleiotropic actions. J Renin Angiotensin Aldosterone Syst 6:121-131 ).
  • Ang I and Ang Il have half lives of approximately 30 seconds in the systemic circulation.
  • For Ang IV the model assumes a half-life of 10 minutes, which is between the reported half lives of Ang Il and Ang(1-7). The concentrations of Ang IV and Ang(1-7) in the systemic circulation were calculated based on the solution of the steady-state equilibrium equations.
  • PRA increases via a regulatory feedback mechanism in response to a reduction in blood pressure, in a relationship that reflects a reduction in Ang Il binding to the AT1 receptors.
  • An analysis of clinical data from trials testing therapies that modulate the RAAS pathway suggests a rapid increase in PRA 24 hours post-treatment, which correlated with the reductions in Ang Il bound to AT1 receptors and blood pressure.
  • the model divides the kidney into two regions: the renal vasculature compartment, comprised of all vascular structures within the kidney (including the blood volume within those structures) and the renal tissue compartment, comprised of all tissue external to vascular structures (including the tubules and interstitial tissue).
  • the model makes the following assumptions and simplifications:
  • RAAS peptides are arterially delivered from the circulation to the renal vascular compartment at concentrations equal to systemic levels, and the peptides flow out of the renal vascular compartment back to the systemic circulation at concentration equal to renal vasculature levels.
  • All angiotensin peptides and all enzymes in the RAAS pathway are also produced locally within each compartment, although the rates of production and enzymatic conversion can vary greatly from those in systemic circulation, as discussed below.
  • a concentration gradient exists between the renal tissue and renal vasculature, such that RAAS peptides produced in the renal tissue diffuse into the renal vasculature. Biopsy data shows that renal tissue levels of Ang I and Ang
  • Kidney lnt Kidney lnt
  • Ang IV and Ang(1-7) levels in the kidney were not specifically modeled because of the limited availability of data. Instead, rates of conversion of Ang I and Ang IV to Ang(1-7) and Ang IV were assumed to be incorporated into the degradation rates of Ang I and Ang II. • Since limited data is available on any changes in the concentrations of AGT and renin within the renal tubules and interstitium, the rate of Ang I synthesis in the renal tissue compartment was assumed to be at equilibrium levels.
  • the model accounts for: 1 ) arterially delivered Ang I and Ang Il peptides and return of these peptides to the systemic circulation; 2) production and utilization of Ang I and Ang Il in the renal vascular bed; 3) diffusion of Ang I and Ang Il from the renal tissue into the renal vasculature; and 4) binding of Ang Il to its receptors.
  • the model takes into consideration: 1 ) production and utilization of Ang I and Ang Il in the renal tissue; 2) diffusion of locally produced peptides into the renal vasculature, and 3) binding of Ang Il to its receptors.
  • Equations (10-13) for the renal vascular RAAS are shown below. These equations are almost identical to those for systemic RAAS sub-module, but the rates are specific for the renal circulation, include additional terms have been added to describe the flow of angiotensin peptides in and out of the kidney at a rate F k , and include the diffusion of angiotensin peptides from the renal tissue compartment to the renal vasculature at a rate of D k .
  • Equations (14-17) for RAAS within the renal tissue compartment are as shown above.
  • the concentration of Ang I at the renal vein is approximately 50% higher than the concentration at the renal artery.
  • the concentration of Ang Il at the renal vein is approximately 50% lower than the concentration at the renal artery.
  • the rate of blood flow to the kidney (F k ) is ⁇ 1 L/min at rest and the blood volume of the kidney is 70 ml, equivalent to a residence time of 4 seconds. • The rate of local Ang I and Ang Il degradation in the kidney is significantly increased over the systemic degradation rate to account for the high rate of angiotensin peptide removal in the renal circulation.
  • the chosen parameters yielded a solution for the dynamical system that satisfied the known constraints of the renal vascular bed.
  • the renal vascular parameters with the same value as their systemic counterpart are not listed in the table.
  • the RAAS pathway within the renal tissue i.e. the tubular compartment
  • the RAAS pathway within the renal tissue was implemented in a similar fashion as the renal vascular RAAS, with identical enzymes, peptides and receptors. Although the concentration and activities of the enzymes were assumed to differ, there is minimal quantitative data for these rates in the published literature.
  • the primary constraint for the renal tissue RAAS is the assumption that the renal tissue should function as a source of Ang I and Ang Il that enters into the renal vasculature.
  • the parameters describing the activity of the renal tissue RAAS pathway was parameterized such that: (i) the equilibrium concentrations of the angiotensin peptides in the tissue pathway were a source of Ang I and Ang Il in the renal vascular compartment; and (ii) the constraints on Ang I and Ang Il concentrations measured by Danser were satisfied.
  • a validation of any model consists of the agreement between model predictions and one or more experimental data sets that were not used to determine the initial parameterization of the model.
  • a validation of the model parameters describing the normotensive Virtual Patient was conducted using a series of published radio-labeled angiotensin peptide infusion experiments (Danser, et al. (1998) Angiotensin l-to-ll conversion in the human renal vascular bed. J Hypertens 16:2051- 2056; and Admiraal, et al. (1993) Regional angiotensin Il production in essential hypertension and renal artery stenosis. Hypertension 21 :173-184).
  • ACE inhibitors were simulated by changing the effect of the rate constant C ACE
  • ARBs angiotensin Il type I receptor blockers
  • DRIs direct renin inhibitors
  • AT1 receptors mediate the majority of Ang Il actions involved in the regulation of blood pressure and blood volume.
  • ACEI blocks the action of ACE competitively and thus the conversion of Ang I to Ang II, thereby reducing circulating and local levels of Ang II.
  • ACEI therapy is associated with a decrease in Ang II, a reactive increase in plasma renin concentration and an increase in plasma Ang I.
  • the reactive increase in plasma renin concentration was also observed in response to ARB and DRI therapy.
  • the simulated ACEI in the model predicted increased concentrations and Ang I and Ang(1-7) and decreased concentrations of Ang II, consistent with reported clinical data (Manhem, et al. (1985) A dose-response study of HOE 498, a new non-sulphydryl converting enzyme inhibitor, on blood pressure, pulse rate and the renin-angiotensin- aldosterone system in normal man. Br J Clin Pharmacol 20:27-35).
  • the time course of the Ang I and Ang Il response predicted an equilibration in the angiotensin peptide concentrations after 5 hours, in agreement with short-term measurements taken in the studies highlighted in Table 5.
  • ARBs act by blocking the binding of Ang Il to the AT1 receptor rather than by inhibiting Ang Il synthesis, their use results in an increase in plasma Ang Il levels.
  • the blockade of AT1 receptors increases renin secretion and the corresponding concentration of plasma Ang I.
  • DRIs have a significant and sustained effect on PRA to reduce the concentration of both Ang I and Ang Il in the circulation.
  • the simulated effects of DRIs in the model predict a decreased concentration of circulating Ang I, Ang Il and Ang(1-7), consistent with results reported in clinical studies (Nussberger, et al. (2007) Plasma renin and the antihypertensive effect of the orally active renin inhibitor aliskiren in clinical hypertension. Int J CHn Pract 61 :1461-1468).
  • Table 2 summarized the wide range of reported clinical values of enzyme activities in the RAAS pathway cascade to reflect the intrinsic variability between human subjects.
  • the values summarized in Table 3 described only one set of parameters for the system of equations that yields a feasible solution.
  • the parameter values in Table 2 can be changed within the observed ranges to generate a new Virtual Patient hypothesis.
  • changing the parameters may yield a mathematically correct steady solution for a new Virtual Patient, the combination of parameter values may not result in steady state concentrations or enzyme activity rates that are consistent with the physiological data. For example, decreasing the rate of Ang Il clearance from the circulation will increase the time it takes for Ang Il to reach an equilibrium. If the resulting Ang Il concentration at equilibrium increases significantly beyond physiological range determined by the infusion studies, then the chosen set of parameters for the Virtual Patient was considered invalid.
  • the verification of the simulated results against plausible data is a valuable step during the process of model building.
  • a collection, or cohort, of multiple feasible Virtual Patients can be generated using a systematic process to explore the parametric space and a method for testing the feasibility criteria of each parameterization.
  • Table 6 summarizes one such method for exploring the parametric space that varies the half lives and enzyme activity rates around the nominal values of the first virtual patient (VP1).
  • a patient hypothesis may be generated by simulating with parameters within the nominal range where the value of 100% is equal to the values chosen for the first Virtual Patient.
  • Table 7 summarizes a set of feasibility criteria for the concentration of angiotensin peptides based on a survey of the literature.
  • the cohort of feasible Virtual Patients can be modified depending on criteria to describe a particular disease phenotype. For example, the feasibility criteria for plasma renin activity can be increased accordingly in patients that exhibit exaggerated renal production of renin leading to increased concentrations of plasma renin. It is important to note that the cohort of Virtual Patients may not follow the same distribution as the clinical population and additional refinement of the patient-generation procedure may be required.
  • Chymase is another enzyme that can convert Ang I to Ang II. Therapy that focuses on the inhibition of ACE activity does not affect the continued conversion of Ang I to Ang Il by chymase. Based on the clinically measured changes in circulating Ang I and Ang Il and the assayed reduction in ACE activity in response to moderate doses of ACEI, the model predicts that ACE is responsible for greater than 95% of Ang Il synthesis in the representative normotensive patient. If the role of ACE in the synthesis of Ang Il was reduced to ⁇ 95%, the model was unable to reproduce the clinically measured reduction in Ang II. [0107] PRA increases in response to ARB or ACEI therapy can be represented by establishing a relationship between decreased Ang Il binding to AT1 receptors and PRA.
  • the kidney possesses all the RAAS components and enzymatic machinery required for the local tissue generation of Ang Il and other RAAS-related peptides.
  • the models described herein comprise a renal function module.
  • the renal module includes a representation of the kidney as an assembly of single nephrons and associated fluid dynamics processes that influence glomerular filtration rate.
  • the renal function module also can comprise a representation of glomerular filtration rate (GFR) and a representation of albuminuria.
  • GFR glomerular filtration rate
  • glomerular filtration permeability is distributed between fenestrated endothelium, GBM and the slit diaphragm.
  • the model represents albumin transport across the glomerular basement membrane as a function, independently, of diffusion and convection (water filtration).
  • GFR is represented as a function of glomerular hydrostatic pressure, oncotic pressure and hydrostatic conductance (K f ).
  • K f in turn, can be represented as a result of integration of multiple effects of physical barriers to filtration in one simplified term representing: podocyte slit diaphragm length, quantity of slits, diaphragm composition, GBM thickness and composition, endothelium integrity and function, and total (capillary) surface area.
  • glomerular hydrostatic pressure can be determined based on afferent and efferent arteriole resistance and blood pressure at the renal artery.
  • the glomerular filter present in the capillary tuft located inside the Bowman's capsule is responsible for the formation of ⁇ 180 L/day of primary urine devoid of macromolecules. This primary filtrate is then modified by the nephron's tubular system and its volume reduced to -1.5 L/day excreted in urine.
  • the glomerular filter/barrier consists of 3 distinct layers 1 ) a fenestrated endothelium, 2) a glomerular basement membrane (GBM) and 3) a slit diaphragm located between the interdigitating foot processes of epithelial podocytes.
  • GBM glomerular basement membrane
  • the anti-clogging capacity of the glomerulus has prompted investigators to postulate various mechanisms where the GBM (gel permeation), the podocyte (size selectivity) and the endothelium (size and charge selectivity) are the relevant components behind the barrier's filtering capacity.
  • GBM gel permeation
  • podocyte size selectivity
  • endothelium size and charge selectivity
  • GFR and albuminuria are the clinical measures used to define normal kidney function and to diagnose renal disease. Both parameters result from a variety of physiological phenomena, some of which are not fully understood and therefore their quantitative nature and relevance cannot be derived directly from the scientific literature.
  • Glomerular filtration rate can be represented as the sum of single nephron GFR (SNGFR) of N nephrons, where N is 2x10e6.
  • SNGFR single nephron GFR
  • the SNGFR of the n th nephron is a flow (in nl/min) that is commonly calculated from the Starling equation: where K f is the hydrostatic conductance , P represents a physical pressure in either the glomerular capillaries or the Bowman's space and ⁇ represents the oncotic pressure (exerted by plasma proteins).
  • the reflection coefficient ( ⁇ ), is often thought as a correction factor for the differences in permeability of body capillaries to large proteins and their contribution to the interstitial fluid oncotic pressure; ⁇ can take values between 0 and 1.
  • Glomerular capillaries have a very low permeability to proteins including albumin, therefore a ⁇ value close to 1 is typically used.
  • hepatic sinusoids are highly permeable to albumin produced by hepatocytes and therefore have a low ⁇ . Strictly speaking, each of the N nephrons would have its own set of these 5 parameters producing a unique SNGFR for each nephron.
  • the glomerular hydrostatic pressure of a specific nephron can be calculated from basic fluid dynamic principles (e.g., a pipe and valve calculation) and will depend on renal perfusion pressure, total renal blood flow resistance, and the resistance presented by the afferent and efferent arterioles of the nephron.
  • the degree of vasodilation / vasoconstriction of the arterioles is of significant interest for this modeling effort as it will be regulated by various factors, most particularly by Ang II.
  • K f The hydrostatic conductance, K f , is the term most closely associated with what are traditionally viewed as the physiological properties of the glomerular membrane determining GFR.
  • Eq (19) demonstrates that K f is the ratio of the flow through a resistance to the pressure difference between the two sides of the resistance.
  • K f represents the effects of a number of complex biological phenomena, including:
  • the model represents GFR as follows:
  • albumin in urine albuminuria
  • albuminuria is typically measured in mg/day. Similar to GFR, albuminuria is represented as the sum of albumin excretion by N nephrons (as for GFR, a single typical nephron manifesting the mean excretion is used as the basis for the model).
  • Excreted albumin is represented as the amount of protein delivered to the proximal tubule that is not reabsorbed, where the amount reabsorbed is a fraction (f) of the amount that enters the tubular system.
  • Albumin tubular reabsorption is a saturable process, thus, loads that exceed the saturation level will be excreted in urine.
  • Single nephron albumin excretion rate (1 - f) * filtered load (22) where the filtered load is the rate at which albumin is delivered from the Bowman's space into the tubule (mg/min).
  • Mass conservation requires that the flow of albumin into the tubule is the product of the albumin concentration in the Bowman's space and the flow rate of fluid into the tubule (SNGFR).
  • the concentration in the Bowman's space is determined using the concept of the sieving coefficient ( ⁇ ) that is the ratio of the Bowman's space concentration to the plasma concentration.
  • albumin excretion rate N*( 1 - f) * SNGFR * ⁇ * [Alb] plasma (23)
  • albuminuria is proportional to GFR. If GFR doubles, albuminuria doubles. Additionally, per Eq (23), albuminuria is proportional to the plasma albumin concentration. While Eq (23) clearly indicates that albuminuria is dependent on GFR, other scenarios in which albuminuria might not depend on GFR should be considered.
  • filtered load is the product of flow and concentration.
  • the sieving coefficient ( ⁇ ) and f are defined empirically: there is an albumin concentration difference between the glomerular Bowman's space and plasma, and for any set of concentrations that ratio is defined as ⁇ .
  • some fraction of albumin (f) is reabsorbed in the proximal tubule.
  • Eq (23) the albumin excretion rate might not depend on GFR. So far, ⁇ and f are assumed to be fixed, yet experimental data suggest otherwise.
  • the filtration coefficient ⁇ is also likely to change with changes in SNGFR.
  • the direction of the change is indeed to decrease with increasing SNGFR in order to maintain albuminuria levels.
  • the changes in ⁇ with SNGFR will partially mitigate the changes in albuminuria induced by changes in SNGFR in Eq (21).
  • ⁇ would need to vary with (1/SNGFR) to cancel the SNGFR in Eq (23).
  • the present model for albuminuria leads to an explicit dependence of albuminuria on SNGFR (Eq (23)) that is a function of the sieving coefficient ( ⁇ ) and tubular readsorption (f) on SNGFR. Furthermore, within the constraints of normal physiological changes in the nephron, the expected dependencies of ⁇ and fon SNGFR will not cancel the dependence of albumin excretion on SNGFR in Eq (23) — the changes in ⁇ may reduce the dependence partially and the changes in f will augment the dependence. The available data do not support the idea that the filtered load of albumin is nearly independent of GFR. Haraldsson et al., Properties of the glomerular barrier and mechanisms of proteinuria. Physiol Rev 2008 April;88(2):451-87.
  • Glomerular filter permeability / selectivity is distributed among the 3 main components of the glomerular filtration barrier (fenestrated endothelium / GBM / slit diaphragm of podocyte foot processes). Other theoretical models of filtration are centered around one layer (e.g., GBM). Smithies, Why the kidney glomerulus does not clog: a gel permeation/diffusion hypothesis of renal function. Proc Natl Acad Sci U S A 2003 April 1 ;100(7):4108-13.
  • GFR is determined by glomerular hydrostatic pressure, oncotic pressure and hydrostatic conductance (K f ).
  • K f is the result of integrating the multiple effects of a series of physical barriers to filtration into one simplified term.
  • the determinants of glomerular hydrostatic pressure are: o afferent and efferent arteriole resistance, o the blood pressure at the renal artery.
  • the sieving coefficient of any solute is the concentration in the filtrate divided by the concentration in the retentate. In the case of glomerular filtration, it is defined as the concentration in the Bowman's capsule by that in plasma.
  • the sieving coefficient of plasma solutes being filtered by the glomerular membrane is determined by a number of factors including 1 ) the intrinsic selectivity of the membrane given by solute size, charge and shape; 2) the filtration rate of water; 3) the solute concentration; and 4) the arrangements of the layers involved in filtration (fenestrated endothelium, GBM and slit diaphragm).
  • albuminuria represented a single-layer glomerular membrane that factors in the sieving coefficient of albumin and implicitly represents the various factors influencing that sieving coefficient.
  • the model treats N, K f , P gbm , and [Alb] p ⁇ aSm a as inputs that will vary in response to various acute and chronic changes in a given patient.
  • the model additionally includes functions for ⁇ and f that have as arguments various values generated by the model:
  • clinical behaviors can be mechanistically modulated to generate high blood pressure, characterize the reported sensitivity to sodium intake and to evaluate responses to a variety of therapies including RAAS and non RAAS-based therapies.
  • the key renal components represented in the model include GFR and glomerular hemodynamics, tubular sodium and water reabsorption, sodium sensing by the macula densa, and modulation of the secretion rate of renin.
  • the cardiovascular hemodynamic components represented in the platform include mean arterial pressure (MAP), cardiac output (CO), total peripheral resistance (TPR), sympathetic nervous activity (SNA), and vascular capacitance.
  • the humoral components with vascular and renal effects can include Angiotensin Il (Ang II), aldosterone, anti-diuretic hormone (ADH), atrial natriuretic peptide (ANP), sodium and potassium.
  • Ang II Angiotensin Il
  • ADH anti-diuretic hormone
  • ADP atrial natriuretic peptide
  • sodium and potassium Compared to the Guyton- Coleman model, the integrated hypertension model disclosed herein comprises a more detailed representation of systemic RAAS-related peptides including Ang I and Ang (1- 7); glomerular and tubular RAAS compartments; renal function (GFR and albuminuria) and the representation of the mechanistic effects of RAAS- and non RAAS-based therapies.
  • the blood pressure regulation module tracks sodium balance and total sodium amount. It also calculates water intake and integrates and tracks water balance and extracellular fluid volume (ECFV).
  • ECFV extracellular fluid volume
  • the blood pressure regulation module contains a simplified representation of cardiac function and peripheral circulation. Based principally on the ECFV-derived blood volume, it calculates MAP and right atrial pressure (RAP). These pressures are modulated by Ang Il and autonomic responses.
  • RAP right atrial pressure
  • the foundation of the blood pressure regulation module is the renal function curve or 'pressure natriuresis'. Pressure natriuresis relates mean arterial pressure (MAP) to blood volume and establishes a steady-state equilibrium for MAP. The equilibrium point between blood volume and MAP is attained through the renal excretion of sodium and water.
  • RAAS and other hormonal factors allow pressure natriuresis to occur over a wider range of blood pressure by up-regulating sodium excretion when the plasma sodium concentration is high and increasing sodium reabsorption when plasma sodium levels are low.
  • the tubuloglomerular feedback pathway participates in regulating these effects and is represented in Figure 9.
  • Sodium levels are sensed by the macula densa, a cellular structure located after the proximal tubule and loop of Henle but before the distal tubule and collecting duct.
  • Low levels of sodium in the glomerular filtrate induce renin release, which promotes Ang Il and aldosterone synthesis.
  • Ang Il acts in the proximal tubule to increase reabsorption of sodium and water to increase blood volume.
  • Aldosterone increases sodium reabsorption in the distal tubule and therefore its actions are physiologically similar to those of Ang II. Increased levels of Ang Il in response to low sodium concentration by the macula densa also result in vasoconstriction of the afferent and efferent arterioles, with a greater effect on the efferent arteriole that results in increased single nephron glomerular filtration rate (SNGFR). High levels of sodium sensed by the macula densa will have the opposite effect - block renin release, lower sodium reabsorption and thus promote further sodium excretion while also lowering SNGFR.
  • SNGFR single nephron glomerular filtration rate
  • MAP is a product of cardiac output (CO, defined as the rate at which blood is ejected by the left ventricle) and arterial (arteriolar) resistance (total peripheral resistance, TPR).
  • CO cardiac output
  • TPR total peripheral resistance
  • RSNA renal sympathetic nervous activity
  • the added representation of the RSNA takes into consideration the more accurate connection between the regulation of arterial pressure and arterial blood volume. This approach allows for the simulation of alternative disease etiologies leading to hypertension. Such profiles will be generated in response to various SNS activity- mediated perturbations of individual vascular bed resistances.
  • the addition of the RSNA to the GC model is a closer approximation to 'essential' hypertension.
  • Clinical behaviors can be mechanistically modulated in the blood pressure regulation module to generate high blood pressure, characterize the reported sensitivity to sodium intake and to evaluate responses to a variety of therapies including RAAS and non RAAS-based therapies.
  • the key renal components represented in the blood pressure regulation model include GFR and glomerular hemodynamics, tubular sodium and water reabsorption, sodium sensing by the macula densa, and modulation of the secretion rate of renin.
  • the cardiovascular hemodynamic components represented in the platform include mean arterial pressure, cardiac output, total peripheral resistance, sympathetic nervous activity, and vascular capacitance.
  • the humoral components with vascular and renal effects include Angiotensin Il (Ang II), aldosterone, anti-diuretic hormone (ADH), atrial natriuretic peptide (ANP), sodium and potassium.
  • the main biological blocks include cardiovascular, renal and signaling (humoral) variables.
  • the primary clinical behaviors that can be mechanistically modulated include • generation of high blood pressure,
  • the key renal components include
  • the blood pressure regulation module can track sodium balance and total sodium amount. It also can calculate water intake to track water balance and extracellular fluid volume (ECFV).
  • ECFV extracellular fluid volume
  • the blood pressure regulation module contains a simplified representation of cardiac function and peripheral circulation. Based principally on the ECFV-derived blood volume, it can calculate MAP and right atrial pressure (RAP). These pressures are modulated by Ang Il and autonomic responses.
  • Figures 8 and 9 delineates the key functions and relationships implemented in the model.
  • the blood pressure regulation module comprises both systemic cardiovascular (Fig. 8) and renal (Fig. 9) aspects.
  • the renal aspect represented in the blood pressure regulation module can be broken down into three functions. The first function is the determination of GFR.
  • GFR is largely dominated by MAP, afferent arteriole resistance and efferent arteriole resistance. Afferent resistance is driven by the external rSNA input and by an internal feedback from the macula densa. GFR determines the load of water entering the tubule, and in conjunction with the externally determined sodium concentration, it determines the sodium entering the tubule.
  • the second function is water reabsorption, which is represented by a single reabsorption process (the sum of proximal tubule, loop of Henle, distal tubule, and collecting duct reabsorption). The reabsorption fraction preferably is modulated by aldosterone and ADH. Urine flow is simply the non-reabsorbed filtrate.
  • the third component of renal sub- module is the reabsorption of sodium, which is handled in three separate regions.
  • the first region is labeled "proximal tubule & LOH Na+ reabsorption" and includes the representation of the reabsorption that occurs in the LoH.
  • Sodium reabsorption also occurs in the distal tubule and the collecting duct.
  • the various reabsorption processes are modulated by Ang II, rSNA, aldosterone and ANP. Note that the reabsorption fraction also depends on the sodium load. Often the sodium load dependence can dominate over the humoral modulators.
  • renin secretion and afferent arteriole resistance are determined based on sodium flow at the macula densa (located just before the entrance to the distal tubule).
  • the effects of the primary hormones involved in the regulation of sodium including ADH, ANP, Ang Il and aldosterone are also represented.
  • the model also includes the modulation of rSNA by MAP, right atrial pressure RAP and the effects of rSNA on renin secretion by the kidney.
  • the present model includes the vascular resistance of interlobar, arcuate, and interlobular arteries (collectively called 'preglomerular resistance'), as well as the resistance of peritubular capillaries and veins. This additional granularity allows one to more accurately describe intrarenal vascular resistance and its effects on blood pressure.
  • Ang Il is a potent vasoconstrictor that has effects both in the kidney and throughout the systemic circulation
  • some implementations include a representation of the effects of Ang Il on the renal vasculature.
  • Ang Il has effects on both renal and systemic circulations.
  • the contribution of Ang Il to the systemic arterial resistance was compared to results obtained using the Quantitative Human Physiology (QHP) software.
  • QHP is a publicly available simulation software from the University of Mississippi developed and maintained by Coleman and colleagues (Hester, et al. A multilevel open source integrative model of human physiology. FASEB J 2008 March 1 ;22(1_MeetingAbstracts):756).
  • QHP version 2008b3 was used to obtain the functional dependence of arterial resistance on Ang Il concentration.
  • the effects of Ang Il on afferent arteriole and total preglomerular resistance were represented as a linear relationship:
  • R R 0 (a + b - C AngII )
  • R 0 is the nominal vascular resistance
  • C An gi ⁇ is the concentration of Ang Il (circulating or bound to a receptor)
  • a and b are fitting constants such that for physiological C An gi ⁇ values the modifier in parenthesis is close to 1.
  • TPR does not explicitly include renal vascular resistance and does not account for its contribution to TPR.
  • certain implementations of the model described here in considers systemic and renal components as parallel resistances with an appropriate calculation of their effect on mean arterial pressure and cardiac output to differentiate between the renal and systemic effects on hypertension. The changes are reflected in the "total peripheral resistance" node.
  • Renal blood flow can be calculated by taking into account that actual pressure drop in the kidney is less than mean arterial pressure.
  • the contribution of renal vein resistance corresponds to a measured value of approximately 4 mm Hg.
  • the current model preferably includes an additional autoregulatory mechanism that constrains GFR values by reducing changes in glomerular pressure that occur in response to changes in MAP. The effect can be implemented via "glomerular pressure autoregulation". When calculated, theoretical glomerular pressure can be adjusted by multiplying it to a transform function.
  • GFR is a function of the number of effective functional nephrons. Functional nephrons may change because of disease progression or simply through the aging process. To account for these effects, total GFR can be computed as a product of an average SNGFR and the total number of nephrons.
  • Sodium reabsorption mechanisms can be added by 1 ) implicitly representing the Loop of Henle, and 2) modifying the effect of the macula densa on the tubuloglomerular feedback. These modifications were implemented to represent the effects of diuretic therapy, particularly loop diuretics (furosemide).
  • the Karaaslan model includes no specific mechanism(s) to account for this regulation.
  • One implementation of the model includes additional feedback to renal water reabsorption in the RAAS model. This feedback mechanism helps to keep plasma sodium concentration within feasible (physiological and pathological) constraints.
  • the reabsorption regulator the following form was chosen:
  • Q and Q 0 is sodium reabsorption rate and its nominal value, respectively.
  • C, Cmax, and Cref are current sodium concentration, and its physiologically maximal and nominal values respectively, S and G are scale and gain factors allowing to fine tune the effect.
  • This feedback has a nonstandard form, similar but not identical to proportional control, whereby a rapid compensatory mechanism is activated as sodium concentrations increase and approach an upper limit.
  • the feedback's gain can be adjusted to prevent oscillatory/unstable behaviors while still maintaining sufficiently tight control over sodium concentration.
  • a more common controller, one that increases water reabsorption proportionately to the sodium concentration relative to a "set-point" could also be implemented as it may also correct for reductions in sodium concentration.
  • This alternate form may be less effective at keeping a "maximum" concentration limit, which was the original issue detected in the Karaaslan model.
  • the invention also provides methods and systems for simulating hypertension.
  • the system of the invention comprises: a) a computer-executable data editor, capable of accepting data describing a subject; b) a computer-executable integrator, capable of executing a computer model of atherosclerosis with the data to generate a set of outputs describing the result of the simulation of atherosclerosis; and c) a computer-executable report generator capable of reporting the set of outputs.
  • the computer model comprises: i) a RAAS pathway module; ii) a renal function module; and iii) a blood pressure regulation module.
  • Methods of simulating RAAS comprise executing the models of the invention, optionally in conjunction with a virtual stimulus.
  • Methods of simulating RAAS can comprise applying a virtual protocol to the computer model to generate a set of outputs to represent a phenotype of the biological system.
  • the phenotype can represent a normal state or a disease state.
  • the methods can further include accepting user input specifying one or more parameters or variables associated with one or more mathematical representations prior to executing the computer model.
  • the user input comprises a definition of a virtual patient or a definition of the virtual protocol, such as administration of a therapy.
  • Running the computer model produces a set of outputs for a biological system represented by the computer model.
  • the set of outputs can represent one or more phenotypes of the biological system, i.e., the simulated subject, and includes values or other indicia associated with variables and parameters at a particular time and for a particular execution scenario.
  • a phenotype is represented by values at a particular time.
  • the behavior of the variables is simulated by, for example, numerical or analytical integration of one or more mathematical relations to produce values for the variables at various times and hence the evolution of the phenotype over time.
  • the level of detail of the output can vary dependent upon the level of sophistication of the target user.
  • Exemplary outputs can range from an exhaustive report including all parameters of the computer model to a simple indicator of likelihood of hypertension or a normotensive blood pressure at a particular point in time. Additional clinically relevant outputs include therapeutic effects on circulating angiotensinogen, glomerular ACE activity or blood volume.
  • the computer executable software code numerically solves the mathematical equations of the model(s) under various simulated experimental conditions. Furthermore, the computer executable software code can facilitate visualization and manipulation of the model equations and their associated parameters to simulate different patients subject to a variety of stimuli. See, e.g., U.S. Patent Number 6,078,739, entitled “Managing objects and parameter values associated with the objects within a simulation model," the disclosure of which is incorporated herein by reference. Thus, the computer model(s) can be used to rapidly test hypotheses and investigate potential drug targets or therapeutic strategies.
  • the computer model can represent a normal state as well as a disease (e.g., hypertensive or diabetic) state of a biological system.
  • the computer model includes parameters that are altered to simulate a disease state or a progression towards the disease state.
  • the parameter changes to represent a disease state are typically modifications of the underlying biological processes involved in the disease state, for example, to represent the genetic or environmental effects of a condition on the underlying physiology.
  • selecting and altering one or more parameters a user modifies a normal state and induces a phenotype of interest. In one implementation, selecting or altering one or more parameters is performed automatically.
  • various mathematical relations of the computer model, along with a modification defined by the virtual stimulus can be solved numerically by a computer using standard algorithms to produce values of variables at one or more times based on the modification. Such values of the variables can, in turn, be used to produce the first set of results of the first set of virtual measurements.
  • the virtual stimulus is a representation of administration of a therapy.
  • One or more virtual patients in conjunction with the computer model can be created based on an initial virtual patient that is associated with initial parameter values.
  • a different virtual patient can be created based on the initial virtual patient by introducing a modification to the initial virtual patient.
  • modification can include, for example, a parametric change (e.g., altering or specifying one or more initial parameter values), altering or specifying behavior of one or more variables, altering or specifying one or more functions representing interactions among variables, or a combination thereof.
  • a parametric change e.g., altering or specifying one or more initial parameter values
  • altering or specifying behavior of one or more variables altering or specifying one or more functions representing interactions among variables, or a combination thereof.
  • other virtual patients e.g., patients possessing certain risk factors for developing high blood pressure, may be created based on the initial virtual patient by starting with the initial parameter values and altering one or more of the initial parameter values.
  • Alternative parameter values can be defined as, for example, disclosed in U.S. Pat. No. 6,078,739. These alternative parameter values can be grouped into different sets of parameter values that can be used to define different virtual patients of the computer model. For certain applications, the initial virtual patient itself can be created based on another virtual patient (e.g., a different initial virtual patient).
  • one or more virtual patients in the computer model can be created based on an initial virtual patient using linked simulation operations as, for example, disclosed in the following publication: "Method and Apparatus for Conducting Linked Simulation Operations Utilizing A Computer-Based System Model", (U.S. Application Publication No. 20010032068, published on October 18, 2001 ).
  • This publication discloses a method for performing additional simulation operations based on an initial simulation operation where, for example, a modification to the initial simulation operation at one or more times is introduced.
  • additional simulation operations can be used to create additional virtual patients in the computer model based on an initial virtual patient that is created using the initial simulation operation.
  • a virtual patient can be customized to represent a particular subject.
  • one or more simulation operations may be performed for a time sufficient to create one or more "stable" virtual patient of the computer model.
  • a "stable" virtual patient is characterized by one or more variables under or substantially approaching equilibrium or steady-state condition.
  • Various virtual patients of the computer model can represent variations of the biological system that are sufficiently different to evaluate the effect of such variations on how the biological system responds to a given scenario.
  • one or more biological processes represented by the computer model can be identified as playing a significant role in modulating biological response to a therapy, and various virtual patients can be defined to represent different modifications of the one or more biological processes.
  • the identification of the one or more biological processes can be based on, for example, experimental or clinical data, scientific literature, results of a computer model, or a combination thereof.
  • various virtual patients can be created by defining different modifications to one or more mathematical relations included in the computer model, which one or more mathematical relations represent the one or more biological processes.
  • a modification to a mathematical relation can include, for example, a parametric change (e.g., altering or specifying one or more parameter values associated with the mathematical relation), altering or specifying behavior of one or more variables associated with the mathematical relation, altering or specifying one or more functions associated with the mathematical relation, or a combination of them.
  • the computer model may be run based on a particular modification for a time sufficient to create a "stable" configuration of the computer model.
  • the model of RAAS is executed while applying a virtual stimulus or protocol representing, e.g., a change in diet or a therapeutic regimen.
  • a virtual stimulus can be associated with a stimulus or perturbation that can be applied to a biological system.
  • Different virtual stimuli can be associated with stimuli that differ in some manner from one another.
  • Stimuli that can be applied to a biological system can include, for example, existing or hypothesized therapeutic agents, treatment regimens, and medical tests. Additional examples of stimuli include exercise and diet. Further examples of stimuli include environmental changes such as those relating to changes in level of exposure to an environmental agent.
  • a virtual protocol e.g., a virtual therapy, representing an actual therapy can be applied to a virtual patient in an attempt to predict how a real-world equivalent of the virtual patient would respond to the therapy.
  • Virtual protocols that can be applied to a biological system can include, for example, existing or hypothesized therapeutic agents and treatment regimens, mere passage of time, changes in lifestyle and the like.
  • a virtual protocol can be created, for example, by defining a modification to one or more mathematical relations included in a model, which one or more mathematical relations can represent one or more biological processes affected by a condition or effect associated with the virtual protocol.
  • a virtual protocol can define a modification that is to be introduced statically, dynamically, or a combination thereof, depending on the particular conditions and/or effects associated with the virtual protocol.
  • the detailed model of hypertension presented herein is the foundation of a platform to investigate the response of this system to multiple RAAS-modulating therapies.
  • the model can be used to predict the relative effects of the different therapies on entities that are difficult to measure clinically and can be used to predict the response to combination therapies for which clinical data is not available.
  • the model also highlights any differences between circulating and renal peptide concentrations, and how therapies that localize in the renal tissue may have different effects than therapies that remain only in the systemic circulation.
  • the predicted concentrations of renal peptides may also yield insight into the changes in local Ang Il in response to therapies without requiring invasive and difficult tissue sampling.
  • the model can be used to investigate questions around the effect of therapies on local tissue Ang Il that, in turn, has an effect on renal function.
  • Using combinations of different classes of RAAS-modulating therapies to treat hypertension is of interest in drug development. Since none of the currently prescribed therapies can block 100% of Ang Il production, it is thought that inhibiting the pathway at multiple points in the pathway and within the tissue may provide a more complete blockade and have a better effect on reducing blood pressure. While there is a large body of RAAS biomarker data available for monotherapies, there is less complete data on the corresponding biomarker response to combination therapy due to a lack of resources to pursue all potential combinations and cost factor attached with any clinical trial.
  • ATI-bound Ang Il is the actual effector of the RAAS pathway and is not measured in the clinic. Instead, the changes in upstream biomarkers are used to estimate and compare the effectiveness of different classes of RAAS modulating therapies.
  • plasma renin activity (PRA) and plasma renin concentration (PRC) are typically measured in clinical trials but different classes of RAAS drugs affect these phenotypic data in different ways (e.g. DRIs reduce PRA, while ARBs and ACEi increase PRA) while still achieve measurable decreases in blood pressure. This makes it difficult to compare the relative level of the reduction in AT-1 bound Ang Il achieved by different mono and combination therapies.
  • the model described herein can be used to fill this gap, by predicting the relative % change in ATI-bound Ang Il (i.e., the effector of downstream changes in blood pressure, glomerular filtration rate, end-organ protection, etc) for different monotherapies and for combination therapies even in the absence of any direct measure or marker of drug efficacy.
  • the model was rigorously calibrated with phenotypic data (PRA and PRC) from a large number of studies for a range of RAAS-modulating monotherapies (e.g. aliskiren, valsartan, losartan, irbesartan, enalapril, ramipril).
  • the model was able to predict the phenotypic (PRA/PRC) response to combinations of RAAS drugs for which data was available, (e.g. aliskiren + valsartan), with no additional changes in model parameters.
  • the model can be used with confidence to predict the change in phenotype for different combination therapies when sufficient clinical data is not available to us. For example, it has been used to predict the phenotypic response for aliskiren 300mg + ramipril 10mg. In addition, the model predicts the relative % inhibition of ATI-bound Ang Il for the different doses and types of RAAS-modulating therapies. The strength of this integrated model lies in the prediction of ATI-bound Ang Il levels, a valuable measure of the primary effector of the downstream response of the RAAS pathway that is difficult to measure in vivo, and even more difficult to measure in the tissue.
  • This invention can include a single computer model that serves a number of purposes.
  • this invention can include a set of large-scale computer models covering a broad range of physiological systems.
  • the system can include complementary computer models, such as, for example, epidemiological computer models or models of related systems, e.g. atherosclerosis and its associated cardiovascular risk.
  • computer models can be designed to analyze a large number of subjects and chemicals.
  • the computer models can be used to create a large number of validated virtual patients and to simulate their responses to a large number of therapeutic regimens or changes in lifestyle.
  • the invention and all of the functional operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structural means disclosed in this specification and structural equivalents thereof, or in combinations of them.
  • the invention can be implemented as one or more computer program products, i.e., one or more computer programs tangibly embodied in an information carrier, e.g., in a machine readable storage device or in a propagated signal, for execution by, or to control the operation of, data processing apparatus, e.g., a programmable processor, a computer, or multiple computers.
  • a computer program (also known as a program, software, software application, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.
  • a computer program does not necessarily correspond to a file.
  • a program can be stored in a portion of a file that holds other programs or data, in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub-programs, or portions of code).
  • a computer program can be deployed to be executed on one computer or on multiple computers at one site or distributed across multiple sites and interconnected by a communication network.
  • processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer.
  • a processor will receive instructions and data from a read only memory (ROM) or a random access memory (RAM) or both.
  • the essential elements of a computer are a processor for executing instructions and one or more memory devices for storing instructions and data.
  • a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks.
  • Information carriers suitable for embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks.
  • semiconductor memory devices e.g., EPROM, EEPROM, and flash memory devices
  • magnetic disks e.g., internal hard disks or removable disks
  • magneto optical disks e.g., CD ROM and DVD-ROM disks.
  • the processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.
  • the invention can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and/or a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer.
  • a display device e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor
  • a keyboard and/or a pointing device e.g., a mouse or a trackball
  • Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input.
  • the invention can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the invention, or any combination of such back end, middleware, or front end components.
  • the components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network ("LAN”) and a wide area network (“WAN”), e.g., the Internet.
  • LAN local area network
  • WAN wide area network
  • the computing system can include clients and servers.
  • a client and server are generally remote from each other and typically interact through a communication network.
  • the relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
  • Example 1 Hypertensive virtual patients [0170] In the context of one implementation of the invention, four exemplary hypertensive virtual patients were developed.
  • HT-1 an essential hypertensive patient with local vasoconstriction and atherosclerosis: Increased preglomerular resistance is a known cause of hypertension, and may be caused by increased sympathetic nervous activity and/or widespread atherosclerosis. While these disease etiologies have a systemic effect, HT-1 was represented in as a local increase in the renal afferent arteriole resistance leading to decreased perfusion of the kidneys to represent patients who may have plaques, obstructions or other factors leading to constriction of the renal artery. Simulations with the present model demonstrated that as the resistance of the afferent arteriole is increased, the GFR initially decreases due to a reduction of perfusion pressure into the glomerulus resulting in decreased sodium and water excretion.
  • HT-2 a diabetic hypertensive patient with diabetic nephropathy/glomerular damage:.
  • K f is the hydrostatic conductance of the glomerular membrane. It is a product of k (specific filtration coefficient), and S (the available surface area for filtration). Patients with nephropathy typically have a reduced K f due to the reduction of both k and S. Loss of endothelial fenestrae, a thickened glomerular basement membrane, and loss of epithelial slits between podocyte foot processes all change the filters integrity by reducing k and the ability to filter water and solutes. Similarly, mesangial expansion and glomerulosclerosis decrease the surface area available for filtration.
  • K f can also increase in the early stages of diabetic nephropathy; the structural change(s) responsible for hyperfiltration in the diabetic setting are unclear, although glomerular
  • K f glomerular filtration coefficient
  • HT-3 an essential hypertensive patient with increased sodium absorption in nephron.
  • a defective increase in sodium reabsorption in the descending portion of the loop of Henle is commonly associated with sodium-insensitive hypertension. Since these sections of the nephron are located upstream of the macula densa it is subjected to regulation by tubuloglomerular feedback (TGF) mechanisms.
  • TGF tubuloglomerular feedback
  • sodium reabsorption is increased in tubular segments located before the macula densa (e.g. LoH), a specialized group of epithelial cells part of the juxtaglomerular apparatus (JGA).
  • the JGA is located in the portion of the distal tubule that comes in close contact with the afferent and efferent arterioles. Increased sodium reabsorption delivers less sodium to the distal tubule and this is sensed by the macula densa. As a result, 1 ) afferent arteriole resistance is decreased (most likely mediated by local production of vasodilators) and, 2) renin production by JG cells is increased. Local generation of Ang Il causes an increase in efferent arteriole resistance. Together, the effects on pre- and post-glomerular resistance increase GFR and bring it back to normal. Direct effects of Ang Il on sodium reabsorption also contribute to restore sodium homeostasis.
  • each nephron excretes less than the amount required to maintain sodium homeostasis.
  • Sodium accumulates slowly over time and eventually suppresses renin release in an effort to increase excretion.
  • the abnormally high level of distal sodium and water reabsorption will continue and increase mean arterial pressure.
  • HT-4 an essential hypertensive patient with increased systemic vascular resistance: Essential hypertension has been traditionally viewed to be a result of increased arterial resistance. Early studies on the use of central antihypertensive agents (e.g. clonidine) demonstrated that a reduction in the central sympathetic outflow translated into reductions in mean arterial pressure. Initial attempts using an increased tubuloglomerular resistance (TPR) to generate hypertension was not successful. The kidney was capable of compensating for any changes in the resistance by altering water volume and ultimately affecting cardiac output. In order to reproduce hypertension due to increased TPR, HT-4 virtual patient is represented by all systemic arteries (including the renal artery) having increased resistance.
  • TPR tubuloglomerular resistance
  • TPR can be expanded to include renal resistance and the actions of Ang Il on both renal and systemic arteries.
  • a representative of essential hypertension was created by modulating total peripheral and renal resistances. Although this hypertensive patient is similar to HT- 1 , this patient will respond differently to therapies that target the total peripheral resistance
  • Atenolol Similar mechanistic grounds were utilized to implement additional non-RAAS and RAAS-based therapies. Renal, vascular and hormonal mechanisms were utilized including handling of sodium by the nephron, direct or indirect effects on renal hemodynamics, and effects on arterial vasoreactivity.
  • the effect of a drug is implemented according to the reported inhibition of a specific pathway, as well as a function of the drug concentration.
  • the latter is approximated by a temporal profile when concentration transitions from its minimal to its maximal value.
  • the normalized profile is multiplied by a certain dose resulting in a net effect.
  • concentration increases from 0 to 1 in the course of 24 hours.
  • the shape of the curve can be adjusted/customized using the appropriate object parameters. Specific functional forms are presented for each drug class.
  • thiazides e.g. hydrochlorotiazide, HCT
  • HCT hydrochlorotiazide
  • thiazide lowers the value of Q re abso P by a factor of (1 - C Th *i) where C is the thiazide normalized concentration and / is the level of inhibition.
  • Parameter / is dependent on the dose and could be calibrated to fit specific data on Na+ reabsorption or high level behavior.
  • the factor (1 - C*i) should be set at values between 0 and 1.
  • thiazides may affect other pathways.
  • the acute effects of thiazide therapy include a reduction of plasma and extracellular fluid volume.
  • prolonged treatment i. e. > 1 month
  • plasma volume and extracellular fluid volume return close to pre-treatment levels. Therefore, the effect on systemic hemodynamics do not fully account for the reduction in blood pressure.
  • a hypothesis formulated in the literature ascribes long-term effects of thiazide therapy to changes in vascular resistance. In the platform, both pathways are represented; their separate or combined action is defined by their respective value sets. Fig.
  • Furosemide is a loop diuretic which acts predominately at the apical membrane in the thick ascending limb of the loop of Henle (LoH); it inhibits Na + and Cl " reabsorption.
  • the furosemide-mediated diuretic effect is represented by reducing Na + reabsorption in the proximal nephron.
  • the filtered sodium load in the proximal tubule is split into two fractions, one of them, F LoH , is ascribed to the LoH; this portion of the sodium reabsorption fraction is affected only by furosemide, (eq. 29). It is known that about 25% of sodium reabsorption happens in the LoH, thus the following range was chosen 0.2 ⁇ F LoH ⁇ 0.3 .
  • ⁇ -Blockers [0185] ⁇ -Blockers (BBs).
  • the antihypertensive action of BBs involves reductions in cardiac output and renin release from the kidneys.
  • Beta blockers also have a central nervous system effect that reduces the activity of the sympathetic nervous system (sympathetic activity outflow).
  • renin release is stimulated by increases in renal sympathetic activity (rSNA), whereas Na+ flow is sensed by the macula densa.
  • rSNA renal sympathetic activity
  • Na+ flow is sensed by the macula densa.
  • rSNA is represented as a normalized baseline value N ⁇ SNA multiplied by the effect of MAP on rSNA and the effect of right atrial pressure (RAP) on rSNA.
  • Beta blockers therapy reduces the value of rSNA, its representation in the platform is similar to thiazide, see Eq (30).
  • the rSNA value was reduced by therapy by 25%.
  • mean arterial pressure was reduced by 5-14 mm Hg in simulations ran in the set of VP treated, and the reductions were in agreement with reported data.
  • CCBs Calcium channel blockers
  • CCB based drugs have multiple effects on the cardiovascular system including reduction in the force of contraction of the myocardium, reduction in heart rate, as well as vasodilation.
  • calcium channel blocker effects are implemented as a reduction in systemic arterial resistance, and renal arterial resistance. Renal arterial resistance is represented as three compartments considered separately preglomerular (pre-afferent arteriole) resistance, and afferent and efferent arteriole resistances. It is assumed that the CCB effect is more pronounced on the efferent arteriole compared to the afferent, allowing more blood filtering through the glomerulus.
  • pre-afferent arteriole preglomerular resistance
  • FIG. 13 shows a mean arterial pressure reduction of approximately 10 mmHg with a CCB therapy applied to a hypertensive VP with elevated preglomerular resistance.
  • the therapy reduced efferent arteriole resistance by 50%, while afferent arteriole resistance was reduced by 15%.
  • ACE inhibitors in the RAAS PhysioLab platform affect several pathways involving different enzymatic activities A mempy . Mathematically, they are all similarly represented as a product of uninhibited activity A 0 and therapy effect, which in turn is defined by the degree of activity inhibition / [0188]
  • ACE inhibition therapy directly affects the activity of ACE, an enzyme that catalyzes the conversion of Ang I to Ang Il both in the systemic circulation and the intrarenal glomerular and tubular compartments. It is hypothesized that peritubular tissue may also contribute to the pool of Ang Il production in the kidney and that fraction also is affected by ACE inhibition therapy.
  • a T1 receptor blocker (ARB) ARBs block the activation of type I Ang Il receptors (AT1 ). In the model disclosed herein, AT1 receptors are split between three compartments.
  • ARB therapy affects Ang Il binding rates and have a similar functional form in all compartments: where r and r 0 are binding rates with and without therapy, T is therapy inhibition effect and C ARB is the concentration of the drug.
  • the values of 7 are selected from calibration experiments and specified in the parameter set describing ARB effects, the values of r 0 are calculated at equilibrium.
  • Additional mechanisms affected by AT1 receptor blocking therapy are included in the model. For instance, ARB therapy may affect Ang Il clearance rate by altering Ang Il degradation time constants.
  • Fig. 14 shows an example on how AT1 receptor blocking therapy changes mean arterial pressure in various virtual patients when binding rates were reduced a factor of 200, while degradation rates were reduced by a factor of only 5.
  • DRIs interrupt the RAAS system by binding and preventing the action of renin and thereby inhibiting the formation of Ang I and Ang II.
  • DRI therapy effects are split into two compartments, a systemic circulation compartment and an intrarenal compartment. In the latter, DRI therapy affects glomerular and tubular angiotensinogen conversion to Ang I by membrane bound renin.
  • inhibition of plasma renin activity by DRI therapy was implemented according to the following equation:
  • Aldosterone Antagonists were lumped into one effect that alters aldosterone secretion rate: CW, where Q° a ido is the nominal aldosterone secretion rate, T a ⁇ d0 is the inhibition effect of the therapy, and C a/(to is the concentration of the drug.
  • Fig. 14 depicts simulation results on MAP changes with an aldosterone antagonist that reduced the normalized secretion rate by 90%.
  • Type 2 diabetic (T2D) disease nephropathy and progression of renal damage was calibrated using clinical data from a study conducted by Nelson et al in Pima Indians (N Eng J Med 335(22): 1636-42 (1996). The study recruited 6 groups of adult subjects with pre-defined characteristics including
  • ITT impaired glucose-tolerance
  • Urinary albumin was measured in mg/l and creatinine in g/l. Microalbuminuria was defined as UACRs of 30-299, whereas macroalbuminuria as UACRs >300. GFR and albumin excretion rates were used to match the reported clinical behavior.
  • RAAS-related peptides in the kidney was simulated using a mathematical model of renal and systemic RAAS kinetics according to the present invention.
  • the model accounts for the renal production and release of Ang I, Ang II, Ang 1-7 and Ang IV.
  • Systemic and local levels of RAAS- related peptides were estimated based on published plasma and whole renal tissue data.
  • the model considers a single renal compartment localized to the glomerulus. Local glomerular rate of renin activity, angiotensin converting enzyme activity (ACE) and degradation rates are different than in the circulation to satisfy constraints observed in radiolabeled Ang I studies by Danser et al., 1998.
  • ACE angiotensin converting enzyme activity
  • renin-angiotensin aldosterone system plays a critical role in blood pressure regulation, renal function and fluid homeostasis.
  • Ang Il concentration in renal tissue is -10 times higher than that of plasma and raises questions about the contribution of intrarenal Ang Il to renal function and disease progression.
  • the model predicted that degradation of locally synthesized Ang I as well as circulating Ang I entering the kidney lowers the local levels of Ang Il but has little measurable impact on their circulating levels.
  • Pharmacological stimulation of renal Ang I degradation and/or inhibition of Ang I to Ang Il paracrine conversion may have therapeutic implications in preventing progression of diabetic and hypertensive nephropathy.

Abstract

The invention encompasses novel computer models of hypertension and systems for predicting development and progression of hypertension and associated disease states, including heart failure, stroke and kidney disease. In particular, the computer model of hypertension comprises a RAAS pathway module, a renal function module, and a blood pressure regulation module.

Description

METHOD AND APPARATUS FOR COMPUTER MODELING HYPERTENSION
1 INTRODUCTION
1.1 Cross Reference to Related Applications [0001] This application claims the benefit of U.S. provisional patent application no.
61/218,779, filed 19 June 2009, and U.S. provisional patent application no. 61/238,653, filed 31 August 2009, each of which is incorporated herein by reference in its entirety.
1.2 Field of the Invention
[0002] The present invention relates generally to the field of computer simulation of hypertension and its associated disease risks, particularly, loss of kidney function, heart failure and stroke.
1.3 Background of the Invention
[0003] Hypertension, the medical condition of elevated blood pressure, is a public health problem that affects both developed and developing nations. Data from the National Health and Nutrition Examination Survey (NHANES) indicate that more than 50 million Americans suffer from elevated blood pressure; worldwide, these figures are close to one billion. The American Heart Association states that hypertension is the most important risk factor for heart disease and stroke in the United States. Despite substantial improvements in public awareness, clinical diagnosis, and treatment, the number of patients diagnosed with hypertension that successfully respond to medications is below optimal (27%). Hypertension has been long recognized to confer increased risk to patients with diabetes, atherosclerotic and atherothrombotic cardiovascular disease leading to an increased likelihood of, myocardial infarction (Ml), stroke, peripheral vascular disease (PVD), renal failure and heart failure (HF). Other risk factors contributing to the complex etiology of hypertension include age, weight, race/ethnicity, genetic predisposition, diabetes and dietary sodium intake.
[0004] Molecular genetics has created new research avenues and improved our understanding of the genetics of hypertension. However, the contribution of these new discoveries to prevention and treatment of a complex polygenic disease are uncertain. Although a great deal is known about the causal risk factors that lead to hypertension, in over 90% of the hypertensive population, no specific mechanism can be identified to account for the elevation in blood pressure to guide preventive measures and effective therapeutic strategies. [0005] Numerous pathophysiological mechanisms of hypertension have been postulated including increased sympathetic nervous system activity, overproduction of sodium-retaining factors and vasoconstrictors (e.g., Angiotensin Il (Ang II) and endothelin), deficiencies of vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI2). A variety of endogenous vasodilators including Ang (1-7), calcitonin gene-related peptide (CGRP), substance P and adrenomedullin, to name a few, have all been implicated in the development and maintenance of high blood pressure. The hypertensinogenic mechanisms mediated by an increased SNS activity involve perturbed baroreflex and chemoreflex pathways at both central and peripheral levels. Indirect clinical evidence of the contribution of the sympathetic nervous system activity to hypertension is the lowering blood pressure effect of centrally acting sympatholytic agents (alpha-adrenergic antagonists). Peripheral resistance is elevated in hypertension due to structural alterations. Remodeling of small arteries and arterioles contributes to the development and maintenance of high blood pressure and the ensuing organ damage. Elevated resistance in these arterioles is caused by an increased wall-to-lumen ratio. Additional pathophysiological mechanisms have been proposed to explain the increased resistance observed in hypertensive subjects including hyperuricemia, arterial stiffness, increased oxidative stress, vascular inflammation and endothelial dysfunction.
[0006] Computational approaches to modeling blood pressure regulation were pioneered by Guyton and Coleman in 1972. These authors published the first model that provided the foundation toward our understanding of the relationship between venous return, cardiac output and the vasculature (Guyton, et al., Ann Biomed Eng 1 :254-281 (1972a), and Guyton et al., Ann Rev Physiol 34:13-46 (1972b)). The original and updated versions of the model focus on the role of the kidney in long-term blood pressure regulation and the effect of blood volume regulation in the development of hypertension, but have been noted to underestimate the influence of the sympathetic nervous system (Osborn et al., Exp Physiol 94: 389-396 (2009). In addition, the representation of the RAAS pathway in the Guyton- Coleman model is oversimplified. The Guyton/Coleman (GC) model does not include vascular remodeling and its effects on vascular geometry and hemodynamics as significant contributors to increased peripheral vascular resistance (Korner and Angus (1997) Vascular remodeling. Hypertension 29:1065-1066; and Korner, et al. (1992) Are cardiac and vascular "amplifiers" both necessary for the development of hypertension? Kidney lnt Suppl 37:S38- S44). To address the under-representation of the sympathetic nervous system, Karaaslan et al, {Ann Biomed Eng 33: 1607-1630 (2005)) published a modified version of the GC model that added the influence of the renal sympathetic nervous activity on the synthesis and release of renin and the afferent arteriolar tone. [0007] The appeal of an integrated model of human physiology in drug discovery and development is the ability to investigate the interactions among multiple biological systems as a whole rather than as individual pieces. Just as the actions of a therapeutic agent extend beyond the binding kinetics at a target site, a systems biology approach to modeling disease can reveal subtleties of the entire physiological system that may not apparent in a model based on the individual physiological components. By extending the focus of the integrated model to encompass both a detailed representation of the mechanism of action and the functional change measured in the clinic, the systems biology approach can provide both meaningful and practical insights to further guide and optimize the process of drug discovery and development.
[0008] The model of hypertension described herein allows one to investigate different hypotheses about the role of angiotensin Il (Ang II) in the physiological function of the kidney, in addition to its recognized role in blood pressure regulation. In particular, hypertensive patients receiving therapies that affect renin-angiotensin aldosterone system (RAAS) may experience delay in onset of glomerulosclerosis and interstitial tubulofibrosis. The model is a powerful tool for quickly testing multiple hypotheses about the physiology that can help answer a wide range of drug development questions. For instance, it can be used to predict the expected changes in blood pressure for specific therapies in clinical trials, or to identify patient types that are most likely to benefit from anti-hypertensive therapies based on specific characteristics or biomarkers (and thus enrich a clinical trial). It can be used to test mechanistic hypotheses that are infeasible or impractical to test clinically, or to test the impact of known or hypothesized drug characteristics (e.g. localization in the kidney, ability to access specific receptors) on end-organ protection, possibly providing support for drug differentiation claims.
2 SUMMARY OF THE INVENTION
[0009] The current disclosure provides the first model to integrate systemic RAAS, renal RAAS, renal function and blood pressure regulation into a single system. The present model can be used to confidently test hypotheses underlying the effects of different diseases on renal disease progression. The relative contributions of glucose, MAP and Ang Il on disease progression in the model are realistic assumptions based on clinical measurements, published data and phenomenological observations.
[0010] One aspect of the invention provides computer models of hypertension comprising a) a RAAS pathway module; b) a renal function module; and c) a blood pressure regulation module. In one implementation, the RAAS pathway module comprises a representation of RAAS in systemic circulation, and a representation of RAAS in the kidney. Optionally, the RAAS pathway module can also comprise a representation of RAAS in heart tissue. In another implementation, the renal function module can comprise a representation of glomerular filtration rate and/or a representation of renal sodium regulation. The renal function module can additional include a representation of disease effects. In yet another implementation, the blood pressure regulation module comprises a representation of cardiac output and a representation of vascular resistance.
[0011] Another aspect of the invention provides systems for simulating hypertension comprising: a) a computer-executable data editor, capable of accepting data describing a subject; b) a computer-executable integrator, capable of executing a computer model of hypertension with the data to generate a set of outputs describing the result of the simulation of hypertension; and c) a computer-executable report generator capable of reporting the set of outputs. The computer model comprises i) a RAAS pathway module; ii) a renal function module; and iii) a blood pressure regulation module. In a preferred implementation, the computer-executable data editor further is capable of accepting a set of parameters describing a virtual patient. In yet another preferred implementation, the computer- executable integrator further is capable of executing the computer model with the set of parameters describing the subject. Preferably, the computer-executable data editor further is capable of accepting a virtual protocol and the computer-executable integrator is capable of executing the computer model with the virtual protocol. [0012] Yet another aspect of the invention provides systems comprising: a) a processor including computer-readable instructions stored thereon that, upon execution by a processor, cause the processor to simulate atherosclerosis; b) a first user terminal, the first user terminal operable to receive a user input specifying one or more parameters associated with one or more mathematical representations defined by the computer readable instructions; and c) a second user terminal, the second user terminal operable to provide the set of outputs to a second user. The computer readable instructions comprise: i) a RAAS pathway module comprising a mathematical representation of a plurality of biological processes associated with RAAS, wherein the plurality of biological processes comprises RAAS in systemic circulation, RAAS in kidney, and optionally, RAAS in cardiac tissue; ii) a renal function module comprising a mathematical representation of a plurality of biological processes associated with renal function, wherein the plurality of biological processes comprises glomerular filtration rate and albuminuria; iii) a blood pressure regulation module comprising a mathematical representation of a plurality of biological processes associated with blood pressure regulation, wherein the plurality of biological processes comprises cardiac output and vascular resistance; iv) defining a set of mathematical relationships between the representations of biological processes associated with RAAS, renal function and blood pressure regulation; and v) applying a virtual protocol to the set of mathematical relationships to generate a set of outputs. The first user may be the same as or different than the second user.
[0013] The model of hypertension can be a tool for investigating the effects of a variety of antihypertensive therapies on lower MAP and the progressive loss of renal function. The limited human data on renal enzyme rates, peptide concentrations and the biology underlying the longitudinal progression of disease was a challenge in constructing the model. Development of the model clearly relies on multiple assumptions of the underlying physiology, but these assumptions have been constrained by both data in the literature and clinical observations of renal function.
[0014] The overall behavior of the hypertension model on GFR, albuminuria and MAP response to therapies is consistent with the wide range of data in the literature. Better constraints on these responses, from either existing individual patient data or better stratification of patient phenotype data, can be useful in additional refinement of model behavior. In light of the available data, the range of responses and the consistency of behavior across the patient cohort are very good.
3 BRIEF DESCRIPTION OF THE DRAWINGS
[0015] Figure 1 provides a Summary Diagram of the computer model of hypertension.
[0016] Figure 2 provides an Effect Diagram of the RAAS pathway in systemic circulation. [0017] Figure 3 provides an Effect Diagram of the RAAS pathway module in kidney, particularly the glomerulus.
[0018] Figure 4 provides an Effect Diagram of the RAAS pathway module in kidney, particularly in tubular tissue.
[0019] Figure 5 provides an Effect Diagram of the RAAS pathway in cardiac (heart) tissue. [0020] Figure 6 provides an Effect Diagram of disease representation and progression in the renal function module.
[0021] Figure 7 provides an Effect Diagram of albumin and creatinine calculations in the renal function module.
[0022] Figure 8 provides an Effect Diagram of systemic blood circulation, baroreceptor activity, and ADH secretion in the blood pressure regulation module.
[0023] Figure 9 provides an Effect Diagram of glomerular filtration, sodium filtration, water handling and renal hemodynamics in the blood pressure regulation module. [0024] Figure 10 provides an Effect Diagram of calculations relating to RAAS and non- RAAS therapies.
[0025] Figure 11 provides an Effect Diagram of calculations relating to clinical outputs.
[0026] Figure 12 provides an Effect Diagram of additional characteristics and conversions for the model.
[0027] Figure 13 illustrates the effect of various non-RAAS therapies on mean arterial pressure. NT: normotensive VP; HT-1 : hypertensive VP with increased preglomerular resistance; HT-2: hypertensive VP with nephropathy; HT-3: hypertensive patient with altered Na+ reabsorption; HT-4: hypertensive patient with increased TPR. [0028] Figure 14 illustrates the effect of different RAAS therapies on mean arterial pressure for normotensive and hypertensive patients. Patient phenotypes as described in Figure 14.
4 DETAILED DESCRIPTION
4.1 Overview [0029] The invention encompasses novel computer models of hypertension and systems for predicting development and progression of hypertension and associated risk for developing diseases, such as heart failure, stroke and kidney disease. In particular, the computer model of hypertension comprises a RAAS pathway module, a renal function module, and a blood pressure regulation module.
4.2 Definitions
[0030] As used herein, a "biological system" can include, for example, a collection of cells such as a cell culture, an organ, a tissue, a multi-cellular organism such as an individual human patient, a subset of cells of a multi-cellular organism, or a population of multi-cellular organisms such as a group of human patients or the general human population as a whole. A biological system can also include, for example, a multi-tissue system such as the nervous system, immune system, or an organ, such as a kidney.
[0031] The term "biological component" refers to a portion of a biological system. A biological component that is part of a biological system can include, for example, an extracellular constituent, a cellular constituent, an intra-cellular constituent, or a combination of them. Examples of suitable biological components, include, but are not limited to, metabolites, DNA, RNA, proteins, surface and intracellular receptors, enzymes, hormones, cells, organs, tissues, portions of cells, tissues, or organs, subcellular organelles, chemically reactive molecules like H+, superoxides, ATP, as well as combinations or aggregate representations of these types of biological variables. In addition, biological components can include therapeutic agents such as an ACE inhibitor or diuretic.
[0032] The term "biological process" is used herein to mean an interaction or series of interactions between biological components. Examples of suitable biological processes, include, but are not limited to, activation, apoptosis or recruitment of certain cells (such as macrophages), inflammation, cytokine production, and the like. The term "biological process" can also include a process comprising one or more therapeutic agents, for example an ACE inhibitor or diuretic. Each biological variable of the biological process can be influenced, for example, by at least one other biological variable in the biological process by some biological mechanism, which need not be specified or even understood.
[0033] The term "parameter" is used herein to mean a value that characterizes the interaction between two or more biological components. Examples of parameters include affinity constants, Km, K0, /ccat, half life, or net flux of water, sodium or proteins.
[0034] The term "variable," as used herein refers to a value that characterizes a biological component. Examples of variables include protein concentrations, such as circulating Ang I or plasma renin concentration, physical measures, such as vascular capacity or extracellular fluid volume.
[0035] The term "phenotype" is used herein to mean the result of the occurrence of a series of biological processes. As the biological processes change relative to each other, the phenotype also undergoes changes. One measurement of a phenotype is the level of activity of variables, parameters, and/or biological processes at a specified time and under specified experimental or environmental conditions.
[0036] A phenotype can include, for example, the state of an individual cell, an organ, a tissue, and/or a multi-cellular organism. Organisms useful in the methods and models disclosed herein include animals. The term "animal" as used herein includes mammals, such as humans. A phenotype can also include, but is not limited to, behavior of the system as a whole, e.g. mean arterial pressure. The conditions defined by a phenotype can be imposed experimentally, or can be conditions present in a patient type. For example a normal phenotype can include a certain amount of circulating Ang Il and sodium and a certain mean arterial pressure. In another example, a disease phenotype can include increased sympathetic nervous activity, increased preglomerular resistance. In yet another example, the phenotype can include the amount of sodium absorption by a nephron or diabetic nephropathy. [0037] The term "simulation" is used herein to mean the numerical or analytical integration of a mathematical model. For example, simulation can mean the numerical integration of the mathematical model of the phenotype defined by the equation, i.e., dx/dt=f(x, p, t).
[0038] The term "biological characteristic" is used herein to refer to a trait, quality, or property of a particular phenotype of a biological system. For example, biological characteristics of the biological systems related to hypertension include clinical signs and diagnostic criteria associated with blood pressure and kidney function. The biological characteristics of a biological system can be measurements of biological variables, parameters, and/or processes. Suitable examples of biological characteristics associated with RAAS include, but are not limited to, measurements of glomerular filtration rates (GFR), mean arterial pressure (MAP) and concentration of certain circulating proteins.
[0039] The term "computer-readable medium" is used herein to include any medium which is capable of storing or encoding a sequence of instructions for performing the methods described herein and can include, but not limited to, optical and/or magnetic storage devices and/or disks.
4.3 Methods of Developing Models of Hypertension
[0040] The present invention provides a mathematical model of hypertension as part of an integrated in s/V/co/experimental approach to the assessment of cardiovascular risk, particularly of heart failure or stroke. The exemplified computer model of hypertension is a large-scale nonlinear ordinary differential equation-based representation of the key biological mechanisms involved in the RAAS pathway, kidney function and blood pressure regulation.
[0041] A computer model can be designed to model one or more biological processes or functions. The computer model can be built using a "top-down" approach that begins by defining a general set of behaviors indicative of a biological condition, e.g. blood pressure. The behaviors are then used as constraints on the system and a set of nested subsystems are developed to define the next level of underlying detail. For example, given a behavior such mean arterial pressure, the specific mechanisms inducing the behavior can each be modeled in turn, yielding a set of subsystems, which can themselves be deconstructed and modeled in detail. The control and context of these subsystems is, therefore, already defined by the behaviors that characterize the dynamics of the system as a whole. The deconstruction process continues modeling more and more biology, from the top down, until there is enough detail to replicate a given biological behavior. Ideally, the model is capable of modeling biological processes that can be manipulated by a drug or other therapeutic agent. [0042] The methods used to develop computer models of hypertension typically begin by identifying one or more biological processes associated with the RAAS pathway in specific tissues (such as systemic circulation, kidney tissue and/or cardiac tissue), one or more biological processes associated with kidney function and one or more biological processes associated with blood pressure regulation. The identification of these biological processes can be informed by data relating to a metabolic, hormonal or organ system or any portion thereof. Optionally, the method can also comprise the step of identifying one or biological processes associated with stability of heart tissue and cardiovascular risk, particularly with myocardial tissue damage. The method next comprises the step of mathematically representing each identified biological process. The biological processes can be mathematically represented in any of a variety of manners. Typically, the biological process is defined by the equation, i.e., dx/dt=f(x, p, t), as described below. The representations of biological processes associated with RAAS pathway, kidney function and blood pressure regulation are combined, thus forming predictive models of hypertension. FIG. 1 provides an overview of the modules that can be utilized in designing a computer model of hypertension.
[0043] In a preferred implementation of the invention, identifying a biological process associated with the RAAS pathway comprises identifying one or more biological processes related the RAAS pathway in systemic circulation, identifying one or more biological processes associated with the RAAS pathway in the kidney, and optionally identifying one or more biological processes associated with the RAAS pathway in heart tissue. In certain implementations, the RAAS pathway in kidney can be separately represented by glomerular RAAS and tubular RAAS. The biological processes related to the RAAS pathway can comprise one or more of angiotensinogen production, processing of angiotensinogen to Ang I, the action of chymase or ACE to generate Ang II, the production of Ang (1-7), inactivation of Ang Il and binding of AT-1 or AT-2 to Ang Il (see Fig. 2-5). The representation of systemic RAAS pathway, in a preferred embodiment, represents the feedback regulation of prorenin synthesis and processing and the equilibrium between prorenin and renin. In certain implementations, the biological processes related to the glomerular RAAS pathway comprise Ang I influx and efflux in the kidney, the interaction between changes of Ang I and/or Ang Il in the kidney on blood volume, or the interaction between blood volume on Ang I and Ang Il synthesis and degradation in the kidney (see Fig. 3).
[0044] In another implementation, identifying a biological process associated with renal function comprise identifying a biological process related to disease progression (see, e.g. Fig. 6) or a biological process related to albumin/creatinine processing (see, e.g. Fig. 7). The biological processes related to disease progression can include, but are not limited to blood pressure effect on filtration, plasma glucose effect on Kf and filtration, glomerular Ang Il effect on Kf and filtration, glomerular pressure effects on nephron loss and the sieving membrane, the rate of disease damage to sieving, rate of sieving membrane repair, reversible and/or permanent damage to the sieving membrane, Ang Il effect on tubular fibrosis, and excess albumin reabsorption and the effect on tubular fibrosis. The biological processes related to albumin/creatinine processing can relate to a single glomerulus and/or the whole kidney. These processes can include, but are not limited to, SNGFR, glomerular albumin sieving coefficient, glomerular filtrate albumin concentration, reabsorption capacity and fraction, tubular fibrosis level, fibrosis effect on albumin reabsorption, fraction of functional nephrons, albumin excretion rate, creatinine clearance rate, creatinine synthesis rate, serum creatinine concentration, and age effect on GFR.
[0045] In yet another implementation identifying a biological process associated with blood pressure regulation comprises identifying one or more biological processes related to ADH secretion, peripheral resistance, cardiac output, extracellular fluid volume and/or vascular capacity (see, e.g. Fig. 8). In certain implementations, identifying a biological process associated with blood pressure regulation comprises identifying one or more biological processes related to water filtration, renal hemodynamics and/or sodium filtration (see, e.g. Fig. 9). In certain implementations, the biological processes related to water filtration can include, but are not limited to, urine flow rate, the effect of aldosterone concentration and/or ADH concentration on tubular water reabsorption rate. The biological processes related to sodium filtration can include, but are not limited to, total sodium amount, extracellular fluid volume, filtered sodium load, proximal tubule and LoH reabsorption, macular densa sodium flows, distal sodium reabsorption, distal tubule sodium outflow, macula densa signal accumulation, and sodium excretion via urine. The biological processes related to renal hemodynamics can include, efferent arteriole resistance, afferent arteriole resistance, renal blood flow, renal vascular resistance, renal sympathetic nerve activity, tubule-glomerular feedback effect and glomerular pressure autoregulation
[0046] Once one or more biological processes are identified in the context of the methods of the invention, each biological process is mathematically represented. For example, the computer model can represent a first biological process using a first mathematical relation and a second biological process using a second mathematical relation. A mathematical relation typically includes one or more variables, the behavior (e.g., time evolution) of which can be simulated by the computer model. More particularly, mathematical relations of the computer model can define interactions among variables describing levels or activities of various biological components of the biological system as well as levels or activities of combinations or aggregate representations of the various biological components. In addition, variables can represent various stimuli that can be applied to the physiological system. The mathematical model(s) of the computer-executable software code represents the dynamic biological processes related to RAAS pathway including kidney function and blood pressure. The form of the mathematical equations employed may include, for example, partial differential equations, stochastic differential equations, differential algebraic equations, difference equations, cellular automata, coupled maps, equations of networks of Boolean or fuzzy logical networks, etc.
[0047] In some implementations, the mathematical equations used in the model are ordinary differential equations of the form: dx/dt=f(x, p, t) where x is an N dimensional vector whose elements represent the biological variables of the system, t is time, dx/dt is the rate of change of x, p is an M dimensional set of system parameters, and f is a function that represents the complex interactions among biological variables. In one implementation, the parameters are used to represent intrinsic characteristics (e.g., genetic factors) as well as external characteristics (e.g., environmental factors) for a biological system.
[0048] In some implementations, the phenotype can be mathematically defined by the values of x and p at a given time. Once a phenotype of the model is mathematically specified, numerical integration of the above equation using a computer determines, for example, the time evolution of the biological variables x{t) and hence the evolution of the phenotype over time.
[0049] The representation of the biological processes are combined to generate a model of RAAS. Generation of models of biological systems are described, for example, in U.S. Patent Nos. 5,657,255 and 5,808,918, entitled "Hierarchical Biological Modeling System and Method"; U.S. Patent No. 5,914,891 , entitled "System and Method for Simulating Operation of Biochemical Systems"; U.S. Patent No. 5,930,154, entitled "Computer-based System and Methods for Information Storage, Modeling and Simulation of Complex Systems Organized in Discrete Compartments in Time and Space"; U.S. Patent No. 6,051 ,029, entitled "Method of Generating a Display for a Dynamic Simulation Model Utilizing Node and Link Representations"; U.S. Patent No. 6,069,629, entitled "Method of Providing Access to Object Parameters Within a Simulation Model"; U.S. Patent No. 6,078,739, entitled "A Method of Managing Objects and Parameter Values Associated With the Objects Within a Simulation Model"; U.S. Patent No. 6,539,347, entitled "Method of Generating a Display For a Dynamic Simulation Model Utilizing Node and Link Representations"; U.S. Patent No. 6,983,237, entitled "Method and Apparatus for Conducting Linked Simulation Operations Utilizing a Computer-Based System Model"; and PCT publication WO 99/27443, entitled "A Method of Monitoring Values within a Simulation Model."
[0050] The methods further can comprise methods for validating the computer models described herein. For example, the methods can include generating a simulated biological characteristic associated with development or progression of hypertension, and comparing the simulated biological characteristic with a corresponding reference biological characteristic measured in vivo. The result of this comparison in combination with known dynamic constraints may confirm some part of the model, or may point the user to a change of a mathematical relationship within the model, which improves the overall fidelity of the model. Methods for validating the various models described herein are taught in U.S. Patent Publication 2002-0193979, entitled "Apparatus And Method For Validating A Computer Model," and in U.S. Patent No. 6,862,561 , entitled "Method and Apparatus for Computer Modeling a Joint."
4.4 Computer Models of Hypertension [0051] The computer model hypertension provides predictive power to rapidly assess, e.g., the efficacy of novel therapeutics prior to investment in large-scale clinical trials. In a preferred implementation, the model contains three modules: an RAAS pathway module, a renal function module and a blood pressure regulation module. The model can be used to establish a population of virtual patients (representing a variety of clinical phenotypes) to rapidly assess the effects of modulating highly-sensitive target pathways on key clinical endpoints. In addition, researchers can assess the efficacy of novel therapeutics, and identify biomarker patterns for predicting long-term clinical efficacy.
[0052] Computer models are being increasingly used in drug discovery and in clinical development to address a range of circumstances in which characterizing the efficacy or safety of a drug effect is dependent on perturbations at the molecular and cellular level. While the variability in drug response among patients can be linked to characteristics routinely collected in demographic surveys including gender and race, some variability can be traced to different protein expression levels, gene expression levels and mutations in relevant biological entities such as drug target receptors or metabolizing enzymes. To this end, mathematical models of signaling and metabolic pathways have been used to elucidate the dynamic behavior of the biological system of interest (Michelson (2006) The impact of systems biology and biosimulation on drug discovery and development. MoI Biosyst 2(6- 7):288-291 ).
[0053] The utility of these models in drug development include: 1 ) identifying and optimizing drug targets within complex pathways via mechanistic dynamic simulations (Aksenov, et al. (2005) An integrated approach for inference and mechanistic modeling for advancing drug development. FEBS Lett 579(8): 1878-1883; Rullmann, et al. (2005) Systems biology for battling rheumatoid arthritis: application of the Entelos PhysioLab platform. Syst Biol (Stevenage) 152(4):256-262; and Michelson, et al. (2006) In silico prediction of clinical efficacy. Curr Opin Biotechnol 17(6):666-670); 2) identifying combinations of targeted therapies that would achieve efficacy without interfering with the biological function of the drugs' targets in normal tissue, thus limiting toxicity (FitzGerald, et al. (2006) The effect of radiation therapy on normal tissue function. Hematol Oncol Clin North Am 20(1 ): 141 -163; and Christopher, et al. (2004) Data-driven computer simulation of human cancer cell. Ann N Y Acad Sci 1020:132-153); 3) characterizing the role that mutations in the drug target have on the overall clinical efficacy (Liu, et al. (2007) A multiscale computational approach to dissect early events in the Erb family receptor mediated activation, differential signaling, and relevance to oncogenic transformations. Ann S/omec/ £ng 35(6):1012-1025); 4) reconciling seemingly contradictory experimental data by showing that different protein expression levels in cell lines and tissues can lead to a largely different behavior of the same signaling network (Schoeberl, et al. (2006) A data-driven computational model of the ErbB receptor signaling network. Con f P roc IEEE Eng Med Biol Soc 1 :53-54); and 5) translating animal data into usable interventions for a corresponding response in human patients (Shoda, et al. (2005) A comprehensive review of interventions in the NOD mouse and implications for translation. Immunity 23(2): 1 15-126).
[0054] The goal of a model is to speed up the development process along the drug development pipeline. Novel therapies can be prioritized based on efficacy early in the drug development process, with multiple dosing regimens and protocols tested and results returned prior to recruiting the first patient in a clinical trial. Combination therapies can also be evaluated in the model to look for potential non-additive effects, and to identify the most potent approach in lowering blood pressure in patients with multiple disease etiologies. A set of biomarkers could be determined that can identify the best responders to different therapeutic approaches for treating hypertension. Ultimately, the model is to provide a versatile tool for pharmaceutical research and development to optimize current approaches to drug development, and to provide new insight into the physiology to reduce the time to bring an effective novel therapy to the market.
[0055] The etiologies of elevated blood pressure are varied and difficult to characterize in any specific patient or clinical subject. Hypertension is postulated to result from numerous pathophysiological mechanisms including increased peripheral resistance, increased sympathetic nervous system activity, overproduction of sodium-retaining factors and vasoconstrictors (e.g., Ang Il and endothelin), increased sodium reabsorption by the kidneys, deficiencies of vasodilators such as atrial natriuretic peptide (ANP), nitric oxide (NO) and prostacyclin (PGI2), or from an imbalance in the regulation of glomerular pressure - all of which are difficult to isolate as the cause of hypertension. Ang Il has been the focus of intensive research aimed at elucidating its role in the control of blood pressure, extracellular fluid and electrolyte homeostasis. Ang Il is a peptide with potent vasoconstricting effects. It is part of the RAAS pathway, a cascade of bioactive peptides and regulatory enzymes. The classical systemic RAAS pathway has been described to start with the synthesis and release of angiotensinogen (AGT) into the systemic circulation by the liver. Renin, a proteolytic enzyme synthesized by the juxtaglomerular cells in the kidney, cleaves AGT to form the decapeptide angiotensin I (Ang I). Angiotensin-converting enzyme (ACE) cleaves Ang I to form Ang II, which is the octapeptide hormone that regulates blood pressure by the modulation of sodium reabsorption in the kidney and by effecting central and peripheral nervous system activity to increase cardiac output and systemic vascular resistance.
[0056] RAAS-modulating therapies directly manipulate this pathway to alter the levels of Ang Il in the systemic circulation to reduce blood pressure. Three classes of RAAS- modulating pharmacological therapies are currently available on the market. Direct renin inhibitors (DRIs) target renin activity; ACE inhibitors block the conversion from Ang I to Ang II; angiotensin-receptor blockers (ARBs) prevent the binding of Ang Il to the Angiotensin 11-1 receptors (AT1 ). All three reduce the systemic activity of Ang II, which leads to vasodilation, decreased renal sodium reabsorption and reduced secretion of vasopressin (from the brain) and aldosterone (from the adrenal cortex). Figure 10 illustrates various modes of representing therapeutic interventions in the present computer model of hypertension. In certain implementations, the model can account for ACE inhibitor effect on systemic and/or renal chymase activity, on systemic and/or glomerular ACE activity, and on Ang(1-7) clearance. In other implementations, the model can account for direct renin inhibitor effects on plasma and glomerular renin activity and the resulting glomerular Ang I production, peritubular ang I synetheis and tubular tissue synthesis of Ang I. In other implementations, the model can account for angiotensin receptor blockers on AT1 receptor binding, renal At1 receptor binding, Ang Il clearance and degradation rate, and Ang III clearance and degradation rate. In yet another implementation, the computer model accounts for diuretic effects on distal tubule sodium reabsorption, proximal tubule and LoH sodium reabsorption and macula densa signaling. In another implementation, the computer model accounts for the effect of calcium channel blockers on efferent arteriole resistance, preglomerular arteriole resistance and systemic arterial resistance. Finally, in some implementations, the computer model accounts for beta blocker effects on renal sympathetic nerve activity. [0057] The computer model described herein represents biological processes at multiple levels and then evaluates the effect of the biological processes on biological processes across all levels. Thus, preferably, the computer model provides a multi-variable view of a biological system. The computer model also, preferably, provides cross-disciplinary observations through synthesis of information from two or more disciplines into a single computer model or through linking a plurality of computer models that represent different disciplines.
[0058] An exemplary computer model reflects a particular biological system, e.g., the vascular system, and anatomical factors relevant to issues to be explored by the computer model. The level of detail incorporated into the model is often dictated by a particular intended use of the computer model. For example, biological components being evaluated often operate at a subcellular level; therefore, the subcellular level can occupy the lowest level of detail represented in the model. The subcellular level includes, for example, biological components such as DNA, proteins, peptides therapeutic agents, and subcellular organelles. Similarly, the model can be evaluated at the multicellular level or even at the level of a whole organism. Because an individual biological system, e.g. a single human, is a common entity of interest with respect to the ultimate effect of the biological components, the individual biological system (e.g., represented in the form of clinical outcomes) is the highest level represented in the system. Chemical and therapeutic interventions are introduced into the model through changes in parameters at lower levels, with clinical outcomes being changed as a result of those lower level changes, as opposed to representing effects by directly changing the clinical outcome variables. Typically, the model represents evolving dynamics of cell populations, rather than the sequence of events for a single cell. [0059] The level of detail reported to a user can vary depending on the level of sophistication of the target user. For a healthcare setting, especially for use by members of the public, it may be desirable to include a higher level of abstraction on top of a computer model. This higher level of abstraction can show, for example, major physiological subsystems and their interconnections, but need not report certain detailed elements of the computer model - at least not without the user explicitly deciding to view the detailed elements. This higher level of abstraction can provide a description of the virtual patient's phenotype and underlying physiological characteristics, but need not include certain parametric settings used to create that virtual patient in the computer model. When representing therapies, this higher level of abstraction can describe what the therapy does but need not include certain parametric settings used to simulate that exposure in the computer model. A subset of outputs of the computer model that is particularly relevant for subjects and doctors can be made readily accessible. In an alternative implementation, the output can comprise an identification of one or more biological processes that most significantly affect whether hypertension develops or whether a certain patient might respond to a selected therapy. In certain implementations, the output may suggest biological assays that can be used to assess the likelihood that a subject may develop high blood pressure.
[0060] The model of hypertension described herein can be used to generate a model for simulating development and progression of high blood pressure and the associated increased risk of adverse effects, such as heart failure, stroke and kidney damage. In such a case, the simulation model may include hundreds or even thousands of objects, each of which can include a number of parameters. In order to perform effective "what-if" analyses using a simulation model, it is useful to access and observe the input values of certain key parameters prior to performance of a simulation operation, and also possibly to observe output values for these key parameters at the conclusion of such an operation. As many parameters are included in the expression of, and are affected by, a relationship between two objects, one may also need to examine certain parameters at either end of such a relationship. For example, one may wish to examine parameters that specify the effects a specific object has on a number of other objects, and also parameters that specify the effects of these other objects upon the specific object. Complex models are also often broken down into a system of sub-models, either using software features or merely by the modeler's convention. It is accordingly often useful to simultaneously view selected parameters contained within a specific sub-model. The satisfaction of this need is complicated by the fact that the boundaries of a sub-model may not be mutually exclusive with respect to parameters, i.e., a single parameter may appear in many sub-models. Further, the boundaries of sub-models often change as the model evolves. [0061] In a preferred implementation, the computer model is configured to allow visual representation of mathematical relations as well as interrelationships between variables, parameters, and biological processes. This visual representation includes multiple modules or functional areas that, when grouped together, represent a large complex model of a biological system. [0062] In one implementation, simulation modeling software is used to provide a computer model, e.g., as described in U.S. Pat. No. 5,657,255, issued Aug. 12, 1997, titled "Hierarchical Biological Modeling System and Method"; U.S. Pat. No. 5,808,918, issued Sep. 15, 1998, titled "Hierarchical Biological Modeling System and Method"; U.S. Pat. No. 6,051 ,029, issued Apr. 18, 2000, titled "Method of Generating a Display for a Dynamic Simulation Model Utilizing Node and Link Representations"; U.S. Pat. No. 6,539,347, issued Mar. 25, 2003, titled "Method of Generating a Display For a Dynamic Simulation Model Utilizing Node and Link Representations"; U.S. Pat. No. 6,078,739, issued Jan. 25, 2000, titled "A Method of Managing Objects and Parameter Values Associated With the Objects Within a Simulation Model"; and U.S. Pat. No. 6,069,629, issued May 30, 2000, titled "Method of Providing Access to Object Parameters Within a Simulation Model". An example of simulation modeling software is found in U.S. Pat. No. 6,078,739.
[0063] Various Diagrams can be used to illustrate the dynamic relationships among the elements of the model of skin sensitization. Examples of suitable diagrams include Effect and Summary Diagrams.
[0064] A Summary Diagram can provide an overview of the various pathways modeled in the methods and models described herein. For example, the Summary Diagram illustrated in FIG. 1 provides an overview of modules that can form the present model of hypertension.
A Summary Diagram also can provide an overview of pathways modeled in a particular module and/or provide links to individual modules of the model. The models represent the relevant components of the phenotype through the use of "state" and "function" nodes whose relations are defined through the use of diagrammatic arrow symbols. Thus, the complex and dynamic mathematical relationships for the various elements of the phenotype are easily represented in a user-friendly manner.
[0065] An Effect Diagram can be a visual representation of the model equations and illustrate the dynamic relationships among the elements of the model. FIG. 3 provides an example of an Effect Diagram illustrating the glomerular RAAS Pathway. The Effect
Diagram is organized into functional areas, which when grouped together represent the large complex physiology of the phenotype being modeled.
[0066] State and function nodes show the names of the variables they represent and their location in the model. The arrows and modifiers show the relationship of the state and function nodes to other nodes within the model. State and function nodes also contain the parameters and equations that are used to compute the values of the variables the represent in simulated experiments. In some embodiments, the state and function nodes are represented according to the method described in U.S. Patent No. 6,051 ,029, entitled "Method of Generating a Display for a Dynamic Simulation Model Utilizing Node and Link Representations," incorporated herein by reference. Examples of state and function nodes are further discussed below.
[0067] State nodes are represented by single-border ovals and represent variables in the system, the values of which are determined by the cumulative effects of inputs over time. "Input" refers to any parameter that can affect the variable being modeled by the state node. For example, input for a state node representing glomerular Ang Il mass can be glomerular Ang Il synthesis and glomerular Ang I mass, regulated by total glomerular ACE activity and chymase activity. State node values are defined by differential equations. The predefined parameters for a state node include its initial value (S0) and its status. In some embodiments, state nodes can have a half-life. In these embodiments, a circle containing an "H" is attached to the node that has a half-life.
[0068] Function nodes are represented by double-border ovals and represent variables in the system, the values of which, at any point in time, are determined by inputs at the same point in time. Function nodes are defined by algebraic functions of their inputs. The predefined parameters for a function node include its initial value (F0) and its status. Setting the status of a node effects how the value of the node is determined. The status of a state or function node can be: 1 ) Computed, i.e., the value is calculated as a result of its inputs; 2) Specified-Locked, i.e., the value is held constant over time; or 3) Specified Data, i.e., the value varies with time according to predefined data points.
[0069] State and function nodes can appear more than once in the module diagram as alias nodes. Alias nodes are indicated by one or more dots (see, e.g., state node
"glomerular Ang II" in FIG. 3). State and Function nodes are also defined by their position, with respect to arrows and other nodes, as being source nodes (S) and/or target nodes (T). Source nodes are located at the tails of arrows and target nodes are located at the heads of arrows. Nodes can be active or inactive. [0070] Arrows link source nodes to target nodes and represent the mathematical relationship between the nodes. Arrows can be labeled with circles that indicate the activity of the arrow. A key to the annotations in the circles is located in the upper left corner of each effect Diagram. If an arrowhead is solid, the effect is positive. If the arrowhead is hollow, the effect is negative. For further description of arrow types, arrow characteristics, and arrow equations, see, e.g., U.S. Patent No. 6,051 ,029, U.S. Patent No. 6,069,629, U.S. Patent No,. 6,078,739, and U.S. Patent No. 6,539,347.
[0071] The fully-integrated computer model of hypertension preferably is capable of representing a breadth of patient phenotypes in terms of their physiological status, additional risk factors for high blood pressure, and alternate genetic and/or hypothesized mechanistic variants. The resulting virtual patients can be used to predict the effect of therapeutic and/or dietary intervention on hypertension and the risk of adverse endpoints, such as heart failure or stroke.
[0072] The methods disclosed herein can be used to form a computer model capable of simulating patient phenotypes and further can incorporate the addition of new components, as well as increased detail in components already modeled. For example, computer models predicting changes in filtration capacity in the kidneys of a diabetic or aging patient.
4.4.1 RAA S Pa thway Module
[0073] The RAAS pathway module incorporates the enzymatic pathways involved in the synthesis and conversion of AGT to Ang I, Ang Il and downstream metabolites, such as Ang(1-7) and Ang IV. The activity of enzymes including renin, ACE, a chymase-like enzyme, and neutral endopeptidase (NEP) were included in the model in addition to the binding rates of Ang Il to the two Ang Il receptors (AT1 and AT2). The inclusion of these peptides and enzymes allows for the investigation antihypertensive therapies that target the RAAS. Each of Figs. 2, 3 and 4 provide a diagrammatic representation of the pathway model, in systemic circulation, glomerulus and tubule, respectively.
[0074] Computational approaches to modeling blood pressure regulation were pioneered by Guyton and Coleman in 1972. These authors published the first model that provided the foundation toward our understanding of the relationship between venous return, cardiac output and the vasculature. The original and updated versions of the model focus on the role of the kidney in long-term blood pressure regulation and the effect of blood volume regulation in the development of hypertension, but have been noted to underestimate the influence of the sympathetic nervous system (Osborn et al., Exp Physiol 94: 389-396 (2009). In addition, the representation of the RAAS pathway in the Guyton-Coleman model is oversimplified. The Guyton/Coleman (GC) model does not include vascular remodeling and its effects on vascular geometry and hemodynamics as significant contributors to increased peripheral vascular resistance To address the under-representation of the sympathetic nervous system, Karaaslan et al, published a modified version of the GC model that added the influence of the renal sympathetic nervous activity on the synthesis and release of renin and the afferent arteriolar tone.
[0075] The Guyton/Karaaslan models for normal blood pressure regulation provided a starting point for the RAAS pathway module with the following extensions:
1 ) Changes in the physiology were represented by different parameter values in the model to capture the transition and progression from normal to diseased states. 2) Addition of a detailed mechanistic representation of renal function (glomerular filtration rate and albuminuria), incorporating concepts from existing models (Lazzara and Deen (2007) Model of albumin reabsorption in the proximal tubule. Am J Physiol Renal Physiol 292:F430-F439; Smithies (2003) Why the kidney glomerulus does not clog: a gel permeation/diffusion hypothesis of renal function. Proc Natl Acad Sci U S A 100:4108-41 13). 3) Inclusion of a detailed representation of the concentration of the systemic circulating RAAS-related peptides including intermediates such as angiotensin I (Ang I), angiotensin (1-7) (Ang(1-7)) and angiotensin IV (Ang IV) and a separate representation of intrarenal RAAS; 4) Incorporation of the effects of Ang II, AT1 and AT2 receptors in hypertension and the pharmacological actions of RAAS-modulating therapies on the RAAS pathway.
4.4.1.1 Systemic RAAS Pathway
[0076] The model that describes the dynamics of the renin-angiotensin system is represented using a system of ordinary differential equations (1 )-(8). Each biochemical reaction has zeroth-order components of production (kn) and first order degradation kinetics expressed through half-life parameters (hn). Binding or enzymatic reactions can be expressed as first-order reactions with parameters (cn). A feedback function, f, relating plasma renin activity (PRA) to ATI-bound Ang Il is also included in the model.
Figure imgf000021_0001
[0077] A range of feasible values for the enzyme activity rates in humans was determined from the available data in the published literature. When a specific range of data could not be found, an assumption was made about the steady-state equilibrium for the angiotensin peptide concentrations to calculate the rates of the remaining unknown parameters. For example in Eq. (2) a steady-state approximation yields:
Figure imgf000022_0001
[0078] As the degradation rate (hAGτ) of AGT and a range of baseline plasma renin activity rates (PRA) are known, a steady-state equilibrium value for AGT (AGT*) was selected from the range known in literature to obtain a value for the rate of AGT synthesis (kAGτ)-
[0079] The variables and parameters with their reported ranges from clinical studies are summarized in Table 1 , as are the parameters where the values are not reported or known.
Figure imgf000022_0002
? : The value is not known.
[0080] A complete parameterization of the model rate constants based upon experimental measurements was not available in the literature. Thus, multiple assumptions about the physiology were made to complete the parameterization of the model structure, as follows. • The baseline plasma renin activity is the rate of AGT conversion to Ang I in healthy subjects. The rate of substrate conversion can change in response to the circulating concentration of AGT and in response to the feedback function ffrom a change in ATI-bound Ang II. These assumptions are based on the detailed kinetic studies in human plasma conducted by Poulsen in 1973 (Scand J CHn Lab Invest 31 :3-86).
PRA is assumed to be proportional to the concentration of its substrate, AGT, because the concentration of AGT is comparable to the Michaelis-Menten constant (Km).
• The activity of ACE and chymase in converting Ang I to Ang Il is assumed proportional to the concentration of the substrate (Ang I). ACE and chymase activity in the vasculature were determined to have Vm values of 222 and 154 pmol/ml/hr, respectively, which was considerably greater than rates (-0.3 pmol/ml/hr) measured in humans (Takai, et al. (1997) Characterization of chymase from human vascular tissues. CHn Chim Acta 265:13-20; Meng, et al. (1995) Sensitive method for quantitation of angiotensin-converting enzyme (ACE) activity in tissue. Biochem
Pharmacol 50:1445-1450). In the current version of the model, ACE was assumed to be responsible for >95% of the conversion of Ang I to Ang II. Human and animal data support the hypothesis of ACE being the primary enzyme responsible for Ang I to Ang Il conversion in normotensive humans. ACE expression and systemic conversion of AGT to Ang I take place primarily in the pulmonary circulation.
• 10% of Ang Il was assumed to be converted to Ang(1-7) and 90% to Ang IV. Since no quantitative data in the literature is available, this assumption was based on measured circulating activity of ACE2, the primary pathway for the conversion of Ang Il to Ang(1-7) compared to the rate of Ang Il degradation to Ang IV. • The instantaneous amount of Ang Il bound to membrane AT1 and AT2 receptors is a small fraction of circulating Ang II. This assumption is based upon the geometric relationship between the volume of the blood and the surface area of the vasculature.
• Ang Il binds preferentially to AT1 rather than AT2 receptors. Data from human smooth muscle cells and renal tissue indicate that AT2 receptors are expressed at lower levels compared to AT1 receptors (Haulica, et al. (2005) Angiotensin peptides and their pleiotropic actions. J Renin Angiotensin Aldosterone Syst 6:121-131 ).
• Ang I and Ang Il have half lives of approximately 30 seconds in the systemic circulation. • For Ang IV, the model assumes a half-life of 10 minutes, which is between the reported half lives of Ang Il and Ang(1-7). The concentrations of Ang IV and Ang(1-7) in the systemic circulation were calculated based on the solution of the steady-state equilibrium equations. • PRA increases via a regulatory feedback mechanism in response to a reduction in blood pressure, in a relationship that reflects a reduction in Ang Il binding to the AT1 receptors. An analysis of clinical data from trials testing therapies that modulate the RAAS pathway suggests a rapid increase in PRA 24 hours post-treatment, which correlated with the reductions in Ang Il bound to AT1 receptors and blood pressure.
4.4.1.2 Renal RAAS Pathways
[0081] In one implementation the model divides the kidney into two regions: the renal vasculature compartment, comprised of all vascular structures within the kidney (including the blood volume within those structures) and the renal tissue compartment, comprised of all tissue external to vascular structures (including the tubules and interstitial tissue). The model makes the following assumptions and simplifications:
• RAAS peptides are arterially delivered from the circulation to the renal vascular compartment at concentrations equal to systemic levels, and the peptides flow out of the renal vascular compartment back to the systemic circulation at concentration equal to renal vasculature levels. • All angiotensin peptides and all enzymes in the RAAS pathway are also produced locally within each compartment, although the rates of production and enzymatic conversion can vary greatly from those in systemic circulation, as discussed below. A concentration gradient exists between the renal tissue and renal vasculature, such that RAAS peptides produced in the renal tissue diffuse into the renal vasculature. Biopsy data shows that renal tissue levels of Ang I and Ang
Il are 10 to 100 fold higher than circulating levels (Navar, et al. (2002) Regulation of intrarenal angiotensin Il in hypertension. Hypertension 39:316-322; Navar and Nishiyama A (2004) Why are angiotensin concentrations so high in the kidney? Curr Opin Nephrol Hypertens 13:107-115; and Metzger, et al. (1999) Angiotensin-converting enzyme in non-neoplastic kidney diseases. Kidney lnt
56:1442-1454).
• Ang IV and Ang(1-7) levels in the kidney were not specifically modeled because of the limited availability of data. Instead, rates of conversion of Ang I and Ang IV to Ang(1-7) and Ang IV were assumed to be incorporated into the degradation rates of Ang I and Ang II. • Since limited data is available on any changes in the concentrations of AGT and renin within the renal tubules and interstitium, the rate of Ang I synthesis in the renal tissue compartment was assumed to be at equilibrium levels.
[0082] Thus, for RAAS concentrations within the renal vasculature compartment (i.e. glomerular compartment), the model accounts for: 1 ) arterially delivered Ang I and Ang Il peptides and return of these peptides to the systemic circulation; 2) production and utilization of Ang I and Ang Il in the renal vascular bed; 3) diffusion of Ang I and Ang Il from the renal tissue into the renal vasculature; and 4) binding of Ang Il to its receptors. For angiotensin peptide concentrations within the renal tissue compartment, the model takes into consideration: 1 ) production and utilization of Ang I and Ang Il in the renal tissue; 2) diffusion of locally produced peptides into the renal vasculature, and 3) binding of Ang Il to its receptors.
[0083] Equations (10-13) for the renal vascular RAAS are shown below. These equations are almost identical to those for systemic RAAS sub-module, but the rates are specific for the renal circulation, include additional terms have been added to describe the flow of angiotensin peptides in and out of the kidney at a rate Fk, and include the diffusion of angiotensin peptides from the renal tissue compartment to the renal vasculature at a rate of Dk.
[0084] Equations (14-17) for RAAS within the renal tissue compartment (i.e. the tubular compartment) are as shown above.
Figure imgf000026_0001
[0085] The parameterization of the RAAS enzyme activities in the renal vascular bed was primarily constrained based on experiments conducted by Danser et al., 1998 (J Hypertens 16:2051-2056). In this study, radio-labeled Ang I was injected into the renal artery of five hypertensive patients while catheters in the abdominal aorta and renal vein were used to sample the concentration of radio-labeled and endogenous Ang I and Ang II. The constraints of the renal RAAS pathway based upon the Danser study can be summarized as follows:
• Of Ang I entering the kidney from the systemic circulation, 70% is degraded, 10% is converted to Ang II, and 20% exits unchanged. • 73% of Ang Il entering the kidney is degraded, and the remainder exits unchanged.
• The concentration of Ang I at the renal vein is approximately 50% higher than the concentration at the renal artery.
• The concentration of Ang Il at the renal vein is approximately 50% lower than the concentration at the renal artery.
[0086] The following assumptions regarding the renal vascular RAAS pathway were made to satisfy these constraints:
• The rate of blood flow to the kidney (Fk) is ~1 L/min at rest and the blood volume of the kidney is 70 ml, equivalent to a residence time of 4 seconds. • The rate of local Ang I and Ang Il degradation in the kidney is significantly increased over the systemic degradation rate to account for the high rate of angiotensin peptide removal in the renal circulation.
• Since the concentration of Ang I leaving the renal circulation is 50% higher than Ang I entering the renal circulation, we assumed a large amount of endogenous Ang I formation. This endogenous Ang I was assumed to be generated in the renal tissue and to diffuse into the renal vasculature.
• The rate of ACE activity is significantly higher in the renal circulation than the systemic circulation, in order to convert 10% of Ang I entering the kidney to Ang [0087] Table 2 provides the parameters calculated based upon these constraints and assumptions, as one possible behavior for the glomerular and peritubular capillary RAAS pathway based on the dynamic system that satisfies the constraints.
Figure imgf000028_0001
[0088] The chosen parameters yielded a solution for the dynamical system that satisfied the known constraints of the renal vascular bed. The renal vascular parameters with the same value as their systemic counterpart are not listed in the table. [0089] The RAAS pathway within the renal tissue (i.e. the tubular compartment) was implemented in a similar fashion as the renal vascular RAAS, with identical enzymes, peptides and receptors. Although the concentration and activities of the enzymes were assumed to differ, there is minimal quantitative data for these rates in the published literature. The primary constraint for the renal tissue RAAS is the assumption that the renal tissue should function as a source of Ang I and Ang Il that enters into the renal vasculature. Therefore, the parameters describing the activity of the renal tissue RAAS pathway was parameterized such that: (i) the equilibrium concentrations of the angiotensin peptides in the tissue pathway were a source of Ang I and Ang Il in the renal vascular compartment; and (ii) the constraints on Ang I and Ang Il concentrations measured by Danser were satisfied.
[0090] Since it is difficult to directly measure the peptide concentrations and enzyme activities of the RAAS within different regions of the kidney, there is a considerable amount of uncertainty around the rates and concentrations of various RAAS components. The model of renal RAAS provides the ability to hypothesize the effects of different scenarios and to determine the sensitivity of renal and systemic ATI-bound Ang Il levels to changes in different model parameters. This approach to hypothesis testing can yield relevant insights on therapy targets that are more likely to result in renal protection, and help in interpreting results of experimental studies. For instance, we have used the model to show that changes in renal RAAS peptide concentrations are not strongly reflected in changes in the concentration of systemic angiotensin peptides. In turn, this suggests that the measured levels of plasma renin activity, Ang I or Ang Il in response to therapy in systemic circulation may not fully capture the changes that occur within the renal tissue, even though local concentrations of Ang Il have a greater effect on renal function than systemic concentrations. In addition, test the effects of different enzyme rates on ATI-bound Ang ll-induced damage to different compartments within the kidney by adding a model of renal disease progression dependent on the effects of local tissue concentrations of Ang Il can be tested. The model can also be used to understand how enhanced localization of RAAS-modulating therapies can selectively affect renal vs. systemic targets and affect the rate of renal disease progression.
4.4.1.3 Calibration of the RAAS Pathway Module and Creation of Normotensive Virtual Patient
[0091] No studies have incorporated both known and hypothesized activity rates for the RAAS pathway cascade into a single dynamic system. Based upon the aforementioned assumptions about the enzyme activities and the existence of a steady- state equilibrium, a single parameterization of this system of equations was derived such that the resulting numerical solution described a feasible normotensive patient (Table 3). It is important to note that the ranges of measured Ang I and Ang Il concentrations in normotensive and hypertensive patients are assumed identical and there is no obvious way to distinguish between normal and elevated blood pressure solely on these concentrations. The steady-state solution of the system described of ordinary differential equations (1 ) to (8) is shown in Table 4 (results derived by numerical methods). This parameter set describes one hypothetical subject or virtual patient (VP), and is the foundation of a framework for conducting hypothesis testing of this physiological system.
l
Figure imgf000030_0001
4.4.1.4 Validation of the RAAS Pathway Module
[0092] A validation of any model consists of the agreement between model predictions and one or more experimental data sets that were not used to determine the initial parameterization of the model. For this model of hypertension, a validation of the model parameters describing the normotensive Virtual Patient was conducted using a series of published radio-labeled angiotensin peptide infusion experiments (Danser, et al. (1998) Angiotensin l-to-ll conversion in the human renal vascular bed. J Hypertens 16:2051- 2056; and Admiraal, et al. (1993) Regional angiotensin Il production in essential hypertension and renal artery stenosis. Hypertension 21 :173-184). The published studies quantified the rates of systemic and tissue Ang Il production and clearance by using a constant infusion of radio-labeled 125l-Ang I and 125l-Ang II. Based upon the known specific radioactivity of 125l-Ang I and 125l-Ang II, the plasma and tissue concentrations of Ang I and Ang Il could be separated by their source (locally synthesized or exogenously delivered). In five human subjects where 125l-Ang I was directly infused at a constant rate, blood samples taken between 5 and 10 minutes after the start of the infusion had constant levels of both 125l-Ang I and 125l-Ang II, which implied that the system reached a steady state within 5 minutes. [0093] The infusion experiment was reproduced by modifying Eq (3) with the addition of a term k2 = 23.1 fmol/ml/hr to represent a constant infusion rate of 125l-Ang I consistent with the experimental protocol based upon the measures of radioactivity. In a time course of both 125l-Ang I and 125l-Ang Il as a steady state is reached in the normotensive VP within 5 minutes, thus confirming the set of chosen parameters (data not shown). [0094] Similar simulation experiments were conducted to reproduce the study by Admiraal et al., in which arterial and venous levels of 125l-Ang I and 125l-Ang Il across a number of vascular beds were measured to determine the local tissue metabolism and production of Ang II. In this study, tracer doses of 125l-Ang I and 125l-Ang Il were infused in hypertensive patients and the study found that equilibrium was achieved within 8 minutes. To reproduce these experiments, equations (3) and (4) were modified with the additional terms k2=26.9 fmol/ml/hr and k3=21.8 fmol/ml/hr respectively.
[0095] In both simulations described above, a steady state was reached within 8 minutes, reinforcing the hypothesis that the chosen parameters in the model that describe a feasible Virtual Patient are consistent with the behavior of a normotensive patient in the clinic. It is important to note that though the comparison was made between measurements in hypertensive patients and model simulations represented normotensive human subjects, the comparison is still justifiable based on data not showing differences between normal and patient populations.
[0096] Additional testing of the model parameterization was conducted by incorporating the effects of the three main RAAS-modulating therapies in the model and comparing the resulting simulated angiotensin peptide concentrations with data. ACE inhibitors (ACEIs) were simulated by changing the effect of the rate constant CACE, angiotensin Il type I receptor blockers (ARBs) were simulated by modulating the effect of the rate constant cAτi, and direct renin inhibitors (DRIs) by altering the overall rate plasma renin activity. In equations (2), (3), (4) and (7) the therapeutic inhibitory effect of ACEI, ARB and DRI were implemented via the use of fractional reductions in enzyme activity, α, β and δ, respectively. For example, equation (7) becomes:
Figure imgf000032_0001
[0097] AT1 receptors mediate the majority of Ang Il actions involved in the regulation of blood pressure and blood volume. Mazzolai et al., 1999 (Hypertension 33:850-855) showed a 90% reduction (β = 0.9) in Ang Il bound to AT1 receptors four hours after a 150 mg dose of irbesartan, an ARB, administered to normotensive patients. ACEI blocks the action of ACE competitively and thus the conversion of Ang I to Ang II, thereby reducing circulating and local levels of Ang II. Data from Manhem et al., 1985 (BrJ CHn Pharmacol 20:27-35) demonstrated a 96% reduction (α = 0.96) in ACE activity four hours following a 20 mg dose of ramipril, an ACE inhibitor. Similarly, Nussberger et al., 2007 (Int J CHn Pract 61 :1461-1468) measured a 60 to 70% reduction in PRA four hours after an 80 mg dose of aliskiren, a DRI, was administered to normotensive patients. Finally, the calibration of the regulatory feedback function fwas based on observations from the literature showing that plasma renin activity increases in response to ACEI, ARB and DRI therapy (Luque, et al. (1996) Effects of captopril related to increased levels of prostacyclin and angiotensin-(1-7) in essential hypertension. J Hypertens 14:799-805). The reactive increase in PRA was hypothesized to be related to the reduction in ATI-bound Ang Il based on the comparable increase observed in ACEI therapy (reduced Ang II) and ARB therapy (increased Ang Il but reduced Ang Il binding to AT1 receptors).
[0098] A comparison of the change in angiotensin peptide concentrations between the model and the literature was used to validate the implementation and parameterization of the antihypertensive therapies. The summary of this comparison is presented in Table 5.
Figure imgf000033_0001
[0099] ACEI therapy is associated with a decrease in Ang II, a reactive increase in plasma renin concentration and an increase in plasma Ang I. The reactive increase in plasma renin concentration was also observed in response to ARB and DRI therapy. The simulated ACEI in the model predicted increased concentrations and Ang I and Ang(1-7) and decreased concentrations of Ang II, consistent with reported clinical data (Manhem, et al. (1985) A dose-response study of HOE 498, a new non-sulphydryl converting enzyme inhibitor, on blood pressure, pulse rate and the renin-angiotensin- aldosterone system in normal man. Br J Clin Pharmacol 20:27-35). The time course of the Ang I and Ang Il response predicted an equilibration in the angiotensin peptide concentrations after 5 hours, in agreement with short-term measurements taken in the studies highlighted in Table 5.
[0100] Since ARBs act by blocking the binding of Ang Il to the AT1 receptor rather than by inhibiting Ang Il synthesis, their use results in an increase in plasma Ang Il levels. The blockade of AT1 receptors increases renin secretion and the corresponding concentration of plasma Ang I. The simulated effect of ARBs in the model predict increased concentrations of circulating Ang I, Ang II, Ang(1-7) and PRA, consistent with published clinical data (Christen, et al. (1991 ) Oral administration of DuP 753, a specific angiotensin Il receptor antagonist, to normal male volunteers. Inhibition of pressor response to exogenous angiotensin I and II. Circulation 83:1333-1342).
[0101] DRIs have a significant and sustained effect on PRA to reduce the concentration of both Ang I and Ang Il in the circulation. The simulated effects of DRIs in the model predict a decreased concentration of circulating Ang I, Ang Il and Ang(1-7), consistent with results reported in clinical studies (Nussberger, et al. (2007) Plasma renin and the antihypertensive effect of the orally active renin inhibitor aliskiren in clinical hypertension. Int J CHn Pract 61 :1461-1468).
4.4.2 Representation of variability across different clinical populations
[0102] Table 2 summarized the wide range of reported clinical values of enzyme activities in the RAAS pathway cascade to reflect the intrinsic variability between human subjects. The values summarized in Table 3 described only one set of parameters for the system of equations that yields a feasible solution. To capture physiological variability observed in the clinic, the parameter values in Table 2 can be changed within the observed ranges to generate a new Virtual Patient hypothesis. Although changing the parameters may yield a mathematically correct steady solution for a new Virtual Patient, the combination of parameter values may not result in steady state concentrations or enzyme activity rates that are consistent with the physiological data. For example, decreasing the rate of Ang Il clearance from the circulation will increase the time it takes for Ang Il to reach an equilibrium. If the resulting Ang Il concentration at equilibrium increases significantly beyond physiological range determined by the infusion studies, then the chosen set of parameters for the Virtual Patient was considered invalid. The verification of the simulated results against plausible data is a valuable step during the process of model building.
[0103] A collection, or cohort, of multiple feasible Virtual Patients can be generated using a systematic process to explore the parametric space and a method for testing the feasibility criteria of each parameterization. Table 6 summarizes one such method for exploring the parametric space that varies the half lives and enzyme activity rates around the nominal values of the first virtual patient (VP1). A patient hypothesis may be generated by simulating with parameters within the nominal range where the value of 100% is equal to the values chosen for the first Virtual Patient. Table 7 summarizes a set of feasibility criteria for the concentration of angiotensin peptides based on a survey of the literature.
Figure imgf000035_0001
Figure imgf000035_0002
[0104] The cohort of feasible Virtual Patients can be modified depending on criteria to describe a particular disease phenotype. For example, the feasibility criteria for plasma renin activity can be increased accordingly in patients that exhibit exaggerated renal production of renin leading to increased concentrations of plasma renin. It is important to note that the cohort of Virtual Patients may not follow the same distribution as the clinical population and additional refinement of the patient-generation procedure may be required.
[0105] In the range of parameter values of the systemic RAAS pathway described in Table 6, the long half life of AGT (In1) compared to Ang I and Ang Il (h2 and h3) indicates a slower rate of AGT turnover compared to Ang I and Ang II. As a result, the concentration of AGT is susceptible to larger changes resulting from increases or decreases in PRA than Ang I or Ang II. Changes in the circulating concentration of AGT may be easier to measure and a better marker of changes to the renin-angiotensin pathway than the more transient Ang II. [0106] ACE is the primary enzyme for the conversion of Ang I to Ang Il in the systemic circulation. Chymase is another enzyme that can convert Ang I to Ang II. Therapy that focuses on the inhibition of ACE activity does not affect the continued conversion of Ang I to Ang Il by chymase. Based on the clinically measured changes in circulating Ang I and Ang Il and the assayed reduction in ACE activity in response to moderate doses of ACEI, the model predicts that ACE is responsible for greater than 95% of Ang Il synthesis in the representative normotensive patient. If the role of ACE in the synthesis of Ang Il was reduced to <95%, the model was unable to reproduce the clinically measured reduction in Ang II. [0107] PRA increases in response to ARB or ACEI therapy can be represented by establishing a relationship between decreased Ang Il binding to AT1 receptors and PRA.
4.4.3 Renal Function Module
[0108] In recent years, there has been additional focus on the role of local tissue- specific RAAS in the development of cardiovascular and renal disease. In particular, the kidney possesses all the RAAS components and enzymatic machinery required for the local tissue generation of Ang Il and other RAAS-related peptides. The models described herein comprise a renal function module. In certain implementations, the renal module includes a representation of the kidney as an assembly of single nephrons and associated fluid dynamics processes that influence glomerular filtration rate. The renal function module also can comprise a representation of glomerular filtration rate (GFR) and a representation of albuminuria. In certain implementations glomerular filtration permeability is distributed between fenestrated endothelium, GBM and the slit diaphragm. In other implementations, the model represents albumin transport across the glomerular basement membrane as a function, independently, of diffusion and convection (water filtration). In some implementations, GFR is represented as a function of glomerular hydrostatic pressure, oncotic pressure and hydrostatic conductance (Kf). Kf, in turn, can be represented as a result of integration of multiple effects of physical barriers to filtration in one simplified term representing: podocyte slit diaphragm length, quantity of slits, diaphragm composition, GBM thickness and composition, endothelium integrity and function, and total (capillary) surface area. In some implementations glomerular hydrostatic pressure can be determined based on afferent and efferent arteriole resistance and blood pressure at the renal artery. [0109] Restricting the passage of albumin and large molecules to the urinary space while filtering low-molecular waste products, and regulating the balance of electrolytes and water in the blood, are the main functions of the kidney in maintaining homeostasis. The glomerular filter present in the capillary tuft located inside the Bowman's capsule is responsible for the formation of ~180 L/day of primary urine devoid of macromolecules. This primary filtrate is then modified by the nephron's tubular system and its volume reduced to -1.5 L/day excreted in urine. The glomerular filter/barrier consists of 3 distinct layers 1 ) a fenestrated endothelium, 2) a glomerular basement membrane (GBM) and 3) a slit diaphragm located between the interdigitating foot processes of epithelial podocytes. The physical properties of this sophisticated multilayer barrier allows for filtration of water and small molecules at high rates and restriction to passage of large molecules and proteins including albumin. The anti-clogging capacity of the glomerulus has prompted investigators to postulate various mechanisms where the GBM (gel permeation), the podocyte (size selectivity) and the endothelium (size and charge selectivity) are the relevant components behind the barrier's filtering capacity.
[0110] GFR and albuminuria are the clinical measures used to define normal kidney function and to diagnose renal disease. Both parameters result from a variety of physiological phenomena, some of which are not fully understood and therefore their quantitative nature and relevance cannot be derived directly from the scientific literature.
4.4.3.1 Glomerular Filtration Rate
[0111] Glomerular filtration rate (GFR) can be represented as the sum of single nephron GFR (SNGFR) of N nephrons, where N is 2x10e6. The SNGFR of the nth nephron is a flow (in nl/min) that is commonly calculated from the Starling equation:
Figure imgf000037_0001
where Kf is the hydrostatic conductance , P represents a physical pressure in either the glomerular capillaries or the Bowman's space and π represents the oncotic pressure (exerted by plasma proteins). The reflection coefficient (σ), is often thought as a correction factor for the differences in permeability of body capillaries to large proteins and their contribution to the interstitial fluid oncotic pressure; σ can take values between 0 and 1. Glomerular capillaries have a very low permeability to proteins including albumin, therefore a σ value close to 1 is typically used. In contrast, hepatic sinusoids are highly permeable to albumin produced by hepatocytes and therefore have a low σ. Strictly speaking, each of the N nephrons would have its own set of these 5 parameters producing a unique SNGFR for each nephron. This distribution of nephrons is represented by the mean behavior; hence the following assumptions are based upon a single typical nephron. [0112] The key terms in Eq (19) are Kf and Pgιom- The pressure in the Bowman's space as a constant. The oncotic pressure gradient can be determined from the relative concentration of albumin, the most abundant plasma protein, on either side of the glomerular barrier. These concentrations are calculated when modeling albumin handling. The oncotic pressure can be treated as a constant. The glomerular hydrostatic pressure of a specific nephron can be calculated from basic fluid dynamic principles (e.g., a pipe and valve calculation) and will depend on renal perfusion pressure, total renal blood flow resistance, and the resistance presented by the afferent and efferent arterioles of the nephron. The degree of vasodilation / vasoconstriction of the arterioles is of significant interest for this modeling effort as it will be regulated by various factors, most particularly by Ang II. For the specific purpose of discussing GFR and albuminuria, these factors aside will be set aside and the glomerular pressure treated as an input to the SNGFR calculation (afferent and efferent arteriole resistances, and thus glomerular hydrostatic pressure, can be captured explicitly in the blood pressure regulation module of the hypertension model). [0113] The hydrostatic conductance, Kf, is the term most closely associated with what are traditionally viewed as the physiological properties of the glomerular membrane determining GFR. Mathematically, Eq (19), demonstrates that Kf is the ratio of the flow through a resistance to the pressure difference between the two sides of the resistance. As stated above, Kf represents the effects of a number of complex biological phenomena, including:
• Podocyte integrity (number and size of slit diaphragms) and function.
• GBM thickness and composition.
• Endothelial cell integrity (number and size of fenestrae) and function.
• Total (capillary) surface area. [0114] At a first glance, explicit representations of all these interacting phenomena would be ideal to better recreate single nephron physiology. However, limited published data and knowledge gaps make its representation a daunting task. A first approach to this problem is to implicitly represent these variables as Kf, a single input to GFR. Changes in Kf will be the result of the integrated changes in all the variables mentioned above. Overall, the model will behave correctly if it is calibrated to published clinical data. However, simulation results cannot be attributed to specific changes in any of the four biological phenomena listed above. Further refinement of this implicit representation can be conducted as a platform enhancement to specifically address mechanistic hypotheses regarding the driving forces behind Kf.
[0115] In summary, the model represents GFR as follows:
Figure imgf000039_0001
4.4.3.2 Albuminuria
[0116] Albumin in urine, albuminuria, is typically measured in mg/day. Similar to GFR, albuminuria is represented as the sum of albumin excretion by N nephrons (as for GFR, a single typical nephron manifesting the mean excretion is used as the basis for the model). Excreted albumin is represented as the amount of protein delivered to the proximal tubule that is not reabsorbed, where the amount reabsorbed is a fraction (f) of the amount that enters the tubular system. Albumin tubular reabsorption is a saturable process, thus, loads that exceed the saturation level will be excreted in urine.
[0117] If the reabsorption fraction, f, is a constant (up to a given filtered load where reabsorption saturates), then, the amount excreted would be the difference between the filtered load and the reabsorbed amount:
Single nephron albumin excretion rate = (1 - f) * filtered load (22) where the filtered load is the rate at which albumin is delivered from the Bowman's space into the tubule (mg/min). Mass conservation requires that the flow of albumin into the tubule is the product of the albumin concentration in the Bowman's space and the flow rate of fluid into the tubule (SNGFR). The concentration in the Bowman's space is determined using the concept of the sieving coefficient (Θ) that is the ratio of the Bowman's space concentration to the plasma concentration.
[0118] Although the mathematical representation of the concentration of albumin in the Bowman's space (Eq. 23) is simple, the underlying phenomena of filtration are quite complex as described in the GFR section. Similar to Kf for GFR, the sieving coefficient (Θ) is the term most closely related to the glomerular phenomena driving albuminuria. If one assumes a fixed Θ and a fixed f, then, albuminuria is a function of SNGFR, the number of functional nephrons, and the plasma albumin concentration: albumin excretion rate = N*( 1 - f) * SNGFR * Θ * [Alb]plasma (23) [0119] For timescales where one can assume that N and [Alb]pιaSma remain constant (in addition to Θ and f), then albuminuria is proportional to GFR. If GFR doubles, albuminuria doubles. Additionally, per Eq (23), albuminuria is proportional to the plasma albumin concentration. While Eq (23) clearly indicates that albuminuria is dependent on GFR, other scenarios in which albuminuria might not depend on GFR should be considered.
[0120] By simple mass conservation, filtered load is the product of flow and concentration. The sieving coefficient (Θ) and f are defined empirically: there is an albumin concentration difference between the glomerular Bowman's space and plasma, and for any set of concentrations that ratio is defined as Θ. For any set of conditions, some fraction of albumin (f) is reabsorbed in the proximal tubule. However, there is one scenario where contrary to Eq (23) the albumin excretion rate might not depend on GFR. So far, Θ and f are assumed to be fixed, yet experimental data suggest otherwise. Under Eq (23), for albuminuria to remain constant as SNGFR increases, either Θ or (1 - f) must decrease with increasing SNGFR in such a way as to cancel the rise in the SNGFR term appearing in Eq (23). If (1 - f) is to decrease, f needs to increase. However, as SNGFR increases, a given bolus of filtrate will spend less time in the proximal tubule, have less time to interact with the active reabsorption process occurring at the base of the tubular microvilli, and therefore the reabsorption fraction f will decrease with increasing SNGFR. Such a decrease will mean that albuminuria increases in a non-linear fashion as SNGFR increases.
[0121] The filtration coefficient Θ is also likely to change with changes in SNGFR. In this case, the direction of the change is indeed to decrease with increasing SNGFR in order to maintain albuminuria levels. As such, the changes in Θ with SNGFR will partially mitigate the changes in albuminuria induced by changes in SNGFR in Eq (21). For albuminuria to have no dependence on SNGFR, Θ would need to vary with (1/SNGFR) to cancel the SNGFR in Eq (23). This is the same as saying that the filtered load of albumin entering the tubule is independent of SNGFR. This is true only in the limited case of pure diffusion. Clearly, this assumption is not valid for glomerular filtration where convection is essential for sieving to occur. Any flow-based transport will increase with increasing SNGFR. Data from rats indicate that a 1.5x increase in SNGFR will lead to a 1.2x increase in filtered load. This is equivalent to saying that a 1.5x increase in SNGFR reduces Θ to 0.8x the original value, the representation of the reabsorption fraction (f) in the present model reflects these concepts.
[0122] In summary, the present model for albuminuria leads to an explicit dependence of albuminuria on SNGFR (Eq (23)) that is a function of the sieving coefficient (Θ) and tubular readsorption (f) on SNGFR. Furthermore, within the constraints of normal physiological changes in the nephron, the expected dependencies of Θ and fon SNGFR will not cancel the dependence of albumin excretion on SNGFR in Eq (23) — the changes in Θ may reduce the dependence partially and the changes in f will augment the dependence. The available data do not support the idea that the filtered load of albumin is nearly independent of GFR. Haraldsson et al., Properties of the glomerular barrier and mechanisms of proteinuria. Physiol Rev 2008 April;88(2):451-87.
[0123] The following assumptions regarding the renal function module were made:
• Glomerular filter permeability / selectivity is distributed among the 3 main components of the glomerular filtration barrier (fenestrated endothelium / GBM / slit diaphragm of podocyte foot processes). Other theoretical models of filtration are centered around one layer (e.g., GBM). Smithies, Why the kidney glomerulus does not clog: a gel permeation/diffusion hypothesis of renal function. Proc Natl Acad Sci U S A 2003 April 1 ;100(7):4108-13.
• Albumin transport across the GBM is due to both diffusion and convection (water filtration) and they proceed independently of each other. Other models emphasize one process over the other. Ibid.
• GFR is determined by glomerular hydrostatic pressure, oncotic pressure and hydrostatic conductance (Kf).
• Kf is the result of integrating the multiple effects of a series of physical barriers to filtration into one simplified term. • The determinants of glomerular hydrostatic pressure are: o afferent and efferent arteriole resistance, o the blood pressure at the renal artery.
[0124] From the various physical properties that govern the glomerular permeability to proteins and macromolecules, those affecting the sieving coefficient (Θ) are the most relevant. The sieving coefficient of any solute is the concentration in the filtrate divided by the concentration in the retentate. In the case of glomerular filtration, it is defined as the concentration in the Bowman's capsule by that in plasma. The sieving coefficient of plasma solutes being filtered by the glomerular membrane is determined by a number of factors including 1 ) the intrinsic selectivity of the membrane given by solute size, charge and shape; 2) the filtration rate of water; 3) the solute concentration; and 4) the arrangements of the layers involved in filtration (fenestrated endothelium, GBM and slit diaphragm). The axial variation in solute concentrations along the glomerular capillary adds a factor to this already complex biological system. One modeling approach to albuminuria represented a single-layer glomerular membrane that factors in the sieving coefficient of albumin and implicitly represents the various factors influencing that sieving coefficient.
[0125] The model treats N, Kf, Pgbm, and [Alb]pιaSma as inputs that will vary in response to various acute and chronic changes in a given patient. The model additionally includes functions for Θ and f that have as arguments various values generated by the model:
Θ = X(SNGFR) (24) f = Y(SNGFR, Θ, [Alb]plasma) (25)
[0126] These functions (X and Y) will also change in response to various chronic and acute changes in a given patient.
4.4.4 Blood Pressure Regulation Module
[0127] In the present model, clinical behaviors can be mechanistically modulated to generate high blood pressure, characterize the reported sensitivity to sodium intake and to evaluate responses to a variety of therapies including RAAS and non RAAS-based therapies. The key renal components represented in the model include GFR and glomerular hemodynamics, tubular sodium and water reabsorption, sodium sensing by the macula densa, and modulation of the secretion rate of renin. The cardiovascular hemodynamic components represented in the platform include mean arterial pressure (MAP), cardiac output (CO), total peripheral resistance (TPR), sympathetic nervous activity (SNA), and vascular capacitance. The humoral components with vascular and renal effects can include Angiotensin Il (Ang II), aldosterone, anti-diuretic hormone (ADH), atrial natriuretic peptide (ANP), sodium and potassium. Compared to the Guyton- Coleman model, the integrated hypertension model disclosed herein comprises a more detailed representation of systemic RAAS-related peptides including Ang I and Ang (1- 7); glomerular and tubular RAAS compartments; renal function (GFR and albuminuria) and the representation of the mechanistic effects of RAAS- and non RAAS-based therapies.
[0128] The blood pressure regulation module tracks sodium balance and total sodium amount. It also calculates water intake and integrates and tracks water balance and extracellular fluid volume (ECFV). The blood pressure regulation module contains a simplified representation of cardiac function and peripheral circulation. Based principally on the ECFV-derived blood volume, it calculates MAP and right atrial pressure (RAP). These pressures are modulated by Ang Il and autonomic responses. [0129] The foundation of the blood pressure regulation module is the renal function curve or 'pressure natriuresis'. Pressure natriuresis relates mean arterial pressure (MAP) to blood volume and establishes a steady-state equilibrium for MAP. The equilibrium point between blood volume and MAP is attained through the renal excretion of sodium and water. In the model representation of pressure natriuresis, water and sodium intake and excretion determine extracellular fluid volume (ECFV) and blood volume and is represented in Figure 9. In this long-term regulation of the set point for MAP, the kidney has a key role in regulating blood volume for any given vascular capacity. The fundamental principle of the model of pressure natriuresis is that sodium and water intake and output must be balanced for the system to operate. An increased intake of sodium temporarily increases blood volume, resulting in a rise in the MAP. In turn, the higher pressure then leads to increasing excretion of sodium and water by the kidney returning MAP to its original set point. Conversely, if sodium intake is limited, the lower blood volume and MAP will decrease the sodium and water excretion until the blood volume and MAP return to normal. [0130] RAAS and other hormonal factors allow pressure natriuresis to occur over a wider range of blood pressure by up-regulating sodium excretion when the plasma sodium concentration is high and increasing sodium reabsorption when plasma sodium levels are low. The tubuloglomerular feedback pathway participates in regulating these effects and is represented in Figure 9. Sodium levels are sensed by the macula densa, a cellular structure located after the proximal tubule and loop of Henle but before the distal tubule and collecting duct. Low levels of sodium in the glomerular filtrate induce renin release, which promotes Ang Il and aldosterone synthesis. Ang Il acts in the proximal tubule to increase reabsorption of sodium and water to increase blood volume.
Aldosterone increases sodium reabsorption in the distal tubule and therefore its actions are physiologically similar to those of Ang II. Increased levels of Ang Il in response to low sodium concentration by the macula densa also result in vasoconstriction of the afferent and efferent arterioles, with a greater effect on the efferent arteriole that results in increased single nephron glomerular filtration rate (SNGFR). High levels of sodium sensed by the macula densa will have the opposite effect - block renin release, lower sodium reabsorption and thus promote further sodium excretion while also lowering SNGFR.
[0131] MAP is a product of cardiac output (CO, defined as the rate at which blood is ejected by the left ventricle) and arterial (arteriolar) resistance (total peripheral resistance, TPR). TPR determines the rate of blood transfer from the arterial to the venous compartment. Long-term blood pressure regulation involves a series of cardiac, vascular and renal mechanisms responsible for the distribution of blood volume between the arterial and venous compartments. Departing from the premise of the Guyton-Coleman model that long-term blood pressure regulation is primarily dependent on pressure natriuresis, the blood pressure regulation module reproduces the additional role of the renal sympathetic nervous activity (RSNA) that was introduced in the Karaaslan model. The added representation of the RSNA takes into consideration the more accurate connection between the regulation of arterial pressure and arterial blood volume. This approach allows for the simulation of alternative disease etiologies leading to hypertension. Such profiles will be generated in response to various SNS activity- mediated perturbations of individual vascular bed resistances. The addition of the RSNA to the GC model is a closer approximation to 'essential' hypertension.
[0132] Clinical behaviors can be mechanistically modulated in the blood pressure regulation module to generate high blood pressure, characterize the reported sensitivity to sodium intake and to evaluate responses to a variety of therapies including RAAS and non RAAS-based therapies. The key renal components represented in the blood pressure regulation model include GFR and glomerular hemodynamics, tubular sodium and water reabsorption, sodium sensing by the macula densa, and modulation of the secretion rate of renin. The cardiovascular hemodynamic components represented in the platform include mean arterial pressure, cardiac output, total peripheral resistance, sympathetic nervous activity, and vascular capacitance. The humoral components with vascular and renal effects include Angiotensin Il (Ang II), aldosterone, anti-diuretic hormone (ADH), atrial natriuretic peptide (ANP), sodium and potassium.
[0133] In certain implementations the main biological blocks include cardiovascular, renal and signaling (humoral) variables. The primary clinical behaviors that can be mechanistically modulated include • generation of high blood pressure,
• characterization of sodium overload, and
• evaluation of responses to therapies. [0134] The key renal components include
• estimations of GFR and albuminuria, • tubular sodium and water reabsorption,
• sensing of sodium reabsorption by the macula densa, and
• modulation of renin secretion rate.
[0135] The blood pressure regulation module can track sodium balance and total sodium amount. It also can calculate water intake to track water balance and extracellular fluid volume (ECFV). In a preferred implementation, the blood pressure regulation module contains a simplified representation of cardiac function and peripheral circulation. Based principally on the ECFV-derived blood volume, it can calculate MAP and right atrial pressure (RAP). These pressures are modulated by Ang Il and autonomic responses. [0136] Figures 8 and 9 delineates the key functions and relationships implemented in the model. The blood pressure regulation module comprises both systemic cardiovascular (Fig. 8) and renal (Fig. 9) aspects. The renal aspect represented in the blood pressure regulation module can be broken down into three functions. The first function is the determination of GFR. GFR is largely dominated by MAP, afferent arteriole resistance and efferent arteriole resistance. Afferent resistance is driven by the external rSNA input and by an internal feedback from the macula densa. GFR determines the load of water entering the tubule, and in conjunction with the externally determined sodium concentration, it determines the sodium entering the tubule. The second function is water reabsorption, which is represented by a single reabsorption process (the sum of proximal tubule, loop of Henle, distal tubule, and collecting duct reabsorption). The reabsorption fraction preferably is modulated by aldosterone and ADH. Urine flow is simply the non-reabsorbed filtrate. The third component of renal sub- module is the reabsorption of sodium, which is handled in three separate regions. The first region is labeled "proximal tubule & LOH Na+ reabsorption" and includes the representation of the reabsorption that occurs in the LoH. Sodium reabsorption also occurs in the distal tubule and the collecting duct. The various reabsorption processes are modulated by Ang II, rSNA, aldosterone and ANP. Note that the reabsorption fraction also depends on the sodium load. Often the sodium load dependence can dominate over the humoral modulators. Finally, renin secretion and afferent arteriole resistance are determined based on sodium flow at the macula densa (located just before the entrance to the distal tubule). The effects of the primary hormones involved in the regulation of sodium including ADH, ANP, Ang Il and aldosterone are also represented. The model also includes the modulation of rSNA by MAP, right atrial pressure RAP and the effects of rSNA on renin secretion by the kidney. [0137] In addition to afferent and efferent arteriole resistance, in certain implementations, the present model includes the vascular resistance of interlobar, arcuate, and interlobular arteries (collectively called 'preglomerular resistance'), as well as the resistance of peritubular capillaries and veins. This additional granularity allows one to more accurately describe intrarenal vascular resistance and its effects on blood pressure.
[0138] Because Ang Il is a potent vasoconstrictor that has effects both in the kidney and throughout the systemic circulation, some implementations include a representation of the effects of Ang Il on the renal vasculature. Ang Il has effects on both renal and systemic circulations. The contribution of Ang Il to the systemic arterial resistance was compared to results obtained using the Quantitative Human Physiology (QHP) software. QHP is a publicly available simulation software from the University of Mississippi developed and maintained by Coleman and colleagues (Hester, et al. A multilevel open source integrative model of human physiology. FASEB J 2008 March 1 ;22(1_MeetingAbstracts):756). QHP (version 2008b3) was used to obtain the functional dependence of arterial resistance on Ang Il concentration. The effects of Ang Il on afferent arteriole and total preglomerular resistance were represented as a linear relationship:
R = R0(a + b - CAngII )
(26) wherein, R0 is the nominal vascular resistance, CAngiι is the concentration of Ang Il (circulating or bound to a receptor), a and b are fitting constants such that for physiological CAngiι values the modifier in parenthesis is close to 1.
[0139] In the Karaaslan model, TPR does not explicitly include renal vascular resistance and does not account for its contribution to TPR. In contrast, certain implementations of the model described here in considers systemic and renal components as parallel resistances with an appropriate calculation of their effect on mean arterial pressure and cardiac output to differentiate between the renal and systemic effects on hypertension. The changes are reflected in the "total peripheral resistance" node.
[0140] Renal blood flow can be calculated by taking into account that actual pressure drop in the kidney is less than mean arterial pressure. In a preferred implementation, the contribution of renal vein resistance corresponds to a measured value of approximately 4 mm Hg. [0141] In the original Karaaslan model, the regulation of cardiac output and mean arterial pressure does not prevent these parameters from rising above physiological limits in order to meet the requirements of GFR and sodium and water balance. The current model preferably includes an additional autoregulatory mechanism that constrains GFR values by reducing changes in glomerular pressure that occur in response to changes in MAP. The effect can be implemented via "glomerular pressure autoregulation". When calculated, theoretical glomerular pressure can be adjusted by multiplying it to a transform function. That adjusted glomerular pressure can be used in calculating GFR (nodes "autoregulated glomerular pressure", "glomerular pressure autoreg.", and "GP autoregulatory adjustment"). [0142] GFR is a function of the number of effective functional nephrons. Functional nephrons may change because of disease progression or simply through the aging process. To account for these effects, total GFR can be computed as a product of an average SNGFR and the total number of nephrons.
[0143] Sodium reabsorption mechanisms can be added by 1 ) implicitly representing the Loop of Henle, and 2) modifying the effect of the macula densa on the tubuloglomerular feedback. These modifications were implemented to represent the effects of diuretic therapy, particularly loop diuretics (furosemide).
[0144] It is known that sodium concentration in the plasma is tightly regulated, however, the Karaaslan model includes no specific mechanism(s) to account for this regulation. One implementation of the model includes additional feedback to renal water reabsorption in the RAAS model. This feedback mechanism helps to keep plasma sodium concentration within feasible (physiological and pathological) constraints. For the reabsorption regulator, the following form was chosen:
Figure imgf000048_0001
where Q and Q0 is sodium reabsorption rate and its nominal value, respectively. C, Cmax, and Cref are current sodium concentration, and its physiologically maximal and nominal values respectively, S and G are scale and gain factors allowing to fine tune the effect.
4.4.4.1 Water and sodium reabsorption
[0145] In the present model, plasma levels of sodium are controlled through a series of RAAS-associated feedbacks on tubular reabsorption and water intake, as well as by coupling of water and sodium flow. In the original implementation of the Karaslaan model (Karaaslan, et al. Long-term mathematical model involving renal sympathetic nerve activity, arterial pressure, and sodium excretion. Ann Biomed Eng. 2005 Nov;33(11):1607-30), increases in distal tubule sodium reabsorption were not sufficiently controlled by the RAAS feedbacks. As a result, sodium concentrations drifted above physiological levels. To prevent this non-physiological response, the present model includes an additional feedback on tubular water reabsorption. This feedback has a nonstandard form, similar but not identical to proportional control, whereby a rapid compensatory mechanism is activated as sodium concentrations increase and approach an upper limit. The feedback's gain can be adjusted to prevent oscillatory/unstable behaviors while still maintaining sufficiently tight control over sodium concentration. This is only one form of sodium controller that could have been implemented. A more common controller, one that increases water reabsorption proportionately to the sodium concentration relative to a "set-point" could also be implemented as it may also correct for reductions in sodium concentration. This alternate form, however, may be less effective at keeping a "maximum" concentration limit, which was the original issue detected in the Karaaslan model. Finally, alternate controller forms that include feedback from the integral and/or rate of change of the difference between sodium and its ideal set-point could be adopted to ensure stability and robustness of control for higher controller gains. [0146] Although the original Karaslaan model explicitly included proximal tubule sodium reabsorption, it did not address the reabsorption occurring in the Loop of Henle. In order to represent furosemide therapy, a common 'background' diuretic therapy taken by hypertensive patients, the original representation of proximal tubule reabsorption has been split into two components, one representing the proximal tubule (PT), and a second one representing the loop of Henle (LoH). Furosemide inhibits reabsorption only in the Loop of Henle. The fraction of the total pre-macula densa (PT + LoH) reabsorption that occurs in the Loop of Henle and the effect of furosemide on this reabsorption can be adjusted to achieve the appropriate clinical behaviors (MAP, GFR).
4.5 Simulating Hypertension and RAAS [0147] The invention also provides methods and systems for simulating hypertension. The system of the invention comprises: a) a computer-executable data editor, capable of accepting data describing a subject; b) a computer-executable integrator, capable of executing a computer model of atherosclerosis with the data to generate a set of outputs describing the result of the simulation of atherosclerosis; and c) a computer-executable report generator capable of reporting the set of outputs. The computer model comprises: i) a RAAS pathway module; ii) a renal function module; and iii) a blood pressure regulation module. Methods of simulating RAAS comprise executing the models of the invention, optionally in conjunction with a virtual stimulus.
[0148] Methods of simulating RAAS can comprise applying a virtual protocol to the computer model to generate a set of outputs to represent a phenotype of the biological system. The phenotype can represent a normal state or a disease state. In certain implementations, the methods can further include accepting user input specifying one or more parameters or variables associated with one or more mathematical representations prior to executing the computer model. Preferably, the user input comprises a definition of a virtual patient or a definition of the virtual protocol, such as administration of a therapy.
[0149] Running the computer model produces a set of outputs for a biological system represented by the computer model. The set of outputs can represent one or more phenotypes of the biological system, i.e., the simulated subject, and includes values or other indicia associated with variables and parameters at a particular time and for a particular execution scenario. For example, a phenotype is represented by values at a particular time. The behavior of the variables is simulated by, for example, numerical or analytical integration of one or more mathematical relations to produce values for the variables at various times and hence the evolution of the phenotype over time. The level of detail of the output can vary dependent upon the level of sophistication of the target user. Exemplary outputs can range from an exhaustive report including all parameters of the computer model to a simple indicator of likelihood of hypertension or a normotensive blood pressure at a particular point in time. Additional clinically relevant outputs include therapeutic effects on circulating angiotensinogen, glomerular ACE activity or blood volume.
[0150] The computer executable software code numerically solves the mathematical equations of the model(s) under various simulated experimental conditions. Furthermore, the computer executable software code can facilitate visualization and manipulation of the model equations and their associated parameters to simulate different patients subject to a variety of stimuli. See, e.g., U.S. Patent Number 6,078,739, entitled "Managing objects and parameter values associated with the objects within a simulation model," the disclosure of which is incorporated herein by reference. Thus, the computer model(s) can be used to rapidly test hypotheses and investigate potential drug targets or therapeutic strategies.
[0151] In one implementation, the computer model can represent a normal state as well as a disease (e.g., hypertensive or diabetic) state of a biological system. For example, the computer model includes parameters that are altered to simulate a disease state or a progression towards the disease state. The parameter changes to represent a disease state are typically modifications of the underlying biological processes involved in the disease state, for example, to represent the genetic or environmental effects of a condition on the underlying physiology. By selecting and altering one or more parameters, a user modifies a normal state and induces a phenotype of interest. In one implementation, selecting or altering one or more parameters is performed automatically.
[0152] In the present implementation of the invention, various mathematical relations of the computer model, along with a modification defined by the virtual stimulus, can be solved numerically by a computer using standard algorithms to produce values of variables at one or more times based on the modification. Such values of the variables can, in turn, be used to produce the first set of results of the first set of virtual measurements. Typically, the virtual stimulus is a representation of administration of a therapy.
4.5.1 Virtual patients
[0153] One or more virtual patients in conjunction with the computer model can be created based on an initial virtual patient that is associated with initial parameter values. A different virtual patient can be created based on the initial virtual patient by introducing a modification to the initial virtual patient. Such modification can include, for example, a parametric change (e.g., altering or specifying one or more initial parameter values), altering or specifying behavior of one or more variables, altering or specifying one or more functions representing interactions among variables, or a combination thereof. For instance, once the initial virtual patient is defined, other virtual patients, e.g., patients possessing certain risk factors for developing high blood pressure, may be created based on the initial virtual patient by starting with the initial parameter values and altering one or more of the initial parameter values. Alternative parameter values can be defined as, for example, disclosed in U.S. Pat. No. 6,078,739. These alternative parameter values can be grouped into different sets of parameter values that can be used to define different virtual patients of the computer model. For certain applications, the initial virtual patient itself can be created based on another virtual patient (e.g., a different initial virtual patient).
[0154] Alternatively, or in conjunction, one or more virtual patients in the computer model can be created based on an initial virtual patient using linked simulation operations as, for example, disclosed in the following publication: "Method and Apparatus for Conducting Linked Simulation Operations Utilizing A Computer-Based System Model", (U.S. Application Publication No. 20010032068, published on October 18, 2001 ). This publication discloses a method for performing additional simulation operations based on an initial simulation operation where, for example, a modification to the initial simulation operation at one or more times is introduced. In the present embodiment of the invention, such additional simulation operations can be used to create additional virtual patients in the computer model based on an initial virtual patient that is created using the initial simulation operation. In particular, a virtual patient can be customized to represent a particular subject. If desired, one or more simulation operations may be performed for a time sufficient to create one or more "stable" virtual patient of the computer model. Typically, a "stable" virtual patient is characterized by one or more variables under or substantially approaching equilibrium or steady-state condition. [0155] Various virtual patients of the computer model can represent variations of the biological system that are sufficiently different to evaluate the effect of such variations on how the biological system responds to a given scenario. In particular, one or more biological processes represented by the computer model can be identified as playing a significant role in modulating biological response to a therapy, and various virtual patients can be defined to represent different modifications of the one or more biological processes. The identification of the one or more biological processes can be based on, for example, experimental or clinical data, scientific literature, results of a computer model, or a combination thereof. Once the one or more biological processes at issue have been identified, various virtual patients can be created by defining different modifications to one or more mathematical relations included in the computer model, which one or more mathematical relations represent the one or more biological processes. A modification to a mathematical relation can include, for example, a parametric change (e.g., altering or specifying one or more parameter values associated with the mathematical relation), altering or specifying behavior of one or more variables associated with the mathematical relation, altering or specifying one or more functions associated with the mathematical relation, or a combination of them. The computer model may be run based on a particular modification for a time sufficient to create a "stable" configuration of the computer model.
[0156] In certain implementations, the model of RAAS is executed while applying a virtual stimulus or protocol representing, e.g., a change in diet or a therapeutic regimen. A virtual stimulus can be associated with a stimulus or perturbation that can be applied to a biological system. Different virtual stimuli can be associated with stimuli that differ in some manner from one another. Stimuli that can be applied to a biological system can include, for example, existing or hypothesized therapeutic agents, treatment regimens, and medical tests. Additional examples of stimuli include exercise and diet. Further examples of stimuli include environmental changes such as those relating to changes in level of exposure to an environmental agent. [0157] A virtual protocol, e.g., a virtual therapy, representing an actual therapy can be applied to a virtual patient in an attempt to predict how a real-world equivalent of the virtual patient would respond to the therapy. Virtual protocols that can be applied to a biological system can include, for example, existing or hypothesized therapeutic agents and treatment regimens, mere passage of time, changes in lifestyle and the like. By applying a virtual protocol to a virtual patient, a set of results of the virtual protocol can be produced, which can be indicative of various effects of a therapy.
[0158] For certain applications, a virtual protocol can be created, for example, by defining a modification to one or more mathematical relations included in a model, which one or more mathematical relations can represent one or more biological processes affected by a condition or effect associated with the virtual protocol. A virtual protocol can define a modification that is to be introduced statically, dynamically, or a combination thereof, depending on the particular conditions and/or effects associated with the virtual protocol.
4.5.2 Hypertension model application in drug development [0159] The detailed model of hypertension presented herein is the foundation of a platform to investigate the response of this system to multiple RAAS-modulating therapies. In particular, after careful parameterization and validation of model behavior with available clinical data, the model can be used to predict the relative effects of the different therapies on entities that are difficult to measure clinically and can be used to predict the response to combination therapies for which clinical data is not available. The model also highlights any differences between circulating and renal peptide concentrations, and how therapies that localize in the renal tissue may have different effects than therapies that remain only in the systemic circulation. The predicted concentrations of renal peptides may also yield insight into the changes in local Ang Il in response to therapies without requiring invasive and difficult tissue sampling. In addition, the model can be used to investigate questions around the effect of therapies on local tissue Ang Il that, in turn, has an effect on renal function. [0160] Using combinations of different classes of RAAS-modulating therapies to treat hypertension is of interest in drug development. Since none of the currently prescribed therapies can block 100% of Ang Il production, it is thought that inhibiting the pathway at multiple points in the pathway and within the tissue may provide a more complete blockade and have a better effect on reducing blood pressure. While there is a large body of RAAS biomarker data available for monotherapies, there is less complete data on the corresponding biomarker response to combination therapy due to a lack of resources to pursue all potential combinations and cost factor attached with any clinical trial. To further compound the problem of quantitation, ATI-bound Ang Il is the actual effector of the RAAS pathway and is not measured in the clinic. Instead, the changes in upstream biomarkers are used to estimate and compare the effectiveness of different classes of RAAS modulating therapies. In particular, plasma renin activity (PRA) and plasma renin concentration (PRC) are typically measured in clinical trials but different classes of RAAS drugs affect these phenotypic data in different ways (e.g. DRIs reduce PRA, while ARBs and ACEi increase PRA) while still achieve measurable decreases in blood pressure. This makes it difficult to compare the relative level of the reduction in AT-1 bound Ang Il achieved by different mono and combination therapies.
[0161] The model described herein can be used to fill this gap, by predicting the relative % change in ATI-bound Ang Il (i.e., the effector of downstream changes in blood pressure, glomerular filtration rate, end-organ protection, etc) for different monotherapies and for combination therapies even in the absence of any direct measure or marker of drug efficacy. To accomplish this analysis, the model was rigorously calibrated with phenotypic data (PRA and PRC) from a large number of studies for a range of RAAS-modulating monotherapies (e.g. aliskiren, valsartan, losartan, irbesartan, enalapril, ramipril).
• Studies of different doses of aliskiren (a direct renin inhibitor) monotherapy provided data on the reduction in PRA as well the corresponding reactive rise in PRC for each dose. This data was used to calibrate a pharmacodynamic (PD) curve relating aliskiren dose to % inhibition of PRA, and was used to calibrate the shape and strength of the feedback on renin with changes in ATI-bound Ang Il
(0-
• After parameterization of this feedback relationship (f), the model was able to capture the PRA/PRC response to ARB and ACEI therapy using only changes in calibration of the % inhibition of AT1 binding rate or ACE activity, respectively. No additional changes in the model, including the feedback from AT1 to PRA, were needed.
• The model was able to predict the phenotypic (PRA/PRC) response to combinations of RAAS drugs for which data was available, (e.g. aliskiren + valsartan), with no additional changes in model parameters.
[0162] The model can be used with confidence to predict the change in phenotype for different combination therapies when sufficient clinical data is not available to us. For example, it has been used to predict the phenotypic response for aliskiren 300mg + ramipril 10mg. In addition, the model predicts the relative % inhibition of ATI-bound Ang Il for the different doses and types of RAAS-modulating therapies. The strength of this integrated model lies in the prediction of ATI-bound Ang Il levels, a valuable measure of the primary effector of the downstream response of the RAAS pathway that is difficult to measure in vivo, and even more difficult to measure in the tissue.
5 PHYSICAL SYSTEMS
[0163] This invention can include a single computer model that serves a number of purposes. Alternatively, this invention can include a set of large-scale computer models covering a broad range of physiological systems. In addition to including a model of hypertension and associated disease states, the system can include complementary computer models, such as, for example, epidemiological computer models or models of related systems, e.g. atherosclerosis and its associated cardiovascular risk. For use in healthcare, computer models can be designed to analyze a large number of subjects and chemicals. In some instances, the computer models can be used to create a large number of validated virtual patients and to simulate their responses to a large number of therapeutic regimens or changes in lifestyle.
[0164] The invention and all of the functional operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structural means disclosed in this specification and structural equivalents thereof, or in combinations of them. The invention can be implemented as one or more computer program products, i.e., one or more computer programs tangibly embodied in an information carrier, e.g., in a machine readable storage device or in a propagated signal, for execution by, or to control the operation of, data processing apparatus, e.g., a programmable processor, a computer, or multiple computers. A computer program (also known as a program, software, software application, or code) can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file. A program can be stored in a portion of a file that holds other programs or data, in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub-programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers at one site or distributed across multiple sites and interconnected by a communication network.
[0165] The processes and logic flows described in this specification, including the method steps of the invention, can be performed by one or more programmable processors executing one or more computer programs to perform functions of the invention by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus of the invention can be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application specific integrated circuit).
[0166] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read only memory (ROM) or a random access memory (RAM) or both. The essential elements of a computer are a processor for executing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto optical disks, or optical disks. Information carriers suitable for embodying computer program instructions and data include all forms of non-volatile memory, including by way of example semiconductor memory devices, e.g., EPROM, EEPROM, and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto optical disks; and CD ROM and DVD-ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry. [0167] To provide for interaction with a user, the invention can be implemented on a computer having a display device, e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor, for displaying information to the user and a keyboard and/or a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any form, including acoustic, speech, or tactile input.
[0168] The invention can be implemented in a computing system that includes a back end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front end component, e.g., a client computer having a graphical user interface or a Web browser through which a user can interact with an implementation of the invention, or any combination of such back end, middleware, or front end components. The components of the system can be interconnected by any form or medium of digital data communication, e.g., a communication network. Examples of communication networks include a local area network ("LAN") and a wide area network ("WAN"), e.g., the Internet.
[0169] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
6 EXAMPLES
6.1 Example 1 : Hypertensive virtual patients [0170] In the context of one implementation of the invention, four exemplary hypertensive virtual patients were developed.
[0171] HT-1 : an essential hypertensive patient with local vasoconstriction and atherosclerosis: Increased preglomerular resistance is a known cause of hypertension, and may be caused by increased sympathetic nervous activity and/or widespread atherosclerosis. While these disease etiologies have a systemic effect, HT-1 was represented in as a local increase in the renal afferent arteriole resistance leading to decreased perfusion of the kidneys to represent patients who may have plaques, obstructions or other factors leading to constriction of the renal artery. Simulations with the present model demonstrated that as the resistance of the afferent arteriole is increased, the GFR initially decreases due to a reduction of perfusion pressure into the glomerulus resulting in decreased sodium and water excretion. This inherent regulation of pressure-natriuresis led to 1 ) a subsequent increase in blood volume and increased arterial pressure, and 2) increased tubuloglomerular feedback that triggers the release of renin and subsequent generation of Ang II. This increased arterial pressure compensates for the previous reduction of salt and water excretion, and will settle at a blood volume and mean arterial pressure necessary to return the excretion levels back to normal (assuming a normal intake of water and sodium). The increased renin- mediated generation of Ang Il will allow for more sodium reabsorption in the proximal tubule. However, as the mean arterial pressure rises, GFR returns to normal, and the RAAS system resets back to normal levels as well. Therefore, hypertension associated with high preglomerular resistance is not sodium-sensitive because the RAAS system was able to respond and adjust to a wide range of sodium intake levels.
[0172] HT-2: a diabetic hypertensive patient with diabetic nephropathy/glomerular damage:. Kf is the hydrostatic conductance of the glomerular membrane. It is a product of k (specific filtration coefficient), and S (the available surface area for filtration). Patients with nephropathy typically have a reduced Kf due to the reduction of both k and S. Loss of endothelial fenestrae, a thickened glomerular basement membrane, and loss of epithelial slits between podocyte foot processes all change the filters integrity by reducing k and the ability to filter water and solutes. Similarly, mesangial expansion and glomerulosclerosis decrease the surface area available for filtration. Of note, Kf can also increase in the early stages of diabetic nephropathy; the structural change(s) responsible for hyperfiltration in the diabetic setting are unclear, although glomerular
(capillary) hypertrophy has been cited as one of the mechanisms, studies in rats suggest that additional mechanisms are involved (Malatiali et al., Phlorizin prevents glomerular hyperfiltration but not hypertrophy in diabetic rats. Exp Diabetes Res 2008;2008:305403).
[0173] Decreasing the glomerular filtration coefficient (Kf) may lead to hypertension because higher glomerular pressures are required to filter the same amount of sodium and water through the glomerulus. Decreasing Kf in isolation of other mechanisms is not a sodium-sensitive mechanism. In fact, as GFR initially declines, renin release is increased due to the lower sodium concentration sensed by the macula densa. However, in these patients, a compensatory increase in mean arterial pressure returns GFR and plasma renin activity to normal levels. Normal or high levels of PRA is not itself a sodium-sensitive mechanism. Lowering renin release, and therefore PRA and Ang Il generation allows the nephron to excrete more sodium; the excess sodium is eliminated and this is reflected in a steep renal output curve. When the RAAS of a given patient is unable to lower renin in order to excrete an increase in sodium intake, that patient is considered 'salt-sensitive'. Decreased Kf can also be associated with progressive nephron loss, which is a sodium-sensitive disorder due to increased perfusion of the remaining functional nephrons. [0174] Hypertensives due to decreased Kf were implemented in the present model by increasing the damage to the glomerulus and decreasing the number of functional nephrons. The increased damage to the glomerular membrane was via a mechanism resulting from high levels of glucose, MAP and Ang II.
[0175] HT-3: an essential hypertensive patient with increased sodium absorption in nephron. A defective increase in sodium reabsorption in the descending portion of the loop of Henle is commonly associated with sodium-insensitive hypertension. Since these sections of the nephron are located upstream of the macula densa it is subjected to regulation by tubuloglomerular feedback (TGF) mechanisms. In response to physiological decreases in GFR, sodium reabsorption is increased in tubular segments located before the macula densa (e.g. LoH), a specialized group of epithelial cells part of the juxtaglomerular apparatus (JGA). The JGA is located in the portion of the distal tubule that comes in close contact with the afferent and efferent arterioles. Increased sodium reabsorption delivers less sodium to the distal tubule and this is sensed by the macula densa. As a result, 1 ) afferent arteriole resistance is decreased (most likely mediated by local production of vasodilators) and, 2) renin production by JG cells is increased. Local generation of Ang Il causes an increase in efferent arteriole resistance. Together, the effects on pre- and post-glomerular resistance increase GFR and bring it back to normal. Direct effects of Ang Il on sodium reabsorption also contribute to restore sodium homeostasis. [0176] Regulation of changes in GFR by TGF mechanisms within physiological parameters minimizes changes in blood volume and MAP. In the presence of a dysregulated TGF mechanism, as may occur in hypertension, increases in sodium reabsorption as a result of lower GFR levels will also augment blood volume and MAP, which will lead to an increase in GFR. As hypertension develops, the GFR would be high enough to compensate for the reduced levels of sodium delivery to the macula densa that resulted from increased reabsorption. Since the sodium delivery to the macula densa has returned to normal levels, the RAAS activity has also returned to normal, thus the patient is not sodium-sensitive but blood pressure remains elevated. It should be noted that the increased GFR at the expense of increased blood pressure in this hypothetical hypertensive patient may lead to additional glomerular damage, namely reductions in Kf and subsequent nephron loss.
[0177] The discussion above included a description of increased sodium reabsorption in the proximal nephron as a mechanism leading to hypertension. It was hypothesized that hypertension may also develop as a result of increases in sodium reabsorption in the distal tubule (DT) and/or the collecting duct (CD), Due to the anatomical location of these structures (DT and CD) distal to the macula densa, and therefore not subjected to RAAS-mediated regulation, a defect in sodium reabsorption in the DT/CD leads to salt- sensitive hypertension. In this condition, it was hypothesized that increased sodium reabsorption occurs regardless of the levels present in the tubular environment. Therefore, each nephron excretes less than the amount required to maintain sodium homeostasis. Sodium accumulates slowly over time and eventually suppresses renin release in an effort to increase excretion. The abnormally high level of distal sodium and water reabsorption will continue and increase mean arterial pressure.
[0178] HT-4: an essential hypertensive patient with increased systemic vascular resistance: Essential hypertension has been traditionally viewed to be a result of increased arterial resistance. Early studies on the use of central antihypertensive agents (e.g. clonidine) demonstrated that a reduction in the central sympathetic outflow translated into reductions in mean arterial pressure. Initial attempts using an increased tubuloglomerular resistance (TPR) to generate hypertension was not successful. The kidney was capable of compensating for any changes in the resistance by altering water volume and ultimately affecting cardiac output. In order to reproduce hypertension due to increased TPR, HT-4 virtual patient is represented by all systemic arteries (including the renal artery) having increased resistance. The representation of TPR can be expanded to include renal resistance and the actions of Ang Il on both renal and systemic arteries. A representative of essential hypertension was created by modulating total peripheral and renal resistances. Although this hypertensive patient is similar to HT- 1 , this patient will respond differently to therapies that target the total peripheral resistance
6.2 EXAMPLE 2: Simulation of Therapy.
[0179] Therapies were implemented by modifying the implemented physiological and pathophysiological mechanisms that led to hypertension in the reference virtual patients, HT- 1 to HT-4, provided that those mechanisms were documented in the scientific literature as being affected by the specific therapies. For example, increased activity of the sympathetic nervous system in the kidney leads to an increased production and release of renin. Increased plasma renin activity (PRA) then leads to cleavage of larger pools of substrate (angiotensinogen) and increased production if Ang II. Since renin production is modulated by renal sympathetic efferent outflow through the activation of beta-adrenergic receptors, renin release by the JGA is amenable to pharmacological blockade by beta-blocker compounds (e.g. atenolol). Similar mechanistic grounds were utilized to implement additional non-RAAS and RAAS-based therapies. Renal, vascular and hormonal mechanisms were utilized including handling of sodium by the nephron, direct or indirect effects on renal hemodynamics, and effects on arterial vasoreactivity.
[0180] Several types of therapeutic interventions approximating the effects of therapies observed in hypertensive patients were implemented in the model. Pharmacological therapies affect various pathways implemented in the platform as reported in the literature. Drug classes, can be divided into two groups, RAAS-based and non RAAS therapies (Table 8).
Figure imgf000061_0001
[0181] Preferably, the effect of a drug is implemented according to the reported inhibition of a specific pathway, as well as a function of the drug concentration. The latter is approximated by a temporal profile when concentration transitions from its minimal to its maximal value. In order to implement different drug doses, the normalized profile is multiplied by a certain dose resulting in a net effect. In a typical normalized concentration profile, concentration increases from 0 to 1 in the course of 24 hours. The shape of the curve can be adjusted/customized using the appropriate object parameters. Specific functional forms are presented for each drug class.
6.2.1 Non-RAA S Therapies
[0182] Thiazides. One of the primary pathways that thiazides (e.g. hydrochlorotiazide, HCT) affect is sodium (Na+) reabsorption in the nephron's distal tubule. In the model, this was calculated as a fraction η of sodium flow past the macula densa:
Figure imgf000062_0001
where fraction η is a product of its nominal value η0 and a function of aldosterone concentration. In the current implementation, thiazide lowers the value of QreabsoP by a factor of (1 - CTh*i) where C is the thiazide normalized concentration and / is the level of inhibition. Parameter / is dependent on the dose and could be calibrated to fit specific data on Na+ reabsorption or high level behavior. The factor (1 - C*i) should be set at values between 0 and 1.
[0183] In addition to altering Na+ reabsorption, clinical data indicate that thiazides may affect other pathways. The acute effects of thiazide therapy include a reduction of plasma and extracellular fluid volume. However, prolonged treatment (i. e. > 1 month) with thiazides results in a sustained reduction in blood pressure, while plasma volume and extracellular fluid volume return close to pre-treatment levels. Therefore, the effect on systemic hemodynamics do not fully account for the reduction in blood pressure. A hypothesis formulated in the literature ascribes long-term effects of thiazide therapy to changes in vascular resistance. In the platform, both pathways are represented; their separate or combined action is defined by their respective value sets. Fig. 13 provides an example of thiazide therapy when reduction of Na+ reabsorption was reduced by 15% and reduction in systemic resistance, pre-arteriole resistance, and afferent arteriole resistance reduced by 15%, 20%, and 20%, respectively. Reductions in MAP ranged from 7- 10 mm Hg among the different categories of hypertensive patients.
[0184] Furosemide is a loop diuretic which acts predominately at the apical membrane in the thick ascending limb of the loop of Henle (LoH); it inhibits Na+ and Cl" reabsorption. The furosemide-mediated diuretic effect is represented by reducing Na+ reabsorption in the proximal nephron. In order to explicitly account for a functional representation of the LoH, the filtered sodium load in the proximal tubule is split into two fractions, one of them, FLoH, is ascribed to the LoH; this portion of the sodium reabsorption fraction is affected only by furosemide, (eq. 29). It is known that about 25% of sodium reabsorption happens in the LoH, thus the following range was chosen 0.2 < FLoH < 0.3 .
Figure imgf000063_0001
[0185] β-Blockers (BBs). The antihypertensive action of BBs involves reductions in cardiac output and renin release from the kidneys. Beta blockers also have a central nervous system effect that reduces the activity of the sympathetic nervous system (sympathetic activity outflow). In the model, renin release is stimulated by increases in renal sympathetic activity (rSNA), whereas Na+ flow is sensed by the macula densa. Thus, a reduction in rSNA as a result of a beta blockers therapy captures both, the reduction in renin release and the reduction in SNA. rSNA is represented as a normalized baseline value NΓSNA multiplied by the effect of MAP on rSNA and the effect of right atrial pressure (RAP) on rSNA. Beta blockers therapy reduces the value of rSNA, its representation in the platform is similar to thiazide, see Eq (30). In the example presented in Fig. 13 the rSNA value was reduced by therapy by 25%. As a result, mean arterial pressure was reduced by 5-14 mm Hg in simulations ran in the set of VP treated, and the reductions were in agreement with reported data.
Figure imgf000063_0002
[0186] Calcium channel blockers (CCBs). CCB based drugs have multiple effects on the cardiovascular system including reduction in the force of contraction of the myocardium, reduction in heart rate, as well as vasodilation. In the model, calcium channel blocker effects are implemented as a reduction in systemic arterial resistance, and renal arterial resistance. Renal arterial resistance is represented as three compartments considered separately preglomerular (pre-afferent arteriole) resistance, and afferent and efferent arteriole resistances. It is assumed that the CCB effect is more pronounced on the efferent arteriole compared to the afferent, allowing more blood filtering through the glomerulus. Fig. 13 shows a mean arterial pressure reduction of approximately 10 mmHg with a CCB therapy applied to a hypertensive VP with elevated preglomerular resistance. In this example, the therapy reduced efferent arteriole resistance by 50%, while afferent arteriole resistance was reduced by 15%.
6.2.2 RAAS therapies [0187] ACE inhibitors: ACEIs in the RAAS PhysioLab platform affect several pathways involving different enzymatic activities Amempy. Mathematically, they are all similarly represented as a product of uninhibited activity A0 and therapy effect, which in turn is defined by the degree of activity inhibition /
Figure imgf000064_0001
[0188] In the platform, ACE inhibition therapy directly affects the activity of ACE, an enzyme that catalyzes the conversion of Ang I to Ang Il both in the systemic circulation and the intrarenal glomerular and tubular compartments. It is hypothesized that peritubular tissue may also contribute to the pool of Ang Il production in the kidney and that fraction also is affected by ACE inhibition therapy. Another hypothesis implemented in the model is the effects of ACE inhibition in the context of a differential conversion of Ang I to Ang Il mediated by both ACE and chymase, an enzyme also generated in the kidney and the heart that also converts Ang I to Ang II. Finally, ACE inhibition therapy alters the rate of degradation of Ang (1-7) peptides. Fig. 14 provides an example of how ACE inhibition therapy reduces MAP in normotensive and hypertensive VPs. [0189] A T1 receptor blocker (ARB) ARBs block the activation of type I Ang Il receptors (AT1 ). In the model disclosed herein, AT1 receptors are split between three compartments. Two of these compartments, glomerular and tubular, represent receptors belonging to the renal circulation, while the rest of AT1 receptors are lumped in the systemic circulation (third compartment). ARB therapy affects Ang Il binding rates and have a similar functional form in all compartments:
Figure imgf000064_0002
where r and r0 are binding rates with and without therapy, T is therapy inhibition effect and CARB is the concentration of the drug. The values of 7 are selected from calibration experiments and specified in the parameter set describing ARB effects, the values of r0 are calculated at equilibrium. [0190] Additional mechanisms affected by AT1 receptor blocking therapy are included in the model. For instance, ARB therapy may affect Ang Il clearance rate by altering Ang Il degradation time constants. The functional form of these mechanisms is similar to eq.5 except that in place of r0 there is a reciprocal of a corresponding degradation time constant. Fig. 14 shows an example on how AT1 receptor blocking therapy changes mean arterial pressure in various virtual patients when binding rates were reduced a factor of 200, while degradation rates were reduced by a factor of only 5.
[0191] Direct renin inhibitors (DRI): DRIs interrupt the RAAS system by binding and preventing the action of renin and thereby inhibiting the formation of Ang I and Ang II. As with other RAAS based drugs in the platform, DRI therapy effects are split into two compartments, a systemic circulation compartment and an intrarenal compartment. In the latter, DRI therapy affects glomerular and tubular angiotensinogen conversion to Ang I by membrane bound renin. In the systemic circulation, inhibition of plasma renin activity by DRI therapy was implemented according to the following equation:
Figure imgf000065_0001
[0192] The difference with previous therapy representations is in the Michaelis-Menten function of effective drug concentration Ch DRι chosen in lieu of a linear relationship. Effective DRI concentration was normalized by the Michaelis-Menten constant Ki, (Ch DRι = C/Ki ), h stands for the Hill coefficient, while TDR, represents the therapy effect. The choice in favor of Michaelis-Menten kinetics was made because it allowed for a direct inclusion of dose-dependency. Similar relationships are implemented for Ang I synthesis by the kidney. Fig. 14 provides an example of simulations with DRI therapy applied to several VPs.
[0193] Aldosterone Antagonists. Implementation of the effects of aldosterone antagonism in the present model was lumped into one effect that alters aldosterone secretion rate: CW,
Figure imgf000066_0001
where Q°aido is the nominal aldosterone secretion rate, Taιd0 is the inhibition effect of the therapy, and Ca/(to is the concentration of the drug. Fig. 14 depicts simulation results on MAP changes with an aldosterone antagonist that reduced the normalized secretion rate by 90%.
6.3 Example 3: Diabetic Phenotype
[0194] Type 2 diabetic (T2D) disease nephropathy and progression of renal damage was calibrated using clinical data from a study conducted by Nelson et al in Pima Indians (N Eng J Med 335(22): 1636-42 (1996). The study recruited 6 groups of adult subjects with pre-defined characteristics including
• a normal glucose-tolerance test,
• an impaired glucose-tolerance (IGT) test within 3 months of the baseline study, with no history of diabetes,
• newly diagnosed diabetes with normal or impaired glucose-tolerance test in the past 3 years, 4) diabetes for at least 5 years with normal urinary albumin excretion ratio (UACR),
• diabetes for at least 5 years with microalbuminuria, and
• diabetes for at least 5 years with macroalbuminuria.
[0195] Urinary albumin was measured in mg/l and creatinine in g/l. Microalbuminuria was defined as UACRs of 30-299, whereas macroalbuminuria as UACRs >300. GFR and albumin excretion rates were used to match the reported clinical behavior.
[0196] Changes in Kf, the filtration coefficient, were implemented to recreate the clinical behavior of diabetic nephropathy. Pathological glomerular changes in T2D are translated into changes in k and S, the determinants of Kf. [0197] As k, the specific filtration coefficient, decreases due to structural damage to the glomerular filtration barrier, S, the glomerular surface area available for filtration may either increase or decrease. For instance, glomerular hypertrophy increases capillary surface, and it will therefore increase S, whereas mesangial cell expansion decreases S, as less area is available for filtration. [0198] Hydrostatic and oncotic pressures are kept constant during progression of diabetic nephropathy. For practical and long-term modeling purposes, changes in hydrostatic pressure and concentration of proteins along the glomerular capillaries were assumed to remain relatively unchanged during progression of diabetic nephropathy. [0199] High levels of glucose have direct damaging structural effects on the glomerular membrane that are reflected in increases in Θ, the sieving coefficient of albumin. Indirect effects of hyperglycemia via Ang Il on the glomerular membrane have been observed; for instance, activation of the RAS by glucose in podocytes. These changes have been represented in the model as Ang-ll-mediated changes via disease effects on renal function. In the current representation, all effects were captured through glucose- mediated actions.
[0200] To capture the diabetic disease states, virtual patients were created by assigning different parameter value sets to each phenotype (IGT, new-onset, microalbuminuric, and macroalbuminuric). Glucose-mediated changes were introduced in parameters k, S and albumin sieving coefficient. VP diversity (e.g. cohorts and populations) was added by further parameterization of S, k and albumin's sieving coefficient.
6.4 Example 3: Simulation of local generation of Ang I and Ang Il
[0201] The contribution of RAAS-related peptides in the kidney to the systemic RAAS pool of peptides was simulated using a mathematical model of renal and systemic RAAS kinetics according to the present invention. The model accounts for the renal production and release of Ang I, Ang II, Ang 1-7 and Ang IV. Systemic and local levels of RAAS- related peptides were estimated based on published plasma and whole renal tissue data. The model considers a single renal compartment localized to the glomerulus. Local glomerular rate of renin activity, angiotensin converting enzyme activity (ACE) and degradation rates are different than in the circulation to satisfy constraints observed in radiolabeled Ang I studies by Danser et al., 1998. The effect of a hypothetical pharmacological therapy that prevented the renal conversion of Ang I from local and systemic sources was implemented by increasing by ten-fold the rate of local Ang I degradation in the kidney. The resulting plasma concentration of RAAS peptides were then predicted using the model. [0202] An increase of local Ang I degradation was translated into lower levels of intrarenal Ang I and Ang II. Plasma levels of Ang I (7.5 vs. 7.4 fmol/ml) Ang Il (4.8 vs. 4.7 fmol/ml), Ang (1-7) (14.0 vs. 13.8 fmol/ml) and Ang IV (1.3 vs. 1.3 fmol/ml) in the absence or presence of therapy, were not affected by changes to Ang I in the kidney. [0203] The renin-angiotensin aldosterone system (RAAS) plays a critical role in blood pressure regulation, renal function and fluid homeostasis. Ang Il concentration in renal tissue is -10 times higher than that of plasma and raises questions about the contribution of intrarenal Ang Il to renal function and disease progression. The model predicted that degradation of locally synthesized Ang I as well as circulating Ang I entering the kidney lowers the local levels of Ang Il but has little measurable impact on their circulating levels. Pharmacological stimulation of renal Ang I degradation and/or inhibition of Ang I to Ang Il paracrine conversion may have therapeutic implications in preventing progression of diabetic and hypertensive nephropathy.
[0204] Although the foregoing invention has been described in some detail by way of illustration and example for purposes of clarity of understanding, it will be apparent to those skilled in the art that certain changes and modifications will be practiced. Therefore, the description and examples should not be construed as limiting the scope of the invention, which is delineated by the appended claims.

Claims

WE CLAIM:
1. A system comprising: a) a processor including computer-readable instructions stored thereon that, upon execution by a processor, cause the processor to simulate the renin-angiotensin aldosterone system, wherein the computer-readable instructions comprise: i) a RAAS pathway module comprising a mathematical representation of a plurality of biological processes associated with RAAS, wherein the plurality of biological processes comprises RAAS in systemic circulation and RAAS in kidney; ii) a renal function module comprising a mathematical representation of a plurality of biological processes associated with renal function, wherein the plurality of biological processes comprises glomerular filtration rate and albuminuria; iii) a blood pressure regulation module comprising a mathematical representation of a plurality of biological processes associated with blood pressure regulation, wherein the plurality of biological processes comprises cardiac output, vascular resistance and regulation of sodium/water balance; iv) a set of mathematical relationships between the representations of biological processes associated with RAAS pathway, renal function and blood pressure regulation; and v) a virtual protocol capable of being applied to the set of mathematical relationships to generate a set of outputs b) a first user terminal, the first user terminal operable to receive a user input specifying one or more parameters associated with one or more mathematical representations defined by the computer readable instructions; and c) a second user terminal, the second user terminal operable to provide the set of outputs to a second user.
2. The system of claim 1 , wherein the RAAS pathway module further comprises a mathematical representation of RAAS in cardiac tissue.
3. The system of claim 1 , wherein the representation of systemic RAAS pathway comprises a representation of feedback regulation of renin activity by prorenin synthesis and conversion and the equilibrium between prorenin and renin.
4. The system of claim 1 , wherein the renal function module further comprises a mathematical representation of disease effects.
5. The system of claim 4, wherein the disease effects are selected from the group consisting of damage to the sieving membrane, decreased amount of nephrons, alteration in glomerular hydrostatic conductance (Kf), tubular albumin reabsorption and tubular fibrosis.
6. The system of claim 1 , wherein the biological processes associated with renal function include a representation of a kidney as an assembly of single nephrons and associated fluid dynamics processes.
7. A system for simulating hypertension comprising: a) a computer-executable data editor, capable of accepting data describing a subject; b) a computer-executable integrator, capable of executing a computer model of RAAS with the data to generate a set of outputs describing the result of the simulation of RAAS, wherein the computer model comprises: i) a RAAS pathway module; ii) a renal function module; and iii) a blood pressure regulation module; and c) a computer-executable report generator capable of reporting the set of outputs.
8. The system of claim 7, wherein the computer-executable data editor further is capable of accepting a set of parameters describing a virtual patient.
9. The system of claim 7, wherein the computer-executable integrator further is capable of executing the computer model with the set of parameters describing the subject.
10. The system of claim 7, wherein the computer-executable data editor further is capable of accepting a virtual protocol and the computer-executable integrator is capable of executing the computer model with the virtual protocol.
11. A computer model of hypertension comprising: a) a RAAS pathway module; b) a renal function module; and c) a blood pressure regulation module.
12. The computer model of claim 11 , wherein the RAAS pathway module comprises a representation of RAAS pathway in systemic circulation and a representation of RAAS pathwayin the kidney.
13. The computer model of claim 11 , wherein the RAAS pathway module further comprises a representation of RAAS pathway in cardiac tissue.
14. The computer model of claim 11 , wherein the renal function module comprises a representation of glomerular filtration rate and a representation of albumin excretion.
15. The computer model of claim 14, wherein the renal function module further comprises a representation of disease effects.
16. The computer model of claim 15, wherein the disease effects are selected from the group consisting of damage to the sieving membrane, decreased amount of nephrons, alteration in glomerular hydrostatic conductance (Kf), tubular albumin reabsorption, and tubular fibrosis.
17. The computer model of claim 11 , wherein the renal module includes a representation of the kidney as an assembly of single nephrons and associated fluid dynamics processes.
18. The computer model of claim 11 , wherein the blood pressure regulation module comprises a representation of cardiac output, a representation of vascular resistance and a representation of regulation of sodium/water balance.
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