Peripheral nerve stimulation threshold prediction method of magnetic resonance gradient coil and application thereof

Abstract

The invention discloses a peripheral nerve stimulation threshold prediction method of a magnetic resonance gradient coil and application thereof. The method comprises the following steps: firstly, designing a reference coil group with differentiated electromagnetic parameters based on a target gradient coil space structure; then combining a high-precision virtual human body anatomical model and an electromagnetic-neurodynamics coupling model, calculating the induction electric field distribution and stimulation threshold of each coil, and positioning sensitive neuron nodes; expressing a stimulation function as a weighted sum of a local magnetic vector potential component, constructing a linear equation set, and solving an optimal coefficient by adopting a least square method; and finally, establishing a linear regression model of a stimulation function and a threshold reciprocal, and defining a prediction function based on a local field. The prediction method provided by the invention has both calculation efficiency and prediction precision, can further derive a magnetic resonance coil peripheral nerve stimulation threshold curve for real-time evaluation of stimulation risks in imaging scanning, and can also introduce a coil design framework to realize electromagnetic optimization design of a high-threshold gradient coil.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance imaging, and in particular to a method for predicting a peripheral nerve stimulation threshold of a magnetic resonance gradient coil and an application thereof. Background Art

[0002] In recent years, the rapid development of high-gradient performance magnetic resonance imaging (MRI) systems has promoted the application of functional MRI (fMRI) and diffusion MRI (dMRI) in neuroscience research. However, the rapid switching of gradient fields can generate induced electric fields in the human body, triggering peripheral nerve stimulation (PNS), leading to muscle twitching or paresthesia. Currently, PNS has become a key safety bottleneck limiting the improvement of gradient performance. In traditional designs, PNS control is mainly achieved through indirect means such as reducing the coil linear area, reducing coil linearity, or using local coils, and the threshold is evaluated through human experiments after the prototype is manufactured. This process has significant defects: the lack of a PNS threshold prediction method in the design phase leads to repeated trial and error and high costs, which is particularly restrictive for the development of ultra-high-performance gradient coils.

[0003] Despite a series of studies on PNS issues in recent years, existing prediction methods still have certain limitations. For example, Roemer et al.'s simplified model based on uniform electrical properties and maximum induced electric field (in compliance with IEC 60601-2-33) is computationally efficient but does not quantitatively analyze the physiological mechanism (PB Roemer et al, Electric field calculation and peripheral nerve stimulation prediction for head and body gradient coils, 2021). Davids' team achieved accurate predictions by simulating the neurodynamic process based on an electromagnetic-neurodynamic coupling model, but the prediction model they introduced requires complex global electromagnetic field calculations and nonlinear neurodynamic simulations, making it difficult to meet the efficiency requirements of industrial design (M. Davids et al, Prediction of peripheral nerve stimulation thresholds of MRI gradient coils using coupled electromagnetic and neurodynamic simulations, 2019). Recent studies have attempted to indirectly alleviate PNS by constraining the local magnetic flux density (M. Davids et al, Peripheral nerve stimulation informed design of a high-performance asymmetric head gradient coil, 2023), but this constraint does not clearly establish a quantitative relationship between the local magnetic field and the PNS threshold, limiting its application in design optimization.

[0004] In summary, the existing technology has the following core problems:

[0005] 1. Efficient and quantitative PNS threshold prediction cannot be achieved during the gradient coil design phase and relies on prototype-based experimental correction, increasing R&D cycle and costs.

[0006] 2. Simplified models ignore physiological mechanisms, while complex models have excessively high computational loads, making it difficult to balance accuracy and efficiency.

[0007] 3. The local field constraint strategy fails to establish an explicit relationship between the local field and the PNS threshold, and cannot achieve quantitative optimization of the threshold. Summary of the Invention

[0008] The present invention provides a method for predicting the peripheral nerve stimulation threshold of a magnetic resonance gradient coil and its application, which can realize efficient quantitative prediction of the PNS threshold.

[0009] The technical solutions of the present invention are as follows:

[0010] A method for predicting a peripheral nerve stimulation threshold of a magnetic resonance gradient coil comprises the following steps:

[0011] S1. Reference gradient coil set construction: Design the reference gradient coil set based on the spatial structural parameters of the target MRI gradient coil;

[0012] S2. Calculation of Induced Electric Field and Threshold: Based on a high-precision virtual human anatomical model, the induced electric field distribution of each reference gradient coil in the human body is simulated using an electromagnetic-neurodynamic coupling model, and the peripheral nerve stimulation threshold th is calculated. The spatial coordinates of all activated neuronal nodes in the high-precision virtual human anatomical model are recorded.

[0013] S3. Stimulation function AF modeling: Define the neuron node stimulation function AF as the first-order spatial differential of the induced electric field projection on the peripheral nerve axis; combine the nerve distribution trajectory and use the induced electric field distribution data obtained in step S2 to solve the AF value of each reference coil at the neuron node;

[0014] S4. Calculation of local magnetic vector potential components: Calculate the local magnetic vector potential and its gradient components generated by each reference coil at the neuron node;

[0015] S5. Construction of linear equations: The neuron node stimulation function AF is expressed as the weighted sum of the local magnetic vector position components, as shown in formula (1):

[0016]

[0017] Wherein, (n) represents a neuron node; A (n) j Represents the local magnetic vector potential A at the location of the neuron node (n) (n) Component in the j direction (j = x, y, z); κ j represents the magnetic vector potential component A (n) j The weighting coefficient of x , j , κ y，j and κ z，j Represent the magnetic vector potential components A (n) j The weighting coefficients of the partial differential terms in the x, y, and z directions; κ cnst Represents a constant term.

[0018] For each activated neuron node, the AF value obtained in step S3 and the local magnetic vector position component obtained in step S4 are substituted into formula (1) to establish a linear equation system containing N equations;

[0019] S6. Coefficient solution: using the least square method to solve the linear equations to determine the weighting coefficient κ of each local magnetic vector position component of each neuron node;

[0020] S7. Linear regression modeling: A linear relationship between the reciprocal of the peripheral nerve stimulation threshold 1 / th and the AF value is established for each neuron node, as shown in formula (2):

[0021] 1 / th (n) =k (n) AF (n) +h (n) (2)

[0022] Where k and h are regression coefficients;

[0023] The regression coefficients k and h were fitted by the least squares method;

[0024] S8. Definition of prediction function PD: 1 / th is defined as the prediction function PD, and the PD value is calculated based on the magnetic vector position distribution of the gradient coil and formulas (1)-(2); the inverse of the maximum PD value of all neuronal nodes in the high-precision virtual human anatomical model is taken as the peripheral nerve stimulation threshold of the predicted magnetic resonance gradient coil.

[0025] In step S1 , the spatial structural parameters of the coil include the distribution layer structure and size; the electromagnetic performance parameters of the coil include gradient efficiency, linearity, shielding, winding spacing, torque, inductance, resistance and magnetic field distribution.

[0026] Preferably, step S1 includes:

[0027] S11. Design and generate an initial coil as a reference coil, wherein the spatial structure and electromagnetic performance parameters of the initial coil are consistent with those of the target magnetic resonance gradient coil;

[0028] S12. Based on a high-precision virtual human anatomical model, the electromagnetic-neurodynamic model was used to screen the 20 neuronal nodes that were most sensitive to peripheral nerve stimulation using the reference coil.

[0029] S13. Perform iterative optimization based on the reference coil, adjusting the coil structure to reduce the magnetic flux density amplitude of the sensitive node selected in step S12 while maintaining the gradient efficiency, linearity, shielding, winding spacing, and torque unchanged, and increasing the inductance by 0.5%-2%, thereby obtaining a reference gradient coil.

[0030] S14, repeating steps S12 and S13 until the number N of differentiated reference gradient coils continuously generated is greater than or equal to 20;

[0031] Each iteration uses the previously generated reference gradient coil as the new baseline coil.

[0032] Preferably, in step S11, the spatial structure electromagnetic performance parameters of the initial coil are consistent with those of the target coil, the coil winding pattern is designed using the finite difference method, and the entire coil design process is described using the following optimization problem framework:

[0033]

[0034] Where Φ is the gradient coil flow function to be solved, L is the inductance matrix, and B z,tar The coil generates a linearly changing spatial magnetic field, ε is the linearity, B stray is the stray field generated by the coil, S1 and S2 are the sensitivity matrices obtained based on the magnetic field constraints, T and D are the sensitivity matrices obtained based on the coil torque and winding spacing constraints, respectively, T max and D min They represent the column vectors obtained based on the set maximum coil torque and minimum winding spacing respectively.

[0035] Preferably, the high-precision virtual human anatomical model has a spatial resolution of no less than 1 mm. Meanwhile, the final stimulus threshold evaluation uses the average of the PD maximum values of multiple virtual human anatomical models to reflect population differences.

[0036] Preferably, the high-precision virtual human anatomical models are "Jeduk" and "Yoon-sun" developed by the Swiss IT'IS Foundation.

[0037] Preferably, the electromagnetic-neurodynamic coupling model includes a coupling solution module of Maxwell's equations and the McIntyre-Richardson-Grill neurodynamic model, and adopts the following parameter configuration:

[0038] a) The electromagnetic field calculation frequency setting range is 500-3000Hz;

[0039] b) The spatial step size when applying the Mack equations to calculate the spatial electromagnetic field distribution is 1 mm;

[0040] c) The waveform of the coil transmission current is a sinusoidal wave or a trapezoidal wave of the same frequency;

[0041] d) The error in solving the neural dynamics model is less than 1%.

[0042] Preferably, in step S13, the coil structure is adjusted by setting magnetic flux density amplitude constraints on the 20 neuron nodes with the lowest PNS thresholds, while keeping the gradient efficiency, linearity, shielding, winding spacing, and torque unchanged. In this case, the coil design optimization problem is:

[0043]

[0044] Among them, FL Φ represents the local magnetic flux density amplitude generated by the coil on the target neuron node, B ref is the local magnetic flux density amplitude generated on the target neuron node of the reference coil, ε B It is an adjustment coefficient between 0 and 1.

[0045] During the design process, while keeping other terms of formula (2b) unchanged, adjust ε B The value increases the total coil magnetic field energy storage by 1% (X / Y axis) or 2% (Z axis), corresponding to a 1% (X / Y axis) or 2% (Z axis) increase in coil inductance.

[0046] In step S3, the first-order spatial differential of the axial projection of the human body induced electric field generated by the gradient coil is defined as the neuron node stimulation function AF; the differential term is approximately calculated using the difference method.

[0047] To simplify the calculation and further improve the efficiency, it is preferred to construct a sensitive point set of neuron nodes based on the lowest PNS threshold corresponding to each reference coil; in the subsequent solution process of the prediction function PD, only the neuron nodes in the sensitive point set are considered.

[0048] Preferably, in step S4, the Biot-Savart law is applied to calculate the local magnetic vector potential A generated by each reference coil at the neuron node in the sensitive point set, as shown below:

[0049]

[0050] Where μ0 and I represent the vacuum magnetic permeability and the transmission current of the coil, respectively; l represents the coil winding element; r and r' represent the spatial position of the local field point and the coil winding element, respectively;

[0051] The magnetic vector potential gradient components are approximately calculated using the spatial difference method.

[0052] Preferably, in step S5, the AF expression is optimized by Coulomb norm, as shown in formula (4):

[0053]

[0054] Preferably, step S6 includes:

[0055] Write the linear equations in matrix form:

[0056] PK=F AF (4a)

[0057] Where K is the column vector consisting of the undetermined weight coefficients κ, P is the coefficient matrix obtained according to formula (4), and F AFis the column vector composed of the stimulus function term AF in formula (4);

[0058] The least squares solution of the linear equations is as follows:

[0059] K=(P T P) -1 P T F AF (4b).

[0060] The present invention also provides a method for constructing a peripheral nerve stimulation threshold curve of a magnetic resonance gradient coil, comprising the following steps:

[0061] (1) Based on the peripheral nerve stimulation threshold prediction method of the magnetic resonance gradient coil, the prediction function PD value of the target gradient coil at at least two different frequencies in the frequency range of 500-3000 Hz is obtained;

[0062] (2) The prediction function PD value at different frequencies is fitted with the corresponding frequency f to generate a peripheral nerve stimulation threshold curve that fits the sinusoidal current waveform. The expression is:

[0063]

[0064] Among them, G′ min is the peripheral nerve stimulation threshold under the sinusoidal current waveform, G0 and τ are the coefficients based on the least squares fitting method;

[0065] (3) Based on the peripheral nerve stimulation threshold curve of the sinusoidal current waveform, the threshold curve of the adaptive trapezoidal current waveform is derived, as shown in formula (6):

[0066]

[0067] Among them, G min is the peripheral nerve stimulation threshold under the trapezoidal current waveform, t is the time for the current to rise from zero to the maximum value, and the trapezoidal wave platform time is not less than 0.5 milliseconds.

[0068] The present invention also provides a method for assessing the risk of peripheral nerve stimulation during magnetic resonance imaging (MRI), comprising: monitoring the actual gradient value of the gradient field in the scanning sequence in real time based on the peripheral nerve stimulation threshold curve; and triggering at least one of the following protection mechanisms if the actual gradient value exceeds a calculated threshold value for the corresponding waveform and frequency:

[0069] a) Gradient field strength or gradient switching rate is forced to decrease;

[0070] b) Scan sequence timing adjustment;

[0071] c) Sound and light alarm and scanning pause.

[0072] Preferably, the forced downward adjustment of the gradient field intensity or the gradient switching rate refers to reducing the gradient field intensity or the switching rate to 80% of the calculation threshold through a hardware interface;

[0073] Scan sequence timing adjustment refers to delaying the rise time of gradient pulses or inserting silent intervals.

[0074] The present invention also provides a real-time monitoring device for peripheral nerve stimulation risk of a magnetic resonance gradient coil, comprising:

[0075] Data import module: imports magnetic resonance gradient coil data, high-precision human anatomical model and determines the relative position of the high-precision human anatomical model and the gradient coil during imaging scanning;

[0076] A threshold curve generation module: applying the method for constructing a peripheral nerve stimulation threshold curve to generate a peripheral nerve stimulation threshold curve for a magnetic resonance gradient coil;

[0077] Dynamic monitoring and feedback module: During the imaging scan, the actual gradient value is compared in real time with the threshold value calculated based on the waveform and frequency corresponding to the peripheral nerve stimulation threshold curve. If the actual gradient value exceeds the calculated threshold value, at least one of the following protection mechanisms is triggered:

[0078] a) Gradient field strength or gradient switching rate is forced to decrease;

[0079] b) Scan sequence timing adjustment;

[0080] c) Sound and light alarm and scanning pause;

[0081] User interaction interface: Visually displays the peripheral nerve stimulation risk level, threshold curve, real-time gradient parameters and triggered protection measures, and provides a manual intervention interface to adjust scanning parameters.

[0082] The present invention also provides a high threshold gradient coil design method, comprising the following steps:

[0083] (i) Take the prediction function PD as a constraint and find the corresponding sensitivity matrix F L ;

[0084] (ii) A hard constraint of max(PD)≤εPD0 is imposed during coil optimization, where PD0 is the maximum PD value before optimization and ε is the introduced constraint scaling factor, ε<1. The coil design optimization problem then becomes:

[0085]

[0086] Where Φ is the gradient coil flow function to be solved, L is the inductance matrix, and B z,tar The coil generates a linearly changing spatial magnetic field, ε is the linearity, Bstray is the stray field generated by the coil, S1 and S2 are the sensitivity matrices obtained based on the magnetic field constraints, T and D are the sensitivity matrices obtained based on the coil torque and winding spacing constraints, respectively, and F L Φ represents the local magnetic flux density amplitude generated by the coil on the target neuron node, PD0 is the maximum PD value before optimization, and λ is the introduced constraint proportional coefficient (λ<1);

[0087] (iii) Iteratively optimize the coil structure to improve the stimulation safety margin while meeting the electromagnetic performance requirements, and obtain a coil winding solution that meets the requirements through continuous iterative solutions.

[0088] Compared with the prior art, the present invention has the following beneficial effects:

[0089] 1. Quantitative PNS prediction based on local fields: The peripheral nerve stimulation threshold prediction method disclosed in the present invention quantitatively describes the relationship between the local field generated by the gradient coil and the PNS threshold, so that the PNS threshold can be very conveniently calculated based on the coil data, which can realize PNS evaluation in the coil design stage.

[0090] 2. High computational efficiency: Using the peripheral nerve stimulation threshold prediction method disclosed in this invention, the PNS threshold can be directly obtained by linearly transforming the local field components, avoiding the complex calculations of the electromagnetic-neurodynamic coupling model. Furthermore, in the process of constructing the prediction model, the method of using the least squares method to fit and correct unknown parameters based on the local field reduces the amount of computation compared to the traditional method using the global field, while avoiding the complex nonlinear processes in the electromagnetic-neurodynamic coupling model, further improving computational efficiency.

[0091] 3. Dynamic Safety Monitoring Capability: The disclosed peripheral nerve stimulation threshold prediction method can be integrated into a PNS threshold curve for assessing scan safety. This curve, when incorporated into the safety assessment module of an MRI system, can assess nerve stimulation risks in real time, triggering protective mechanisms such as imaging sequence adjustment and scan pause, thereby improving imaging scan safety.

[0092] 4. Adaptability of the gradient coil design framework: Since the prediction model disclosed in the present invention can be calculated through linear transformation of the local field, it can be introduced as a linear constraint into the traditional gradient coil design framework, and gradient coils with high PNS thresholds can be obtained by iterative optimization during the coil design stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] Figure 1 A flowchart was constructed for a prediction model of peripheral nerve stimulation thresholds for magnetic resonance gradient coils.

[0094] Figure 2 This is a cross-sectional diagram of the spatial structure of a head-specific magnetic resonance gradient coil.

[0095] Figure 3 Schematic diagram of PNS sensitive points generated by the gradient coil in the human body model.

[0096] Figure 4 Figure 3 is a graphical representation of the relationship between the maximum fitting error of the stimulation function AF and the number of reference coils.

[0097] Figure 5 is the linear fitting result between the inverse of the PNS threshold and the stimulation function.

[0098] Figure 6 This is a comparison chart of the PNS threshold curve of the magnetic resonance gradient coil and the experimental value.

[0099] Figure 7 The winding patterns of the magnetic resonance gradient coil before (A) and after (B) optimization.

[0100] Figure 8 The induced electric field distribution generated by the magnetic resonance gradient coil in the human body before (A) and after (B) optimization.

[0101] Figure 9 To optimize the PNS threshold of the magnetic resonance gradient coil before and after the change curve based on the gradient pulse frequency. DETAILED DESCRIPTION

[0102] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be noted that the following examples are intended to facilitate understanding of the present invention and do not have any limiting effect on the present invention.

[0103] The present invention provides a method for predicting the threshold of peripheral nerve stimulation using a magnetic resonance gradient coil. This method combines the simplicity and ease of use of indirectly describing the PNS threshold based on the local field with the accuracy of a quantitative electromagnetic-neurodynamic model, ultimately achieving direct settlement of the PNS threshold through the local field, making it possible to perform efficient and quantitative threshold prediction based on magnetic resonance gradient coil data. Here, the local field refers to the local magnetic field (magnetic flux density, magnetic vector position, etc.) components on the main peripheral neuron nodes of the human body, as well as their corresponding spatial first-order differential and other derivative physical quantities. The construction process of the peripheral nerve stimulation threshold prediction model using a magnetic resonance gradient coil is as follows: Figure 1 The following will take the gradient coil in the head-specific magnetic resonance system as an example to specifically illustrate the implementation method and effect of each step of the technical solution:

[0104] S1. Construction of reference gradient coil set

[0105] First, define the spatial structure of the target magnetic resonance gradient coil. Figure 2As shown, the head-specific MRI gradient coil used in this embodiment is a three-layer cylindrical structure, comprising a main coil layer 2, an intermediate coil layer 3, and a shield coil layer 4. This provides sufficient design freedom to meet the performance requirements of ultra-high gradient field MRI. The imaging region 1 has a diameter of 200 mm and is located in the middle near one end of the main coil layer 2, substantially covering the human brain. In this embodiment, the main parameters of the coil structure (including the cylindrical diameter d and length l) are as follows: the diameter d1 of the main coil layer 2 is 46 cm, the diameter d2 of the intermediate coil layer 3 is 62 cm, the diameter d3 of the shield coil layer 4 is 75 cm, the length l1 of the main coil layer 2 is 66 cm, the length l2 of the intermediate coil layer 3 is 112 cm, and the length l3 of the shield coil layer 4 is 120 cm. Furthermore, the design targets for the main performance parameters of the coil are as follows: coil efficiency of 0.15 mT / m / A, linearity deviation of 5%, stray field generated per unit current of no more than 1 μT, maximum coil torque generated of 0.1 Nm, and minimum distance between coil windings of 7 mm.

[0106] To calibrate the PNS prediction model, this technical solution designed a set of reference gradient coils. These coils share the same spatial structure as the target coils, but their electromagnetic performance parameters are designed differently. Ideally, the reference coils should align with the target coils' key performance parameters. Therefore, this technical solution achieves this by controlling the magnetic flux density amplitude at the stimulation-sensitive peripheral neuronal nodes, as follows:

[0107] S11. Design and generate an initial coil as a reference coil. The spatial structure and electromagnetic performance parameters of the initial coil are consistent with those of the target magnetic resonance gradient coil.

[0108] In this embodiment, the spatial structure and main performance parameters of the initial coil are consistent with those of the target coil. The coil winding pattern is designed using the finite difference method. The entire coil design process can be described using the following optimization problem framework:

[0109]

[0110] Where Φ is the gradient coil flow function to be solved, L is the inductance matrix, and B z,tar The coil generates a linearly changing spatial magnetic field, ε is the linearity, B stray is the stray field generated by the coil, S1 and S2 are the sensitivity matrices obtained based on the magnetic field constraints, and T and D represent the sensitivity matrices obtained based on the coil torque and winding spacing constraints, respectively. max and D min They represent the column vectors obtained based on the set maximum coil torque and minimum winding spacing respectively.

[0111] S12. The 20 neuronal nodes that are most sensitive to peripheral nerve stimulation of the benchmark coil are screened using the electromagnetic-neurodynamic model.

[0112] The electromagnetic-neurodynamic model was used to simulate the coil-induced electric field and PNS thresholds. Virtual human anatomical models of "Jeduk" (33 years old, male) and "Yoon-sun" (26 years old, female), developed by the Swiss IT'IS Foundation, were used. These models had a spatial resolution of 0.1 × 0.1 × 0.2 mm. The simulation involved solving the coil-induced electric field distribution in the human body using Maxwell's equations and then integrating this distribution into the McIntyre-Richardson-Grill (MRG) neurodynamic model to calculate the PNS threshold. Considering the common MRI pulse sequence frequency range (in the kilohertz range), the electromagnetic frequency used in the simulation was 500–3000 Hz with a step size of 250 Hz. Furthermore, the spatial step size of the human model was 1 mm, and the coil current was a sinusoidal wave with the same electromagnetic frequency. The maximum error in the neurodynamic solution was 1%. Figure 3 The figure shows the 20 PNS neuron nodes with the lowest thresholds located by the three-axis gradient coil on the human body model "Jeduk", that is, the points most sensitive to stimulation. Due to the close distance, some nodes are Figure 3 There is some overlap when displayed in .

[0113] S13. Perform iterative optimization based on the reference coil and adjust the coil structure to reduce the magnetic flux density amplitude at the sensitive nodes screened in S11, while maintaining the gradient efficiency, linearity, shielding, winding spacing, and torque unchanged, and increasing the inductance by 0.5%-2%.

[0114] In the subsequent reference coil design process of this embodiment, the coil structure is adjusted by setting magnetic flux density amplitude constraints on the 20 neuron nodes with the lowest PNS thresholds, while keeping the main performance objectives of the coil unchanged. At this time, the optimization problem of coil design becomes:

[0115]

[0116] Among them, F L Φ represents the local magnetic flux density amplitude generated by the coil on the target neuron node, B ref is the local magnetic flux density amplitude generated on the target neuron node of the reference coil, ε B is an adjustment coefficient between 0 and 1. During the design process, while keeping other terms of formula (2b) unchanged, adjust ε B The value increases the total coil magnetic field energy storage by 1% (X / Y axis) or 2% (Z axis), corresponding to a 1% (X / Y axis) or 2% (Z axis) increase in coil inductance.

[0117] S14. Repeat the optimization process of steps S12 and S13, using the previously generated reference gradient coil as a new reference coil in each iteration, and continue to generate differentiated reference gradient coils until the number of generated reference gradient coils N is greater than or equal to 20, ensuring that the least squares method solution converges.

[0118] The previously designed reference gradient coil is used as the new baseline coil, and steps S12 and S13 are repeated. In this embodiment, 26 reference coils (N=26) are ultimately designed for each axis. The inductance of these coils relative to the initial coil ranges from 1 to 1.25 (X / Y axes) or 1 to 1.5 (Z axis).

[0119] S2. Induction electric field and threshold calculation

[0120] During the design of the reference coils in this example, the electromagnetic-neurodynamic model was used to calculate the induced electric field distribution and PNS thresholds generated by most reference gradient coils (except for the last reference coil generated in each axis). In this step, the same method was used to further simulate and record the induced electric fields and PNS thresholds generated by the remaining reference coils in the human body.

[0121] S3. Stimulus Function AF Modeling

[0122] The first-order spatial differential of the induced electric field generated by the gradient coils, projected onto the axial direction of the peripheral nerves, is defined as the neuron node stimulation function (AF). Based on the peripheral nerve distribution trajectory in the virtual human body model and the induced electric field distribution generated by each reference coil in S2, the first-order spatial differential of the induced electric field projected along the peripheral nerve distribution direction at each peripheral nerve node is calculated. The differential term is approximated using the difference method.

[0123] In order to simplify the calculation and further improve the efficiency, this embodiment constructs a set of neuron nodes with the lowest PNS threshold corresponding to each reference coil, namely the sensitive point set. At the same time, in the subsequent solution process of the prediction function PD, only the neuron nodes in the sensitive point set are considered, thereby achieving the purpose of reducing the amount of calculation. The points included in the sensitive point set constructed in this embodiment are as follows: Figure 2 As shown, it includes PNS sensitive point A15 / PNS sensitive point A26 (X axis), PNS sensitive point B17 / PNS sensitive point B28 (Y axis), and PNS sensitive point C19 / PNS sensitive point C210 (Z axis).

[0124] S4. Calculation of local magnetic vector potential components

[0125] The Biot-Savart law is applied to calculate the local magnetic vector potential A generated by each reference coil at the neuron node in the sensitive point set, as shown below:

[0126]

[0127] where μ0 and I represent the vacuum magnetic permeability and the transmission current of the coil, respectively; l represents the coil winding element; r and r' represent the spatial position of the local field point and the coil winding element, respectively.

[0128] The magnetic vector potential gradient component is approximately calculated by the spatial difference method as shown below (taking the gradient component in the x direction as an example):

[0129]

[0130] In this embodiment, Δx is the spatial step length, and Δx is set to 2 mm; A j (x, y, z) represents the component of the magnetic vector potential A along the j direction (j = x, y, z) at the position with spatial coordinates (x, y, z).

[0131] S5. Construction of linear equations

[0132]

[0133] Where (n) represents a specific neuron node; A (n) j Represents the local magnetic vector potential A at the location of the neuron node (n) (n) Component in the j direction (j = x, y, z); κ j represents the magnetic vector potential component A (n) j The weighting coefficient of x，j , κ y，j and κ z，j Represent the magnetic vector potential components A (n) j The weighting coefficients of the partial differential terms in the x, y and z directions; κ cnst Represents a constant term.

[0134] The AF is approximated using the weighted sum of the local magnetic vector position components as shown in formula (1) or formula (4), where the weighting coefficient κ is determined based on the magnetic vector position components generated by the reference coil at the neuron node and the AF fitting. Substituting the magnetic vector position components (obtained in S4) and the stimulation function AF (obtained in S3) generated by all 26 reference coils designed for each axis at the neuron node in the sensitive point set into formula (1), 26 linear equations are obtained. In addition, there are 13 undetermined coefficients in formula (1), and formula (4) has 13 undetermined coefficients due to the application of the Coulomb norm. One of the undetermined coefficients is eliminated, making the calculation simpler. Therefore, this embodiment uses formula (4) to fit AF.

[0135] S6. Coefficient solution

[0136] Write the linear equations constructed in S5 into matrix form:

[0137] PK=F AF (4a)

[0138] Where K is the column vector consisting of the undetermined weight coefficients κ, P is the coefficient matrix obtained according to formula (4), and F AF is the column vector of the stimulus function AF in formula (4). The least squares solution of this linear equation system is as follows:

[0139] K=(P T P) -1 P T F AF (4b)

[0140] The relationship between the maximum fitting error of the stimulation function AF in formula (4) and the number of reference coils used to construct formula (4a) is as follows: Figure 4 As shown in the figure, for the main stimulation sensitive points in the sensitive point set, when the number of reference coils N is not less than 20, the fitting error can be less than 1%, which basically meets the requirements of practical applications.

[0141] S7. Linear regression modeling

[0142] Applying formula (2), for the neuron nodes in the sensitive point set, a linear relationship between the inverse of the stimulation threshold (1 / th) and the stimulation function AF is established:

[0143] 1 / th (n) =k (n) AF (n) +h (n) (2)

[0144] On this basis, a linear regression model is constructed based on the AF obtained in S3 and the PNS threshold obtained in S1-S2, and the linear coefficients k and h in formula (2) are solved by the least squares fitting method similar to that in S6.

[0145] Figure 5 The relationship between the inverse PNS threshold and the stimulation function obtained by linear regression modeling is shown. The circles in the figure mark the inverse PNS threshold and stimulation function generated by 26 reference coils. The curve is based on the main stimulation sensitive points in the sensitive point set. It was obtained by least squares fitting. In the figure, the higher r 2 The value (greater than 0.96) shows that the use of a linear model to fit the relationship between the inverse of the PNS threshold (1 / th) and the stimulation function AF is reasonable.

[0146] S8. Definition of prediction function PD

[0147] 1 / th is defined as the prediction function PD, which can be calculated based on the gradient coil magnetic vector position distribution and formulas (1)-(2). In this embodiment, the inverse of the maximum PD value of all neuronal nodes in the sensitive point set (1 / PD) is the predicted peripheral nerve stimulation threshold of the magnetic resonance gradient coil.

[0148] S9. Calculate the PNS threshold curve of the magnetic resonance gradient coil

[0149] The constructed PNS threshold prediction model of the magnetic resonance gradient coil can be used to calculate the PNS threshold curve of the magnetic resonance gradient coil. The curve is defined as the minimum magnetic flux density change rate (dB / dt) required to induce PNS in the human body when the gradient coil is driven by a bidirectional trapezoidal current pulse, or the minimum gradient field strength (G min ), a function curve of the time from zero to maximum intensity of the current pulse. The plateau period of the trapezoidal current pulse is 0.5ms. In this embodiment, G min To describe the PNS threshold curve. The steps of applying the prediction function PD to construct the PNS threshold curve are as follows:

[0150] S91. Based on the peripheral nerve stimulation threshold prediction model for the magnetic resonance gradient coil provided by the present invention, obtain prediction function (PD) values for the target gradient coil at at least two different frequencies within the frequency range of 500-3000 Hz. In this embodiment, 11 PDs within the range of 500-3000 Hz (with a step size of 250 Hz) are constructed.

[0151] S92. Fit the PD values at different frequencies to the corresponding frequency f to generate a peripheral nerve stimulation threshold th0 curve that fits the sinusoidal current waveform. The expression is:

[0152]

[0153] Among them, G′ min is the peripheral nerve stimulation threshold under the sinusoidal current waveform, G0 and τ are the coefficients based on the least squares fitting method.

[0154] S93. Based on the coefficients G0 and τ in the fitted sinusoidal current waveform threshold curve, derive a threshold curve adapted to the trapezoidal current waveform:

[0155]

[0156] Among them, G min is the peripheral nerve stimulation threshold under the trapezoidal current waveform, t is the time for the current to rise from zero to the maximum value, and the trapezoidal wave platform time is not less than 0.5 milliseconds.

[0157] Figure 6 The figure shows a comparison between the threshold curve fitted in this example and the experimental value. The experiment was conducted on the United Imaging uMRNeuroFrontier platform. It can be seen that the threshold curve fitted is in good agreement with the experimental results.

[0158] The constructed PNS threshold curve can be used to monitor the actual gradient value of the gradient field during the scanning sequence in real time. The real-time monitoring module obtains the actual gradient value of the current scanning sequence (including gradient strength and switching rate) through the gradient controller of the magnetic resonance system and compares it with the safety threshold value in the threshold curve. If the actual gradient value exceeds the safety threshold of the threshold curve, the following protection mechanism is triggered:

[0159] a) reducing the gradient field strength or switching rate to 80% of the threshold through the hardware interface;

[0160] b) Delay the rise time of the gradient pulse or insert a silent interval;

[0161] c) Alert the operator through sound and light alarms and suspend scanning until parameter adjustment is completed.

[0162] In actual implementation, the gradient is first adjusted downward. If the limit is still exceeded, the scan is paused and an audible and visual alarm is issued. The operator adjusts the parameters and then scans again.

[0163] Based on the constructed peripheral nerve stimulation threshold curve of the magnetic resonance gradient coil, the present invention provides a real-time monitoring device for the peripheral nerve stimulation risk of the magnetic resonance gradient coil, including the following modules:

[0164] a) Data Import Module: Supports importing gradient coil parameters (such as inductance and resistance) and high-precision human body models (resolution 1mm) from files or databases. The relative positions of the model and coils are automatically aligned using the MRI system coordinate system.

[0165] b) Threshold curve generation module: calling the threshold curve generation algorithm provided by the present invention, inputting coil parameters, and automatically generating and storing sinusoidal wave and trapezoidal wave threshold curves.

[0166] c) Dynamic monitoring and feedback module: embedded in the MRI control software, during the imaging scan, the actual value of the gradient field is compared with the safety threshold in the threshold curve in real time. If the threshold is exceeded, the protection mechanism described in the magnetic resonance imaging peripheral nerve stimulation risk assessment method provided by the present invention is triggered.

[0167] d) User interface: The interface displays real-time gradient parameters, threshold curves, and risk levels (green / yellow / red color symbols), and provides a manual adjustment slider to modify the gradient field limit value.

[0168] S10, high threshold gradient coil design

[0169] Based on the constructed PNS threshold function for magnetic resonance gradient coils, the present invention also provides a high-threshold gradient coil design method for designing high-stimulation threshold gradient coils. In this embodiment, a set of gradient coils with high PNS thresholds was designed based on the target coil spatial structure and performance parameters when constructing the threshold function PD. The specific steps are as follows:

[0170] S101, the PD function obtained is used as a constraint condition, and the corresponding sensitivity matrix is obtained. In the solution process, the coil space structure and performance parameter target selected are consistent with those used in the previous PD function generation process. The final sensitivity matrix obtained is F L .

[0171] S102. Apply the hard constraint of max(PD)≤εPD0 in the coil optimization, where PD0 is the maximum PD value before optimization and λ is the introduced constraint proportional coefficient (λ<1). At this point, the coil design optimization problem becomes:

[0172]

[0173] S103. Iteratively optimize the coil structure to improve the stimulation safety margin while meeting electromagnetic performance requirements. Based on the constructed coil design optimization problem, a coil winding solution that meets the requirements is obtained through continuous iterative solution. Figure 7 To adopt this technical solution, the winding style of the front and rear coils is optimized; Figure 8 To optimize the distribution of the induced electric field generated by the front and rear coils on the human body; Figure 9 The following curves show the change in PNS threshold based on gradient pulse frequency before and after optimization. As shown in the figure, the inductances of the coils on the X, Y, and Z axes were 261μH (before optimization) / 298μH (after optimization), 261μH (before optimization) / 300μH (after optimization), and 182μH (before optimization) / 273μH (after optimization), respectively. Simultaneously, the PNS thresholds under 1000Hz sinusoidal excitation on the X, Y, and Z axes increased from 102mT / m, 63mT / m, and 96mT / m to 190mT / m, 138mT / m, and 164mT / m, respectively. Thus, while maintaining most coil performance, a 15% increase in coil inductance increased the PNS threshold to 219% of the original value (with 1000Hz sinusoidal excitation), significantly improving the gradient coil's stimulation safety margin.

[0174] The embodiments described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for predicting the peripheral nerve stimulation threshold of a magnetic resonance gradient coil, characterized in that: The following steps are involved: S1. Reference gradient coil set construction: Design the reference gradient coil set based on the spatial structural parameters of the target MRI gradient coil; S2. Calculation of Induced Electric Field and Threshold: Based on a high-precision virtual human anatomical model, the induced electric field distribution of each reference gradient coil in the human body is simulated using an electromagnetic-neurodynamic coupling model, and the peripheral nerve stimulation threshold th is calculated. The spatial coordinates of all activated neuronal nodes in the high-precision virtual human anatomical model are recorded. S3. Stimulation function AF modeling: Define the neuron node stimulation function AF as the first-order spatial differential of the induced electric field projection on the peripheral nerve axis; combine the nerve distribution trajectory and use the induced electric field distribution data obtained in step S2 to solve the AF value of each reference coil at the neuron node; S4. Calculation of local magnetic vector potential components: Calculate the local magnetic vector potential and its gradient components generated by each reference coil at the neuron node; S5. Construction of linear equations: The neuron node stimulation function AF is expressed as the weighted sum of the local magnetic vector position components, as shown in formula (1): Where (n) represents a neuron node; Represents the local magnetic vector potential A at the location of the neuron node (n) (n) Component in the j direction (j = x, y, z); κ j represents the magnetic vector potential component The weighting coefficient of x，j , κ y，j and κ z，j Represent the magnetic vector potential components The weighting coefficients of the partial differential terms in the x, y, and z directions; κ cnst represents a constant term; For each activated neuron node, the AF value obtained in step S3 and the local magnetic vector position component obtained in step S4 are substituted into formula (1) to establish a linear equation system containing N equations; S6. Coefficient solution: using the least square method to solve the linear equations to determine the weighted coefficients of each local magnetic vector position component of each neuron node; S7. Linear regression modeling: A linear relationship between the reciprocal of the peripheral nerve stimulation threshold 1 / th and the AF value is established for each neuron node, as shown in formula (2): 1 / th (n) =k (n) ·OF (n) +h (n) (2) Where k and h are regression coefficients; The regression coefficients k and h were fitted by the least squares method; S8. Definition of prediction function PD: 1 / th is defined as the prediction function PD, and the PD value is calculated based on the magnetic vector position distribution of the gradient coil and formulas (1)-(2); the inverse of the maximum PD value of all neuronal nodes in the high-precision virtual human anatomical model is taken as the peripheral nerve stimulation threshold of the predicted magnetic resonance gradient coil.

2. The method for predicting the peripheral nerve stimulation threshold of the magnetic resonance gradient coil according to claim 1, characterized in that: Step S1 includes: S11. Design and generate an initial coil as a reference coil, wherein the spatial structure and electromagnetic performance parameters of the initial coil are consistent with those of the target magnetic resonance gradient coil; S12. Based on a high-precision virtual human anatomical model, the electromagnetic-neurodynamic model was used to screen the 20 neuronal nodes that were most sensitive to peripheral nerve stimulation using the reference coil. S13. Perform iterative optimization based on the reference coil, adjusting the coil structure to reduce the magnetic flux density amplitude of the sensitive node selected in step S12 while maintaining the gradient efficiency, linearity, shielding, winding spacing, and torque unchanged, and increasing the inductance by 0.5%-2%, thereby obtaining a reference gradient coil. S14, repeating steps S12 and S13 until the number N of differentiated reference gradient coils continuously generated is greater than or equal to 20; Each iteration uses the previously generated reference gradient coil as the new baseline coil.

3. The method for predicting the peripheral nerve stimulation threshold of the magnetic resonance gradient coil according to claim 1, characterized in that: The high-precision virtual human anatomical model has a spatial resolution of no less than 1 mm.

4. The method for predicting the peripheral nerve stimulation threshold of the magnetic resonance gradient coil according to claim 1, characterized in that: The electromagnetic-neurodynamic coupling model includes a coupling solution module for Maxwell's equations and the McIntyre-Richardson-Grill neurodynamic model, and uses the following parameter configuration: a) The electromagnetic field calculation frequency setting range is 500-3000Hz; b) The spatial step size when applying the Mack equations to calculate the spatial electromagnetic field distribution is 1 mm; c) The waveform of the coil transmission current is a sinusoidal wave or a trapezoidal wave of the same frequency; d) The error in solving the neural dynamics model is less than 1%.

5. The method for predicting the peripheral nerve stimulation threshold of the magnetic resonance gradient coil according to claim 1, characterized in that: In step S4, the Biot-Savart law is applied to calculate the local magnetic vector potential A generated by each reference coil at the neuron node in the sensitive point set, as shown below: Where μ0 and I represent the vacuum magnetic permeability and the transmission current of the coil, respectively; l represents the coil winding element; r and r' represent the spatial position of the local field point and the coil winding element, respectively; The magnetic vector potential gradient components are approximately calculated using the spatial difference method.

6. The method for predicting the peripheral nerve stimulation threshold of the magnetic resonance gradient coil according to claim 1, characterized in that: In step S5, the AF expression is optimized by Coulomb norm, as shown in formula (4):

7. A method for constructing a peripheral nerve stimulation threshold curve for a magnetic resonance gradient coil, characterized in that: The following steps are involved: (1) Based on the peripheral nerve stimulation threshold prediction method of the magnetic resonance gradient coil according to any one of claims 1 to 6, the prediction function PD value of the target gradient coil at at least two different frequencies in the frequency range of 500-3000 Hz is obtained; (2) The prediction function PD value at different frequencies is fitted with the corresponding frequency f to generate a peripheral nerve stimulation threshold curve that fits the sinusoidal current waveform. The expression is: Among them, G′ min is the peripheral nerve stimulation threshold under the sinusoidal current waveform, G0 and τ are the coefficients based on the least squares fitting method; (3) Based on the peripheral nerve stimulation threshold curve of the sinusoidal current waveform, the threshold curve of the adaptive trapezoidal current waveform is derived, as shown in formula (6): Among them, G min is the peripheral nerve stimulation threshold under the trapezoidal current waveform, t is the time for the current to rise from zero to the maximum value, and the trapezoidal wave platform time is not less than 0.5 milliseconds.

8. A method for assessing the risk of peripheral nerve stimulation using magnetic resonance imaging, characterized in that: include: Based on the peripheral nerve stimulation threshold curve constructed by the construction method of claim 7, the actual gradient value of the gradient field in the scanning sequence is monitored in real time; if the actual gradient value exceeds the calculated threshold value under the corresponding waveform and frequency, at least one of the following protection mechanisms is triggered: a) Gradient field strength or gradient switching rate is forced to decrease; b) Scan sequence timing adjustment; c) Sound and light alarm and scanning pause.

9. A real-time monitoring device for peripheral nerve stimulation risk of magnetic resonance gradient coil, characterized in that: include: Data import module: imports magnetic resonance gradient coil data, high-precision human anatomical model and determines the relative position of the high-precision human anatomical model and the gradient coil during imaging scanning; A threshold curve generating module: applying the method for constructing a peripheral nerve stimulation threshold curve according to claim 7 to generate a peripheral nerve stimulation threshold curve for a magnetic resonance gradient coil; Dynamic monitoring and feedback module: During the imaging scan, the actual gradient value is compared in real time with the threshold value calculated based on the waveform and frequency corresponding to the peripheral nerve stimulation threshold curve. If the actual gradient value exceeds the calculated threshold value, at least one of the following protection mechanisms is triggered: a) Gradient field strength or gradient switching rate is forced to decrease; b) Scan sequence timing adjustment; c) Sound and light alarm and scanning pause; User interaction interface: Visually displays the peripheral nerve stimulation risk level, threshold curve, real-time gradient parameters and triggered protection measures, and provides a manual intervention interface to adjust scanning parameters.

10. A high threshold gradient coil design method, characterized in that: The following steps are involved: (i) Using the prediction function PD obtained by the peripheral nerve stimulation threshold prediction method described in claim 1 as a constraint condition, and obtaining the corresponding sensitivity matrix F L ; (ii) A hard constraint of max(PD)≤εPD0 is imposed during coil optimization, where PD0 is the maximum PD value before optimization and ε is the introduced constraint scaling factor, ε<1. The coil design optimization problem is then: Where Φ is the gradient coil flow function to be solved, L is the inductance matrix, and B z,tar The coil generates a linearly changing spatial magnetic field, ε is the linearity, B stray is the stray field generated by the coil, S1 and S2 are the sensitivity matrices obtained based on the magnetic field constraints, T and D are the sensitivity matrices obtained based on the coil torque and winding spacing constraints, respectively, T max and D min They represent the column vectors obtained based on the set maximum coil torque and minimum winding spacing, F L Φ represents the local magnetic flux density amplitude generated by the coil on the target neuron node, PD0 is the maximum PD value before optimization, λ is the introduced constraint proportional coefficient, λ<1; (iii) Iteratively optimize the coil structure to improve the stimulation safety margin while meeting the electromagnetic performance requirements, and obtain a coil winding solution that meets the requirements through continuous iterative solutions.

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