A liver deformation simulation method and device and a storage medium

Abstract

The application discloses a liver deformation simulation method and device and a storage medium, and belongs to the technical field of soft tissue deformation simulation. The method comprises the following steps: after acquiring a multi-modal liver image, constructing and segmenting to obtain a tissue probability distribution graph, splicing and fusing a feature vector, and then performing parameter mapping based on physical constraints to obtain a non-homogeneous material parameter distribution field, calculating a macroscopic total Cauchy stress tensor based on the tissue probability distribution graph and the non-homogeneous material parameter distribution field, and if at least one of the gradient modulus values of each parameter in the macroscopic total Cauchy stress tensor and the non-homogeneous material parameter distribution field exceeds the corresponding gradient threshold value, performing progressive homogenization, otherwise directly outputting; and based on the above data, constructing a liver tetrahedral finite element grid and updating to complete deformation simulation. The application ensures that the parameters conform to real mechanical laws and image features through physical constraints, so as to describe the non-homogeneity of liver tissue, and the progressive homogenization is performed on the regions meeting the conditions, so that the simulation precision is improved.

Description

Technical Field

[0001] This invention relates to a method, apparatus, and storage medium for simulating liver deformation, belonging to the field of soft tissue deformation simulation technology. Background Technology

[0002] The liver is a vital organ in the human body with complex physiological structures and mechanical properties. Its internal tissues exhibit significant heterogeneity, especially in liver tumor regions, where mechanical parameters such as tissue stiffness, elastic modulus, and damage threshold differ significantly from those of normal liver tissue. Accurately establishing a liver model that reflects the differences in mechanical properties in tumor regions is a key technical challenge in fields such as virtual surgical simulation, preoperative planning, surgical navigation, and tumor biomechanical behavior analysis.

[0003] Currently, liver deformation simulation requires liver modeling as a foundation. Liver modeling methods based on medical imaging mainly fall into two categories: The first is the traditional finite element method based on geometric and material homogeneity assumptions. This type of method typically treats the liver as a homogeneous material and uses uniform material parameters for finite element analysis. Although this method is computationally efficient, it cannot accurately describe the heterogeneous characteristics of liver tumor regions, leading to significant deviations between the mechanical response and actual biological tissue behavior during simulated surgical cutting, puncture, or compression, severely affecting the realism and credibility of the simulation results. The second category is modeling methods based on mapping image grayscale values ​​to material properties. This type of method utilizes grayscale information from medical images such as CT and MRI to assign heterogeneous material properties to the liver by establishing empirical or statistical relationships between grayscale values ​​and mechanical parameters such as Young's modulus. CT refers to computed tomography (CT) scans, and MRI refers to magnetic resonance imaging (MRI). However, existing methods often rely on simplified linear models or region divisions to establish the mapping relationship between grayscale values ​​and mechanical parameters, failing to fully consider the influence of multiple factors such as tissue type, density, and microstructure, resulting in limited mapping accuracy.

[0004] In summary, existing technologies still suffer from low simulation accuracy when simulating liver deformation. Summary of the Invention

[0005] The purpose of this invention is to provide a method, apparatus, and storage medium for simulating liver deformation, thereby solving the problem of low simulation accuracy in existing technologies due to the difficulty in describing heterogeneity when simulating liver deformation.

[0006] To achieve the above objectives, the present invention employs the following technical solution: In a first aspect, the present invention provides a method for simulating liver deformation, comprising: After acquiring multimodal liver images, a fused feature vector is constructed through multimodal image registration and feature fusion. The fused feature vector is then input into a trained image segmentation network to obtain a tissue probability distribution map of the liver. The fused feature vector and the organization probability distribution map are concatenated and then input into the trained physical constraint neural network model to obtain the parameter distribution field of the heterogeneous material; the loss function used by the physical constraint neural network model during training includes volume incompressibility constraint terms and stress-strain monotonicity constraint terms; Hyperelastic stress is calculated based on the parameter distribution field of heterogeneous materials, and viscoelastic stress is calculated based on the probability distribution map of the microstructure. The macroscopic total Cauchy stress tensor is calculated based on the hyperelastic stress and viscoelastic stress. If at least one of the gradient moduli of the macroscopic total Cauchy stress tensor and each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is asymptotically homogenized to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor and is output. If neither the macroscopic total Cauchy stress tensor nor the gradient moduli of each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is output. Based on the tissue probability distribution map, the parameter distribution field of the heterogeneous material, and the tensor K, a tetrahedral finite element mesh of the liver is constructed. The tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization. The external force vector based on the external force on the liver is obtained. The liver tetrahedral finite element mesh is solved by GPU parallel finite element method based on the external force vector. The liver tetrahedral finite element mesh is updated according to the solution results to obtain the liver deformation tetrahedral finite element mesh, thus completing the liver deformation simulation.

[0007] Furthermore, the expression for the loss function used during the training of the physical constraint neural network model is as follows: ; in, This represents the loss function used during the training of a physically constrained neural network. Indicates the mean square error loss. This represents the volume incompressibility constraint term. This represents the stress-strain monotonicity constraint term. This represents the weighting coefficient corresponding to the volume incompressibility constraint term. This represents the weighting coefficient corresponding to the stress-strain monotonicity constraint term; The expression for the volumetric incompressibility constraint term is: ; in, Indicates the first The volumetric deformation penalty parameter at the individual unit that is related to the bulk modulus. This indicates the set critical volume ratio threshold. This indicates taking the maximum value; The expression for the stress-strain monotonicity constraint term is: ; in, Indicates the first The first individual element Principal stress components in each principal direction Indicates the first The first corresponding to the individual element Principal strain components in each principal direction Indicates the principal direction index of the principal stress component or principal strain component.

[0008] Through the aforementioned further technical solutions, this invention simultaneously introduces a volume incompressibility constraint term and a stress-strain monotonicity constraint term into the loss function of the physically constrained neural network. This ensures that the network not only minimizes parameter prediction errors during training but is also explicitly constrained by fundamental biomechanical laws. Specifically, the volume incompressibility constraint term forces the output material parameters to satisfy the near-incompressibility characteristics of liver tissue, avoiding volumetric deformation responses that violate physical laws. Furthermore, the stress-strain monotonicity constraint term guarantees that the material parameters satisfy the mechanical stability requirement of monotonically increasing stress with strain in all principal directions. Therefore, the trained network can map accurate material parameters from multimodal image features that conform to both image information and mechanical laws, fundamentally ensuring the numerical stability and biofidelity of subsequent finite element deformation simulations, thereby improving simulation accuracy.

[0009] Furthermore, the calculation of hyperelastic stress based on the parameter distribution field of heterogeneous materials is performed using the following formula: ; ; in, Indicates the first hyperelastic stress at individual elements Indicates the first The strain energy density function at the individual element. Indicates the first isochoric invariant. This represents the second isochoric invariant. Let be the determinant of the deformation gradient tensor. Indicates the first Mooney-Rivlin model parameters related to shearing behavior at individual units. Indicates the first Mooney-Rivlin model parameters at individual units that are related to the large deformation behavior of materials. Indicates the first The volumetric deformation penalty parameter at the individual unit that is related to the bulk modulus. For the deformation gradient tensor, Indicates transpose. This represents the right Cauchy-Green tensor.

[0010] Through the above-described further technical solutions, the present invention addresses the parameter distribution field of heterogeneous materials. , and These are respectively used as material parameters in the Mooney-Rivlin model, and vary with the first... Variations in individual element numbers reflect the heterogeneity of liver tumor tissue, thereby improving simulation accuracy.

[0011] Furthermore, in a heterogeneous material parameter distribution field, the parameters , and The value of satisfies the following condition: Tumor necrosis core area Larger than the active edge region active edge region Larger than normal liver tissue area To reflect the high stiffness characteristics of the tumor necrosis core region, the transitional mechanical behavior of the active edge region, and the low stiffness characteristics of the normal liver tissue region; fibrotic areas It is positively correlated with the degree of fibrosis, reflecting the enhanced anisotropy caused by fibrosis in fibrotic regions; Among them, the normal liver tissue area, the tumor necrosis core area, the active edge area, and the fibrotic area are all regions in the liver; in, Indicates the first Mooney-Rivlin model parameters related to shearing behavior at individual units. Indicates the first Mooney-Rivlin model parameters at individual units that are related to the large deformation behavior of materials. Indicates the first The volumetric deformation penalty parameter at the individual element that is related to the bulk modulus.

[0012] Through the above-mentioned further technical solutions, the present invention limits the material parameters of each region of the liver according to the characteristics of each region, thereby improving the accuracy of describing the different hyperelastic properties of each region of the liver and thus improving the simulation accuracy.

[0013] Furthermore, the calculation of viscoelastic stress based on the tissue probability distribution map includes: The values ​​of each parameter in the three-unit generalized Maxwell model used to describe the viscoelastic properties of the liver are determined based on the tissue probability distribution map. Based on the parameters of the three-element generalized Maxwell model, the viscoelastic stress is calculated using the following formula: ; in, Indicates the current time Next viscoelastic stress at individual units For the first The first individual element Shear modulus of a Maxwell element For the first The first individual element The relaxation time of a Maxwell cell. For the partial strain tensor, For the current time, For integration variables, This is the index of the Maxwell cell.

[0014] Through the above-mentioned further technical solutions, the present invention adopts a three-unit generalized Maxwell model to describe the viscoelastic properties of liver tissue, which can effectively characterize the stress relaxation and creep behavior of soft tissue, thereby improving the simulation accuracy.

[0015] Furthermore, determining the values ​​of each parameter in the three-unit generalized Maxwell model used to describe the viscoelastic properties of the liver based on the tissue probability distribution map includes: Based on the tissue probability distribution map, the liver is divided into regions: normal liver tissue region, tumor necrosis core region, active edge region, and fibrotic region. The shear modulus of the tumor necrosis core region is made smaller than that of the active edge region to reflect that the viscosity effect of the tumor necrosis core region is less significant than that of the active edge region. The shear modulus of the tumor necrosis core region is made smaller than that of the normal liver tissue region to reflect that the viscosity effect of the tumor necrosis core region is less significant than that of the normal liver tissue region. The relaxation time of the tumor necrosis core region should be shorter than that of the active edge region, and the relaxation time of the tumor necrosis core region should be shorter than that of the normal liver tissue region. The shear modulus and relaxation time of the fibrotic region are positively correlated with the degree of fibrosis to reflect the enhanced anisotropy caused by fibrosis in the fibrotic region.

[0016] Through the above-mentioned further technical solutions, the present invention assigns regional values ​​to the shear modulus and relaxation time of different regions of the liver based on the tissue probability distribution map, thereby improving the accuracy of the description of different viscoelastic properties of different regions of the liver and thus improving the simulation accuracy.

[0017] Furthermore, the calculation of the macroscopic total Cauchy stress tensor based on hyperelastic stress and viscoelastic stress is performed using the following formula: ; in, Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor at the location. Indicates macroscopic spatial location hyperelastic stress at the location, Indicates the current time Lower macroscopic spatial position viscoelastic stress at the point, Indicates macroscopic spatial location Injection pressure at the point, For unit tensors, Indicates the first The macroscopic spatial location corresponding to an individual element; The injection pressure is calculated using the following formula: ; in, Based on the injection pressure, The coupling coefficient is... Location of CT images in macroscopic space The first-order gradient vector at that point, Macroscopic spatial location The micro displacement field at that location, This indicates the search for the Euclidean norm.

[0018] Through the above-mentioned further technical solutions, this invention combines hyperelastic stress and viscoelastic stress to calculate the macroscopic total Cauchy stress tensor, and constructs a viscoelastic coupled stress response to improve simulation accuracy.

[0019] Furthermore, the asymptotic homogenization of the macroscopic total Cauchy stress tensor to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor is performed using the following formula: ; in, Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor after asymptotic homogenization. This represents the volume of a microscopic volume element. Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor at the location. This represents a micro-volume element within a micro-representation volume element. Here, the micro-representative volume element is a volume element centered at the macroscopic spatial location corresponding to the macroscopic total Cauchy stress tensor, and the scale of the micro-representative volume element is sufficient to contain the microstructure in the liver.

[0020] Through the above-mentioned further technical solutions, the present invention further performs progressive homogenization on the qualified region, namely the region where the mechanical gradient and material parameters change drastically, corresponding to the key region in liver tissue where tissue types change rapidly, local load concentration is concentrated, and vascular perfusion is significantly affected. That is, micro-representative volume elements are embedded to obtain a more stable macroscopic stress input in the above-mentioned key region when performing finite element solution, thereby improving the simulation accuracy.

[0021] In a second aspect, the present invention provides a liver deformation simulation device, comprising: The image acquisition and segmentation module is configured to: acquire multimodal liver images, construct a fusion feature vector through multimodal image registration and feature fusion, input the fusion feature vector into the trained image segmentation network, and obtain a tissue probability distribution map of the liver. The heterogeneous material parameter calculation module is configured to: concatenate the fused feature vector and the organization probability distribution map and input them into the trained physical constraint neural network model to obtain the heterogeneous material parameter distribution field; wherein, the loss function used by the physical constraint neural network model during training includes volume incompressibility constraint terms and stress-strain monotonicity constraint terms; The macroscopic total Cauchy stress tensor calculation module is configured to: calculate hyperelastic stress based on the parameter distribution field of the heterogeneous material, calculate viscoelastic stress based on the microstructure probability distribution map, calculate the macroscopic total Cauchy stress tensor based on the hyperelastic stress and viscoelastic stress, and if at least one of the gradient magnitudes of the macroscopic total Cauchy stress tensor and each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, then the macroscopic total Cauchy stress tensor is asymptotically homogenized to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor and is output; if neither the macroscopic total Cauchy stress tensor nor the gradient magnitudes of each parameter in the heterogeneous material parameter distribution field exceed their corresponding gradient thresholds, then the macroscopic total Cauchy stress tensor is output. The finite element mesh construction and deformation simulation module is configured to: construct a liver tetrahedral finite element mesh based on the tissue probability distribution map, the non-homogeneous material parameter distribution field, and tensor K, where tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization; obtain the external force vector based on the external forces acting on the liver; perform GPU parallel finite element solution on the liver tetrahedral finite element mesh based on the external force vector; update the liver tetrahedral finite element mesh according to the solution results to obtain the liver deformation tetrahedral finite element mesh, and complete the liver deformation simulation.

[0022] Thirdly, the present invention provides a computer-readable storage medium having a computer program / instructions stored thereon, which, when executed by a processor, implements the steps of the liver deformation simulation method described in any one of the first aspects.

[0023] Compared with the prior art, the beneficial effects achieved by the present invention are: This invention provides a method, device, and storage medium for simulating liver deformation. By introducing volume incompressibility constraints and stress-strain monotonicity constraints, it ensures that all parameters in the heterogeneous material parameter distribution field simultaneously conform to the actual mechanical laws of liver tissue and the imaging characteristics of the liver, thereby describing the heterogeneity of liver tissue and improving simulation accuracy. Based on the heterogeneous material parameter distribution field, it calculates hyperelastic stress to reflect the heterogeneity of liver tumor tissue and describes the instantaneous nonlinear elastic response of liver tissue. Based on the tissue probability distribution map, it calculates viscoelastic stress to establish a voxel-dependent regionalized viscoelastic response and describes the time-dependent stress relaxation behavior of liver tissue. Based on hyperelastic stress and viscoelastic stress measurement... The macroscopic total Cauchy stress tensor was calculated, and the viscoelastic coupled stress response within the liver region was constructed. For regions where at least one of the gradient moduli of each parameter in the macroscopic total Cauchy stress tensor and the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, due to the drastic changes in mechanical gradient and material parameters in these regions, which correspond to key areas in the liver tissue with rapid transitions in tissue type, concentrated local loads, and significant influences on vascular perfusion, a progressive homogenization process was performed to provide a more stable macroscopic stress input for the finite element solution. This provides suitable, continuous, and physically meaningful macroscopic stress input for the finite element solution of each region. Through the above-mentioned macroscopic total Cauchy stress tensor calculation process, the overall simulation accuracy is improved. Attached Figure Description

[0024] Figure 1 This is a flowchart of a liver deformation simulation method corresponding to Embodiment 1 of the present invention; Figure 2 This is a flowchart of a liver deformation simulation method corresponding to Embodiment 2 of the present invention. Detailed Implementation

[0025] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solution of the present invention more clearly, and should not be used to limit the scope of protection of the present invention.

[0026] Example 1 like Figure 1 As shown, this embodiment provides a method for simulating liver deformation, including: After acquiring multimodal liver images, a fused feature vector is constructed through multimodal image registration and feature fusion. The fused feature vector is then input into a trained image segmentation network to obtain a tissue probability distribution map of the liver. The fused feature vector and the organization probability distribution map are concatenated and then input into the trained physical constraint neural network model to obtain the parameter distribution field of the heterogeneous material; Hyperelastic stress is calculated based on the parameter distribution field of heterogeneous materials, and viscoelastic stress is calculated based on the probability distribution map of the microstructure. The macroscopic total Cauchy stress tensor is calculated based on the hyperelastic stress and viscoelastic stress. If at least one of the gradient moduli of the macroscopic total Cauchy stress tensor and each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is asymptotically homogenized to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor and is output. If neither the macroscopic total Cauchy stress tensor nor the gradient moduli of each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is output. Based on the tissue probability distribution map, the parameter distribution field of the heterogeneous material, and the tensor K, a tetrahedral finite element mesh of the liver is constructed. The tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization. The external force vector based on the external force on the liver is obtained. The liver tetrahedral finite element mesh is solved by GPU parallel finite element method based on the external force vector. The liver tetrahedral finite element mesh is updated according to the solution results to obtain the liver deformation tetrahedral finite element mesh, thus completing the liver deformation simulation.

[0027] This invention introduces volumetric incompressibility and stress-strain monotonicity constraints to ensure that all parameters in the heterogeneous material parameter distribution field simultaneously conform to the actual mechanical laws of liver tissue and the imaging characteristics of the liver, thereby describing the heterogeneity of liver tissue and improving simulation accuracy. Based on the heterogeneous material parameter distribution field, hyperelastic stress is calculated to reflect the heterogeneity of liver tumor tissue and describe the instantaneous nonlinear elastic response of liver tissue. Viscoelastic stress is calculated based on the tissue probability distribution map to establish a voxel-dependent regionalized viscoelastic response and describe the time-dependent stress relaxation behavior of liver tissue. Finally, the macroscopic total Cauchy stress tensor is calculated based on the hyperelastic and viscoelastic stresses. The viscoelastic coupled stress response within the liver region was constructed. For regions where at least one of the gradient moduli of each parameter in the macroscopic total Cauchy stress tensor and the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, due to the drastic changes in mechanical gradient and material parameters in these regions, which correspond to key areas in the liver tissue with rapid transition of tissue types, concentrated local loads, and significant influence of vascular perfusion, a progressive homogenization process was performed to provide a more stable macroscopic stress input for finite element solution. This provides suitable, continuous, and physically meaningful macroscopic stress input for finite element solution in each region. Through the above-mentioned macroscopic total Cauchy stress tensor calculation process, the overall simulation accuracy is improved.

[0028] Example 2 like Figure 2 As shown, this embodiment provides a method for simulating liver deformation, including the following steps S1 to S5.

[0029] Step S1, Multimodal Image Fusion and Tissue Subregion Segmentation: After acquiring multimodal liver images, a fused feature vector of all voxels is constructed through multimodal image registration and feature fusion. The fused feature vectors are input into the trained image segmentation network to obtain the tissue probability distribution map of all voxels of the liver. .

[0030] Step S1 can be further divided into steps S1.1 to S1.4.

[0031] Step S1.1: Acquire CT images covering the liver region T1 weighted image T2 weighted image and strain diagram .

[0032] In this embodiment, T1-weighted and T2-weighted images are obtained through MRI technology, i.e., two different weighted images obtained through magnetic resonance imaging. T1-weighted images clearly display tissues such as fat, while T2-weighted images clearly display tissues with high fluid content, such as edema and tumors. Combining the two provides richer tissue information. The strain map is obtained through ultrasound elastography. The CT images and both T1-weighted and T2-weighted images are the original images before stress was applied.

[0033] Step S1.2: Use the B-spline-based elastic registration method to transform all images to the same coordinate system to achieve image registration.

[0034] In this embodiment, using the CT image as a reference, an elastic registration method based on B-splines is adopted to transform images of other modalities to the coordinate system of the CT image. In this process, the optimization objective is to maximize mutual information.

[0035] When transforming the T1-weighted image to the coordinate system of the CT image, the expression for the optimization objective is: ; in, Indicates the optimization objective. This means finding the entity that maximizes mutual information. , Represents a spatial transformation field. This represents the calculation of mutual information, which measures the statistical correlation between two images. This indicates the composition of functions. This indicates that the T1-weighted image is... After spatial transformation field The image obtained by resampling.

[0036] When transforming other images to the coordinate system of the CT image, the optimization objective is based on the formula above.

[0037] Step S1.3: After image registration is completed, all modal images are aligned to a unified anatomical space. Based on this, images numbered as follows are then registered. The voxel construction incorporates a fused feature vector containing grayscale and texture information. , Voxel index, used to represent the voxel index in an image. The numbering of individual voxels is performed using the following formula: ; in, Indicates the first The fused feature vector at the individual element. Indicates the CT image at the 1st Image intensity value at individual pixels, Indicates the T1 weighted image at the th Image intensity value at individual pixels, Indicates the T2-weighted image at the th Image intensity value at individual pixels, The strain diagram is shown in the first... Image intensity value at individual pixels, This indicates the search for the Euclidean norm. Indicates the CT image at the 1st The first-order gradient vector at the individual element. express The second-order gradient vector is used to capture tissue boundaries and internal texture information. Indicates transpose. This indicates finding the first-order gradient vector. This indicates the calculation of the second-order gradient vector.

[0038] The fused feature vector corresponding to all voxels is used This indicates that it serves as the input for step S1.4.

[0039] Step S1.4: Obtain the fused feature vector from step S1.3 Then, it is input into a pre-trained image segmentation network, specifically a 3D U-Net, to perform tissue compression area recognition and segmentation, thereby obtaining a tissue probability distribution map of the liver. .

[0040] 3D U-Net employs an encoder-decoder architecture. The encoder consists of four downsampling layers, each composed of two 3×3×3 convolutional layers and a ReLU activation function, followed by a 2×2×2 max pooling layer. The decoder restores spatial resolution through upsampling and skip connections, and finally outputs the tissue probability distribution map of five tissue types in the liver through a softmax layer. , No. The expression for the tissue probability distribution map at individual elements is: , , , , and These correspond to the background area, normal liver tissue area, tumor necrosis core area, active edge area, and fibrosis area, respectively. This indicates transpose.

[0041] In this embodiment, the expression for the total loss function used by 3D U-Net during training is: ; in, Represents the total loss function. This indicates Dice's loss. Represents cross-entropy loss, This represents the weighting coefficients corresponding to the Dice loss. This represents the weight coefficient corresponding to the cross-entropy loss.

[0042] Step S2, Intelligent Mapping and Optimization of Gray-Scale-Mechanical Parameters: Fusing Feature Vectors of All Voxels Organizational probability distribution map After being spliced ​​together, the data is input into a trained physical constraint neural network model to obtain the heterogeneous material parameter distribution field of all voxels. .

[0043] Obtain the tissue probability distribution map of all voxels. Then, it is fused with the feature vector of all voxels. The data is then concatenated and input into a physical constraint neural network. The heterogeneous material parameter distribution field of all voxels was obtained. .

[0044] Physically constrained neural networks are lightweight fully connected networks, where the input is the first... Tissue probability distribution at individual elements With the Fusion feature vector at individual elements When stitching together images, the output is the first... hyperelastic material parameter vector corresponding to individual elements The hyperelastic material parameter vectors corresponding to all voxels constitute the heterogeneous material parameter distribution field. .

[0045] Physically constrained neural networks calculate the parameter vector of hyperelastic materials. The process is carried out using the following formula: ; in, Indicates the first The hyperelastic material parameter vector at the individual element. Indicates the first The fused feature vector at the individual element. Indicates the first Tissue probability distribution at individual elements. The weights of the physical constraint neural network are represented. This represents the bias term of a physically constrained neural network. Represents a physically constrained neural network. Indicates transpose. Indicates the first Mooney-Rivlin model parameters related to shearing behavior at individual units. Indicates the first Mooney-Rivlin model parameters at individual units that are related to the large deformation behavior of materials. Indicates the first The volumetric deformation penalty parameter at the individual element that is related to the bulk modulus.

[0046] In this embodiment, to ensure that the mapped parameters conform to the true mechanical laws of biological tissues, the physical constraint neural network is trained using a loss function that includes physical constraints, within the standard mean squared error loss. Based on this, a volume incompressibility constraint term is introduced. and stress-strain monotonicity constraint terms Composite loss function The expression is: ; in, This represents the loss function used during the training of a physically constrained neural network. This represents the mean squared error loss. This represents the volume incompressibility constraint term. This represents the stress-strain monotonicity constraint term. This represents the weighting coefficient corresponding to the volume incompressibility constraint term. This represents the weighting coefficient corresponding to the stress-strain monotonicity constraint term.

[0047] Mean square error loss Defined as: ; in, Indicates the first The hyperelastic material parameter vector at the individual element. Indicates the first The true material parameter vector at the individual element. This represents finding the square of the Euclidean norm.

[0048] Volume incompressibility constraint Defined as: ; in, Indicates the first The volumetric deformation penalty parameter at the individual unit that is related to the bulk modulus. This indicates the set critical volume ratio threshold. This indicates taking the maximum value.

[0049] Stress-strain monotonicity constraint term Defined as: ; in, Indicates the first The first individual element Principal stress components in each principal direction Indicates the first The first individual element Principal strain components in each principal direction This indicates taking the maximum value. Indicates the principal direction index of the principal stress component or principal strain component. These correspond to three mutually perpendicular main directions.

[0050] when When, it represents the first principal direction, i.e., the maximum principal stress or the maximum principal strain; when When, it represents the second principal direction, that is, the intermediate principal stress or intermediate principal strain; when When , it represents the third principal direction, that is, the minimum principal stress or the minimum principal strain.

[0051] Using the optimized loss function described above, the physical constraint neural network can output a non-homogeneous material parameter distribution field that conforms to both image features and biomechanical laws. .

[0052] Step S3: Calculate hyperelastic stress based on the microstructure probability distribution map and the heterogeneous material parameter distribution field; calculate viscoelastic stress based on the microstructure probability distribution map; calculate the macroscopic total Cauchy stress tensor based on the hyperelastic stress and viscoelastic stress; if at least one of the gradient magnitudes of the macroscopic total Cauchy stress tensor and the gradient magnitudes of each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, then perform asymptotic homogenization on the macroscopic total Cauchy stress tensor to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor; otherwise, output the macroscopic total Cauchy stress tensor.

[0053] The multiscale viscohyperelastic constitutive model is a model that can realistically reflect the mechanical properties of liver tumors. In the multiscale viscohyperelastic constitutive model, the Mooney-Rivlin model is used to describe the hyperelastic properties of the liver, and the three-unit generalized Maxwell model is used to describe the viscoelastic properties of the liver.

[0054] Based on the heterogeneous material parameter distribution field output in step S2 , Composed of multiple Composition, in which, , By transposing the model, a multi-scale viscoelastic constitutive model that can realistically reflect the mechanical properties of liver tumors is constructed. The distribution field of heterogeneous material parameters is input into this model to obtain the macroscopic total Cauchy stress tensor of key and non-key regions of the liver model. Indicates the current time. In the parameter distribution field of a heterogeneous material. , and These are respectively used as material parameters in the Mooney-Rivlin model, and vary with the first... Variations in individual element numbers reflect the heterogeneity of liver tumor tissue.

[0055] For each voxel number Step S3 can be further divided into steps S3.1 to S3.5.

[0056] Step S3.1: Calculate hyperelastic stress based on the parameter distribution field of heterogeneous materials .

[0057] Based on the tissue probability distribution map output in step S1 It can distinguish different areas of the liver, including corresponding Normal liver tissue area, corresponding The core area of ​​tumor necrosis, corresponding active edge region and corresponding The fibrous regions are described. For each of these regions, the Mooney-Rivlin model is used to describe its mechanical behavior.

[0058] The strain energy density function of the Mooney-Rivlin model Defined as: ; in, Indicates the first The strain energy density function at the individual element. Let be the determinant of the deformation gradient tensor. , The deformation gradient tensor describes the local deformation mapping of a material point from its initial configuration to its current configuration. It is obtained by differentiating the macroscopic displacement field during the finite element solution process. For the right Cauchy-Green tensor, , Indicates transpose; Indicates the first isochoric invariant. , This represents the second isochoric invariant. ; Indicates the first Mooney-Rivlin model parameters related to shearing behavior at individual units. Indicates the first Mooney-Rivlin model parameters at individual units that are related to the large deformation behavior of materials. Indicates the first The volumetric deformation penalty parameter at the individual element that is related to the bulk modulus.

[0059] because , , Satellite numbering The parameter values ​​vary in different regions of the heterogeneous material parameter distribution field obtained in step S2. exist The dominant tumor necrosis core region, i.e., if the first Individuals are located in the core region of tumor necrosis. A larger value reflects the high stiffness characteristics of the tumor necrosis core region; exist The dominant active edge region, i.e., if the first Individuals are located in the active edge region. A suitable value reflects the transitional mechanical behavior of the active edge region; exist The dominant normal liver tissue area, i.e., if the first Individuals are located in areas of normal liver tissue. Smaller values ​​reflect the low stiffness characteristics of normal liver tissue areas; exist The dominant fibrotic region, i.e., if the first Individuals are located in fibrotic regions. The value is dynamically adjusted appropriately according to the degree of fibrosis, reflecting the enhanced anisotropy caused by fibrosis in the fibrotic region, that is, in the fibrotic region The value is positively correlated with the degree of fibrosis.

[0060] From the strain energy density function Differentiating the deformation gradient tensor yields the hyperelastic stress. : ; in, Indicates the first hyperelastic stress at individual elements Indicates the first The strain energy density function at the individual element. Let be the determinant of the deformation gradient tensor. For the deformation gradient tensor, Indicates transpose. Represents the right Cauchy-Green tensor. .

[0061] Step S3.2: Calculate viscoelastic stress based on the tissue probability distribution map .

[0062] The viscoelastic properties of liver tissue were described using a three-element generalized Maxwell model. This model consists of three Maxwell elements connected in parallel, each containing a spring and a damper connected in series, effectively characterizing the stress relaxation and creep behavior of soft tissue.

[0063] For different regions of the liver, viscoelastic parameters and Also with the Individual changes, For the first The first individual element Shear modulus of a Maxwell element For the first The first individual element The relaxation time of each Maxwell cell, and based on the tissue probability distribution plot. Perform regionalized assignment: exist The dominant tumor necrosis core region exhibits a weaker viscosity effect. Smaller values ​​reflect a lower degree of significance in the viscosity effect within the tumor necrosis core region. The value is relatively short; exist Dominant active edge regions and In the predominantly normal liver tissue areas, a significant viscosity effect was observed. Larger values ​​are used to reflect a higher degree of significance in the viscosity effect of the tumor necrosis core region. The value is relatively long; exist In the predominantly fibrous region, the shear modulus and relaxation time are dynamically adjusted appropriately according to the degree of fibrosis, reflecting the enhanced anisotropy caused by fibrosis in the fibrous region. That is, the values ​​of shear modulus and relaxation time in the fibrous region are positively correlated with the degree of fibrosis.

[0064] viscoelastic stress The time domain is expressed as: ; in, Indicates the current time Next viscoelastic stress at individual units For the first The first individual element Shear modulus of a Maxwell element For the first The first individual element The relaxation time of a Maxwell cell. For the partial strain tensor, For the current time, For integration variables, This is the index of the Maxwell cell. .

[0065] Using the above method, step S3.2, based on the tissue region division results obtained in step S1, establishes a system for classifying tissue regions according to the order of tissue division. The regionalized viscoelastic response of individual element variations provides input for the further coupling of the hyperelastic model, viscoelastic model, and infusion pressure term in step S3.3.

[0066] Step S3.3: Calculate the macroscopic total Cauchy stress tensor based on hyperelastic stress and viscoelastic stress.

[0067] Using only voxel numbering Since it is no longer possible to clearly represent a specific location in continuous space, macroscopic spatial location is introduced. As the first The position coordinates of the individual element.

[0068] The hyperelastic model constructed in step S3.1 is coupled with the viscoelastic model constructed in step S3.2, while considering the influence of microvascular perfusion pressure on tissue mechanical behavior, and the macroscopic spatial position is... By coupling the hyperelastic and viscoelastic stresses at a given location, the macroscopic spatial position of non-critical regions can be obtained. The macroscopic total Cauchy stress tensor at the location.

[0069] Therefore, the total macroscopic Cauchy stress tensor in this step is calculated using the following formula: ; in, Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor at the location. Indicates macroscopic spatial location Hyperelastic stress at a point describes the instantaneous nonlinear elastic response of liver tissue. Indicates the current time Lower macroscopic spatial position The viscoelastic stress at the site describes the time-related stress relaxation behavior of liver tissue. Indicates macroscopic spatial location Injection pressure at the point, It is a unit tensor.

[0070] Defined as the local CT grayscale gradient and micro displacement field The relevant quantities are calculated using the following formula: ; in, Based on the injection pressure, The coupling coefficient is... Location of CT images in macroscopic space The first-order gradient vector at that point, Macroscopic spatial location The micro displacement field at that location, This indicates the search for the Euclidean norm.

[0071] Using the above method, step S3.3, based on the regional modeling results of steps S3.1 and S3.2, constructs the viscoelastic coupled stress response of non-critical regions within the liver region.

[0072] S3.4: Voxels within the liver region Corresponding macroscopic spatial location The liver is divided into key and non-key regions for modeling.

[0073] Based on the distribution field of heterogeneous material parameters corresponding to the macroscopic spatial location and the macroscopic total Cauchy stress tensor associated with that location, it is determined whether the location belongs to a critical region or a non-critical region. If the first... Macroscopic spatial location corresponding to individual elements If it belongs to a non-critical region, then the macroscopic total Cauchy stress tensor obtained in step S3.3 will be used. As the output of step S3; if the... Macroscopic spatial location corresponding to individual elements If it belongs to a key area, then in terms of macro-spatial location Microscopic representative volume elements are embedded at the key region, and then progressive homogenization is performed on them in step S3.5 to obtain the macroscopic total Cauchy stress tensor of the key region. And use it as the output of step S3.

[0074] However, to facilitate the description of the finite element nonlinear solution process in step S4, the responses of critical and non-critical regions are expressed using the macroscopic total Cauchy stress tensor. To indicate that if the first Macroscopic spatial location corresponding to individual elements If it belongs to a critical area, then for If the first Macroscopic spatial location corresponding to individual elements If it belongs to a non-critical area, then for Based on the judgment conditions, the total macroscopic Cauchy stress tensor of the corresponding region is automatically substituted into step S4 to solve for the element internal force vector and the element tangent stiffness matrix.

[0075] The macroscopic spatial locations corresponding to each voxel within the liver region are divided to obtain key and non-key regions for liver modeling, including: To clarify the criteria for determining drastic changes in the mechanical gradient, the output of step S2 is defined as follows: Individual elements correspond to macroscopic spatial locations The material parameters at that location are , and ,for , and The gradient thresholds were set as follows: , and The total macroscopic Cauchy stress tensor obtained in step S3.4 is... The gradient threshold is set to . , and Based on statistical results from training samples and experimental calibration results, this is used to determine whether the gradient of material parameters or the gradient of the macroscopic total Cauchy stress tensor exceeds a predetermined range. Indicates macroscopic spatial location The Mooney-Rivlin model parameters related to shear behavior at the location, Indicates macroscopic spatial location The Mooney-Rivlin model parameters related to the large deformation behavior of materials at a given location. Indicates macroscopic spatial location The volumetric deformation penalty parameter related to the bulk modulus at that location.

[0076] The following formula is used to determine the first... Macroscopic spatial location corresponding to individual elements Whether a region belongs to a critical area is determined based on the distribution field of heterogeneous material parameters corresponding to that macroscopic spatial location and the gradient threshold set for that macroscopic spatial location. Specifically, a determination parameter is first calculated using the following formula: ; in, Indicates macroscopic spatial location The corresponding decision parameters, This indicates the search for the Euclidean norm. This indicates finding the first-order gradient vector. Indicates macroscopic spatial location The Mooney-Rivlin model parameters related to shear behavior at the location, Indicates macroscopic spatial location The Mooney-Rivlin model parameters related to the large deformation behavior of materials at a given location. Indicates macroscopic spatial location The volumetric deformation penalty parameter related to the bulk modulus at that location. Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor at the location. This indicates taking the maximum value. Represented as Set gradient threshold, Represented as Set gradient threshold, Represented as Set gradient threshold, Represented as The set gradient threshold.

[0077] like That is, if the material parameters , , and the macroscopic total Cauchy stress tensor If at least one of the gradient magnitudes exceeds its corresponding gradient threshold, then the macroscopic spatial location is determined. This is a critical area; proceed to step S3.5. like That is, if the material parameters , , and the macroscopic total Cauchy stress tensor When the gradient magnitudes of all gradients do not exceed their respective gradient thresholds, the macroscopic spatial location is determined. If it belongs to a non-critical area, the result of step S3.4 will be used as the output of step S3.

[0078] Key areas for liver modeling include, but are not limited to: the boundary between the tumor necrosis core area and the active edge area, the transition area between the active edge area and the normal liver tissue area, the boundary between the fibrotic area and the normal liver tissue area, the area adjacent to the tumor blood vessels, the localized load concentration area near the puncture point or compression point, and the area of ​​abrupt curvature change on the liver surface or the protruding edge area of ​​the tumor.

[0079] S3.5: The critical region is progressively homogenized and, together with the response of the non-critical region, forms a globally unified macroscopic total Cauchy stress tensor.

[0080] In step S3.4, for non-critical regions, the hyperelastic model and viscoelastic model have already been coupled. Since the changes in material parameters and stress are relatively gradual, the asymptotic homogenization process based on microscopic representative volume elements is no longer performed; instead, the macroscopic total Cauchy stress tensor obtained in step S3.4 is directly used. This serves as the local macroscopic response at this location. Because liver tissue exhibits significantly different microstructural characteristics in different regions, especially in key areas with rapid tissue type transitions, concentrated local loads, and significant influences from vascular perfusion, simply using the microscopic stress expression from step S3.4 is insufficient to directly provide a stable macroscopic equivalent stress input for organ-scale finite element solutions. Therefore, the total macroscopic Cauchy stress tensor is obtained in step S3.4. Based on this, for each macroscopic spatial location within the key area We construct the corresponding microscopic representative volume element and obtain the macroscopic total Cauchy stress tensor at this location using existing asymptotic homogenization methods. A gradual homogenization process is performed to obtain the macroscopic total Cauchy stress tensor at that location. .

[0081] If the first Macroscopic spatial location corresponding to individual elements For key regions in liver modeling, a [structure / mechanism] is embedded at this macroscopic spatial location. The microscopic representative volume element at the center is much smaller than the size of the macroscopic unit, but large enough to contain microstructures such as microvessels and extracellular matrix.

[0082] By asymptotically homogenizing the microscopic representative volume element, the macroscopic total Cauchy stress tensor obtained in step S3.4 is... Equivalent to the macroscopic scale, we obtain the macroscopic total Cauchy stress tensor. It is represented by the total Cauchy stress tensor inside the microscopic volume element. The volume average is obtained as follows: ; in, Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor after asymptotic homogenization. This represents the volume of a microscopic volume element. Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor at the location. This represents a micro-volume element within a micro-representation volume element.

[0083] Since step S4 involves a finite element nonlinear solution for the entire liver, the constitutive model responses obtained from the critical and non-critical regions are combined to form a globally unified macroscopic total Cauchy stress tensor. As the sole stress input for the overall finite element nonlinear solution in step S4, the total Cauchy stress tensor of the corresponding region is automatically selected based on the judgment conditions. ; in, This represents the set of macroscopic locations corresponding to key regions. This represents the set of macroscopic locations corresponding to non-critical areas. Indicates the first in the whole liver The macroscopic spatial location corresponding to an individual element.

[0084] Using the above method, step S3.5 obtains the macroscopic total Cauchy stress tensor in step S3.4. Based on this, microscopic representative volume elements are introduced to locally enhance the characterization of key regions, and the obtained microscopic equivalent results are fed back to the macroscopic scale, thereby obtaining the macroscopic total Cauchy stress tensor that can be directly used for subsequent finite element solutions of key regions. .

[0085] Thus, step S3 completes the entire process from the results of tissue partitioning and the parameter mapping results of heterogeneous materials to the microscopic viscoelastic coupling modeling and the macroscopic homogenization correction of key regions, providing continuous and physically meaningful macroscopic stress response inputs for the finite element nonlinear solution of key and non-key regions in step S4.

[0086] Step S4: Construct a tetrahedral finite element mesh for the liver based on the tissue probability distribution map, the distribution field of heterogeneous material parameters, and tensor K. Tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization. Obtain the external force vector based on the external force acting on the liver. Perform GPU parallel finite element solution on the tetrahedral finite element mesh for the liver based on the external force vector. Update the tetrahedral finite element mesh for the liver based on the solution results to obtain the tetrahedral finite element mesh for liver deformation, thus completing the liver deformation simulation.

[0087] Based on the tissue probability distribution map output in step S1, the heterogeneous material parameter distribution field output in step S2, and the globally unified macroscopic total Cauchy stress tensor output in step S3, a tetrahedral finite element mesh of the entire liver is established. Within each current load step or simulation time step, the external force components generated by the force feedback device are processed to obtain the external force vector. A GPU-parallelized finite element solution method is used to iteratively solve the entire liver, obtaining the macroscopic displacement field and the nodal coordinates after deformation. All of the above processes are implemented using existing technologies in the field. Specifically, the surface mesh extraction during the construction of the liver tetrahedral finite element mesh is achieved using the moving cube algorithm; the liver volume tetrahedral partitioning is achieved using Delaunay triangulation; the nonlinear deformation solution uses the Newton-Raphson method finite element iterative framework; and the parallel solution of linear subproblems uses sparse matrix assembly and the preconditional conjugate gradient method under GPU.

[0088] Step S4 can be further divided into steps S4.1 to S4.3.

[0089] Step S4.1: Based on the organizational probability distribution map Generate a tetrahedral finite element mesh for the liver and map the parameters of the heterogeneous material.

[0090] Based on the tissue probability distribution map output in step S1, the moving cubes algorithm is used to extract the surface mesh of liver tissue from the segmentation results. During extraction, the sum of the probability values ​​of normal liver tissue, tumor necrosis core, active edge, and fibrotic region is greater than a background threshold as an extraction condition to ensure that the generated surface mesh completely encompasses all liver tissue regions. After obtaining the surface mesh, Delaunay triangulation is used to tetrahedronize the liver volume region enclosed by the surface mesh, generating a mesh containing... Each node and Unit The liver tetrahedral finite element mesh, each element It consists of four nodes, which together determine the geometry and spatial extent of a tetrahedral unit.

[0091] After obtaining the tetrahedral finite element mesh of the liver, the heterogeneous material parameter distribution field output in step S2 is... Mapped to each unit For each unit According to the spatial position of the voxel , and Assign material parameters to this element. Thus, each element... All of these methods obtain material parameters consistent with the local tissue type and local imaging characteristics, thereby enabling the heterogeneous material parameter distribution field obtained in step S2 to truly enter the liver tetrahedral finite element mesh.

[0092] To facilitate subsequent GPU parallel computing, all units were further classified according to their material properties. Grouping is performed on units with the same or similar material properties. Material blocks are stored contiguously in memory, and then a CUDA kernel is launched for each material block, with all units within the block... The internal force vectors and tangent stiffness matrices of each element are calculated in parallel and then accumulated into the global matrix and vectors through atomic operations to reduce branch divergence and improve parallel computing efficiency.

[0093] Step S4.2: Assemble the external force components obtained from the force feedback device to form a global external force vector, perform GPU parallel finite element solution, and obtain the macroscopic displacement field and the node coordinates after deformation.

[0094] Since step S3 has unified the constitutive responses of the critical and non-critical regions into a single global macroscopic total Cauchy stress tensor, we no longer need to establish two separate finite element models for the critical and non-critical regions. Instead, we assemble and solve them uniformly on the same global tetrahedral mesh.

[0095] At each simulation time step Internally, the input force signal is converted into the corresponding external force components at the nodes through a force feedback device. Then, all external force contributions are assembled according to the nodal degrees of freedom to form the global external force vector at the current time step. Subsequently, the Newton-Raphson method is used to iteratively solve the global nonlinear finite element equilibrium equation. Thus, the mapping of the heterogeneous material parameter field to the liver tetrahedral finite element mesh and the GPU parallel finite element solution are completed, providing high-precision displacement field and post-deformation geometric data for subsequent real-time deformation simulation.

[0096] Step S4.3: In each simulation time step, read the node coordinates after deformation and continuously update the node positions of the liver tetrahedral finite element mesh accordingly. Use the updated node positions as the vertex coordinates of the liver tetrahedral finite element mesh to generate the liver deformation tetrahedral finite element mesh. At this point, the liver deformation simulation can be completed.

[0097] After obtaining the finite element mesh of the liver deformation tetrahedron, it can be sent to the graphics rendering pipeline for display, realizing the continuous dynamic deformation display of liver tissue under the current external force.

[0098] Thus, this invention completes the entire processing flow from inputting the original multimodal medical images to outputting the deformed tetrahedral finite element mesh of the liver, realizing high-precision modeling and real-time deformation simulation of the heterogeneous mechanical properties of liver tumors.

[0099] Example 3 This embodiment provides a liver deformation simulation device, including: The image acquisition and segmentation module is configured to: acquire multimodal liver images, construct a fusion feature vector through multimodal image registration and feature fusion, input the fusion feature vector into the trained image segmentation network, and obtain a tissue probability distribution map of the liver. The heterogeneous material parameter calculation module is configured to: concatenate the fused feature vector and the organization probability distribution map and input them into the trained physical constraint neural network model to obtain the heterogeneous material parameter distribution field; wherein, the loss function used by the physical constraint neural network model during training includes volume incompressibility constraint terms and stress-strain monotonicity constraint terms; The macroscopic total Cauchy stress tensor calculation module is configured to: calculate hyperelastic stress based on the parameter distribution field of the heterogeneous material, calculate viscoelastic stress based on the microstructure probability distribution map, calculate the macroscopic total Cauchy stress tensor based on the hyperelastic stress and viscoelastic stress, and if at least one of the gradient magnitudes of the macroscopic total Cauchy stress tensor and each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, then the macroscopic total Cauchy stress tensor is asymptotically homogenized to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor and is output; if neither the macroscopic total Cauchy stress tensor nor the gradient magnitudes of each parameter in the heterogeneous material parameter distribution field exceed their corresponding gradient thresholds, then the macroscopic total Cauchy stress tensor is output. The finite element mesh construction and deformation simulation module is configured to: construct a liver tetrahedral finite element mesh based on the tissue probability distribution map, the non-homogeneous material parameter distribution field, and tensor K, where tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization; obtain the external force vector based on the external forces acting on the liver; perform GPU parallel finite element solution on the liver tetrahedral finite element mesh based on the external force vector; update the liver tetrahedral finite element mesh according to the solution results to obtain the liver deformation tetrahedral finite element mesh, and complete the liver deformation simulation.

[0100] Example 4 This embodiment provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the liver deformation simulation method provided in Embodiment 1: After acquiring multimodal liver images, a fused feature vector is constructed through multimodal image registration and feature fusion. The fused feature vector is then input into a trained image segmentation network to obtain a tissue probability distribution map of the liver. The fused feature vector and the organization probability distribution map are concatenated and then input into the trained physical constraint neural network model to obtain the parameter distribution field of the heterogeneous material; the loss function used by the physical constraint neural network model during training includes volume incompressibility constraint terms and stress-strain monotonicity constraint terms; Hyperelastic stress is calculated based on the parameter distribution field of heterogeneous materials, and viscoelastic stress is calculated based on the probability distribution map of the microstructure. The macroscopic total Cauchy stress tensor is calculated based on the hyperelastic stress and viscoelastic stress. If at least one of the gradient moduli of the macroscopic total Cauchy stress tensor and each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is asymptotically homogenized to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor and is output. If neither the macroscopic total Cauchy stress tensor nor the gradient moduli of each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is output. Based on the tissue probability distribution map, the parameter distribution field of the heterogeneous material, and the tensor K, a tetrahedral finite element mesh of the liver is constructed. The tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization. The external force vector based on the external force on the liver is obtained. The liver tetrahedral finite element mesh is solved by GPU parallel finite element method based on the external force vector. The liver tetrahedral finite element mesh is updated according to the solution results to obtain the liver deformation tetrahedral finite element mesh, thus completing the liver deformation simulation.

[0101] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0102] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0103] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0104] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0105] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for simulating liver deformation, characterized in that, include: After acquiring multimodal liver images, a fused feature vector is constructed through multimodal image registration and feature fusion. The fused feature vector is then input into a trained image segmentation network to obtain a tissue probability distribution map of the liver. The fused feature vector and the organization probability distribution map are concatenated and then input into the trained physical constraint neural network model to obtain the parameter distribution field of the heterogeneous material; the loss function used by the physical constraint neural network model during training includes volume incompressibility constraint terms and stress-strain monotonicity constraint terms; Hyperelastic stress is calculated based on the parameter distribution field of heterogeneous materials, and viscoelastic stress is calculated based on the probability distribution map of the microstructure. The macroscopic total Cauchy stress tensor is calculated based on the hyperelastic stress and viscoelastic stress. If at least one of the gradient moduli of the macroscopic total Cauchy stress tensor and each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is asymptotically homogenized to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor and is output. If neither the macroscopic total Cauchy stress tensor nor the gradient moduli of each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, the macroscopic total Cauchy stress tensor is output. Based on the tissue probability distribution map, the parameter distribution field of the heterogeneous material, and the tensor K, a tetrahedral finite element mesh of the liver is constructed. The tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization. The external force vector based on the external force on the liver is obtained. The liver tetrahedral finite element mesh is solved by GPU parallel finite element method based on the external force vector. The liver tetrahedral finite element mesh is updated according to the solution results to obtain the liver deformation tetrahedral finite element mesh, thus completing the liver deformation simulation.

2. The liver deformation simulation method according to claim 1, characterized in that, The expression for the loss function used during the training of the physical constraint neural network model is as follows: ； in, This represents the loss function used during the training of a physically constrained neural network. This represents the mean squared error loss. This represents the volume incompressibility constraint term. This represents the stress-strain monotonicity constraint term. This represents the weighting coefficient corresponding to the volume incompressibility constraint term. This represents the weighting coefficient corresponding to the stress-strain monotonicity constraint term; The expression for the volumetric incompressibility constraint term is: ； in, Indicates the first The volumetric deformation penalty parameter at the individual unit that is related to the bulk modulus. This indicates the set critical volume ratio threshold. This indicates taking the maximum value; The expression for the stress-strain monotonicity constraint term is: ； in, Indicates the first The first individual element Principal stress components in each principal direction Indicates the first The first individual element corresponding to the Principal strain components in each principal direction Indicates the principal direction index of the principal stress component or principal strain component.

3. The liver deformation simulation method according to claim 1, characterized in that, The calculation of hyperelastic stress based on the parameter distribution field of heterogeneous materials is performed using the following formula: ； ； in, Indicates the first hyperelastic stress at individual elements Indicates the first The strain energy density function at the individual element. Indicates the first isochoric invariant. This represents the second isochoric invariant. Let be the determinant of the deformation gradient tensor. Indicates the first Mooney-Rivlin model parameters related to shearing behavior at individual units. Indicates the first Mooney-Rivlin model parameters at individual units that are related to the large deformation behavior of materials. Indicates the first The volumetric deformation penalty parameter at the individual unit that is related to the bulk modulus. For the deformation gradient tensor, Indicates transpose. This represents the right Cauchy-Green tensor.

4. The liver deformation simulation method according to claim 1, characterized in that, In a non-homogeneous material parameter distribution field, the parameters , and The value of satisfies the following condition: Tumor necrosis core area Larger than the active edge region active edge region Larger than normal liver tissue area To reflect the high stiffness characteristics of the tumor necrosis core region, the transitional mechanical behavior of the active edge region, and the low stiffness characteristics of the normal liver tissue region; fibrotic areas It is positively correlated with the degree of fibrosis, reflecting the enhanced anisotropy caused by fibrosis in fibrotic regions; Among them, the normal liver tissue area, the tumor necrosis core area, the active edge area, and the fibrotic area are all regions in the liver; in, Indicates the first Mooney-Rivlin model parameters related to shearing behavior at individual units. Indicates the first Mooney-Rivlin model parameters at individual units that are related to the large deformation behavior of materials. Indicates the first The volumetric deformation penalty parameter at the individual element that is related to the bulk modulus.

5. The liver deformation simulation method according to claim 1, characterized in that, The calculation of viscoelastic stress based on the tissue probability distribution map includes: The values ​​of each parameter in the three-unit generalized Maxwell model used to describe the viscoelastic properties of the liver are determined based on the tissue probability distribution map. Based on the parameters of the three-element generalized Maxwell model, the viscoelastic stress is calculated using the following formula: ； in, Indicates the current time Next viscoelastic stress at individual units For the first The first individual element Shear modulus of a Maxwell element For the first The first individual element The relaxation time of a Maxwell cell. For the partial strain tensor, For the current time, For integration variables, This is the index of the Maxwell cell.

6. The liver deformation simulation method according to claim 5, characterized in that, The determination of the values ​​of each parameter in the three-unit generalized Maxwell model used to describe the viscoelastic properties of the liver based on the tissue probability distribution map includes: Based on the tissue probability distribution map, the liver is divided into regions: normal liver tissue region, tumor necrosis core region, active edge region, and fibrotic region. The shear modulus of the tumor necrosis core region is made smaller than that of the active edge region to reflect that the viscosity effect of the tumor necrosis core region is less significant than that of the active edge region. The shear modulus of the tumor necrosis core region is made smaller than that of the normal liver tissue region to reflect that the viscosity effect of the tumor necrosis core region is less significant than that of the normal liver tissue region. The relaxation time of the tumor necrosis core region should be shorter than that of the active edge region, and the relaxation time of the tumor necrosis core region should be shorter than that of the normal liver tissue region. The shear modulus and relaxation time of the fibrotic region are positively correlated with the degree of fibrosis to reflect the enhanced anisotropy caused by fibrosis in the fibrotic region.

7. The liver deformation simulation method according to claim 1, characterized in that, The macroscopic total Cauchy stress tensor is calculated based on hyperelastic and viscoelastic stress using the following formula: ； in, Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor at the location. Indicates macroscopic spatial location hyperelastic stress at the location, Indicates the current time Lower macroscopic spatial position viscoelastic stress at the point, Indicates macroscopic spatial location Injection pressure at the point, For unit tensors, Indicates the first The macroscopic spatial location corresponding to an individual element; The injection pressure is calculated using the following formula: ； in, Based on the injection pressure, The coupling coefficient is... Location of CT images in macroscopic space The first-order gradient vector at that point, Macroscopic spatial location The micro displacement field at that location, This indicates the search for the Euclidean norm.

8. The liver deformation simulation method according to claim 1, characterized in that, The asymptotic homogenization of the macroscopic total Cauchy stress tensor to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor is performed using the following formula: ； in, Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor after asymptotic homogenization. This represents the volume of a microscopic volume element. Indicates the current time Lower macroscopic spatial position The macroscopic total Cauchy stress tensor at the location. This represents a micro-volume element within a micro-representation volume element. Here, the micro-representative volume element is a volume element centered at the macroscopic spatial location corresponding to the macroscopic total Cauchy stress tensor, and the scale of the micro-representative volume element is sufficient to contain the microstructure in the liver.

9. A liver deformation simulation device, characterized in that, include: The image acquisition and segmentation module is configured to: acquire multimodal liver images, construct a fusion feature vector through multimodal image registration and feature fusion, input the fusion feature vector into the trained image segmentation network, and obtain a tissue probability distribution map of the liver. The heterogeneous material parameter calculation module is configured to: concatenate the fused feature vector and the organization probability distribution map and input them into the trained physical constraint neural network model to obtain the heterogeneous material parameter distribution field; wherein, the loss function used by the physical constraint neural network model during training includes volume incompressibility constraint terms and stress-strain monotonicity constraint terms; The macroscopic total Cauchy stress tensor calculation module is configured to: calculate hyperelastic stress based on the parameter distribution field of the heterogeneous material, calculate viscoelastic stress based on the microstructure probability distribution map, calculate the macroscopic total Cauchy stress tensor based on the hyperelastic stress and viscoelastic stress, and if at least one of the gradient magnitudes of the macroscopic total Cauchy stress tensor and each parameter in the heterogeneous material parameter distribution field exceeds its corresponding gradient threshold, then the macroscopic total Cauchy stress tensor is asymptotically homogenized to obtain the asymptotically homogenized macroscopic total Cauchy stress tensor and is output; if neither the macroscopic total Cauchy stress tensor nor the gradient magnitudes of each parameter in the heterogeneous material parameter distribution field exceed their corresponding gradient thresholds, then the macroscopic total Cauchy stress tensor is output. The finite element mesh construction and deformation simulation module is configured to: construct a liver tetrahedral finite element mesh based on the tissue probability distribution map, the non-homogeneous material parameter distribution field, and tensor K, where tensor K is the macroscopic total Cauchy stress tensor or the macroscopic total Cauchy stress tensor after asymptotic homogenization; obtain the external force vector based on the external forces acting on the liver; perform GPU parallel finite element solution on the liver tetrahedral finite element mesh based on the external force vector; update the liver tetrahedral finite element mesh according to the solution results to obtain the liver deformation tetrahedral finite element mesh, and complete the liver deformation simulation.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the liver deformation simulation method according to any one of claims 1 to 8.

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