A costimulated optimization design method for costal cartilage graft interface microstructure with cross-scale collaborative optimization capability
Patent Information
- Application Number
- CN202610938135.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-06-26
- Publication Date
- 2026-10-30
AI Technical Summary
[0005]本发明提供了一种具有跨尺度协同优化能力的肋软骨移植物界面微结构优化设计方法，通过在界面微结构优化设计中创新性地引入伴随法，并构建AI代理模型实现微观几何参数与宏观力学响应的耦合，有效解决了传统优化设计方法计算量大、收敛效率低、难以兼顾跨尺度优化的问题
[0025]1、通过引入伴随法获得目标函数对界面微结构几何参数及类型松弛参数的灵敏度信息，使优化过程由依赖大量正向试错转变为基于梯度信息的定向迭代，从而提高优化收敛效率并降低计算成本。
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Abstract
Description
Technical Field
[0001] This invention relates to an interface microstructure optimization design method, specifically to a rib cartilage graft interface microstructure optimization design method with cross-scale collaborative optimization capabilities. Background Technology
[0002] In my country, the number of osteoarthritis patients exceeds 100 million. Osteoarthritis often leads to degenerative changes and defects in cartilage. For large-area cartilage defects, autologous rib cartilage transplantation has become a popular alternative treatment option in the field of cartilage defect repair due to its relatively abundant donor source, similar tissue composition to articular cartilage, and low risk of immune rejection. However, rib cartilage and host articular cartilage differ in elastic modulus, permeability, and layered mechanical properties. After transplantation, stress concentration, stress shielding, or abnormal distribution of liquid phase pressure can easily occur at the lateral bonding interface between the graft and the host cartilage, thereby deteriorating the interfacial mechanical microenvironment. This is detrimental to the adhesion, proliferation, differentiation, and matrix secretion of cartilage repair-related cells such as mesenchymal stem cells and chondrocyte progenitor cells, thus affecting the structural integration and rehabilitation process of the transplanted cartilage.
[0003] Existing research has shown that microscale stress, strain, and flow fields can influence cell adhesion, spreading, growth, and differentiation. Therefore, constructing controllable microstructures at the graft interface holds promise for improving the mechanical microenvironment of cartilage graft interfaces by adjusting local equivalent stiffness, permeability, and surface topological features. However, existing interface microstructure optimization design methods still have shortcomings: topology optimization and shape optimization methods are mostly based on local objectives at the microscale representative unit level, lacking coupling with joint-scale porous elastic models, and failing to reflect the influence of microstructures on the solid-phase stress and liquid-phase pressure distribution of the graft interface under macroscopic physiological loads. On the other hand, particle swarm optimization and genetic algorithms can search for equivalent material parameters at the macroscopic scale, but they usually rely on a large number of forward problem trials, lack explicit gradient information, and have long computation time and low convergence efficiency; moreover, if optimization is only performed in the equivalent material parameter space, equivalent material parameters that are difficult to achieve from the actual microstructure geometry may be obtained.
[0004] Therefore, in order to solve the problems of difficult optimization convergence, insufficient coupling between microstructure parameters and macroscopic mechanical response, and insufficient feasibility of equivalent material parameters in the microstructure optimization design of rib cartilage graft interfaces, it is necessary to construct an interface microstructure optimization design method that takes into account both cross-scale modeling and gradient information. Summary of the Invention
[0005] This invention provides a method for optimizing the microstructure of rib cartilage graft interfaces with cross-scale collaborative optimization capabilities. By innovatively introducing the adjoint method into the interface microstructure optimization design and constructing an AI surrogate model to couple microscopic geometric parameters with macroscopic mechanical responses, it effectively solves the problems of large computational load, low convergence efficiency, and difficulty in taking cross-scale optimization into account in traditional optimization design methods.
[0006] The objective of this invention is achieved through the following technical solution:
[0007] A method for optimizing the microstructure of rib cartilage graft interfaces with cross-scale collaborative optimization capabilities includes the following steps:
[0008] Step 1: Construct an equivalent material parameter prediction surrogate model:
[0009] Step 11: Perform batch simulations of the equivalent representative elements of the microstructure using COMSOL Multiphysics, measure the equivalent material properties of the equivalent representative elements under different microstructure types and geometric parameters, and construct a database of the correspondence between microstructure parameters and equivalent material properties for training the equivalent material parameter prediction surrogate model.
[0010] Step 12: When constructing the positive prediction model, train the positive prediction model separately for different types of microstructures. Each positive prediction model takes the geometric parameters of the microstructure of that type as input and the equivalent stiffness matrix and equivalent permeability matrix as output.
[0011] Step 2: Determine the optimization domain:
[0012] The space near the transplantation interface between the rib cartilage graft and the host articular cartilage, that is, the thin layer of space formed by extending symmetrically and equidistantly to both sides along the normal of the interface plane, is defined as the microstructure optimization domain.
[0013] Step 3: Obtain residual derivative information:
[0014] A porous elastic finite element model was constructed, comprising a rib cartilage graft, host articular cartilage, and an interface optimization domain. The state variables included solid-phase displacement. and liquid phase pressure Residuals are preserved during the assembly and solution of forward problems. Solid displacement in the optimization domain Liquid phase pressure The derivative information is obtained, and at the same time, the objective function of the optimization task is constructed;
[0015] Step 4: Update and optimize the domain microstructure parameters based on the adjoint method:
[0016] Step 41: Based on the solution to the forward problem obtained in Step 3, obtain the partial derivatives of the objective function with respect to the equivalent stiffness matrix and the equivalent permeability matrix using the adjoint method.
[0017] Step 42: Use PyTorch's automatic differentiation tool to perform reverse chain propagation on the forward prediction neural network to obtain the partial derivatives of the equivalent material parameters with respect to the continuous geometric parameters of the microstructure.
[0018] Step 43: For discrete type parameters, use the softmax relaxation method to represent discrete types as continuous type weights. ,in and , This indicates that the microstructure is the first The probability or weight of a microstructure, and the mixed equivalent material parameters are expressed as follows: , ,in For the first Continuous geometric parameters corresponding to microstructures and The output of the positive prediction network for this type of microstructure;
[0019] Step 44: After optimization and convergence, select the type with the largest weight as the actual microstructure type;
[0020] Step 5: Predict the updated mechanical field using the residual increment equation:
[0021] After updating the continuous geometric parameters and type weights of the microstructure, the new state variables are predicted using the residual linearized incremental equation, thereby updating the displacement field, liquid pressure field, and solid-phase force field obtained from the constitutive relation; if the prediction error of the updated residual norm or objective function is greater than the preset threshold, the porous elastic positive problem is solved again to correct the error generated by the linearization prediction.
[0022] Step 6: Repeat until convergence:
[0023] Repeat steps 4 and 5 until the change in the objective function is less than the preset convergence threshold or the maximum number of iterations is reached. Finally, output the microstructure type, continuous geometric parameters, equivalent stiffness matrix, equivalent permeability matrix, and corresponding solid-phase stress and liquid-phase pressure distribution of each partition in the optimization domain.
[0024] Compared with the prior art, the present invention has the following advantages:
[0025] 1. By introducing the adjoint method, the sensitivity information of the objective function to the geometric parameters and type relaxation parameters of the interface microstructure is obtained, so that the optimization process changes from relying on a large number of positive trial and error to directional iteration based on gradient information, thereby improving the optimization convergence efficiency and reducing the computational cost.
[0026] 2. By establishing the mapping relationship between microstructure type parameters, geometric parameters and equivalent stiffness matrix and equivalent permeability matrix through a neural network surrogate model, and coupling it to the macroscopic porous elastic model, the synergistic optimization of microstructure design and macroscopic interface mechanical response is achieved, thereby improving the physical realizability of the optimization results. Attached Figure Description
[0027] Figure 1 The flowchart shows a method for optimizing the microstructure of rib cartilage graft interfaces with cross-scale collaborative optimization capabilities. Detailed Implementation
[0028] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.
[0029] This invention provides a method for optimizing the microstructure of rib cartilage graft interfaces with cross-scale collaborative optimization capabilities. First, a surrogate model for predicting microstructure material parameters is constructed based on a multilayer perceptron (MLP). Then, the optimization domain is determined and a porous elastic forward problem under joint-scale loading is solved. Next, the gradient information of the objective function with respect to design variables is obtained based on the adjoint method. Thus, efficient optimization of the surface microstructure containing gradient information is achieved through a finite-degree forward problem solution combined with multi-step adjoint method iteration. The objective function is a scalar function, composed of the actual and design values of solid-phase stress, liquid-phase pressure, and liquid-phase flow velocity in the region near the graft interface, as well as a regularization term. The design variables are the type of microstructure (discrete parameters) and geometric parameters (continuous parameters). Figure 1 As shown, the specific steps are as follows:
[0030] Step 1: Construct an equivalent material parameter prediction surrogate model:
[0031] Batch simulations of equivalent representative elements of microstructures were performed using COMSOL Multiphysics to measure the equivalent material properties of these representative elements under different microstructure types and geometric parameters. A database of the correspondence between microstructure parameters and equivalent material properties was constructed to train a surrogate model for predicting equivalent material parameters. Specifically: the microstructure parameters include discrete and continuous structural parameters; the discrete parameters include micropores, microgrooves, micropillars, or combinations thereof, encoded using one-heat encoding; the continuous structural parameters include period, aperture, pillar diameter, groove width, depth, height, and tilt angle; the equivalent material properties include the equivalent stiffness matrix. and equivalent permeability matrix .
[0032] When constructing the forward prediction model, separate forward prediction models are trained for different types of microstructures (micropores, micropillars, microgrooves, etc.). Each forward prediction model takes the geometric parameters of that type of microstructure as input and outputs the equivalent stiffness matrix and equivalent permeability matrix. A positive definiteness constraint term is added to the model's loss function to ensure that the output of the forward prediction model has physical realism.
[0033] Step 2: Determine the optimization domain:
[0034] The space near the transplantation interface between the rib cartilage graft and the host articular cartilage, i.e., the thin layer of space formed by symmetrically extending equidistantly to both sides along the normal of the interface plane, is defined as the microstructure optimization domain, wherein: the thickness of the optimization domain is 10~200 micrometers; the optimization domain is divided into several partitions along the joint surface depth direction and its orthogonal direction based on the transplantation interface, and each partition has independent microstructure type parameters and continuous geometric parameters.
[0035] Step 3: Obtain residual derivative information:
[0036] A porous elastic finite element model was constructed, comprising a rib cartilage graft, host articular cartilage, and an interface optimization domain. The state variables included solid-phase displacement. and liquid phase pressure Residuals are preserved during the assembly and solution of forward problems. Solid displacement in the optimization domain Liquid phase pressure The derivative information is obtained. Simultaneously, the objective function for the optimization task is constructed. This objective function is a function that explicitly depends on the state variables in the optimization domain and is set according to the optimization objective.
[0037] Step 4: Update and optimize the domain microstructure parameters based on the adjoint method:
[0038] Based on the solution to the forward problem obtained in step 3, the partial derivatives of the objective function with respect to the equivalent stiffness matrix and the equivalent permeability matrix are obtained using the adjoint method. Subsequently, the forward predictive neural network is propagated backward using PyTorch's automatic differentiation tool to obtain the partial derivatives of the equivalent material parameters with respect to the continuous geometric parameters of the microstructure. For discrete-type parameters, a softmax relaxation method is used to represent discrete-type parameters as continuous-type weights. ,in and , This indicates that the microstructure is the first The probability or weight of a microstructure. Hybrid equivalent material parameters are expressed as... , ,in For the first Continuous geometric parameters corresponding to microstructures and The output is from the positive prediction network for this type of microstructure. After optimization and convergence, the type with the largest weight is selected as the actual microstructure type.
[0039] Step 5: Predict the updated mechanical field using the residual increment equation:
[0040] After updating the continuous geometric parameters and type weights of the microstructure, the new state variables (solid phase displacements) are predicted using the residual linearized incremental equation. and liquid phase pressure This updates the displacement field, liquid phase pressure field, and solid phase force field obtained from the constitutive relation. If the updated residual norm or objective function prediction error exceeds a preset threshold, the porous elastic positive problem is resolved to correct the error generated by linearization prediction.
[0041] Step 6: Repeat until convergence:
[0042] Repeat steps 4 and 5 until the change in the objective function is less than the preset convergence threshold, or the maximum number of iterations is reached. The final output includes the microstructure type, continuous geometric parameters, equivalent stiffness matrix, equivalent permeability matrix, and corresponding solid-phase stress and liquid-phase pressure distribution at the transplantation interface for each partition within the optimization domain. This achieves gradient-based microstructure optimization design of the rib cartilage graft interface.
[0043] The above method not only solves the problem that existing methods for optimizing the microstructure of rib cartilage graft interfaces often rely on gradient-free global search, making it difficult to obtain the sensitivity information of the objective function to the microstructure design parameters, resulting in large optimization computation and low convergence efficiency; it also solves the problem that existing methods cannot directly utilize the mapping relationship between microstructure geometric parameters and equivalent stiffness matrix and equivalent permeability matrix, making it difficult to establish a connection between the macroscopic mechanical response of the transplant interface and the microstructure geometry, thus making it impossible to achieve physically realizable cross-scale optimization design.
[0044] Example:
[0045] This embodiment focuses on the lateral interface between the rib cartilage graft and the host articular cartilage. Manufacturable surface microstructures are constructed in the neighborhood of the interface to ensure that the solid-phase stress distribution and liquid-phase pressure distribution at the transplantation interface closely approximate the design target. The microstructure type, continuous geometric parameters, equivalent stiffness matrix, and equivalent permeability matrix of each region are output. The specific steps are as follows:
[0046] Step 1: Construct an equivalent material parameter prediction surrogate model:
[0047] First, an equivalent representative metadata database of microstructures is constructed. Micropores, microgrooves, and micropillars are selected as candidate microstructure types. Discrete type parameters are represented using one-hot encoding, while continuous structure parameters are determined according to the specific structure type. For example, the spacing, diameter, depth, and tilt angle of micropores; the spacing, width, depth, and tilt angle of microgrooves; and the spacing, diameter, height, and tilt angle of micropillars.
[0048] In COMSOL Multiphysics, equivalent representative meta-models of various microstructures are established, and batch simulations are performed on different types and combinations of continuous geometric parameters. For each set of samples, unit strain and unit pressure gradient conditions are applied respectively, and the volume average stress and volume average velocity are calculated to obtain the equivalent stiffness matrix and equivalent permeability matrix. .
[0049] Each sample in the database contains microstructure type, continuous geometric parameters, equivalent stiffness matrix, and equivalent permeability matrix. If the candidate microstructure has a total of... Class, then the first The unique heat type encoding of microstructures can be represented as: .
[0050] Considering that different types of microstructures have different numbers and physical meanings of continuous geometric parameters, this embodiment trains a separate positive prediction network for each type of microstructure. The forward prediction network for microstructure-like structures takes the continuous geometric parameters of the structure as input and outputs the equivalent stiffness matrix and equivalent permeability matrix, denoted as:
[0051]
[0052] in, For the first A continuous vector of geometric parameters of microstructures. The network weights are used for this type of positive prediction network. In this embodiment, the positive prediction network adopts a multilayer perceptron structure. The input layer dimension is equal to the number of continuous geometric parameters of this type of microstructure. The hidden layer uses four fully connected layers with 128, 128, 64, and 64 neurons in each layer, respectively. The activation function is GELU or Tanh, and a dropout layer is set after the first two layers with a dropout ratio of 0.05~0.20. The output layer outputs 27 parameters, of which 21 outputs correspond to the 21 independent parameters of the sixth-order equivalent stiffness matrix, and 6 outputs correspond to the 6 independent parameters of the third-order equivalent permeability matrix.
[0053] To ensure the physical realism of the proxy model's output, this embodiment uses the Cholesky parameterization method to output a positive definite matrix. Specifically, the network output is first filled with a lower triangular matrix. and Then construct the equivalent stiffness matrix. and equivalent permeability matrix .
[0054]
[0055] in, and This is the positive definiteness margin, and its value range is usually [value range missing]. , It is the identity matrix. Alternatively, the independent components of the matrix can be directly output, and a minimum eigenvalue penalty term can be added to the loss function.
[0056] loss function In the design, normalized mean square error is used as the main fitting error, and symmetry constraints and weight regularization terms are added.
[0057]
[0058]
[0059]
[0060]
[0061]
[0062]
[0063] in, and The equivalent stiffness matrix and equivalent permeability matrix obtained from COMSOL simulation are... , , , This represents a matrix normalized to the mean and standard deviation of the training set, where the subscripts are... Indicates the output of the prediction model, subscript This represents the equivalent material parameters obtained from the simulation. This is the loss weight.
[0064] During training, the dataset for each type of microstructure is divided into training and test sets, for example, 80% and 20% respectively. Continuous geometric parameters and equivalent material parameters are normalized. The optimizer used is Adams, with an initial learning rate of 1e-3 and a batch size of 64 or 128. Cosine annealing is used to adjust the learning rate based on the validation set loss. Training is stopped early when the training set loss no longer decreases within a certain number of consecutive rounds. After training, the relative error, minimum eigenvalue, and positive definite matrix proportion are calculated for the test set. Only prediction models that meet the requirements for prediction error and positive definiteness proceed to the subsequent optimization process.
[0065] Step 2: Determine the optimization domain:
[0066] In the joint-scale model, the space near the lateral interface between the rib cartilage graft and the host articular cartilage is designated as the microstructure optimization domain. The thickness of the optimization domain is set to 30 μm. Based on the graft interface, the optimization domain is divided into several sections along the depth direction of the articular surface and the tangential direction of the interface orthogonal to it.
[0067] Each partition has independent microstructure design variables. Let the optimization domain be divided into... The partition, the first The design variables for each partition include type weights and continuous geometric parameters for various microstructures, expressed as follows:
[0068]
[0069] in, For the first The type weight vector of each partition, For the first in this partition The continuous geometric parameters corresponding to the microstructure. The continuous geometric parameters satisfy the manufacturing process constraints, such as minimum aperture, minimum groove width, maximum aspect ratio, minimum period range, etc.
[0070] Step 3: Obtain residual derivative information:
[0071] A three-dimensional porous elastic finite element model was constructed, comprising a rib cartilage graft, host articular cartilage, and an interface optimization domain. State variables included solid-phase displacement. and liquid phase pressure The merger is represented as:
[0072]
[0073] This embodiment uses a quasi-static porous elastic control equation to describe the coupling relationship between the solid-phase skeleton of cartilage and the liquid-phase flow. The solid-phase equilibrium equation and the liquid-phase continuity equation can be written as:
[0074]
[0075]
[0076] in, For physical force or equivalent external load, This is the liquid phase source term. The solid phase stress is determined by both the equivalent stiffness matrix and the liquid phase pressure, expressed as:
[0077]
[0078]
[0079] Taking the residuals from the above governing equations and discretizing them using the finite element method, we obtain the discrete residual equations:
[0080]
[0081]
[0082] The process of solving the forward problem preserves the derivative information of the residuals with respect to state variables and material parameters, mainly including:
[0083]
[0084] In this embodiment, the boundary conditions can be set according to the joint compression conditions. For example, a fixed constraint can be applied to the distal end of the host cartilage, a normal compressive displacement or equivalent contact load can be applied to the joint surface, and a flow-free or pressure-given boundary can be set at the lateral boundary. The specific boundary conditions can be replaced according to the actual joint location and load conditions, but it should be ensured that the solid-phase stress and liquid-phase pressure at the transplant interface can be extracted and used for the objective function calculation.
[0085] The objective function consists of the solid-phase stress distribution error and the liquid-phase pressure distribution error at the transplantation interface, which can be expressed as follows in this embodiment:
[0086]
[0087]
[0088]
[0089] in, This indicates the error in the distribution of the corresponding force in the solid. Indicates the error in liquid phase pressure distribution. For porting the interface, and These are the actual solid phase pressure and the target liquid phase pressure, respectively. and These are the target solid phase stress and the target liquid phase pressure, respectively. and These are the weighting coefficients.
[0090] Step 4: Update and optimize the domain microstructure parameters based on the adjoint method:
[0091] Based on the solution to the forward problem obtained in step 3, solve the discrete adjoint equation.
[0092] set up:
[0093]
[0094] make:
[0095]
[0096] Obtain the adjoint equation:
[0097]
[0098] After obtaining the accompanying variables, since the residual equation is always physically equal to 0, it can be proven that...
[0099]
[0100] Therefore, the sensitivities of the objective function to the equivalent stiffness matrix and the equivalent permeability matrix are respectively:
[0101]
[0102]
[0103] Subsequently, the forward prediction network trained in step 1 is subjected to back-chain propagation using PyTorch's automatic differentiation tool, transferring the macroscopic adjoint sensitivity to the continuous geometric parameters of the microstructure. For discrete-type parameters, the softmax function is used to represent discrete types as continuous-type weights.
[0104]
[0105]
[0106]
[0107] in, For the first The type score for microstructures is 1. This is a temperature parameter. The hybrid equivalent material parameters of each optimized partition are expressed as follows:
[0108]
[0109]
[0110] in, Indicates the first The first region The weights of the microstructure-like structure They represent the use of the first Forward prediction models of microstructures with geometric parameters of The equivalent stiffness matrix and equivalent permeability matrix predicted at that time.
[0111] The objective function for the first The gradients of continuous geometric parameters are obtained using the chain rule:
[0112]
[0113]
[0114]
[0115]
[0116] in, and They represent the objective function with respect to the first... The derivatives of the equivalent stiffness matrix and equivalent permeability matrix for each region. and They represent the first The equivalent stiffness matrix and equivalent permeability matrix of each region affect the continuous geometric parameters of the microstructure. The partial derivatives of .
[0117] The gradient of the objective function with respect to the type weights can be written as:
[0118]
[0119]
[0120]
[0121] The gradient is then passed to the type using the derivative of softmax. During optimization, continuous type weights are used for relaxation. After convergence, the type with the largest weight is selected as the actual microstructure type, and the corresponding continuous geometric parameters are output as manufacturing parameters.
[0122]
[0123]
[0124] in, That is, the actual microstructure type parameters. These are the continuous geometric parameters of the actual microstructure.
[0125] To avoid the intermediate mixed state obtained by continuous relaxation from failing to correspond to the real microstructure, this embodiment re-performs the equivalent representative element simulation or surrogate model verification of the microstructure type and geometric parameters obtained by projection after convergence, confirming that its equivalent stiffness matrix, equivalent permeability matrix and manufacturing constraints all meet the requirements.
[0126] Step 5: Predict the updated mechanical field using the residual increment equation:
[0127] After updating the microstructure geometric parameters and type weights, new state variables are predicted based on the residual linearized incremental equation. Let the material parameter increment be... The increment of the state variable is Then we have:
[0128]
[0129]
[0130] in, and Residuals For state variables and material parameters The partial derivatives of .
[0131] This yields a new approximate value for the state variable:
[0132]
[0133] in, For the first The solution to the forward problem or the corrected state field at the next iteration. Based on the predicted displacement field and liquid pressure field, the solid-state force field is updated using constitutive relations:
[0134]
[0135] in, For the first The equivalent stiffness matrix after the next iteration and That is, the first The state variables obtained in the next iteration.
[0136] To control the linearization prediction error, the residual norm prediction error is calculated after each iteration step. When the updated residual norm exceeds a preset threshold, the porous elastic positive problem is resolved, and the predicted state field is replaced with the newly obtained state field.
[0137]
[0138] in, This is the residual threshold. This step essentially updates displacement, pressure, and stress based on the residual increment equation, rather than directly updating the mechanical field by the adjoint method; the adjoint method is used to provide the optimization sensitivity of microstructure parameters.
[0139] Step 6: Repeat until convergence:
[0140] Repeat steps 4 and 5 to iteratively update the weights of each partition's microstructure type and continuous geometric parameters. Optimization stops when the change in the objective function is less than the preset convergence threshold or when the maximum number of iterations is reached.
[0141]
[0142] The final output includes the microstructure type, continuous geometric parameters, equivalent stiffness matrix, equivalent permeability matrix, and corresponding solid-phase stress and liquid-phase pressure distribution at the transplantation interface for each partition within the optimization domain. For the output microstructure scheme, further verification can be performed using equivalent representative elements, three-dimensional joint models, and processing constraints to form a final, manufacturable rib cartilage graft interface microstructure design scheme.
[0143] Through the above embodiments, the present invention integrates the neural network surrogate model, the three-dimensional porous elastic positive problem, discrete adjoint sensitivity analysis, softmax type relaxation, and residual incremental update and correction into the same optimization process, so that the microstructure parameters can be updated in a directional manner under the objective constraints of the solid phase stress and liquid phase pressure of the macroscopic transplantation interface, thereby realizing the microstructure optimization design of the rib cartilage graft interface based on gradient information.
[0144] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.
Claims
1. A method for optimizing the microstructure of rib cartilage graft interfaces with cross-scale collaborative optimization capabilities, characterized in that... The method includes the following steps: Step 1: Construct a surrogate model for predicting equivalent material parameters: Step 11: Perform batch simulations of the equivalent representative elements of the microstructure using COMSOL Multiphysics, measure the equivalent material properties of the equivalent representative elements under different microstructure types and geometric parameters, and construct a database of the correspondence between microstructure parameters and equivalent material properties for training the equivalent material parameter prediction surrogate model. Step 12: When constructing the positive prediction model, train the positive prediction model separately for different types of microstructures. Each positive prediction model takes the geometric parameters of the microstructure of that type as input and the equivalent stiffness matrix and equivalent permeability matrix as output. Step 2: Determine the optimization domain: The space near the transplantation interface between the rib cartilage graft and the host articular cartilage, that is, the thin layer of space formed by extending symmetrically and equidistantly to both sides along the normal of the interface plane, is defined as the microstructure optimization domain. Step 3: Obtain residual derivative information: A porous elastic finite element model was constructed, comprising a rib cartilage graft, host articular cartilage, and an interface optimization domain. The state variables included solid-phase displacement. and liquid phase pressure Residuals are preserved during the assembly and solution of forward problems. Solid displacement in the optimization domain Liquid phase pressure The derivative information is obtained, and at the same time, the objective function of the optimization task is constructed; Step 4: Update and optimize the domain microstructure parameters based on the adjoint method: Step 41: Based on the solution to the forward problem obtained in Step 3, obtain the partial derivatives of the objective function with respect to the equivalent stiffness matrix and the equivalent permeability matrix using the adjoint method. Step 42: Use PyTorch's automatic differentiation tool to perform reverse chain propagation on the forward prediction neural network to obtain the partial derivatives of the equivalent material parameters with respect to the continuous geometric parameters of the microstructure. Step 43: For discrete type parameters, use the softmax relaxation method to represent discrete types as continuous type weights. ,in and , This indicates that the microstructure is the first The probability or weight of a microstructure, and the mixed equivalent material parameters are expressed as follows: , ,in For the first Continuous geometric parameters corresponding to microstructure-like structures and The output of the positive prediction network for this type of microstructure; Step 44: After optimization and convergence, select the type with the largest weight as the actual microstructure type; Step 5: Predict the updated mechanical field using the residual increment equation: After updating the continuous geometric parameters and type weights of the microstructure, the new state variables are predicted using the residual linearized incremental equation, thereby updating the displacement field, liquid pressure field, and solid-phase force field obtained from the constitutive relation; if the prediction error of the updated residual norm or objective function is greater than the preset threshold, the porous elastic positive problem is solved again to correct the error generated by the linearization prediction. Step 6: Repeat until convergence: Repeat steps 4 and 5 until the change in the objective function is less than the preset convergence threshold or the maximum number of iterations is reached. Finally, output the microstructure type, continuous geometric parameters, equivalent stiffness matrix, equivalent permeability matrix, and corresponding solid-phase stress and liquid-phase pressure distribution of each partition in the optimization domain.
2. The method for optimizing the microstructure of rib cartilage graft interface with cross-scale collaborative optimization capability according to claim 1, characterized in that... In step 1-1, the microstructure parameters include discrete type parameters and continuous structure parameters; discrete type parameters include micropores, microgrooves, micropillars, or combinations thereof, using one-hot encoding; continuous structure parameters include period, pore diameter, pillar diameter, groove width, depth, height, and tilt angle; equivalent material properties include the equivalent stiffness matrix. and equivalent permeability matrix .
3. The method for optimizing the microstructure of rib cartilage graft interface with cross-scale collaborative optimization capability according to claim 1, characterized in that... In steps 1-2, a positive definiteness constraint term is added to the loss function of the model to ensure that the output of the positive prediction model has physical authenticity.
4. The method for optimizing the microstructure of rib cartilage graft interface with cross-scale collaborative optimization capability according to claim 1, characterized in that... The loss function The expression is: in, and The equivalent stiffness matrix and equivalent permeability matrix obtained from COMSOL simulation are... , , , This represents a matrix normalized to the mean and standard deviation of the training set, where the subscripts are... Indicates the output of the prediction model, subscript This represents the equivalent material parameters obtained from the simulation. This is the loss weight.
5. The method for optimizing the microstructure of rib cartilage graft interface with cross-scale collaborative optimization capability according to claim 1, characterized in that... In step 2, the thickness of the optimization domain is 10~200 micrometers; the optimization domain is divided into several partitions along the joint surface depth direction and its orthogonal direction, with the transplantation interface as the reference. Each partition has independent microstructure type parameters and continuous geometric parameters.
6. The method for optimizing the microstructure of rib cartilage graft interface with cross-scale collaborative optimization capability according to claim 1, characterized in that... In step 3, the objective function is a function that explicitly depends on the state variables in the optimization domain, and consists of the solid phase stress distribution error and the liquid phase pressure distribution error at the transplantation interface, expressed as: in, This indicates the error in the distribution of the corresponding force in the solid. Indicates the error in liquid phase pressure distribution. For porting the interface, and These are the actual solid phase pressure and the target liquid phase pressure, respectively. and These are the target solid phase stress and the target liquid phase pressure, respectively. and These are the weighting coefficients.
7. The method for optimizing the microstructure of rib cartilage graft interface with cross-scale collaborative optimization capability according to claim 1, characterized in that... In step 43 The expression is: in, For the first The type score for microstructures is 1. This refers to the temperature parameter.
8. The method for optimizing the microstructure of rib cartilage graft interface with cross-scale collaborative optimization capability according to claim 1, characterized in that... In step 5, the material parameter increment is set to... The increment of the state variable is Then we have: in, and Residuals For state variables and material parameters The partial derivatives; This yields a new approximate value for the state variable: in, For the first The solution to the forward problem or the corrected state field at the next iteration; Based on the predicted displacement field and liquid pressure field, the solid phase stress field is updated using constitutive relations: in, For the first The equivalent stiffness matrix after the next iteration and That is, the first The state variables obtained in the next iteration; To control the linearization prediction error, the residual norm prediction error is calculated after each iteration step. When the updated residual norm exceeds a preset threshold, the porous elastic positive problem is resolved, and the predicted state field is replaced with the newly obtained state field. in, This is the residual threshold.