Hybrid multi-coil collaborative optimization low-field NMR automatic shimming method and system

Abstract

The invention provides a low-field NMR automatic shimming method and system for hybrid multi-coil collaborative optimization. The system comprises an optimization strategy control unit, and a coarse shimming unit, a fine shimming unit, an FID processing and evaluation index calculation unit, a current fitting and optimization unit and a shimming execution and signal acquisition unit which are respectively connected with the optimization strategy control unit. The optimization strategy control unit is used for controlling the overall operation of the system and managing the switching and matching of the coarse homogenizing unit and the fine homogenizing unit; the coarse homogenizing unit and the fine homogenizing unit are used for processing FID signals of a nuclear magnetic resonance spectrometer hardware system, assistance can be achieved through the FID processing and evaluation index calculation unit, and the FID processing and evaluation index calculation unit is used for converting collected original FID into numerical indexes capable of being used for quantifying magnetic field uniformity; the current fitting and optimizing unit is used for providing a basis for each shimming coil to analyze and solve the optimal current, and the shimming execution and signal acquisition unit is used for being connected with a lower computer.

Description

TECHNICAL FIELD

[0001] The application relates to a low-field NMR, in particular to a low-field NMR automatic shimming method and system based on Bayesian optimization and hybrid multi-coil collaborative optimization of secondary moments. BACKGROUND

[0002] Nuclear magnetic resonance (NMR) is a physical phenomenon that occurs between matter in an alternating magnetic field and a stationary strong magnetic field. For low-field nuclear magnetic resonance (LF-NMR), also known as low-resolution nuclear magnetic resonance, it is commonly used for physical property determination of matter. In simple terms, the low-energy state atomic nucleus magnetic moment, under the interaction of constant field strength and alternating field strength, after absorbing the energy provided by the alternating field strength, will jump to a high-energy state, thereby generating a nuclear magnetic resonance signal. According to the field strength, nuclear magnetic resonance can be divided into three types: high-field nuclear magnetic resonance, medium-field nuclear magnetic resonance and low-field nuclear magnetic resonance.

[0003] The low-field nuclear magnetic resonance (LF-NMR) device mainly detects hydrogen protons in the sample. After the sample is placed in a magnetic field, a certain frequency of radio frequency pulse is emitted to make the hydrogen protons resonate and absorb the radio frequency pulse energy. When the radio frequency pulse ends, the hydrogen protons will release the absorbed radio frequency energy, and through a special coil, the process of hydrogen protons releasing energy can be detected, which is the nuclear magnetic resonance signal.

[0004] A uniform magnetic field is the basis for obtaining fine structure information in nuclear magnetic resonance (NMR). The traditional NMR analysis automatic shimming method uses a single coil for coarse adjustment and a multi-coil fine adjustment iterative method, which has the disadvantages of long time consumption, insufficient accuracy, and high dependence on the central point of the uniformity of the magnetic field space magnetic force line distribution.

[0005] The current secondary moment algorithm for automatic shimming has the advantages of strong mathematical analysis and fast calculation speed when used in high-field NMR (such as 400MHz) and above, but has the disadvantages of being easily trapped in local optimal solution and requiring high accuracy of the magnetic field model when used in low-field NMR. Although the Bayesian optimization algorithm has the advantages of strong global convergence and strong robustness to noise and model errors, it also has the disadvantage of high computational cost.

[0006] For a low-field 20MHz NMR system, the intrinsic uniformity of the magnetic field is poor, and it is more susceptible to environmental interference than high-field NMR, so the automatic shimming challenge is huge. The existing technology mainly has several problems, one is that under low field, due to low signal-to-noise ratio and large magnetic field model error, the traditional gradient descent search algorithm is easily trapped in a local optimal solution, and cannot achieve the best global shimming effect, and lacks collaborative optimization of the coupling effect between different shimming coils (such as spherical harmonic function terms); two is that although the genetic algorithm has strong global search ability, it requires a large number of sampling points (NMR signal acquisition), which consumes a lot of time and is difficult to apply in practice.

[0007] In addition, the gradient coil plays an important role in the MRI system, and its main function is to generate a gradient magnetic field for image positioning and tomography. In a conventional superconducting MRI system, the gradient coil is placed in the center of the magnet and deep into the magnet hole, and the purpose is to generate a fine-tuned main magnetic field. In order to meet the fine needs of scanning, these gradient coils must be able to linearly change and harmonically superimpose with the main magnetic field. It is known that the gradient plays a role in the X, Y, Z three directions, so the gradient coil is also composed of three groups of orthogonal coils. The Z-direction gradient coil uses a solenoid winding to generate a Z-direction magnetic field according to Ampere's theorem. The X, Y direction gradient coil uses a Halbach coil design to generate a magnetic field orthogonal to the Z direction through the Biot-Savart law. By combining X, Y, Z three groups of coils into a cylinder, the basic circuit structure of the gradient coil is formed. The combination of X, Y, Z gradient coils on the outer surface of a cylinder forms the basic circuit structure of the gradient coil. The gradient coil is connected to the gradient amplifier through a group of positive and negative terminals, and by adjusting the output current, the gradient field is flexibly generated by using the principle of vector superposition. The X, Y, Z three groups of coils in the gradient coil respectively lead out a group of positive and negative terminals, and these terminals control the output current through the gradient amplifier, thereby adjusting the size of the gradient field. By adjusting the current intensity of the X, Y, Z direction gradient coil, any direction gradient field can be flexibly generated by using the principle of vector superposition. SUMMARY

[0008] The application provides a hybrid multi-coil collaborative optimization low-field NMR automatic shimming method and system, which solves the problem of processing the shimming method of low-field NMR by using the algorithm based on Bayesian optimization and second moment, and realizes the shimming method. The technical scheme is as follows: A hybrid multi-coil collaborative optimization low-field NMR automatic shimming system, comprising an optimization strategy control unit, and a coarse shimming unit, a fine shimming unit, an FID processing and evaluation index calculation unit, a current fitting and optimization unit, and a shimming execution and signal acquisition unit connected with the optimization strategy control unit respectively; the optimization strategy control unit is used for controlling the overall operation of the system and managing the switching and cooperation of the coarse shimming unit and the fine shimming unit; the coarse shimming unit and the fine shimming unit are used for processing the FID signal of the nuclear magnetic resonance spectrometer hardware system, and can be assisted by the FID processing and evaluation index calculation unit; the FID processing and evaluation index calculation unit is used for converting the original FID collected into a numerical index that can be used for quantifying the uniformity of the magnetic field; the current fitting and optimization unit is used for providing basis for analyzing and solving the optimal current of each shimming coil; and the shimming execution and signal acquisition unit is used for the interface with the lower computer.

[0009] The FID signal from the hardware system of the nuclear magnetic resonance spectrometer is received by the coarse homogeneity unit, and the second moment is calculated after processing. The current value corresponding to the lowest point of the parabola is found by fitting the parabola, and fast convergence is realized. The calculation result is sent to the optimization strategy control unit. The second moment is as follows: The coarse homogeneity unit sets the current increment to -x 0 , 0 and x 0 , respectively, to obtain the absorption line shape second moment I - 、I 0 and I + under the corresponding conditions; since the current increment d and the absorption line shape second moment are in a quadratic function relationship I = A d + B d + C 2 f = a * (F50) + b * (F10) + g * |1 - S| + d * (1 / SNR) C , the parameters A, B and C are obtained, and then the current increment d min that makes the absorption line shape second moment at the minimum value I opt (the bottom of the parabola) is obtained; the values of the three parameters are: ; The corresponding optimal current increment is: ; By collecting FID in real time and performing FFT, the magnetic field uniformity is evaluated at three half-peak widths of 50%, 10% and 0.5%. The coarse adjustment prioritizes the Z, Z 2 , Y and X coils.

[0010] The fine homogeneity unit receives the FID signal from the hardware system of the nuclear magnetic resonance spectrometer, designs a multi-objective optimization function, improves the second moment and the spectral peak width and the signal-to-noise ratio, constructs a comprehensive objective function and uses Bayesian optimization.

[0011] The FID processing and evaluation index calculation unit converts the collected original FID into a numerical index that can be used to quantify the magnetic field uniformity. The numerical index includes the second moment, symmetry, half-peak width and signal-to-noise ratio, which provides the optimization target for the coarse homogeneity unit. At the same time, other spectral performance parameters required by the multi-objective fusion function of the fine homogeneity unit are also calculated.

[0012] The fine homogeneity unit includes a multi-objective fusion function evaluation module, a Gaussian process proxy module and an acquisition function optimization module that process the data in sequence; The multi-objective fusion function evaluation module fuses multiple spectral performance indicators into a single, scalar objective function value fTypical functions + Δd, d , where α, β, γ, δ are weighting coefficients, F50 is 50% half-width at half-maximum, F10 is 10% half-width at half-maximum, S is symmetry, and SNR is signal-to-noise ratio; The Gaussian process proxy module is used to collaboratively optimize variables and automatically handle the coupling effect between coils; the acquisition function optimization module uses the EI function. The acquisition function optimization module is used to establish the search step path for each set of shimming coils.

[0013] The search step of the acquisition function optimization module is to set the current magnetic field X, Y, Z, Z... 2 The current values ​​of the eight sets of shimming coils on the axis are respectively E n ( 01 E 01， E 02， E 03，…, E 08 ), d k This is the search step size for each set of shimming coils; a magnetic field space matrix M with a search step size of 8×9 is constructed using a table. x ij ), where 8 columns correspond to 8 sets of shimming coils, and each row vector in M ​​( x i1， x i2， x i3，…， x i8 ) constitute a spatial point; the first row ( x=0 This indicates a magnetic field state where there is no current in any of the coils. x The line represents the first x The coil group is increased to d x The subsequent magnetic field state, the first x (x∈{1-8}) represents the row of... x The current of the coils in groups 1-8 increases by a small amount. d x The magnetic field state afterward.

[0014] A hybrid multi-coil collaborative optimization method for automatic shimming in low-field NMR includes the following steps: S1: Shrinking Initialization: Uses the historical shrinking coil current values ​​or manually set coil current values. d 0And the optimization strategy control unit configures the parameters of the coarse and fine homogeneity stages; S2: Perturbation sampling: for each set of shim coils, at its current current value d cuurrent 2-5 times small perturbation is made nearby, and the perturbation mode is implemented according to the implementation, that is d cuurrent - Δd cuurrent Crit , and Δd refers to the perturbation current. After each perturbation, the FID signal is collected, and the corresponding magnetic field homogeneity index is calculated Crit ; S3: Fitting calculation: for each set of coils i , 2-3 sets of current-homogeneity data obtained in step S2 d, Ii = A ) are independently fitted to a quadratic function Ii i * d i 2 + B i * d i + C i ; said i refers to the i-th set of coils, said A i 、 B i and C i is the coefficient of the i-th set of coils, d i is the current increment of the i-th set of coils; S4: Analytical optimization: for each set of coils i , directly according to the fitted parabolic coefficient A i 、 B i and C i , the quadratic moment f = a * (F50) + b * (F10) + g * |1 - S| + d * (1 / SNR) optimal current value d i_best = - B i / ( 2 * A i ) is calculated by the coarse homogeneity unit; S5: Current update: according to the optimal current value d i_best solved in step S4, the current of the 8 sets of shim coils is updated synchronously through the current fitting and optimization unit; S6: Verify evaluation: under the newly set shim coil current, re-acquire FID, calculate the overall uniformity and judge whether it meets the coarse shim requirement, if it meets, enter fine shim; if it does not meet, return to step S2; S7: Set prior: the optimal current combination Q 0 = [d 1_best , d 2_best , ..., d 8_best ] As the initial point of Bayesian optimization and the prior mean of the Gaussian process model; S8: Calculate the confidence interval, process through the fine shim uniform field unit, calculate the sensitivity coefficient, define the acceptable change range of the objective function, calculate the current disturbance range of the single coil group, and obtain the fine shim search interval; S9: Bayesian optimization iteration: predict the current data mean according to the historical data, and give the prediction variance; S10: Fusion target evaluation: define and calculate the multi-objective fusion function GP GP Where α, β, γ, δ are weight coefficients, F50 is the 50% half peak width, F10 is the 10% half peak width, S is the symmetry, SNR is the signal-to-noise ratio; for any current combination, construct 3 objective functions, f1 Calculate the line width, f2 Calculate the symmetry, f3 Calculate the signal-to-noise ratio, and based on the 3 Gaussian process GP proxy models, wherein GP lw Predict the expected line width and its uncertainty under any current combination, Δd se Predict the expected symmetry error and its uncertainty under any current combination, Tv snr Predict the expected signal-to-noise ratio error and its uncertainty under any current combination; then obtain the Pareto optimal solution set, finally calculate the membership function of each target and calculate the comprehensive satisfaction to obtain the final solution; S11: Terminate the shim: repeat the iteration until the function f Converges or reaches the maximum number of times, output the globally optimal current configuration, and exit the shim process.

[0015] Further, in step S8, the confidence interval is calculated, and the fine shim uniform field unit is processed, the sensitivity coefficient is calculated, the acceptable change range of the objective function is defined, and the current disturbance range of the single coil group is calculated to obtain the fine shim search interval, including the following steps: S11: Calculate the sensitivity coefficient; establish the magnetic field space matrix M around Q0. x ij Q0 is the optimal current combination obtained from the coarse uniform field unit; since the sensitivity of magnetic field uniformity to changes in the current of each coil group is different, it is necessary to calculate the sensitivity coefficient S of each coil. i For the first i The magnetic field-current response matrix H is established by the coil group. x ij This is approximately the case where, when the currents of other coils remain constant, only the first coil... i The coil current undergoes a slight change Tv The change in the objective function caused by the time; S12: Define the acceptable range of variation for the objective function; assume the objective function value during the fine-tuning stage represents the uniformity of the magnetic field in Hz, and assume this variable is... Tv An acceptable deviation value Δ is set based on empirical values. Tv accept Therefore, fine homogenization results are acceptable in [ Tv , Tv + Δ Tv accept Within the range; S13: Calculate the current disturbance range of a single coil group; for the first... i For a set of coils, the change in the objective function caused by its individual variation should not exceed Δ. Tv accept The range of its current variation d i Should meet: S i * |Δ d i | ≤ Δ Tv accept ; Therefore, the allowable disturbance amplitude Δ of the coil current can be calculated. d i = Δ i group accept / S i ; where Δ d i This is the allowable current disturbance amplitude for the i-th (out of 8) group of coils; Δ Figure 1 accept This refers to the range of tolerances for magnetic field uniformity, such as 180 Hz; S i It is the sensitivity coefficient of the i-th group of coils.

[0016] S14: Determine the search interval for fine shimming; finally used in the second-moment algorithm for the fine shimming process. Figure 2 The current search range of the coil is based ond i_best for the center, and Δ d i for the radius d i_best - Δ d i , d i_best + Δ d i ].

[0017] Further, the Bayesian optimization iteration in step S9 predicts the current data mean value according to historical data, and simultaneously gives a prediction variance, and the implementation manner is that firstly, a kernel function is selected, which can generate a smooth enough response surface and is not sensitive to slight noise in the low-field NMR data; then, the result of the rough shimming is taken as the prior mean value of the Gaussian process, so that the model believes that the optimal solution is near the point from the beginning, and the convergence is accelerated; finally, after each new current fusion function value evaluation is completed, the data point is added to the historical observation data set, and the posterior distribution of the Gaussian process is recalculated, so that the model becomes more and more accurate; and the EI function is used to optimize the acquisition function, and the Bayesian iteration is iterated until the convergence end condition is met.

[0018] The mixed multi-coil collaborative optimization low-field NMR automatic shimming method and system has the following advantages: (1) Efficient fusion of global convergence and local fast convergence. The quadratic moment algorithm with local fast convergence is creatively combined with the Bayesian optimization algorithm. The quadratic moment algorithm is used to quickly approach a “better” local area in the initial stage, and then the Bayesian optimization is used to finely explore the area. This mixed strategy not only utilizes the speed advantage of the quadratic moment, but also overcomes the fatal defect of being easy to fall into local optimum through the Bayesian optimization, and realizes the unity of “fast” and “accurate”.

[0019] (2) Multi-coil collaborative optimization and coupling effect compensation. Traditional methods often adjust the shim coils one by one or ignore the coupling therebetween. The invention first proposes a collaborative optimization strategy for multiple groups of shim coils (X, Y, Z, XY, XZ, YZ, Z 2 , X 2 -Y 2 ). The low-order coils and the high-order coils are divided into two groups (L group and H group), and the method of first low and then high is used to construct a multi-dimensional optimization objective function. The algorithm simultaneously evaluates the influence of the L group and the H group coil current combination on the overall uniformity of the magnetic field in each iteration, and uses an effective compensation mechanism to reduce the influence of the electromagnetic coupling effect between the coils, and finds the truly global optimal current configuration, which cannot be achieved by general sequential optimization.

[0020] (3) High robustness. The Bayesian optimization algorithm kernel (such as Gaussian process using Matern kernel function) has no requirement for the mathematical form of the objective function (magnetic field uniformity), and has natural smoothing and tolerance ability to measurement noise (signal fluctuation caused by low SNR of low-field NMR). This makes the application still work stably and reliably in the low-field NMR environment with low signal-to-noise ratio, which is significantly better than the traditional gradient algorithm which is sensitive to model error and noise. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 3 is a schematic diagram of the principle of the nuclear magnetic resonance spectrometer; Figure 4 is a schematic diagram of the structure of the mixed multi-coil collaborative optimization low-field NMR automatic shimming system; Figure 5 is a schematic diagram of the quadratic function between the current increment d in the shimming coil and the second moment of the absorption profile I; Figure 6 is a workflow diagram of the fine shimming unit; Figure 1 is a schematic diagram of the magnetic field space matrix with a search step of 8x9; Figure 2 is a schematic diagram of the flow of the mixed multi-coil collaborative optimization low-field NMR automatic shimming method. DETAILED DESCRIPTION

[0022] As shown in I = A d + B d + C , the nuclear magnetic resonance spectrometer refers to the study of the absorption of radio frequency radiation by atomic nuclei, and is one of the most powerful tools for qualitative analysis of the composition and structure of various organic and inorganic substances, and sometimes quantitative analysis can also be performed. Its working principle is that in a strong magnetic field, atomic nuclei undergo energy level splitting, and when absorbing external electromagnetic radiation, nuclear energy level transitions occur, i.e. the so-called NMR phenomenon. Its working process is: the sample is loaded into the sample tube, placed in the slit between the two stages of the magnet, and rotated at a uniform speed (50-60 Hz), so that the sample is subjected to a uniform magnetic field strength. In this process, the coil of the radio frequency generator (or also known as the radio frequency oscillator) emits electromagnetic waves of a fixed frequency (such as hydrogen spectrum: 20 / 60 MHz) to the sample outside the sample tube, and the radio frequency receiver is used to detect the absorption signal of nuclear magnetic resonance through the radio frequency receiving coil, and the magnetic field strength is continuously changed by the scan generator coil to perform scanning from low field to high field. The receiver and recorder amplify and record the resonance absorption signal into a nuclear magnetic resonance spectrum.

[0023] On this basis, the field coil (also known as the Gauβ coil) is a device for compensating for small changes in the main magnetic field in nuclear magnetic resonance spectrometer and magnetic resonance imaging equipment, which maintains the magnetic field uniformity around the sample by generating an additional magnetic field; it generates a compensation magnetic field by adjusting the current to offset the main magnetic field fluctuations, and plays a key role in maintaining the uniformity of the magnetic field in nuclear magnetic resonance experiments and atomic magnetometers.

[0024] As shown in f = a * (F50) + b * (F10) + g * |1 - S| + d * (1 / SNR) The mixed multi-coil collaborative optimization low-field NMR automatic shimming system includes an optimization strategy control unit, and a coarse shimming unit, a fine shimming unit, an FID processing and evaluation index calculation unit, a current fitting and optimization unit, and a shimming execution and signal acquisition unit connected with the optimization strategy control unit respectively; the optimization strategy control unit is used to control the overall operation of the system and manage the switching and cooperation of the coarse shimming unit and the fine shimming unit; the coarse shimming unit and the fine shimming unit are used to process the FID signal of the nuclear magnetic resonance spectrometer hardware system, which can be assisted by the FID processing and evaluation index calculation unit, which is used to convert the original FID collected into a numerical index that can be used to quantify the magnetic field uniformity; the current fitting and optimization unit is used to provide a basis for solving the optimal current of each shimming coil, and the shimming execution and signal acquisition unit is used to interface with the lower computer.

[0025] The optimization strategy control unit as the brain of the system can set parameters of the system, including the number of iterations, convergence conditions, threshold values, etc. The optimization strategy control unit is responsible for managing the switching, cooperation and data flow direction of the two coarse shimming and fine shimming units, and making the final decision. After the final shimming instruction is determined, it is output to the shimming power supply of the nuclear magnetic resonance spectrometer through the shimming execution and signal acquisition unit to drive the corresponding shimming coil.

[0026] The coarse shimming unit is an analytical calculator based on a physical model. It receives the FID signal from the nuclear magnetic resonance spectrometer hardware system, processes and calculates to obtain the second moment I. It actively uses the known strong mathematical constraint of the quadratic function to fit the parabola with a few sampling points and directly find the current value corresponding to the lowest point, realize fast convergence, and the calculation result is sent to the optimization strategy control unit. Among them, the sampling points are a series of continuous sample amplitude signals related to time characteristics, composed of horizontal coordinate time and vertical coordinate amplitude, and finally drawn into an FID curve. The number of sampling points is generally a power of 2, such as 1024, 2048, 4096 sampling points. These sampling points can be collected in a few hundred microseconds to a few tens of milliseconds, so they are called a few.

[0027] The fine homogeneity unit is a data-driven probabilistic model optimizer, which receives the same FID signal from the hardware system of the nuclear magnetic resonance spectrometer, but calculates a more complex multi-objective fusion function. It does not assume the specific form of the objective function, but learns and predicts the complex "current-performance" relationship through a Gaussian process, thereby performing global refinement based on the coarse homogeneity field, and the calculated recommended parameters are sent to the optimization strategy control unit. The specific calculation process of the global refinement based on the coarse homogeneity field can be described in steps S7-S11 below, and the recommended parameters are the predicted current data after Bayesian optimization, and the predicted variance calculated at the same time. The fine homogeneity unit improves the second moment (including high-order moment correction term) and spectral peak width, signal-to-noise ratio (SNR) by designing a multi-objective optimization function, constructs a comprehensive objective function, and improves the homogeneity accuracy. The half-peak width, signal-to-noise ratio, and second moment function are introduced into the weight coefficient, and a noise reduction algorithm is introduced according to the influence of noise, which is conducive to better exerting the advantages of the second moment algorithm. The optimization uses Bayesian optimization.

[0028] The FID processing and evaluation index calculation unit is the "sensory organ" of the algorithm, responsible for converting the collected original FID into numerical indicators that can be used to quantify the uniformity of the magnetic field. The numerical indicators include the second moment, symmetry, half-peak width, and signal-to-noise ratio, which provide optimization targets for the coarse homogeneity unit; at the same time, it also calculates other spectral performance parameters required by the multi-objective fusion function of the fine homogeneity unit. The other spectral performance parameters include the symmetry of the main peaks in the spectrum (such as methyl and methylene when the sample is ethylbenzene, and the water peak when the sample is water), the smoothness of the baseline, etc., but generally included is the symmetry, which has a lower priority than the 50% half-peak width.

[0029] The current fitting and optimization unit works independently for each homogeneity coil, and its function is to establish a quantitative mathematical relationship between the current increment d of the coil and the magnetic field uniformity (represented by the second moment I) Figure 3 2 I = A d + B d By fitting the coefficients A and B, it provides a basis for the next step of analytical solution of the optimal current. Current optimization is to analytically and one-time calculate the theoretical optimal current value that minimizes the second moment I based on the fitted quadratic function model, thereby achieving fast convergence.

[0030] The present application takes the performance index of the Lorentz absorption line shape (including 10% half-peak width, 50% half-peak width, symmetry, second moment) and signal-to-noise ratio as evaluation index. Among them, the symmetry and half-peak width are obtained by collecting FID of the standard sample (ethylbenzene, copper sulfate, n-heptane and pure water, etc.) and through FFT, phase correction, baseline correction and peak search algorithm processing, and the second moment is the value of three or five points (usually three points) measured by the actual absorption line shape. The relationship between the current increment in the shimming coil and the quadratic function is fitted using these second moment values.

[0031] As shown in Figure 4 , by setting the current increment to -x 0 , 0 and x 0 , the absorption line shape second moment I - 、I 0 and I + under the corresponding conditions can be obtained respectively. Since the current increment d and the absorption line shape second moment are in a quadratic function relationship f = a * (F50) + b * (F10) + g * |1 - S| + d * (1 / SNR) 2 Figure 5 +C , the current increment d min that makes the absorption line shape second moment at the minimum value I opt (the bottom of the parabola) can be obtained by solving the coefficients A, B and C. The values of the three parameters are: ; The corresponding optimal current increment is: ; By collecting FID in real time and performing FFT, the magnetic field uniformity is evaluated at 50%, 10% and 0.5% half-peak width, and the coarse adjustment is preferentially realized for the magnetic field Z, Z 2 , Y and X coils, and the fine adjustment is mainly aimed at high-order non-uniformity (such as X 2 -Y 2 , XY), and the improved second moment optimization is adopted.

[0032] The shimming execution and signal acquisition unit is a series of interface programs with the lower computer, responsible for sending shimming instructions, acquisition instructions and obtaining FID raw data.

[0033] As shown in Figure 6 , the fine shimming unit includes the following modules: including a multi-target fusion function evaluation module, a Gaussian process agent module and an acquisition function optimization module processed in turn.

[0034] The multi-objective fusion function evaluation module, the task of processing Bayesian optimization is to minimize this fusion function, which is responsible for fusing multiple spectral map performance indicators into a single, scalar target function value f , typical function f = + Δd, d Where α, β, γ, δ are weight coefficients, F50 is the 50% half-peak width, F10 is the 10% half-peak width, S is the symmetry, and SNR is the signal-to-noise ratio. The purpose of this is to guide the Bayesian optimization process to find a current configuration that performs well on multiple indicators, avoiding spectral distortion (such as poor symmetry) that may result from optimizing a single indicator (such as line width), thereby obtaining the best overall quality spectral map.

[0035] The Gaussian process proxy module is based on the Gaussian process model and the expected improvement (EI) acquisition function, and recommends the next set of 8 groups of coil current parameters that can maximize X, Y, Z, Z 2 .

[0036] The innovation lies in the cooperative optimization of 8 variables, which automatically handles the coupling effect between coils, which is not solved in the shimming stage. As described in the following step S10: first, 3 Gaussian process (GP) proxy models are used to obtain 3 groups of data, then the Pareto optimal solution set is obtained, and finally the membership function of each target (such as using linear or piecewise function) is calculated and the overall satisfaction is calculated to obtain the final solution.

[0037] The acquisition function optimization module, based on the prediction data (mean and variance) provided by the Gaussian process proxy module, "exploits" and "explores" the next set of current parameters to be tested. "Exploitation" refers to sampling in areas where the model predicts a small value, i.e. the current value parameter predicted by the model is in the range of 0.02mA-0.1mA, rather than a wide range of amperes. "Exploration" refers to sampling in areas where the model has high uncertainty to obtain new information. The acquisition function optimization module can use the EI (Expected Improvement, EI) function. Correspondingly, the model has high uncertainty, which means that although the magnetic field distribution spherical harmonic function is solved and simulated to give a prediction model current value adjustment step interval, there is still a difference between the actual magnetic field distribution and the theoretical distribution prediction due to manufacturing process and other unavoidable factors. Such differences are common in practice, that is, the error is often > 50%, and more precise shimming is needed in the above "small" range.

[0038] As shown in - Δd , the search path of the acquisition function optimization module: set the current current values of the 8 groups of magnetic field shim coils toE n ( 01 E 01， E 02， E 03，…, E 08 ), d k It is the search step size for each set of shimming coils.

[0039] The table is constructed using a magnetic field space matrix M with a search step size of 8×9. x ij ), where 8 columns correspond to 8 sets of shimming coils, and each row vector in M ​​( x i1， x i2， x i3，…， x i8 () constitutes a spatial point. The first line () x=0 This indicates a magnetic field state where there is no current in any of the coils; it is actually field B0. x The line represents the first x The magnitude of the coil current increment is d x The subsequent magnetic field state. x (x∈{1-8}) represents the row of... x The current of the coils in groups 1-8 increases by a small amount. d x The magnetic field state afterward.

[0040] ,like Crit As shown, the detailed flowchart of the automatic shimming method provided by the present invention includes the following steps: S1: Shrinking Initialization: Uses the historical shrinking coil current values ​​or manually set coil current values. d 0 The optimization strategy control unit configures the parameters for the coarse and fine uniformization stages, such as the convergence threshold, maximum number of iterations, and Bayesian optimization search range.

[0041] S2: Perturbation Sampling: For each group of shim coils, at its current current value d cuurrent Two to five small perturbations are made in the vicinity, and the perturbations are implemented in pairs, that is... d cuurrent Crit cuurrent Ii = A, Ad is the perturbation current, FID signal is collected after each perturbation, and the corresponding magnetic field homogeneity index is calculated Ii .

[0042] S3: Fitting calculation: for each set of coils i , the quadratic function d, Δd ) is fitted independently based on the 2-3 sets of current-homogeneity data obtained in step S2 Δd i ×d i 2 + B i × d i + C i . i refers to the i-th set of coils, and the A i , B i and C i are the coefficients of the i-th set of coils, d i is the current increment of the i-th set of coils, and this step is characterized by decomposing the multivariate problem into multiple single-variable problems for parallel processing, with the advantage of fast speed.

[0043] S4: Analytical optimization: for each set of coils i , the parabolic coefficients A i , B i and C i are directly calculated by the coarse homogeneity unit, and the optimal current value WHM50 that makes the second moment d i_best = - B i / ( 2 * A i ) is calculated.

[0044] S5: Current update: based on the current value solved in step S4, the currents of the 8 sets of shim coils X, Y, Z, Z 2 are updated synchronously by the current fitting and optimization unit.

[0045] S6: Verification and evaluation: under the newly set shim coil currents, FID is re-collected, the overall homogeneity is calculated, and it is judged whether it meets the coarse shim requirements (such as reaching the predetermined threshold). If it meets, go to fine shim; if it does not meet, return to step S2, but at this time, since the starting point has been optimized, the perturbation current≈ |WHM50( Need to be smaller.

[0046] S7: Set the prior: the optimal current combination obtained by the coarse shimming unit Q 0 = [d 1_best , d 2_best , ..., d 8_best ] As the initial point of Bayesian optimization and the prior mean of the Gaussian process model, so as to improve the subsequent optimization efficiency.

[0047] S8: Calculate the confidence interval, and process it through fine shimming, including the following steps: S11: Calculate the sensitivity wash; around the optimal current combination Q 0 , the magnetic field space matrix M( x ij ) is established. Since the magnetic field uniformity is sensitive to the change of each group of coil current, it is necessary to calculate the sensitivity coefficient S i of each coil. Similar to M( x ij ), the magnetic field-current corresponding matrix H( i x ij ) is established for the first i group of coils, that is, when other coil currents remain unchanged and only the first + Δd) - WHM50 ( group of coil currents changes slightly )) / Δd| , the change of the objective function (such as half peak width, second moment, symmetry) caused by the change. Taking 50% half peak width as an example, assuming that the half peak width objective function is Ii , the sensitivity coefficient S i d i_best Δd d i_best Tv . The said d i_best refers to the optimal current value of the second moment Tv , and Tv refers to the disturbance current.

[0048] S12: Define the acceptable change range of the objective function; assuming that the value of the target function in the fine shimming stage is expressed in Hz to represent the uniformity of the magnetic field, assuming that the variable of the uniformity of the magnetic field is Tv , an acceptable deviation value Δ Tv accept is set through experience value, so the acceptable fine shimming result is in [Tv , Tv + Δ Tv accept Within the range.

[0049] S13: Calculate the current disturbance range of a single coil group; for the first... i For a set of coils, the change in the objective function caused by its individual variation should not exceed Δ. Tv accept The range of its current variation d i Should satisfy: S i * |Δ d i | ≤ Δ i group accept； Therefore, the allowable disturbance amplitude Δ of the coil current can be calculated. d i = Δ f = a * (F50) + b * (F10) + g * |1 - S| + d * (1 / SNR) accept / S i ; Where, Δ d i This is the allowable current disturbance amplitude for the i-th (out of 8) group of coils; Δ GP accept is the range of deviations in magnetic field uniformity, for example, 180Hz; Si is the sensitivity coefficient of the i-th group of coils.

[0050] S14: Determine the search interval for fine shimming; finally, the second moment algorithm is used to perform fine shimming. GP The current search range of the coil is as follows: d i_best Centered on Δ d i For radius [ d i_best - Δ d i , d i_best + Δ d i In fact, coarse and even texture already provides a good starting point, so this range is relatively narrow.

[0051] S9: Bayesian optimization iteration: replace the real objective function (i.e. "multi-objective fusion function" F) which is costly to evaluate (need to actually sample FID) with a probabilistic model. Its role is to predict the current data (mean) and also give the prediction variance (uncertainty) based on historical data. The implementation is as follows: first, choose a kernel function, such as Matern 5 / 2 kernel (can produce a sufficiently smooth response surface and is not sensitive to slight noise in the low-field NMR data, more robust than the commonly used radial basis function); the second step is to use the results of the rough shimming as the prior mean of the Gaussian process, so that the model believes from the beginning that the optimal solution is near this point, accelerating convergence; the last step is to add the data point to the historical observation data set every time a new current fusion function value is evaluated, and recalculate the posterior distribution of the Gaussian process, so that the model becomes more and more accurate. The EI function is used to optimize the acquisition function. Bayesian iteration is iterated until the convergence end condition is met.

[0052] S10: Fusion objective evaluation: define and calculate the multi-objective fusion function GP ​ where a, b, g, d are weight coefficients, F50 is the 50% half-peak width, F10 is the 10% half-peak width, S is the symmetry, and SNR is the signal-to-noise ratio. For any current combination, construct three objective functions, f1 calculate the line width, f2 calculate the symmetry, f3 calculate the signal-to-noise ratio, and based on three Gaussian process (GP) surrogate models, ​ lw predict the expected line width and its uncertainty under any current combination, ​ se predict the expected symmetry error and its uncertainty under any current combination, ​ snr predict the expected signal-to-noise ratio error and its uncertainty under any current combination. Then obtain the Pareto optimal solution set, and finally calculate the membership function of each objective (such as using a linear or piecewise function) and calculate the comprehensive satisfaction to obtain the final solution. The innovation of the fusion objective evaluation is to integrate multiple spectral indicators, not just the second moment or line width, which can more comprehensively represent the spectral quality and avoid the defects of a single indicator.

[0053] S11: terminate shimming: repeat iteration until the function f converges or reaches the maximum number of times, output the globally optimal current configuration, and exit the shimming process.

[0054] The application introduces a fusion optimization objective function, takes the second moment as a core evaluation index of Bayesian optimization, processes nonlinear interference (such as eddy current effect, nonlinear response of a probe and the like), takes the Bayesian optimization result as an initial value, and executes a gradient descent algorithm to realize fine adjustment of the second moment.

Claims

1. A low-field NMR automatic shimming system with hybrid multi-coil collaborative optimization, characterized in that: The system includes an optimization strategy control unit, and coarse homogenization unit, fine homogenization unit, FID processing and evaluation index calculation unit, current fitting and optimization unit, and shimming execution and signal acquisition unit, all connected to the optimization strategy control unit. The optimization strategy control unit controls the overall operation of the system and manages the switching and coordination of the coarse and fine homogenization units. The coarse and fine homogenization units process the FID signals of the nuclear magnetic resonance spectrometer hardware system, assisted by the FID processing and evaluation index calculation unit, which converts the acquired raw FID signals into numerical indicators that can be used to quantify magnetic field uniformity. The current fitting and optimization unit provides a basis for analytically solving for the optimal current for each shimming coil, and the shimming execution and signal acquisition unit serves as the interface with the lower-level computer.

2. The low-field NMR automatic shimming system with hybrid multi-coil collaborative optimization according to claim 1, characterized in that: The coarse homogenizing unit receives the FID signal from the nuclear magnetic resonance spectrometer hardware system, processes and calculates it to obtain the second moment, and achieves rapid convergence by fitting a parabola and directly finding the current value corresponding to its minimum point. The calculation result is sent to the optimization strategy control unit; the obtained second moment is as follows: The coarsening unit sets current increments respectively -x 0 , 0 and x 0 The absorption linear quadratic moments for the corresponding cases were obtained respectively. I - 、I 0 and I + Due to the increase in current d It has a quadratic function relationship with the absorption linear quadratic moment. I=Ad 2 +Bd+C Therefore, by obtaining parameters A, B, and C, we can then obtain the value of I that minimizes the second moment of the absorbing line. min The current increment d at time (bottom of the parabola) opt The values ​​of the three parameters are: ； The corresponding optimal current increment is: ； By acquiring FID data in real time and performing FFT, the magnetic field uniformity is evaluated at three half-peak widths: 50%, 10%, and 0.5%. Coarse adjustment is prioritized to achieve the desired magnetic field Z and Z values. 2 The coils of Y, X.

3. The low-field NMR automatic shimming system with hybrid multi-coil collaborative optimization according to claim 1, characterized in that: The fine uniform unit receives the FID signal from the nuclear magnetic resonance spectrometer hardware system. By designing a multi-objective optimization function, it improves the quadratic moment, spectral peak width, and signal-to-noise ratio, constructs a comprehensive objective function, and uses Bayesian optimization.

4. The low-field NMR automatic shimming system with hybrid multi-coil collaborative optimization according to claim 1, characterized in that: The FID processing and evaluation index calculation unit converts the collected raw FID into numerical indices that can be used to quantify the magnetic field uniformity. These numerical indices include the second moment, symmetry, half-maximum width, and signal-to-noise ratio, providing optimization targets for the coarse uniformity unit. At the same time, it also calculates other spectral performance parameters required for the multi-objective fusion function of the fine uniformity unit.

5. The low-field NMR automatic shimming system with hybrid multi-coil collaborative optimization according to claim 3, characterized in that: The fine-tuning unit includes a multi-objective fusion function evaluation module, a Gaussian process proxy module, and an acquisition function optimization module that process the data sequentially. The multi-objective fusion function evaluation module fuses multiple spectral performance indicators into a single, scalable objective function value. f Typical functions f =α* (F50) + β * (F10) + γ * |1 - S| + δ * (1 / SNR) , where α, β, γ, δ are weighting coefficients, F50 is 50% half-width at half-maximum, F10 is 10% half-width at half-maximum, S is symmetry, and SNR is signal-to-noise ratio; The Gaussian process proxy module is used to collaboratively optimize variables and automatically handle the coupling effect between coils; the acquisition function optimization module uses the EI function. The acquisition function optimization module is used to establish the search step path for each set of shimming coils.

6. The low-field NMR automatic shimming system with hybrid multi-coil collaborative optimization according to claim 5, characterized in that: The search step of the acquisition function optimization module is to set the current magnetic field X, Y, Z, Z... 2 The current values ​​of the eight sets of shimming coils on the axis are respectively E n ( 01 E 01， E 02， E 03，…, E 08 ), d k This is the search step size for each set of shimming coils; a magnetic field space matrix M with a search step size of 8×9 is constructed using a table. x ij ), where 8 columns correspond to 8 sets of shimming coils, and each row vector in M ​​( x i1， x i2， x i3，…， x i8 ) constitute a spatial point; the first row ( x=0 This indicates a magnetic field state where there is no current in any of the coils. x (x∈{1-8}) represents the row of... x The current in the coils, i.e., the coils in groups 1-8, increases by a small amount. d x The magnetic field state afterward.

7. A hybrid multi-coil collaborative optimization method for automatic shimming in low-field NMR, comprising the following steps: S1: Shrinking Initialization: Uses the historical shrinking coil current values ​​or manually set coil current values ​​d. 0 The parameters for the coarse and fine uniformization stages are configured by the optimization strategy control unit. S2: Disturbance Sampling: For each group of shim coils, sample their current current value. d cuurrent Perform 2-5 small disturbances in the vicinity, with the disturbance method implemented accordingly. d cuurrent +Δd、d cuurrent -Δd Δd refers to the disturbance current. After each disturbance, the FID signal is collected, and the corresponding magnetic field uniformity index is calculated. Crit ; S3: Fitting calculation: For each group of coils i The 2-3 sets of current-uniformity data obtained in step S2 ( d, Crit Independently fit the quadratic function Ii = A i * d i 2 + B i * d i + C i The i refers to the i-th group of coils. A i , B i and C i It is the coefficient of coil i, d i It is the current increment of coil i; S4: Analytical optimization: For each group of coils i Directly based on the fitted parabolic coefficients A i , B i and C i The quadratic moment is calculated analytically using coarse uniform elements. Ii Optimal current value d i_best = - B i / ( 2 * A i ); S5: Current Update: Based on the optimal current value obtained in step S4. d i_best The current of the eight shimming coils is updated synchronously through the current fitting and optimization unit; S6: Verification and Evaluation: Under the newly set shimming coil current, re-acquire FID, calculate the overall uniformity and determine whether it meets the coarse shimming requirements. If it does, proceed to fine shimming; if it does not, return to step S2. S7: Setting Priorities: Using the optimal current combination Q obtained from the coarse uniform element. 0 = [d1_best , d 2_best , ..., d 8_best ] As the initial point for Bayesian optimization and the prior mean of the Gaussian process model; S8: Calculate the confidence interval by processing the fine uniform field. The fine uniform field search interval is obtained by calculating the sensitivity coefficient, defining the acceptable range of variation of the objective function, and calculating the current disturbance range of a single coil. S9: Bayesian optimization iteration: Predict the mean of current data based on historical data, and provide the prediction variance; S10: Fusion Objective Evaluation: Define and compute the multi-objective fusion function f =α* (F50) + β * (F10) + γ * |1 - S| + δ * (1 / SNR) Where α, β, γ, and δ are weighting coefficients, F50 is 50% HWHM, F10 is 10% HWHM, S is symmetry, and SNR is signal-to-noise ratio; for any set of current combinations, three objective functions are constructed. f1 Calculate line width, f2 Calculate symmetry, f3 The signal-to-noise ratio was calculated based on three Gaussian process GP surrogate models, where GP lw Predicting the expected linewidth and its uncertainty under arbitrary current combinations. GP se Predicting the expected symmetry error and its uncertainty under arbitrary current combinations. GP snr Predict the expected signal-to-noise ratio error and its uncertainty under arbitrary current combinations; then obtain the Pareto optimal solution set; finally calculate the membership function of each objective and calculate the overall satisfaction to obtain the final solution. S11: Terminating the homogenization: Repeat iterations until the function... f Once the convergence reaches the maximum number of iterations, the globally optimal current configuration is output, and the shimming process is terminated.

8. The low-field NMR automatic shimming method and system with hybrid multi-coil collaborative optimization according to claim 7, characterized in that: In step S8, the confidence interval is calculated by processing the fine shimming single coil. This involves calculating the sensitivity coefficient, defining the acceptable range of variation for the objective function, and calculating the current disturbance range of a single coil group to obtain the fine shimming search interval. This includes the following steps: S11: Calculate the sensitivity coefficient; establish the magnetic field space matrix M around Q0. x ij Q0 is the optimal current combination obtained from the coarse uniform field unit; since the sensitivity of magnetic field uniformity to changes in the current of each coil group is different, it is necessary to calculate the sensitivity coefficient S of each coil. i For the first i The magnetic field-current response matrix H is established by the coil group. x ij This is approximately the case where, when the currents of other coils remain constant, only the first coil... i The coil current undergoes a slight change Δd The change in the objective function caused by the time; S12: Define the acceptable range of variation for the objective function; assume the objective function value during the fine-tuning stage represents the uniformity of the magnetic field in Hz, and assume this variable is... TV An acceptable deviation value Δ is set based on empirical values. TV accept Therefore, fine homogenization results are acceptable in [ TV , TV + Δ TV accept Within the range; S13: Calculate the current disturbance range of a single coil group; for the first... i For a set of coils, the change in the objective function caused by its individual variation should not exceed Δ. TV accept The range of its current variation d i It should meet the following requirements: S i * |D d i | ≤ D TV accept ; Therefore, the allowable disturbance amplitude Δ of the coil current can be calculated. d i = Δ TV accept / S i ; Where, Δ d i This is the allowable current disturbance amplitude for the i-th (out of 8) group of coils; Δ TV accept It represents the range of deviations in magnetic field uniformity, for example, 180Hz; Si is the sensitivity coefficient of the i-th group of coils; S14: Determine the search interval for fine shimming; finally used in the second-moment algorithm for the fine shimming process. i group The current search range of the coil is as follows: d i_best Centered on Δ d i For radius [ d i_best - Δ d i , d i_best + Δ d i ].

9. The low-field NMR automatic shimming method and system with hybrid multi-coil collaborative optimization according to claim 7, characterized in that: The Bayesian optimization iteration in step S9 predicts the mean of the current data based on historical data and provides the prediction variance. This is achieved by first selecting a kernel function that can produce a sufficiently smooth response surface and is insensitive to slight noise in low-field NMR data; then using the result of coarse shimming as the prior mean of the Gaussian process so that the model believes from the beginning that the optimal solution is near this point, thus accelerating convergence; finally, after each new current fusion function value evaluation, the data point is added to the historical observation dataset, and the posterior distribution of the Gaussian process is recalculated, making the model increasingly accurate. The EI function is used to optimize the acquisition function, and the Bayesian iteration continues until the convergence termination condition is met.

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