A method for fast prediction of mechanical response of carpal tunnel structure based on agent model

Abstract

This invention provides a rapid prediction method for the mechanical response of carpal tunnel structures based on a surrogate model, belonging to the field of biomechanical analysis technology. The method includes: constructing a complete three-dimensional geometric model of the carpal tunnel structure and applying palmar tensile loads and harmonic excitation loads; generating multiple sets of material property parameter combinations through random sampling, and constructing static and dynamic training datasets by combining the corresponding static and dynamic displacement responses; training a PCE surrogate model based on the static training dataset, and training both the PCE surrogate model and the SVR surrogate model based on the dynamic training dataset; inputting the material property parameters of the carpal tunnel structure to be predicted into the corresponding trained surrogate models, and outputting the predicted static and dynamic displacement responses of the carpal tunnel structure. This method overcomes the shortcomings of low efficiency and high computational cost in traditional finite element analysis, significantly improving computational efficiency while maintaining prediction accuracy, providing a scientific basis for the assessment of carpal tunnel syndrome.

Description

Technical Field

[0001] This invention relates to the field of biomechanical analysis technology, and in particular to a rapid prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model. Background Technology

[0002] The diagnostic criteria for occupational carpal tunnel syndrome pay special attention to the impact of biomechanical factors such as prolonged repetitive or forceful wrist work on manufacturing workers. When the wrist is exposed to different types and degrees of mechanical loads during occupational activities, the median nerve in the carpal tunnel can be damaged. Existing technology can use finite element analysis software to analyze the response of biological tissues by simulating mechanical scenarios, and it has been applied to biomechanical analysis.

[0003] In practical applications, there are significant individual differences in the structural parameters of the carpal tunnel, resulting in high inconsistency. Due to the objective existence of individual differences, large-scale finite element modeling and analysis are required when diagnosing and treating multiple patients with different conditions. This leads to increasingly serious problems of computational resource consumption and inefficiency, severely restricting its application efficiency in rapid clinical assessment and personalized prediction.

[0004] Therefore, this invention proposes a fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model. Summary of the Invention

[0005] This invention provides a rapid prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model. It uses the method of constructing a surrogate model to replace a large number of finite element simulation calculations. It only requires a few finite element calculations to construct training samples, and can obtain the mapping relationship between input variables and mechanical response. While ensuring prediction accuracy, it greatly improves computational efficiency and provides the possibility for large-scale clinical application.

[0006] This invention provides a fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model, comprising: Step 1: Import the reconstructed models of each wrist bone, the simplified model of the cartilage, the solid model of the transverse carpal ligament, and the spring model of the interosseous ligament into the 3D modeling software SolidWorks, and construct a complete 3D geometric model of the carpal tunnel structure according to the anatomical relationship of the human wrist. Step 2: Apply palmar tensile load to the three-dimensional geometric model to observe the carpal tunnel structure and extract the static displacement response of key nodes of the transverse carpal ligament. At the same time, apply harmonic excitation load to the three-dimensional geometric model and extract the dynamic displacement response of key nodes of the transverse carpal ligament within a specified frequency range. Step 3: For static and dynamic working conditions, generate multiple sets of material property parameter combinations by random sampling, and construct static training datasets and dynamic training datasets by combining the corresponding static displacement response and dynamic displacement response. Step 4: Train the PCE surrogate model based on the statics training dataset, and train the PCE surrogate model and the SVR surrogate model based on the dynamics training dataset respectively; Step 5: Input the material property parameters of the carpal tunnel structure to be predicted into the corresponding surrogate model after training, and output the static and dynamic displacement response prediction results of the carpal tunnel structure.

[0007] Preferably, a complete three-dimensional geometric model of the carpal tunnel structure is constructed, including: The wrist bone model obtained from the CT scanner is saved as an STL file. The STL file is then imported into the Spaceclaim module of the finite element software ANSYS to separate and remove discrete patches, repair surface depressions and high curvature areas, and perform reverse modeling using the Autoskin command to obtain the reconstructed model of each wrist bone. The reconstructed model is imported into SolidWorks and each bone is assembled to its corresponding position. A cross section is generated at the joint space using spline curves, which are then stretched to form a columnar solid and the interference portion is removed to obtain a simplified model of the cartilage. Based on the morphological characteristics and modeling requirements of different types of ligaments, solid models of the transverse carpal ligament and spring models of the interosseous ligaments were established respectively. The models are assembled according to the anatomical structure of the human wrist. Overlapping areas are eliminated by interference detection to obtain a three-dimensional geometric model of the carpal tunnel structure, in which the transverse carpal ligament arches along the palmar side as the positive Y-axis.

[0008] Preferably, the static displacement response of key nodes of the transverse carpal ligament is extracted, including: The carpal bones, cartilage, and transverse carpal ligament of the three-dimensional geometric model are all meshed with tetrahedral meshes, and element erasure, boundary fusion, and local mesh optimization are performed at the connection points of each part. The bones, cartilage, and transverse carpal ligament are designed as uniform isotropic linear elastic bodies and given elastic modulus and Poisson's ratio. At the same time, the interosseous ligament springs are given stiffness coefficients. The carpal bones, cartilage and transverse carpal ligament contact parts are bound face to face, and three non-ligament attachment nodes are selected on each of the eight carpal bones to constrain the displacement degrees of freedom. Five unit surfaces were selected at the midpoint of the midline of the transverse carpal ligament. A concentrated load of 100N along the positive Y-axis was applied, and the displacement of the carpal tunnel structure along the Y-axis was extracted as the static displacement response.

[0009] Preferably, the dynamic displacement response of key nodes of the transverse carpal ligament within a specified frequency range is extracted, including: Remove the interosseous ligament spring model from the three-dimensional geometric model of the carpal tunnel structure, and set the bottom surface of each carpal bone as a fixed boundary; At the center of the transverse carpal ligament, a small area consisting of 5 unit surfaces is selected, and a sinusoidal load with an amplitude of 20N is applied with a frequency range of 400Hz to 700Hz. The structural damping ratio is set to 0.1. Frequency points were uniformly selected within the 450-550Hz frequency band, and the Y-direction displacement response of the proximal, middle, and distal nodes of the transverse carpal ligament was extracted as the dynamic displacement response.

[0010] Preferably, the random sampling adopts the Latin hypercube sampling method; The static training dataset has a 6-input, 1-output structure. The inputs are the elastic modulus and Poisson's ratio of bone, cartilage, and transverse carpal ligament, and the output is the static displacement of key nodes of the transverse carpal ligament. The dynamic training dataset has a 10-input, 1-output structure. The inputs are the elastic modulus, Poisson's ratio, bone density, and frequency points of the bone, cartilage, and transverse carpal ligament. The output is the dynamic displacement of key nodes of the transverse carpal ligament.

[0011] Preferably, the construction of the PCE proxy model includes: Hermite polynomials are used as orthogonal polynomial basis functions, and the undetermined coefficients are solved by least squares regression. The construction of the SVR agent model includes: Radial basis functions are used as kernel functions, and Lagrange multipliers and bias terms are solved through Lagrange dual optimization. The penalty factor and error tolerance are adjusted to ensure that the training accuracy meets the requirements.

[0012] Compared with the prior art, the beneficial effects of this application are: (1) This technical solution constructs a complete carpal tunnel structure and obtains the displacement response of the carpal tunnel structure under palmar tensile force and sinusoidal load by means of finite element method, providing a biomechanical theoretical basis for the pathogenesis and pathological evolution of carpal tunnel syndrome. (2) The prediction accuracy of the PCE surrogate model and the SVR surrogate model for nonlinear problems were compared under dynamic conditions. The average relative error of SVR at the three reference points was significantly lower than that of the PCE surrogate model, which verified that SVR has a stronger fitting ability for nonlinearity. (3) This technical solution introduces surrogate model technology for the first time in the field of carpal tunnel biomechanics analysis. It achieves rapid calculation through two surrogate models: PCE completes a single prediction in less than 1 ms, and SVR completes a single prediction in 1.13 ms, which is much shorter than the finite element calculation time, while ensuring prediction accuracy. Compared with the traditional finite element method, the computational efficiency is greatly improved, which can meet the needs of rapid prediction and large-scale calculation in clinical work.

[0013] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description and the accompanying drawings.

[0014] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of a fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model, as described in an embodiment of the present invention. Figure 2 This is a reverse modeling diagram of the wrist bones in an embodiment of the present invention, wherein (a) is the hamate bone, (b) is the scaphoid bone, (c) is the capitate bone, (d) is the trapezium bone, (e) is the lunate bone, (f) is the trapezium argenteus, (g) is the triquetrum bone, and (h) is the pisiform bone. Figure 3 These are partial cartilage model illustrations from embodiments of the present invention; Figure 4 This is a geometric model diagram of the transverse carpal ligament in an embodiment of the present invention; Figure 5 This is a model diagram of the interosseous ligament spring in an embodiment of the present invention; Figure 6 This is a complete three-dimensional geometric model of the carpal tunnel structure in an embodiment of the present invention; Figure 7 This is a finite element model diagram of the carpal tunnel structure in an embodiment of the present invention; Figure 8 This is a displacement contour map of the transverse carpal ligament under static conditions in an embodiment of the present invention; Figure 9 This is a diagram showing the displacement frequency response curve in the Y direction in an embodiment of the present invention; Figure 10 This is a comparison between the prediction results of the PCE proxy model test set and the finite element results under static working conditions in an embodiment of the present invention, wherein (a) is the near end, (b) is the middle part, and (c) is the far end; Figure 11 The test set results of two proxy models for near-end nodes in this embodiment of the invention are compared with the finite element results. Among them, (a) is the PCE prediction result and (b) is the SVR prediction result. Detailed Implementation

[0016] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0017] This invention provides a fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model, such as... Figure 1 As shown, it includes: Step 1: Import the reconstructed models of each wrist bone, the simplified model of the cartilage, the solid model of the transverse carpal ligament, and the spring model of the interosseous ligament into the 3D modeling software SolidWorks, and construct a complete 3D geometric model of the carpal tunnel structure according to the anatomical relationship of the human wrist. Step 2: Apply palmar tensile load to the three-dimensional geometric model to observe the carpal tunnel structure and extract the static displacement response of key nodes of the transverse carpal ligament. At the same time, apply harmonic excitation load to the three-dimensional geometric model and extract the dynamic displacement response of key nodes of the transverse carpal ligament within a specified frequency range. Step 3: For static and dynamic working conditions, generate multiple sets of material property parameter combinations by random sampling, and construct static training datasets and dynamic training datasets by combining the corresponding static displacement response and dynamic displacement response. Step 4: Train the PCE surrogate model based on the statics training dataset, and train the PCE surrogate model and the SVR surrogate model based on the dynamics training dataset respectively; Step 5: Input the material property parameters of the carpal tunnel structure to be predicted into the corresponding surrogate model after training, and output the static and dynamic displacement response prediction results of the carpal tunnel structure.

[0018] Preferably, a complete three-dimensional geometric model of the carpal tunnel structure is constructed, including: The wrist bone model obtained from the CT scanner is saved as an STL file. The STL file is then imported into the Spaceclaim module of the finite element software ANSYS to separate and remove discrete patches, repair surface depressions and high curvature areas, and perform reverse modeling using the Autoskin command to obtain the reconstructed model of each wrist bone. The reconstructed model is imported into SolidWorks and each bone is assembled to its corresponding position. A cross section is generated at the joint space using spline curves, which are then stretched to form a columnar solid and the interference portion is removed to obtain a simplified model of the cartilage. Based on the morphological characteristics and modeling requirements of different types of ligaments, solid models of the transverse carpal ligament and spring models of the interosseous ligaments were established respectively. The models are assembled according to the anatomical structure of the human wrist. Overlapping areas are eliminated by interference detection to obtain a three-dimensional geometric model of the carpal tunnel structure, in which the transverse carpal ligament arches along the palmar side as the positive Y-axis.

[0019] Preferably, the static displacement response of key nodes of the transverse carpal ligament is extracted, including: The carpal bones, cartilage, and transverse carpal ligament of the three-dimensional geometric model are all meshed with tetrahedral meshes, and element erasure, boundary fusion, and local mesh optimization are performed at the connection points of each part. The bones, cartilage, and transverse carpal ligament are designed as uniform isotropic linear elastic bodies and given elastic modulus and Poisson's ratio. At the same time, the interosseous ligament springs are given stiffness coefficients. The carpal bones, cartilage and transverse carpal ligament contact parts are bound face to face, and three non-ligament attachment nodes are selected on each of the eight carpal bones to constrain the displacement degrees of freedom. Five unit surfaces were selected at the midpoint of the midline of the transverse carpal ligament. A concentrated load of 100N along the positive Y-axis was applied, and the displacement of the carpal tunnel structure along the Y-axis was extracted as the static displacement response.

[0020] Preferably, the dynamic displacement response of key nodes of the transverse carpal ligament within a specified frequency range is extracted, including: Remove the interosseous ligament spring model from the three-dimensional geometric model of the carpal tunnel structure, and set the bottom surface of each carpal bone as a fixed boundary; At the center of the transverse carpal ligament, a small area consisting of 5 unit surfaces is selected, and a sinusoidal load with an amplitude of 20N is applied with a frequency range of 400Hz to 700Hz. The structural damping ratio is set to 0.1. Frequency points were uniformly selected within the 450-550Hz frequency band, and the Y-direction displacement response of the proximal, middle, and distal nodes of the transverse carpal ligament was extracted as the dynamic displacement response.

[0021] Preferably, the random sampling adopts the Latin hypercube sampling method; The static training dataset has a 6-input, 1-output structure. The inputs are the elastic modulus and Poisson's ratio of bone, cartilage, and transverse carpal ligament, and the output is the static displacement of key nodes of the transverse carpal ligament. The dynamic training dataset has a 10-input, 1-output structure. The inputs are the elastic modulus, Poisson's ratio, bone density, and frequency points of the bone, cartilage, and transverse carpal ligament. The output is the dynamic displacement of key nodes of the transverse carpal ligament.

[0022] Preferably, the construction of the PCE proxy model includes: Hermite polynomials are used as orthogonal polynomial basis functions, and the undetermined coefficients are solved by least squares regression. The construction of the SVR agent model includes: Radial basis functions are used as kernel functions, and Lagrange multipliers and bias terms are solved through Lagrange dual optimization. The penalty factor and error tolerance are adjusted to ensure that the training accuracy meets the requirements.

[0023] In this embodiment, the key nodes are the three feature nodes: near, middle, and far.

[0024] In this embodiment, the carpal bone geometry model was obtained using a spiral CT scanner. The carpal bone model obtained by the CT scanner is saved as an STL file with a large number of facets and chaotic topology. Furthermore, the file data contains numerous floating fragments. Directly importing it into CAD or CAE software can lead to modeling failures and mesh generation failures. Therefore, it is necessary to reverse engineer the CT-reconstructed 3D model: First, the STL file obtained from the carpal bone scan is imported into the Spaceclaim module in ANSYS. Using the separation command, the internal discrete facets are separated from the main model, and the discrete facets inside the model are removed. Then, for depressions caused by chaotic surface topology, local facets are deleted and reconstructed. Next, for areas with excessive surface curvature, the curvature is reduced using the shrink and flatten commands to improve smoothness. Finally, the repaired facets are used to generate a 3D solid covered by multiple curved surfaces using the Autoskin command, completing the reverse engineering of the carpal bone model. The reconstructed carpal bones are shown below. Figure 2 As shown, (a) is the hamate bone, (b) is the scaphoid bone, (c) is the capitate bone, (d) is the trapezium bone, (e) is the lunate bone, (f) is the trapezium argenteus, (g) is the triquetrum bone, and (h) is the pisiform bone.

[0025] Cartilage tissue has a low density and produces darker grayscale images, making it impossible to obtain a well-defined model using CT scans. Therefore, this technical solution utilizes the 3D modeling software SolidWorks for manual modeling. First, the pre-modeled 3D wrist bone model is imported into SolidWorks, and each bone is assembled into its corresponding position to facilitate the positioning of the cartilage model. Then, spline curves are used to generate the cartilage cross-sectional shape at the joint space, and the extrusion command is used to create columnar solids between the wrist bones. Finally, the surface cut command is used to delete interfering parts of the solids to form a simplified cartilage model. A portion of the cartilage model is shown below (the darker colored areas). Figure 3 As shown.

[0026] Similar to cartilage, wrist ligaments are low-density soft tissues, with a density similar to surrounding tendons and cartilage. Their complex anatomical location makes it difficult to identify clear morphological boundaries using CT images. Due to these limitations, this technical solution primarily reconstructs wrist ligaments by establishing simplified models. Based on the morphological characteristics and modeling requirements of different ligament types, this solution establishes solid models of the transverse carpal ligament and spring models of the interosseous ligaments to describe their roles in mechanical response.

[0027] The transverse carpal ligament (TCL) is located on the palmar side of the wrist, originating from the scaphoid tubercle and trapezium on the radial side, crossing the carpal tunnel, and reaching the pisiform and uncinate processes of the hamate on the ulnar side. It is a relatively thick fibrous plate. Compared to other ligaments in the wrist, the TCL is wider and thicker, therefore a 3D solid model was constructed in SolidWorks. First, based on the established carpal bone geometry model, a rectangular cross-section was drawn at the bone attachment location of the TCL. Referring to relevant literature, the thickness of the TCL was assumed to be 2mm, meaning the width of the rectangular cross-section was 2mm. Then, guide lines were drawn using 3D drawing, and the TCL geometry model was generated using the scan command. Finally, the interference between solids was removed using the delete command, thus constructing the TCL geometry model, as shown below. Figure 4 As shown.

[0028] Compared to the transverse carpal ligament, interosseous ligaments are smaller and located in narrow gaps between bones, making their geometry and attachment locations more difficult to determine. Therefore, this paper replaces each interosseous ligament with a nonlinear spring element that is only subjected to tension, not compression. Instead of creating a specific geometric model in SolidWorks, this is achieved in finite element software by setting spring constraints. The tensile stiffness and attachment locations will be discussed in detail later; here, only the interosseous ligament spring model is shown. Figure 5 As shown.

[0029] The established geometric models of the carpal bones, interosseous cartilage, transverse carpal ligament, and interosseous ligament were imported into the 3D modeling software SolidWorks. They were then precisely assembled according to their anatomical relationships in the actual human wrist to construct a complete 3D geometric model of the carpal tunnel structure. During the assembly process, to avoid difficulties in mesh generation and subsequent finite element analysis errors caused by geometric interference, the interference detection function in SolidWorks was used to check the contact relationships of each part of the model, promptly identifying and addressing any potential overlapping areas. After interference processing and detail adjustments, a complete 3D geometric model of the carpal tunnel structure was finally obtained, as shown below. Figure 6 As shown.

[0030] In this embodiment, under static conditions, when the carpal tunnel structure satisfies the quasi-static equilibrium condition, the basic governing equations for solving the nodal displacements can be expressed as: ,in, This represents the overall stiffness matrix of the carpal tunnel structure. This represents the displacement of the node to be determined; the specific number of nodes is determined by the finite element mesh type and mesh density. This represents the external load vector, which is the palmar tensile force in the static analysis of this paper.

[0031] In this embodiment, the finite element model of the carpal tunnel structure after mesh generation is as follows: Figure 7 As shown.

[0032] In reality, biological tissues are usually anisotropic nonlinear structures. However, current basic experiments cannot provide constitutive equations for bone, cartilage, and ligaments. Therefore, we assume that bone, cartilage, and the transverse carpal ligament are homogeneous, isotropic linear elastic bodies. The elastic modulus and Poisson's ratio of each tissue are shown in Table 1. Table 1. Biomechanical parameters of various tissues in the wrist (statics) The interosseous ligament is assumed to be a nonlinear spring under tension but not compression, with both ends of the spring connected to the nodes on the surface of the bone element. The stiffness coefficient is set with reference to existing literature.

[0033] In this embodiment, the displacement of the carpal tunnel structure along the Y-axis is extracted to obtain the displacement contour map of the model under static conditions, such as... Figure 8 As shown in the simulation results, under palmar tensile force, the transverse carpal ligament is the primary deforming structure and exhibits significant non-uniform deformation characteristics. The transverse carpal ligament arches upwards in an arc shape, and along the midline, the displacement amplitude of the proximal transverse carpal ligament is significantly greater than that of the distal one. This indicates that under the same loading conditions, the asymmetry of the carpal tunnel structure in terms of geometry and constraints leads to uneven displacement distribution in different regions. This phenomenon is highly consistent with the clinical observation of median nerve compression—the distal region of the carpal tunnel has poor deformability and is more prone to nerve compression under load. These simulation results not only verify the biomechanical rationality of the finite element model but also provide a mechanical theoretical explanation for the pathogenesis of carpal tunnel syndrome.

[0034] In actual industrial production, workers frequently operate machinery, and their hands are often subjected to long-term vibration loads. To study the mechanical response behavior of the carpal tunnel structure under vibration loads, a sinusoidal load was applied to the transverse carpal ligament, and the dynamic response of the carpal tunnel structure was analyzed using finite element method software.

[0035] Under dynamic conditions, the effects of inertia and damping on the carpal tunnel structure need to be considered. The load applied in this paper is a sinusoidal alternating load, and both the excitation and response can be expressed in complex form. At this time, the frequency domain equation has the following form: ,in These are the mass matrix, damping matrix, and stiffness matrix of the carpal tunnel structure, respectively. Indicates the excitation angular frequency. The imaginary unit; This represents the sinusoidal load applied to the carpal tunnel structure; This represents the frequency domain response of the displacement at each node.

[0036] In this embodiment, the mechanical parameters of various tissues in the wrist—elastic modulus and Poisson's ratio—remain consistent with those in the static model, and the bone density is set according to relevant literature as shown in Table 2. Table 2. Mechanical parameters (kinetics) of various tissues in the wrist. Since harmonic response analysis can only identify linear systems, and the nonlinear mechanical properties of the interosseous ligament spring model make it difficult to perform finite element calculations within this analytical framework, and the deformation of the carpal bones and interosseous ligaments is minimal compared to the deformation of the transverse carpal ligament, the interosseous ligament spring model is removed under dynamic conditions.

[0037] In this embodiment, considering that the relative displacement between carpal bones is much smaller than the displacement of the transverse carpal ligament, the bottom surface of each carpal bone is set as a fixed boundary for the purpose of simplifying the model. The main analysis focuses on the frequency domain response of the displacement of the transverse carpal ligament under sinusoidal excitation.

[0038] In this embodiment, three nodes—proximal, middle, and distal—of the transverse carpal ligament are selected along the midline direction, and the displacement frequency response curve in the Y direction is plotted, as shown below. Figure 9 As shown, the selected nodes exhibit significant frequency correlation within this frequency range. All curves show peak responses in the 450Hz-550Hz frequency band, indicating a resonance tendency within this range. The proximal resonance peak is the highest, suggesting a stronger vibration response and a higher likelihood of injury in the proximal region at this frequency. Furthermore, the amplitude distribution of the three frequency response curves shows that within the 450Hz-550Hz frequency band, the displacement response amplitude at the proximal and mid-positions is significantly higher than that at the distal end, which is largely consistent with characteristics observed in statics. This result suggests that in occupational groups frequently exposed to vibrating tools, the mid-proximal transverse carpal ligament may be more prone to structural damage due to repetitive vibration excitation, offering some explanation for the pathological evolution of carpal tunnel syndrome.

[0039] In this embodiment, considering the inconsistency of material parameters caused by individual differences, traditional finite element analysis methods require multiple repeated simulations, resulting in significant time costs. To address this issue, a surrogate model is constructed to replace repeated finite element simulations. This method can obtain the mapping relationship between input variables and mechanical responses with only a few finite element calculations to construct training samples, significantly improving computational efficiency while maintaining high prediction accuracy.

[0040] The basic principle of surrogate modeling is to construct a mathematical model of the structural response function using regression or classification, and then use this mathematical model to perform analysis in place of the actual model. There are several common surrogate models; this article mainly introduces the PCE surrogate model and the Support Vector Regression (SVR) surrogate model.

[0041] The core idea of ​​PCE lies in using orthogonal polynomials to expand stochastic processes or random fields into a polynomial sequence of random variables. The PCE surrogate model treats the uncertain inputs in the stochastic model as random variables and expands the response values ​​into a linear combination of a set of orthogonal polynomials of the input variables, specifically in the following form: ,in It is a vector form of random variables; The proxy model response value; These are orthogonal polynomial basis functions; the orthogonal polynomial basis functions vary depending on the distribution of the random variable. The key to constructing the PCE proxy model lies in the undetermined coefficients, which are all the terms to be expanded. The determination of random variables. In practical modeling, random variables... The dimensions and distribution of the variables are usually known. Multiple sets of random variables are obtained through random sampling, and the response value of each set is calculated using finite element software, ultimately forming multiple sets of parameter combinations corresponding to the input and output. These parameter combinations are used as a dataset, and the undetermined coefficients are solved using the least squares regression method, finally yielding the complete PCE surrogate model expression.

[0042] SVR (Survey-Regression Hyperplane) is a regression method based on statistical theory. Its core idea is to find a regression hyperplane that minimizes prediction error and has good generalization ability within a given tolerance range of error. For nonlinear problems, it generally has the following form: ,in They are Lagrange multipliers, For kernel function, Indicates the first training sample vectors, This is the bias term. Kernel functions come in many forms; this paper uses a radial basis function kernel, whose main form is: Radial basis function kernels possess strong fitting capabilities and wide applicability, especially suitable for complex and nonlinear mapping relationships in high-dimensional spaces. The key to constructing an SVR surrogate model lies in solving for the Lagrange multipliers. and bias terms Essentially, it is a constrained convex optimization problem, which can be expressed as: ; The constraints are expressed as follows: ; in In this paper, the value represents the response calculated using the finite element method. Regression weights representing higher-dimensional space; Represents the implicit mapping of kernel functions; The set error tolerance; For slack variables, representing the sample size that is allowed to exceed the error tolerance; This serves as a penalty factor, controlling the model's tolerance for samples exceeding the error threshold. Ultimately, the process is transformed into solving for the multipliers through Lagrange dual optimization. This yields the complete regression function. In actual model building, only the penalty factor and error tolerance need to be adjusted to ensure the training accuracy is within an acceptable range.

[0043] Taking into full account the differences in material properties among the various parts of the carpal tunnel, it is assumed that the elastic modulus and Poisson's ratio of the bone, cartilage, and transverse carpal ligament, a total of six variables, follow a normal distribution. The standard deviation and mean are shown in Table 3. Table 3. Normal distribution of random input variables for carpal tunnel structure under static conditions. First, using the aforementioned variables as input, multiple combinations of different material property parameters are generated through Latin hypercube sampling. Then, a parametric script is used to iteratively input these parameters into the finite element software for calculation. Next, nodes at proximal, mid-, and distal positions are selected along the midline of the transverse carpal ligament, and nodal displacements are extracted from the post-processing results. Finally, material properties are used as input, and nodal displacement responses are used as output to construct a 6-input, 1-output dataset. Since the random variables follow a normal distribution, Hermite polynomials are chosen as basis functions to construct the PCE surrogate model. The main form of the Hermite polynomial is: ; The dataset was divided into training and test sets in a 4:1 ratio. A PCE surrogate model was constructed using samples from the training set. Subsequently, the input data from the test set was substituted into the established surrogate model to obtain the corresponding predicted response.

[0044] Based on the established finite element model of displacement frequency domain response, considering the differences in carpal tunnel structure material properties among different individuals, it is assumed that all variables follow a normal distribution. Unlike static conditions, the influence of mass on the displacement frequency domain response needs to be considered in harmonic response analysis. In finite element software, the mass of an object is calculated using volume and density; therefore, density is added as a variable in the dynamic condition. The mean and standard deviation of each variable are shown in Table 4. Table 4 Normal distribution of random input variables for the carpal tunnel structure under dynamic conditions First, Latin hypercube sampling is used to randomly generate sample data with different material properties within a set probability distribution range. Then, a parametric script is used to iteratively input the data into the finite element software, which solves the problem according to boundary conditions and loads. Next, multiple frequency points are uniformly selected within a specified frequency range (450Hz-550Hz), and the displacement responses at the corresponding frequency points of the proximal, middle, and distal ends of the transverse carpal ligament are extracted from the post-processed file. Finally, material properties and frequency points are used as input variables, and the displacement responses of the three nodes are used as outputs to construct a 10-input, 1-output dataset. Based on this dataset, two surrogate models, PCE and SVR, are trained respectively.

[0045] To verify the prediction accuracy of the model, the prediction results of the PCE model were compared with the actual response values ​​obtained from the finite element analysis, and the relative error at each point was recorded in the form of a bar chart. The results are as follows: Figure 10 As shown, (a) is the proximal end, (b) is the middle end, and (c) is the distal end.

[0046] The average relative error at three locations of the transverse carpal ligament was calculated, and the time to complete a single finite element calculation and PCE model prediction was recorded, as shown in Table 5: Table 5 Comparison of PCE and Finite Element Calculation Results under Static Conditions As shown in the table, the average relative error of the PCE model at both the near and far nodes is controlled within 1%, while the error at the intermediate node is slightly higher at 2.42%, but still within an acceptable range. Overall, the prediction accuracy is high and meets the accuracy requirements of static analysis. Furthermore, compared to the approximately 12 seconds required for each finite element calculation, the PCE surrogate model's single prediction time is less than 1 millisecond, demonstrating extremely high computational efficiency. Therefore, the PCE-based static displacement response model for the wrist transverse ligament not only possesses excellent accuracy performance but also significantly improves computational speed, making it suitable for scenarios involving rapid prediction and large-scale parameter analysis.

[0047] In this embodiment, the prediction accuracy of the proxy model in the test set is demonstrated using a near-end node as an example. Figure 11 As shown, (a) is the PCE prediction result and (b) is the SVR prediction result.

[0048] Using the finite element results as a blank control group, the average relative error and computational efficiency of the two surrogate models were compared, and the relevant results are recorded in Table 6. Table 6. Comparison of the effects of two proxy models and finite element calculation under dynamic conditions. In summary, it can be seen that for the nonlinear problem of displacement frequency domain response prediction in dynamics, the SVR surrogate model is generally superior to the PCE model in terms of prediction accuracy, with a lower overall average relative error and stronger fitting ability. It is demonstrated that for highly nonlinear problems, the SVR surrogate model can more effectively capture the nonlinear mapping relationship between samples, achieving higher fitting accuracy compared to the PCE surrogate model. In terms of computational efficiency, the finite element software requires 121 seconds to complete a single calculation, while both surrogate models can achieve millisecond-level prediction. Considering both accuracy and computational efficiency, the constructed SVR surrogate model balances computational accuracy and efficiency for the displacement frequency domain response prediction problem of carpal tunnel structures, meeting the needs of rapid prediction and large-scale computation.

[0049] In this invention, the prediction accuracy of the surrogate model depends on the reliability of the finite element calculation data, and the mesh quality directly determines the accuracy of the finite element results. If the mesh has geometric distortions or topological conflicts, it will lead to errors in the mechanical response calculation (such as displacement response deviation exceeding 10%), thereby affecting the effectiveness of the training dataset and reducing the generalization ability of the surrogate model. Therefore, this invention also includes: At the junctions of each part, element erasure, boundary merging, and local mesh optimization are performed, including: Extract the connection interface at each connection point after fusion. Three-dimensional curved surface , and the preset ideal reference surface based on standard anatomical morphology Perform spatial registration and point cloud comparison, and calculate... Each sampling point Compared to The instantaneous geometric difference vector of the corresponding point A geometric difference field is constructed based on the geometric difference vectors of all points and using a weighted kernel density estimation method. ; For the geometric difference field Multi-level threshold segmentation is performed, and the percentage of the difference loss area within each difference level interval is calculated to form a hierarchical difference ratio group that characterizes the overall deviation features of the surface. ,in, Let be the proportion of the k-th level difference, and k = 1, 2, ..., n, where n is the total number of difference levels; Based on the aforementioned graded difference ratio group By using principal component analysis and spatial filtering, a set of geometric feature ridges representing the main deformation trends is extracted from high-order difference regions. ,in, The total number of geometric feature ridges; For each characteristic ridge line Sampling line position points along its length direction ; For each line position point , because of its original curved surface Using the projection point as the center, select its eight neighboring point sets to construct a local micro-surface patch. ; Calculate each micro-surface patch unit normal vector and its relationship with the ridge line exist Tangent vector at point The included angle Define this included angle as the local curvature coupling angle; Based on the local curvature coupling angle at each point Geometric difference vector , ridge line Adaptively expand to both sides to generate feature influence band surfaces that are strongly correlated with mechanical deformation. This is a key area of ​​focus for mechanics-grid co-optimization; For the connection interface Feature influence zone surface Apply a set of standardized basic load conditions Finite element analysis was performed to extract and fuse the stress flux matrix between nodes under multiple working conditions, and an integrated mechanical correlation matrix was constructed. ; Combined with the aforementioned geometric difference field With characteristic influence zone surface For the matrix Constrained spectral clustering analysis was performed to identify m1 key transmission sub-regions that are dually coupled with geometric anomalies and mechanical sensitivity. ; For each key transmission sub-region Units within Simultaneous calculation of geometric distortion index Mechanical sensitivity Topological conflict degree and geometric feature correlation ,in, From unit It is determined by the distance to the nearest feature ridge and the geometric difference field gradient at its location; Each unit is based on a learned classifier. Dynamically categorized into geometric repair type (G type), mechanical enhancement type (M type), topological reconstruction type (T type), or feature synergy type (FC type); Based on the element classification results, the corresponding optimization rule base is invoked to perform fine-tuning operations. For feature-cooperative (FC) elements, a geometry-mechanical guided joint optimization is performed: the objective is to minimize the deviation from the ideal geometry of the feature influence zone, while aligning the element's principal direction with the principal stress direction of the region. The optimization process is constrained by constraint functions. : ,in, For unit Geometric difference field gradient at the center; These are the principal directions of the element and the directions of the local principal stresses, respectively. , This is the balance coefficient; After optimization, the geometric conformance loss function Lge and the mechanical transmission fidelity function Fme are calculated, and a composite convergence determination is performed. The optimization iteration continues until the dual convergence conditions of geometry and mechanics are satisfied, thus obtaining the optimized mesh.

[0050] In this embodiment, the average side length of the tetrahedral mesh element is 0.5 mm, the maximum side length does not exceed 0.8 mm, and the minimum side length is not less than 0.3 mm. The mesh quality evaluation standard is a distortion index ≤ 0.3 (distortion index calculation method: the ratio of element volume to circumscribed sphere volume, the ideal tetrahedral distortion index is 1, and the actual value ≥ 0.7 is a high-quality element, and ≥ 0.5 is a qualified element). After dissection, the number of carpal bone mesh elements is approximately 8000-10000, the number of cartilage mesh elements is approximately 3000-5000, and the number of transverse carpal ligament mesh elements is approximately 6000-8000. The overall qualified element ratio of the mesh is ≥ 95%.

[0051] In this embodiment, the connection interface The contact surfaces between the various components of the carpal tunnel structure (such as the carpal bones and cartilage, ligaments and bones) are key areas for mesh optimization. For example, the articular contact interface between the carpal bones and cartilage covers the entire joint contact area, with an area of ​​approximately [area missing]. .

[0052] Three-dimensional curved surface It is the actual curved surface of the connection interface in the actual constructed model. Due to scanning noise and modeling errors, it will deviate from the ideal shape. The curved surface data of the connection interface between the wrist bone and cartilage after assembly is extracted by the ANSYS Spaceclaim module and saved as a point cloud format. The point spacing is set to 0.1mm to ensure data accuracy.

[0053] Preset ideal reference surface based on standard anatomical morphology It is an error-free connected interface surface constructed based on standard human anatomical data, and a smooth surface constructed using SolidWorks software, referencing the standard articular surface morphology of wrist bones and cartilage in human anatomical atlases.

[0054] Spatial registration was performed in MATLAB using the iterative nearest point algorithm, with the registration error controlled within 0.05 mm.

[0055] Point cloud comparison is the process of matching point cloud data of two surfaces one-to-one and analyzing the positional differences.

[0056] Sampling points Is Evenly selected feature points are used to accurately capture deviations, such as at 0.5mm intervals. 1000 sampling points were selected, and the three-dimensional coordinates of each point were recorded.

[0057] Instantaneous geometric difference vector It is the positional deviation vector of each sampling point relative to the corresponding point on the ideal surface, including the magnitude and direction of the deviation. For example, if the coordinates of a sampling point are (10.2, 5.3, 3.1) mm and the coordinates of the ideal corresponding point are (10.0, 5.2, 3.0) mm, the difference vector is (0.2, 0.1, 0.1) mm, which intuitively reflects the deviation of the point in three directions.

[0058] The weighted kernel density estimation method is a statistical method that integrates discrete difference vectors into a continuous field. The weight of sampling points in the joint center region is set to 1.2, and the weight of sampling points in the edge region is set to 0.8, highlighting the deviation in key areas.

[0059] In this embodiment, the geometric difference field It is a continuous field characterizing the distribution of deviations across the entire connection interface. For example, deviations of 0.3-0.5 mm were observed at the joint edge region and 0.1-0.2 mm at the center region, providing a target basis for subsequent optimization.

[0060] In this embodiment, multi-level threshold segmentation is a processing method that classifies deviations into levels based on their magnitude. For example, deviations are divided into three levels: 0-0.2mm, 0.2-0.5mm, and >0.5mm, quantifying the proportion of regions with different degrees of deviation. The difference level interval is the range of deviations that are divided, and each interval corresponds to a type of deviation degree.

[0061] In this embodiment, the difference loss area is the area of ​​the region where the deviation exceeds the ideal shape within each grade range. For example, the loss area for the 0.2-0.5mm grade is... Graded difference ratio group It is a set of percentages of the loss area of ​​each level relative to the total area of ​​the connection interface, where n is the total number of levels, such as the total area. hour, =70% (0-0.2mm) =24% (0.2-0.5mm) =6% (>0.5mm), clearly showing the overall deviation characteristics.

[0062] Principal component analysis is a data dimensionality reduction method that extracts the main deformation trends of the difference field. The data is processed by the princomp function in MATLAB, and the cumulative contribution rate of the first two principal components is over 90%.

[0063] Spatial filtering is an operation that filters out noise and preserves core features. Gaussian filtering (standard deviation 0.3 mm) is used to eliminate random scanning errors. High-order difference regions refer to areas with higher deviation levels (>0.2 mm), where deformation is significant.

[0064] Geometric feature ridge set It is a set of curves that characterize the main deformation trend, such as extracting two ridge lines. , These correspond to the main deformation areas at the joint edges.

[0065] Characteristic ridge line It is a curve that connects the extreme points of deviation in the higher-order difference region, such as Extending along the edge where the carpal bone connects to the cartilage, with a length of approximately 15 mm, it connects multiple extreme points with deviations >0.4 mm, reflecting the main direction of deformation.

[0066] In this embodiment, the line position point These are analysis points uniformly selected along the characteristic ridge line, such as... Select 15 points at 1mm intervals to accurately locate local areas.

[0067] The projection point is the point on the line that is perpendicularly projected onto the original surface. The points on the surface are used to ensure the accurate center position of the micro-curved surface patch.

[0068] The eight-neighbor point set is a collection of eight sampling points within a 0.3mm radius around the projected point, forming a point cloud set for a local region.

[0069] Local micro-curved surface patches It is a small-scale surface patch formed by fitting an eight-neighbor point set, each with an area of ​​approximately It can accurately reflect local geometric characteristics.

[0070] Unit normal vector It is a normalized vector perpendicular to the micro-surface patch, calculated using MATLAB's surfnorm function, such as (0.2, 0.6, 0.8) (already normalized), representing the orientation of the surface patch.

[0071] Ridge tangent vector It is along the characteristic ridge line in The tangent direction vector at a point, such as The tangent vector at a certain point (0.9, 0.1, 0.0) reflects the direction of the ridge line.

[0072] The local curvature coupling angle ranges from 0° to 90°, relating the curvature of the local surface to the direction of the ridge line.

[0073] In this embodiment, adaptive expansion is an operation that adjusts the ridge expansion width according to the coupling angle and the difference vector. Areas with large coupling angles and large difference vectors are expanded by 1.5mm, and vice versa, by 0.8mm, to ensure that the influence band covers the critical areas.

[0074] Feature influence zone surface It is a surface with a mechanically sensitive region surrounding the ridgeline, and the area of ​​each influence zone is approximately This is the core target for subsequent optimization.

[0075] Standardized basic load conditions Three representative static loads are used: F1 is a 50N concentrated load in the positive Y-axis direction, F2 is a 30N concentrated load in the positive X-axis direction, and F3 is a 40N concentrated load in the negative Z-axis direction, simulating common stress scenarios in the wrist. The stress flux matrix between nodes is a quantified matrix of stress transfer between nodes in the influence zone after finite element calculation. For example, 300 nodes form a 300×300 matrix with element values ​​ranging from 0 to 5 MPa.

[0076] Integrated mechanical correlation matrix It is a comprehensive matrix after integrating multiple working condition matrices. The larger the value, the closer the mechanical transmission between nodes, providing a mechanical basis for cluster analysis.

[0077] In this embodiment, the constrained spectral clustering analysis is a clustering algorithm incorporating geometric difference fields and influence band constraints, implemented using the MATLAB function `spectclust`, with a cluster size of m1=2. The key transmission sub-region is characterized by dual coupling of geometric anomalies and mechanical sensitivity. It is a region where both large geometric deviations and strong mechanical transmission characteristics exist simultaneously, such as This refers to the area at the junction of the carpal bones and cartilage, with an area of... Geometric deviation of 0.3-0.5mm and mechanical correlation value >3MPa are the core targets for mesh optimization.

[0078] Units within the key conduction subregion These are tetrahedral mesh cells divided within the critical region, such as... It contains 80 elements, each 0.5 mm in size, and is the basic unit for finite element analysis.

[0079] Geometric Distortion Index The degree to which a unit deviates from an ideal tetrahedron is characterized by an ideal value of 1. The ratio of the unit volume to the volume of the circumscribed sphere is calculated. For example, a unit has G=0.85 (excellent morphology) and another unit has G=0.4 (severe distortion).

[0080] Mechanical sensitivity It reflects the sensitivity of the element to load changes and is calculated by the stress change rate when the load changes by 10%. For example, if the stress change rate of a certain element is 20%, then M=20%.

[0081] Topological conflict degree The degree of topological conflict between a cell and its neighboring cells is characterized by calculating the ratio of the conflict surface area to the total area of ​​the cells. For example, T=5% indicates that there is a slight conflict.

[0082] Geometric feature correlation Determined by the distance from the element to the ridge and the gradient of the difference field, the formula is: If the unit distance from the ridge is 0.3 mm and the gradient is 0.4, then F = 1.37.

[0083] The learning classifier is a machine learning model based on support vector machine (SVM), trained with 200 labeled units, achieving an accuracy of 92%. The units are divided into geometric repair type (G type, G<0.6), mechanical enhancement type (M type, M>25%), topological reconstruction type (T type, T>8%), and feature co-operation type (FC type, all four exponents are moderate).

[0084] The optimization rule base is a set of preset optimization operations for various cells, such as adjusting vertex coordinates to reduce distortion for G-type cells and encrypting the mesh to improve accuracy for M-type cells.

[0085] Geometry-mechanism-guided joint optimization is an optimization method for FC-type elements, which takes into account both geometric shape and mechanical transfer characteristics.

[0086] constraint functions These are the constraints for optimization. =0.6、 =0.4, The absolute value of the gradient of the difference field. The angle between the principal direction of the element and the principal stress direction is the angle between the two directions. Optimization requires minimizing this function value.

[0087] The geometric conformality loss function Lge characterizes the deviation of the optimized element from the ideal shape, calculating the volume difference percentage, with a convergence condition of Lge < 3%. The mechanical transmission fidelity function Fme characterizes the degree of agreement between the mechanical transmission and the actual situation, obtained by comparing with experimental results, with a convergence condition of Fme > 95%. The composite convergence criterion is to simultaneously check Lge and Fme; optimization stops when both conditions are met. The final optimized mesh element distortion index is all > 0.7, and the mechanical calculation deviation is < 5%.

[0088] In this embodiment, a four-order progressive optimization logic is constructed, consisting of geometric precision diagnosis → mechanical-geometric coupling analysis → intelligent unit classification → strategy collaborative optimization. For the first time, the macroscopic anatomical deviations (geometric difference field, characteristic ridge line) of the connection interface are explicitly correlated and coupled with the microscopic mechanical conduction characteristics, forming a complete causal chain and technical closed loop from macroscopic morphology diagnosis to microscopic mesh optimization.

[0089] In this embodiment, the overall deviation pattern is quantified by constructing a graded difference ratio group, and the geometric feature ridge line is extracted as the main deformation path. By calculating the local curvature coupling angle and generating the feature influence band, the abstract geometric lines are given a clear mechanical analysis meaning, making them a bridge connecting the geometric shape and the mechanical response.

[0090] By introducing geometric difference fields and characteristic influence zones as hard constraints into the cluster analysis of mechanical transmission paths, the key regions can be accurately calibrated, and the correlation of geometric features can be increased, thus achieving a fundamental leap in optimization guidance from a single mechanical dimension to a geometric-mechanical dual dimension.

[0091] The beneficial effects of the above technical solution are: through deep fusion, the final mesh not only meets the accuracy requirements of mechanical calculations, but also actively conforms to the individualized deformation characteristics of anatomical structures at the geometric level. This ensures that the training data of the surrogate model generated based on this mesh can simultaneously contain individual geometric features and general mechanical laws, significantly improving the generalization ability and prediction accuracy of the surrogate model in practical applications.

[0092] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model, characterized in that, include: Step 1: Import the reconstructed models of each wrist bone, the simplified model of the cartilage, the solid model of the transverse carpal ligament, and the spring model of the interosseous ligament into the 3D modeling software SolidWorks, and construct a complete 3D geometric model of the carpal tunnel structure according to the anatomical relationship of the human wrist. Step 2: Apply palmar tensile load to the three-dimensional geometric model to observe the carpal tunnel structure and extract the static displacement response of key nodes of the transverse carpal ligament. At the same time, apply harmonic excitation load to the three-dimensional geometric model and extract the dynamic displacement response of key nodes of the transverse carpal ligament within a specified frequency range. Step 3: For static and dynamic working conditions, generate multiple sets of material property parameter combinations by random sampling, and construct static training datasets and dynamic training datasets by combining the corresponding static displacement response and dynamic displacement response. Step 4: Train the PCE surrogate model based on the statics training dataset, and train the PCE surrogate model and the SVR surrogate model based on the dynamics training dataset respectively; Step 5: Input the material property parameters of the carpal tunnel structure to be predicted into the corresponding surrogate model after training, and output the static and dynamic displacement response prediction results of the carpal tunnel structure.

2. The fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model according to claim 1, characterized in that, Construct a complete three-dimensional geometric model of the carpal tunnel structure, including: The wrist bone model obtained from the CT scanner is saved as an STL file. The STL file is then imported into the Spaceclaim module of the finite element software ANSYS to separate and remove discrete patches, repair surface depressions and high curvature areas, and perform reverse modeling using the Autoskin command to obtain the reconstructed model of each wrist bone. The reconstructed model is imported into SolidWorks and each bone is assembled to its corresponding position. A cross section is generated at the joint space using spline curves, which are then stretched to form a columnar solid and the interference portion is removed to obtain a simplified model of the cartilage. Based on the morphological characteristics and modeling requirements of different types of ligaments, solid models of the transverse carpal ligament and spring models of the interosseous ligaments were established respectively. The models are assembled according to the anatomical structure of the human wrist. Overlapping areas are eliminated by interference detection to obtain a three-dimensional geometric model of the carpal tunnel structure, in which the transverse carpal ligament arches along the palmar side as the positive Y-axis.

3. The fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model according to claim 1, characterized in that, Extracting the static displacement response of key nodes of the transverse carpal ligament, including: The carpal bones, cartilage, and transverse carpal ligament of the three-dimensional geometric model are all meshed with tetrahedral meshes, and element erasure, boundary fusion, and local mesh optimization are performed at the connection points of each part. The bones, cartilage, and transverse carpal ligament are designed as uniform isotropic linear elastic bodies and given elastic modulus and Poisson's ratio. At the same time, the interosseous ligament springs are given stiffness coefficients. The carpal bones, cartilage and transverse carpal ligament contact parts are bound face to face, and three non-ligament attachment nodes are selected on each of the eight carpal bones to constrain the displacement degrees of freedom. Five unit surfaces were selected at the midpoint of the midline of the transverse carpal ligament. A concentrated load of 100N along the positive Y-axis was applied, and the displacement of the carpal tunnel structure along the Y-axis was extracted as the static displacement response.

4. The fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model according to claim 1, characterized in that, Extract the dynamic displacement response of key nodes of the transverse carpal ligament within a specified frequency range, including: Remove the interosseous ligament spring model from the three-dimensional geometric model of the carpal tunnel structure, and set the bottom surface of each carpal bone as a fixed boundary; At the center of the transverse carpal ligament, a small area consisting of 5 unit surfaces is selected, and a sinusoidal load with an amplitude of 20N is applied with a frequency range of 400Hz to 700Hz. The structural damping ratio is set to 0.

1. Frequency points were uniformly selected within the 450-550Hz frequency band, and the Y-direction displacement response of the proximal, middle, and distal nodes of the transverse carpal ligament was extracted as the dynamic displacement response.

5. The fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model according to claim 1, characterized in that, The random sampling method used is the Latin hypercube sampling method.

6. The fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model according to claim 1, characterized in that, The static training dataset has a 6-input, 1-output structure. The inputs are the elastic modulus and Poisson's ratio of bone, cartilage, and transverse carpal ligament, and the output is the static displacement of key nodes of the transverse carpal ligament. The dynamic training dataset has a 10-input, 1-output structure. The inputs are the elastic modulus, Poisson's ratio, bone density, and frequency points of the bone, cartilage, and transverse carpal ligament. The output is the dynamic displacement of key nodes of the transverse carpal ligament.

7. The fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model according to claim 1, characterized in that, The construction of the PCE agent model includes: Hermite polynomials are used as orthogonal polynomial basis functions, and the undetermined coefficients are solved by least squares regression.

8. The fast prediction method for the mechanical response of the carpal tunnel structure based on a surrogate model according to claim 1, characterized in that, The construction of the SVR agent model includes: Radial basis functions are used as kernel functions, and Lagrange multipliers and bias terms are solved through Lagrange dual optimization. The penalty factor and error tolerance are adjusted to ensure that the training accuracy meets the requirements.

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