Prediction method for peripheral nerve stimulation threshold of magnetic resonance gradient coil, and use thereof

Abstract

Disclosed in the present invention are a prediction method for a peripheral nerve stimulation threshold of a magnetic resonance gradient coil, and the use thereof. The method comprises: first, on the basis of a spatial structure of target gradient coils, designing a reference coil group having differentiated electromagnetic parameters; then, making use of a high-precision virtual human anatomical model and an electromagnetic-neurodynamic coupling model to calculate an induced electric field distribution and a stimulation threshold for each coil and locate sensitive neuron nodes; then, expressing a stimulation function as a weighted sum of local magnetic vector potential components to construct a linear equation system, and using a least square method to solve an optimal coefficient; and finally, establishing a linear regression model for the stimulation function and a reciprocal of the threshold, and defining a local field-based prediction function. The prediction method provided by the present invention has both calculation efficiency and prediction accuracy, can further derive a peripheral nerve stimulation threshold curve of a magnetic resonance coil for real-time evaluation of a stimulation risk during imaging scan, and can also introduce a coil design framework to realize electromagnetic optimization design of a high-threshold gradient coil.

Description

Methods for predicting peripheral nerve stimulation thresholds using magnetic resonance gradient coils and their applications Technical Field

[0001] This invention relates to the field of magnetic resonance imaging technology, and in particular to a method for predicting the peripheral nerve stimulation threshold of a magnetic resonance gradient coil and its application. Background Technology

[0002] In recent years, the rapid development of high-gradient magnetic resonance imaging (MRI) systems has driven the application of functional MRI (fMRI) and diffused MRI (dMRI) in neuroscience research. However, rapid switching of gradient fields can generate induced electric fields in the human body, triggering peripheral nerve stimulation (PNS) and leading to muscle spasms or sensory abnormalities. 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 linear region of the coil, decreasing coil linearity, or using local coils, and the threshold is evaluated through human trials after prototype manufacturing. This process has significant drawbacks: the lack of PNS threshold prediction methods during the design phase leads to repeated trial and error, high costs, and particularly restricts the development of ultra-high-performance gradient coils.

[0003] Despite a series of studies on peripheral nerve stimulation (PNS) in recent years, existing prediction methods still have certain limitations. For example, while Roemer et al.'s simplified model based on uniform electrical properties and the maximum induced electric field (compliant with IEC 60601-2-33 standard) is computationally efficient, it does not quantitatively analyze the physiological mechanisms (PBRoemer et al, Electric field calculation and peripheral nerve stimulation prediction for head and body gradient coils, 2021). Davids' team, based on an electromagnetic-neurodynamic coupling model, achieves accurate prediction by simulating neurodynamic processes, but their prediction model requires complex global electromagnetic field calculations and nonlinear neurodynamic simulations, making it difficult to meet the high-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 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 has not clearly established a quantitative relationship between the local magnetic field and the PNS threshold, which limits 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 in the gradient coil design stage, relying on prototype-based experimental correction, which increases the R&D cycle and cost.

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

[0007] 3. The local field constraint strategy failed to establish an explicit relationship between the local field and the PNS threshold, thus failing to achieve quantitative optimization of the threshold. Summary of the Invention

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

[0009] The technical solution of the present invention is as follows:

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

[0011] S1. Construction of the reference gradient coil group: Design of the reference gradient coil group based on the spatial structure parameters of the target magnetic resonance gradient coil;

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

[0013] S3. Modeling of the stimulation function AF: Define the neuron node stimulation function AF as the first spatial differential of the projection of the induced electric field onto the peripheral nerve axis; combine the nerve distribution trajectory and use the induced electric field distribution data obtained in step S2 to solve for 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 the linear equation system: The neuron node stimulation function AF is expressed as a weighted sum of local magnetic vector positional components, as shown in formula (1):

[0016] Where (n) represents a neuron node; A (n) j The local magnetic vector A represents the location of the neuron node (n). (n) The component in the j-direction (j = x, y, z); κ j Represents the magnetic vector potential component A (n) j The weighting coefficients; κ x，j κ y，j With κ z， j Representing 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 This represents a constant term.

[0017] 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 system of N equations.

[0018] S6. Coefficient Determination: The linear equation system is solved using the least squares method to determine the weighting coefficient κ of each local magnetic vector component of each neuron node.

[0019] S7. Linear Regression Modeling: Establish a linear relationship between the reciprocal of the peripheral nerve stimulation threshold 1 / th and the AF value for each neuron node, as shown in formula (2): 1 / th (n) =k (n) ·AF (n) +h (n) (2)

[0020] Where k and h are regression coefficients;

[0021] The regression coefficients k and h were fitted using the least squares method;

[0022] S8. Definition of prediction function PD: Define 1 / th as prediction function PD. Calculate PD value based on gradient coil magnetic vector position distribution and formulas (1)-(2). Take the reciprocal of the maximum value of PD of all neuronal nodes in the high-precision virtual human anatomy model as the peripheral nerve stimulation threshold of the predicted magnetic resonance gradient coil.

[0023] In step S1, the spatial structure 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.

[0024] Preferably, step S1 includes:

[0025] 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.

[0026] S12. Based on a high-precision virtual human anatomy model, the 20 neuronal nodes that are most sensitive to peripheral nerve stimulation by the benchmark coil are selected through an electromagnetic-neurodynamic model.

[0027] S13. Based on the reference coil, perform iterative optimization, adjust the coil structure to reduce the magnetic flux density amplitude of the sensitive nodes selected in step S12, while keeping the gradient efficiency, linearity, shielding, winding spacing and torque unchanged, and increasing the inductance value by 0.5%-2% to obtain the reference gradient coil.

[0028] S14. Repeat steps S12 and S13 until the number of differentiated reference gradient coils N ≥ 20 is continuously generated.

[0029] Each iteration uses the previously generated reference gradient coil as the new reference coil.

[0030] Preferably, in step S11, the spatial structure electromagnetic performance parameters of the initial coil are consistent with those of the target coil, and the coil winding pattern is designed using the finite difference method. The entire coil design process is described using the following optimization problem framework:

[0031] Where Φ is the gradient coil current function to be solved, L is the inductance matrix, and B... z,tar To generate a linearly varying spatial magnetic field for the coil, where ε is the linearity and B is the linearity. stray S1 and S2 are the sensitivity matrices obtained based on magnetic field constraints, and T and D represent the sensitivity matrices obtained based on coil torque and winding spacing constraints, respectively. max and D min These represent column vectors obtained based on the set maximum coil torque and minimum winding spacing, respectively.

[0032] Preferably, the high-precision virtual human anatomy model has a spatial resolution of no less than 1 mm. Furthermore, the final stimulation threshold assessment uses the average of the maximum PD values ​​from multiple virtual human anatomy models to reflect population differences.

[0033] Preferably, the high-precision virtual human anatomy model is “Jeduk” and “Yoon-sun” developed by the Swiss IT'IS Foundation.

[0034] Preferably, the electromagnetic-neurodynamic coupling model includes a coupled solution module for Maxwell's equations and the McIntyre-Richardson-Grill neurodynamic model, and is configured with the following parameters:

[0035] a) The frequency setting range for electromagnetic field calculation is 500-3000Hz;

[0036] b) The spatial step size for calculating the spatial electromagnetic field distribution using the McEquations is 1 mm;

[0037] c) The waveform of the coil current is a sinusoidal wave or a trapezoidal wave of the same frequency;

[0038] d) The solution error of the neurodynamic model is less than 1%.

[0039] Preferably, in step S13, the coil structure is adjusted by setting magnetic flux density amplitude constraints on the 20 neurons with the lowest PNS thresholds, while keeping gradient efficiency, linearity, shielding, winding spacing, and torque constant. The optimization problem for the coil design then becomes:

[0040] Among them, F L Φ represents the amplitude of the local magnetic flux density generated by the coil at the target neuron node, B refε represents the amplitude of the local magnetic flux density generated at the target neuron node of the reference coil. B The adjustment coefficient is between 0 and 1.

[0041] During the design process, while keeping all other terms of formula (2b) unchanged, adjust ε B The value increases the total magnetic field energy stored in the coil by 1% (X / Y axis) or 2% (Z axis), corresponding to a 1% (X / Y axis) or 2% (Z axis) increase in coil inductance.

[0042] In step S3, the first-order spatial differential of the human body induced electric field generated when the gradient coil is working, projected onto the peripheral nerve axis, is defined as the neuron node stimulation function AF; the differential term is approximated using the finite difference method.

[0043] To simplify calculations and further improve efficiency, as a preferred approach, a set of sensitive points for neuron nodes is constructed based on the lowest PNS threshold corresponding to each reference coil; in the subsequent solution of the prediction function PD, only the neuron nodes in the set of sensitive points are considered.

[0044] 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:

[0045] Where μ0 and I represent the vacuum permeability and the coil transmission current, respectively; l represents the coil winding element; and r and r' represent the spatial positions of the local field point and the coil winding element, respectively.

[0046] The magnetic vector potential gradient components are approximated using the spatial difference method.

[0047] As a preferred embodiment, in step S5, the AF expression, after Coulomb specification optimization, is as shown in formula (4):

[0048] Preferably, step S6 includes:

[0049] The aforementioned system of linear equations can be written in matrix form: PK = F AF (4a)

[0050] Where K is a column vector composed of undetermined weighting coefficients κ, P is the coefficient matrix obtained according to formula (4), and F AF The column vector consisting of the stimulus function terms AF in formula (4);

[0051] The least squares solution to the linear equation system is as follows: K = (P T P) -1 P T F AF (4b)

[0052] This invention also provides a method for constructing a peripheral nerve stimulation threshold curve using a magnetic resonance gradient coil, comprising the following steps:

[0053] (1) Based on the peripheral nerve stimulation threshold prediction method of the magnetic resonance gradient coil, obtain the prediction function PD value of the target gradient coil at at least two different frequencies within the frequency range of 500-3000Hz.

[0054] (2) Fit the prediction function PD values ​​at different frequencies to the corresponding frequency f to generate a peripheral nerve stimulation threshold curve that fits the sinusoidal current waveform. Its expression is:

[0055] Among them, G′ min G0 and τ are the peripheral nerve stimulation thresholds under sinusoidal current waveforms, respectively, and the coefficients are fitted based on the least squares method.

[0056] (3) Based on the peripheral nerve stimulation threshold curve of the sinusoidal current waveform, the threshold curve adapted to the trapezoidal current waveform is derived, as shown in formula (6):

[0057] Among them, G min The threshold for peripheral nerve stimulation under the trapezoidal current waveform is t, where t is the time it takes for the current to rise from zero to its maximum value, and the plateau time of the trapezoidal wave is not less than 0.5 milliseconds.

[0058] This invention also provides a method for assessing the risk of peripheral nerve stimulation in magnetic resonance imaging (MRI), comprising: real-time monitoring of the actual gradient value of the gradient field in the scan sequence based on the peripheral nerve stimulation threshold curve; if the actual gradient value exceeds the calculated threshold at the corresponding waveform and frequency, triggering at least one of the following protection mechanisms:

[0059] a) Forcefully reduce the gradient field strength or gradient switching rate;

[0060] b) Timing adjustment of the scan sequence;

[0061] c) Audible and visual alarms and scanning paused.

[0062] As a preferred option, forcibly reducing the gradient field strength or gradient switching rate means reducing the gradient field strength or switching rate to 80% of the calculation threshold through a hardware interface.

[0063] Scan sequence timing adjustment refers to delaying the rise time of gradient pulses or inserting silent intervals.

[0064] This invention also provides a real-time monitoring device for the risk of peripheral nerve stimulation using a magnetic resonance gradient coil, comprising:

[0065] Data import module: Imports magnetic resonance gradient coil data and high-precision human anatomical models, and determines the relative position of the high-precision human anatomical models with the gradient coils during imaging scanning;

[0066] Threshold curve generation module: Using the method described above for constructing peripheral nerve stimulation threshold curves, a peripheral nerve stimulation threshold curve for a magnetic resonance gradient coil is generated.

[0067] Dynamic monitoring and feedback module: During the imaging scan, the actual gradient value is compared in real time with the calculated threshold based on the waveform and frequency corresponding to the peripheral nerve stimulation threshold curve. If the actual gradient value exceeds the calculated threshold, at least one of the following protection mechanisms is triggered:

[0068] a) Forcefully reduce the gradient field strength or gradient switching rate;

[0069] b) Timing adjustment of the scan sequence;

[0070] c) Audible and visual alarms and scanning paused;

[0071] User interface: Visually displays the risk level of peripheral nerve stimulation, threshold curve, real-time gradient parameters and triggered protective measures, and provides a manual intervention interface to adjust scanning parameters.

[0072] This invention also provides a high-threshold gradient coil design method, comprising the following steps:

[0073] (i) Using the prediction function PD as a constraint, the corresponding sensitivity matrix F is obtained. L ;

[0074] (ii) Apply a hard constraint of max(PD)≤εPD0 in the coil optimization, where PD0 is the maximum PD value before optimization, and ε is the introduced constraint scaling factor, ε<1; at this time, the optimization problem of coil design becomes:

[0075] Where Φ is the gradient coil current function to be solved, L is the inductance matrix, and B... z,tar To generate a linearly varying spatial magnetic field for the coil, where ε is the linearity and B is the linearity. stray S1 and S2 are the sensitivity matrices obtained based on magnetic field constraints, and T and D represent the sensitivity matrices obtained based on coil torque and winding spacing constraints, respectively. F represents the stray field generated by the coil. L Φ represents the amplitude of the local magnetic flux density generated by the coil at the target neuron node, PD0 is the maximum PD value before optimization, and λ is the introduced constraint scaling factor (λ<1).

[0076] (iii) Iteratively optimize the coil structure to improve the safety margin of stimulation while meeting the electromagnetic performance requirements. The coil winding scheme that meets the requirements is obtained by iteratively solving the problem.

[0077] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0078] 1. Quantitative PNS prediction based on local field: The peripheral nerve stimulation threshold prediction method disclosed in this 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 easily calculated based on coil data, and PNS evaluation can be realized in the coil design stage.

[0079] 2. High computational efficiency: Applying 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 fitting and correcting unknown parameters based on the local field using the least squares method reduces the computational load 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.

[0080] 3. Dynamic Safety Monitoring Capability: The peripheral nerve stimulation threshold prediction method disclosed in this invention can be integrated into a PNS threshold curve for assessing scanning safety. Importing this into the safety assessment module of an MRI system allows for real-time assessment of nerve stimulation risks, triggering protective mechanisms such as imaging sequence adjustment and scan pause, thereby improving the safety of imaging scans.

[0081] 4. Adaptability of the gradient coil design framework: Since the prediction model disclosed in this invention can be calculated through linear transformation of the local field, it can be introduced into the traditional gradient coil design framework as a linear constraint, and a gradient coil with a high PNS threshold can be obtained through iterative optimization in the coil design stage. Attached Figure Description

[0082] Figure 1 is a flowchart of the construction of the peripheral nerve stimulation threshold prediction model of magnetic resonance gradient coil.

[0083] Figure 2 is a cross-sectional view of the spatial structure of the head-specific magnetic resonance gradient coil.

[0084] Figure 3 is a schematic diagram of the PNS sensitive points generated by the gradient coil in the human body model.

[0085] Figure 4 illustrates the relationship between the maximum fitting error of the stimulus function AF and the number of reference coils.

[0086] Figure 5 shows the linear fit results between the reciprocal of the PNS threshold and the stimulation function.

[0087] Figure 6 is a comparison between the PNS threshold curve of this magnetic resonance gradient coil and the experimental value.

[0088] Figure 7 shows the winding patterns of the magnetic resonance gradient coil before (A) and after (B) optimization.

[0089] Figure 8 shows the distribution of the induced electric field generated by the magnetic resonance gradient coil in the human body before (A) and after (B) optimization.

[0090] Figure 9 shows the curves of the PNS threshold of the magnetic resonance gradient coil before and after optimization, based on the gradient pulse frequency. Detailed Implementation

[0091] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not limit it in any way.

[0092] This invention provides a method for predicting peripheral nerve stimulation (PNS) thresholds using magnetic resonance gradient coils. This method combines the ease of use of indirect PNS threshold description based on local fields with the accuracy of quantitative electromagnetic-neurodynamic models. Ultimately, it achieves direct calculation of the PNS threshold through local fields, making efficient quantitative threshold prediction based on magnetic resonance gradient coil data possible. Here, the local field refers to the components of the local magnetic field (magnetic flux density, magnetic vector potential, etc.) at the main peripheral neuronal nodes of the human body, as well as their corresponding spatial first-order differential and other derived physical quantities. The construction process of the peripheral nerve stimulation threshold prediction model using magnetic resonance gradient coils is shown in Figure 1. The following will use a gradient coil in a head-specific magnetic resonance imaging (MRI) system as an example to specifically illustrate the implementation methods and effects of each step of this technical solution:

[0093] S1. Construction of the reference gradient coil group

[0094] First, the spatial structure of the target magnetic resonance gradient coil is defined. As shown in Figure 2, the head-specific magnetic resonance gradient coil selected in this embodiment is a three-layer cylindrical structure, including a main coil layer 2, an intermediate coil layer 3, and a shielding coil layer 4, to provide sufficient design freedom to meet the performance requirements of ultra-high gradient field magnetic resonance imaging. The imaging region 1 has a diameter of 200 mm and is located in the middle near the end of the main coil layer 2, basically covering the human brain region. In this embodiment, the main parameters of the coil structure (including the cylinder diameter d and length l) are as follows: diameter of main coil layer 2 d1 = 46 cm, diameter of intermediate coil layer 3 d2 = 62 cm, diameter of shielding coil layer 4 d3 = 75 cm, length of main coil layer 2 l1 = 66 cm, length of intermediate coil layer 3 l2 = 112 cm, and length of shielding coil layer 4 l3 = 120 cm. In addition, the design targets for the main performance parameters of the coil are set as follows: coil efficiency of 0.15mT / m / A, linearity deviation of 5%; stray field generated per unit current not exceeding 1μT, maximum coil torque of 0.1Nm; minimum distance between coil windings of 7mm.

[0095] To fit and calibrate the PNS prediction model, this technical solution designs a set of reference gradient coils. These coils have the same spatial structure as the target coil, but their electromagnetic performance parameters are designed differently. Ideally, the reference coils should have the same main performance parameters as the target coil. Therefore, this technical solution achieves the design of the reference coils by controlling the amplitude of the magnetic flux density at the peripheral neuron nodes that are sensitive to stimuli, as follows:

[0096] 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.

[0097] 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:

[0098] Where Φ is the gradient coil current function to be solved, L is the inductance matrix, and B... z,tar To generate a linearly varying spatial magnetic field for the coil, where ε is the linearity and B is the linearity. stray S1 and S2 are the sensitivity matrices obtained based on magnetic field constraints, and T and D represent the sensitivity matrices obtained based on coil torque and winding spacing constraints, respectively. max and D min These represent column vectors obtained based on the set maximum coil torque and minimum winding spacing, respectively.

[0099] S12. Using an electromagnetic-neurodynamic model, select the 20 neuronal nodes that are most sensitive to peripheral nerve stimulation from the baseline coil.

[0100] When simulating the induced electric field generated by the coil and the PNS threshold using an electromagnetic-neurodynamic model, the virtual human anatomical models selected were "Jeduk" (33 years old, male) and "Yoon-sun" (26 years old, female), developed by the IT'IS Foundation in Switzerland. These models have a spatial resolution of 0.1 × 0.1 × 0.2 mm. The simulation involved two steps: solving for the induced electric field distribution generated by the coil in the human body using Maxwell's equations, and importing this distribution into the McIntyre-Richardson-Grill (MRG) neurodynamic model to calculate the PNS threshold. Considering the frequency range of commonly used magnetic resonance imaging pulse sequences (on the order of kilohertz), the electromagnetic frequency used in the simulation was 500–3000 Hz, with a step size of 250 Hz. In addition, the spatial step size of the human body model selected for the simulation was 1 mm, the coil current was a sine wave with the same frequency as the electromagnetic field, and the maximum error of the neurodynamic solution was 1%. Figure 3 shows the 20 neurons with the lowest PNS thresholds located by the three-axis gradient coils in the human model "Jeduk," which are the most sensitive points to stimulation. Due to their proximity, some nodes overlap slightly when shown in Figure 3.

[0101] S13. Based on the reference coil, perform iterative optimization, adjust the coil structure to reduce the magnetic flux density amplitude of the sensitive nodes selected in S11, while keeping the gradient efficiency, linearity, shielding, winding spacing and torque unchanged, and increase the inductance value by 0.5%-2%.

[0102] 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 neurons with the lowest PNS thresholds, while keeping the main performance objectives of the coil unchanged. At this point, the optimization problem of the coil design becomes:

[0103] Among them, F L Φ represents the amplitude of the local magnetic flux density generated by the coil at the target neuron node, B ref ε represents the amplitude of the local magnetic flux density generated at the target neuron node of the reference coil. B ε is an adjustment coefficient between 0 and 1. During the design process, while keeping all other terms of formula (2b) unchanged, adjust ε... B The value increases the total magnetic field energy stored in the coil by 1% (X / Y axis) or 2% (Z axis), corresponding to a 1% (X / Y axis) or 2% (Z axis) increase in coil inductance.

[0104] S14. Repeat the optimization process of steps S12 and S13. In each iteration, use the previously generated reference gradient coil as the new reference coil and continue to generate differentiated reference gradient coils until the number of generated reference gradient coils N≥20, to ensure that the least squares method solution converges.

[0105] Using the previously designed reference gradient coil as the new reference coil, S12 and S13 are repeated. In this embodiment, 26 reference coils (N=26) are finally designed for each axis, and the inductance of these coils is in the range of 1 to 1.25 (X / Y axis) or 1 to 1.5 (Z axis) relative to the initial coil.

[0106] S2, Induced Electric Field and Threshold Calculation

[0107] In the design of the reference coils in this embodiment, an electromagnetic-neurodynamic model was used to calculate the induced electric field distribution and PNS threshold of most of the reference gradient coils (except for the last reference coil generated on each axis) in the human body. In this step, the same method is used to further simulate and record the induced electric field and PNS threshold of the remaining reference coils in the human body.

[0108] S3, Stimulus Function AF Modeling

[0109] The first-order spatial differential of the projection of the induced electric field generated by the gradient coil on the peripheral nerve axis 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 projection of the induced electric field on each peripheral nerve node along the peripheral nerve distribution direction is calculated. The differential term is approximated using the finite difference method.

[0110] To simplify calculations and further improve efficiency, this embodiment constructs a set of neurons with the lowest PNS threshold corresponding to each reference coil, i.e., a set of sensitive points. Furthermore, in the subsequent solution of the prediction function PD, only neurons in the set of sensitive points are considered, thereby reducing the computational load. The points included in the set of sensitive points constructed in this embodiment are shown in Figure 2, including PNS sensitive points A15 / A26 (X-axis), B17 / B28 (Y-axis), and C19 / C210 (Z-axis).

[0111] S4. Calculation of local magnetic vector potential components

[0112] The local magnetic vector potential A generated by each reference coil at the neuron node in the sensitive point set is calculated using the Biot-Savart law, as shown below:

[0113] Where μ0 and I represent the vacuum permeability and the coil transmission current, respectively; l represents the coil winding element; and r and r' represent the spatial positions of the local field point and the coil winding element, respectively.

[0114] The magnetic vector potential gradient components are approximated using the spatial difference method, as shown below (taking the gradient component in the x-direction as an example):

[0115] In this embodiment, Δx is the spatial step size, and Δx is set to 2mm; A j (x,y,z) represents the component of the magnetic vector A along the j direction at the position with spatial coordinates (x,y,z) (j=x,y,z).

[0116] S5. Construction of Linear Equations

[0117] Where (n) represents a specific neuron node; A (n) j The local magnetic vector A represents the location of the neuron node (n). (n) The component in the j-direction (j = x, y, z); κ j Represents the magnetic vector potential component A (n) j The weighting coefficients; κ x，j , κ y，j With κ z，j Representing 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 This represents a constant term.

[0118] The AF is approximated by a weighted sum of the local magnetic vector potential components as shown in Equation (1) or Equation (4), where the weighting coefficient κ is determined based on the magnetic vector potential components generated by the reference coils at the neuron nodes and the AF fitting. Substituting the magnetic vector potential components generated by all 26 reference coils designed for each axis at the neuron nodes in the sensitive point set (obtained in S4) and the stimulation function AF (obtained in S3) into Equation (1) yields a system of 26 linear equations. In addition, Equation (1) has 13 undetermined coefficients, while Equation (4) is simpler to calculate because it eliminates one of the undetermined coefficients by applying the Coulomb specification (▽·A=0). Therefore, this embodiment uses Equation (4) to fit the AF.

[0119] S6, Solving for coefficients

[0120] Rewrite the system of linear equations constructed in S5 in matrix form: PK = F AF (4a)

[0121] Where K is a column vector composed of undetermined weighting coefficients κ, P is the coefficient matrix obtained according to formula (4), and F AF Let be the column vector consisting of the stimulus function terms AF in formula (4). The least squares solution of this system of linear equations is as follows: K = (P T P) -1 P T F AF (4b)

[0122] Figure 4 shows the relationship between the maximum fitting error of the stimulus function AF in formula (4) and the number of reference coils used to construct formula (4a). It can be seen that, for the main stimulus 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.

[0123] S7, Linear Regression Modeling

[0124] Applying formula (2), for the neuron nodes in the sensitive point set, a linear relationship is established between the reciprocal of the stimulation threshold (1 / th) and the stimulation function AF: 1 / th (n) =k (n) ·AF (n) +h (n) (2)

[0125] Based on this, a linear regression model is constructed using the AF obtained in S3 and the PNS threshold obtained in S1 to S2. The linear coefficients k and h in formula (2) are fitted and solved using a method similar to the least squares method in S6.

[0126] Figure 5 illustrates the relationship between the reciprocal of the PNS threshold and the stimulus function obtained through linear regression modeling. The circles in the figure mark the reciprocal of the PNS threshold and the stimulus function generated by the 26 reference coils. This curve is based on the principal stimulus-sensitive points in the sensitive point set. Least squares fitting was used. In the figure, higher r... 2 A value greater than 0.96 indicates that using a linear model to fit the relationship between the reciprocal of the PNS threshold (1 / th) and the stimulus function AF is reasonable.

[0127] S8. Definition of Prediction Function PD

[0128] 1 / th is defined as the prediction function PD, which can be calculated based on the magnetic vector distribution of the gradient coil and formulas (1)-(2). In this embodiment, the reciprocal of the maximum value of PD (1 / PD) of all neuronal nodes in the sensitive point set is the peripheral nerve stimulation threshold of the predicted magnetic resonance gradient coil.

[0129] S9. Calculate the PNS threshold curve of the magnetic resonance gradient coil.

[0130] The constructed PNS threshold prediction model for magnetic resonance gradient coils can be used to calculate the PNS threshold curve of magnetic resonance gradient coils. This curve is defined as: the rate of change (dB / dt) of the minimum magnetic flux density 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) required. min The curve represents the time it takes for a current pulse to reach its maximum intensity from zero. The plateau period of the trapezoidal current pulse is 0.5 ms. In this embodiment, G will be used. min To describe the PNS threshold curve. The steps for constructing the PNS threshold curve using the prediction function PD are as follows:

[0131] S91. Based on the peripheral nerve stimulation threshold prediction model of the magnetic resonance gradient coil provided by the present invention, obtain the prediction function (PD) values ​​of the target gradient coil at at least two different frequencies within the frequency range of 500-3000Hz. In this embodiment, 11 PDs are constructed within the range of 500-3000Hz (step size 250Hz).

[0132] S92. Fit the PD values ​​at different frequencies to the corresponding frequencies f to generate the peripheral nerve stimulation threshold th0 curve that adapts to the sinusoidal current waveform. Its expression is:

[0133] Among them, G′ min G0 represents the peripheral nerve stimulation threshold under a sinusoidal current waveform, and G0 and τ are the coefficients fitted using the least squares method.

[0134] S93. Based on the coefficients G0 and τ in the fitted sinusoidal current waveform threshold curve, derive the threshold curve for the adapted trapezoidal current waveform:

[0135] Among them, G min The threshold for peripheral nerve stimulation under the trapezoidal current waveform is t, where t is the time it takes for the current to rise from zero to its maximum value, and the plateau time of the trapezoidal wave is not less than 0.5 milliseconds.

[0136] Figure 6 shows a comparison between the threshold curve obtained by fitting in this embodiment and the experimental value. The experiment was conducted on the United Imaging uMR NeuroFrontier platform. It can be seen that the fitted threshold curve has a good agreement with the experimental results.

[0137] The constructed PNS threshold curve can be used to monitor the actual gradient value of the gradient field in the scan sequence in real time. The real-time monitoring module obtains the actual gradient field value (including gradient intensity and switching rate) of the current scan sequence through the gradient controller of the magnetic resonance system and compares it with the safety threshold in the obtained threshold curve. If the actual gradient value exceeds the safety threshold of the threshold curve, the following protection mechanism is triggered:

[0138] a) Reduce the gradient field strength or switching rate to 80% of the threshold through a hardware interface;

[0139] b) Delay the rise time of the gradient pulse, or insert a silent interval;

[0140] c) The operator will be alerted by an audible and visual alarm, and the scanning will be paused until the parameters are adjusted.

[0141] In practice, the gradient is first adjusted downwards. If the limit is still exceeded, the scan is paused and an audible and visual alarm is issued. The scan is then restarted after the operator adjusts the parameters.

[0142] Based on the constructed peripheral nerve stimulation threshold curve of the magnetic resonance gradient coil, this invention provides a real-time monitoring device for the risk of peripheral nerve stimulation of the magnetic resonance gradient coil, comprising the following modules:

[0143] a) Data Import Module: Supports importing gradient coil parameters (such as inductance and resistance) and high-precision human models (1mm resolution) from files or databases. The relative positions of the model and coils are automatically aligned using the MRI system coordinate system.

[0144] b) Threshold curve generation module: After calling the threshold curve generation algorithm provided by this invention and inputting the coil parameters, it automatically generates and stores sine wave and trapezoidal wave threshold curves.

[0145] 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 scanning peripheral nerve stimulation risk assessment method provided by this invention is triggered.

[0146] d) User interface: The interface displays real-time gradient parameters, threshold curves, and risk levels (indicated by green, yellow, and red colors), and provides a slider for manually adjusting gradient field limits.

[0147] S10, High Threshold Gradient Coil Design

[0148] Based on the constructed PNS threshold function of the magnetic resonance gradient coil, this 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 is designed using the target coil spatial structure and performance parameters when constructing the threshold function PD. The specific steps are as follows:

[0149] S101. Using the solved PD function as a constraint, the corresponding sensitivity matrix is ​​obtained. During the solution process, the selected coil space structure and performance parameters are consistent with those used in the previous PD function generation process. The final sensitivity matrix obtained is F.L .

[0150] S102. In coil optimization, apply a hard constraint that max(PD) ≤ εPD0, where PD0 is the maximum PD value before optimization, and λ is the introduced constraint scaling factor (λ < 1). At this point, the coil design optimization problem becomes:

[0151] S103. Iterative optimization of the coil structure to improve the safety margin of stimulation while meeting electromagnetic performance requirements. Based on the constructed coil design optimization problem, a coil winding scheme that meets the conditions is obtained through continuous iterative solution. Figure 7 shows the coil winding pattern before and after optimization using this technical solution; Figure 8 shows the distribution of the induced electric field generated by the coil on the human body before and after optimization; Figure 9 shows the change curve of the PNS threshold based on the gradient pulse frequency before and after optimization. As shown in the figure, the inductance of the coil on the X, Y, and Z axes are 261μH (before optimization) / 298μH (after optimization), 261μH (before optimization) / 300μH (after optimization), and 182μH (before optimization) / 273μH (after optimization), respectively. At the same time, the PNS threshold under 1000Hz sine wave excitation on the X, Y, and Z axes is optimized and improved from 102mT / m, 63mT / m, and 96mT / m to 190mT / m, 138mT / m, and 164mT / m, respectively. Therefore, it is possible to increase the PNS threshold to 219% of the original value (1000Hz sine wave excitation) while keeping most of the coil performance unchanged and increasing the coil inductance by 15%, thereby significantly improving the stimulation safety margin of the gradient coil.

[0152] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the peripheral nerve stimulation threshold using a magnetic resonance gradient coil, characterized in that, Includes the following steps: S1. Construction of the reference gradient coil group: Design of the reference gradient coil group based on the spatial structure parameters of the target magnetic resonance gradient coil; S2. Induced Electric Field and Threshold Calculation: Based on a high-precision virtual human anatomy model, the induced electric field distribution of each reference gradient coil in the human body is simulated through an electromagnetic-neurodynamic coupling model, and the peripheral nerve stimulation threshold th is calculated; the spatial coordinates of all activated neuron nodes in the high-precision virtual human anatomy model are recorded. S3. Modeling of the stimulation function AF: Define the neuron node stimulation function AF as the first spatial differential of the projection of the induced electric field onto the peripheral nerve axis; combine the nerve distribution trajectory and use the induced electric field distribution data obtained in step S2 to solve for 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 the linear equation system: The neuron node stimulation function AF is expressed as a weighted sum of local magnetic vector positional components, as shown in formula (1): where (n) denotes a neuron node; A (n) j denotes the local magnetic vector potential A at the position of the neuron node (n) (n) the component in the j direction (j = x, y, z); κ j denotes the magnetic vector potential component A (n) j the weighting factor of the partial differential term; κ x， j , κ y，j and κ z，j denote the magnetic vector potential components A (n) j the weighting factor of the partial differential term in the x, y and z directions; κ cnst denotes the 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 system of N equations. S6. Solving for coefficients: The linear equations are solved using the least squares method to determine the weighting coefficients of each local magnetic vector component of each neuron node. S7. Linear regression modeling: Establish a linear relationship between the reciprocal of the peripheral nerve stimulation threshold 1 / th and the AF value 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 using the least squares method; S8. Definition of prediction function PD: Define 1 / th as prediction function PD. Calculate PD value based on gradient coil magnetic vector position distribution and formulas (1)-(2). Take the reciprocal of the maximum value of PD of all neuronal nodes in the high-precision virtual human anatomy model as the peripheral nerve stimulation threshold of the predicted magnetic resonance gradient coil.

2. The method for predicting the peripheral nerve stimulation threshold of a 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. 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 anatomy model, the 20 neuronal nodes that are most sensitive to peripheral nerve stimulation by the benchmark coil are selected through an electromagnetic-neurodynamic model. S13. Based on the reference coil, perform iterative optimization, adjust the coil structure to reduce the magnetic flux density amplitude of the sensitive nodes selected in step S12, while keeping the gradient efficiency, linearity, shielding, winding spacing and torque unchanged, and increasing the inductance value by 0.5%-2% to obtain the reference gradient coil. S14. Repeat steps S12 and S13 until the number of differentiated reference gradient coils N ≥ 20 is continuously generated. Each iteration uses the previously generated reference gradient coil as the new reference coil.

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

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

5. The method for predicting the peripheral nerve stimulation threshold of a 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 permeability and the coil transmission current, respectively; l represents the coil winding element; and r and r' represent the spatial positions of the local field point and the coil winding element, respectively. The magnetic vector potential gradient components are approximated using the spatial difference method.

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

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

8. A method for assessing the risk of peripheral nerve stimulation via magnetic resonance imaging, characterized in that, include: The peripheral nerve stimulation threshold curve constructed based on the construction method described in claim 7 is used to monitor the actual gradient value of the gradient field in the scanning sequence in real time; if the actual gradient value exceeds the calculated threshold under the corresponding waveform and frequency, at least one of the following protection mechanisms is triggered: a) Forcefully reduce the gradient field strength or gradient switching rate; b) Timing adjustment of the scan sequence; c) Audible and visual alarms and scanning paused.

9. A real-time monitoring device for the risk of peripheral nerve stimulation using a magnetic resonance gradient coil, characterized in that, include: Data import module: Imports magnetic resonance gradient coil data and high-precision human anatomical models, and determines the relative position of the high-precision human anatomical models with the gradient coils during imaging scanning; Threshold curve generation module: Using the method for constructing the peripheral nerve stimulation threshold curve as described in claim 7, a peripheral nerve stimulation threshold curve of the magnetic resonance gradient coil is generated; Dynamic monitoring and feedback module: During the imaging scan, the actual gradient value is compared in real time with the calculated threshold based on the waveform and frequency corresponding to the peripheral nerve stimulation threshold curve. If the actual gradient value exceeds the calculated threshold, at least one of the following protection mechanisms is triggered: a) Forcefully reduce the gradient field strength or gradient switching rate; b) Timing adjustment of the scan sequence; c) Audible and visual alarms and scanning paused; User interface: Visually displays the risk level of peripheral nerve stimulation, threshold curve, real-time gradient parameters and triggered protective measures, and provides a manual intervention interface to adjust scanning parameters.

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

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