A high-performance cardiac biomechanics numerical simulation method, system and terminal

Abstract

The application discloses a high-performance cardiac biomechanics numerical simulation method and system and a terminal, is based on nonlinear anisotropic myocardial mechanics model, and through regional decomposition strategy optimization parallel computing efficiency, can realize accurate simulation of myocardium under physiological and various pathological conditions on a high-performance computing platform; through the optimized parallel computing strategy, the application supports simulation calculation of a grid of the order of tens of millions to hundreds of millions of units using ten thousand computing cores on a supercomputing platform, significantly improves the simulation accuracy and speed, effectively reduces the calculation time and saves the computing resources, and supports higher spatial resolution, fully utilizes the high-performance computing platform, to support the accurate simulation of the myocardial mechanical behavior under physiological and various pathological conditions.

Description

Technical Field

[0001] This invention relates to the field of numerical simulation technology, and in particular to a high-performance numerical simulation method, system, terminal, and computer-readable storage medium for cardiac biomechanics. Background Technology

[0002] Biomechanical modeling and numerical simulation of the myocardium is a complex and crucial research area. With the development of medical imaging technology, the anatomical structure and mechanical properties of the myocardium can be accurately depicted using high-resolution images and experimental data. However, relying solely on traditional imaging methods is insufficient to comprehensively capture the dynamic mechanical characteristics of the myocardium under different pathological conditions. Therefore, numerical simulation techniques to model the mechanical behavior of the myocardium under various pathological conditions have become an important tool for in-depth research into the mechanisms of myocardial diseases and for assisting clinical diagnosis. Biomechanical simulations in this field are typically based on nonlinear elasticity theory, treating the myocardium as an anisotropic material. Nonlinear anisotropic myocardial mechanical models are widely used in modeling to accurately represent the deformation and stress distribution of the myocardium under stress, providing theoretical support for analyzing the movement patterns of the myocardium under physiological and pathological conditions.

[0003] Currently, most methods for simulating myocardial biomechanics employ the finite element method (FEM) and the finite difference method (FDM) for discretization. The FEM, due to its excellent geometric adaptability, is widely used to simulate myocardial tissue with complex geometries and material heterogeneity. In 3D simulations, the FEM can construct myocardial mechanical models on fine meshes to analyze the stress-strain relationships of the myocardium under various conditions. Furthermore, spatial discretization using the FEM is often combined with temporal discretization using the finite difference method (FDM). Additionally, to improve simulation speed, parallel computing methods have been widely adopted in recent years. By implementing distributed computing on high-performance computing platforms, the solution speed can be significantly accelerated, making it suitable for large-scale 3D simulations of myocardial tissue and capable of handling myocardial mechanical responses under various pathological conditions. Existing numerical simulation techniques typically achieve a mesh size of millions of elements, roughly achieving a spatial resolution of 2-3 millimeters, capturing relatively detailed myocardial mechanical characteristics.

[0004] While the finite element method and finite difference method are widely used in the numerical simulation of myocardial biomechanics, these methods still have some shortcomings in accurately and efficiently simulating the mechanical behavior of myocardium under complex pathological conditions. Currently, commonly used numerical simulation techniques can typically only achieve a spatial resolution of 2-3 millimeters, which is insufficient to meet certain requirements. On the other hand, while increasing the spatial resolution can capture more detailed myocardial mechanical features, the resulting increase in the computational grid size will significantly increase computational resources and time costs. Simultaneously, existing parallel computing methods are not ideally efficient for large-scale problems on high-performance computing platforms. When using simulations with hundreds to thousands of computational cores, further increasing the number of cores makes it difficult to further shorten the computation time, thus limiting the application potential of numerical simulation.

[0005] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0006] The main objective of this invention is to provide a high-performance numerical simulation method, system, terminal, and computer-readable storage medium for cardiac biomechanics, aiming to solve the problems of insufficient spatial resolution accuracy, low computational efficiency, and waste of computational resources in existing biomechanical numerical simulations.

[0007] To achieve the above objectives, the present invention provides a high-performance numerical simulation method for cardiac biomechanics, which includes the following steps:

[0008] Acquire high-resolution medical image data, and generate a three-dimensional myocardial geometric model based on the high-resolution medical image data using image segmentation and geometric reconstruction.

[0009] Based on the aforementioned three-dimensional myocardial geometry model, a tetrahedral unstructured mesh is generated using mesh generation software, and then mesh subdivision is performed.

[0010] Based on the theory of elasticity, a nonlinear anisotropic elastic dynamics model describing myocardial motion is established according to the structural characteristics of myocardial tissue.

[0011] The finite element method was used to numerically discretize the equations of the nonlinear anisotropic elastic dynamics model of the heart, resulting in a set of algebraic equations suitable for computer solving.

[0012] Set the total simulation duration and number of time steps, and set the initial conditions and chamber surface boundary conditions according to the simulation task environment and the nature of the heart itself;

[0013] The direction of myocardial fibers at any point in the computational grid is determined based on the three-dimensional geometry of the heart, and is estimated based on physiological and anatomical data or implemented using an interpolation method based on heart geometry.

[0014] Within each time step, based on the myocardial displacement and velocity obtained in the previous time step, the deformation and stress distribution of each element at the current moment are calculated using nonlinear elastic theory and combined with a nonlinear anisotropic elastic dynamics model.

[0015] The calculated deformation and stress distribution are substituted into the discrete equation system, and the Newton-Krylov-Schwarz method is used to solve the algebraic equation system to obtain the updated elastic dynamic state of myocardial tissue.

[0016] Output and save the simulation results of the current time step. The simulation results represent the displacement and velocity of all nodes of the heart finite element mesh at the current moment, obtain the shape of the heart at the current moment, and calculate the deformation and stress magnitude at any position of the myocardium. The simulation ends when all time step calculations are completed.

[0017] Optionally, the high-performance cardiac biomechanical numerical simulation method, wherein generating a tetrahedral unstructured mesh based on the three-dimensional myocardial geometry model using mesh generation software and performing mesh subdivision, specifically includes:

[0018] Based on the aforementioned three-dimensional myocardial geometry model, tetrahedral unstructured meshes are generated using an adaptive refinement method via mesh generation software.

[0019] On the supercomputing platform, computing node resources are allocated, and each node creates an independent computing process. On the main process, a multi-level partitioning strategy based on graph theory is used to achieve efficient 3D unstructured mesh partitioning through local balancing and minimum cut optimization, resulting in a set of non-overlapping sub-regions. By mutually expanding the cells of adjacent sub-regions, overlapping sub-regions are obtained. The main process sends the sub-region mesh to other computing processes, and the data synchronization rules between adjacent sub-regions are determined based on the overlapping parts between the sub-region meshes.

[0020] Optionally, the high-performance cardiac biomechanical numerical simulation method, wherein the establishment of a nonlinear anisotropic elastic dynamics model describing myocardial motion based on elasticity theory and the structural characteristics of myocardial tissue specifically includes:

[0021] Based on myocardial fibers and layered structure, a nonlinear anisotropic elastic dynamics model is constructed. This nonlinear anisotropic elastic dynamics model takes into account the directional properties of myocardium and emphasizes the different stress-strain relationships of myocardial fibers and transverse fibers to accurately reflect the mechanical response under various loading conditions.

[0022] According to the principles of elastic dynamics, the displacement d and velocity v of any point in the heart tissue at any given time satisfy the following equation:

[0023]

[0024] in, Let P represent the gradient, Ω represent the first Piola-Kirchhoff stress currently applied, ρ represent the space occupied by the myocardial tissue, ρ represent the material density of the myocardial tissue, and T represent the simulation termination time.

[0025] Optionally, the high-performance cardiac biomechanical numerical simulation method, wherein the step of numerically discretizing the cardiac nonlinear anisotropic elastic dynamics model equations using the finite element method to obtain a set of algebraic equations suitable for computer solving specifically includes:

[0026] Based on the principles of the finite element method, consider the following variational form:

[0027]

[0028] in, The generalized function representing the elastic dynamic energy is expressed in the following form:

[0029]

[0030] Where X represents the spatial independent variable, Let these represent the discrete displacement function and discrete velocity function at the representative nth time step. Finite element mesh node values ​​of displacement and velocity With basis function {φ i The expansion form of} i = 1, 2, ..., NV is defined as follows:

[0031]

[0032] Where Δt represents the simulation time step, N represents the test function. V This indicates the total number of nodes contained in the computational grid;

[0033] By By replacing each basis function one by one and calculating the numerical integral, the original differential equation is transformed into a system of algebraic equations, thus completing the numerical discretization. After discretization, the unknowns to be solved are a finite set of nodal values.

[0034] Optionally, in the high-performance cardiac biomechanical numerical simulation method, the initial conditions are determined by cardiac physiological parameters and pathological characteristics, and the chamber surface boundary conditions are determined by pressure distribution data in the early stage of the simulation.

[0035] Optionally, the high-performance cardiac biomechanical numerical simulation method, wherein, within each time step, based on the myocardial displacement and velocity obtained in the previous time step, calculates the deformation and stress distribution of each element at the current moment using nonlinear elasticity theory combined with a nonlinear anisotropic elastic dynamics model, specifically including:

[0036] Calculate the gradient tensor of the displacement

[0037] Calculate the deformation gradient tensor Where I represents the second-order unit tensor;

[0038] Calculate the Green-Lagrange strain tensor E, which represents the magnitude of myocardial deformation:

[0039]

[0040] Construct a local rectangular coordinate system within the unit, wherein the three coordinates of the local rectangular coordinate system are mutually orthogonal, and the first coordinate axis must coincide with the direction of the myocardial fibers of the unit;

[0041] calculate:

[0042]

[0043] Where Q represents a number, and each E ij This represents the component value of the strain tensor E measured in the element's local coordinate system, b. f b t b fs These represent model parameters, which respectively represent the overall stiffness of the material and the stiffness along each fiber axis;

[0044] Calculate the determinant J = det F of tensor F;

[0045] Calculate the passive stress S caused by myocardial deformation p :

[0046] S p =Ce Q A*E+κln JC -1 ;

[0047] Where C represents the basic stiffness of myocardial tissue, κ represents the incompressibility coefficient of myocardial tissue, the operator * indicates the element-wise multiplication of the matrix, and the material parameter matrix A is defined as:

[0048]

[0049] Calculate the active stress S caused by spontaneous contraction of the myocardium. a :

[0050]

[0051] Among them, T a denoted by , where represents the intensity of active contractile stress, and f represents a unit vector along the direction of myocardial fibers;

[0052] Calculate the second Piola-Kirchhoff stress tensor S:

[0053] S = S a +S p ;

[0054] Calculate the first Piola-Kirchhoff stress tensor P:

[0055] P = FS.

[0056] Optionally, the high-performance cardiac biomechanical numerical simulation method, wherein substituting the calculated deformation and stress distribution into a discrete equation system and solving the algebraic equation system using the Newton-Krylov-Schwarz method to obtain the updated elastic dynamic state of myocardial tissue, specifically includes:

[0057] Within each time step, based on the finite element discretization scheme, the stress data of all elements in the calculated mesh are substituted to form a system of nonlinear algebraic equations:

[0058]

[0059] in, This represents the set of all unknowns to be solved in the system.

[0060] Solving systems of nonlinear algebraic equations using the Newton-Krylov-Schwarz method:

[0061] Using the Newton method, a system of nonlinear algebraic equations is transformed into a series of linear equations that are solved sequentially. The solutions from the previous step are used to construct the coefficient matrix of the next system of equations. Each linear equation is generally represented as:

[0062] Ax = b;

[0063] Wherein, the right-hand vector Given an initial conjecture solution The calculation shows that A represents the coefficient matrix obtained by linearization;

[0064] Using the Krylov subspace method and a parallel computing model, the linear equation system Ax = b is solved iteratively. Data communication is performed between adjacent sub-regions based on the grid partitioning structure and synchronization rules.

[0065] Based on the obtained mesh partitioning structure, construct the Schwarz preprocessing operator M for solving Ax = b.-1 This accelerates the convergence speed of solving linear equation systems. Each computational process constructs and solves subproblems on its own sub-region grid, and the results are obtained through integration.

[0066]

[0067] in, This describes the process of solving a problem for a subregion. and Let represent two projection operators that project any vector defined over the entire region onto a non-overlapping subregion and a subregion with δ-layer overlapping units, respectively. The transpose of represents the corresponding extended operator;

[0068] The preprocessor M obtained by construction -1 Integrating into the iterative solution of Ax = b in the Krylov subspace, the original problem is transformed into solving the following system of equations:

[0069] (AM -1 (Mx) = b;

[0070] The preprocessed system of equations has the same solution as the original system of equations.

[0071] Furthermore, to achieve the above objectives, the present invention also provides a high-performance cardiac biomechanical numerical simulation system, wherein the high-performance cardiac biomechanical numerical simulation system comprises:

[0072] A geometric model construction module is used to acquire high-resolution medical image data and generate a three-dimensional myocardial geometric model based on the high-resolution medical image data using image segmentation and geometric reconstruction.

[0073] The mesh processing module is used to generate a tetrahedral unstructured mesh based on the three-dimensional myocardial geometry model using mesh generation software, and to perform mesh subdivision.

[0074] The dynamic model construction module is used to establish a nonlinear anisotropic elastic dynamic model describing myocardial motion based on the theory of elasticity and the structural characteristics of myocardial tissue.

[0075] The numerical discretization module is used to numerically discretize the equations of the nonlinear anisotropic elastic dynamics model of the heart using the finite element method, and obtain a set of algebraic equations suitable for computer solving.

[0076] The parameter setting module is used to set the total simulation duration and number of time steps, and to set the initial conditions and chamber surface boundary conditions according to the simulation task environment and the nature of the heart itself.

[0077] The orientation determination module is used to determine the orientation of myocardial fibers at any point in the computational grid based on the three-dimensional geometry of the heart. This can be achieved by estimating based on physiological and anatomical data or by using an interpolation method based on heart geometry.

[0078] The myocardial stress calculation module is used to calculate the deformation and stress distribution of each element at each time step, based on the myocardial displacement and velocity obtained in the previous time step, using nonlinear elastic theory and combined with a nonlinear anisotropic elastic dynamics model.

[0079] The equation solving module is used to substitute the calculated deformation and stress distribution into the discrete equation system, and use the Newton-Krylov-Schwarz method to solve the algebraic equation system to obtain the updated elastic dynamic state of myocardial tissue.

[0080] The simulation result output module is used to output and save the simulation results of the current time step. The simulation results represent the displacement and velocity of all nodes of the heart finite element mesh at the current moment, obtain the shape of the heart at the current moment, and calculate the deformation and stress magnitude at any position of the myocardium. The simulation ends when all time step calculations are completed.

[0081] In addition, to achieve the above objectives, the present invention also provides a terminal, wherein the terminal includes: a memory, a processor, and a high-performance cardiac biomechanical numerical simulation program stored in the memory and executable on the processor, wherein when the high-performance cardiac biomechanical numerical simulation program is executed by the processor, it implements the steps of the high-performance cardiac biomechanical numerical simulation method as described above.

[0082] Furthermore, to achieve the above objectives, the present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a high-performance cardiac biomechanical numerical simulation program, which, when executed by a processor, implements the steps of the high-performance cardiac biomechanical numerical simulation method as described above.

[0083] In this invention, high-resolution medical image data is acquired, and a three-dimensional myocardial geometric model is generated based on the high-resolution medical image data using image segmentation and geometric reconstruction. Based on the three-dimensional myocardial geometric model, a tetrahedral unstructured mesh is generated using mesh generation software, and the mesh is then subdivided. Based on elasticity theory, a nonlinear anisotropic elastic dynamics model describing myocardial motion is established according to the structural characteristics of myocardial tissue. The equations of the cardiac nonlinear anisotropic elastic dynamics model are numerically discretized using the finite element method to obtain a set of algebraic equations suitable for computer solution. The total simulation duration and number of time steps are set, and initial conditions and chamber surface boundary conditions are set according to the simulation task environment and the properties of the heart itself. The direction of myocardial fibers at any point in the computational mesh is determined based on the three-dimensional geometric structure of the heart. The simulation is achieved by estimating the data from the profiling data or using interpolation methods based on cardiac geometry. Within each time step, based on the myocardial displacement and velocity obtained from the previous time step, the deformation and stress distribution of each element at the current moment are calculated using nonlinear elasticity theory combined with a nonlinear anisotropic elastic dynamics model. The calculated deformation and stress distribution are substituted into a discrete equation system, and the Newton-Krylov-Schwarz method is used to solve the algebraic equation system to obtain the updated elastic dynamic state of the myocardial tissue. The simulation results for the current time step are output and saved. These results represent the displacement and velocity of all nodes in the cardiac finite element mesh at the current moment, obtaining the shape of the heart at the current moment. The deformation and stress magnitude at any location of the myocardium are also calculated. The simulation ends after all time step calculations are completed. This invention, through an optimized parallel computing strategy, supports simulation calculations on meshes of tens of millions to hundreds of millions of elements using tens of thousands of computing cores on a supercomputing platform. This significantly improves simulation accuracy and speed, effectively reduces computation time, saves computing resources, and supports higher spatial resolution. It fully utilizes high-performance computing platforms to support accurate simulation of myocardial mechanical behavior under physiological and various pathological conditions. Attached Figure Description

[0084] Figure 1 This is a flowchart of a preferred embodiment of the high-performance cardiac biomechanics numerical simulation method of the present invention;

[0085] Figure 2 This is a flowchart of the parallel simulation steps based on the Newton-Krylov-Schwarz method using an unstructured mesh, in a preferred embodiment of the high-performance cardiac biomechanics numerical simulation method of the present invention.

[0086] Figure 3 This is a schematic diagram of a three-dimensional geometric model of the human heart reconstructed from medical images in a preferred embodiment of the high-performance cardiac biomechanical numerical simulation method of the present invention.

[0087] Figure 4This is a schematic diagram of the cardiac unstructured mesh (right) and domain decomposition (left) in a preferred embodiment of the high-performance cardiac biomechanical numerical simulation method of the present invention;

[0088] Figure 5 This is a schematic diagram of the simulation results of cardiac deformation at several typical moments within a cardiac cycle in a preferred embodiment of the high-performance cardiac biomechanics numerical simulation method of the present invention.

[0089] Figure 6 This is a schematic diagram illustrating the computation time of large-scale parallel simulation testing in a preferred embodiment of the high-performance cardiac biomechanics numerical simulation method of the present invention.

[0090] Figure 7 This is a schematic diagram illustrating the parallel efficiency of large-scale parallel simulation testing in a preferred embodiment of the high-performance cardiac biomechanics numerical simulation method of the present invention.

[0091] Figure 8 This is a structural diagram of a preferred embodiment of the high-performance cardiac biomechanics numerical simulation system of the present invention;

[0092] Figure 9 This is a structural diagram of a preferred embodiment of the terminal of the present invention. Detailed Implementation

[0093] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0094] The purpose of this invention is to provide a high-performance numerical simulation method for solving nonlinear elastic dynamics models of myocardium. Through an optimized parallel computing strategy, it supports simulation calculations on a supercomputing platform using tens of thousands of computing cores across meshes with tens of millions to hundreds of millions of cells, significantly improving simulation accuracy and speed to support accurate simulation of myocardial mechanical behavior under physiological and various pathological conditions. To this end, this invention introduces a domain decomposition strategy to optimize the parallel computing method, thereby ensuring the efficiency of parallel computing when solving large-scale problems. This method effectively reduces computation time, saves computing resources, supports higher spatial resolution, and fully utilizes high-performance computing platforms, providing scientific support for strategy optimization.

[0095] The high-performance cardiac biomechanics numerical simulation method described in the preferred embodiment of the present invention, such as... Figure 1 and Figure 2 As shown, the high-performance cardiac biomechanics numerical simulation method includes the following steps:

[0096] Step S10: Acquire high-resolution medical image data, and generate a three-dimensional myocardial geometric model based on the high-resolution medical image data using image segmentation and geometric reconstruction.

[0097] Specifically, based on high-resolution medical imaging data, a three-dimensional myocardial geometric model is generated using image segmentation and geometric reconstruction techniques (treating the myocardium as an anisotropic elastic material and determining initial parameters and boundary conditions). This model is then subjected to necessary smoothing to obtain a model that more closely resembles the actual anatomical structure, providing an accurate geometric basis for subsequent simulations. During the construction process, the anatomical details and fiber orientation of the myocardial structure are realized based on cardiac geometric features and data interpolation methods, ensuring the model's accuracy. The constructed geometric model will serve as the basis for myocardial biomechanical analysis in numerical simulations.

[0098] Step S20: Based on the three-dimensional myocardial geometry model, generate a tetrahedral unstructured mesh using mesh generation software, and then perform mesh subdivision.

[0099] Specifically, such as Figure 3 As shown, based on the three-dimensional myocardial geometry model, a tetrahedral unstructured mesh is generated using an adaptive refinement method through mesh generation software to improve computational accuracy in the lesion region. A three-dimensional finite element mesh of the myocardial tissue is generated using the same software to adapt to complex myocardial geometry, providing a high-resolution spatial discretization basis for subsequent simulations. This mesh generation technology can not only handle complex geometric structures but also supports flexible adjustment of different resolutions. On the supercomputing platform, computing node resources are allocated, with each node creating an independent computing process. A graph-based multi-level partitioning strategy is used in the main process, achieving efficient three-dimensional unstructured mesh partitioning through local equilibrium and minimum cut optimization. First, a set of non-overlapping sub-regions is obtained. Then, by mutually expanding the elements of adjacent sub-regions, overlapping sub-regions are obtained. The main process sends the sub-region meshes to other computing processes. Based on the overlapping portions between the sub-region meshes, data synchronization rules between adjacent sub-regions are determined. Let N be the total number of nodes in the mesh. V The number of sub-regions after partitioning (same as the number of computational cores) is n. p And assume that the number of overlapping unit layers between adjacent sub-regions is δ.

[0100] Step S30: Based on the theory of elasticity, establish a nonlinear anisotropic elastic dynamics model to describe myocardial motion according to the structural characteristics of myocardial tissue.

[0101] Specifically, based on the myocardial fibers and layered structure, a nonlinear anisotropic elastic dynamics model is constructed. This model considers the directional properties of the myocardium and emphasizes the different stress-strain relationships between myocardial fibers and transverse fibers to accurately reflect the mechanical response under various loading conditions. According to the principles of elastic dynamics, the displacement d and velocity v at any point in the cardiac tissue satisfy the following equations at any time:

[0102]

[0103] in, Let P represent the gradient, where P represents the first Piola-Kirchhoff stress currently experienced, derived from the deformation gradient of the myocardium at the current moment. The decision is as follows: Ω represents the space occupied by the myocardial tissue, ρ represents the material density of the myocardial tissue, and T represents the termination time of the simulation.

[0104] Step S40: Use the finite element method to numerically discretize the equations of the nonlinear anisotropic elastic dynamics model of the heart, and obtain a set of algebraic equations suitable for computer solution.

[0105] Specifically, the model is discretized spatially using the finite element method and temporally using the backward Euler method, transforming the original infinite-dimensional partial differential equations into a system of finite-dimensional algebraic equations. Based on the principles of the finite element method, the following variational form is considered:

[0106]

[0107] in, The generalized function representing the elastic dynamic energy is expressed in the following form:

[0108]

[0109] Where X represents the spatial independent variable, Let these represent the discrete displacement function and discrete velocity function at the representative nth time step. Finite element mesh node values ​​of displacement and velocity With basis function {φ i} i = 1, 2, ..., N V Definition of expansion form:

[0110]

[0111] Where Δt represents the simulation time step, N represents the test function. V This indicates the total number of nodes contained in the computational grid.

[0112] By By replacing each basis function one by one and calculating the numerical integral, the original differential equation is transformed into a system of algebraic equations. This completes the numerical discretization. After discretization, the unknowns to be solved are a finite set of nodal values.

[0113] In a high-performance computing environment, each computing core executes computing tasks by creating an independent process. The main process reads the mesh file, divides the mesh into regions, and assigns each sub-region to a different computing process. This region decomposition strategy ensures efficient parallelization of the computing process.

[0114] Each sub-region generates corresponding ghost cells based on the initial and boundary conditions set in the model, initializes the node information of each mesh cell (including center point position, area, normal vector and adjacent cell information), and allocates a buffer to handle inter-process data exchange.

[0115] Step S50: Set the total simulation duration and number of time steps. Based on the simulation task environment and the nature of the heart itself, set the initial conditions and chamber surface boundary conditions.

[0116] Specifically, the total simulation duration and number of time steps are set. Based on the simulation task environment and the properties of the heart itself, initial conditions and chamber surface boundary conditions are set (the purpose is to reflect the properties of the simulated object and the simulation environment), including the initial stress and strain distribution of the myocardium and the load conditions of the inner and outer surfaces of the heart chambers. The initial conditions are determined by cardiac physiological parameters and pathological characteristics, while the chamber surface boundary conditions are determined by the pressure distribution data in the early stage of the simulation, ensuring that the initial state of the simulation is close to the real myocardial state.

[0117] Based on the simulation scenario, the initial state of the myocardial biomechanics model is set, including the initial position, displacement, stress and strain distribution, to ensure that the initial distribution of physical quantities in each sub-region conforms to the set physiological or pathological state.

[0118] Step S60: Determine the direction of myocardial fibers at any point in the computational grid based on the three-dimensional geometry of the heart, and estimate it based on physiological and anatomical data or use an interpolation method based on heart geometry.

[0119] Specifically, the direction of myocardial fibers at any point in the computational grid is determined based on the three-dimensional geometry of the heart. This can be estimated based on physiological and anatomical data or achieved using methods such as interpolation based on cardiac geometry.

[0120] Step S70: In each time step, based on the myocardial displacement and velocity obtained in the previous time step, use nonlinear elasticity theory and combine it with a nonlinear anisotropic elastic dynamics model to calculate the deformation and stress distribution of each element at the current moment.

[0121] Specifically, within each time step, based on the myocardial displacement and velocity obtained from the previous time step, the deformation and stress distribution of each element at the current moment are calculated using nonlinear elasticity theory combined with a nonlinear anisotropic elastic dynamics model. The steps are as follows:

[0122] (1) Calculate the gradient tensor of the displacement

[0123] (2) Calculate the deformation gradient tensor Where I represents the second-order unit tensor;

[0124] (3) Calculate the Green-Lagrange strain tensor E, which represents the magnitude of myocardial deformation:

[0125]

[0126] (4) Construct a local rectangular coordinate system within the unit. The three coordinates of the local rectangular coordinate system are orthogonal to each other, and the first coordinate axis must coincide with the direction of the myocardial fibers of the unit.

[0127] (5) Calculation:

[0128]

[0129] Where Q represents a number, and each E ij This represents the component value of the strain tensor E measured in the element's local coordinate system, b. f b t b fs These represent model parameters, which respectively represent the overall stiffness of the material and the stiffness along each fiber axis;

[0130] (6) Calculate the determinant J = detF of tensor F;

[0131] (7) Calculate the passive stress S caused by myocardial deformation. p :

[0132] S p =Ce Q A*E+κln JC -1 ;

[0133] Where C represents the basic stiffness of myocardial tissue, κ represents the incompressibility coefficient of myocardial tissue, the operator * indicates the element-wise multiplication of the matrix, and the material parameter matrix A is defined as:

[0134]

[0135] (8) Calculate the active stress S caused by spontaneous contraction of the myocardium. a :

[0136]

[0137] Among them, T a denoted by , where represents the intensity of active contractile stress, and f represents a unit vector along the direction of myocardial fibers;

[0138] (9) Calculate the second Piola-Kirchhoff stress tensor S:

[0139] S = S a +S p ;

[0140] (10) Calculate the first Piola-Kirchhoff stress tensor P:

[0141] P = FS.

[0142] Step S80: Substitute the calculated deformation and stress distribution into the discrete equation system, and use the Newton-Krylov-Schwarz method to solve the algebraic equation system to obtain the updated elastic dynamic state of the myocardial tissue.

[0143] Specifically, within each time step, according to the finite element discretization scheme, the stress data of all elements in the mesh obtained from the calculation are substituted to form a system of nonlinear algebraic equations. That is, within each time step, according to the finite element discretization scheme of step S40, the stress data of all elements in the mesh obtained from step S70 are substituted to form a large-scale nonlinear equation system:

[0144]

[0145] in, This represents the set of all unknowns to be solved in the system.

[0146] Next, the Newton-Krylov-Schwarz method is used to solve the system of nonlinear algebraic equations:

[0147] Using the Newton method, a system of nonlinear algebraic equations is transformed into a series of linear equations that are solved sequentially. The solutions from the previous step are used to construct the coefficient matrix of the next system of equations. Each linear equation is generally represented as:

[0148] Ax = b;

[0149] Wherein, the right-hand vector Given an initial conjecture solution The calculation shows that A represents the coefficient matrix obtained by linearization;

[0150] Using the Krylov subspace method and a parallel computing model, the linear equation system Ax = b is solved iteratively. Data communication is performed between adjacent sub-regions based on the grid partitioning structure and synchronization rules.

[0151] Based on the obtained mesh partitioning structure, construct the Schwarz preprocessing operator M for solving Ax = b. -1 This accelerates the convergence speed of solving linear equation systems. Each computational process constructs and solves subproblems on its own sub-region grid, and the results are obtained through integration.

[0152]

[0153] in, This describes the process of solving a problem for a subregion. and Let represent two projection operators that project any vector defined over the entire region onto a non-overlapping subregion and a subregion with δ-layer overlapping units, respectively. The transpose of represents the corresponding extended operator;

[0154] The preprocessor M obtained by construction -1 Integrating into the iterative solution of Ax = b in the Krylov subspace, the original problem is transformed into solving the following system of equations:

[0155] (AM -1 (Mx) = b;

[0156] The preprocessed system of equations has the same solution as the original system of equations, and the condition number is greatly reduced, so the number of iterations required to solve the problem using the Krylolv subspace method can be significantly reduced.

[0157] At each time step, based on the anisotropic properties of the model, the stress and strain distribution within each grid cell is calculated and substituted into a discrete set of equations. The Newton-Krylov-Schwarz method is used to solve the algebraic equations to obtain the updated elastic dynamic state of the myocardial tissue. In a parallel computing environment, each process exchanges data with processes in neighboring sub-regions according to a domain decomposition strategy, updating the information of boundary cells to ensure the continuity of mechanical information.

[0158] Step S90: Output and save the simulation results of the current time step. The simulation results represent the displacement and velocity of all nodes of the heart finite element mesh at the current moment, obtain the shape of the heart at the current moment, and calculate the deformation and stress magnitude at any position of the myocardium. The simulation ends when all time step calculations are completed.

[0159] Specifically, the simulation results for the current time step are output and saved (stress data can be considered intermediate data; they are calculated to construct discrete equations, and the solution obtained by solving these discrete equations is the simulation result). This includes the displacement and velocity of all nodes in the heart's finite element mesh at the current moment, obtaining the heart's shape at that moment. Based on this, the deformation and stress magnitude at any location of the myocardium can be calculated. The simulation checks whether all time steps have been calculated. If all time steps have been completed, the simulation program terminates; otherwise, it continues execution until all time steps have been calculated.

[0160] like Figure 3 and Figure 4 As shown, human cardiac CT images are imported into geometric reconstruction software and mesh generation software to generate unstructured tetrahedral conformal meshes, and the mesh files are exported. Boundary conditions are set: blood pressure is set on the inner surface of the heart, and motion inhibition is set on the outer surface. The distribution of myocardial fibers is set, the initial displacement and initial velocity of the myocardium are set, the number of parallel execution processes is set to 1024, and the total simulation time is set. Parallel computation begins, and the simulation results of the current time step are output after each time step is completed. Figure 5 The deformation of the heart at several typical moments within a cardiac cycle is presented. To test parallel performance, this invention was tested on a supercomputer at a national supercomputing center. Three meshes with different numbers of cells (Mesh1, Mesh2, and Mesh3) were used, with corresponding simulation unknowns of 36,104,852, 127,038,200, and 235,341,978, respectively. The parallel speedup and efficiency are shown below. Figure 6 and Figure 7 As shown.

[0161] The key points of this invention are as follows:

[0162] (1) This invention proposes a numerical simulation method for heart deformation based on biomechanical theory. Its innovation lies in using an unstructured mesh based on the three-dimensional geometry of the real human heart, and employing the finite element method and backward Euler method to spatiotemporally discretize the model equations. On this basis, a domain decomposition strategy is adopted, and the Newton-Krylov-Schwarz method is used to solve the discretized nonlinear algebraic equations using high-performance parallel computation, thereby obtaining the deformation process of the heart under physiological and pathological conditions.

[0163] (2) Based on the unstructured grid parallel computing region division, and based on the overlapping parts between the grids of each sub-region, the data synchronization rules between adjacent sub-regions are determined. Its innovation lies in the use of a multi-level partitioning strategy based on graph theory. Through local balance and minimum cutting optimization methods, efficient three-dimensional unstructured grid partitioning is achieved, ensuring the parallel efficiency of large-scale flow field grid partitioning.

[0164] (3) At each time step, the Newton method is used to transform the nonlinear equation system into a series of linear equation systems, and the Krylov subspace iteration method is used to solve each linear equation system. Based on this, a domain decomposition strategy is adopted to construct a Schwarz preprocessor to act on the Krylov subspace iteration method, which greatly accelerates the computational convergence process and maintains good parallel efficiency.

[0165] (4) Based on the above theory, numerical equation programs are written for supercomputer hardware architecture and software environment. By generating a computing grid and executing numerical algorithms in parallel, the biomechanical elastic deformation simulation results of the heart under physiological and pathological conditions are obtained.

[0166] Existing numerical simulation techniques for human cardiac biomechanics suffer from limitations in accuracy and computational efficiency, making it difficult to efficiently simulate myocardial biomechanical behavior under complex pathological conditions. The advantages of this proposed solution are as follows:

[0167] (1) Based on human medical image modeling, it can be used to simulate the high-fidelity geometric structure of the human heart.

[0168] (2) This invention provides a parallel algorithm for human heart biomechanics using the three-dimensional unstructured mesh finite element method, which can be used to simulate the deformation process of the heart under various physiological and pathological conditions.

[0169] (3) Compared with traditional simulation methods, this invention is based on unstructured grids and adopts the Newton-Krylov-Schwarz large-scale parallel computing method based on domain decomposition. It supports numerical calculations using more than 10,000 computing cores and hundreds of millions of unknown computing grids, which can achieve high-precision and high-efficiency simulation of human heart biomechanics.

[0170] Furthermore, such as Figure 8 As shown, based on the above-mentioned high-performance cardiac biomechanical numerical simulation method, the present invention also provides a high-performance cardiac biomechanical numerical simulation system, wherein the high-performance cardiac biomechanical numerical simulation system includes:

[0171] The geometric model construction module 51 is used to acquire high-resolution medical image data and generate a three-dimensional myocardial geometric model based on the high-resolution medical image data using image segmentation and geometric reconstruction.

[0172] The mesh processing module 52 is used to generate a tetrahedral unstructured mesh based on the three-dimensional myocardial geometry model using mesh generation software, and to perform mesh subdivision.

[0173] The dynamic model construction module 53 is used to establish a nonlinear anisotropic elastic dynamic model describing myocardial motion based on the theory of elasticity and the structural characteristics of myocardial tissue.

[0174] The numerical discretization module 54 is used to numerically discretize the equations of the nonlinear anisotropic elastic dynamics model of the heart using the finite element method, so as to obtain a set of algebraic equations suitable for computer solving.

[0175] The parameter setting module 55 is used to set the total simulation duration and number of time steps, and to set the initial conditions and chamber surface boundary conditions according to the simulation task environment and the nature of the heart itself.

[0176] The orientation determination module 56 is used to determine the orientation of myocardial fibers at any point in the computational grid based on the three-dimensional geometry of the heart, which is estimated based on physiological and anatomical data or implemented using an interpolation method based on heart geometry.

[0177] The myocardial stress calculation module 57 is used to calculate the deformation and stress distribution of each element at the current time step based on the myocardial displacement and velocity obtained in the previous time step, using nonlinear elastic theory and combined with a nonlinear anisotropic elastic dynamics model.

[0178] The equation solving module 58 is used to substitute the calculated deformation and stress distribution into the discrete equation system, and use the Newton-Krylov-Schwarz method to solve the algebraic equation system to obtain the updated elastic dynamic state of myocardial tissue.

[0179] The simulation result output module 59 is used to output and save the simulation results of the current time step. The simulation results represent the displacement and velocity of all nodes of the heart finite element mesh at the current moment, obtain the shape of the heart at the current moment, and calculate the deformation and stress magnitude at any position of the myocardium. The simulation ends when all time step calculations are completed.

[0180] Furthermore, such as Figure 9 As shown, based on the above-mentioned high-performance cardiac biomechanics numerical simulation method and system, the present invention also provides a terminal, which includes a processor 10, a memory 20 and a display 30. Figure 9 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0181] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc. Further, the memory 20 may include both internal and external storage devices. The memory 20 is used to store application software and various types of data installed on the terminal, such as program code installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output. In one embodiment, the memory 20 stores a high-performance cardiac biomechanical numerical simulation program 40, which can be executed by the processor 10 to implement the high-performance cardiac biomechanical numerical simulation method of this application.

[0182] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as executing the high-performance cardiac biomechanical numerical simulation method.

[0183] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. The display 30 is used to display information on the terminal and to display a visual user interface. The components 10-30 of the terminal communicate with each other via a system bus.

[0184] In one embodiment, when the processor 10 executes the high-performance cardiac biomechanical numerical simulation program 40 in the memory 20, it implements the steps of the high-performance cardiac biomechanical numerical simulation method described above.

[0185] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a high-performance cardiac biomechanical numerical simulation program, which, when executed by a processor, implements the steps of the high-performance cardiac biomechanical numerical simulation method as described above.

[0186] In summary, this invention provides a high-performance numerical simulation method, system, terminal, and storage medium for cardiac biomechanics. The method includes: acquiring high-resolution medical image data; generating a three-dimensional myocardial geometric model based on the high-resolution medical image data using image segmentation and geometric reconstruction; generating a tetrahedral unstructured mesh based on the three-dimensional myocardial geometric model using mesh generation software and performing mesh subdivision; establishing a nonlinear anisotropic elastic dynamics model describing myocardial motion based on elasticity theory and the structural characteristics of myocardial tissue; numerically discretizing the equations of the cardiac nonlinear anisotropic elastic dynamics model using the finite element method to obtain a set of algebraic equations suitable for computer solution; setting the total simulation duration and number of time steps; setting initial conditions and chamber surface boundary conditions based on the simulation task environment and the properties of the heart itself; and determining the three-dimensional geometric structure of the heart. The orientation of myocardial fibers at any point in the computational mesh is estimated based on physiological and anatomical data or achieved using interpolation methods based on cardiac geometry. Within each time step, based on the myocardial displacement and velocity obtained from the previous time step, the deformation and stress distribution of each element at the current moment are calculated using nonlinear elasticity theory combined with a nonlinear anisotropic elastic dynamics model. The calculated deformation and stress distribution are substituted into a discrete equation system, and the Newton-Krylov-Schwarz method is used to solve the algebraic equation system to obtain the updated elastic dynamic state of the myocardial tissue. The simulation results of the current time step are output and saved, representing the displacement and velocity of all nodes in the cardiac finite element mesh at the current moment, obtaining the shape of the heart at the current moment, and calculating the deformation and stress magnitude at any location of the myocardium. The simulation ends after all time step calculations are completed. This invention, through an optimized parallel computing strategy, supports simulation calculations on meshes of tens of millions to hundreds of millions of elements using tens of thousands of computing cores on a supercomputing platform, significantly improving simulation accuracy and speed, effectively reducing computation time, saving computational resources, and supporting higher spatial resolution. It fully utilizes high-performance computing platforms to support accurate simulation of myocardial mechanical behavior under physiological and various pathological conditions.

[0187] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal that includes that element.

[0188] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The computer-readable storage medium can be a memory, magnetic disk, optical disk, etc.

[0189] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A high-performance numerical simulation method for cardiac biomechanics, characterized in that, The high-performance cardiac biomechanics numerical simulation method includes: Acquire high-resolution medical image data, and generate a three-dimensional myocardial geometric model based on the high-resolution medical image data using image segmentation and geometric reconstruction. Based on the aforementioned three-dimensional myocardial geometry model, a tetrahedral unstructured mesh is generated using mesh generation software, and then mesh subdivision is performed. Based on the theory of elasticity, a nonlinear anisotropic elastic dynamics model describing myocardial motion is established according to the structural characteristics of myocardial tissue. The finite element method was used to numerically discretize the equations of the nonlinear anisotropic elastic dynamics model of the heart, resulting in a set of algebraic equations suitable for computer solving. Set the total simulation duration and number of time steps, and set the initial conditions and chamber surface boundary conditions according to the simulation task environment and the nature of the heart itself; The direction of myocardial fibers at any point in the computational grid is determined based on the three-dimensional geometry of the heart, and is estimated based on physiological and anatomical data or implemented using an interpolation method based on heart geometry. Within each time step, based on the myocardial displacement and velocity obtained in the previous time step, the deformation and stress distribution of each element at the current moment are calculated using nonlinear elastic theory and combined with a nonlinear anisotropic elastic dynamics model. Substitute the calculated deformation and stress distribution into the discrete equation system, and use the Newton-Krylov-Schwarz method to solve the algebraic equation system to obtain the updated elastic dynamic state of myocardial tissue. Output and save the simulation results of the current time step. The simulation results represent the displacement and velocity of all nodes of the heart finite element mesh at the current moment, obtain the shape of the heart at the current moment, and calculate the deformation and stress magnitude at any position of the myocardium. The simulation ends when all time step calculations are completed.

2. The high-performance cardiac biomechanics numerical simulation method according to claim 1, characterized in that, The step of generating a tetrahedral unstructured mesh based on the three-dimensional myocardial geometric model using mesh generation software and performing mesh subdivision specifically includes: Based on the aforementioned three-dimensional myocardial geometry model, tetrahedral unstructured meshes are generated using an adaptive refinement method via mesh generation software. On the supercomputing platform, computing node resources are allocated, and each node creates an independent computing process. On the main process, a multi-level partitioning strategy based on graph theory is used to achieve efficient 3D unstructured mesh partitioning through local balancing and minimum cut optimization, resulting in a set of non-overlapping sub-regions. By mutually expanding the cells of adjacent sub-regions, overlapping sub-regions are obtained. The main process sends the sub-region mesh to other computing processes, and the data synchronization rules between adjacent sub-regions are determined based on the overlapping parts between the sub-region meshes.

3. The high-performance cardiac biomechanics numerical simulation method according to claim 1, characterized in that, The aforementioned nonlinear anisotropic elastic dynamics model describing myocardial motion, based on the theory of elasticity and the structural characteristics of myocardial tissue, specifically includes: Based on myocardial fibers and layered structure, a nonlinear anisotropic elastic dynamics model is constructed. This nonlinear anisotropic elastic dynamics model takes into account the directional properties of myocardium and emphasizes the different stress-strain relationships of myocardial fibers and transverse fibers to accurately reflect the mechanical response under various loading conditions. According to the principles of elastic dynamics, the displacement d and velocity v of any point in the heart tissue at any given time satisfy the following equation: in, Let P represent the gradient, Ω represent the first Piola-Kirchhoff stress currently applied, ρ represent the space occupied by the myocardial tissue, ρ represent the material density of the myocardial tissue, and T represent the simulation termination time.

4. The high-performance cardiac biomechanics numerical simulation method according to claim 3, characterized in that, The method of numerically discretizing the equations of the nonlinear anisotropic elastic dynamics model of the heart using the finite element method yields a set of algebraic equations suitable for computer solving, specifically including: Based on the principles of the finite element method, consider the following variational form: in, The generalized function representing the elastic dynamic energy is expressed in the following form: Where X represents the spatial independent variable, Let these represent the discrete displacement function and discrete velocity function at the representative nth time step. Finite element mesh node values ​​of displacement and velocity With basis function {φ i }i=1,2,...,N V Definition of the expansion form: Where Δt represents the simulation time step, N represents the test function. V This indicates the total number of nodes contained in the computational grid; By By replacing each basis function one by one and calculating the numerical integral, the original differential equation is transformed into a system of algebraic equations, thus completing the numerical discretization. After discretization, the unknowns to be solved are a finite set of nodal values.

5. The high-performance cardiac biomechanics numerical simulation method according to claim 1, characterized in that, The initial conditions are determined by cardiac physiological parameters and pathological characteristics, and the chamber surface boundary conditions are determined by pressure distribution data from the initial stage of simulation.

6. The high-performance cardiac biomechanics numerical simulation method according to claim 1, characterized in that, Within each time step, based on the myocardial displacement and velocity obtained from the previous time step, the deformation and stress distribution of each element at the current moment are calculated using nonlinear elasticity theory combined with a nonlinear anisotropic elastic dynamics model. Specifically, this includes: Calculate the gradient tensor of the displacement Calculate the deformation gradient tensor Where I represents the second-order unit tensor; Calculate the Green-Lagrange strain tensor E, which represents the magnitude of myocardial deformation: Construct a local rectangular coordinate system within the unit, wherein the three coordinates of the local rectangular coordinate system are mutually orthogonal, and the first coordinate axis must coincide with the direction of the myocardial fibers of the unit; calculate: Where Q represents a number, and each E ij This represents the component value of the strain tensor E measured in the element's local coordinate system, b. f b t b fs These represent model parameters, which respectively represent the overall stiffness of the material and the stiffness along each fiber axis; Calculate the determinant J = detF of tensor F; Calculate the passive stress S caused by myocardial deformation p : S p =What Q A*E+κln JC -1 ; Where C represents the basic stiffness of myocardial tissue, κ represents the incompressibility coefficient of myocardial tissue, the operator * indicates the element-wise multiplication of the matrix, and the material parameter matrix A is defined as: Calculate the active stress S caused by spontaneous contraction of the myocardium. a : Among them, T a denoted by , where represents the intensity of active contractile stress, and f represents a unit vector along the direction of myocardial fibers; Calculate the second Piola-Kirchhoff stress tensor S: S=S a +S p ; Calculate the first Piola-Kirchhoff stress tensor P: P = FS.

7. The high-performance cardiac biomechanics numerical simulation method according to claim 1, characterized in that, The process involves substituting the calculated deformation and stress distribution into a discrete system of equations, and then using the Newton-Krylov-Schwarz method to solve the algebraic equations to obtain the updated elastic dynamic state of the myocardial tissue. Specifically, this includes: Within each time step, based on the finite element discretization scheme, the stress data of all elements in the calculated mesh are substituted to form a system of nonlinear algebraic equations: in, This represents the set of all unknowns to be solved in the system. Solving systems of nonlinear algebraic equations using the Newton-Krylov-Schwarz method: Using the Newton method, a system of nonlinear algebraic equations is transformed into a series of linear equations that are solved sequentially. The solutions from the previous step are used to construct the coefficient matrix of the next system of equations. Each linear equation is generally represented as: Ax = b. Wherein, the right-hand vector Given an initial conjecture solution The calculation shows that A represents the coefficient matrix obtained by linearization; Using the Krylov subspace method and a parallel computing model, the linear equation system Ax = b is solved iteratively. Data communication is performed between adjacent sub-regions based on the grid partitioning structure and synchronization rules. Based on the obtained mesh partitioning structure, construct the Schwarz preprocessing operator M for solving Ax = b. -1 This accelerates the convergence speed of solving linear equation systems. Each computational process constructs and solves subproblems on its own sub-region grid, and the results are obtained through integration. in, This describes the process of solving a problem for a subregion. and Let represent two projection operators that project any vector defined over the entire region onto a non-overlapping subregion and a subregion with δ-layer overlapping units, respectively. The transpose of represents the corresponding extended operator; The preprocessor M obtained by construction -1 Integrating into the iterative solution of Ax = b in the Krylov subspace, the original problem is transformed into solving the following system of equations: (AM -1 )(Mx)=b; The preprocessed system of equations has the same solution as the original system of equations.

8. A high-performance numerical simulation system for cardiac biomechanics, characterized in that, The high-performance cardiac biomechanics numerical simulation system includes: A geometric model construction module is used to acquire high-resolution medical image data and generate a three-dimensional myocardial geometric model based on the high-resolution medical image data using image segmentation and geometric reconstruction. The mesh processing module is used to generate a tetrahedral unstructured mesh based on the three-dimensional myocardial geometry model using mesh generation software, and to perform mesh subdivision. The dynamic model construction module is used to establish a nonlinear anisotropic elastic dynamic model describing myocardial motion based on the theory of elasticity and the structural characteristics of myocardial tissue. The numerical discretization module is used to numerically discretize the equations of the nonlinear anisotropic elastic dynamics model of the heart using the finite element method, and obtain a set of algebraic equations suitable for computer solving. The parameter setting module is used to set the total simulation duration and number of time steps, and to set the initial conditions and chamber surface boundary conditions according to the simulation task environment and the nature of the heart itself. The orientation determination module is used to determine the orientation of myocardial fibers at any point in the computational grid based on the three-dimensional geometry of the heart. This can be achieved by estimating based on physiological and anatomical data or by using an interpolation method based on heart geometry. The myocardial stress calculation module is used to calculate the deformation and stress distribution of each element at each time step, based on the myocardial displacement and velocity obtained in the previous time step, using nonlinear elastic theory and combined with a nonlinear anisotropic elastic dynamics model. The equation solving module is used to substitute the calculated deformation and stress distribution into the discrete equation system, and use the Newton-Krylov-Schwarz method to solve the algebraic equation system to obtain the updated elastic dynamic state of myocardial tissue. The simulation result output module is used to output and save the simulation results of the current time step. The simulation results represent the displacement and velocity of all nodes of the heart finite element mesh at the current moment, obtain the shape of the heart at the current moment, and calculate the deformation and stress magnitude at any position of the myocardium. The simulation ends when all time step calculations are completed.

9. A terminal, characterized in that, The terminal includes: a memory, a processor, and a high-performance cardiac biomechanical numerical simulation program stored in the memory and executable on the processor. When the high-performance cardiac biomechanical numerical simulation program is executed by the processor, it implements the steps of the high-performance cardiac biomechanical numerical simulation method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a high-performance cardiac biomechanical numerical simulation program, which, when executed by a processor, implements the steps of the high-performance cardiac biomechanical numerical simulation method as described in any one of claims 1-7.

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