A soft tissue deformation simulation method, device, storage medium and equipment

Abstract

This invention discloses a method, apparatus, storage medium, and device for simulating soft tissue deformation, belonging to the field of soft tissue deformation simulation technology. The method includes: firstly, performing positional correction on the surface vertices to be corrected in the initial 3D model based on geometric information to obtain a corrected 3D model; when the corrected 3D model undergoes deformation, calculating the Jacobian determinant of the volume element, and accordingly calculating the additional potential energy term and regularization force, mapping the regularization force to the equivalent internal force acting on each vertex of the volume element; finally, updating the corrected 3D model based on the equivalent internal force to obtain the final 3D model after deformation. This invention improves the propagation of boundary conditions and displacement fields by introducing positional correction based on geometric information, and introduces a volume constraint mechanism through the design of the additional potential energy term and regularization force to suppress the stability of the volume element deformation process, thereby achieving the synergy between geometric representation and numerical stability in the soft tissue deformation simulation process.

Description

Technical Field

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

[0002] In interactive virtual surgery and preoperative rehearsals, high-fidelity deformation simulation of soft tissues is crucial for enhancing surgical immersion and operational credibility. This places stringent demands on the real-time performance, geometric fidelity, and numerical stability of algorithms. However, accurately characterizing lesion features with significant local heterogeneity in soft tissues under limited computational resources, while maintaining numerical robustness under large deformation conditions, remains a pressing issue in the field of soft tissue simulation. This problem is increasingly prominent in delicate surgical procedures such as hepatocellular carcinoma: while the liver presents a smooth morphology macroscopically, lesion areas often exhibit highly irregular geometric details and complex curvature changes due to tumor nodular proliferation or tissue necrosis and collapse.

[0003] Existing methods typically enhance geometric representation through volume mesh refinement or surface resolution enhancement. Regarding volume mesh refinement, while global refinement improves accuracy, the exponential increase in computational scale severely restricts interactive real-time performance. Local adaptive refinement, while reducing overhead, easily introduces non-uniform element size distributions, leading to a deterioration of the stiffness matrix condition number and weakening the stability of numerical solutions. Surface subdivision methods, although able to improve surface accuracy while maintaining volume mesh topological consistency, alter the spatial distribution characteristics of the displacement field by adjusting the boundary discretization criteria. Under large deformation or extreme deformation conditions, this non-uniform displacement field distribution caused by surface-volume coupling may lead to local deformation concentration, exacerbating volume element distortion, causing the Jacobian determinant to degenerate, and thus severely weakening the stability of numerical solutions. Summary of the Invention

[0004] The purpose of this invention is to provide a method, apparatus, storage medium, and device for simulating soft tissue deformation, thereby solving the problem of numerical solution stability in existing technologies for simulating soft tissue deformation.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] In a first aspect, the present invention provides a method for simulating soft tissue deformation, comprising:

[0007] Obtain an initial 3D model of the soft tissue;

[0008] The composite feature intensity of each surface vertex is calculated based on the geometric information of each surface vertex in the initial 3D model. An adaptive threshold is determined based on the composite feature intensity of each surface vertex and the statistical quantile method. Feature surface vertices are selected from all surface vertices of the initial 3D model based on the adaptive threshold. The surface of the initial 3D model is subdivided to obtain a subdivided 3D model. The parts to be corrected are selected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and their positions are corrected to obtain a corrected 3D model.

[0009] In response to the deformation generated by the modified 3D model, the following calculations are performed on each volume element in the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex in the volume element.

[0010] All equivalent internal forces are assembled into a global force vector. Explicit dynamic equations are constructed and solved based on the global force vector to obtain the displacement of each vertex. The modified 3D model is then updated based on the displacement of each vertex to obtain the final 3D model after deformation.

[0011] Furthermore, the calculation of the composite feature intensity of each surface vertex based on the geometric information of each surface vertex in the initial three-dimensional model includes:

[0012] Based on the geometric information of each surface vertex in the initial 3D model, calculate and normalize the geometric eigenvalues ​​of each surface vertex. The geometric eigenvalues ​​include the maximum normal angle, the average curvature magnitude, and the centroid offset distance. Perform the following operation on each surface vertex to obtain the composite feature intensity of each surface vertex: calculate the weighted sum of all normalized geometric eigenvalues ​​of the surface vertex as the composite feature intensity of that surface vertex.

[0013] Based on the above-mentioned further technical solutions, the introduced maximum normal angle can characterize the difference in normal direction between adjacent vertices, exhibiting high sensitivity to local geometric changes on the surface. It can effectively respond to rough features such as sharp edges and wrinkles, and normalization eliminates the influence of mesh density differences and noise on the maximum normal angle, improving the correction effect. The introduced average curvature amplitude can characterize the spatial trend of curvature, effectively capturing the mesoscale boundary structure formed when the lesion area transitions from flat to raised or concave, effectively characterizing the local geometric strength of the surface. It has extremely high sensitivity and robustness for soft tissue lesion detection, compared to principal curvature or Gaussian curvature. The rate, which can be efficiently solved by the discrete Laplacian operator without complex coordinate transformations or feature estimation, is more suitable for rapid feature extraction and screening in large-scale clinical models. The introduced centroid offset distance can reflect the degree of convexity or concavity of the surface vertex relative to its neighborhood. Based on the introduced maximum normal angle, the surface vertex is corrected to improve the problem of blurred lesion details. The maximum normal angle is sensitive to surface creases and sharp edges, the average curvature amplitude reflects the degree of curvature, and the centroid offset distance describes the overall morphological changes of local bulges. Therefore, the weighted sum of the three is used as the composite feature intensity to ensure the stability and accuracy of feature point detection to the greatest extent.

[0014] Furthermore, the step of filtering out the parts to be corrected from the surface vertices of the subdivided 3D model based on the geometric information of the feature surface vertices and surface vertices includes:

[0015] In a subdivided 3D model, the minimum geodesic distance from a surface vertex to the set of feature surface vertices is calculated using the following formula:

[0016] ;

[0017] in, Represents surface vertices The minimum geodesic distance to the set of vertices of the characteristic surface. Represents the set of vertices on the feature surface. Represents surface vertices and feature surface vertices The geodesic distance between them along the surface of the triangular grid. This indicates taking the minimum value;

[0018] The weights of surface vertices are calculated based on the minimum geodesic distance from a surface vertex to the set of feature surface vertices, using the following formula:

[0019] ;

[0020] in, Represents surface vertices The weight, Represents an exponential function. This represents the scale parameter used to control the range of influence of the feature;

[0021] If surface vertex weight If not 0, then the surface vertex It is the surface vertex to be corrected, otherwise it is the surface vertex. This is not a surface vertex to be corrected.

[0022] Based on the above-mentioned further technical solutions, a selection scheme for surface vertices is designed according to the minimum geodesic distance from the surface vertex to the set of feature surface vertices. This can accurately characterize the topological proximity relationship between surface vertices and feature regions on the curved manifold, thereby avoiding the cross-regional misassociation problem caused by Euclidean distance under complex geometric structures. Furthermore, by combining the exponential function as the Gaussian decay function, the discrete feature point set can be mapped into a continuous and smooth spatial weight field, realizing the smooth propagation and natural decay of feature influence on the curved surface, thereby ensuring the continuity and stability of the local geometric correction process.

[0023] Furthermore, the position correction is performed using the following method:

[0024] If surface vertex To be corrected, the surface vertices should be calculated using the following formula. Correction magnitude coefficient:

[0025] ;

[0026] in, Represents surface vertices The correction factor, This represents the preset feature enhancement coefficient;

[0027] Calculate the surface vertices using the following formula. Local height correction amount:

[0028] ;

[0029] in, Represents surface vertices Local height correction amount, Represents the vertex of the feature surface The unit normal vector, Represents the vertex of the feature surface The position vector, Represents surface vertices The position vector, Represents surface vertices The unit normal vector, Indicates transpose;

[0030] Along surface vertex The normal direction is calculated for the surface vertices using the following formula. Corrected position vector:

[0031] ;

[0032] in, Represents surface vertices The corrected position vector, Indicates the weight of the subdivision operator;

[0033] Subdivide the surface vertices in the 3D model The position vector is updated to the surface vertex. The corrected position vector completes the surface vertex. Position correction.

[0034] Based on the above-mentioned further technical solutions, by introducing feature enhancement coefficients, the problems of surface distortion, local self-intersection, and mesh quality degradation caused by excessive geometric perturbation are avoided. Furthermore, a smaller feature enhancement coefficient is beneficial to maintaining surface smoothness and structural stability, while a larger feature enhancement coefficient is used to enhance the local geometric representation ability of the lesion region, thereby achieving a balance between geometric fidelity and mesh quality. The above-mentioned geometric correction process corrects the local geometric structure weakened by the subdivision process, avoids the problem of blurred lesion details caused by excessive smoothing in traditional subdivision methods, and improves the uniformity of boundary node distribution, alleviating the abrupt change in displacement field gradient caused by non-uniform discretization.

[0035] Furthermore, the calculation of the additional potential energy term based on the Jacobian determinant is performed using the following formula:

[0036] ;

[0037] in, Indicates the first Additional potential energy term of individual unit, Indicates the first Jacobian determinant of individual units, Represents the volume regularization modulus. , Represents the numerical stability parameter. The bulk modulus of the material.

[0038] The above-mentioned further technical solution is to improve the numerical stability under large deformation conditions. As can be seen from the calculation formula of the additional potential energy term, when the Jacobian determinant is close to the degenerate state, the additional potential energy term grows rapidly, thereby generating a forced recovery effect in the simulation process, and finally feeding back to the explicit dynamic equation through the equivalent internal force of the vertex, so as to achieve active suppression of the collapse of the bulk element and the degeneration of the Jacobian determinant under extreme deformation conditions.

[0039] Furthermore, the calculation of the regularization force based on the additional potential energy term is performed using the following formula:

[0040] ;

[0041] in, Indicates the first The regularizing force of individual units, Indicates the first Additional potential energy term of individual unit, Indicates the first Jacobian determinant of individual units.

[0042] Based on the above-mentioned further technical solution, after obtaining the additional potential energy term, partial derivative calculations are performed on it to characterize the intensity of the mechanical response caused by the volume change.

[0043] Furthermore, mapping the regularized force to the equivalent internal force acting on each vertex of the volume element includes:

[0044] The current volume of the volume element is calculated using the following formula:

[0045] ;

[0046] in, Indicates the first The current volume of the individual unit. Indicates the first Jacobian determinant of individual units, Indicates the first The initial volume of an individual unit;

[0047] The equivalent internal forces at each vertex of a solid element are calculated based on its current volume using the following formula:

[0048] ;

[0049] in, Indicates the first Vertex in individual unit The equivalent internal force, Indicates the first The regularizing force of individual units, Indicates the first The current volume of the individual unit. Represents vertices The coordinate vector.

[0050] Based on the above further technical solution, the partial derivative of the regularization force with respect to the coordinate vector of each vertex in the volume element is performed, and the mapping of the regularization based on the volume change of the volume element to the discrete vertices is realized, thereby realizing the conversion from the volume response at the volume element level to the force at the vertex level.

[0051] In a second aspect, the present invention provides a soft tissue deformation simulation device, comprising:

[0052] The model acquisition module is configured to acquire an initial 3D model of the soft tissue.

[0053] The model correction module is configured to: calculate the composite feature intensity of each surface vertex based on the geometric information of each surface vertex in the initial 3D model; determine an adaptive threshold based on the composite feature intensity of each surface vertex and the statistical quantile method; filter out feature surface vertices from all surface vertices of the initial 3D model based on the adaptive threshold; subdivide the surface of the initial 3D model to obtain a subdivided 3D model; and filter out the parts to be corrected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and perform position correction to obtain the corrected 3D model.

[0054] The deformation mapping module is configured to perform the following calculations for each volume element in the modified 3D model in response to deformation of the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex of the volume element.

[0055] The model update module is configured to: assemble all equivalent internal forces into a global force vector, construct and solve explicit dynamic equations based on the global force vector to obtain the displacement of each vertex, and update the modified 3D model based on the displacement of each vertex to obtain the final 3D model after deformation.

[0056] 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 soft tissue deformation simulation method described in any one of the first aspects.

[0057] Fourthly, the present invention provides a computer device, comprising:

[0058] Memory, used to store computer programs / instructions;

[0059] A processor for executing the computer program / instructions to implement the steps of the soft tissue deformation simulation method described in any one of the first aspects.

[0060] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0061] This invention provides a soft tissue deformation simulation method, apparatus, storage medium, and device. Addressing the primary instability mechanism of volumetric degradation in 3D models under extreme deformation conditions, it constructs an additional potential energy term based on the Jacobian determinant from an energy perspective. This transforms the volumetric compression process of the volumetric elements into a controllable energy penalty problem, i.e., an energy constraint problem, thereby generating a forced recovery effect during the simulation. Ultimately, this is fed back to the explicit dynamic equations through the equivalent internal forces at the vertices, actively suppressing volumetric element collapse and Jacobian determinant degradation under extreme deformation conditions, thus improving the stability of the numerical solution. A regularizing force is constructed based on the additional potential energy term to characterize the degree of mechanical response caused by volume changes, forming a volume constraint mechanism. This mechanism suppresses the stability of the volumetric element deformation process, further improving the stability of the numerical solution. The regularizing force is mapped to the equivalent internal forces acting on each vertex of the volumetric element, realizing the mapping of the regularizing action based on volumetric element volume changes to discrete vertices. This achieves the conversion from volumetric response at the volumetric level to force at the vertex level, allowing the equivalent internal forces to be assembled into the global force vector and participate in the explicit dynamic equations. The solution process of the dynamic equations is described to constrain the volume of the volume element, thereby improving the stability of the numerical solution. The volume degradation state is characterized by the Jacobian determinant, and the volume degradation state is transformed into an energy penalty by adding a potential energy term. The added potential energy term is then regularized into an equivalent internal force, thus transforming the geometric constraint into a mechanical action that can participate in the dynamic solution. Furthermore, after subdivision, surface vertex correction based on geometric information is introduced to correct the local geometric structure weakened by the subdivision process, avoiding the problem of blurred lesion details caused by excessive smoothing in traditional subdivision methods. At the same time, it improves the uniformity of boundary node distribution, alleviates the abrupt change in displacement field gradient caused by non-uniform discretization, realizes geometric correction of the surface vertices of the 3D model, and achieves adaptive reconstruction of boundary geometry. Without changing the topology of the volume element, it improves the distribution characteristics of the displacement field in the spatial domain, thereby improving the stability of the numerical solution. In summary, geometric correction mainly improves the propagation of boundary conditions and displacement field, while the volume constraint mechanism suppresses the stability of the volume element deformation process, thus achieving the synergy between geometric expression and numerical stability in the simulation of soft tissue deformation. Attached Figure Description

[0062] Figure 1 This is a flowchart of a soft tissue deformation simulation method provided in an embodiment of the present invention;

[0063] Figure 2 This is a schematic diagram of the process for correcting an initial three-dimensional model provided in an embodiment of the present invention;

[0064] Figure 3 This is a schematic diagram of the process of mapping deformation in a modified three-dimensional model to equivalent internal forces, provided by an embodiment of the present invention. Detailed Implementation

[0065] 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.

[0066] Example 1

[0067] like Figure 1 As shown, this embodiment provides a method for simulating soft tissue deformation, including:

[0068] Obtain an initial 3D model of the soft tissue;

[0069] The composite feature intensity of each surface vertex is calculated based on the geometric information of each surface vertex in the initial 3D model. An adaptive threshold is determined based on the composite feature intensity of each surface vertex and the statistical quantile method. Feature surface vertices are selected from all surface vertices of the initial 3D model based on the adaptive threshold. The surface of the initial 3D model is subdivided to obtain a subdivided 3D model. The parts to be corrected are selected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and their positions are corrected to obtain a corrected 3D model.

[0070] In response to the deformation generated by the modified 3D model, the following calculations are performed on each volume element in the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex in the volume element.

[0071] All equivalent internal forces are assembled into a global force vector. Explicit dynamic equations are constructed and solved based on the global force vector to obtain the displacement of each vertex. The modified 3D model is then updated based on the displacement of each vertex to obtain the final 3D model after deformation.

[0072] This invention addresses the primary instability mechanism of volumetric degradation in 3D models under extreme deformation conditions. From an energy perspective, it constructs an additional potential energy term based on the Jacobian determinant, transforming the volumetric compression process of the volume element into a controllable energy penalty problem, i.e., an energy constraint problem. This generates a forced recovery effect during the simulation and ultimately feeds back to the explicit dynamic equations through the equivalent internal forces at the vertices, actively suppressing volumetric collapse and Jacobian determinant degradation under extreme deformation conditions, thereby improving the stability of the numerical solution. A regularizing force is constructed based on the additional potential energy term to characterize the degree of mechanical response caused by volume changes, forming a volume constraint mechanism. This mechanism suppresses the stability of the volumetric deformation process, further improving the stability of the numerical solution. The regularizing force is mapped to the equivalent internal forces acting on each vertex of the volume element, realizing the mapping of the regularizing action based on volumetric changes to discrete vertices. This achieves the conversion from volumetric response at the volume element level to force at the vertex level, allowing the equivalent internal forces to be assembled into the global force vector and participate in the solution process of the explicit dynamic equations. Constraining the volume of the bulk element further improves the stability of the numerical solution. The volume degradation state is characterized by the Jacobian determinant, and this degradation state is transformed into an energy penalty through an additional potential energy term. This additional potential energy term is then regularized into an equivalent internal force, thus transforming the geometric constraint into a mechanical action that can participate in the dynamic solution. Furthermore, geometric correction based on surface vertices is introduced after subdivision to correct the weakened local geometry during the subdivision process, avoiding the problem of blurred details caused by excessive smoothing in traditional subdivision methods. This also improves the uniformity of boundary node distribution, alleviates the abrupt changes in displacement field gradient caused by non-uniform discretization, and achieves geometric correction of the 3D model surface vertices, enabling adaptive reconstruction of boundary geometry. This improves the distribution characteristics of the displacement field in the spatial domain without changing the topology of the bulk element, thereby enhancing the stability of the numerical solution. In summary, geometric correction mainly affects the propagation of boundary conditions and the displacement field, while the volume constraint mechanism suppresses the stability of the bulk element deformation process, thus achieving a synergy between geometric representation and numerical stability in soft tissue deformation simulation.

[0073] Example 2

[0074] This embodiment provides a method for simulating soft tissue deformation, specifically including the following steps S1 to S4.

[0075] Step S1: Obtain the initial three-dimensional model of the soft tissue.

[0076] The initial three-dimensional model of the soft tissue was constructed based on CT and MRI images of the soft tissue.

[0077] Step S2: Design an adaptive point-line method based on vertex labeling to correct the initial 3D model. Calculate the composite feature intensity of each surface vertex based on its geometric information. Determine an adaptive threshold based on the composite feature intensity and statistical quantile method. Based on the adaptive threshold, select feature surface vertices from all surface vertices of the initial 3D model. Subdivide the surfaces of the initial 3D model to obtain a subdivided 3D model. Based on the feature surface vertices and their geometric information, select the surface vertices to be corrected from the surface vertices of the subdivided 3D model and perform position correction to obtain the corrected 3D model.

[0078] like Figure 2 As shown, step S2 can be further divided into steps S2.1 to S2.6. In step S2, any processing or calculation involving vertices refers to the processing or calculation of surface vertices, using symbolic representations. To refer to any vertex of the surface, using the symbol To refer to the surface vertex any surface vertex in the set of neighboring surface vertices.

[0079] Step S2.1: Calculate and normalize the geometric feature values ​​of each surface vertex based on the geometric information of each surface vertex in the initial 3D model. The geometric feature values ​​include the maximum normal angle, the average curvature amplitude, and the centroid offset distance.

[0080] The maximum angle between the normals at the surface vertices is calculated based on their geometric information using the following formula:

[0081] ;

[0082] in, Represents surface vertices The maximum angle between the normals, This indicates taking the maximum value. Represents the inverse cosine function. Represents surface vertices The set of vertices of the neighborhood surface. Represents surface vertices The unit normal vector, Represents surface vertices The unit normal vector.

[0083] The maximum normal angle reflects the degree of change in the normal direction at the surface vertex. In order to eliminate the influence of mesh density differences and noise on the maximum normal angle, Min-Max normalization is used to unify the scale of the maximum normal angle to obtain the normalized maximum normal angle.

[0084] For surface vertices Maximum normal angle The surface vertices are obtained by performing Min-Max normalization using the following formula. Maximum normal angle after normalization:

[0085] ;

[0086] in, Represents surface vertices The maximum angle between normalized normals, Represents surface vertices The maximum angle between the normals, This represents the global minimum normal angle. This represents the global maximum normal angle.

[0087] The maximum normal angle can characterize the difference in the normal direction between adjacent vertices and is highly sensitive to local geometric changes on the surface. It can effectively respond to rough features such as sharp edges and wrinkles. Based on the above considerations, in this embodiment, the maximum normal angle is used as one of the geometric feature values ​​for calculating the intensity of composite features.

[0088] The average curvature vector of the surface vertices is calculated based on their geometric information using the following formula:

[0089] ;

[0090] in, Represents surface vertices The average curvature vector, To express summation, Represents surface vertices The position vector, Represents surface vertices The position vector, Represents surface vertices Local area weights of the position vectors Represents surface vertices The set of vertices of the neighborhood surface. Indicates the relationship with the edge In an adjacent triangle with side Interior angles at opposite vertices, Indicates the relationship with the edge In another adjacent triangle with side Interior angles at opposite vertices, This represents the cotangent function.

[0091] about and Further explanation: In the initial 3D model, with edges The two adjacent triangles are respectively and ,triangle The three vertices are ,triangle The three vertices are , It is a triangle Center and edge relative vertices The interior angle at that point, It is a triangle Center and edge relative vertices The interior angle at that location.

[0092] The average curvature magnitude of a surface vertex is calculated based on its average curvature vector using the following formula:

[0093] ;

[0094] in, Represents surface vertices The average curvature amplitude, Represents surface vertices The average curvature vector, This indicates the search for the Euclidean norm.

[0095] For surface vertices average curvature amplitude The surface vertices are obtained by performing Min-Max normalization using the following formula. Normalized mean curvature amplitude:

[0096] ;

[0097] in, Represents surface vertices Normalized mean curvature amplitude, Represents surface vertices The average curvature amplitude, This represents the global minimum average curvature amplitude. This represents the global maximum average curvature amplitude.

[0098] The mean curvature amplitude can characterize the spatial variation trend of curvature, effectively capturing the mesoscale boundary structure formed when a lesion transitions from flat to raised or depressed areas. Furthermore, the mean curvature amplitude effectively characterizes the local geometric strength of a surface, exhibiting extremely high sensitivity and robustness for soft tissue lesion detection. Healthy tissue surfaces are smooth with near-zero curvature, while the protrusions or depressions caused by lesions lead to a significant surge in curvature amplitude. Compared to principal curvature or Gaussian curvature, this index can be efficiently solved using the discrete Laplacian operator, without the need for complex coordinate transformations or feature estimation, making it more suitable for rapid feature extraction and screening in large-scale clinical models. Based on these considerations, in this embodiment, the mean curvature amplitude is used as one of the geometric feature values ​​for calculating the composite feature intensity.

[0099] The centroid offset distance of a surface vertex is calculated based on its geometric information using the following formula:

[0100] ;

[0101] in, Represents surface vertices The distance of the centroid offset, Represents surface vertices The position vector, Represents surface vertices The position vector, Represents surface vertices The set of vertices of the neighborhood surface. This indicates the search for the Euclidean norm. To express summation, This indicates the number of elements in a set.

[0102] For surface vertices centroid offset distance The surface vertices are obtained by performing Min-Max normalization using the following formula. Normalized centroid offset distance:

[0103] ;

[0104] in, Represents surface vertices Normalized centroid offset distance, Represents surface vertices The distance of the centroid offset, This represents the global minimum centroid offset distance. This represents the global maximum centroid offset distance.

[0105] The centroid offset distance can reflect the degree of convexity or concavity of a surface vertex relative to its neighborhood. Based on the above considerations, in this embodiment, the centroid offset distance is used as one of the geometric feature values ​​for calculating the composite feature intensity.

[0106] Step S2.2: After obtaining the above three normalized geometric eigenvalues, calculate their weighted sum as the composite feature intensity of the surface vertex.

[0107] ;

[0108] in, Represents surface vertices The composite characteristic intensity, Represents surface vertices The maximum angle between normalized normals, Represents surface vertices Normalized mean curvature amplitude, Represents surface vertices Normalized centroid offset distance, express The weight, express The weight, express The weight.

[0109] Because the three geometric feature values ​​have different effects in detecting abrupt changes in surface regions; among them, the maximum normal angle is sensitive to surface creases and sharp edges, the average curvature amplitude reflects the degree of curvature, and the centroid offset distance characterizes the overall morphological changes of local bulges. Therefore, to balance local details and overall trends, this invention selects a weighting ratio of [missing value]. This ensures the stability and accuracy of feature point detection.

[0110] Step S2.3: Determine the adaptive threshold based on the composite feature intensity of each surface vertex and the statistical quantile method.

[0111] The adaptive threshold is determined using the following formula:

[0112] ;

[0113] in, Indicates an adaptive threshold. Represents surface vertices The composite characteristic intensity, Represents the quantile function. For quantile parameters, This indicates the number of vertices on the surface.

[0114] The quantile parameter can be interpreted as the percentage of vertex on the feature surface. Its value is set according to the geometric complexity of the initial 3D model. This strategy can be adaptively adjusted according to the local geometric distribution of different models or lesions. In this embodiment, the value of the quantile parameter is 0.1.

[0115] Step S2.4: Select feature surface vertices from all surface vertices of the initial 3D model based on an adaptive threshold. Surface vertices with composite feature strength greater than the adaptive threshold are selected as feature surface vertices, thus constructing a set of feature surface vertices. .

[0116] Step S2.5: Subdivide the surface of the initial 3D model to obtain a subdivided 3D model. Based on the feature surface vertices and the geometric information of the surface vertices, select the surface vertices to be corrected from the surface vertices of the subdivided 3D model.

[0117] The surface of the initial 3D model is subdivided using the Loop subdivision rule to obtain a subdivided 3D model.

[0118] For all surface vertices in the subdivided 3D model, the minimum geodesic distance from each surface vertex to the set of feature surface vertices is calculated using the following formula:

[0119] ;

[0120] in, Represents surface vertices The minimum geodesic distance to the set of vertices of the characteristic surface. Represents the set of vertices on the feature surface. Represents surface vertices and feature surface vertices The geodesic distance between them along the surface of the triangular grid. This indicates taking the minimum value.

[0121] The weights of surface vertices are calculated based on the minimum geodesic distance from a surface vertex to the set of feature surface vertices, using the following formula:

[0122] ;

[0123] in, Represents surface vertices The weight, This represents an exponential function used to achieve non-linear decay of weights. Represents surface vertices The minimum geodesic distance to the set of vertices of the characteristic surface. This represents the scale parameter used to control the range of influence of the feature.

[0124] In the subdivision of the 3D model, the surface vertices are judged, if the surface vertices weight If not 0, then the surface vertex These are the surface vertices to be corrected; this completes the filtering of whether surface vertices need correction.

[0125] Step S2.6: Correct the position of the surface vertices to be corrected in the subdivided 3D model to obtain the corrected 3D model.

[0126] If surface vertex If correction is needed, calculate the correction magnitude coefficient using the following formula:

[0127] ;

[0128] in, Represents surface vertices The correction factor, Represents surface vertices The weight, This represents the preset feature enhancement coefficient, which is 0.3 in this embodiment.

[0129] The feature enhancement coefficient does not change the meaning of the feature weights but directly affects the geometric correction process, serving as a key factor controlling the scale of surface reconstruction. Since this correction directly impacts the local surface morphology and the quality of subsequent volume mesh generation, a trade-off must be struck between geometric enhancement capability and numerical stability to avoid excessive geometric perturbation leading to surface distortion, local self-intersection, and mesh quality degradation. In practical applications, a value of 0.3 is beneficial for maintaining surface smoothness and structural stability, while larger values ​​are used to enhance the local geometric representation of lesion regions, thereby achieving a balance between geometric fidelity and mesh quality.

[0130] Along the surface vertex The surface vertices are obtained by correcting the position of the normal direction. The corrected position vector is obtained using the following formula:

[0131] ;

[0132] in, Represents surface vertices The corrected position vector, Represents surface vertices The position vector, Represents surface vertices The correction factor, Represents face vertices Local height correction amount, Represents surface vertices The unit normal vector, Indicates the weight of the subdivision operator. This represents the set of vertices on the feature surface.

[0133] The local height correction amount is calculated using the following formula:

[0134] ;

[0135] in, Represents surface vertices Local height correction amount, Represents the vertex of the feature surface The unit normal vector, Represents the vertex of the feature surface The position vector, Represents surface vertices The position vector, Represents surface vertices The unit normal vector, This indicates transpose.

[0136] Subdivide the surface vertices in the 3D model The position vector is updated to the calculated surface vertex. The corrected position vector completes the surface vertex. Position correction. After all the surface vertices to be corrected in the subdivided 3D model have been corrected, the corrected 3D model is obtained.

[0137] Step S3: Local soft spring stabilization strategy based on force level regularization. In response to the deformation generated by the modified 3D model, the following calculations are performed on each volume element in the modified 3D model: calculate the deformation gradient and Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex of the volume element.

[0138] like Figure 3 As shown, for each volume element in the modified 3D model, step S3 can be specifically expanded into steps S3.1 to S3.4. In step S3, when processing or calculating vertices, this involves processing or calculating all existing vertices in the modified 3D model, using symbolic representations. To refer to any vertex, the symbol is used. No longer limited to surface vertices.

[0139] Step S3.1: Calculate the deformation gradient and Jacobian determinant of the volume element.

[0140] The calculation of deformation gradient is a prior art and will not be elaborated here; the Jacobian determinant is calculated based on the deformation gradient using the following formula:

[0141] ;

[0142] in, Indicates the first Individual units in Deformation gradient at time step, This indicates that a determinant operation is performed on the tensor. Indicates the first Jacobian determinant of individual units.

[0143] In the reference configuration, the Jacobian determinant is 1. However, during complex virtual surgical interactions, such as when soft tissue is subjected to strong compression or traction, the volumetric elements will undergo significant geometric distortion. At this point, when the Jacobian determinant approaches the zero critical value, the system will lose the feasibility of real-time simulation due to an explosion in stress values ​​or a significant reduction in the steady-state time step. To address this deficiency, an additional potential energy term is introduced in this embodiment, and a regularized force is constructed.

[0144] Step S3.2: Calculate the additional potential energy term based on the Jacobian determinant.

[0145] The additional potential energy term is calculated using the following formula:

[0146] ;

[0147] in, Indicates the first Additional potential energy term of individual unit, Indicates the first Jacobian determinant of individual units, Represents the volume regularization modulus. , Represents the numerical stability parameter. The bulk modulus of the material.

[0148] The construction of the additional potential energy term follows strict boundary constraints: it satisfies the zero energy point and generates no stress at the reference configuration, and approaches infinity when the volume approaches the singularity, thus mathematically guaranteeing the positive definiteness of the element volume. Specifically, this embodiment addresses the main instability mechanism of volumetric degradation in the 3D model under extreme deformation conditions. From an energy perspective, an additional potential energy term based on the Jacobian determinant is constructed, transforming the volumetric compression process of the element into a controllable energy penalty problem, i.e., an energy constraint problem. When the Jacobian determinant approaches the degenerate state, the additional potential energy term grows rapidly, thereby generating a forced recovery effect during the simulation. Ultimately, it is fed back to the explicit dynamic equations through the equivalent internal force at the vertices, achieving active suppression of element collapse and Jacobian determinant degradation under extreme deformation conditions, thereby improving the stability of the numerical solution.

[0149] Step S3.3: Calculate the regularization force based on the additional potential energy term.

[0150] The regularization force is calculated using the following formula:

[0151] ;

[0152] in, Indicates the first The regularizing force of individual units, Indicates the first Additional potential energy term of individual unit, Indicates the first Jacobian determinant of individual units.

[0153] In continuum mechanics, the internal force vector is the negative gradient of the strain energy density with respect to the coordinates. In this embodiment, an additional potential energy term related to the Jacobian determinant is defined. According to the principle of energy conservation and virtual work, this potential energy must correspond to a physical resistance force.

[0154] Substituting the expression for the additional potential energy term into the expression for the regularization force, we obtain the final expression for the regularization force:

[0155] ;

[0156] in, Indicates the first The regularizing force of individual units, Represents the volume regularization modulus. Indicates the first Jacobian determinant of individual units.

[0157] Rewriting the regularization force as a function of the Jacobian determinant not only physically directly constrains the volumetric degradation of the volume element, but also mathematically achieves consistency with the direct Jacobian derivation path in the direct Jacobian total Lagrangian explicit dynamics finite element algorithm. Under extreme compression, the Jacobian determinant of the volume element... It may rapidly approach zero, at which point the regularization force will exhibit a highly nonlinear growth, used to characterize the degree of mechanical response caused by volume changes, forming a volume constraint mechanism. Through the volume constraint mechanism, the stability of the deformation process of the volume element is suppressed, further improving the stability of the numerical solution.

[0158] Step S3.4: Map the regularized force as an equivalent internal force acting on each vertex of the volume element.

[0159] Calculate the first The current volume of an individual unit is determined by the following formula:

[0160] ;

[0161] in, Indicates the first The current volume of the individual unit. Indicates the first Jacobian determinant of individual units, Indicates the first The initial volume of an individual unit.

[0162] For the correction of the 3D model, the first Vertex in individual unit The equivalent internal force is calculated using the following formula:

[0163] ;

[0164] in, Indicates the first Vertex in individual unit The equivalent internal force, Indicates the first Additional potential energy term of individual unit, Represents vertices The coordinate vector.

[0165] It can also be expressed as:

[0166] ;

[0167] in, Indicates the first Vertex in individual unit The equivalent internal force, Indicates the first The regularizing force of individual units, Indicates the first The current volume of the individual unit. Represents vertices The coordinate vector.

[0168] It can also be expressed as:

[0169] ;

[0170] in, Indicates the first Vertex in individual unit The equivalent internal force, Represents the volume regularization modulus. Indicates the first Jacobian determinant of individual units, Indicates the first The current volume of the individual unit. Represents vertices The coordinate vector.

[0171] When the volume unit is compressed, that is When <1, there is and Therefore, the regularization force becomes positive. and In the same direction, this generates equivalent expansionary internal forces at the four vertices, increasing the volume and effectively suppressing volume collapse and Jacobian determinant degradation. Furthermore, since the Jacobian determinant is determined only by the deformation gradient, The regularized force is determined solely by the geometry of the current volume element, thus it is an internal force term. The calculation is independent of the absolute position, and the force vectors at the four vertices within the element satisfy the condition that the resultant force is 0.

[0172] In step S3, the reason for designing to first calculate the additional potential energy term, then the regularizing force, and finally the equivalent internal force is as follows: the volume degradation state is characterized by the Jacobian determinant, the volume degradation state is transformed into an energy penalty by the additional potential energy term, and the additional potential energy term is transformed into an equivalent internal force by the regularizing force, thereby transforming the geometric constraint into a mechanical action that can participate in the dynamic solution.

[0173] Step S4: Assemble all equivalent internal forces into a global force vector, construct and solve explicit dynamic equations based on the global force vectors, obtain the displacement of each vertex by solving the explicit dynamic equations, and update the modified three-dimensional model based on the displacement of each vertex to obtain the final three-dimensional model after deformation.

[0174] Step S4 can be further divided into steps S4.1 to S4.3.

[0175] Step S4.1: Assemble all equivalent internal forces into a global force vector.

[0176] The expression for the global force vector is:

[0177] ;

[0178] in, Represents the global force vector. Indicates the first Vertex in individual unit Assembly operator, Indicates transpose. Indicates the first Vertex in individual unit The equivalent internal force, Represents a set of volumetric units.

[0179] Step S4.2: Construct the following explicit dynamic equations based on the global force vector:

[0180] ;

[0181] in, This represents the global quality matrix of soft tissue. Represents the global vertex acceleration vector. This represents the vector of nodal forces applied externally. This represents the sum of internal forces within a single element. For the first Individual units in The internal force vector contributed at each moment, Indicates time, Represents the global force vector. Represents the damping matrix. This represents the global vertex velocity vector.

[0182] Step S4.3: Solve the explicit dynamic equations to obtain the displacements of each vertex, and update the modified 3D model based on the displacements of each vertex to obtain the final 3D model after deformation. This step is implemented using existing technology and will not be described in detail here.

[0183] Example 3

[0184] This embodiment provides a soft tissue deformation simulation device, including:

[0185] The model acquisition module is configured to acquire an initial 3D model of the soft tissue.

[0186] The model correction module is configured to: calculate the composite feature intensity of each surface vertex based on the geometric information of each surface vertex in the initial 3D model; determine an adaptive threshold based on the composite feature intensity of each surface vertex and the statistical quantile method; filter out feature surface vertices from all surface vertices of the initial 3D model based on the adaptive threshold; subdivide the surface of the initial 3D model to obtain a subdivided 3D model; and filter out the parts to be corrected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and perform position correction to obtain the corrected 3D model.

[0187] The deformation mapping module is configured to perform the following calculations for each volume element in the modified 3D model in response to deformation of the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex of the volume element.

[0188] The model update module is configured to: assemble all equivalent internal forces into a global force vector, construct and solve explicit dynamic equations based on the global force vector to obtain the displacement of each vertex, and update the modified 3D model based on the displacement of each vertex to obtain the final 3D model after deformation.

[0189] Example 4

[0190] 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 soft tissue deformation simulation method provided in Embodiment 1:

[0191] Obtain an initial 3D model of the soft tissue;

[0192] The composite feature intensity of each surface vertex is calculated based on the geometric information of each surface vertex in the initial 3D model. An adaptive threshold is determined based on the composite feature intensity of each surface vertex and the statistical quantile method. Feature surface vertices are selected from all surface vertices of the initial 3D model based on the adaptive threshold. The surface of the initial 3D model is subdivided to obtain a subdivided 3D model. The parts to be corrected are selected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and their positions are corrected to obtain a corrected 3D model.

[0193] In response to the deformation generated by the modified 3D model, the following calculations are performed on each volume element in the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex in the volume element.

[0194] All equivalent internal forces are assembled into a global force vector. Explicit dynamic equations are constructed and solved based on the global force vector to obtain the displacement of each vertex. The modified 3D model is then updated based on the displacement of each vertex to obtain the final 3D model after deformation.

[0195] Example 5

[0196] This embodiment provides a computer device, including:

[0197] Memory, used to store computer programs / instructions;

[0198] A processor is configured to execute the computer program / instructions to implement the steps of the soft tissue deformation simulation method provided in Embodiment 1:

[0199] Obtain an initial 3D model of the soft tissue;

[0200] The composite feature intensity of each surface vertex is calculated based on the geometric information of each surface vertex in the initial 3D model. An adaptive threshold is determined based on the composite feature intensity of each surface vertex and the statistical quantile method. Feature surface vertices are selected from all surface vertices of the initial 3D model based on the adaptive threshold. The surface of the initial 3D model is subdivided to obtain a subdivided 3D model. The parts to be corrected are selected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and their positions are corrected to obtain a corrected 3D model.

[0201] In response to the deformation generated by the modified 3D model, the following calculations are performed on each volume element in the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex in the volume element.

[0202] All equivalent internal forces are assembled into a global force vector. Explicit dynamic equations are constructed and solved based on the global force vector to obtain the displacement of each vertex. The modified 3D model is then updated based on the displacement of each vertex to obtain the final 3D model after deformation.

[0203] 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.

[0204] 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.

[0205] 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.

[0206] 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 1One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0207] 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 soft tissue deformation, characterized in that, include: Obtain an initial 3D model of the soft tissue; The composite feature intensity of each surface vertex is calculated based on the geometric information of each surface vertex in the initial 3D model. An adaptive threshold is determined based on the composite feature intensity of each surface vertex and the statistical quantile method. Feature surface vertices are selected from all surface vertices of the initial 3D model based on the adaptive threshold. The surface of the initial 3D model is subdivided to obtain a subdivided 3D model. The parts to be corrected are selected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and their positions are corrected to obtain a corrected 3D model. In response to the deformation generated by the modified 3D model, the following calculations are performed on each volume element in the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex in the volume element. All equivalent internal forces are assembled into a global force vector. Explicit dynamic equations are constructed and solved based on the global force vector to obtain the displacement of each vertex. The modified 3D model is then updated based on the displacement of each vertex to obtain the final 3D model after deformation.

2. The soft tissue deformation simulation method according to claim 1, characterized in that, The calculation of the composite feature intensity of each surface vertex based on the geometric information of each surface vertex in the initial 3D model includes: Based on the geometric information of each surface vertex in the initial 3D model, calculate and normalize the geometric eigenvalues ​​of each surface vertex. The geometric eigenvalues ​​include the maximum normal angle, the average curvature magnitude, and the centroid offset distance. Perform the following operation on each surface vertex to obtain the composite feature intensity of each surface vertex: calculate the weighted sum of all normalized geometric eigenvalues ​​of the surface vertex as the composite feature intensity of that surface vertex.

3. The soft tissue deformation simulation method according to claim 1, characterized in that, The part to be corrected is selected from the surface vertices of the subdivided 3D model based on the geometric information of the feature surface vertices and surface vertices, including: In a subdivided 3D model, the minimum geodesic distance from a surface vertex to the set of feature surface vertices is calculated using the following formula: ； in, Represents surface vertices The minimum geodesic distance to the set of vertices of the characteristic surface. Represents the set of vertices on the feature surface. Represents surface vertices and feature surface vertices The geodesic distance between them along the surface of the triangular grid. This indicates taking the minimum value; The weights of surface vertices are calculated based on the minimum geodesic distance from a surface vertex to the set of feature surface vertices, using the following formula: ； in, Represents surface vertices The weight, Represents an exponential function. This represents the scale parameter used to control the range of influence of the feature; If surface vertex weight If not 0, then the surface vertex It is the surface vertex to be corrected, otherwise it is the surface vertex. This is not a surface vertex to be corrected.

4. The soft tissue deformation simulation method according to claim 3, characterized in that, The position correction is performed using the following method: If surface vertex To be corrected, the surface vertices should be calculated using the following formula. Correction magnitude coefficient: ； in, Represents surface vertices The correction factor, This represents the preset feature enhancement coefficient; Calculate the surface vertices using the following formula. Local height correction amount: ； in, Represents surface vertices Local height correction amount, Represents the vertex of the feature surface The unit normal vector, Represents the vertex of the feature surface The position vector, Represents surface vertices The position vector, Represents surface vertices The unit normal vector, Indicates transpose; Along surface vertex The normal direction is calculated for the surface vertices using the following formula. Corrected position vector: ； in, Represents surface vertices The corrected position vector, Indicates the weight of the subdivision operator; Subdivide the surface vertices in the 3D model The position vector is updated to the surface vertex. The corrected position vector completes the surface vertex. Position correction.

5. The soft tissue deformation simulation method according to claim 1, characterized in that, The calculation of the additional potential energy term based on the Jacobian determinant is performed using the following formula: ； in, Indicates the first Additional potential energy term of individual unit, Indicates the first Jacobian determinant of individual units, Represents the volume regularization modulus. , Represents the numerical stability parameter. The bulk modulus of the material.

6. The soft tissue deformation simulation method according to claim 1, characterized in that, The calculation of the regularized force based on the additional potential energy term is performed using the following formula: ； in, Indicates the first The regularizing force of individual units, Indicates the first Additional potential energy term of individual unit, Indicates the first Jacobian determinant of individual units.

7. The soft tissue deformation simulation method according to claim 1, characterized in that, The mapping of regularized forces to equivalent internal forces acting on each vertex of the volume element includes: The current volume of the volume element is calculated using the following formula: ； in, Indicates the first The current volume of the individual unit. Indicates the first Jacobian determinant of individual units, Indicates the first The initial volume of an individual unit; The equivalent internal forces at each vertex of a solid element are calculated based on its current volume using the following formula: ； in, Indicates the first Vertex in individual unit The equivalent internal force, Indicates the first The regularizing force of individual units, Indicates the first The current volume of the individual unit. Represents vertices The coordinate vector.

8. A soft tissue deformation simulation device, characterized in that, include: The model acquisition module is configured to acquire an initial 3D model of the soft tissue. The model correction module is configured to: calculate the composite feature intensity of each surface vertex based on the geometric information of each surface vertex in the initial 3D model; determine an adaptive threshold based on the composite feature intensity of each surface vertex and the statistical quantile method; filter out feature surface vertices from all surface vertices of the initial 3D model based on the adaptive threshold; subdivide the surface of the initial 3D model to obtain a subdivided 3D model; and filter out the parts to be corrected from the surface vertices of the subdivided 3D model based on the feature surface vertices and the geometric information of the surface vertices, and perform position correction to obtain the corrected 3D model. The deformation mapping module is configured to perform the following calculations for each volume element in the modified 3D model in response to deformation of the modified 3D model: calculate the Jacobian determinant of the volume element, calculate the additional potential energy term based on the Jacobian determinant, calculate the regularization force based on the additional potential energy term, and map the regularization force to the equivalent internal force acting on each vertex of the volume element. The model update module is configured to: assemble all equivalent internal forces into a global force vector, construct and solve explicit dynamic equations based on the global force vector to obtain the displacement of each vertex, and update the modified 3D model based on the displacement of each vertex to obtain the final 3D model after deformation.

9. 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 soft tissue deformation simulation method according to any one of claims 1 to 7.

10. A computer device, characterized in that, include: Memory, used to store computer programs / instructions; A processor for executing the computer program / instructions to implement the steps of the soft tissue deformation simulation method according to any one of claims 1 to 7.

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