WO2003079894A1

WO2003079894A1 - Method of analysis of circadian rhythms

Info

Publication number: WO2003079894A1
Application number: PCT/AU2003/000358
Authority: WO
Inventors: Geoffrey Albert Head; Elena Vladimirovna Lukoshkova
Original assignee: Baker Medical Research Institute
Priority date: 2002-03-25
Filing date: 2003-03-25
Publication date: 2003-10-02
Also published as: AUPS133102A0

Abstract

A method of analysis of a circadian rhythm, including the steps of: receiving data indicative of the circadian rhythm; and performing a statistical fit of the data to provide a non-symmetrical approximation curve representative of the circadian rhythm.

Description

METHOD OF ANALYSIS OF CIRCADIAN RHYTHMS

FIELD OF THE INVENTION

The present invention relates to a method of analysis of human circadian rhythms. More particularly, the invention relates to a non-symmetrical method for analysing diurnal blood pressure and heart rate recordings.

BACKGROUND OF THE INVENTION

Ambulatory blood pressure (ABP) monitoring devices are now routinely used throughout the world. In today's health care environment there is an ever-increasing importance on quickly and accurately identifying patient problems before they become critical and require hospitalization. More and more often, the 24 hour blood pressure variation information of a patient is being sought as a better indicator of a patient's cardiovascular health than clinically acquired blood pressure measurements. The clinically acquired blood pressure measurements have a limited usefulness due to phenomena such as white coat hypertension. Many physicians use ABP monitoring to detect such phenomena and to adjust drug therapy for hypertensive patients. It has become recognised that 24 hour monitoring of blood pressure provides a better indicator of the likely impact of blood pressure on the degree of enlargement of the heart and thickening of the blood vessels. These factors are critical in the prediction of cardiovascular events.

The diurnal variation in blood pressure has been well described. Blood pressure tends to be the highest in the morning, decreasing gradually during the day and reaching its lowest values at night. Physical activity and periods of rest strongly influence the diurnal blood pressure pattern. However, a major characteristic of the diurnal variation is the fall in blood pressure and heart rate during the night.

Known methods of analysis of circadian rhythms have generally involved averaging blood pressure records at fixed clock times or synchronising records relative to the time of waking. Thus the data is segmented into a higher pressure period, approximating the daytime awake period and a low pressure period corresponding to the night time sleep period. The difference in these two blood pressure levels constitutes the major circadian variation in blood pressure. However, this approach is rather limited, and a more robust method is desirable. The most common approach in this regard has been the Minnesota Cosinor method which assumes that the high and low blood pressure periods have the same length and that the diurnal pattern follows, in principle, a sine wave and that the transition is smooth, symmetrical and continuous. An extension of this approach has been to apply a Fourier analysis which constitutes the superposition of multiple cosine functions of different amplitude and frequency. A recent method has involved the application of a simple square wave mathematical model which involves the estimation of the daytime and night time plateau with a vertical transition between the two periods, resulting in a square wave pattern. While this method has been shown to be better than the cosinor method, it assumes an abrupt and complete transition within one time point which is clearly not the case in practice.

To date there have been no methods which separately determine the rate of increase in blood pressure and heart rate in the morning and the rate of decrease in the evening. Indeed, a considerable need has arisen to provide a robust method of analysis of circadian changes in cardiovascular parameters since it has become clear that the occurrence of strokes, cardiac infarcts and subarachnoid haemorrhage is unevenly distributed over the day with the highest incidence in the morning when blood pressure is rising from low overnight values. Each of the known methods uses a symmetrical approximation curve when fitting the measured data to a circadian rhythmic form.

SUMMARY OF THE INVENTION

The present invention provides a method of analysis of a circadian rhythm, including the steps of: receiving data indicative of the circadian rhythm; and performing a statistical fit of the data to provide a non-symmetrical approximation curve representative of the circadian rhythm.

Preferably, the approximation curve includes a first transitional curve indicative of a transition of the circadian rhythm from a night-time level to a day-time level and a second transitional curve indicative of a transition of the circadian rhythm from a day-time level to a night-time level. Preferably, the first transition curve has a negative slope and the second transitional curve has a positive slope different in magnitude to that of the negative slope.

Preferably, the step of performing a statistical fit is performed using the following equation:

- DI ^{P2 P2} = ^pl + ₁_ ₊ . _e ,P33,(,P4*_-,x). + ._{1 + e}«("-*>

where PI is a day-time plateau level of the circadian rhythm; P2 is the difference between the day-time plateau and a night-time plateau;

P3 is a rate of transition from the day to night plateaus, having units 1 /hours;

P4 is a centre location (in time) of a transition period from day to night;

P5 is a rate of transition from the night to day plateaus, having units 1/nours;

P6 is a centre location (in time) of a transition period from night to day; x is a sample time; and y is the approximation curve.

Preferably, the method further includes the step of using the approximation curve to facilitate assessment of the likelihood of a cardiac event.

Preferably, the statistical fit is a least squares fit. Preferably, the least squares fit uses an initial parameter set to reduce the number of iterations required by the least squares fit to achieve a desired curve fitting accuracy level. Preferably, the initial parameter set is generated by performing a least squares fit of the data according to a sine curve model.

Preferably, the circadian rhythm is a cardiovascular rhythm. Preferably, the circadian rhythm is a human cardiovascular rhythm. Preferably, the circadian rhythm includes one of a diastolic blood pressure level, a systolic blood pressure level, a mean blood pressure level or a heart rate.

The present invention further provides a system for analysing a circadian rhythm, including: means for receiving data indicative of the circadian rhythm; and means for performing a statistical fit of the data to provide a non-symmetrical approximation curve representative of the circadian rhythm.

Preferably, the system includes means for collecting the data indicative of the circadian rhythm and transmitting the data to the means for receiving. Preferably, the means for collecting data is an ambulatory blood pressure monitor. Preferably, the means for performing a statistical fit of the data is a personal computer configured to interface with the ambulatory blood pressure monitor.

Advantageously, embodiments of the invention may assist medical practitioners in forming prognoses in relation to risk of cardiac disease and in more accurately titrating cardiovascular medication for a patient.

The present invention also provides a computer readable storage medium having stored thereon program code for causing a computer to execute the steps of the above method.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the invention are described in further detail hereinafter, by way of example only, with reference to the accompanying drawings, wherein: Figure 1 shows a system for analysing a circadian rhythm;

Figure 2 is a flow diagram illustrating a method of obtaining initial parameter estimates for use in the method of an embodiment of the invention; Figure 3 is a flow diagram illustrating the method of an embodiment of the invention applied to diastolic blood pressure information;

Figure 4 shows sample approximation curves of different kinds of circadian rhythms, plotted in accordance with an embodiment of the invention; and

Figure 5 shows a comparative analysis of approximation curves produced by an embodiment of the present invention and approximation curves produced by the Cosinor method using the same data. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to Figure 1, there is shown a system for analysing a circadian rhythm, generally designated by the reference numeral 2, including a recording device 6 and a computer 8, such as a personal computer or a manufacturer or server. The recording device 6 may be an Ambulatory Blood Pressure Monitor, Model 90207 by Spacelabs Medical, preferably used in combination with a Report Management System, Model 90121-1 by Spacelabs Medical (to enable direct cabling of the blood monitor pressure to the computer 8). The recording device 6 records information from a subject 4 relating to the subject's circadian rhythms and, in real time or in batch processing, feeds this information into the computer 8 for processing and analysis. Alternatively, the recorded information may be stored in data storage, such as a disk, tape or distributed database, for archival and subsequent transmission to the computer 8. This allows the computer 8 and recording device 6 to be location independent. Software installed on the computer 8 performs a statistical fit according to a known curve fitting algorithm, such as least squares fitting, to generate a non-symmetrical approximation curve of the circadian rhythm information gathered from the subject 4.

The computer 8 applies a curve fitting procedure to ambulatory blood pressure (ABP) recordings in order to determine the rate of change in systolic (SBP) and diastolic blood pressure (DBP) and heart rate (HR) from the day to night values separately from the night to day transition. The ABP recordings are fitted to a six parameter curve fitting equation. Two sigmoid equations ((1) and (2) below) are used as the basis for forming the curve fitting equation (3) below.

tracks the night to day transition part of the circadian rhythm, and

P2 y = ^{pι +} s 1 +. e _,'«„,,. (2) tracks the day to night transition, where:

PI is the day time rhythm plateau; P2 is the difference between the day and night plateau and the night plateau is therefore P1-P2; the rate of transition between these plateaus is controlled by the value of P3 and RJ for the day to night and night to day transition respectively and have units of 1 /hours; the parameters P4 and P6 give the centre location of the transition periods with P4 being the middle of the day to night transition and P6 the middle of the night to day transition; x is a sample time; and y is the approximation curve.

The maximum rate of change for each of these transitions is calculated as P2*P3/4 and P2*P5/4 for equations (1) and (2) respectively while an average rate of change (between inflection points) can be calculated as P2*P3/4.562 and R2*R5/4.562 for equations (1) and (2) respectively.

The combination of equations (1) and (2) give the following six parameter equation:

R2 R2

A v = Rl + ₁. ₊ . _g _P«3((P«4--xx) ^■ + ) + ^■ ₁ , ₊ . _e _-P5(P6-x) ( V3- )

To make the resulting curve quasiperiodic, four additional terms, related to changes in the preceding and the following days may be added to equation (3). A compensating parameter q is also added to the equation such that q — -2 when P4 is less than P6 (i.e., if the data began with the day to night transition) and q = -3 when P4 is greater than P6 (i.e., if the data began with the night to day transition). The quasiperiodic equation is as follows:

R2 P2 y = Pl + - ^■ + ^■ l _{+ e}"⁽«-*⁾ \ + _e ^{P5 P6}-^χ)

R2

+- R2

^■ + -

1 _{+ e}PH 4-*-24) J _{+ e}P5(P6-x-24)

(4)

R2 P2

+ 1 _{+ e}« T (T/T^>Γ4.-jr+24) + j _{+ e}P_(P6-x₊24)

+P2 * q 1 -

Initial estimates of the parameters may be made from a visual inspection of the data or from a simple sine wave fitting method as shown in equation (5) in order to reduce the number of iterations necessary under the least squares method to achieve the desired accuracy.

„ , . ,2 *πX . y = d + αsιn( + c) (5)

For determining the initial values of the six parameters of the non-symmetrical fit, the parameters a, b, c and d are obtained from the least squares fitted data according to equation (5). Thus, PI = a + d (where a is the peak amplitude of the sine wave relative to the mean and d is the mean of the sine wave); P2 = 2*a (twice the amplitude of the sine wave); P4 = 1.25*b - b*c/2*7T + 6 (where b is the time between peaks of the sine wave and c is a location parameter of the sine wave peak); P6 = P4 + b/2 (hours). Estimates for the slope coefficients P3 and P5 may be taken as -0.5 and 0.5 respectively.

Once the data is collected from the subject 4 by the recording device 6 and received by the computer 8, the computer 8 performs the analysis method as shown in Figures 2 and 3. The sample diastolic blood pressure measurements used to illustrate the method are shown in Table 1 below. The blood pressure measurements were taken at regular hourly or half hourly intervals. At step 105, the data is received and input. At step 110 a least squares fit of a standard sine wave equation (5) is performed as illustrated at step 115. The resulting four parameters from the sine wave fit at step 120 are used to calculate the initial parameters at step 125. The raw data in combination with the initial parameters are used to perform the least squares fitting of the nonsymmetrical approximation equation (3) (termed a double logistic equation in Figure 3 at step 130). From the least squares fitting, the final parameter estimates are calculated at step 135 and are used at step 140 to plot the resulting approximation curve as shown at step 145. Figure 4 shows sample plots for systolic blood pressure, mean BP and heart rate (next to the plot of diastolic pressure 145 as shown in Figure 2 and 3), together with the relevant parameter estimates. Table 1

Figure 5 makes a comparative illustration of the approximation curves produced by the present method (shown by the thick line) and the corresponding sine curves (shown by the thin line) for systolic arterial pressure (SAP), diastolic arterial pressure (DAP), mean arterial pressure (MAP) and heart rate (HR). Information as to the statistical fit of the respective curves to the data is also tabulated in Figure 5.

A significant advantage of the preferred method of analysis is that it can separately determine the slope of the decrease in blood pressure and heart rate when the subject goes to sleep from the increase in the same variables when the patient is waking up. Thus the method defines two plateaus (waking and sleeping) and the different rates of change from one to the other. Analysis of a large number of data files taken from the Alfred Baker Medical Unit Risk Evaluation Clinic (Melbourne, Australia) has uncovered a difference in the rate at which heart rate changes as the patient goes to sleep and when the patient arises in the morning. Data from over 200 patients have been analysed using the above-described curve fitting method and the fit has consistently been shown to be robust and to fit the data in a manner superior to the existing methods. It will be understood by persons skilled in the art that alterations and modifications may be made to some features of the described embodiments of the invention without departing from the spirit and scope of the invention.

Claims

THE CLAIMS:

1. A method of analysis of a circadian rhythm, including the steps of: receiving data indicative of the circadian rhythm; and performing a statistical fit of the data to provide a non-symmetrical approximation curve representative of the circadian rhythm.

2. The method of claim 1, further including the steps of, prior to said receiving, collecting the data indicative of the circadian rhythm and storing the data.

3. The method of claim 2, further including the step of communicating the stored data to a data receiving means.

4. The method of any one of claims 1 to 3, wherein said approximation curve includes a first transitional curve indicative of a transition of the circadian rhythm from a night-time level to a day-time level and a second transitional curve indicative of a transition of the circadian rhythm from a day-time level to a night-time level.

5. The method of claim 4, wherein said first transition curve has a negative slope and the second transitional curve has a positive slope different in magnitude to that of the negative slope.

6. The method of any one of claims 1 to 5, wherein the step of performing a statistical fit is performed using the following equation:

- n. ^{P1 P1}

I + _e ⁽P4-* I _{+ e} HP6-x)

where PI is a day-time plateau level of the circadian rhythm;

P2 is the difference between the day-time plateau and a night-time plateau; P3 is a rate of transition from the day to night plateaus; P4 is a centre location (in time) of a transition period from day to night;

P5 is a rate of transition from the night to day plateaus; P6 is a centre location (in time) of a transition period from night to day; x is a sample time; and y is an approximation curve generated from the statistical fit.

7. The method of any one of claims 1 to 6, further including the step of using the approximation curve to facilitate assessment of the likelihood of a cardiac event.

8. The method of any of the preceding claims, wherein said statistical fit is a least squares fit.

9. The method of claim 8, wherein said least squares fit uses an initial parameter set to reduce the number of iterations required by the least squares fit to achieve a desired curve approximation level.

10. The method of claim 9, wherein said initial parameter set is generated by performing a least squares fit of the data according to a sine curve model.

11. The method of any one of the preceding claims, wherein said circadian rhythm is a cardiovascular rhythm.

12. The method of claim 11, wherein said circadian rhythm is a human cardiovascular rhythm.

13. The method of any one of the preceding claims, wherein said circadian rhythm includes one of a diastolic blood pressure level, a systolic blood pressure level, a mean blood pressure level or a heart rate.

14. A system for analysing a circadian rhythm, including: means for receiving data indicative of the circadian rhythm; and means for performing a statistical fit of the data to provide a non-symmetrical approximation curve representative of the circadian rhythm.

15. The system of claim 14, further including means for collecting the data, the means for receiving being adapted to communicate with the means for collecting to receive the data therefrom.

16. The system of claim 15, wherein said means for collecting data is an ambulatory blood pressure monitor.

17. The system of claim 16, wherein said means for performing a statistical fit of the data is a computer configured to interface with the ambulatory blood pressure monitor.

18. The system of any one of claims 14 to 17, wherein said circadian rhythm is a cardiovascular rhythm.

19. The system of claim 18, wherein said circadian rhythm is a human cardiovascular rhythm.

20. The system of any one of claims 14 to 19, wherein said circadian rhythm includes one of a diastolic blood pressure level, a systolic blood pressure level, a mean blood pressure level or a heart rate.

21. Computer readable storage media or medium having stored thereon program code for causing a computer to execute the method of any one of claims 1 to 13.