WO2012138902A1

WO2012138902A1 - B0-based modulation of b1 excitation in mri

Info

Publication number: WO2012138902A1
Application number: PCT/US2012/032387
Authority: WO
Inventors: Jozef H. Duyn
Original assignee: The United States Of America As Represented By The Secretary, Department Of Health & Human Services
Priority date: 2011-04-08
Filing date: 2012-04-05
Publication date: 2012-10-11

Abstract

In high field MRI, RF flip angle inhomogeneity due to wavelength effects can lead to spatial variations in contrast and sensitivity. Systems and methods, disclosed herein relate to the use of non-linear B₀ shims to improve excitation flip angle uniformity in high field MRI. The disclosed system and methods can be used in conjunction with existing multi-dimension excitation methods, including those that use parallel excitation to improve contrast and sensitivity in gradient echo magnetic resonance imaging.

Description

Bo-BASED MODULATION OF Bl EXCITATION IN MRI

BACKGROUND

[0001] Magnetic resonance imaging (MRI) is an often used research and diagnostic tool. MRI typically involves exposing an object to be imaged to a static magnetic field (B₀ field) that aligns the nuclear spins of hydrogen atoms within the object. The object is also exposed to a radio frequency (RF) field (Bi field) transverse to the Bo field, at a resonance frequency known as the "Larmor frequency" that flips the nuclear spins by a predetermined angle. To collect and construct images of the object, a decay signal emitted by the flipped nuclear spins is collected and measured.

[0002] MRI systems and apparatuses that operate in the range of 1.5-3.0 T have generally been used in some hospitals and research institutes to acquire images. In order to acquire high resolution images, MRI systems and apparatuses operating with an ultra-high B₀ field of around 7.0T have been used. In MRI systems operating in the lower range and the higher range, imperfections in the Bi field can lead to undesired spatial variations in the signal to noise ratio (SNR) and contrast of the acquired image. The variations become increasingly apparent at higher Bo field strengths, where the wavelength of the Bi field are shortened, thus leading to increased spatial variations in the amplitude and phase of the Bi field. The Bi field imperfections are significant when imaging most of the human body using a B₀ field of around 3T and when imaging the human head with a Bo field of around 7T. At these levels for the Bo fields, the wavelengths of the RF pulses within the Bi fields approach and/or become smaller than the dimensions of the imaging target.

[0003] There is a trend to use higher-powered B₀ fields in order to improve the spatial resolution of MRI. However, as the strength of the Bo field increases, the wavelength of the Bi field decreases and its amplitude distribution within the object to be imaged becomes less homogeneous. Moreover, In addition, the B₀ field may have its own inhomogeneity, which further induces artifacts in the collected decay signal. The problem caused by induced artifacts is further heighted by increasing the strength of the Bo field.

[0004] A common response to the Bo field inhomogeneity issue described above includes the use of adiabatic excitation pulses that have reduced sensitivity of the excitation flip angle to Bi inhomogeneity. However, it is difficult to design such pulses to include spatial selectivity, which is generally required in MRI. In addition, adiabatic excitation pulses typically require a high level of RF radiation that may expose the subject to unacceptable levels of associated tissue heating. Conversely, limiting or reducing the power of the B field may still produce images with artifacts and/or reduced tissue contrast and resolution. Furthermore, when the power of the Bi field is limited, the inhomogeneity of the B₀ further reduces the ability to generate high-contrast and artifact- free images.

[0005] An alternative approach to overcome flip angle variations due to Bi field inhomogeneity is to design RF pulses that have a spatial selectivity to compensate for the Bi field imperfections. This can be accomplished only by manipulating the B₀ field with gradient coils or shim coils and applying a spectrally- selective (i.e. Bo-selective) RF pulse. In this approach, the precise shape of the Bo field is dictated by both the Bo field manipulation and the desired flip angle correction.

[0006] The methods described above attempt to correct generally non-linear spatial variations in the Bi field using only linear gradients of the Bo field, thereby requiring elaborate designs that resulted in a lengthy RF pulse length. Here we improve this situation by using both linear and non-linear spatial variations in the B₀ field

[0007] Improved Bi field homogeneity can be achieved through multi-dimensional excitation; however, long radio frequency pulse durations limit the practical applications of MRI. Therefore, it may be impractical and difficult to correct for Bi and Bo field inhomogeneity through manipulation of the Bi field alone.

SUMMARY

[0008] According to one aspect, a system is provided for correcting inhomogeneity of a B₀ field. The system includes a first coil to generate a B₀ field along a first axis during an MRI process. A second coil generates a radio frequency field along a second axis that is transverse to the first axis.

[0009] The system further includes a plurality of shim coils, each configured to generate an auxiliary B₀ field having a particular strength, that are used to correct inhomogeneity of the Bo field. The system further includes a database comprising static magnetization map data, the static magnetization map data corresponding to static magnetization (i.e., Bo field) measurements during the application of a predefined current to each of the individual shim coils.

[0010] The system further includes a processor to determine a desired B₀ field distribution required to generate a uniform, pre-defined effective flip angle of the at least two radio frequency pulses based on the radio frequency field map data and a duration, a shape, and an amplitude of the at least two radio frequency pulses. The processor determines the combination of static magnetic fields of the individual shim coils that optimally match the desired field distribution for the particular object. In another aspect, the processor calculates the fields that optimize the flip angle uniformity over the object. The processor also calculates a corresponding auxiliary magnetic field strength for each of the plurality of shims to correct the inhomogeneity in the B₀ field and determines a corresponding current level to apply to each of the a plurality of shim coils to achieve the corresponding auxiliary magnetic field strength. The system also includes a control system to supply the corresponding current level to each of the plurality of shim coils.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Fig. 1 depicts an exemplary MRI system for correcting inhomogeneity of a static magnetic field.

[0012] Figs. 2A-B depict Bi field shimming pulse sequences according to an embodiment of the present disclosure.

[0013] Fig. 3 A depicts the relationship between the effective flip angle and phase distribution according to an embodiment of the present disclosure.

[0014] Fig. 3B depicts the optimization of the effective flip angle (FA) at different combinations of pulse phases and individual flip angles according to an embodiment of the present disclosure.

[0015] Fig. 4 is a flowchart depicting an exemplary embodiment of B₀-based modulation, according to one embodiment of the present disclosure.

[0016] Fig. 5 depicts the application of shims x, z² and x²-y² during the image acquisition of an oil phantom, according to one embodiment of the present disclosure.

DETAILED DESCRIPTION

[0017] As previously described, one strategy to mitigate the imperfections of the radio frequency (RF) field (Bi field) is based on the notion that a uniform flip angle for the RF pulses in a sequence does not necessarily require a uniform Bi field. Therefore, RF pulses can be designed to be spatial selective in multiple spatial dimensions such that the pulses have an in- plane spatial selectivity that compensates for the inhomogeneities of the field. While the use of a spatially selective pulse provides flip angle uniformity, it also requires a prohibitively lengthy pulse duration that may result in significant sensitivity to off-resonance effects. The present disclosure relates to a system and method to shorten the required duration of a multidimensional selective RF pulse by the use of static magnetic field (Bo field) shim coils. In particular, the system uses both linear and non-linear spatial variations in the Bo field to correcting inhomogeneity of a B₀ field .

[0018] Figure 1 depicts an exemplary MRI system 100 for correcting inhomogeneity of a Bo field. The MRI system 100 includes, for example, a MRI scanner device ("MRI device") 102 that enables the visualization of organs, organ function, and/or other tissue within a body of a subject, such as a patient. The MRI device 102 includes a primary magnet or coil 104 that generates a uniform magnetic field that is applied across the body of the subject under observation.

[0019] After the subject is properly positioned for analysis by the MRI device 102, a body or RF coil 106 of the MRI device 102 emits a RF pulse signal. The RF pulse signal causes the nuclei within the body of the subject to transition their spin orientation, or precess. The frequency of the energy at which this transition occurs is known as the Larmor Frequency.

When the RF coil 106 is not providing the RF radiation field, the hydrogen nuclei hydrogen atoms transition back to a lower energy state and reemits the electromagnetic energy at the RF wavelength.

[0020] The MRI system 100 also includes gradient coils or magnets 107 that allow the magnetic field Bo to be altered very precisely. The gradient magnetic fields generated by the gradient magnets allow image "slices" of the body to be created. By altering the gradient magnetic fields, the magnetic field can be specifically encoded on a selected part of the body. In addition, multiple shim coils 108 each apply an auxiliary magnetic field having a particular strength.

[0021] The MRI system 100 further includes a control system 109 for controlling the auxiliary magnetic field strength of each shim coil 108. The control system 109 includes a database 110 that stores static magnetization map data 112. According to one aspect, the static magnetization map data corresponds to static magnetization (i.e., Bo field) measurements that have been previously collected along a first axis during the application of at least one test pulse generated by the RF coil 106.

[0022] By way of example and not limitation, the B₀ field measurements may be obtained by measuring at least two gradient gradient echo signals generated in response to the test pulse. The phase difference between the echo signals may be used to calculate the frequency of the gradient echo signals, which in turn may be used to determine the magnetic strength at various locations of the B₀ field. In other examples, other methods of determining the B₀ field strength to generate the static magnetization map data 112 may be used.

[0023] A measurement system 1 12 is used to collect Bi map data for a particular object. The Bi map data corresponds to the amplitude of RF measurements taken along the second axis. In one aspect, one or more test pulses may be generated along the second axis. The test pulse and the acquired signal are used to determine the amplitude of the radio frequency field. In one example, a single RF pulses is generated to acquire two or more measurements from which the amplitude of the Bi field may be determined. In other examples, other methods of determining the Bi field strength may be used.

[0024] The MRI system 100 includes a processor 114 that calculates an effective flip angle of the at least two radio frequency pulses based on the radio frequency field map data and a duration, a shape, and an amplitude of the at least two radio frequency pulses. The processor 114 also calculates a radio frequency phase distribution for the particular object as a function of the determined effective flip angle.

[0025] The processor 114 further calculates a corresponding auxiliary magnetic field strength for each of the plurality of shims 108 to correct the inhomogeneity in the Bo field based on the radio frequency phase distribution and determines a corresponding current level to apply to each of the a plurality of shim coils to achieve the corresponding auxiliary magnetic field strength. The control system 109 supplies the corresponding current level to each of the plurality of shim coils.

[0026] By way of example, and not limitation, the method may be described with reference to a Bi field shimming pulse sequence 200 as shown in Figure 2A. The pulse sequence 100 includes a dual pulse slice- selective RF excitation 202 having a slice-selecting gradient of the Bo field indicated generally by 204. [0027] The dual RF pulses 202 excite the same slice (not shown) of the subject or object being imaged. The spins of the hydrogen atoms of the selected slice experience a combined effective flip angle that is dependent on the individual flip angles CLi and a ₂, as well as the accumulated phase (φ) 206 between the pulses. The time between each pulse in the pulse sequence 202 is represented by (ΔΤ) 208.

[0028] Similarly, Figure IB depicts an alternate Bi field shimming pulse sequence 210 with reduced pulse spacing 202. In this pulse sequence 210, ΔΤ 208 between the pulses is minimized by inverting the polarity of the slice-selection gradient 204 of the Bo field.

[0029] In each sequence 200 and 210, an in-slice position-dependent phase accumulation is indicated by the trapezoidal shim pulse (S) 212 in the B₀ field. The shim pulse 212 represents a temporary spatially-dependent frequency- shift produced by a combination of the transmitter frequency shift ΔΒο, χ-, y-, and z- gradients of x-, y-, and z-, and other higher order shims. The shim pulse 212 is produced during the time (ΔΤ) 208 between each pulse in the pulse sequences 200 and 210.

[0030] For purposes of illustration only, The effective flip angle (FA) induced by the pulse sequences 200 and 210 can be calculated by:

1 - sin 6tr(cos ^+ l) where d = (X ₂ = (X, and a and φ are dependent on spatial location r.

[0031] Figure 3A is a graph 300 showing the relationship between the effective flip angle and the phase 106 between pulses 202. As shown, when the phase 106 (φ) = 0, the effective flip angle of the excitation becomes 2a, or equal to the sum of the individual flip angles. Conversely, when the phase (φ) is non-zero, the effective flip angle is reduced. As shown, The fractional reduction in the effective flip angle with increasing φ appears to be proportional for various flip angles a, until a approaches 90°. Thus, Figure 2A illustrates the dependence of the effective flip angle on φ at selected values of a as determined using the Bloch- Siegert method as represented in Equation (1). The effective flip angle of the 2-pulse excitation reduces with increasing φ; therefore, the relationship between effective flip angle and φ is dependent on a. As a approaches and equals 90°, the effective flip angle becomes inversely proportional to φ.

[0032] According to another aspect, the flip angle a is proportional to the spatial variation of the Bi field according to:

a(r) = \ c(t)B_lt (r)dt = CB_lt (r) (2) where the integral runs over the sub-pulse duration, C represents the modulation amplitude (i.e. voltage) of the pulse and incorporates the gyromagnetic ratio, and B_lt represents the amplitude of the transmitted Bi field per unit voltage.

[0033] In one aspect, the method of the present disclosure includes generating a spatial distribution cp(r) that counteracts the effects of a(r) on the effective flip angle such that the effective flip angle is constant over space. To achieve this a target phase at the location r ((p_target (r) is generated according to: l + cos 2or(r) - 2cos ¾

target (O = iJICCOS (3)

l - cos2ar(r)

[0034] Figure 3B is a graph 302 illustrating that the optimization of the effective flip angle can be determined at different combinations of pulse phases and individual flip angles when plotted as φ vs. a. As shown, the lowest transmitted radio frequency power required for optimizing the effective flip angle corresponds to a phase of 0 for the individual flip angle. Furthermore, for low φ and effective flip angle values, relatively large changes in the phase φ are needed to compensate for changes in a.

[0035] In one aspect, the method includes optimizing the currents to the shim coils to correct the inhomogeneity of the Bo field. The shim optimization is represented by c _shi_m (r) that approximates (p_target(r) as provided in Equation (3). c _shi_m (r) is determined by applying current pulses (Si) at a time (t) to a number individual shim coils (n) indexed by "i" according to:

shim (4) where the time integral runs over a period of time (ΔΤ). The current applied to the shim coils can be optimized by minimizing the root mean square difference between cp_shim(r) and (ptarget(r) of Equation (2) based on a multi-linear regression using the field associated with each shim coil as independent variables or regressors.

[0036] In one aspect, knowledge of the field generated by each shim coil is obtained from shim coil calibration scans. In example, knowledge of the field generated by each shim may be obtained during the initial set-up of the MRI system. In another example, knowledge of the field generated by each shim may be obtained during calibration scans performed prior to scanning the desired object.

[0037] Figure 4 illustrates an exemplary method of modulation of the B field using Bo-based shimming according to one aspect of the present disclosure. By way of example and not limitation, the method will be described with reference to image acquisitions and scans of one or more phantoms and a human brain using a 7T Siemens^® whole body scanner employing an Agilent Technologies^® shielded-magnet design.

[0038] In this example, the scanner system used five second-order shims having functional shim terms of z 2 , zx, zy, xy, x 2 -y 2 with a maximum strength of 1.6 kHz/cm 2. In one aspect, a continuous current was supplied to the second-order shims. In another aspect, current was provided to the second-order shims intermittently, as necessary.

[0039] In one aspect, the scanner system also includes zero-order shim term and one or more linear gradient coils for the B₀ field, for example, to effectively achieve at least 9 degrees of shimming for the Bo field. Therefore, the number of individual shim coils (n) used to determine flip angle optimization according to Equation (3) is nine. In one example, the zero- order shim term is effectuated through phase adjustments of the RF pulses. In another example, the zero-order shim term is effectuated through a frequency shift by a RF synthesizer. Other examples exist. In various other aspects, other scanners, shims, and/or shim terms may be used.

[0040] In one aspect, the method 400 includes calibrating each of the individual shim terms at 402, based on applying a known current (S) applied to the individual shims. In this aspect, the calibration of each shim coil includes acquiring a B₀ field map during the application of S, as shown in FIGS 2A-B. Similar to the determination of the static magnetization map data 112, the calibration of the individual shims includes determining the phase difference between two gradient echo signals to determine the frequency and shimmed Bo field strength. [0041] The calibration may be performed on a phantom. In one aspect, the phantom has a low dielectric constant. For example, the phantom may include silicon oil. By way of example and not limitation, the B₀ field maps may be acquired by applying a gradient echo pulse sequence where the two echo pulses are separated by a time interval ΔΤ. In one example, the time interval may be 2 ms. In one aspect, the known current pulse (S) is applied during the time interval ΔΤ.

[0042] At 404, shim calibration frequency maps are generated for each shim term. In one aspect, the phase for each gradient echo signal generated at 402 are subtracted from each other to determine a frequency, that is then divided by their time interval to generate the calibrated shim Bo field map. For each shim term, the Bo field maps are acquired at two different shim current amplitudes, 406. For example, the shim current amplitudes may be at half of a maximum current and its inverse (max/2 and -max/2) or at half of the maximum current and zero (max/2 and 0). The shim calibration, in terms of a generated frequency shift per unit current, is obtained by dividing the difference between the Bo field maps by the difference in the shim currents. According to other aspects, the operations at 402, 404, and 406 are performed simultaneously.

[0043] For each object to be scanned, B field frequency maps are used at 408 to determine the flip angle at a location (a(r)) as described by Equation (2). In one aspect, the B frequency maps are determined using the Bloch-Siegert method, based upon an 8 ms irradiation pulse at a frequency of 4 kHz and 2 shifts at +8 kHz and -8 kHz respectively.

[0044] The B field mapping can then be used to obtain an object- specific frequency map (Bl(r)). The object- specific frequency map (Bl(r)) may then be used to determine a(r) by multiplying the object- specific frequency map by a factor C. C is determined from the duration, shape, and amplitude of the gradient echo pulse sequence applied at 402.

[0045] At 410, the target phase distribution (cptarget (r)) is determined using Equation (3) that is based in part upon the (r), determined at 408. In one aspect, the target phase distribution (cptarget (r)) includes a correction for imperfections in the background field Bo. In this aspect, the correction is derived from the spatially-varied magnetic susceptibility of the object being scanned, which causes additional phase accumulation in the object (cpobject(r)).

Therefore, in this aspect, it is preferred that cpobjectO^") is subtracted from ( _target (r) provide by Equation (3) prior to calculating the calibrated shim strengths. [0046] According to one aspect, multi-linear regression is used to determine the desired shim strengths at 412. In one example, the shim calibration frequency maps generated at 404 are converted to phase shifts (cpshim) by multiplying the time integral of the modulation pulse (S) amplitude, applied at 402, over the time integral ΔΤ. In another example, the desired effective flip angle may be used to determine the current that is to be applied to the individual shims. In other aspect, other methods to calculate and determined the desired shim strength may be used.

[0047] In various other aspects, determining the shim strengths requires a particular RF sub-pulse amplitude as this determines the phase accumulation (cp_smm) that is needed to induce the desired effective flip angle. In one aspect, the minimum RF sub-pulse amplitude is the value for which (r_Bmin) = FA/2 and c _shi_m(rBmin) = 0, where r_Bmi_n represents the spatial location where the strength of the B field is minimal. Due to the non-linear nature of Equation (2), greater values of (r_Bmi_n) require varied shim distributions. Therefore, it is preferred to optimize the uniformity of the effective flip angle over a range of RF sub-pulse amplitudes and select the sub-pulse amplitude that induces the greatest uniformity in the effective flip angle. In another aspect, it is preferred that the minimal sensitivity to changes in or temporal variations to the (pobject(r) distribution.

[0048] At 414, the Bo field is modulated by activation of the optimized and calibrated shims to reduce inhomogeneity of the Bo field. In one aspect, the optimized shims are applied only during the sub-pulse interval (ΔΤ). In other aspects, the optimized shims may be applied continuously. Continuous application of the shims may be necessary when the switching speed of the shim hardware is limited.

[0049] Fig. 5 depicts the application of shims x, z² and x²-y² during an image acquisition sequence 500 of an oil phantom. The acquired images 502-512 demonstrate the flexibility of the proposed method in manipulating the effective flip angle within an axial slice selected in a phantom. In one aspect, linear, circular, and ellipsoidal flip angle distributions were generated by applying the x gradient, the z 2 shim, and a combination of the z 2 and x 2 -y 2 shims, respectively. As shown, strong spatial variations can be generated with each of these cp_shim(r) distributions. [0050] The images were acquired using a two-pulse excitation along with continued application of shim terms. The variations in intensity reflect the effective flip angle, as both the RF transmission fields and receiver fields were uniform.

[0051] There is some flexibility in optimization of the effective flip angle with respect to the choice of ( _shim(rBmin)- This choice affects both the amount of RF power required for the excitation, as well as the sensitivity to temporal variations in resonance frequency or spatial variations related to magnetic susceptibility effects. Choice of ( _shim(rBmin) can be left up to the optimization process by inclusion of a B₀ map and possibly also including a cost terms for required RF power and sensitivity to temporal variations in resonance frequency.

[0052] Another consideration for the optimization is the choice of inter-pulse spacing D. Choosing too large of a value for D may result in a range of susceptibility-induced phase accumulation over the object that exceeds 2π. Shorter spacing values of D reduces sensitivity to T₂* decay and off resonance, but increases the required shim strength, gradient switching rates, and may require shorter sub-pulse durations. The latter increases RF peak power and overall power deposition. The 2 ms spacing used above was limited by gradient slew rate. By way of example, and not limitation, the minimal inter-pulse spacing for slice thickness selection during a dual-pulse sequence as shown in FIGS. 2A-B ranges from about 1.0 ms for 5mm slices to about 2.3ms for 1mm slices.

[0053] Good effective flip angle uniformity may also be achieved without the use of higher order shim terms, either by extending the pulse length through the addition of one or more RF sub-pulses (spokes), or through the addition of independent RF channels. By way of example and not limitation, two- spoke designs that make use of independent RF channels have been shown to provide good effective flip angle uniformity in a human brain at 7T. The results suggest that this performance may be achieved without the need for independent radio frequency channels. In addition, the level of performance may be increased by combining the two methods. In another aspect, this method may relax the requirements for transmit coil uniformity, and therefore lessen the burden on coil design.

[0054] Although the experiments described here were performed on a single axial slice, in various aspects, the methods described herein are extendable to multi-slice imaging with oblique orientations. Extending the image acquisition to multi-slice two dimensional images will require switching of the higher order shims. In one aspect, this is accomplished by a manipulation of the pulse S, as shown in Figure 1. In another aspect, the pulse S may be extended over the time interval between the radio frequency sub-pulses. In various other aspects, the pulse S may extend across and/or beyond the radio-frequency sub-pulses.

[0055] In various other aspects, shim hardware capable of millisecond- scale switching times may be used for dynamic shimming applications. The methods disclosed herein, may also be used in three dimensional scanning. In one aspect, additional second order shims (e.g. five additional shims, in addition), and possibly additional higher order shims are used. Due in part to the spherical symmetry of shim terms generated with many shim designs, the methods disclosed herein may also be used for acquiring oblique slices.

[0056] Those skilled in the art will appreciate that variations from the specific embodiments disclosed above are contemplated by the invention. The invention should not be restricted to the above embodiments, but should be measured by the following claims.

Claims

CLAIMS In the claims:

1. A system for correcting inhomogeneity of a static magnetic field:

a first coil to generate a static magnetic field along a first axis during a magnetic resonance

imaging (MRI) process;

a second coil to generate a radio frequency field along a second axis, the second axis being

transverse to the first axis;

a database comprising static magnetization map data, the static magnetization map data

corresponding to static magnetization measurements along the first axis during application of at least two radio frequency pulses generated by the second coil;

a plurality of shim coils each configured to generate an auxiliary magnetic field having a

particular strength, the auxiliary magnetic fields to correct inhomogeneity of the static magnetic field;

a measurement system to collect radio frequency field map data for a particular object, the radio frequency field map data corresponding to radio frequency measurements along the second axis and based on a phase difference and a time difference between the at least two radio frequency pulses; and

a processor to:

determine an effective flip angle of the at least two radio frequency pulses based on the radio frequency field map data and a duration, a shape, and an amplitude of the at least two radio frequency pulses;

determine a radio frequency phase distribution for the particular object as a function of the determined effective flip angle;

calculate a corresponding auxiliary magnetic field strength for each of the plurality of shims coils to correct the inhomogeneity in the static magnetic field based on the radio frequency phase distribution;

determine a corresponding current level to apply to each of the plurality of shim coils to achieve the corresponding auxiliary magnetic field strength; and supply the corresponding current level to each of the plurality of shim coils

2. The system of claim 1 wherein the static magnetization measurements comprise static magnetic field strength measurements, .wherein the static magnetic field strength measurements are obtained by:

measuring at least two gradient echo signals generated in response to the at least two radio frequency pulses generated by the second coil;

calculating another phase difference between the echo signals to determine a particular frequency of each of the at least two gradient echo signals; and

determining the static magnetic field strength measurements at various locations of the static magnetic field along based on the particular frequency of each of the at least two gradient echo signals .

3. The system of claim 1 wherein the second coil generates a shimming pulse sequence, the shimming pulse sequence comprising dual pulse slice-selective radio frequency excitation having a slice- selecting gradient of the static magnetic field.

4. The system of claim 1 wherein the radio frequency measurements comprise one or more amplitudes of radio frequency measurements taken along the second axis in response the at least two radio frequency pulses.

5. The system of claim 1 wherein the particular strength of a corresponding auxiliary magnetic field of each of plurality of shim coils is calculated by applying a predetermined current to each of plurality of shim coils.

6. The system of claim 1 wherein the processor determines the effective flip angle of each of the at least two radio frequency pulses by executing the following algorithm:

1 - sin or(cos ^+ l) where a is an individual flip angle and φ is an accumulated phase that are each dependent on a corresponding spatial location.

7. The system of claim 1 wherein the processor determines the individual flip angle by executing the following algorithm: a{r) = \ c{t)B_lt{r)dt = CB_lt{r) ) wherein C represents the modulation amplitude of each of the at least two radio frequency pulses and incorporates a gyromagnetic ratio, and B_lt represents an amplitude of the transmitted a radio frequency field per unit voltage.

8. The system of claim 7 wherein the processor determines the radio frequency phase distribution for the particular object by executing the following algorithm: l + cos2ar(r) - 2cos ¾

W_tW = arccos

l -cos2ar(r)

9. A method for correcting inhomogeneity of a static magnetic field comprising: generating a static magnetic field along a first axis at a first coil during a magnetic resonance imaging (MRI) process;

generating a radio frequency field along a second axis at a second coil, the second axis being transverse to the first axis;

comprising retrieving static magnetization map data from a database , the static magnetization map data corresponding to static magnetization measurements along the first axis during application of at least two radio frequency pulses generated by the second coil;

generating an auxiliary magnetic field having a particular strength at each of a plurality of shim coils , the auxiliary magnetic fields correcting inhomogeneity of the static magnetic field;

collecting radio frequency field map data for a particular object at a measurement system, the radio frequency field map data corresponding to radio frequency measurements along the second axis and based on a phase difference and a time difference between the at least two radio frequency pulses;

determining, at a processor, an effective flip angle of the at least two radio frequency pulses based on the radio frequency field map data and a duration, a shape, and an amplitude of the at least two radio frequency pulses; determining, at the processor, a radio frequency phase distribution for the particular object as a function of the determined effective flip angle;

calculating, at the processor, a corresponding auxiliary magnetic field strength for each of the plurality of shims coils to correct the inhomogeneity in the static magnetic field based on the radio frequency phase distribution; and

determining, at the processor, a corresponding current level to apply to each of the plurality of shim coils to achieve the corresponding auxiliary magnetic field strength; and supplying the corresponding current level from a control system to each of the plurality of shim coils

10. The method of claim 9 wherein the static magnetization measurements comprise static magnetic field strength measurements, and wherein the method further comprises obtaining static magnetic field strength measurements by:

11. The method of claim 9 wherein generating the radio frequency field comprises generating a shimming pulse sequence at the second coil, the shimming pulse sequence comprising dual pulse slice- selective radio frequency excitation having a slice-selecting gradient of the static magnetic field.

12. The method of claim 9 wherein the radio frequency measurements retrieved from the database comprise one or more amplitudes of radio frequency measurements previously collected along the second axis in response the at least two radio frequency pulses.

13. The method of claim 9 wherein the particular strength of a corresponding auxiliary magnetic field of each of plurality of shim coils is calculated by applying a predetermined current to each of plurality of shim coils.

14. The system of claim 9 wherein determining the effective flip angle of each of the at least two radio frequency pulses comprises executing at the processor the following algorithm:

15. The method of claim 15 wherein determining the individual flip angle comprises executing at the processor the following algorithm: a{r) = \ c{t)B_lt {r)dt = CB_lt {r) ) wherein C represents the modulation amplitude of each of the at least two radio frequency pulses and incorporates a gyromagnetic ratio, and B_lt represents an amplitude of the transmitted a radio frequency field per unit voltage.

16. The method of claim 15 wherein the determining the radio frequency phase distribution for the particular object comprises executing at the processor the following algorithm:

l -cos2ar(r)

17. A magnetic resonance imaging system for correcting inhomogeneity of a static magnetic field:

a magnetic resonance imaging device comprising:

a primary coil to generate a static magnetic field along a first axis during a magnetic resonance imaging (MRI) process; a radio frequency coil to generate a radio frequency field along a second axis, the second axis being transverse to the first axis;

a database comprising static magnetization map data, the static magnetization map data corresponding to static magnetization measurements along the first axis during application of at least two radio frequency pulses generated by the second coil; and

a plurality of shim coils each configured to generate an auxiliary magnetic field having a particular strength, the auxiliary magnetic fields to correct inhomogeneity of the static magnetic field;

a control system comprising at least one processor to:

collect radio frequency field map data for a particular object, the radio frequency field map data corresponding to radio frequency measurements along the second axis and based on a phase difference and a time difference between the at least two radio frequency pulses;

determine a corresponding current level to apply to each of the plurality of shim coils to achieve the corresponding auxiliary magnetic field strength; and supply the corresponding current level to each of the plurality of shim coils.

18. The magnetic resonance imaging system of claim 17 wherein the at least one processor determines the effective flip angle of each of the at least two radio frequency pulses by executing the following algorithm: FA =

19. The magnetic resonance imaging system of claim 18 wherein the at least one processor determines the individual flip angle by executing the following algorithm: a{r) = \ c{t)B_lt {r)dt = CB_lt {r) ) wherein C represents the modulation amplitude of each of the at least two radio frequency pulses and incorporates a gyromagnetic ratio, and B_lt represents an amplitude of the transmitted a radio frequency field per unit voltage.

20. The magnetic resonance imaging system of claim 19 wherein the at least one processor determines the radio frequency phase distribution for the particular object by executing the following algorithm: l + cos2ar(r) - 2cos ¾

t (>") = arccos

l - cos2ar(r)