Eddy current compensation method for digital gradient pre-enhancement in ultra-high field MRI system

Abstract

The present invention discloses a digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system, comprising: obtaining a nonlinear eddy current function and an eddy current transfer function of the eddy current in each direction that changes with time; the eddy current transfer function includes a direct eddy current transfer function and a cross-term eddy current transfer function; establishing a relationship between the magnetic resonance eddy current transfer function and the digital gradient pre-enhancement unit transfer function; respectively calculating the amplitude constant and time constant of the digital gradient cross-term pre-enhancement unit transfer function and the direct-term pre-enhancement unit transfer function in each direction of the eddy current; by verification and implementation through FPGA, the digital gradient pre-enhancement eddy current compensation for the ultra-high field nuclear magnetic resonance imaging system can be realized. The present invention provides a faster and more accurate eddy current compensation solution for the ultra-high field nuclear magnetic resonance imaging system, which can effectively improve the imaging quality.

Description

Technical Field

[0001] The invention belongs to the technical field of magnetic resonance imaging (MRI), and in particular relates to a digital gradient pre-enhancement eddy current compensation method for an ultra-high field magnetic resonance imaging system. Background Art

[0002] MRI systems can be divided into low-field, high-field and ultra-high-field systems according to their main magnetic field strength. Among them, the ultra-high-field MRI system with the largest main magnetic field strength has the best imaging effect and can produce magnetic resonance images with the highest resolution and signal-to-noise ratio. The ultra-high-field MRI system also has a higher-performance gradient system that can speed up imaging.

[0003] The nuclear magnetic resonance imaging system uses a gradient system to generate a gradient magnetic field that usually changes linearly, and realizes spatial encoding functions such as layer selection and frequency encoding and phase encoding in the three directions of xyz, so that the magnetic resonance signal can be easily reconstructed into an intuitive image and can distinguish the different spatial position information of the target to be measured.

[0004] Due to Faraday's law of electromagnetic induction, this changing gradient magnetic field will induce eddy currents in the conductor structure of the MRI system. According to the Biot-Savart law, eddy currents will generate eddy magnetic fields in the conductor structure. And because of Lenz's law, the eddy current field will always hinder the change of its source - the gradient field, causing the gradient field waveform output by the gradient system to be distorted, the spatial encoding to be biased, and ultimately causing artifacts in the reconstructed magnetic resonance image. Therefore, the gradient eddy current effect will have an adverse effect on the imaging quality of the MRI system.

[0005] Existing research has proposed a variety of compensation schemes for the gradient eddy currents of MRI systems. One method is to add an additional shielding coil to the gradient coil through electromagnetic field design and simulation, and to offset the eddy currents generated by the gradient magnetic field through passive shielding (self-shielding) or active shielding. This method has a good compensation effect, but it requires high system processing accuracy and high hardware costs. Another mainstream method is to superimpose an additional gradient current on the input conventional gradient waveform through analog or digital gradient pre-enhancement, so that the final output gradient waveform can be consistent with the conventional set gradient waveform after being affected by eddy currents. This method only requires a simple expansion of the hardware circuit or the implementation of the corresponding function through software in the existing digital device for gradient calculation. The hardware cost is low and the application range is wide. It can also be used with systems with shielded coils. However, different pre-enhancement gradient waveform implementation methods will have a greater impact on the eddy current compensation effect: CN109765512A proposes a magnetic resonance gradient system and its eddy current compensation method and device, but this method requires additional hardware to measure the gradient waveform. The nonlinear fitting method used is sensitive to the initial value, and the pre-enhancement parameter calculation may be wrong or inaccurate, resulting in the inability to better reduce the eddy current. In addition, this method does not consider the main magnetic field direction B 0 CN112881959A provides a gradient eddy current compensation method and system for magnetic resonance imaging, but this method needs to set a time range for the decay time constant T when using least squares fitting. Inaccurate time range will lead to large errors in fitting results.

[0006] Most existing technical solutions use fitting-iteration methods for compensation, which is prone to cumulative errors. The compensation process is complex and time-consuming, and the main magnetic field B 0 The measurement and compensation of eddy current terms generally adopt separate solutions, without joint compensation with eddy current direct terms and cross terms. The separate compensation device and compensation method make the eddy current compensation system very complicated and the compensation efficiency low. Summary of the invention

[0007] The present invention proposes a digital gradient pre-enhancement eddy current compensation method suitable for an ultra-high field nuclear magnetic resonance imaging system, and realizes the eddy current compensation function through FPGA, providing a faster and more accurate eddy current compensation solution for the ultra-high field nuclear magnetic resonance imaging system, so as to effectively improve its imaging quality.

[0008] The technical solution adopted by the present invention is as follows:

[0009] The present invention provides a digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system, the method comprising the following steps:

[0010] 1) Obtain the eddy current in all directions (x, y, z and B) 0) a nonlinear eddy current function and an eddy current transfer function varying with time on the surface of the vortex generator, wherein the eddy current transfer function includes a direct eddy current transfer function and a cross eddy current transfer function;

[0011] In specific implementation, the present invention adopts a method for measuring eddy currents through magnetic resonance signals to obtain a nonlinear eddy current function. The method includes the following steps:

[0012] The gradient echoes with different delay times after the ultra-high field NMR imaging system turns off the gradient pulse are used as the eddy current measurement pulse sequence and preset into the spectrometer of the ultra-high field NMR imaging system. The excited sample is moved in the x, y, z target axis directions and the main magnetic field B. 0 A magnetic resonance signal is generated in the direction which varies with the delay time;

[0013] In the x, y, z axis and B 0 A readout gradient is applied to the coil in each direction to obtain the magnetic resonance signal in each direction. The nonlinear eddy current in each direction can be analyzed from the phase information of the magnetic resonance signal. At the same time, the time variation curve of the nonlinear eddy current in each direction can be obtained. The nonlinear eddy current function is characterized by a series of exponential functions containing multi-component time constants and amplitude constants (Equation (6)).

[0014] Use a nonlinear multi-exponential model to fit the eddy current and extract the amplitude constants used to characterize the multi-exponential model of the eddy current and time constant Then, when the input gradient is a unit step function u(t), the eddy current multi-exponential model (nonlinear eddy current function) of the eddy current field of the magnetic resonance system is expressed as:

[0015]

[0016] In formula (6): m = x, y, z, B 0 , represents the direction (axis) of the induced eddy current source, where B 0 Indicates the direction of the main magnetic field; n = x, y, z, B 0 , represents the direction of the induced eddy current. When m=n, the eddy current multi-exponential model represents the eddy current direct term, and when m≠n, it represents the eddy current cross term; It represents the eddy current field generated by the source in the m direction and changes with time t in the n direction by induction; A represents the amplification factor of the magnetic field generated by the current, which is related to the coil parameters; i = 1, 2, · -, C, represents the i-th exponential component, and the eddy current field can be characterized by C exponential components; represents the eddy current amplitude constant of the i-th exponential component of the induced eddy current field in the n direction by the source in the m direction; represents the eddy current time constant of the i-th exponential component of the induced eddy current field in the n direction generated by the source in the m direction; u(t) represents the form The unit step function of .

[0017] From the perspective of the signal system, the MRI system is a time-invariant system with a linear response. The eddy current field can be expressed by the current i(t) of the input gradient amplifier and the impulse response function. The convolution representation of is:

[0018]

[0019] in, Represents the convolution calculation symbol;

[0020] When A = 1, the eddy current transfer function can be obtained by Laplace transform.

[0021]

[0022] Among them, n e The number of exponential components of the eddy current transfer function is represented by n e exponential components to characterize the eddy current transfer function; s is the complex frequency; I(s) is the image function of the current i(t); Eddy current field The image function of

[0023] 2) establishing a relationship between a magnetic resonance eddy current transfer function and a digital gradient pre-enhancement unit transfer function; the magnetic resonance eddy current system includes a direct eddy current system and a cross-term eddy current system, and the digital gradient pre-enhancement unit includes a digital gradient direct pre-enhancement unit and a digital gradient cross-term pre-enhancement unit;

[0024] According to the nonlinear eddy current function and eddy current transfer function that vary with time in each direction of the eddy current, the magnetic resonance eddy current system transfer function corresponding to each direction of the linear time-invariant MRI system is calculated (Equation (9)), and the relationship between the digital gradient pre-enhancement unit transfer function and the magnetic resonance eddy current transfer function is established (Equation (12)).

[0025] For an ideal MRI system that does not generate eddy currents, the input gradient current should be completely converted into the output gradient field, and the transfer function of the system is equal to 1. For an MRI system that generates eddy currents, when the eddy current direction is the same as the gradient direction, the transfer function of the straight eddy current system is:

[0026]

[0027] in, is the direct eddy current transfer function, is the transfer function of the direct eddy current system;

[0028] The relationship between the magnetic resonance direct eddy current system transfer function and the digital gradient direct pre-enhancement unit transfer function established by the digital gradient pre-enhancement eddy current compensation process is expressed as follows:

[0029]

[0030] in, is the transfer function of the direct pre-enhancement unit in the m direction;

[0031] The cross-term pre-enhancement unit transfer function is:

[0032]

[0033] in, is the transfer function of the cross-term pre-enhancement unit in the m-direction to the n-direction, and They are the transfer function of the eddy current system in the n-direction direct term and the transfer function of the eddy current system in the m-direction cross term to the n-axis respectively;

[0034] 3) according to the digital gradient cross-term pre-enhancement unit transfer function and the direct-term pre-enhancement unit transfer function, respectively calculate the amplitude constant and time constant of the digital gradient cross-term pre-enhancement unit transfer function and the direct-term pre-enhancement unit transfer function in each direction of the eddy current;

[0035] 31) According to the digital gradient cross-term pre-enhancement unit transfer function, the amplitude constant and time constant of the digital gradient cross-term pre-enhancement unit transfer function in each direction of the eddy current are calculated;

[0036] The present invention uses a quantitative solution method to calculate the x, y, z directions and the main magnetic field B 0 The amplitude constant and time constant of the transfer function of the digital gradient direct term pre-enhancement unit in the direction are obtained by fitting calculation, and then the amplitude constant and time constant of the transfer function of the digital gradient cross term pre-enhancement unit in each direction are obtained by fitting calculation.

[0037] 31) The calculation process of the amplitude constant and time constant of the digital gradient cross-term pre-enhancement unit transfer function is as follows:

[0038] 311) expressing the gradient current after the cross-term pre-enhancement unit in the form of a multi-component exponential function;

[0039] The transfer function of the cross-term pre-enhancement unit obtained by direct calculation is complex. Consider simplifying it so that the gradient current after the cross-term pre-enhancement unit can also be expressed in the form of a multi-component exponential function:

[0040]

[0041] in, and are the amplitude constant and time constant of the cross-term pre-enhancement unit transfer function from m to n, respectively. The cross-term pre-enhancement unit transfer function is expressed as It is characterized by an index component;

[0042] 312) placing a cross-term pre-enhancement unit before the direct-term pre-enhancement unit to obtain a representation of the gradient current after passing through the cross-term pre-enhancement unit;

[0043] Formula (13) shows that the cross-term pre-enhancement unit transfer function is related to the three sets of magnetic resonance eddy current system transfer functions. Formula (14) gives the transfer function H of the magnetic resonance eddy current system with similar form under Laplace transform. e mn (s) and cross-term pre-enhancement unit transfer function Therefore, the amplitude constant and time constant of the cross-term pre-enhancement unit transfer function can be obtained by model fitting. At this time, the gradient current I m (s) becomes after the cross-term pre-enhancement unit:

[0044]

[0045] in, represents the inverse Laplace transform, represents the gradient current after the cross-term pre-enhancement unit;

[0046] 32) calculating the amplitude constant and time constant of the digital gradient direct term pre-enhancement unit transfer function in each direction of the eddy current through the digital gradient direct term pre-enhancement unit transfer function;

[0047] The present invention provides a method for obtaining the amplitude constant and the time constant of a direct pre-enhancement unit transfer function by direct calculation.

[0048] 321) Amplitude constant of the direct pre-enhancement unit transfer function Gradient pre-enhancement time constant and eddy current amplitude constant Eddy current time constant The relationship is derived by establishing the following model:

[0049]

[0050] The direct pre-enhancement unit transfer function is actually the inverse of the magnetic resonance eddy current system transfer function, which can be further written as follows:

[0051]

[0052] in The transfer function of the direct pre-enhancement unit in the m direction is expressed as It is characterized by an index component.

[0053] 322) The calculation of the direct pre-enhancement unit transfer function is as follows: Based on the measured eddy current amplitude constant and time constant Calculate the polynomial parameters, where c k It can be obtained by iteration:

[0054]

[0055] In this way, starting from n=1, the corresponding iteration parameters are calculated by continuously increasing n. Finally, when n=n PE mm When c k Parameter, d k The parameter can be obtained by n=n PE mm c k Parameters to determine:

[0056]

[0057] Indication command When n=n PE mm c k Parameters, combined with the above c k Parameter calculation formula (18) can be obtained The calculation formula is:

[0058]

[0059] Similarly, when i is determined, the corresponding iterative parameters are calculated by continuously increasing n starting from n=1 Finally, when n=n PE mm When , we get Parameters, calculated according to the above formula to get d k Parameters, the time constant of the direct pre-enhancement unit transfer function is obtained by taking the root of the following polynomial

[0060]

[0061] After determining the time constant, which is the root of the polynomial, the amplitude constant of the direct pre-enhancement unit transfer function can be further obtained.

[0062]

[0063] Note that when i=0:

[0064]

[0065] The calculated Not all of them are 1 as previously assumed, so the amplitude constant of the direct pre-enhancement unit transfer function calculated needs to be Normalize.

[0066] 4) Verify the obtained digital gradient pre-enhancement unit transfer function amplitude constant and time constant (i.e., eddy current compensation effect) by simulation method;

[0067] Since the real gradient is not an ideal step function and has a certain rise time and fall time, after obtaining the amplitude constant and time constant of the digital gradient pre-enhancement unit transfer function based on the above steps, the present invention proposes a simulation method, in which the input current waveform, the digital gradient pre-enhancement unit transfer function and the nonlinear eddy current function are discretized, and MATLAB is used to simulate the transfer function of the magnetic resonance eddy current system to obtain the pre-enhanced gradient, which is compared with the ideal gradient waveform to verify the eddy current compensation effect.

[0068] 5) The parameters (amplitude constant and time constant) of the verified digital gradient pre-enhancement unit transfer function can be further verified in real life. The current passes through the gradient coil and then through the magnetic resonance system to obtain the actual magnetic resonance system gradient.

[0069] 6) In specific implementation, the present invention also proposes a magnetic resonance imaging gradient system that implements a digital gradient pre-enhancement eddy current compensation method, which is composed of a gradient waveform generator and a gradient coil composed of a gradient power amplifier and a magnet part, as well as analog circuit parts such as a digital analog conversion (DAC) device. The gradient waveform generator includes a gradient calculation module; the gradient calculation module of the gradient waveform generator includes a direct pre-enhancement unit and a cross-term pre-enhancement unit. In order to reduce the number of cross-term pre-enhancement units in each direction and reduce the complexity of system design, the present invention sets the cross-term pre-enhancement unit before the direct pre-enhancement unit. After receiving the gradient waveform control instruction of the pulse sequence generator, the gradient waveform generator calculates and outputs the three gradient directions of x, y, and z or the main magnetic field B through the gradient calculation module. 0 The digital gradient data of the direction is generated by the DAC device to generate an analog gradient waveform voltage, which is then amplified to a suitable current by the gradient power amplifier and finally input to the gradient coil in the corresponding direction to generate a gradient magnetic field. The direct pre-enhancement unit transfer function of the target axis to the target axis and the target axis to the non-target axis and B are calculated quickly and in real time through the programmable logic device (Field Programmable Gate Array, FPGA). 0The transfer function of the cross-term pre-enhancement unit in the direction can respectively obtain the current after passing through the direct-term pre-enhancement unit and the current after passing through the cross-term pre-enhancement unit. The two types of currents are added as the gradient pre-enhancement current of the target axis to compensate the magnetic resonance imaging gradient system.

[0070] Through the above steps, the digital gradient pre-enhancement eddy current compensation of the ultra-high field nuclear magnetic resonance imaging system can be realized.

[0071] The technical solution of the present invention has the following advantages:

[0072] 1. The eddy current measurement method adopted in the present invention does not require additional hardware, and the nonlinear eddy current function (Formula 6) can be obtained based on the magnetic resonance signal.

[0073] 2. The transfer function of the magnetic resonance eddy current system can be calculated based on the nonlinear eddy current function (Equation 9). By establishing the relationship between the transfer function of the magnetic resonance eddy current system and the transfer function of the digital gradient pre-enhancement unit (Equation (12)), the corresponding relationship between the pre-enhancement parameters and the amplitude and time constant as well as the accurate calculation method are given. This can quickly and accurately calculate the important parameters for realizing digital eddy current compensation of the ultra-high field nuclear magnetic resonance imaging system, avoid the errors caused by iteration in the traditional fitting method, and effectively improve the efficiency and accuracy of the pre-enhancement method for compensating the gradient eddy current of the ultra-high field nuclear magnetic resonance imaging system.

[0074] 3. The digital gradient pre-enhancement method provided by the present invention further compensates for the eddy current cross-term on the basis of using the digital gradient direct-term pre-enhancement unit to compensate for the eddy current direct term. By setting the cross-term pre-enhancement unit before the direct-term pre-enhancement unit, the number of units in each direction is reduced, which can effectively improve the stability of the system. In addition, the present invention uses the same method to compensate for the main magnetic field eddy current B 0 The term is also digitally gradient pre-enhancement compensated.

[0075] 4. The simulation verification method provided by the present invention uses MATLAB to simulate the transfer function of the magnetic resonance eddy current system and the transfer function of the digital gradient pre-enhancement unit to obtain the gradient after pre-enhancement, which can verify the correctness of the amplitude constant and time constant of the transfer function of the digital gradient pre-enhancement unit before actual application, avoiding human errors.

[0076] 5. The present invention uses an FPGA device to implement a gradient calculation module of a gradient waveform generator. By reasonably allocating and using FPGA calculation units, the use of FPGA calculation resources can be reduced. The direct-term pre-enhancement unit and the cross-term pre-enhancement unit are optimized and designed on the FPGA to improve the calculation efficiency, shorten the time consumption of the ultra-high field nuclear magnetic resonance imaging system to compensate for the gradient eddy current, and is suitable for an ultra-high field nuclear magnetic resonance imaging system with rapid gradient switching. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 A diagram of an eddy current measurement method provided by an embodiment of the present invention;

[0078] in, Figure 1 a is a flow chart of an eddy current measurement method provided by an embodiment of the present invention; Figure 1 b is a gradient echo pulse sequence diagram for eddy current measurement provided by an embodiment of the present invention.

[0079] Figure 2 This is a straight-term fitting curve diagram of the z-direction eddy current provided by an embodiment of the present invention.

[0080] Figure 3 A fitting curve diagram of the eddy current cross term in the z-direction to the y-direction provided in an embodiment of the present invention.

[0081] Figure 4 A diagram of a digital gradient pre-enhancement eddy current system provided in an embodiment of the present invention.

[0082] Figure 5 A flow chart of a cross-term gradient pre-enhancement parameter calculation program provided by an embodiment of the present invention.

[0083] Figure 6 A flow chart of a direct gradient pre-enhancement parameter calculation program provided by an embodiment of the present invention.

[0084] Figure 7 A flow chart of a eddy current direct term pre-enhancement compensation simulation program provided by an embodiment of the present invention;

[0085] Figure 8 A flow chart of a simulation program for eddy current cross-term pre-enhancement compensation provided by an embodiment of the present invention;

[0086] Fig. 9 A simulation curve of eddy current direct compensation in the z direction provided by an embodiment of the present invention;

[0087] Fig.10 A simulation curve for compensation of eddy current cross terms in the z direction for the y direction provided by an embodiment of the present invention;

[0088] Fig.11 A physical picture of a gradient calculation module board equipped with FPGA provided in an embodiment of the present invention;

[0089] Fig.12 A basic flow chart of a gradient calculation program provided by an embodiment of the present invention;

[0090] Fig.13 The internal computing unit structure implemented based on FPGA in the embodiment of the present invention; Fig.14 The curve after the z-direction eddy current direct compensation provided by the embodiment of the present invention;

[0091] Fig.15 This is a curve after eddy current compensation for the cross term in the z direction to the y direction provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0092] The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be noted that the embodiments herein are only used to illustrate the implementation steps of the present invention, rather than being specific limitations of the present invention.

[0093] The present invention takes one of the shafts as an example to illustrate the implementation process of the eddy current compensation method proposed in the present invention. Step 1 of the embodiment is the eddy current measurement process:

[0094] like Figure 1 As shown in a, the present invention takes the eddy current measurement process of applying a test gradient echo pulse sequence - collecting magnetic resonance gradient echo signals - extracting phase information - fitting an eddy current multi-exponential model as an example to illustrate the method of using a nuclear magnetic resonance spectrometer to obtain a nonlinear eddy current function;

[0095] Passing current through the gradient coil of the magnetic resonance system can generate a gradient magnetic field. The changing gradient field will induce eddy currents in the conductor structure of the MRI system, which can be expressed as follows through Taylor expansion:

[0096]

[0097] B 0e (t) is the zero-order eddy current term. The zero-order eddy current will affect the main magnetic field B 0 The effect is to produce a frequency shift, also known as B 0 vortex; It is the first-order eddy term. The first-order eddy changes linearly with the spatial distribution and is also called linear eddy; Indicates spatial distance;

[0098] Eddy currents can be measured using gradient echoes in the spectrometer of an ultra-high field MRI system. Figure 1 b describes the gradient echo eddy current measurement pulse sequence. The excited sample produces a magnetic resonance signal that is only affected by the gradient eddy current. A readout gradient is applied to the target axis to obtain the above magnetic resonance signal. The eddy current magnetic field can be calculated based on the phase information contained in the signal. In the MRI system, the relationship between the phase of the magnetic resonance signal and the magnetic field that changes with spatial position and time is:

[0099]

[0100] Where γ is the gyromagnetic ratio, φ 0 It is the initial phase change caused by non-magnetic field factors and is usually regarded as a constant.

[0101] Depend on Figure 1The gradient echo sequence shown in b applies a rectangular RF pulse (hard pulse) with the pulse center time t = t RF , the echo time is TE, then the phase of the magnetic resonance signal affected only by the eddy current generated after the test gradient is turned off can be expressed as:

[0102]

[0103] When TE is small enough, we can get:

[0104] φ e (r,t RF )≈γTE·(B 0e (t RF )+rG e (t RF )) (4)

[0105] In the signal acquisition window, the linear phase difference in the effective signal area is calculated, and then the linear eddy current can be extracted by taking the derivative of the distance r:

[0106]

[0107] φ e (n,t RF ) represents the signal phase of the nth sampling point, SI is the number of sampling points, G r is the maximum value of the readout gradient amplitude, and BW is the imaging bandwidth. RF , we can get the nonlinear eddy current function that varies with time. Use the nonlinear multi-exponential model to fit the eddy current and extract the amplitude constant used to characterize the multi-exponential model of the eddy current. and time constant Then, when the input gradient is a unit step function u(t), the eddy current multi-exponential model of the magnetic resonance system is expressed as:

[0108]

[0109] In formula (6): m = x, y, z, B 0 , represents the direction of the induced eddy current source, where B 0 Indicates the direction of the main magnetic field; n = x, y, z, B o , represents the direction of the induced eddy current. When m=n, the eddy current multi-exponential model represents the eddy current direct term, and when m≠n, it represents the eddy current cross term; It represents the eddy current field generated by the source in the m direction and changes with time t in the n direction by induction; A represents the amplification factor of the magnetic field generated by the current, which is related to the coil parameters; i = 1, 2, .., C, represents the i-th exponential component, and the eddy current field can be characterized by C exponential components; represents the eddy current amplitude constant of the i-th exponential component of the induced eddy current field in the n direction by the source in the m direction; represents the eddy current time constant of the i-th exponential component of the induced eddy current field in the n direction generated by the source in the m direction; u(t) represents the form The unit step function of .

[0110] Taking the z-axis as an example, Table 1 shows the parameters of the direct and cross-term nonlinear eddy current functions in the z-direction, where the measurement process of the direct nonlinear eddy current function is:

[0111] The gradient echo eddy current measurement pulse sequence first applies a test gradient waveform in the z-axis direction. After the test gradient is turned off, the interval time t RF A readout gradient is applied in the z-axis direction, and samples are collected in the z-axis direction. RF The signal at the moment, calculate the phase information in the signal, and continuously increase the interval time t RF The direct nonlinear eddy current function is obtained, Figure 2 To fit the curve graph using a multi-exponential fitting function model;

[0112] The measurement process of the cross-term nonlinear eddy current function is:

[0113] The gradient echo eddy current measurement pulse sequence first applies a test gradient waveform in the z-axis direction. After the test gradient is turned off, the interval time t RF On the x-axis, y-axis and main magnetic field B 0 Apply a readout gradient in the direction, collect the signal of the sample in each direction, calculate the phase information in the signal, and continuously increase the interval time t RF The cross-term nonlinear eddy current function is obtained, Figure 3 To fit the curve graph in the y direction using a multi-exponential fitting function model;

[0114] Table 1 z-direction gradient eddy current parameters

[0115]

[0116] The second step of implementation is the digital gradient pre-enhancement eddy current compensation process:

[0117] From the perspective of the signal system, the MRI system is a time-invariant system with a linear response. The eddy current field can be expressed by the current i(t) of the input gradient amplifier and the impulse response function h of the eddy current system. e The convolution representation of (t) is:

[0118]

[0119] Where A represents the amplification factor of the gradient field and the current input to the gradient amplifier. Represents the convolution calculation symbol; when A = 1, the eddy current transfer function can be obtained by Laplace transform

[0120]

[0121] Among them, n e The eddy current transfer function is represented by n e It is characterized by an index component;

[0122] For an ideal MRI system, the transfer function of the system is equal to 1. For an MRI system that generates eddy currents, when the eddy current direction is the same as the gradient direction, the transfer function of the magnetic resonance direct eddy current system is:

[0123]

[0124] When the eddy current direction is different from the gradient direction, the magnetic resonance cross-term eddy current system transfer function is:

[0125]

[0126] The eddy current amplitude constant obtained by fitting in step 1 and the eddy current time constant Can be used to calculate the digital gradient pre-enhancement unit amplitude constant and time constant Considering the unit step function u(t) as input, the digital gradient pre-enhancement unit model is shown in equation (11):

[0127]

[0128] In formula (11):

[0129] m=x,y,z,B 0 , indicating the direction in which pre-enhancement is applied;

[0130] n=x,y,z,B 0 , represents the direction in which the pre-enhancement is applied. When m is equal to n, it represents the direct term pre-enhancement used to compensate for the eddy current direct term. When m is not equal to n, it represents the cross term pre-enhancement used to compensate for the eddy current cross term.

[0131] It indicates that the pre-enhancement current in the m direction is applied to the n direction and changes with time t;

[0132] i = 1, 2, …, C, represents the i-th exponential component, which is consistent with the corresponding eddy current field;

[0133] represents the pre-enhancement amplitude constant of the i-th exponential component applied in the m direction to the n direction;

[0134] represents the pre-enhancement time constant of the i-th exponential component applied in the m direction to the n direction;

[0135] u(t) represents the unit step function.

[0136] The digital gradient pre-enhancement unit proposed in the present invention is as follows Figure 4 As shown, the digital gradient pre-enhancement unit amplitude constant Time constant and the eddy current function amplitude constant Time constant The relationship is derived by establishing the following model:

[0137] The relationship between the transfer function of the magnetic resonance direct eddy current system and the transfer function of the digital gradient direct pre-enhancement unit established through the digital gradient pre-enhancement eddy current compensation process is:

[0138]

[0139] Figure 4 The digital gradient eddy current compensation method shown in the figure can reduce the number of units in each direction, reduce the complexity of the pre-enhancement system, and improve the stability of the pre-enhancement system by setting a cross-term pre-enhancement unit before the straight-term pre-enhancement unit. For example, if the x-axis affects the y-axis, setting the cross-term pre-enhancement unit in the y-direction requires 2 units, and if four directions are considered, a total of 8 units are required. If it is set in the x-direction, a total of 4 units are required if four directions are considered. Figure 5 This is the flow chart of the calculation of the eddy current cross-term pre-enhancement unit parameters. The calculation process is as follows:

[0140] exist Figure 4 In the digital gradient eddy current compensation method shown in FIG. , the transfer function of the digital gradient cross-term pre-enhancement unit is:

[0141]

[0142] Consider simplifying it so that the gradient current after the cross-term pre-enhancement unit can also be expressed in the form of a multi-component exponential function:

[0143]

[0144] Formula (13) shows that the cross-term pre-enhancement unit transfer function is related to the three sets of magnetic resonance eddy current system transfer functions. Formula (14) gives the eddy current transfer function H with similar form under Laplace transform. e mn (s) and the cross-term pre-enhancement unit transfer function H PE mn(s), so the amplitude constant and time constant of the cross-term pre-enhancement unit can be obtained by model fitting. At this time, the gradient current becomes:

[0145]

[0146] In traditional methods, the use of fitting models for calculation is easily limited by real-time calculation, and there is a problem that the cumulative error gradually increases with the number of iterations. For digital gradient direct pre-enhancement units with high accuracy and rate requirements, the direct pre-enhancement unit transfer function is only related to the nonlinear eddy current function. Therefore, the present invention proposes a method for obtaining the direct pre-enhancement unit amplitude constant and time constant by direct calculation. Time constant and the amplitude constant of the nonlinear eddy current function Eddy current time constant The relationship is derived by establishing the following model:

[0147]

[0148] Therefore, the transfer function of the digital gradient direct pre-enhancement unit is actually the inverse of the transfer function of the magnetic resonance eddy current system, which can be further written in a form similar to equation (16):

[0149]

[0150] in Figure 6 This is a flow chart for the calculation of the parameters of the direct pre-enhancement unit, based on the measured nonlinear eddy current amplitude constant and time constant The polynomial parameters can be calculated, where c k It can be obtained by iteration:

[0151]

[0152] In this way, starting from n=1, the corresponding iteration parameters are calculated by continuously increasing n. Finally, when n=n PE mm When c k Parameter, d k The parameter can be obtained by n=n PE mm c k Parameters to determine:

[0153]

[0154] Indication command When n=n PE mm c k Parameters, combined with the above c k Parameter calculation formula (18) can be obtained The calculation formula is:

[0155]

[0156] Similarly, when i is determined, the corresponding iterative parameters are calculated by continuously increasing n starting from n=1 Finally, when n=n PE mm When , we get Parameters, calculated according to the above formula to get d k Parameters, the time constant of the direct pre-enhancement unit is obtained by taking the root of the following polynomial

[0157]

[0158] After determining the time constant, which is the root of the polynomial, the amplitude constant of the direct pre-enhancement can be further obtained:

[0159]

[0160] Note that when i=0:

[0161]

[0162] The calculated Not all of them are 1 as previously assumed, so the calculated direct pre-enhancement unit amplitude constant needs to be Normalize.

[0163] Taking the z-axis and y-axis as examples, the above process is implemented through the program. Table 2 shows the amplitude constant and time constant of the cross-term pre-enhancement unit in the z-direction to the y-direction. The calculation process is:

[0164] The first step is to obtain the amplitude constants of the zz and yy direct eddy current functions through fitting. and time constant The magnitude constant of the cross-term eddy current function in the z-direction to the y-direction and time constant These parameters are used as input parameters for the program calculation, and the zz and yy magnetic resonance eddy current direct system transfer functions are constructed according to equations (9) and (10): and the zy magnetic resonance eddy current cross-term system transfer function Finally, the zy cross-term pre-enhancement unit transfer function is calculated according to formula (13): According to equations (14) and (15), the step response current of the cross-term pre-enhancement unit is calculated: And the cross-term pre-enhancement unit parameters are obtained by fitting and

[0165] Table 2 z-direction gradient pre-enhancement parameters

[0166]

[0167] Taking the z-axis as an example, Table 2 shows the amplitude constant and time constant of the direct pre-enhancement unit transfer function in the z-direction. The calculation process can be briefly described as follows:

[0168] The first step is to obtain the amplitude constant of the zz direct eddy current function through fitting. and time constant According to formula (17), the direct pre-enhancement unit transfer function can be obtained, and c can be calculated according to formula (18), (19), (20) respectively. k ,d k and c k i Parameter iteration matrix. According to formula (21), the coefficient is d k The zero point of the polynomial function is the time constant of the direct pre-enhancement unit After determining the time constant, the amplitude constant of the direct pre-enhancement unit can be further obtained according to formula (22):

[0169] It should be noted that the amplitude constant needs to be obtained from equation (23) Normalize.

[0170] Implementation step three is the simulation process of digital gradient pre-enhancement eddy current compensation effect:

[0171] Since the real gradient is not an ideal step function and has a certain rise time and fall time, before the pre-enhancement parameters are input into the multiplier of the digital gradient eddy current compensation subsystem, in order to verify the effectiveness of the eddy current compensation effect of the pre-enhancement gradient system, the present invention proposes a simulation method.

[0172] The digital gradient pre-enhancement unit proposed in the present invention is discretized, and the current after passing through the direct pre-enhancement unit is the sum of the original current and the pre-enhancement current:

[0173]

[0174] In formula (24):

[0175] N represents the discretized ordinal number;

[0176] ΔT represents the update time of the digital gradient waveform;

[0177] Exponential pre-enhancement time parameters set to simplify digital signal system calculations;

[0178] The pre-enhanced part of the current can be expressed in the discrete domain as:

[0179]

[0180] Performing Z transform on equation (25) yields the transfer function of the discrete pre-enhancement unit, as shown in equation (26):

[0181]

[0182] Then perform an inverse Z transform on equation (26) to obtain the differential equation required by the digital signal system, as shown in equation (27):

[0183]

[0184] The total current after superimposing the original current is:

[0185]

[0186] Similarly, the total cross-term current can be obtained as:

[0187]

[0188] For the linear gradient, taking the x direction as an example, the total gradient after the digital gradient pre-enhancement unit is:

[0189]

[0190] B 0 The total gradient output after the gradient pre-enhancement unit in the direction is:

[0191]

[0192] It can be proved that the discrete signal system shown in formula (24) is a linear time-invariant system. Therefore, for different gradient input waveforms, the difference equation (27) determined by the system function of formula (26) can obtain a suitable output. The number of subsystems can also be expanded according to the number of components of the eddy current multi-exponential model, and the outputs of each subsystem can be superimposed as the total output.

[0193] After determining the parameters of the gradient pre-enhancement unit, the above differential equation can be implemented in MATLAB software. Taking the coaxial as an example, the magnetic resonance eddy current system is discretized in the same way to obtain a differential equation with a similar form but different coefficients:

[0194]

[0195] Therefore, the eddy current difference equation can be expressed by equation (32) and used as the eddy current system in the simulation program.

[0196] The eddy current compensation simulation proposed in the present invention can verify the parameters of the digital gradient pre-enhancement unit before actual application. The eddy current compensation simulation program flow chart is as follows: Figure 7 and Figure 8 The z-direction direct compensation simulation process can be briefly described as follows:

[0197] First, the parameters of the magnetic resonance eddy current system and the digital gradient pre-enhancement unit are input, and then the initial gradient waveform is set. The differential equations calculated by the pre-enhancement unit parameters of different components are respectively inserted, and the gradient output of each component is calculated respectively, and the total gradient output is superimposed. Then, the total gradient output is used as the input of the differential equation of the magnetic resonance eddy current system, and the gradient output of each component is calculated. The outputs of each component are superimposed, and finally the eddy current compensation simulation results are obtained. Fig. 9 This is the simulation result diagram. The results show that the gradient after the direct pre-enhancement unit is consistent with the ideal gradient, which verifies the feasibility of this method.

[0198] The process of simulating the cross-term eddy current compensation in the z direction to the y direction can be briefly described as follows:

[0199] First, input the z-axis current, cross-term eddy current system transfer function Cross-term pre-enhancement unit transfer function Direct eddy current system transfer function Parametric, direct pre-enhancement unit transfer function Calculate the coefficients of the differential equations corresponding to each part respectively. The z-axis current passes through the cross-term pre-enhancement unit differential equation to obtain the pre-enhancement current, which is superimposed on the y-axis to offset the cross-term eddy current of the z-axis to the y-axis. Therefore, the pre-enhancement current passes through the y-axis direct eddy current system. The differential equation is used to obtain the cross-term pre-enhancement gradient waveform. Then, the outputs of the pre-enhancement units of each component are superimposed to obtain the eddy current compensation simulation results. Fig.10 This is a simulation result diagram. The results show that the current after passing through the cross-term pre-enhancement unit can effectively compensate for the cross-term eddy current.

[0200] Step 4 of the embodiment is to implement the digital gradient pre-enhancement eddy current compensation FPGA:

[0201] In order to implement the digital gradient pre-enhancement system in FPGA and reduce the difficulty of developing the actual FPGA program, the present invention uses the Xilinx company's System Generator associated with MATLAB's Simulink tool, which is consistent in design logic, to implement the system module design. The digital gradient pre-enhancement unit is integrated in the gradient waveform calculation module and implemented based on FPGA. The model of FPGA is EP2C50F484I8 of the Cyclone series of Altera company, and the FPGA program is written using the hardware description language VHDL. Fig.11 The figure shows the actual gradient calculation module board equipped with the above FPGA.

[0202] Different from the eddy current compensation simulation program, writing an FPGA program to implement a digital gradient pre-enhancement unit requires focusing on timing design and effective use of device resources. Therefore, the present invention optimizes the use of device resources, saves computing time, and accurately and quickly implements pre-enhancement gradient calculation and waveform generation. Fig.12 The basic flow of the gradient calculation program is shown, in which the time for implementing the gradient pre-enhancement calculation is less than 1 microsecond. From the perspective of practical implementation, the gradient pre-enhancement should be performed after the gradient calculation module completes reading the gradient waveform data and calculating the rotation matrix transformation, and before completing the parallel-to-serial conversion of the calculated gradient waveform data.

[0203] In the gradient calculation program, the initialization execution mainly includes: clock initialization, gradient pre-enhancement clearing, dual-port SRAM initialization configuration, FPGA_RAM working mode configuration, waveform output emergency shutdown control configuration, and indicator light control configuration. Clock initialization divides the system clock through the counter to generate 2, 4, and 8 divided clocks; gradient pre-enhancement unit initialization clears all data registers used by the pre-enhancement unit calculation to prepare for data update.

[0204] The dual-port SRAM is divided into the FPGA side and the DSP side. The FPGA side configures the SRAM to the "read" working mode, and the port output configuration is enabled. The "read" or "write" of the SRAM on the DSP side is controlled by the DRW signal, and the port output configuration is enabled. When DWTRB=0 and the output address is 0x500000, the SRAM chip select is enabled. When the FPGA_RAM working mode is configured as "read", the address is sent to the FPGA_RAM by the DSP or by other registers in the FPGA, and then the required data in the FPGA_RAM is read out; when configured as "write", the write operation is mainly to write the rotation matrix data to the FPGA_RAM by the DSP, and the written address and data are sent to the FPGA through the data bus DD by the DSP. The waveform emergency shutdown configuration is mainly to configure the waveform output enable port to control the opening and closing of the waveform output according to the situation. The DSP sends the instruction address and generates the corresponding gate signal, and sends the control signal to the RENA of the FPGA and outputs it. The control configuration of the indicator light is sent by the DSP to generate a gate signal, send the control signal to the FPGA LED [2..1] and output it to control the state of the indicator light LED [2..1]. The remaining 4 indicator lights LED [6..3] are controlled by 4 waveform status words.

[0205] The gradient waveform data reading part mainly performs the reading of rotation matrix data, the reading of logic waveform first address and address length, the reading of logic waveform gain, the reading of DC bias parameters, the reading of gradient pre-enhancement unit parameters, and the reading of some counter configuration parameters.

[0206] To read the rotation matrix data, the DSP needs to send the instruction address and generate the corresponding gating signal, read the rotation matrix number, perform the corresponding calculation using the rotation matrix number, obtain the address where the matrix data is stored in FPGA_RAM, and finally use the counter to read out the data at the address.

[0207] To read the logic waveform related data, the DSP needs to send the corresponding instruction address and generate the corresponding gating signal, and then the bus DD sends the logic waveform first address and address length reading, logic waveform gain reading, DC bias parameter reading, and the cycle parameter of the global counter GLB_DC to the FPGA. Similarly, to read the gradient pre-enhancement unit parameters, the DSP also sends the corresponding instruction address and generates the corresponding gating signal, and then the bus DD sends the digital gradient pre-enhancement unit amplitude constant, time constant, and scale parameter data to the FPGA.

[0208] The gradient waveform calculation includes rotation matrix transformation and gradient pre-enhancement unit parameter calculation. The rotation matrix transformation mainly needs to read the logical gradient waveform data matrix from the SRAM, multiply it by the waveform gain, and then perform matrix multiplication with the rotation matrix to calculate the physical gradient waveform matrix data. The gradient pre-enhancement unit calculation uses the physical gradient waveform data, the pre-enhancement unit amplitude constant and the time constant to calculate the gradient waveform in the form of a single component exponential, and superimposes the calculation result on the original physical gradient waveform data, and finally adds the DC bias required to achieve the first-order uniform field. The parallel-to-serial conversion of the gradient waveform data uses a serial shift register and a shift counter to realize the serial output of the final parallel physical gradient waveform data. The shift clock uses the 2-frequency clock of the system clock, and transmits the data to the DAC through the corresponding timing control.

[0209] Since the present invention uses a 16-bit DAC device, the gradient waveform data is represented by a 16-bit signed fixed-point number. The highest bit of a 16-bit signed fixed-point number is the sign bit, and the actual representation range is -2 15 To 2 15 -1. The pre-enhancement amplitude constant or digital pre-enhancement time constant will be temporarily expanded to more digits during gradient waveform calculation, and finally truncated to 16-bit fixed-point representation according to requirements when output. In practice, the spectrometer software will convert the pre-enhancement unit amplitude constant expressed as a percentage of the input decimal number by dividing it by 100 to a proportional representation, and then process it into a 16-bit signed fixed-point number; the pre-enhancement unit time constant will first be processed into an exponential function form under a 32-bit unsigned integer.

[0210] The gradient calculation module uses FPGA as the main processor to implement the calculation process of the gradient pre-enhancement unit. The gradient pre-enhancement unit includes the direct pre-enhancement units in the three directions of X, Y, and Z, the first-order cross-term pre-enhancement units in the three directions, and the B 0 The pre-enhancement unit is characterized by large amount of calculation and similar calculation process. Therefore, FPGA is selected as the main processor to realize large amount of data calculation in a short time by using its multi-module parallel calculation capability. Fig.13 The structure of the internal computing unit of FPGA is shown. There are 14 computing units in FPGA, and 4 computing units are used for the related calculations in the three directions of X, Y and Z. 0 The relevant calculation uses two computing units. Different parameters are input into the computing units in a pipeline manner, and the output results of each computing unit are accumulated as needed to obtain the final calculation result.

[0211] Table 3 Comparison of the RMS value of the amplitude ratio before and after eddy current compensation

[0212]

[0213] In order to test the function of the digital gradient pre-enhancement unit realized by hardware, the output end of the gradient calculation module board, which should usually be connected to the gradient power amplifier, is connected to an oscilloscope, and the gradient waveform voltage signal directly output by the gradient calculation module board is observed on the oscilloscope.

[0214] Fig.14 and Fig.15 The eddy current diagrams of the z-direction straight eddy current and the z-direction cross-term eddy current after compensation by the pre-enhancement unit are shown respectively, and Table 3 shows the root mean square (RMS) of the eddy current amplitude ratio data calculated before and after compensation. The results show that the gradient pre-enhancement method proposed in the present invention can effectively reduce the eddy current, and the measured eddy current compensation effect exceeds 50%.

Claims

1. A digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system, comprising the following steps: 1) Obtain the nonlinear eddy current function and eddy current transfer function of the eddy current in each direction with time; the eddy current transfer function includes the direct eddy current transfer function and the cross eddy current transfer function; each direction includes the target axis direction x, y, z and the main magnetic field direction B 0 ; 11) Obtaining nonlinear eddy current function by measuring eddy current through magnetic resonance signals; include: 111) using the gradient echoes with different delay times after the ultra-high field nuclear magnetic resonance imaging system turns off the gradient pulse as an eddy current measurement pulse sequence, presetting the eddy current measurement pulse sequence into the ultra-high field nuclear magnetic resonance imaging system spectrometer, and the excited sample generates magnetic resonance signals in all directions that vary with the delay time; 112) applying gradients to the coils in various directions, obtaining magnetic resonance signals respectively, analyzing and obtaining nonlinear eddy currents in various directions, and obtaining the curves of the nonlinear eddy currents in various directions changing with time; 113) The magnetic resonance eddy current includes a direct eddy current and a cross-term eddy current; a nonlinear multi-exponential model is used to fit the magnetic resonance eddy current, and an amplitude constant and a time constant used to characterize the eddy current multi-exponential model are extracted; an exponential function containing multi-component time constants and amplitude constants is used to represent the nonlinear eddy current function; 12) Then obtain the eddy current transfer function s is the complex frequency; 2) establishing a relationship between a magnetic resonance eddy current transfer function and a digital gradient pre-enhancement unit transfer function; the digital gradient pre-enhancement unit includes a digital gradient direct term pre-enhancement unit and a digital gradient cross term pre-enhancement unit; The relationship between the magnetic resonance direct and cross-term eddy current system transfer functions and the digital gradient direct and cross-term pre-enhancement unit transfer functions established through the digital gradient pre-enhancement eddy current compensation process, The transfer function of the direct pre-enhancement unit is expressed as: The cross-term pre-enhancement unit transfer function is: Wherein, m represents the direction of the induced eddy current source; n represents the direction in which the induced eddy current is generated; when m=n, the nonlinear eddy current function represents the eddy current direct term, and when m≠n, it represents the eddy current cross term; and They are the transfer function of the direct term pre-enhancement unit in the m direction and the transfer function of the cross term pre-enhancement unit in the m direction to the n direction, and They are the transfer function of the eddy current system in the n-direction direct term and the transfer function of the eddy current system in the m-direction cross term to the n-axis respectively; 3) According to the digital gradient cross-term pre-enhancement unit transfer function and the direct-term pre-enhancement unit transfer function, the amplitude constant and time constant of the digital gradient cross-term pre-enhancement unit transfer function and the direct-term pre-enhancement unit transfer function in each direction of the eddy current are calculated respectively; including: 31) According to the digital gradient cross-term pre-enhancement unit transfer function, the amplitude constant and time constant of the digital gradient cross-term pre-enhancement unit transfer function in each direction of the eddy current are calculated; the calculation process includes: 311) expressing the gradient current after the cross-term pre-enhancement unit in the form of a multi-component exponential function; The gradient current after the cross-term pre-enhancement unit is expressed in the form of a multi-component exponential function: in, and are the amplitude constant and time constant of the transfer function of the cross-term pre-enhancement unit in the m-direction to the n-direction, respectively; The cross-term pre-enhancement unit transfer function is expressed as It is characterized by an index component; 312) placing a cross-term pre-enhancement unit before the direct-term pre-enhancement unit, obtaining the amplitude constant and time constant of the transfer function of the cross-term pre-enhancement unit by model fitting, and then obtaining the representation of the gradient current after passing through the cross-term pre-enhancement unit; 32) Calculate the amplitude constant and time constant of the digital gradient direct term pre-enhancement unit transfer function in each direction of the eddy current through the digital gradient direct term pre-enhancement unit transfer function; including: 321) The direct pre-enhancement unit transfer function is expressed as: in, The transfer function of the direct pre-enhancement unit in the m direction is expressed as It is characterized by an index component; is the amplitude constant of the direct pre-enhancement unit transfer function; is the gradient pre-enhancement time constant; 322) calculates the direct pre-enhancement unit transfer function, specifically: According to the measured eddy current amplitude constant and the eddy current time constant The polynomial parameters are calculated, where c is obtained by iteration k : Starting from n=1, calculate the corresponding iteration parameters by increasing n Finally, when n=n PE mm When c k ; Then through n = n PE mm c k To determine d k : Indication command When n=n PE mm c k parameter; The calculation is expressed as: When i is determined, the corresponding iterative parameters are calculated by continuously increasing n starting from n=1 Finally, when n=n PE mm When , we get According to the above formula, we can calculate d k Parameters, by taking the root of the following polynomial, the time constant of the direct pre-enhancement unit transfer function is obtained The roots of the polynomial are the time constants; According to the obtained time constant, the amplitude constant of the direct pre-enhancement unit transfer function is further obtained. It is expressed as: Calculate the amplitude constant when i = 0 The value of the direct pre-enhancement unit transfer function is then calculated to Normalize; The obtained digital gradient pre-enhancement unit transfer function amplitude constant and time constant are verified by simulation method; specifically, after discretizing the input current waveform, the digital gradient pre-enhancement unit transfer function and the nonlinear eddy current function, MATLAB is used to simulate the transfer function of the magnetic resonance eddy current system to obtain the pre-enhancement gradient, which is compared with the ideal gradient waveform to verify the eddy current compensation effect; Further physical verification can be carried out, where the current passes through the gradient coil and then through the magnetic resonance system to obtain the actual gradient of the system; Through the above steps, the digital gradient pre-enhancement eddy current compensation of the ultra-high field nuclear magnetic resonance imaging system can be realized.

2. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 1, Its characteristics are: Specifically, the programmable logic device FPGA is used to quickly and in real time calculate the direct pre-enhancement unit transfer function of the target axis to the target axis and the target axis to the non-target axis and B 0 The cross-term pre-enhancement unit transfer function in the direction is used to obtain the current after passing through the direct-term pre-enhancement unit and the current after passing through the cross-term pre-enhancement unit respectively; The two types of currents are added together as the gradient pre-enhancement current of the target axis to compensate the magnetic resonance imaging gradient system.

3. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 1, Its characteristics are: In step 11), the eddy current field of the ultra-high field nuclear magnetic resonance imaging system is used to calculate the current i(t) of the input gradient amplifier and the impulse response function The convolution is expressed as formula (7): Where i(t) is the current; is the impulse response function.

4. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 3, Its characteristics are: In step 113), an exponential function containing multiple component time constants and amplitude constants is used to represent the nonlinear eddy current function as follows: Wherein, m represents the direction of the induced eddy current source; n represents the direction in which the induced eddy current is generated; when m=n, the nonlinear eddy current function represents the eddy current direct term, and when m≠n, it represents the eddy current cross term; represents the eddy current field generated by the source in the m direction and changes with time t in the n direction by induction; A represents the amplification factor of the magnetic field generated by the current; i = 1, 2, ..., C, represents the i-th exponential component, and the eddy current field is characterized by C exponential components; represents the eddy current amplitude constant of the i-th exponential component of the induced eddy current field in the n direction by the source in the m direction; It represents the eddy current time constant of the i-th exponential component of the induced eddy current field in the n direction generated by the source in the m direction; u(t) is the unit step function; When A = 1, the eddy current transfer function is obtained It is expressed as: Among them, n e is the number of exponential components of the eddy current transfer function; s is the complex frequency; I(s) is the image function of the current i(t); Eddy current field The image function.

5. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 4, Its characteristics are: In step 2), for the MRI system that generates eddy currents, when the eddy current direction is the same as the gradient direction, the direct eddy current system transfer function is: in, is the direct eddy current transfer function, is the transfer function of the direct eddy current system.

6. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 5, Its characteristics are: Gradient current I m (s) is expressed as follows after the cross-term pre-enhancement unit: in, represents the inverse Laplace transform, represents the gradient current after the cross-term pre-enhancement unit.

7. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 1, Its characteristics are: The simulation method in step 4) includes: 41) The digital gradient pre-enhancement unit is discretized, and the current after the direct pre-enhancement unit is the sum of the original current and the pre-enhancement current, which is expressed as: Where: N represents the discretized ordinal number; ΔT represents the update time of the digital gradient waveform; Exponential pre-enhancement time parameters set to simplify digital signal system calculations; 42) The pre-enhancement part of the current is expressed in the discrete domain as: 43) Perform Z transform on equation (25) to obtain the transfer function of the discrete pre-enhancement unit, as shown in equation (26): 44) Then perform an inverse Z transform on equation (26) to obtain the differential equation required by the digital signal system, as shown in equation (27): 45) The total current after superimposing the original current is: 46) The total cross-term current is: 47) For the linear gradient, taking the x direction as an example, the total gradient after the digital gradient pre-enhancement unit is: 48)B 0 The total gradient output after the gradient pre-enhancement unit in the direction is: After determining the parameters of the gradient pre-enhancement unit, the above difference equations were implemented using the MATLAB application.

8. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 7, Its characteristics are: The simulation process of direct compensation in z direction is as follows: First, the parameters of the magnetic resonance eddy current system and the digital gradient pre-enhancement unit are input; then the initial gradient waveform is set, and the differential equations calculated by the pre-enhancement unit parameters of different components are respectively inserted, and the gradient output of each component is calculated respectively, and the total gradient output is superimposed; then the total gradient output is used as the input of the differential equation of the magnetic resonance eddy current system, the gradient output of each component is calculated, and the outputs of each component are superimposed, and finally the eddy current compensation simulation results are obtained.

9. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system as claimed in claim 7, Its characteristics are: The simulation process of eddy current compensation for cross-terms in the z direction and the y direction is as follows: Firstly, input the z-axis current, the cross-term eddy current system transfer function, the cross-term pre-enhancement unit transfer function, the direct-term eddy current system transfer function parameters, and the direct-term pre-enhancement unit transfer function, and calculate the coefficients of the corresponding differential equations of each part respectively; The z-axis current is passed through the cross-term pre-enhancement unit differential equation to obtain the pre-enhancement current, which is superimposed on the y-axis to offset the cross-term eddy current of the z-axis to the y-axis; The pre-enhancement current passes through the y-axis direct eddy current system differential equation to obtain the cross-term pre-enhancement gradient waveform; then the outputs of the pre-enhancement units of each component are superimposed to obtain the eddy current compensation simulation result.

10. The digital gradient pre-enhancement eddy current compensation method for an ultra-high field nuclear magnetic resonance imaging system according to claim 1, Its characteristics are: The method is used to realize a digital gradient pre-enhancement system in FPGA; specifically, Xilinx's SystemGenerator is associated with MATLAB's Simulink tool, and a digital gradient pre-enhancement unit is integrated into a gradient waveform calculation module based on FPGA; the FPGA model is EP2C50F484I8 of Altera's Cyclone series, and the FPGA program is written in hardware description language VHDL.

Images