Systems and methods for calibrating asymmetric gradient adjoint field correction parameters

Abstract

The present invention is entitled "System and Method for Calibrating Asymmetric Gradient Companion Field Correction Parameters." A method for correcting for companion gradient field effects in a magnetic resonance imaging (MRI) system includes determining a plurality of first phase difference measurements between two acquisitions using a plurality of first bipolar gradient waveforms applied to a first gradient coil. A first gradient coil constant is determined based on the plurality of first phase difference measurements, and a compensation gradient waveform is determined based on the first gradient coil constant. The compensation gradient waveform is applied to the gradient coil along with a target gradient waveform to compensate for the companion gradient field.

Description

Technical Field

[0001] The field of the present disclosure relates generally to systems and methods for magnetic resonance imaging (MRI), and more particularly, to systems and methods for calibrating asymmetric gradient adjoint field correction parameters in MRI. Background Art

[0002] MRI has proven useful in the diagnosis of many diseases. MRI provides detailed images of soft tissue, abnormal tissue (such as tumors), and other structures that cannot be easily imaged by other imaging modalities such as computed tomography (CT). In addition, MRI operates without exposing the patient to the ionizing radiation experienced in modalities such as CT and X-rays.

[0003] In an MRI system, a large magnet generates a very strong magnetic field on the patient's body. The magnetic field generated by the large magnet is very uniform, or homogeneous. Gradient coils in the MRI system generate gradients that distort this uniform magnetic field. Typically, the gradients cause the strength of the magnetic field to vary from one point to another within the patient's body.

[0004] In some MRI systems, high gradient amplitude coils are used to achieve higher image quality or when good spatial resolution is required. High gradient amplitude coils are capable of generating magnetic gradient fields up to 400 mT / m and / or may have a coil efficiency of η = 0.13-0.32 mT / m / A. This compares to the coil efficiency of conventional gradient coils of η = 0.08-0.10 mT / m / A. An example of such a gradient coil is a 300 mT / m maximum gradient amplitude (G max ) of the connection group gradient, with G max =80mT / m compact 3T MRI system and G max =MAGNUS (for microstructural anatomical gradients using ultrafast scanning neuroimaging) with a gradient of 200-400 mT / m, depending on the maximum current output of the gradient driver. Compact 3T and MAGNUS gradient coils are asymmetric gradient coils for smaller head sizes. Therefore, the maximum gradient fields generated by high-gradient coils far exceed those of conventional gradient coils. This presents a daunting systems engineering challenge, as gradient coils and the associated gradient field correction depend on accurate and proper calibration of the gradient coil parameters. Gradient field correction must compensate for the nonlinearity in the gradient field strength, which worsens with distance from the magnetic field isocenter.

[0005] Therefore, there is a need for an improved magnetic resonance imaging system and method. Summary of the Invention

[0006] According to an embodiment of the present technology, a method for correcting for the effects of a companion gradient in a magnetic resonance imaging (MRI) system is provided. The method comprises determining a plurality of first phase difference measurements between two acquisitions using a plurality of first bipolar gradient waveforms applied to a first gradient coil axis or direction. A first gradient coil axis constant is determined based on the plurality of first phase difference measurements. Using the determined first gradient coil (axis) constant, a compensation gradient waveform associated with the gradient coil axis is determined. Finally, a compensation gradient waveform is applied along with a target gradient waveform to compensate for the companion gradient field. The compensation waveform may also be applied to other gradient axes in addition to the first gradient coil axis.

[0007] According to another embodiment of the present technology, a method for correcting for concomitant gradient effects in an MRI system is provided. The method includes determining a plurality of first phase difference measurements between two acquisitions using a plurality of first bipolar gradient waveforms applied to a first gradient coil (axis). The method further includes determining a plurality of second phase difference measurements between the two acquisitions using a plurality of second bipolar gradient waveforms applied to a second gradient coil (axis). A first gradient coil constant and a second gradient coil constant are determined based on the plurality of first phase difference measurements and the plurality of second phase difference measurements, respectively. The method further includes determining a compensation gradient waveform based on the first gradient coil constant and the second gradient coil constant, and applying the compensation gradient waveform along with the target gradient waveform to compensate for the concomitant gradient field.

[0008] According to another embodiment of the present disclosure, an MRI system is provided. The MRI system includes: a magnet configured to generate a polarizing magnetic field around at least a portion of a subject disposed in the MRI system; and a gradient coil assembly including a plurality of gradient coils configured to apply at least one gradient field to the polarizing magnetic field. The MRI system further includes: a radio frequency (RF) system configured to apply an RF field to the subject and receive magnetic resonance signals from the subject; and a processing system. The processing system is programmed to determine a plurality of phase difference measurements between two acquisitions using a plurality of bipolar gradient waveforms applied to at least one gradient coil of the plurality of gradient coils. The processing system is also programmed to determine at least one gradient coil constant based on the plurality of phase difference measurements, and to determine a compensating gradient waveform based on the at least one gradient coil constant. The processing system is further programmed to apply the compensating gradient waveform to the plurality of gradient coils to compensate for the accompanying gradient field. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] These and other features, aspects, and advantages of the present invention will be better understood when the following detailed description is read with reference to the accompanying drawings, in which like characters represent like parts throughout, and in which:

[0010] Figure 1is a vector graph of the gradient field computed according to aspects of the present method;

[0011] Figure 2 is a schematic diagram of an exemplary MRI system according to aspects of the present method;

[0012] Figure 3 is a graphical plot of a typical bipolar phase contrast flow encoding the imaging waveform for phase contrast MRI;

[0013] Figure 4 is another graphical plot of a bipolar phase contrast imaging gradient waveform with an associated zeroth-order companion gradient field in accordance with an embodiment of the present technology;

[0014] Figure 5 is a graphical plot of a single-sided bipolar gradient encoding type imaging waveform with an associated zero-order companion gradient field in accordance with an embodiment of the present technology;

[0015] Figure 6 is a graphical plot of bipolar gradient pulse patterns of different polarities according to an embodiment of the present technology;

[0016] Figure 7 is a graphical plot of measured phase error for phase difference acquisition according to an embodiment of the present technology;

[0017] Figure 8 is a graphical graph of experimental results according to an embodiment of the present technology;

[0018] Figure 9 is a graphical plot of residual error in phase error as a function of the value of an offset constant for the x-gradient axis in accordance with an embodiment of the present technology;

[0019] Figure 10A and Figure 10B is a graphical plot of a desired or applied gradient waveform used with a compensation field to reduce first-order adjoint gradient field effects according to an embodiment of the present technology;

[0020] Figure 11 is a schematic diagram of a system for correcting a gradient waveform according to an embodiment of the present technology;

[0021] Figure 12 is a schematic diagram of a system for correcting a gradient waveform according to an embodiment of the present technology; and

[0022] Figure 13 is a flow chart depicting a method for correcting for incidental gradient effects in an MRI system in accordance with an embodiment of the present technology. DETAILED DESCRIPTION

[0023] One or more specific embodiments will be described below. In order to provide a concise description of these embodiments, not all features of an actual implementation may be described in the specification. It should be understood that in the development of any such actual implementation, as in any engineering or design project, many implementation-specific decisions must be made to achieve the developer's specific goals, such as complying with system-related and business-related constraints that may vary from implementation to implementation. Furthermore, it should be understood that such development efforts may be complex and time-consuming, but remain a routine task of design, fabrication, and manufacturing for those of ordinary skill having the benefit of this disclosure.

[0024] When introducing elements of various embodiments of the present embodiment, the articles "a," "an," "the," and "said" are intended to mean that there are one or more of these elements. The terms "comprising," "including," and "having" are intended to be inclusive and mean that additional elements may be present in addition to the listed elements. Furthermore, any numerical examples in the following discussion are intended to be non-limiting, and thus the additional numerical values, ranges, and percentages are within the scope of the disclosed embodiments. Furthermore, the terms "circuit," "circuitry," and "controller" may include a single component or multiple components that are active and / or passive and are connected or otherwise coupled together to provide the described functionality.

[0025] In magnetic resonance imaging (MRI), a subject is placed in a magnet. When the subject is in the magnetic field generated by the magnet, the magnetic moments of nuclei (such as protons) attempt to align with the magnetic field, but precess in a random order around the magnetic field at the nucleus' Larmor frequency. The magnetic field of the magnet is called B0 and extends in the longitudinal or z-direction. During the acquisition of MR images, a magnetic field in the xy plane close to the Larmor frequency (called the excitation field B1) is generated by a radio frequency (RF) coil and can be used to align the net magnetic moment M of the nuclei. z Rotation or "tilt" from the z direction toward the lateral or xy plane. After the excitation signal B1 ends, the nucleus emits a signal, which is called an MR signal. In order to use the MR signal to generate an image of the object, a magnetic field gradient pulse (G x , G y and G z Gradient pulses are used to scan through k-space, the space of spatial frequencies or distances. A Fourier relationship exists between the acquired MR signals and the image of the object, so an image of the object can be derived by reconstructing the MR signals.

[0026] In MRI, the effects of the companion gradient fields become more pronounced when the gradient fields are applied at higher amplitudes. The companion fields are the result of the applied linear gradient field, with additional fields that nominally vary only in the z-direction, or in the direction of the main static magnetic field, and have nonlinear spatial variations in the x-direction or y-direction. These companion fields are a direct consequence of the need to satisfy Maxwell's equations, which determine the absence of magnetic monopoles. Or field As a current source in the z direction, a pure linear x or y or z gradient is applied (i.e. or The off-axis gradient field is established as a result of are the unit vectors in the x, y and z directions respectively. For example, a pure linear x gradient field G is applied to a symmetric gradient coil. x ,turn out

[0027]

[0028] That is, an additional field that varies spatially along the z direction, and where is the main static magnetic field. Similarly, for a pure linear z gradient field G z ,turn out

[0029]

[0030] where ∝ is the symmetry parameter and describes the relationship along the x-axis and y-axis to the applied G z The resulting field strength of the gradient field. For a typical MRI gradient coil with cylindrical symmetry, ∝ = 0.5. In short, satisfying Maxwell's equations results in the creation of an additional companion field that distorts the primary applied field. This additional field generates a nonlinear, spatially varying field that contributes to phase errors or spatial offsets in MRI applications ranging from echo planar imaging (EPI) to phase contrast flow imaging and quantitative diffusion.

[0031] Figure 1 A vector diagram 100 for calculating the additional adjoint gradient field is shown. The vector diagram 100 shows the main magnetic field vector B0 along the z direction. The vector diagram 100 also shows the desired gradient field vector along the z direction It is the result of applying a pure linear x or y or z gradient field along the z direction. As previously mentioned, the application of a pure linear gradient field creates a vector diagram 100 consisting of a vector adjoint field B c Furthermore, as shown in the vector diagram 100, the accompanying field vector B c The amplitude is That is, the magnitude of the magnetic field that deviates from the z-axis. The added adjoint field vector B c and the main magnetic field vector B0 and the desired gradient field vector Generates a total magnetic field vector Therefore, the total magnetic field vector The amplitude of is greater than the expected magnetic field amplitude, that is,

[0032] It should be noted that for both symmetric and asymmetric gradient coils, additional companion gradient fields are generated. In symmetric coils, the magnetic and physical isocenters are configured to be arranged in a common plane, such as the patient's eye or the patient's heart. On the other hand, asymmetric gradient coils are asymmetric with respect to the z-direction, and therefore, their magnetic and physical isocenters are not arranged in a common plane. It has been noted that asymmetric gradient coil designs produce additional zero-order and first-order companion gradient fields compared to symmetric gradient coils that have a large number of second-order terms. The invention described herein relates to the calibration of asymmetric gradient coils after installation, because the correction factors depend on parameters specific to the gradient coil installation. In particular, the invention described allows the correction factors to be calibrated to ensure that the correct companion gradient factors are applied. When the insertion position of the gradient coil can vary, these parameters can vary from system to system. Therefore, a fast and accurate method for determining these offsets is important.

[0033] Figure 2 A schematic diagram of an exemplary MRI system 10 is shown. In an exemplary embodiment, the MRI system 10 includes a workstation 12 having a display 14 and a keyboard 16. The workstation 12 includes a processor 18, such as a commercially available programmable machine running a commercially available operating system. The workstation 12 provides an operator interface that allows scanning plans to be entered into the MRI system 10. The workstation 12 is coupled to a pulse sequence server 20, a data acquisition server 22, a data processing server 24, and a data storage server 26. The workstation 12 and each of the servers 20, 22, 24, and 26 communicate with each other and together can be referred to as a processing system.

[0034] In the exemplary embodiment, the pulse sequence server 20 operates the gradient system 28 and the radio frequency ("RF") system 30 in response to instructions downloaded from the workstation 12. The instructions are used to generate gradient waveforms and RF waveforms in an MR pulse sequence. The RF coil 38 and the gradient coil assembly 32 are used to execute the prescribed MR pulse sequence. The RF coil 38 is shown as a whole-body RF coil. The RF coil 38 can also be a local coil that can be placed near the anatomical structure to be imaged, or a coil array including multiple coils.

[0035] In the exemplary embodiment, gradient waveforms for performing a prescribed scan are generated and applied to a gradient system 28, which includes gradient amplifiers and energizes the gradient coils in a gradient coil assembly 32 to generate magnetic field gradients G for position encoding the MR signals. x , G y and Gz The gradient coil assembly 32 forms part of a magnet assembly 34, which also includes a polarizing magnet 36 and an RF coil 38. The magnet assembly 34 forms a bore 35 in which an object 37 (such as a patient) is received and scanned. The magnet 36 generates a polarizing magnetic field around the patient, and the gradient coil assembly 32 applies a magnetic gradient field to the polarizing magnetic field. Further,

[0036] In an exemplary embodiment, the RF system 30 includes an RF transmitter for generating RF pulses used in MR pulse sequences. The RF transmitter responds to the scan plan and direction from the pulse sequence server 20 to generate RF pulses with a desired frequency, phase, and pulse amplitude waveform. The generated RF pulses are applied by the RF system 30 to an RF coil 38, which applies an RF field to the patient. The responsive MR signals detected by the RF coil 38 are received by the RF system 30 and amplified, demodulated, filtered, and digitized according to commands generated by the pulse sequence server 20. The RF coil 38 is depicted as both a transmitter and receiver coil, such that the RF coil 38 transmits RF pulses and detects MR signals. In one embodiment, the MRI system 10 may include a transmitter RF coil for transmitting RF pulses and a separate receiver coil for detecting MR signals. The transmit channels of the RF system 30 may be connected to the RF transmit coil, and the receiver channels may be connected to separate RF receiver coils. Typically, the transmit channels are connected to the whole-body RF coil 38, and each receiver segment is connected to a separate local RF coil.

[0037] In the exemplary embodiment, the RF system 30 also includes one or more RF receiver channels. Each RF receiver channel includes an RF amplifier that amplifies the MR signals received by the RF coil 38 to which the channel is connected; and a detector that detects and digitizes the I and Q quadrature components of the received MR signals. The magnitude M of the received MR signal can then be determined as the square root of the sum of the squares of the I and Q components, as shown in equation (3) below:

[0038]

[0039] And the phase φ of the received MR signal can also be determined as shown in the following equation (4):

[0040]

[0041] In an exemplary embodiment, the digitized MR signal samples generated by the RF system 30 are received by the data acquisition server 22. The data acquisition server 22 can operate in response to instructions downloaded from the workstation 12 to receive real-time MR data and provide buffer memory so that no data is lost due to data overflow. In some scans, the data acquisition server 22 only passes the acquired MR data to the data processing server 24. However, in scans where information derived from the acquired MR data is needed to control further execution of the scan, the data acquisition server 22 is programmed to generate the required information and transmit it to the pulse sequence server 20. For example, during a pre-scan, MR data is acquired and used to calibrate the pulse sequence executed by the pulse sequence server 20. In addition, navigator signals can be acquired during the scan and used to adjust operating parameters of the RF system 30 or gradient system 28, or to control the order in which views are sampled in k-space.

[0042] In an exemplary embodiment, the data processing server 24 receives MR data from the data acquisition server 22 and processes the MR data according to instructions downloaded from the workstation 12. Such processing may include, for example, Fourier transforming the raw k-space MR data to produce two-dimensional or three-dimensional images, applying filters to reconstructed images, performing backprojection image reconstruction on the acquired MR data, generating functional MR images, and computing motion or flow images.

[0043] With the previous discussion of the MRI system 10 in mind, we can return to the discussion of the companion field. As previously mentioned, the application of a linear gradient field in the z-direction results in the generation of a companion field, i.e., an additional field that varies nonlinearly, spatially, along the x- or y-direction. The invention described herein relates to the calibration of asymmetric gradient coils, which can be used to compensate for the companion field.

[0044] Apply a static magnetic field along the main Direction-guided high-amplitude gradient field results in a spatially varying modification of the main magnetic field, where the magnetic field is desired

[0045]

[0046] The result is the following total magnetic field vector:

[0047]

[0048] This results in a non-zero component of the field along the x or y direction. In the above equation, The first component associated is B x ,and The associated second component is B y , and with The associated third component is B zIn addition, G x , G y and G z are the applied gradient fields that vary spatially along the x, y, and z directions, respectively. 0x and z 0y is the offset of the gradient field components relative to the isocenter of the magnet. Specifically, x0 and y0 are the offsets of the z gradient coil in the x and y directions, respectively, and z 0x and z 0y are the offsets in the z direction (x and y gradient coils), respectively. In general, for symmetric gradient coils, x0 = y0 = z 0x =z 0y = 0, since they coincide with the isocenter of the magnet.

[0049] For an asymmetric gradient coil, z 0x ≠0 and z 0y ≠ 0. In addition, it is possible that z 0x ≠z 0y , that is, the shifts in the lateral gradients may not necessarily be the same. However, in most cases, z 0x =z 0y The techniques described herein allow for determining whether z 0x =z 0y If not, determine z 0x and z 0y Individual values of (for z 0x ≠z 0y ). Although 0x and z 0y Typically determined during the design phase of the gradient coil (i.e., default values), but manufacturing tolerances as well as gradient coil assembly and installation may result in variations in the value of z 0x and z 0y Deviation from expected or designed values. In the discussion that follows, the z gradient coils (and not the x or y gradient coils) are assumed to be symmetrical. There are practical reasons why the z gradient coils are symmetrical, as it is desirable for the offsets of the asymmetric coils from the isocenter to be aligned as closely as possible. In other words, although it is possible to have completely asymmetric gradient coils in all three axes (x, y and z), it is common for only the transverse axes (x and y) to be asymmetric because it is difficult to align the transverse axis gradient coils with the z gradient coils to avoid significant eddy currents and to facilitate adequate force and torque balance. Therefore, for a symmetric z gradient coil, x0=y0. The invention described herein then relates to the z 0x and z 0y These are gradient coil constants specific to the transverse gradient axis and can be used to correct the gradient coil waveform to compensate for the accompanying magnetic field.

[0050] like Figure 1As shown in equation (6), the magnitude of the total magnetic field can be written as:

[0051]

[0052] Among them B x 、B y and B z They are The x, y and z components of the desired field are z , using Taylor series expansion,

[0053]

[0054] Equation (7) can be replaced by To solve. Therefore,

[0055]

[0056] Among them B x 、B y and B z is given in Equation (6). In addition to the desired field, the adjoint field can then be obtained from Equation (7), in

[0057]

[0058] The zero-order (0 th ), first order (1 st ), second order (2 nd ) and higher-order companion gradient fields. The order of the companion gradient field represents the order of spatial variation. That is, the zero-order companion field is independent of spatial position, the first-order varies linearly with spatial position, the second-order varies quadratically with spatial position, and the third-order varies cubically with spatial position. Similar relationships apply to higher-order companion fields.

[0059] With low performance gradient coils, it can be assumed that the higher order terms are negligible and only the zeroth, first and second order corrections may be required. However, with higher performance gradient coils, third order corrections may also be required. High performance gradient coils are capable of generating magnetic gradient fields up to 400 mT / m and / or may have a coil efficiency of η = 0.13-0.32 mT / m / A. To quantify the significance of the higher order terms, equation (10) can be expanded using the definition of equation (6) as follows

[0060]

[0061] in

[0062]

[0063] and

[0064]

[0065] Collecting the terms from equation (11) and using the definitions from equations (12) to (14), we can define the zero-order, first-order, second-order, and third-order spatial terms that accompany the gradient. Thus, the zero-order term is

[0066]

[0067] Since symmetric gradients (e.g., z gradient coils) do not have zero-order and odd-order adjoints, asymmetric gradient coils (i.e., x and y) typically have only asymmetric transverse x and y gradients and a symmetric z gradient. It is difficult to align an asymmetric z gradient with an asymmetric transverse (x and y) gradient, and it is preferable to make the z gradient symmetric to simplify the force and torque balance in the gradient design. Therefore, for high-performance head gradient adjoint correction (as an example), only the asymmetric transverse gradient is considered. Therefore, in Equation (15) we set x0 = y0 = 0, and z 0x ≠0, z 0y ≠0, so that the zero-order adjoint gradient field for the asymmetric transverse gradient and the symmetric z gradient is:

[0068]

[0069] Where α = 0.5. Assume B z ≈B0, (because B0>>(G x x+G y y+G z z)), then the zero-order error field is

[0070]

[0071] Similarly, the first-order adjoint field is

[0072]

[0073] In an asymmetric transverse gradient coil with a symmetric z-gradient of x0=y0=0 and y0=0 and α=0.5 this simplifies to

[0074]

[0075] Note that for symmetric transverse gradient coils (x and y axes), equations (18) and (20) vanish, i.e., there are no zero-order or first-order adjoint fields for a perfectly symmetric gradient coil, since z 0x =z 0y =0.

[0076] The second-order adjoint field is:

[0077]

[0078] And this is approximately

[0079]

[0080] It is common and constant in symmetric as well as asymmetric gradient coils, where α=0.5.

[0081] The third-order spatial component in equation (11) according to the Taylor series expansion may be significant, but the fourth-order spatial component can be ignored because The term is dominant. Therefore, in the case of x0 = y0 = 0, the third-order adjoint field for the asymmetric transverse gradient is

[0082]

[0083] If we ignore the xz and yz cross terms in Eq. (23), the third-order adjoint term that contributes to the spatial variation of the measurable phase in the MRI image can be approximated as the error field that varies spatially in the z direction

[0084]

[0085] According to an embodiment of the present technology, after determining the first-order and second-order companion field components, these components can be corrected in the MRI system by a correction field along the z gradient, which is generated by gradient pre-emphasis, i.e., a compensation gradient waveform. However, the third-order companion field cannot be corrected by gradient pre-emphasis or the correction field along z, but will be considered in post-processing. It can be observed from the above equations that in order to determine the first-order, second-order, and third-order companion field components, we first need to determine two parameters z 0x and z 0y , which are the gradient coil constants specific to the transverse gradient axis.

[0086] According to an embodiment of the present technology, in order to determine the gradient coil constant z 0x and z 0y , utilizing a method based on phase contrast MRI acquisition. Phase contrast MRI is a method of encoding the velocity of flowing spins in a patient by using a dual acquisition scheme with a bipolar gradient reversing polarity between the two acquisitions of the flow encoding gradient. The phase difference between the two acquisitions is then acquired. The stationary spins result in zero phase, whereas the flowing spins will differentially accumulate phase during the application of bipolar gradients of different polarity. In an embodiment of the present technique, we image a stationary phantom. After applying the bipolar gradient, we expect a zero phase from the phase difference method. However, the additional companion gradient field produces a non-zero phase in the stationary phantom, which can be measured and the gradient coil constant z can then be determined 0x and z 0y.

[0087] Figure 3 A graphical graph 200 of a phase contrast imaging waveform for phase contrast MRI is shown. Figure 3 , graph 202 shows the flow encoding gradient (X gradient), graph 204 shows the phase encoding gradient (Y gradient), and graph 206 shows the slice selection gradient (Z gradient). In this example, the readout gradient 224 is also in the same direction as the flow encoding gradient (X gradient). The horizontal axis 212 and the vertical axis 214 in all graphs 202, 204 and 206 show time in microseconds and gradient amplitude in gauss / cm, respectively. The flow encoding gradient 202 is a bipolar gradient waveform that switches between positive (+) polarity 208 and negative (-) polarity 210. From Figure 3 It can be seen that the positive polarity gradient waveform 208 has two lobes, i.e., triangular or trapezoidal pulse regions, with a positive lobe 216 followed by a negative lobe 218. Furthermore, the negative polarity gradient waveform 210 also has two lobes, with a negative lobe 220 followed by a positive lobe 222. It should be noted that the positive lobe 222 is followed by a readout gradient pulse 224. However, for the purpose of accompanying field calculations, the gradient pulse 224 can be ignored because any phase contribution from this and other extraneous gradients (except the bipolar gradient) is cancelled when the phase difference is taken. For the purpose of measuring the gradient coil constant z 0x and z 0y For the purpose of this study, we focus on the effects of the zero-order companion gradient field. Therefore, after taking the phase difference, the resulting zero-order companion gradient field is derived from the other gradient waveforms that are unchanged and canceled. The method described in this technique varies the amplitude of the bipolar gradient and measures the resulting phase difference. By plotting the resulting phase difference as a function of the bipolar gradient amplitude, the gradient coil constant z can be determined. 0x and z 0y .

[0088] Taking the phase difference between the two acquisitions 208 and 210 produces a net phase because the phase of the static spin is opposite to the polarity change. Considering the zero-order adjoint gradient effect from equation (17), it can be seen that the net effect of the adjoint gradient is positive, regardless of the given gradient polarity, and the gradient amplitude term is squared in equation (17). In addition, due to the fact that the bipolar flow encoding lobes, i.e., the pulse regions, are generally unequal in pulse width and amplitude in order to minimize the echo time (i.e., TE time), the zero-order adjoint gradient amplitude can be different for positive and negative polarities. Therefore, since the zero-order adjoint gradient generates a uniform, spatially invariant additional magnetic field, there is a net phase accumulation for the flow encoding gradient. This phase accumulation Can be identified as:

[0089]

[0090] where γ = 267.552 × 10 6 rad / s / T is the gyromagnetic ratio, and τ is the total time of the flow encoding gradient. Taking the phase difference between the two acquisitions 208 and 210, the net phase is then

[0091]

[0092] where the (+) and (-) signs represent the positive and negative polarities of the bipolar flow encoding gradient. Equation (26) can be obtained by inserting the zero-order error field B from equation (17) 误差 ,0th x gradient value to further modify. Therefore,

[0093]

[0094] Among them G x1 and G x2 These are positive and negative bipolar gradient waveforms respectively.

[0095] Figure 4 Another graphical graph 300 of a phase contrast imaging waveform is shown in accordance with an embodiment of the present technology. Figure 4 In FIG. 3 , graph 302 shows the readout gradient direction, where the bipolar gradient is applied in the same direction; graph 304 shows the zeroth order companion gradient field due to the associated positive bipolar encoding gradient 308. And graph 306 shows the associated zero-order companion gradient field due to the negative polarity bipolar encoding gradient 310 Horizontal axis 312 and vertical axis 314 in graph 302 show time in microseconds and gradient amplitude in gauss / cm, respectively. Additionally, horizontal axis 316 and vertical axis 318 in graphs 304 and 306 show time in microseconds and field amplitude in gauss, respectively. Figure 3 Likewise, the stream encoding gradient 302 is a bipolar gradient waveform that switches between positive (+) polarity 308 and negative (-) polarity 310. Note that Figure 4 The associated zero-order companion field from only the bipolar flow encoding gradient is shown. and This is because after taking the phase difference, the resulting zeroth-order companion gradient fields from the other gradient waveforms cancel out since they do not change with the change in polarity of the bipolar gradient.

[0096] Instead of using Figure 3 The standard flow coding scheme shown, in one embodiment, can use a single-sided flow coding type gradient waveform to simplify the calculation. Figure 3 In the stream coding scheme, it may be necessary to increase the gradient flow of the coded gradient amplitude in order to obtain sufficient phase difference value. Figure 5 A graphical plot 400 of a single-sided bipolar encoding type imaging waveform similar to a flow encoding waveform is shown. Unlike a flow encoding waveform where the bipolar waveform amplitude and waveform pulse width are calculated to match some velocity encoding value, the gradient waveform amplitude and pulse width of a bipolar encoding waveform only need to meet the criteria that the net gradient zero-order moment (or gradient amplitude x time) needs to be equal to the gradient lobe 418. The area or zero-order moment of the gradient lobe 418 is the dephasing gradient region that provides the readout gradient 430. Figure 5 In FIG. 4 , graph 402 shows the readout gradient waveform and the switched bipolar encoding waveform; graph 404 shows the associated zero-order companion gradient field due to the positive bipolar encoding gradient 410. And graph 406 shows the associated zero-order companion gradient field due to the negative bipolar encoding gradient 408 The horizontal axis 412 and the vertical axis 414 in the graph 402 show time in microseconds and gradient amplitude in gauss / cm, respectively. In addition, the horizontal axis 416 and the vertical axis 418 in the graphs 404 and 406 show time in microseconds and field amplitude in gauss, respectively. Figure 3 Similarly, the bipolar encoding gradient shown in 402 is a bipolar gradient waveform that switches between positive (+) polarity 408 and negative (-) polarity 410. However, unlike Figure 3 In contrast, the positive bipolar gradient waveform 408 has only one lobe, negative lobe 418, to provide a dephasing gradient region of the readout gradient in the x-direction. Furthermore, the negative bipolar gradient waveform 410 has two lobes, negative lobe 420 followed by positive lobe 422.

[0097] If the gradient is in the y direction (i.e., along the phase encoding direction) instead of Figure 5 If applied along the x-direction as shown, negative (-) encoding will have zero gradient amplitude. Similarly, if the gradient is applied along the z-direction (slice encoding direction), negative (-) encoding will only have slice rephasing gradients. Positive (+) polarity encoding gradients typically have a net gradient area (zeroth-order moment) equal to the area required to dephase spins before the readout gradient (x-direction), a net phase encoding gradient area or zero gradient area (y-direction), or a gradient area required to rephases slice select gradient spins (z-direction).

[0098] From equation (27), we can see that The term is a constant term that is pulled out of the integral, and the bipolar gradient G x A single measurement of can directly determine the value of this constant. However, in order to better take into account other miscellaneous errors, it is preferable to vary the applied bipolar gradient G xThe amplitude of the (bipolar gradient 420) is collected, a series of measurements are collected, and the resulting data are fitted to equation (27) to minimize the effects of noise or spatially varying eddy currents. This is achieved by using a one-sided approach to measure the phase difference, such as Figure 5 shown.

[0099] Figure 6 A graphical graph 500 is shown of a gradient waveform diagram according to an embodiment of the present technology. Graph 500 shows a positive (+) polarity bipolar encoding gradient 502, and a negative (-) polarity bipolar encoding gradient 504. If we denote the gradient amplitude, pulse width, and waveform ramp time of the (+) polarity encoding gradient 502 as g1, g2, t p；1 , t p；2 , t r；1 , t r；2 and (-) polarity encoding gradient 504 is represented as g3, g4, t p；3 , t p；4 , t r；3 , t r；4 , since the phase obtained from the zero-order adjoint field of the bipolar gradient is

[0100]

[0101] and

[0102]

[0103] It should be noted that the previous analysis is only for the x-gradient axis, but similar analysis can be performed for the y-gradient axis and the z-gradient axis. Figure 5 The proposed method mentioned sets g1 = 0 so that there is only one lobe for the positive polarity gradient. Then, the phase difference is

[0104]

[0105] in and where g3 is the same as -g t ,…,+g T The maximum phase difference is changed so that |Δφ| < 2π, i.e., to avoid aliasing. In equation (30), we further assume that the pulse width and ramp time of the bipolar encoding gradient 502 are the same as those of the bipolar encoding gradient 504 to simplify to equation (30). We note that if the pulse width and ramp time of the bipolar encoding gradients 502 and 504 are different, the same analysis can be performed without loss of specificity. Therefore, in equation (30), we set t p；3 =t p；1 , tp；4 =t p；2 , t r；3 =t r；1 , and t r；4 =t r；2 It should be noted that g4 is related to g3 by:

[0106]

[0107] Where A2=g3(t p,2 +t r,2 ) is the area or zeroth order moment of the readout dephasing gradient 430. Similarly, to determine z 0y To find the correct value of , a bipolar gradient waveform is applied to the y-axis (phase encoding direction), and the phase difference is then determined as:

[0108]

[0109] Since for the bipolar waveform applied in the phase encoding direction, g1 = g2 = 0, z 0y It can be determined from equation (32) by fitting the measured phase difference as the gradient amplitude, with g3 and g4 varying.

[0110] Equation (32) assumes that the phase encoding gradient is separated from the bipolar waveform (i.e., not combined as in the method of minimizing TE time). Therefore, z can be determined independently 0x and z 0y Both. Furthermore, equation (32) assumes that for a particular scan plane orientation, the frequency readout direction remains fixed, while the bipolar encoding direction changes from the readout direction to the phase encoding direction. However, if the frequency direction also changes with the bipolar encoding direction, then either equation (30) or equation (32) can be used to determine z 0x and z 0y It should also be noted that if the phase encoding gradient is not separated from the bipolar waveform, then the analysis of equations (28), (29), and (32) still applies because the associated concomitant gradient field effects from the phase encoding gradient lobes cancel in terms of phase difference. This emphasizes the advantage of the present technique because it eliminates or substantially reduces the concomitant contributions of gradient waveforms other than the bipolar encoding gradient waveform.

[0111] As an example, since the gradient waveform is applied only along the physical x and / or y axis, z 0x and z 0y The offset is relevant and the scanning protocol is for axial plane acquisition. 0x , the frequency encoding direction is set to the right / left (R / L) direction, and the bipolar encoding is also set to the R / L direction. In this way, gradients g2, g3, and g4 are applied along the x-axis (where g1 = 0). In order to determine z0y , setting the frequency encoding direction in the axial plane acquisition to the anterior / posterior (A / P) direction, and also in the A / P direction for the bipolar encoding gradient. Gradients g2, g3, and g4 are now applied along the y-axis. Therefore, fitting the measurement to equation (30) will allow the determination of z 0y The same procedure is relevant if a unilateral bipolar waveform is applied to the phase encoding direction without changing the frequency encoding direction, where the measurements will then be fitted to equation (32).

[0112] Figure 7 A graphical plot 600 of measured phase error or phase difference as a function of gradient amplitude g3, in accordance with an embodiment of the present technology, is shown. In graphical plot 600, horizontal axis 602 represents g3 gradient amplitude in gauss / cm, and vertical axis 604 represents measured phase difference or phase error in radians. The plot includes a first curve 606 without accompanying field correction and a second curve 608 with accompanying field correction.

[0113] As can be seen from curve 606, several measurements of the gradient amplitude of g3 vary from g3 = -7, ..., +7 Gauss / cm, and the corresponding phase differences or phase errors are obtained. Since the measurement is of a stationary phantom, a zero phase difference is expected. However, due to the accompanying gradient field effect, a non-zero phase difference is measured. This non-zero phase difference constitutes the phase error due to the accompanying gradient field effect. By fitting the measured data points to equation (30), the gradient coil offset z can be determined by using typical data fitting methods (such as least squares fitting or polynomial fitting). 0x In a similar manner, the axis of the applied bipolar gradient is adjusted, z 0y It can be determined by fitting the corresponding measured data points to Equation (31) or Equation (32), depending on whether the readout gradient direction is changed. 0x and z 0y Also related to the correction of the first-order adjoint gradient effects (as indicated by equation (20)), it is sufficient to use these equations to correct the system only for the zero-order adjoint field effects. 0x and z 0y Then, a gradient compensation waveform is generated to compensate for the satellite field effect for both zero-order and first-order corrections. Curve 608 shows that after compensating for the satellite field, the phase error or phase difference remains approximately zero radians.

[0114] The above techniques were evaluated in experimental studies. Experiments were performed on a GE MR750 3.0T MRI scanner (GE Healthcare, Waukesha, WI) using microstructural anatomical gradients for neuroimaging with ultrafast scanning (MAGNUS) gradient coils (G max=200mT / m and SR max =500T / m / s) to replace the standard whole-body gradient and transmit / receive RF coils. A compact 3T head gradient coil (G max =80mT / m and SR max =700 T / m / s). Similar results were obtained with the MAGNUS system, which has an asymmetric transverse gradient coil and a symmetric z-gradient coil, and the peripheral nerve stimulation threshold is substantially higher than that of the whole-body gradient system, allowing echo planar imaging (EPI) to be performed using the maximum slew rate. A 32-channel receive coil (NOVA Medical, Wilmington, MA) was used in all studies. A spherical oil phantom with a diameter of 14 cm was placed in the coil and allowed to settle for several hours to allow the phantom to temperature equilibrate in the magnet bore and also to minimize any thermal convection.

[0115] A standard ungated gradient echo phase contrast acquisition was modified and used in the experiment. The scan parameters used were: 24 cm image field of view; 10 mm slice thickness; 256 × 128 matrix; TR (repetition time) = 20 ms; 15° flip angle; axial plane; frequency direction = R / L; ±15.65 kHz bandwidth; VENC (velocity encoding value) = 100 mm / s. Note that the VENC value is only used to establish the bipolar encoding gradient waveform pulse width and ramp time. Using the minimum TE (echo time) setting, this results in TE = 6.4 ms. Table 1 lists the corresponding Figure 6 The pulse width of the resulting waveform in is . The amplitude of g3 varies between -7, …, +7 G / cm, where the value of g4 changes according to equation (31). The average signal intensity in the relevant region acquired at the center of the phase difference image is recorded for each value of g3. The maximum amplitude of g3 is such that the maximum phase difference is |Δφ| < 2π to avoid aliasing.

[0116] Waveform Amplitude (G / cm) Ramp time (μs) Flat top time (μs) <![CDATA[g1]]> +8.10 700 4 <![CDATA[g2]]> -9.87 672 4 <![CDATA[g3]]> -10.84 700 4 <![CDATA[g4]]> +9.87 672 4

[0117] Table 1

[0118] The results of the above experiments are Figure 8 In the graphical graph 650, the horizontal axis 652 represents the g3 gradient amplitude in gauss / cm and the vertical axis 654 represents the phase error or phase difference in radians. The first graph 656 is a graph using the theoretical design or default gradient coil constant z 0x= 12.0 cm predicted expected phase error or phase difference, and the second graph 658 is the actual phase error or phase difference determined from measurements (without accompanying field correction). Dashed line 660 shows the result of a second-order polynomial fit of equation (30) to the measured data 658. The actual gradient coil constant z is shown by measurement. 0x = 12.9 cm, which differs from that determined by theoretical design or electromagnetic analysis. As previously mentioned, the z position of the gradient coils may vary during installation, and if default design parameters are used, this will introduce errors in the accompanying gradient field correction factors. This is in addition to manufacturing tolerances, which may introduce additional errors. Therefore, post-installation calibration of the accompanying gradient correction factors is necessary.

[0119] As can be seen from the graph 650, the measured phase error or phase difference as a function of g3 increases as the amplitude of g3 increases. It can be noted that when the default or designed gradient coil constant z 0x When used in equation (30), the expected phase error or phase difference (i.e., curve 656) underestimates the actual measurement (i.e., curve 658). This indicates that the z of 12 cm 0x The default value is incorrect. Fitting the measured data to equation (30), the gradient offset z 0x It can be determined by using typical data fitting methods, such as with a second-order polynomial y=a1x 2 The least squares fit of +a2x+a3. The fit of the coefficient of the quadratic term in g3 is given by

[0120]

[0121] And the result is z 0x =12.9±0.2cm. This indicates that the z 0x The default value is offset by about 1 cm. It should be noted that instead of a second-order polynomial, z 0x or z 0y It can also be determined by fitting to a linear or constant term. However, the confidence intervals for the fit of each of the coefficients of the second-order polynomial can be used as a guide to which fit is most accurate.

[0122] Figure 9 A graphical plot 670 is shown of the residual error in the phase difference measurement from the expected zero phase. In the graphical plot 670, the horizontal axis 672 represents the gradient correction offset z in mm. 0x , the vertical axis 674 represents the residual error in the phase error in radians 2. In general, if the offset z 0x or z 0y Far from the correct value, such as Figure 8As shown, the correction applied will not be effective and a large error will be obtained in the phase after correction. However, in the example provided, z 0x A variation of ±3 mm produces a fairly narrow minimum, as seen in graph 670. This demonstrates that the above technique for determining the gradient coil correction constants is quite accurate.

[0123] Determine the gradient coil constants x0, y0, z 0x and z 0y The importance of the correct values of lies in the use of these constants in the adjoint gradient correction. Correction of adjoint gradient effects can be performed by adjusting the frequencies of the MRI receiver and transmitter (for zero-order correction) or by gradient pre-emphasis for first-order effects. As an example, referring to the first-order correction of equation (20) for an asymmetric gradient, the pulse amplitude is G x The x gradient of will result in a spatially varying adjoint field in the z direction, so that the error field is

[0124]

[0125] in is essentially equal to the gradient applied in the z direction. Therefore, if an x gradient is applied, the accompanying correction will require a small compensating gradient pre-emphasis applied to the z gradient so that at any time t is expressed as The gradient waveform at the end is

[0126]

[0127] Among them G x (t) is the gradient amplitude command and is usually given by I c (t)×η x,y,z Given. x,y,z are the coil gains or coil efficiencies of the x, y, and z gradient coils, respectively, and I c (t) is the command current for generating the target gradient field amplitude. From equation (34), it can be seen that for the standard gradient amplitude command G x (t), compensated gradient pre-emphasis Applied to the z gradient to correct for first-order adjoint gradient field effects.

[0128] Similarly, for G y The expected y gradient of , and the gradient applied in the case of pre-emphasis is

[0129]

[0130] In other words, for the standard gradient amplitude command G y (t), pre-emphasize the compensation gradient should be applied to the z gradient. In addition, it should be noted that for G zIf there are no other gradients applied simultaneously, the pre-emphasis can be neglected. However, if there are gradients applied in the x and y directions, the overall correction at each time point is

[0131]

[0132] In equation (36), x (t), G y (t) and G z The additional terms outside of (t)) represent compensation terms or correction terms. In other words, the compensating gradient waveform is applied to the gradient coils so that a companion correction gradient field is generated in the same direction as the companion gradient field.

[0133] Figure 10A and Figure 10B A graphical graph 700 of a gradient waveform according to an embodiment of the present technology is shown. Figure 10A and Figure 10B In FIG. 7 , graphs 702 and 704 represent the desired x, y, and z gradient waveforms that need to be applied to the gradient windings of the MR machine, i.e., the target gradients required for normal operation. However, as described above, with the present technique, correction or pre-emphasis gradients are applied to correct for the effects of the satellite gradients. These pre-emphasis gradients are shown in corresponding graphs 706 and 708. Note that the pre-emphasis gradients of graphs 706 and 708 should be applied to the z gradient to correct for first-order satellite field effects.

[0134] Given that we have a programmable waveform with a certain digital resolution in terms of time and amplitude, the digital command sent to the gradient amplifier is essentially that in equation (36). The corrected waveform can be Figure 11 The typical MRI pulse sequence shown is pre-calculated in memory, or the correction can also be performed by a dedicated pre-emphasis board that is based on Figure 12 The system input / controller transfer function shown performs the correction of equation (36). In other words, Figure 11 A system for correcting gradient in a method of illustrative embodiments utilizes a stored gradient waveform that is a combination of a target gradient waveform and a gradient correction waveform. Figure 12 The system used to correct gradients in

[15] modifies the target gradient waveform in real time by applying gradient correction factors using a dedicated circuit board.

[0135] It should be noted that the effects of the zero-order adjoint gradient field (Eq. (17)) can be corrected by changing the MRI transmitter and receiver frequency specifications in the waveform control board. This can be done using an external FPGA (field programmable gate array) board as a real-time frequency correction. In this case, for the gradients applied in the x and y directions, the zero-order correction is a frequency adjustment such that

[0136]

[0137] in is the RF frequency offset in Hz, which is used to compensate for the zeroth-order satellite field.

[0138] In one embodiment, the zero-order adjoint gradient correction can also be performed as a pre-calculation in the frequency pulse sequencer board. In this case, the correction can be applied as a time-varying frequency offset during the slice select or readout gradient (i.e., during the data acquisition window) if there are gradients applied in the x or y direction during these pulse sequence periods. This type of correction is useful if the amplitude of the applied gradient is large enough so that the frequency offset (as given by equation (36)) exceeds the correction range of the FPGA. In another embodiment, if the applied gradient is outside the slice select RF pulse window or data acquisition period, the accumulated phase can be added to the receiver offset in the waveform pulse sequencer.

[0139] Figure 13 800 is a flowchart illustrating a method for correcting for concomitant gradient effects in an MRI system. The method includes, at step 802, determining a plurality of phase difference measurements between two acquisitions using a plurality of bipolar gradient waveforms. For example, a first bipolar gradient waveform is applied to a first gradient, such as an x-gradient, and then a second bipolar gradient waveform is independently applied to a second gradient, such as a y-gradient. The first bipolar gradient waveform and the second bipolar gradient waveform include two gradient lobes of positive and negative polarity. Note that at least one of the bipolar gradient waveforms in each acquisition is reduced to a single gradient lobe depending on whether the gradient coil is in readout mode or phase encoding mode.

[0140] Furthermore, the plurality of phase difference measurements include a first phase difference measurement and a second phase difference measurement corresponding to the x-gradient and the y-gradient, respectively. At step 804, the method includes determining gradient coil constants based on the plurality of phase difference measurements. The gradient coil constants include a first gradient coil constant determined based on the first phase difference measurement and a second gradient coil constant determined based on the second phase difference measurement. The first gradient coil constant and the second gradient coil constant are determined by fitting the first phase difference measurement and the second phase difference measurement data to a mathematical expression corresponding to a phase difference generated by one of a zero-order companion gradient field, a first-order companion gradient field, or a second-order companion gradient field.

[0141] At step 806, a compensating gradient waveform is determined based on the gradient coil constants. In one embodiment, the compensating gradient waveform compensates for the first-order companion field and the second-order companion field. In one embodiment, the compensating gradient waveform can be pre-calculated in the MRI pulse sequence memory. In another embodiment, the compensating gradient waveform can be calculated in real time in the pre-emphasis board. Finally, in step 808, the compensating gradient waveform is applied to the gradient coil to compensate for the companion gradient field. The compensating gradient waveform is applied to the gradient coil in combination with the target gradient waveform. The method further includes correcting the third-order companion gradient field in post-processing of the acquired data acquired after applying the compensating gradient waveform together with the target gradient waveform. Furthermore, the zero-order component of the companion gradient field is corrected by adjusting the frequency of the MRI system receiver and transmitter.

[0142] An advantage of this technique is that once the gradient coil constants are determined through measurement, they can be loaded into appropriate configuration files for accurate correction of concomitant gradient effects. Furthermore, image quality can be improved when applying high-amplitude gradient fields in asymmetric gradient coils. Furthermore, using this technique, artifacts from improperly inserted asymmetric gradient coils can be quickly identified, and corrective action can be taken. Furthermore, this technique ensures that the gradient coil parameters are valid and applicable for the full range of gradient amplitudes from +maximum to -maximum, including zero amplitude.

[0143] This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any included methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insignificant differences from the literal language of the claims.

Claims

1. A method for correcting for incident gradient field effects in a magnetic resonance imaging (MRI) system, the method comprising: determining a plurality of first phase difference measurements between the two acquisitions using a plurality of first bipolar gradient waveforms applied to the first gradient coil; determining a first gradient coil constant based on the plurality of first phase difference measurements; determining a compensation gradient waveform based on the first gradient coil constant; as well as The compensation gradient waveform is applied together with the target gradient waveform to compensate for the companion gradient field. The method of claim 1 , wherein the first gradient coil is an asymmetric gradient coil.

3. The method of claim 1, wherein the compensating gradient waveform compensates for first-order and second-order components of the companion gradient field. 4 . The method according to claim 1 , wherein second-order components and third-order components of the companion gradient field are corrected for use in post-processing of acquisition data acquired after applying the compensation gradient waveform together with the target gradient waveform. 5 . The method of claim 1 , further comprising determining a second gradient coil constant based on a plurality of second phase difference measurements between two acquisitions using a plurality of second bipolar gradient waveforms applied to a second gradient coil. The method of claim 1 , wherein the plurality of first bipolar gradient waveforms comprises two gradient lobes of positive and negative polarity. 7 . The method of claim 6 , wherein at least one of the first bipolar gradient waveforms in each acquisition is reduced to a single gradient lobe depending on whether the first gradient coil is in readout mode or phase encoding mode. 8 . The method of claim 7 , wherein the gradient lobes of the plurality of first bipolar gradient waveforms that are not reduced to the single gradient lobe are varied in a stepwise manner such that the first phase difference is less than 2π.

9. The method of claim 1 , wherein determining the first gradient coil constant comprises fitting the plurality of first phase difference measurement data to a mathematical expression corresponding to a phase difference generated by one of a zero-order companion gradient field, a first-order companion gradient field, or a second-order companion gradient field.

10. The method of claim 1, wherein the zero-order component of the companion gradient field is corrected by adjusting the frequency of the MRI system receiver and transmitter.

11. The method according to claim 1, wherein the compensation gradient waveform is pre-calculated in an MRI pulse sequence memory or calculated in real time in a pre-emphasis board.

12. A method for correcting for incident gradient field effects in a magnetic resonance imaging (MRI) system, the method comprising: determining a plurality of first phase difference measurements between the two acquisitions using a plurality of first bipolar gradient waveforms applied to the first gradient coil; determining a plurality of second phase difference measurements between the two acquisitions using a plurality of second bipolar gradient waveforms applied to a second gradient coil; determining a first gradient coil constant and a second gradient coil constant based on the plurality of first phase difference measurements and the plurality of second phase difference measurements, respectively; determining a compensation gradient waveform based on the first gradient coil constant and the second gradient coil constant; as well as The compensation gradient waveform is applied together with the target gradient waveform to compensate for the companion gradient field. 13 . The method of claim 12 , wherein the first bipolar gradient waveform and the second bipolar gradient waveform each include two gradient lobes of positive and negative polarity.

14. The method of claim 13, wherein at least one of the first bipolar gradient waveforms in each acquisition is reduced to a single gradient lobe depending on whether the gradient coil is in a readout direction or a phase encoding direction. 15 . The method of claim 14 , wherein the gradient lobes of the plurality of first bipolar gradient waveforms that are not reduced to the single gradient lobe are varied in a stepwise manner such that the phase difference is less than 2π.

16. The method of claim 12, wherein determining the first and second gradient coil constants comprises fitting the plurality of first and second phase difference measurement data to a mathematical expression corresponding to a phase difference generated by one of a zero-order companion gradient field, a first-order companion gradient field, or a second-order companion gradient field.

17. The method of claim 12, wherein the zero-order component of the companion gradient field is corrected by adjusting the frequency of the MRI system receiver and transmitter.

18. The method of claim 12, wherein the compensation gradient waveform is pre-calculated in an MRI pulse sequence memory or calculated in real time in a pre-emphasis board.

19. A magnetic resonance imaging (MRI) system comprising: a magnet configured to generate a polarized magnetic field around at least a portion of a subject disposed in the MRI system; a gradient coil assembly comprising a plurality of gradient coils configured to apply at least one gradient field to the polarizing magnetic field; a radio frequency (RF) system configured to apply an RF field to the subject and receive magnetic resonance signals from the subject; A processing system programmed to: determining a plurality of phase difference measurements between two acquisitions using a plurality of bipolar gradient waveforms applied to at least one gradient coil of the plurality of gradient coils; determining at least one gradient coil constant based on the plurality of phase difference measurements; determining a compensation gradient waveform based on the at least one gradient coil constant; as well as The compensating gradient waveform is applied to the plurality of gradient coils to compensate for the companion gradient field.

20. The MRI system of claim 19, wherein the processing system is programmed to determine a compensating gradient waveform based on the at least one gradient coil constant to generate a companion correction gradient field in the same direction as the companion gradient field.

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