Rapid myocardial material parameter estimation method based on deep neural network

Abstract

The invention relates to the technical field of myocardial material parameter estimation, in particular to a rapid myocardial material parameter estimation method based on a deep neural network. The method comprises the following steps: reconstructing a three-dimensional closed surface of left ventricular myocardium based on a left ventricular myocardium image obtained by segmentation; the method comprises the following steps: carrying out myocardial material modeling, describing a nonlinear elastic behavior of a myocardial by the model based on a myocardial microstructure, carrying out inverse finite element analysis, and optimizing eight material parameters in a Holzapfel-Ogden constitutive model in combination with an iterative optimization algorithm; a high-confidence reference standard is generated through a simulation optimization process and used for training a deep neural network model, left ventricle three-dimensional point cloud data is processed by adopting a DGCNN graph neural network so as to learn a mapping relation between a myocardial geometrical morphology and a material parameter, and a rapid myocardial material parameter estimation model is obtained. According to the method, myocardial material parameter prediction can be completed in an extremely short time, so that the feasibility of clinical application is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of myocardial material parameter estimation, and particularly to a method for rapidly estimating myocardial material parameters based on a deep neural network. Background Art

[0002] Myocardial material parameters are important indicators for evaluating the biomechanical properties of the heart and are of great significance for studying the physiological mechanisms of myocardial lesions and formulating personalized treatment plans. Currently, the most commonly used parameter estimation method is based on inverse finite element (Inverse FE), which inversely calculates the material parameters of the myocardium through non-linear optimization iteration. However, this method has a high computational complexity, relies on expensive high-performance computing resources, and has a long calculation time, making it difficult to meet the real-time requirements of clinical applications.

[0003] In recent years, deep learning has made remarkable progress in the fields of medical image processing and computational modeling, and can efficiently learn complex biomechanical relationships through data-driven methods. Although existing research has explored the application of deep learning in cardiac finite element simulations, there is still a lack of an effective method for directly and rapidly estimating myocardial material parameters from routine cardiac magnetic resonance imaging (CMRI) data.

[0004] Therefore, there is an urgent need for an efficient, accurate and low-cost algorithm for estimating myocardial material parameters to promote the application of this technology in medical image analysis and personalized cardiovascular diagnosis and treatment. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for rapidly estimating myocardial material parameters based on a deep neural network: to solve the problems in the prior art that the calculation complexity is high, high-performance computing resources are occupied, and the calculation time is long due to the use of non-linear optimization iteration to inversely calculate myocardial material parameters, making it difficult to meet the real-time requirements of clinical applications.

[0006] The purpose of the present invention can be achieved by the following technical solutions:

[0007] A method for rapidly estimating myocardial material parameters based on a deep neural network, the method comprising:

[0008] Using a deep neural network to perform image segmentation on short-axis cardiac magnetic resonance images to obtain the left ventricular myocardial region; based on the segmented left ventricular myocardial images, using the Marching Cubes algorithm to reconstruct the three-dimensional closed surface of the left ventricular myocardium; based on a registration method, aligning the reconstructed three-dimensional left ventricular structure with a left ventricular template that has been pre-divided into hexahedral meshes to provide a geometric structure for subsequent analysis;

[0009] The Holzapfel-Ogden constitutive model is used for myocardial material modeling. This model describes the non-linear elastic behavior of the myocardium based on its microstructure. Inverse finite element analysis is carried out based on the MATLAB-ABAQUS joint simulation framework. Combining with an iterative optimization algorithm, eight material parameters in the Holzapfel-Ogden constitutive model are optimized. Through the simulation optimization process, a reference standard with high confidence is generated for training the deep neural network model.

[0010] The DGCNN graph neural network is used to process the three-dimensional point cloud data of the left ventricle to learn the mapping relationship between the myocardial geometric morphology and material parameters, and a rapid estimation model of myocardial material parameters is obtained. After training, the new short-axis cardiac magnetic resonance image is input into this model, and the myocardial material parameters are output.

[0011] Furthermore, a convolutional neural network is used to perform image segmentation on the short-axis cardiac magnetic resonance image to obtain the left ventricular myocardial region image, which specifically includes the following process:

[0012] It is assumed that the convolutional neural network consists of K convolutional kernels. The graph mapping module is used to map the short-axis cardiac magnetic resonance image into a topological graph. The nodes in the graph represent different regions in the image, and the edges represent the similarity or relationship between regions.

[0013] The graph pruning technique is used for the topological graph to remove redundant parameters and optimize the graph structure, obtaining a more discriminative weighted undirected graph.

[0014] The similarity of the pruned weighted undirected graph is calculated. The reciprocal of the similarity is the distance between the graphs. Based on the graph distance, the short-axis cardiac magnetic resonance image is segmented to obtain the left ventricular myocardial region image.

[0015] Furthermore, based on the segmented left ventricular myocardial image, the Marching Cubes algorithm is used to reconstruct the three-dimensional closed surface of the left ventricular myocardium, which specifically includes the following process:

[0016] Based on the segmented left ventricular myocardial image, the Marching Cubes algorithm is used to reconstruct the three-dimensional closed surface of the left ventricular myocardium.

[0017] Furthermore, before using the Holzapfel-Ogden constitutive model for myocardial material modeling, the method also includes an individualized left ventricular mesh generation method based on the deformation field registration method:

[0018] Step 1: Perform an affine transformation to perform a preliminary alignment based on the overall morphology of the left ventricular myocardium, including position, scale, and rotation adjustment. The general structure of the template mesh is consistent with the target heart morphology, reducing the error caused by large-scale deformation.

[0019] Step 2: Local registration. Based on the global registration, the free-form deformation method is adopted to make the mesh structure more accurately match the anatomical shape of the individual left ventricle.

[0020] Step 3: Update of mesh node coordinates. After local registration, directly update the node coordinates of the template mesh to match the myocardial shape of the target left ventricle.

[0021] Furthermore, the specific process of myocardial material modeling using the Holzapfel-Ogden constitutive model includes the following:

[0022] The passive properties of the left ventricular myocardium during diastole are described by the Holzapfel-Ogden constitutive model, which is established based on the microscopic structure of the myocardium. Its strain energy function ψ is as follows:

[0023]

[0024] where a, b, a f , b f , a s , b s , a fs , b fs are 8 material parameters to be estimated, which reflect the elastic and anisotropic mechanical properties of the myocardium; I1, I 4f , I 4s , I 8fs are 4 strain invariants used to characterize the deformation state of the myocardial tissue;

[0025] Parameter grouping and scaling: The parameters are divided into two groups: a G ={a, a f , a s , a fs}, b G ={b, b f , b s b fs}. The two groups of parameters are standardized using the scaling factors Ca and Cb to reduce the model complexity:

[0026]

[0027] where and represent the initial parameters of the 8 material parameters.

[0028] Governing equations and boundary conditions: The governing equations of the left ventricle can be described by the mechanical equilibrium equations and boundary conditions:

[0029]

[0030] Among them, σ represents the Cauchy stress tensor, which describes the stress state inside the myocardium; b is the body force density per unit volume; Ω is the computational domain defined by the left ventricular mesh; n is the normal vector of the endocardial surface; p endo represents the left ventricular filling pressure, which is used to simulate the load at the end of diastole; is the Neumann boundary; u z is the displacement of the basal surface in the z direction; represents the Dirichlet boundary;

[0031] Among them, the end-diastolic pressure is set to 8 mmHg, that is, p endo = 8 mmHg, which is used as the loading condition for the finite element simulation.

[0032] Furthermore, inverse finite element analysis is carried out based on the MATLAB-ABAQUS joint simulation framework. Combining with the iterative optimization algorithm, 8 material parameters in the Holzapfel-Ogden constitutive model are optimized. The specific process includes the following:

[0033] Initial simulation: Set the initial parameters of the Holzapfel-Ogden constitutive model, and perform finite element calculation through MATLAB background calling ABAQUS to obtain the left ventricular deformation;

[0034] Error calculation: Compare the error between the left ventricular volume change obtained by finite element calculation and the measurement value of magnetic resonance imaging;

[0035] Parameter update: Use the sequential quadratic programming optimization algorithm to adjust the material parameters to make the simulation results approximate the imaging measurement values;

[0036] Convergence determination: If the error meets the convergence condition, output the final material parameters, otherwise continue the optimization iteration.

[0037] Furthermore, the DGCNN graph neural network is used to process the left ventricular three-dimensional point cloud data to learn the mapping relationship between the myocardial geometric morphology and material parameters, and a rapid estimation model of myocardial material parameters is obtained. The specific content includes the following:

[0038] Network model: Based on the DGCNN graph neural network, it receives the point cloud data corresponding to the closed surface of the left ventricular myocardium in the early diastole and end diastole. Each sample contains point coordinates of (N, 3) dimensions. Based on the point cloud data, a k-nearest neighbor graph is constructed: during the forward propagation of the network, k-nearest neighbors are dynamically calculated for the point cloud data to construct the topological structure of the point cloud. Based on the EdgeConv module, local point features are extracted, and the spatial relationship of the point cloud is learned through convolution operations. Local and global information is aggregated layer by layer to generate a high-dimensional feature representation, and global geometric information is extracted through max pooling to obtain the myocardial microstructure.

[0039] Loss function: Mean Square Error is used to measure the error between the predicted parameters and the true values;

[0040] Optimizer: Adam optimizer;

[0041] Hyperparameter settings: Learning rate: 1e-3 to 1e-8; Batch size: 16, 32, 64; Number of nearest neighbors: k = 10;

[0042] Training device: Core TM i9-14900KF processor, NVIDIA RTX 4090 GPU.

[0043] Compared with the traditional scheme, the beneficial effects achieved by the present invention are:

[0044] The present invention uses a convolutional neural network to perform image segmentation on short-axis cardiac magnetic resonance images to obtain the left ventricular myocardial region; based on the segmented left ventricular myocardial images, the Marching Cubes algorithm is used to reconstruct the three-dimensional closed surface of the left ventricular myocardium; the Holzapfel-Ogden constitutive model is used for myocardial material modeling, and this model describes the nonlinear elastic behavior of the myocardium based on the myocardial microstructure. This method can complete the prediction of myocardial material parameters in an extremely short time, thereby improving the feasibility of clinical applications.

[0045] The traditional finite element method usually relies on a high-performance computing cluster (HPC) for simulation, while the method of the present invention can run on a conventional GPU device, greatly reducing the computing resource requirements and improving the usability. Description of the Drawings

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments recorded in the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings.

[0047] Figure 1 is the workflow diagram of a myocardial material parameter estimation method based on the traditional inverse finite element in an embodiment of the present invention;

[0048] Figure 2 is the workflow diagram of another myocardial material parameter rapid estimation method based on a deep neural network in an embodiment of the present invention. Detailed Embodiments

[0049] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0050] In addition, the described features, structures, or characteristics may be combined in any suitable manner in one or more example embodiments. In the following description, numerous specific details are provided to give a thorough understanding of the example embodiments of the present disclosure. However, those skilled in the art will recognize that the technical solutions of the present disclosure may be practiced without one or more of the specific details, or other methods, components, steps, etc. may be used. In other cases, well-known structures, methods, implementations, or operations are not shown or described in detail to avoid obscuring aspects of the present disclosure.

[0051] This embodiment provides a method for estimating myocardial material parameters based on traditional inverse finite element. Figure 1 It is a flowchart of a method for estimating myocardial material parameters based on traditional inverse finite element in an embodiment of the present invention, as Figure 1 shown. The method includes the following steps:

[0052] Step S101: Use a convolutional neural network to perform image segmentation on short-axis cardiac magnetic resonance images to obtain the left ventricular myocardial region; based on the segmented left ventricular myocardial images, use the Marching Cubes algorithm to reconstruct the three-dimensional closed surface of the left ventricular myocardium.

[0053] Step S102: Based on the registration method, align the reconstructed three-dimensional left ventricular structure with the left ventricular template that has been pre-meshed with hexahedrons to provide a geometric structure for subsequent analysis.

[0054] Step S103: Use the Holzapfel-Ogden constitutive model to perform myocardial material modeling. This model describes the nonlinear elastic behavior of the myocardium based on the myocardial microstructure; perform inverse finite element analysis based on the MATLAB-ABAQUS joint simulation framework, and combine the iterative optimization algorithm to optimize the eight material parameters in the Holzapfel-Ogden constitutive model, thereby obtaining the material parameters of the myocardium.

[0055] In summary, the present invention uses a convolutional neural network to perform image segmentation on short-axis cardiac magnetic resonance images to obtain the left ventricular myocardial region; based on the segmented left ventricular myocardial images, the Marching Cubes algorithm is used to reconstruct the three-dimensional closed surface of the left ventricular myocardium; the Holzapfel-Ogden constitutive model is used for myocardial material modeling, and inverse finite element analysis is performed based on the MATLAB-ABAQUS joint simulation framework. Combining with an iterative optimization algorithm, eight material parameters in the Holzapfel-Ogden constitutive model are optimized, and this method can more accurately complete the prediction of myocardial material parameters.

[0056] In some embodiments, Figure 2 is a flowchart of a method for quickly estimating myocardial material parameters based on a deep neural network according to an embodiment of the present invention. As Figure 2 shown, on the basis of obtaining myocardial material parameters by traditional inverse finite element, using the DGCNN graph neural network to quickly estimate myocardial material parameters specifically includes the following processes:

[0057] Step S201: Generate a reference standard with high confidence through a traditional method for estimating myocardial material parameters based on inverse finite element to train a deep neural network model;

[0058] Step S202: Use the DGCNN graph neural network to process the three-dimensional point cloud data of the left ventricle to learn the mapping relationship between myocardial geometric morphology and material parameters, and obtain a rapid estimation model of myocardial material parameters; after training, input new short-axis cardiac magnetic resonance images into this model and output myocardial material parameters.

[0059] Specifically: Based on the DGCNN network architecture, extract the point cloud data corresponding to the closed surface of the left ventricular myocardium at the early diastolic and end-diastolic phases. Each sample contains point coordinates of (N, 3) dimensions. Construct a k-nearest neighbor graph based on the point cloud data: During the forward propagation of the network, dynamically calculate k-nearest neighbors for the point cloud data, construct the topological structure of the point cloud, extract local point features based on the EdgeConv module, and learn the spatial relationship of the point cloud through convolutional operations. Aggregate local and global information layer by layer to generate a high-dimensional feature representation, and extract global geometric information through max pooling to obtain the myocardial microstructure.

[0060] In some embodiments, using a convolutional neural network to perform image segmentation on short-axis cardiac magnetic resonance images to obtain the left ventricular myocardial region specifically includes the following processes:

[0061] Set that the convolutional neural network consists of K convolutional kernels, and use the graph mapping module to map the short-axis cardiac magnetic resonance image into a topological graph;

[0062] Specifically, calculate the mean or sum of the weight matrix of the convolution kernel to obtain a new weight matrix; at this time, it can be directly mapped to a weighted undirected graph, where the weight of the edge is the corresponding weight matrix value, and the graphs of all convolutional neural network layers form the weighted undirected graph of the model.

[0063] Prune the topological graph using graph pruning techniques to remove redundant parameters and obtain a more discriminative weighted undirected graph.

[0064] Specifically, during the pruning process, set the corresponding pruning rate to perform pruning, and calculate the weight difference between the convolution kernel and the model to determine the pruning threshold. Remove the edges in the weighted undirected graph whose weights are less than the threshold, and retain the edges whose weights are greater than the threshold. Thus, the redundant edges of the weighted undirected graph can be removed, and the redundant information of the local model can be pruned to obtain a more discriminative weighted undirected graph.

[0065] Calculate the similarity of the pruned weighted undirected graph. The reciprocal of the similarity is the distance between the graphs. Based on the graph distance, perform image segmentation on the short-axis cardiac magnetic resonance image to obtain the left ventricular myocardial region.

[0066] Specifically, use the method of the pyramid matching kernel function to calculate the graph similarity:

[0067] Construct a pyramid:

[0068] For each image, construct a multi-layer pyramid, and each layer of the pyramid corresponds to a different scale.

[0069] In each layer of the pyramid, the feature points are arranged according to their positions.

[0070] Match the feature points:

[0071] For each layer of the pyramid, use the distance threshold to match the feature points of two images.

[0072] If a certain feature point cannot find a directly matching point in another image, but there is a close point (within the distance threshold), then establish a matching relationship through the "pyramid matching" strategy. Specifically, it is allowed that the feature points have a certain offset between different layers as long as they meet certain distance conditions.

[0073] Calculate the number of matching pairs:

[0074] Count the number of pairs of matching feature points in all layers.

[0075] Calculate the similarity:

[0076] According to the number of matching pairs and the descriptor information of the feature points, calculate the similarity score between two images. Usually, the more the number of matching pairs and the smaller the difference in descriptors, the higher the similarity score.

[0077] Performing image segmentation on short-axis cardiac magnetic resonance images based on graph distance to obtain the left ventricular myocardial target image:

[0078] Denote the image part with graph distance less than the preset threshold as the left ventricular myocardial target area.

[0079] In some embodiments, before using the Holzapfel-Ogden constitutive model for myocardial material modeling, the method further includes implementing individualized left ventricular mesh generation based on a deformation field registration method:

[0080] Step 1: Perform an affine transformation to perform a preliminary alignment based on the overall morphology of the left ventricular myocardium, including position, scale, and rotation adjustment. The general structure of the template mesh is consistent with the target heart morphology, reducing errors caused by large-scale deformations;

[0081] Step 2: Local registration. Based on the global registration, use the free-form deformation method to make the mesh structure more accurately match the individualized left ventricular anatomical morphology;

[0082] Step 3: Update the mesh node coordinates: After local registration, directly update the node coordinates of the template mesh to match the target left ventricular myocardial morphology.

[0083] In some embodiments, using the Holzapfel-Ogden constitutive model for myocardial material modeling specifically includes the following process:

[0084] The passive properties of the left ventricular myocardium during diastole are described by the Holzapfel-Ogden constitutive model, which is established based on the myocardial microstructure. Its strain energy function ψ is as follows:

[0085]

[0086] where a, b, a f , b f , a s , b s , a fs , b fs are 8 material parameters to be estimated, which reflect the elastic and anisotropic mechanical properties of the myocardium; I1, I 4f , I 4s , I 8fs are 4 strain invariants used to characterize the deformation state of the myocardial tissue;

[0087] Parameter grouping and scaling: Divide the parameters into two groups: a G ={a, a f , a s , a fs}, b G ={b, bf , b s b fs}. The two sets of parameters are normalized using scaling factors Ca and Cb to reduce the model complexity:

[0088]

[0089] where and represent the initial parameters of the 8 material parameters, including a0, b0, a f0 , b f0 , a s0 , b s0 , a fs0 , b fs0 The values are as follows in the table:

[0090]

[0091] Furthermore, the governing equations and boundary conditions: The governing equation of the left ventricle can be described by the mechanical equilibrium equation and boundary conditions:

[0092]

[0093] where σ represents the Cauchy stress tensor, describing the stress state inside the myocardium; b is the body force density per unit volume; Ω is the computational domain defined by the left ventricle mesh; n is the normal vector of the endocardial surface; p endo represents the left ventricle filling pressure, used to simulate the load at the end of diastole; is the Neumann boundary; u z is the displacement of the basal surface in the z direction; represents the Dirichlet boundary;

[0094] where, the end-diastolic pressure is set to 8 mmHg, i.e., p endo = 8 mmHg, which is used as the loading condition for the finite element simulation.

[0095] In some embodiments, based on the MATLAB-ABAQUS joint simulation framework, inverse finite element analysis is performed, combined with an iterative optimization algorithm, to optimize the 8 material parameters in the Holzapfel-Ogden constitutive model. The specific process includes the following:

[0096] Initial simulation: Set the initial parameters of the Holzapfel-Ogden constitutive model, and perform finite element calculations through MATLAB background calling ABAQUS to obtain the left ventricle deformation;

[0097] Error calculation: Compare the error between the left ventricle volume change obtained from the finite element calculation and the measurement value of the magnetic resonance imaging;

[0098] Parameter update: The sequential quadratic programming optimization algorithm is used to adjust the material parameters to make the simulation results approximate the image measurement values;

[0099] Convergence determination: If the error meets the convergence condition, the final material parameters are output; otherwise, the optimization iteration continues.

[0100] In some embodiments, the training strategy of the myocardial material parameter rapid estimation model specifically includes the following process:

[0101] Network model: Based on the DGCNN graph neural network, the point cloud data corresponding to the diastolic early and diastolic end of the closed surface of the left ventricular myocardium is received. Each sample contains the point coordinates of the (N, 3) dimension. Based on the point cloud data, a k-nearest neighbor graph is constructed: during the forward propagation of the network, the k-nearest neighbor is dynamically calculated for the point cloud data, and the topological structure of the point cloud is constructed. Based on the EdgeConv module, local point features are extracted, and the spatial relationship of the point cloud is learned through convolution operations. The local and global information is aggregated layer by layer to generate a high-dimensional feature representation, and the global geometric information is extracted through max pooling to obtain the myocardial microstructure.

[0102] Loss function: The mean square error is used to measure the error between the predicted parameters and the true values;

[0103] Optimizer: Adam optimizer;

[0104] Hyperparameter settings: Learning rate: 1e-3 - 1e-8; Batch size: 16, 32, 64; Number of k-nearest neighbors: k = 10;

[0105] Training device: Core TM i9-14900KF processor, NVIDIA RTX 4090 GPU.

[0106] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, the processes or functions described in the embodiments of the present application are generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center by wired (such as infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server or a data center that contains one or more collections of available media. The available medium can be a magnetic medium (such as a floppy disk, a hard disk, or a magnetic tape), an optical medium (such as a DVD), or a semiconductor medium. The semiconductor medium can be a solid-state drive.

[0107] Those of ordinary skill in the art will appreciate that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or in a combination of computer software and electronic hardware. Whether these functions are executed in hardware or software depends on the specific application and design constraints of the technical solution. Skilled artisans can use different methods for each specific application to implement the described functions, but such implementation should not be considered to exceed the scope of the present application.

[0108] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, devices, and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0109] In several embodiments provided in the present application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only for some logical function divisions, and there can be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces, and the indirect couplings or communication connections of the devices or units can be in electrical, mechanical, or other forms.

[0110] The unit described as a separation component may or may not be physically separated. The component displayed as a unit may or may not be a physical unit, that is, it may be located in one place or may be distributed across multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0111] As described above, the above is only the specific implementation manner of this application, but the protection scope of this application is not limited thereto. Any person skilled in the art within the technical scope disclosed in this application can easily think of changes or substitutions, which should be covered within the protection scope of this application. Therefore, the protection scope of this application should be subject to the protection scope of the claimed rights.

Claims

1. A rapid estimation method for myocardial material parameters based on a deep neural network, characterized in that The method includes: Performing image segmentation on short-axis cardiac magnetic resonance images using a convolutional neural network to obtain the left ventricular myocardial region; based on the segmented left ventricular myocardial images, using the Marching Cubes algorithm to reconstruct the three-dimensional closed surface of the left ventricular myocardium; based on a registration method, aligning the reconstructed three-dimensional left ventricular structure with a left ventricular template that has been pre-divided into hexahedral meshes to provide a geometric structure for subsequent analysis; Adopting the Holzapfel-Ogden constitutive model for myocardial material modeling, which describes the non-linear elastic behavior of the myocardium based on its microscopic structure; performing inverse finite element analysis based on the MATLAB-ABAQUS joint simulation framework, and combining with an iterative optimization algorithm to optimize the eight material parameters in the Holzapfel-Ogden constitutive model; through the simulation optimization process, generating a high-confidence reference standard for training a deep neural network model. Using a DGCNN graph neural network to process the three-dimensional point cloud data of the left ventricle to learn the mapping relationship between myocardial geometric morphology and material parameters, and obtaining a rapid estimation model of myocardial material parameters; after training is completed, inputting new short-axis cardiac magnetic resonance images into the model to output myocardial material parameters.

2. A rapid estimation method for myocardial material parameters based on a deep neural network according to claim 1, characterized in that, Performing image segmentation on short-axis cardiac magnetic resonance images using a convolutional neural network to obtain the left ventricular myocardial region specifically Includes the following processes: Setting that the convolutional neural network consists of K convolutional kernels, and using a graph mapping module to map the short-axis cardiac magnetic resonance images into a topological graph; Pruning the topological graph using graph pruning techniques to remove redundant parameters and obtain a more discriminative weighted undirected graph; Calculating the similarity of the pruned weighted undirected graph. The reciprocal of the similarity is the distance between the graphs. Based on the graph distance, perform image segmentation on the short-axis cardiac magnetic resonance images to obtain the left ventricular myocardial region.

3. A rapid estimation method of myocardial material parameters based on a deep neural network according to claim 1, characterized in that Based on the segmented left ventricular myocardial images, using the Marching Cubes algorithm to reconstruct the three-dimensional closed surface of the left ventricular myocardium specifically includes the following processes; based on a registration method, aligning the reconstructed three-dimensional left ventricular structure with a left ventricular template that has been pre-divided into hexahedral meshes to provide a geometric structure for subsequent analysis: Based on the segmented left ventricular myocardial images, using the Marching Cubes algorithm to reconstruct the three-dimensional closed surface of the left ventricular myocardium; Receiving the point cloud data of the early diastolic and end-diastolic phases corresponding to the closed surface of the left ventricular myocardium based on the DGCNN network architecture. Each sample contains point coordinates in the (N, 3) dimension. Construct a k-nearest neighbor graph based on the point cloud data: during the forward propagation of the network, dynamically calculate the k-nearest neighbors for the point cloud data, construct the topological structure of the point cloud, extract local point features based on the EdgeConv module, and learn the spatial relationship of the point cloud through convolutional operations, aggregating local and global information layer by layer to generate a high-dimensional feature representation, and extracting global geometric information through max pooling to obtain the myocardial microscopic structure.

4. A rapid estimation method for myocardial material parameters based on a deep neural network according to claim 1, characterized in that, Before adopting the Holzapfel-Ogden constitutive model for myocardial material modeling, the method also includes implementing individualized left ventricular mesh division based on a deformation field registration method: Step 1: Perform an affine transformation to perform preliminary alignment based on the overall morphology of the left ventricular myocardium, including position, scale, and rotation adjustment. The general structure of the template grid is consistent with the target heart morphology, reducing the error caused by large-scale deformation. Step 2: Local registration. On the basis of global registration, use the free-form deformation method to make the grid structure more accurately match the anatomical morphology of the individual left ventricle. Step 3: Update the grid node coordinates: After local registration, directly update the node coordinates of the template grid to match the morphology of the target left ventricular myocardium.

5. A rapid estimation method of myocardial material parameters based on a deep neural network according to claim 1, characterized in that Use the Holzapfel-Ogden constitutive model to model the myocardial material. Specifically Include the following processes: The passive properties of the left ventricular myocardium during diastole are described by the Holzapfel-Ogden constitutive model, which is based on the microstructure of the myocardium. Its strain energy function ψ is as follows: Among them, a, b, a f , b f , a s , b s , a fs , b fs are 8 material parameters to be estimated, which reflect the elastic and anisotropic mechanical properties of the myocardium; I1, I 4f , I 4s , I 8fs are 4 strain invariants used to characterize the deformation state of myocardial tissue; Parameter grouping and scaling: The parameters are divided into two groups: a G ={a, a f , a s , a fs}, b G ={b, b f , b s b fs}. The two groups of parameters are normalized using scaling factors Ca and Cb to reduce the model complexity: Among them and represent the initial parameters of eight material parameters; Governing equations and boundary conditions: The governing equations of the left ventricle can be described by the mechanical equilibrium equations and boundary conditions: where, σ represents the Cauchy stress tensor, describing the internal stress state of the myocardium; b is the body force density per unit volume; Ω is the computational domain defined by the left ventricular mesh; n is the normal vector of the endocardial surface; p endo represents the left ventricular filling pressure, used to simulate the load at the end of diastole; Γ N is the Neumann boundary; u z is the displacement of the basal surface in the z direction; represents the Dirichlet boundary; Among them, the end-diastolic pressure is set to 8 mmHg, that is, p endo = 8 mmHg, which is used as the loading condition for the finite element simulation.

6. The rapid estimation method of myocardial material parameters based on a deep neural network according to claim 1, characterized in that Based on the MATLAB-ABAQUS joint simulation framework, perform inverse finite element analysis. Combining with the iterative optimization algorithm, optimize the 8 material parameters in the Holzapfel-Ogden constitutive model. Specifically, it includes the following processes: Initial simulation: Set the initial parameters of the Holzapfel-Ogden constitutive model, and perform finite element calculations through MATLAB background calling of ABAQUS to obtain the left ventricular deformation. Error calculation: Compare the error between the left ventricular volume change obtained by finite element calculation and the measurement value of magnetic resonance imaging. Parameter update: Use the sequential quadratic programming optimization algorithm to adjust the material parameters to make the simulation results approach the imaging measurement values. Convergence determination: If the error meets the convergence condition, output the final material parameters, otherwise continue the optimization iteration.

7. The rapid estimation method of myocardial material parameters based on a deep neural network according to claim 6, characterized in that, The training strategy of the rapid estimation model for myocardial material parameters specifically includes the following processes: Network model: Based on the DGCNN graph neural network, receive the point cloud data corresponding to the closed surface of the left ventricular myocardium at the early diastolic and end-diastolic phases. Each sample contains point coordinates in the (N, 3) dimension. Construct a k-nearest neighbor graph based on the point cloud data: During the forward propagation of the network, dynamically calculate the k-nearest neighbors for the point cloud data, construct the topological structure of the point cloud, extract local point features based on the EdgeConv module, and learn the spatial relationship of the point cloud through convolutional operations. Aggregate local and global information layer by layer to generate a high-dimensional feature representation, and extract the global geometric information through max pooling to obtain the myocardial microstructure. Loss function: Use the mean square error to measure the error between the predicted parameters and the true values. Optimizer: Adam optimizer Hyperparameter settings: Learning rate: 1e-3 - 1e-8; Batch size: 16, 32, 64; Number of k-nearest neighbors: k = 10 Training equipment: Core TM i9-14900KF processor, NVIDIA RTX 4090 GPU.

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