Calibration transfer method for quantitative analysis model of magnetic resonance tissue based on symbolic regression

Abstract

The present application relates to a kind of calibration migration method of nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression, the method includes: obtaining the nuclear magnetic relaxation signal data of same group M calibration samples collected on source equipment and target equipment, and obtaining the known reference value of target tissue component in the M calibration samples;Based on the nuclear magnetic relaxation signal data and its corresponding reference value collected on source equipment, establish the quantitative analysis model for predicting target tissue component content, and extract the key parameter set of model;The nuclear magnetic signal data of same group calibration samples collected on source equipment and the target equipment are used as the input-output pair of symbolic regression;An explicit mathematical conversion function f is automatically searched and constructed using symbolic regression algorithm;For the nuclear magnetic signal data of unknown sample collected on target equipment, the model parameters of source equipment are extracted, and the target tissue component content prediction value of unknown sample is calculated by combining conversion function f.

Description

Technical Field

[0001] This invention relates to the fields of analytical instrument calibration and chemometrics, and particularly to cross-instrument model transfer of time-domain nuclear magnetic resonance (NMR) technology. Specifically, it refers to a calibration transfer method, apparatus, processor, and computer-readable storage medium for a NMR tissue quantitative analysis model based on symbolic regression. Background Technology

[0002] Time-domain nuclear magnetic resonance (TD-NMR or relaxation NMR) technology has been widely used in biomedicine, food, and materials science, for example, to non-destructively and rapidly determine the content of fat, water (free water), and lean meat (protein) in live animal or tissue samples. This technology is an indirect test, requiring the establishment of a quantitative regression model (such as partial least squares regression PLSR) between the NMR relaxation signal (e.g., T1, T2 relaxation time distribution) and the content of the target component based on a calibrated sample with known components.

[0003] However, in practical applications, a robust quantitative model is often tied to a specific instrument (referred to as the "source device" or "master device"). Due to inherent physical differences between different NMR devices, such as the strength and homogeneity of the static magnetic field (B0), the efficiency of the radio frequency field (B1), the probe quality factor (Q value), electronic gain, and dead time, the signals acquired from the same set of samples on different devices (referred to as the "target device" or "slave device") exhibit systematic differences (i.e., "instrument drift"). This causes the accurate model built on the source device to suffer a significant decrease in prediction accuracy or even complete failure when directly applied to data from the target device.

[0004] To address this issue, model calibration transfer technology has emerged. Existing technologies are mainly divided into two categories: Standard transfer methods (such as direct standardized DS and piecewise direct standardized PDS) require measuring a set of identical standard samples on both master and slave instruments, and then performing correction by establishing a linear or piecewise linear transformation relationship between the signal matrices. These methods are intuitive in principle, but they rely on transferred samples, have limited ability to correct complex nonlinear drift, and are computationally complex and prone to overfitting in high-dimensional data.

[0005] Standardless / Model Update Methods: These methods adapt to new instrument data by updating model parameters or incorporating machine learning algorithms. While reducing reliance on standard samples, they are often sensitive to drift and the correlation with the target variable. Parameter selection is subjective, and the models are often "black boxes" lacking physical interpretability, failing to meet the regulatory transparency requirements for instrument calibration.

[0006] Especially in the field of TD-NMR, the signal generation and attenuation processes involve complex physical mechanisms (such as exponential decay, logarithmic response, phase-dependent trigonometric functions, etc.), and the differences between instruments are often nonlinear and coupled. Existing transfer methods based on the linear assumption of Lambert-Beer's law, which are borrowed from fields such as near-infrared spectroscopy, are difficult to accurately characterize and correct for this complex drift.

[0007] Symbolic Regression (SR) is a machine learning method that automatically discovers hidden mathematical formulas (expressions) in data. It does not pre-define a model form; instead, it searches the expression space comprised of basic operators (addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric functions, etc.) to find the explicit functional relationship that best fits the data. This characteristic makes it highly suitable for discovering inherent, potentially nonlinear, mappings between complex systems (such as different NMR instruments).

[0008] Currently, there is no publicly available technology that applies symbolic regression to cross-device calibration transfer of quantitative NMR models. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a calibration migration method, apparatus, processor and computer-readable storage medium for a nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression.

[0010] To achieve the above objectives, the present invention provides a calibration migration method, apparatus, processor, and computer-readable storage medium for a nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression, as follows: The calibration transfer method of this nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression is characterized by its applicability to time-domain nuclear magnetic resonance systems that include at least source and target devices. The method includes the following steps: (1) Data acquisition: acquire nuclear magnetic relaxation signal data of the same group of M calibration samples collected on the source device and target device, and acquire known reference values ​​of the target tissue components in the M calibration samples; wherein, M is an integer greater than 1; (2) Source device modeling: Based on the nuclear magnetic relaxation signal data collected on the source device and its corresponding reference values, a quantitative analysis model for predicting the content of target tissue components is established, and the key parameter set of the model is extracted; (3) Symbolic regression mapping construction: The NMR signal data of the same set of calibration samples collected by the source device and the target device, or the feature data obtained by projecting the NMR signal data through the quantitative analysis model, are used as the input-output pair of symbolic regression; an explicit mathematical transformation function f is automatically searched and constructed using the symbolic regression algorithm, so that the data of the target device can be mapped to the data space of the source device through the transformation function f; (4) Model transfer and prediction: For the NMR signal data of the unknown sample collected on the target device, the model parameters of the source device extracted in step (2) are used in combination with the transformation function f to calculate the predicted value of the target tissue component content of the unknown sample.

[0011] Preferably, the nuclear magnetic resonance relaxation signal data is T1-T2 two-dimensional relaxation data acquired by an FSR-CPMG sequence.

[0012] Preferably, the quantitative analysis model established in step (2) is a partial least squares regression model, a principal component regression model, or a Bayesian regression model; the key parameter set includes one or more of the regression coefficient matrix, loading matrix, and score matrix.

[0013] Preferably, step (3) specifically includes the following steps: (3.1) The nuclear magnetic resonance signal data collected on the source device and the target device are projected onto the load space of the quantitative analysis model of the source device, respectively, to obtain the source device score matrix T_A and the target device initial score matrix T_B_raw; (3.2) Taking the source device score matrix T_A as input and the target device initial score matrix T_B_raw as the expected output, the gene expression programming algorithm is used to perform symbolic regression to search for the optimal transformation function f, which satisfies T_B_corrected = f(T_A) and minimizes the error between T_B_corrected and T_B_raw, where T_B_corrected is the corrected target device score matrix.

[0014] Preferably, the fitness function of the symbolic regression algorithm comprehensively considers prediction error, expression complexity, and correlation, and its expression is: Fitness = α·(1-RMSE) + β·(1 / Complexity) + γ·Correlation Where RMSE is the root mean square error, Complexity is the total number of nodes in the expression, Correlation is the correlation coefficient, and α, β, and γ are the weighting coefficients.

[0015] Preferably, step (4) specifically includes the following steps: (4.1) Project the nuclear magnetic signal data X_B_new collected by the unknown sample on the target device onto the load matrix P_A space of the source device to obtain the prediction score T_B_pred = X_B_new · P_A ·(P_A^T · P_A)^{-1}; (4.2) Correct the predicted score using the transformation function f: T_B_corrected = f(T_B_pred); (4.3) Using the regression coefficient matrix B_A of the source device, calculate the predicted value of the tissue component content of the unknown sample: Y_B_pred = T_B_corrected · B_A^T.

[0016] Preferably, the target tissue component includes at least one of lean meat, fat, and water.

[0017] The migration device for this nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression is characterized in that the device comprises: A processor is configured to execute computer-executable instructions; The memory stores one or more computer-executable instructions, which, when executed by the processor, implement the steps of the calibration migration method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression described above.

[0018] The main feature of this transfer processor for the symbolic regression-based quantitative analysis model of nuclear magnetic resonance tissue is that the processor is configured to execute computer-executable instructions, which, when executed by the processor, implement the steps of the calibration transfer method for the symbolic regression-based quantitative analysis model of nuclear magnetic resonance tissue described above.

[0019] The computer-readable storage medium is characterized in that it stores a computer program that can be executed by a processor to implement the steps of the calibration migration method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression described above.

[0020] The calibration migration method, apparatus, processor, and computer-readable storage medium of the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression of the present invention have the following advantages compared with the prior art: High data efficiency: Compared with traditional methods, the amount of standard samples used is reduced by 60%, and stable migration can be achieved with M≥15.

[0021] Accuracy Improvement: After migration, RMSEP is reduced by 35-50% to address the nonlinear characteristics of one-dimensional and multi-dimensional relaxation signals in time-domain NMR, with R²>0.95.

[0022] High interpretability: Explicit mathematical formulas express the essential physical differences between instruments, with outstanding ability to correct nonlinear distortions, supporting quantitative review and physical mechanism research.

[0023] Good versatility: Suitable for migration between NMR devices of different brands, field strengths (0.125T-21T), and sequences (CPMG, IR, T1-T2). Attached Figure Description

[0024] Figure 1 This is a schematic diagram of a two-dimensional relaxation spectrum of a sample acquired on a source device in an embodiment of the present invention.

[0025] Figure 2 This is a schematic diagram of the two-dimensional relaxation spectrum of the same calibration sample collected on the target device in an embodiment of the present invention.

[0026] Figure 3 This is a schematic diagram of the two-dimensional relaxation spectrum of the same calibration sample collected on the verification device in an embodiment of the present invention.

[0027] Figure 4 This is a schematic diagram of the actual chemical properties of the reference sample used to establish the quantitative analysis model in this embodiment of the invention.

[0028] Figure 5 This is a schematic diagram illustrating the principal component optimization process and the number of principal components for each modeling component when establishing a quantitative analysis model in an embodiment of the present invention.

[0029] Figure 6 This is a diagram illustrating the modeling effect of establishing a quantitative analysis model in an embodiment of the present invention. Detailed Implementation

[0030] To more clearly describe the technical content of the present invention, the following description is provided in conjunction with specific embodiments.

[0031] Before describing the embodiments of the present invention in detail, it should be noted that, in the following, the terms “comprising,” “including,” or any other variations are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed or inherent to such process, method, article, or apparatus.

[0032] The following will further explain the processing steps of the calibration migration method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression in this technical solution: Step S1: Nuclear Magnetic Resonance Signal Acquisition Two-dimensional NMR signals of the sample system were acquired using a T1-T2 NMR two-dimensional relaxation sequence.

[0033] M samples were continuously acquired. Acquisition parameters: echo time: 0.1-2ms; number of flip-recovery times: 10-100; flip-recovery time range: 1ms-5000ms; number of accumulations: 2-1024; sampling bandwidth: 10kHz-5000kHz; multiple devices were used for acquisition, with the same number of samples per device. Step S2: Standardized Reading of Multi-Source NMR Data The source device (A) and the target device (B) respectively read the M×N-dimensional relaxation signal matrix X and the M×Z-dimensional reference chemical value matrix Y, where M is the number of calibration samples, N is 1024-40960 relaxation time points, and Z is 3 (lean, fat, water).

[0034] Step S3: Establishing the regression analysis model For each component z∈{lean, fat, water}, PLSR (Partial Least Squares), BR (Bayesian Regression), and PCR (Principal Component Regression) models were independently established. Monte Carlo cross-validation (MCCV) was used to determine the latent variables and the number of principal components L∈[1,20]. Record the model parameters: regression coefficient matrix B_z (N×1), loading matrix P_z (N×L), and score matrix T_z (M×L).

[0035] Step S4: Signed Regression Mapping Discovery Using the source device score matrix T_A and the target device initial score matrix T_B_raw as the input-output pair for symbolic regression, the Genetic Expression Programming (GEP) algorithm is employed to search for the optimal transformation function f. in, Let K be the basis functions (including +, -, ×, ÷, exp, log, sqrt, ^2), where c_i is the coefficient, and K≤20.

[0036] The fitness function is: Fitness = α·(1-RMSE) + β·(1 / Complexity) + γ·Correlation(T_B_raw,f(T_A)) The complexity is the total number of nodes in the expression, where α=0.6, β=0.2, and γ=0.2.

[0037] It is understandable that in step S4 above, the input-output pair of symbolic regression can use the score matrix (T_A, T_B_raw) or the raw nuclear magnetic resonance relaxation signal data that has been properly preprocessed as input. The core of both is to find the mapping function f between devices through the symbolic regression algorithm.

[0038] Step S5: Model Transfer and Correction For T_B_raw obtained by projecting the calibration samples during the training phase: T_B_raw = X_B_calibration · P_A · (P_A^T · P_A)^{-1} For the new sample X_B_new of the target device, first project it onto the payload space of the source device: T_B_pred = X_B_new·P_A·(P_A^T·P_A)^{-1} Then apply the symbol conversion function: T_B_corrected = f(T_B_pred) Final predicted chemical values: Y_B_pred = T_B_corrected·B_A^T X_B_new comes from the third host.

[0039] It is understandable that the projection operation on the new samples during the prediction phase (resulting in T_B_pred) uses the same source device model parameters (specifically P_A) as the projection operation on the calibration samples during the training phase (resulting in T_B_raw).

[0040] Step S6: Evaluation of the transfer effect of the tissue component model Calculate the evaluation indicators for the three levels: RMSE before and after migration: improved by more than 30%; After migrating the piano, R 2 Score level: Improvement of 30% or more.

[0041] Step S7: Symbolic Regression Results The mathematical expressions, model parameters, and evaluation metrics generated by symbolic regression are encapsulated into a standard XML file, which includes a digital signature and timestamp.

[0042] The implementation of this technical solution will be further explained below with reference to specific embodiments: This embodiment uses the determination of fat, lean meat, and water in animal tissue as an example to illustrate the specific implementation of the present invention. The experiment involves three low-field TD-NMR instruments: Instrument A (source device / main unit), Instrument B (target device / slave 1), and Instrument C (verification device / slave 2). The calibration sample is a mixture of artificially prepared chicken breast (simulated lean meat), low-erucic acid rapeseed oil (simulated fat), and physiological saline (simulated free water).

[0043] Step S1: Data Acquisition 1. Sample Preparation: Accurately prepare 30 sets (M=30) of calibration samples with different mass ratios. The specific composition design is shown in Table 1 below: ; For each of the above samples, the actual weight (reference value) of lean meat, fat and water was accurately weighed and recorded.

[0044] 2. Data Acquisition: The 30 calibration samples were measured sequentially on both device A and device B using an FSR-CPMG sequence (which can simultaneously acquire T1 and T2 information). Acquisition parameters: echo time 1 ms, 50 inversion recovery times (10-3000 ms), 4 accumulations, and sampling bandwidth 50 kHz. Ultimately, a two-dimensional relaxation signal matrix was obtained for each sample on each device.

[0045] Step S2: Source device modeling 1. Preprocess the two-dimensional NMR signal data of 30 samples collected by device A (such as amplitude normalization, data dimensionality reduction, etc.) to form a signal matrix X_A (30×N, where N is the number of feature points).

[0046] 2. Using reference values ​​for fat, lean meat, and water as dependent variables Y_fat, Y_lean, and Y_water respectively, three independent quantitative analysis models were established using partial least squares regression (PLSR). The optimal number of latent variables (LV) was determined through Monte Carlo cross-validation.

[0047] Fat model: LV=9, modeling set RMSEC=0.82%, R²=0.999.

[0048] Lean meat model: LV=5, modeling set RMSEC=0.82%, R²=0.998.

[0049] Moisture model: LV=5, modeling set RMSEC=0.82%, R²=0.992.

[0050] 3. Extract the key parameters for each model: regression coefficient matrix B_A, loading matrix P_A, and score matrix T_A.

[0051] Step S3: Construction of symbolic regression mapping (taking the fat model as an example) 1. Project the signal matrix X_B of the 30 samples collected by device B onto the load matrix P_A_fat space of the fat model of device A to obtain the initial score matrix T_B_raw_fat of device B.

[0052] 2. Prepare the input-output pairs for symbolic regression: The input is the score matrix T_A_fat (30×9) of device A, and the expected output is T_B_raw_fat (30×9).

[0053] 3. The Gene Expression Programming (GEP) algorithm is used for symbolic regression search. The function set is set as {+, -, ×, ÷, exp, log, sqrt, ^2}, and the fitness function is defined as: Fitness = 0.6·(1-RMSE) + 0.2·(1 / Complexity) + 0.2·Correlation, where Complexity is the total number of nodes in the expression tree.

[0054] 4. After the GEP algorithm runs, it outputs an optimal explicit mathematical transformation function f_fat.

[0055] 5. Similarly, construct separate conversion functions f_lean and f_water for the lean meat and water models.

[0056] Step S4: Model Transfer and Prediction 1. For a new sample with unknown composition collected on device C (another target device), obtain its NMR signal X_C_new.

[0057] 2. Fat prediction: a) Project X_C_new onto the fat model load space of device A: T_C_pred_fat = X_C_new · P_A_fat · (P_A_fat^T · P_A_fat)^{-1}.

[0058] b) Apply the symbolic regression transformation function for correction: T_C_corrected_fat = f_fat(T_C_pred_fat).

[0059] c) Calculate the predicted fat content: Y_C_pred_fat = T_C_corrected_fat · B_A_fat^T.

[0060] 3. Repeat step 2, using the corresponding loading matrix, transformation function and regression coefficients to predict the lean meat and moisture content of the sample.

[0061] In a specific embodiment of the present invention, the relevant parameter indicators obtained by device B before migration are shown in Table 2: The results show that the method of the present invention significantly improves the prediction accuracy (R² increases to 0.978, RMSE decreases to 1.20%) while reducing the number of calibration samples required. Furthermore, the generated transformation function f has a clear mathematical form, which is easy to understand and apply directly.

[0062] In practical applications, this technical solution, in the process of establishing a quantitative analysis model, uses the actual chemical indicators of the reference sample, the principal component optimization process and the number of principal components for each modeling component, and the modeling effect, as shown below. Figures 4 to 6 As shown, the modeling effect diagram represents the true level of the modeling effect and is used to analyze the modeling results and interactive verification results.

[0063] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution device.

[0064] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0065] The storage media mentioned above can be read-only memory, disk, or optical disk, etc.

[0066] In the description of this specification, references to terms such as "an embodiment," "some embodiments," "example," "specific example," or "embodiment," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0067] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

[0068] In this specification, the invention has been described with reference to specific embodiments thereof. However, it will be apparent that various modifications and variations can be made without departing from the spirit and scope of the invention. Therefore, the specification and drawings should be considered illustrative rather than restrictive.

Claims

1. A calibration transfer method for a nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression, characterized in that, Applied to a time-domain nuclear magnetic resonance system comprising at least a source device and a target device, the method includes the following steps: (1) Data acquisition: acquire nuclear magnetic relaxation signal data of the same group of M calibration samples collected on the source device and target device, and acquire known reference values ​​of the target tissue components in the M calibration samples; wherein, M is an integer greater than 1; (2) Source device modeling: Based on the nuclear magnetic relaxation signal data collected on the source device and its corresponding reference values, a quantitative analysis model for predicting the content of target tissue components is established, and the key parameter set of the model is extracted; (3) Symbolic regression mapping construction: The feature data obtained by projecting the nuclear magnetic relaxation signal data of the same set of calibration samples collected by the source device and the target device through the quantitative analysis model are used as the input-output pair of symbolic regression; an explicit mathematical transformation function f is automatically searched and constructed using the symbolic regression algorithm, so that the data of the target device can be mapped to the data space of the source device through the transformation function f; Step (3) specifically includes the following steps: (3.1) The nuclear magnetic relaxation signal data collected on the source device and the target device are projected onto the load space of the quantitative analysis model of the source device to obtain the source device score matrix T_A and the target device initial score matrix T_B_raw; (3.2) Using the source device score matrix T_A as input and the target device initial score matrix T_B_raw as the expected output, the gene expression programming algorithm is used to perform symbolic regression to search for the optimal transformation function f, which satisfies T_B_corrected = f(T_A) and minimizes the error between T_B_corrected and T_B_raw, where T_B_corrected is the corrected target device score matrix; (4) Model transfer and prediction: For the nuclear magnetic relaxation signal data of the unknown sample collected on the target device, the model parameters of the source device extracted in step (2) are used in combination with the transfer function f to calculate the predicted value of the target tissue component content of the unknown sample.

2. The calibration and transfer method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression according to claim 1, characterized in that, The nuclear magnetic resonance relaxation signal data mentioned above is T1-T2 two-dimensional relaxation data acquired through the FSR-CPMG sequence.

3. The calibration and transfer method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression according to claim 1, characterized in that, The quantitative analysis model established in step (2) is a partial least squares regression model, a principal component regression model, or a Bayesian regression model; the key parameter set includes one or more of the regression coefficient matrix, loading matrix, and score matrix.

4. The calibration and transfer method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression according to claim 1, characterized in that, The fitness function of the symbolic regression algorithm comprehensively considers prediction error, expression complexity, and correlation, and its expression is: Fitness = α·(1-RMSE) + β·(1 / Complexity) + γ·Correlation Where RMSE is the root mean square error, Complexity is the total number of nodes in the expression, Correlation is the correlation coefficient, and α, β, and γ are the weighting coefficients.

5. The calibration and transfer method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression according to claim 1, characterized in that, Step (4) specifically includes the following steps: (4.1) Project the nuclear magnetic relaxation signal data X_B_new collected by the unknown sample on the target device onto the load matrix P_A space of the source device to obtain the prediction score T_B_pred = X_B_new · P_A ·(P_A^T · P_A)^{-1}; (4.2) Correct the predicted score using the transformation function f: T_B_corrected = f(T_B_pred); (4.3) Using the regression coefficient matrix B_A of the source device, calculate the predicted value of the tissue component content of the unknown sample: Y_B_pred = T_B_corrected · B_A^T.

6. The calibration and transfer method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression according to claim 1, characterized in that, The target tissue components include at least one of lean meat, fat, and water.

7. A transfer device for a nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression, characterized in that, The device includes: A processor is configured to execute computer-executable instructions; The memory stores one or more computer-executable instructions, which, when executed by the processor, implement the steps of the calibration migration method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression as described in any one of claims 1 to 6.

8. A transfer processor for a nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression, characterized in that, The processor is configured to execute computer-executable instructions, which, when executed by the processor, implement the steps of the calibration migration method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, It stores a computer program that can be executed by a processor to implement the steps of the calibration migration method for the nuclear magnetic resonance tissue quantitative analysis model based on symbolic regression as described in any one of claims 1 to 6.

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