A blood flow simulation boundary condition calculation method with 2nd order accuracy

Abstract

The application is suitable for the technical field of computational fluid dynamics, and provides a blood flow simulation boundary condition calculation method with 2nd order precision. The method uses a 2nd order implicit difference format as a specific numerical method to discretize a ternary Windkessel equation. Compared with a backward Euler method used in the past research, the method has higher calculation precision and has little influence on calculation efficiency. A storage medium storing the method and a processor running the method also have the same technical effects.

Description

Technical Field

[0001] This application belongs to the field of computational fluid dynamics technology, and in particular relates to a method for calculating boundary conditions in blood flow simulation with second-order accuracy, a storage medium, and a processor. Background Technology

[0002] In existing technologies, when using computational fluid dynamics (CFD)-based blood flow simulations to assess the risk of abdominal aortic aneurysm rupture, the accuracy of the model and simulation results can be reduced due to errors in data acquisition, limitations of reconstruction algorithms, and the inherent characteristics of the object itself. This affects the overall accuracy of the simulation results. In particular, when using the backward Euler scheme to discretize the ternary Windkessel equations, the scheme only has first-order accuracy, meaning the error in calculating the analytical solution can only be guaranteed to be below 5%, which is a relatively large error range. Therefore, existing technologies have shortcomings. Summary of the Invention

[0003] The purpose of this application is to provide a method, storage medium, and processor for calculating blood flow simulation boundary conditions with second-order accuracy, aiming to solve the technical problem of insufficient calculation accuracy in the backward Euler method used in the prior art.

[0004] On the one hand, this application provides a method for calculating boundary conditions in blood flow simulation with second-order accuracy, including three-dimensional reconstruction of the abdominal aorta using medical computed tomography imaging data; then, meshing the reconstructed model to discretize the continuous intravascular environment into a finite number of units; the method further includes the following steps:

[0005] s1. When performing fluid dynamics simulations, a second-order implicit difference scheme is used to discretize the ternary Windkessel equations;

[0006] s2. Solve the discretized ternary Windkessel equation to obtain the inlet and outlet boundary conditions of the discretized unit, so as to simulate the blood flow environment in a real blood vessel;

[0007] s3. Based on the calculation results of the fluid dynamics simulation, the hemodynamic parameters of the model are calculated using Paravierw, including: blood flow velocity, pressure, shear stress, shear oscillation index and relative residence time.

[0008] Furthermore, in step s2, the output of one cardiac cycle is used as the inlet boundary condition, and the output and pressure changes within one cardiac cycle are used to obtain the initial conditions and various calculation parameters for solving the ternary Windkessel equation.

[0009] Furthermore, in step s2, for the unit with a complex geometry having multiple outlets, a boundary condition of the ternary Windkessel equation is applied to each outlet, and the simulated pressure is brought to a normal physiological value by adjusting the values ​​of total drag and total compliance.

[0010] Furthermore, in step s2, when implementing the Windkessel model using ANSYS CFX, four additional variables are defined to temporarily store the pressure and flow rate of each outlet in the previous time step, as well as the pressure and flow rate of each outlet in the previous two time steps, so that these four data can be passed to the next time step in ANSYS CFX.

[0011] Furthermore, in step s3, the various hemodynamic parameters of Paravierw are calculated using a numerical integration method.

[0012] Furthermore, the medical computed tomography imaging data includes data on normal abdominal aorta and data on abdominal aorta with aneurysms.

[0013] Furthermore, during the three-dimensional reconstruction of the abdominal aorta, real-time processing and multimodal fusion are employed to achieve rapid processing and integration of various imaging data.

[0014] Furthermore, during the three-dimensional reconstruction of the abdominal aorta, advanced image segmentation algorithms are used to ensure clear model boundaries, and post-processing is performed on the model to remove noise and increase details.

[0015] Furthermore, during the three-dimensional reconstruction of the abdominal aorta, the accuracy of the reconstruction was verified by comparing simulations with the physical model.

[0016] Furthermore, during the three-dimensional reconstruction of the abdominal aorta, the model is regularly updated incorporating the latest clinical data to improve its accuracy and reliability.

[0017] On the other hand, this application also provides a storage medium storing a program file capable of implementing the above-described method for calculating blood flow simulation boundary conditions with second-order accuracy.

[0018] On the other hand, this application also provides a processor for running a program, wherein the program executes the above-described method for calculating blood flow simulation boundary conditions with second-order accuracy.

[0019] This application employs a specific numerical method (second-order implicit difference scheme) to discretize the ternary Windkessel equation. This method offers higher computational accuracy compared to the backward Euler method, which has been used extensively in research, while having minimal impact on computational efficiency. Furthermore, this application uses the output of one cardiac cycle as the ingress boundary condition. By utilizing the changes in output and pressure within one cardiac cycle to obtain the initial conditions for solving the ternary Windkessel equation and to calculate the various parameters, this approach also helps to improve the approximation of the final analytical solution. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the blood flow simulation using the method described in this application;

[0021] Figure 2 This is a schematic diagram of the ternary Windkessel boundary conditions in this application;

[0022] Figure 3 This is a comparison chart of the experimental model and parameter curves provided in Embodiment 4 of this application;

[0023] Figure 4 This is a schematic diagram of the global mesh generation of the three-dimensional model of the abdominal aorta used in this application;

[0024] Figure 5 This is the main flowchart of the blood flow simulation boundary condition calculation method with second-order accuracy provided in Embodiment 1 of this application. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0026] The specific implementation of this application will be described in detail below with reference to specific embodiments:

[0027] Example 1:

[0028] Figures 1 to 5 The main implementation flow of the blood flow simulation boundary condition calculation method with second-order accuracy provided in Embodiment 1 of this application is shown. For ease of explanation, only the parts related to the embodiments of this application are shown, and are described in detail below:

[0029] On the one hand, such as Figure 5 As shown, this application provides a method for calculating boundary conditions in blood flow simulation with second-order accuracy, including as follows: Figure 4The method illustrates the three-dimensional reconstruction of the abdominal aorta using medical computed tomography (CT) imaging data; then, the reconstructed model is meshed, discretizing the continuous intravascular environment into a finite number of units; the method also includes, for example... Figure 5 The following steps are shown:

[0030] s1. In the fluid dynamics simulation, a second-order implicit difference scheme is used to discretize the ternary Windkessel equation; the accuracy of blood flow simulation is improved by leveraging the second-order accuracy of the second-order implicit difference scheme.

[0031] s2. Solve the discretized ternary Windkessel equation to obtain the inlet and outlet boundary conditions of the discretized unit, so as to simulate the blood flow environment in a real blood vessel;

[0032] s3. Based on the calculation results of the fluid dynamics simulation, the hemodynamic parameters of the model are calculated using Paraview, including: blood flow velocity, pressure, shear stress, shear oscillation index and relative residence time.

[0033] In practical implementation, using Paraview for post-processing has the following advantages:

[0034] A.Paraview offers a variety of visualization technologies and provides multiple visualization methods, such as isosurfaces, streamlines, and particle tracking, which help this application to intuitively observe the spatial distribution of various parameters.

[0035] B.Paraview has powerful data analysis capabilities. In addition to visualization, Paraview also provides a wealth of data analysis tools, such as statistical analysis, data filtering, and data extraction, to help this application calculate hemodynamic parameters.

[0036] C.Paraview can export visualization results to various formats (such as images, animations, data files, etc.), facilitating the reporting and sharing of results in this application.

[0037] Appendix Figure 1 This demonstrates the complete process of this application, from data acquisition to 3D modeling and then to specific blood flow simulation. The numerical calculation portion employs a second-order implicit difference scheme, which effectively improves the accuracy of the blood flow simulation.

[0038] As attached Figure 2 The schematic diagram of the ternary Windkessel boundary condition is shown, where Ci represents the total compliance of each outlet. This represents the near-end resistance of each exit. Qi represents the far-end resistance of each outlet, Qi represents the flow rate of each outlet, and Pi represents the pressure of each outlet.

[0039] This application uses a second-order implicit difference scheme instead of the backward Euler scheme used in previous studies because the second-order implicit difference scheme can provide second-order accuracy. The detailed proof of its second-order accuracy is as follows:

[0040] Consider the differential equation: Here, y represents all twice differentiable functions, corresponding to the two derivative terms of the ternary Windkessel equation (Qi represents the flow rate at each outlet and Pi represents the pressure at each outlet).

[0041] The formula for the second-order implicit difference scheme is defined as follows: nn represents the current time step.

[0042] Prove that for y n and y n-2 Perform a Taylor expansion:

[0043]

[0044] Substituting the formula for the second-order implicit difference scheme, we get:

[0045]

[0046] After simplification, we get:

[0047]

[0048] Expanding the right side of the equation using Taylor series, we get:

[0049]

[0050] Simplifying, we get:

[0051]

[0052] Where t represents time, used to simulate blood flow time within one cardiac cycle; Δt represents the time step, O(Δt) 2 ) and O(Δt 3 ) represent second-order infinitesimals and third-order infinitesimals, respectively. and Let these represent the first and second derivatives of y with respect to t, respectively. and Let f represent the partial derivatives of f with respect to y and f with respect to t, respectively.

[0053] Therefore, error E n =|y n -y(t n )|~O(Δt 2 ), representing the error E n With the second-order infinitesimal O(Δt) 2Since the error generated by the second-order implicit difference scheme is second-order at each step, it can be concluded that the second-order implicit difference scheme has second-order accuracy.

[0054] It is evident that, compared to the backward Euler scheme used in existing technologies which only has first-order accuracy, discretizing the ternary Windkessel equation using a second-order implicit difference scheme can provide higher computational accuracy.

[0055] In practical implementation, the ternary Windkessel equation is as follows:

[0056]

[0057] Among them, such as Figure 2 As shown, at the outlet of the blood vessel, C i This indicates the overall compliance of each export. This represents the near-end resistance of each exit. Q represents the far-end resistance of each outlet. i P represents the flow rate at each outlet. i This indicates the pressure on each export channel.

[0058] After discretization, we can obtain:

[0059]

[0060] Where Δt represents the time step, P i n and P represents the pressure and flow rate at each outlet at the current time step. i n-1 and P represents the pressure and flow rate at each outlet in the previous time step. i n-2 and These represent the pressure and flow rate at each outlet in the first two time steps, respectively, and P... i n As a pressure boundary condition for exports.

[0061] The parameters of the ternary Windkessel equation are calculated as follows:

[0062] Based on the average pressure P at the inlet m Average flow rate Q m and the surface area S of each outlet i (representing the surface area of ​​the i-th outlet) is used to calculate the resistance and compliance parameters of the i-th outlet. This completes the boundary condition calculation for all blood vessel outlets.

[0063] The detailed calculation formula is as follows:

[0064]

[0065]

[0066] The two formulas mentioned above indicate that the parameters of "each" outlet are calculated based on the "total" parameters and the area of ​​"each" outlet.

[0067]

[0068] Among them, R total C represents the total resistance. total Let M represent the total compliance, M represent the number of outlets, and τ represent the pressure drop constant, where τ = 1.79 seconds.

[0069] Furthermore, in step s2, the flow rate of one cardiac cycle is used as the inlet boundary condition, and the initial flow rate and average flow rate Q within one cardiac cycle are used. m and initial pressure and average pressure P m The initial conditions and calculation parameters for solving the ternary Windkessel equation are obtained.

[0070] Furthermore, in step s2, for the unit with a complex geometry having multiple outlets, a boundary condition of the ternary Windkessel equation is applied to each outlet to simulate real pulsating pressure. By adjusting the values ​​of total resistance and total compliance, the range of blood flow simulation pressure is made within the normal physiological range of humans or matches clinical measurements, making the blood flow simulation closer to the real situation and the conclusion more convincing.

[0071] Furthermore, in step s2, when implementing the Windkessel model using ANSYS CFX, four additional variables are defined to temporarily store the pressure and flow rate of each outlet in the previous time step, as well as the pressure and flow rate of each outlet in the previous two time steps, so that these four data can be passed to the next time step in ANSYS CFX.

[0072] Specifically, when implementing the Windkessel model in ANSYS CFX, due to P n-1 (Pressure at each outlet in the previous time step), Q n-1 (Flow rate at each exit in the previous time step), P n-2 (Pressures at each outlet in the first two time steps) and Q n-2 The flow rates at each outlet in the first two time steps are not directly available in ANSYS CFX. This application defines four additional variables to temporarily store the outlet pressures and flow rates for the previous and first two time steps, and then passes them to the next time step.

[0073] Additionally, in CFX, add the code "Update Loop = Trans_loop" to the command editor for additional variables to read the pressure and flow values ​​from the previous and two previous time steps.

[0074] In other preferred embodiments, the command language and expression language in ANSYS CFX are used to calculate the flow rate at the current time step, and the discretized ternary Windkessel equation can also be obtained through the expression.

[0075] Furthermore, in step s3, the various hemodynamic parameters of Paravierw are calculated using surface integrals via numerical integration. In hemodynamics, surface integrals typically represent the sum or average of blood flow, pressure, or other physiological parameters within a specific region (such as a blood vessel or ventricle). This integration can be used to calculate flow rate, blood velocity, or other dynamic characteristics. The core of numerical integration is to simplify complex mathematical models into computable forms. By discretizing continuous functions, these hemodynamic phenomena can be simulated on a computer. This method is particularly useful when dealing with nonlinear, complex equations that are often difficult to solve analytically. In biological hemodynamics, blood vessels and ventricles typically have complex geometries. Numerical integration methods can adapt to these complex shapes, making the analysis of the flow field more realistic.

[0076] Furthermore, during the three-dimensional reconstruction of the abdominal aorta, real-time processing and multimodal fusion were employed to achieve rapid processing and integration of various imaging data. Real-time processing refers to the ability to process the acquired imaging data immediately to obtain results quickly.

[0077] For 3D reconstruction of the abdominal aorta, this process can be achieved through the following methods: Efficient algorithms: Using fast image processing algorithms (such as Fast Fourier Transform, Fast Edge Detection, etc.), which can process large amounts of image data in a short time. Parallel computing: Utilizing multi-core processors and graphics processing units (GPUs) for parallel computing can significantly accelerate data processing. For example, GPU-accelerated image segmentation and reconstruction can process multiple image frames simultaneously. Real-time image streaming: Employing streaming processing technology, which can receive and process data frame by frame and segment by segment, avoiding waiting for the entire dataset to load. This can be applied to imaging techniques such as ultrasound, CT, or MRI to analyze and dynamically monitor changes in the abdominal aorta in real time. Multimodal fusion refers to integrating data from different imaging modalities to construct a more comprehensive 3D model of the abdominal aorta. Fusion methods typically include: Image registration: Before multimodal fusion, data from different imaging modalities need to be registered to ensure that the same anatomical structure is aligned on different images. This can be achieved through feature matching, rigid or non-rigid transformation algorithms. Data fusion algorithms: Fusion algorithms, such as weighted fusion, principal component analysis, or wavelet transform, are used to integrate data from different imaging sources. For example, when fusing CT and MRI data, the high resolution of CT and the soft tissue contrast advantage of MRI can be utilized to obtain comprehensive information. Deep learning models: Image fusion is performed using deep learning techniques. By training convolutional neural network models, data from different modalities can be better extracted and fused, improving the quality and accuracy of the final 3D reconstruction. Information augmentation: During the fusion process, it is crucial to preserve the details of important anatomical structures to ensure the clarity and effectiveness of the final model.

[0078] Furthermore, during the 3D reconstruction of the abdominal aorta, advanced image segmentation algorithms were used to ensure clear model boundaries, and post-processing was performed to remove noise and enhance details. Advanced image segmentation algorithms demonstrate their superiority in several aspects, primarily as follows:

[0079] Deep learning techniques: In recent years, deep learning methods such as convolutional neural networks have demonstrated extremely high accuracy in image segmentation tasks. Multi-scale feature extraction: Advanced algorithms often employ multi-scale feature extraction techniques, which can effectively capture both large-scale and small-scale structural information, making them crucial for processing target objects with different sizes and shapes.

[0080] Fully Automated Segmentation: Modern algorithms enable fully automated segmentation without human intervention or prior knowledge, making its applications more widespread and efficient. Especially in medical image processing, it can reduce the workload of doctors and provide a highly efficient auxiliary tool.

[0081] Adaptive learning: Deep learning-based segmentation algorithms can gradually adapt to different image content and types by training on a large amount of labeled data, thereby improving the versatility and adaptability of the algorithm.

[0082] Use of large-scale datasets: Some algorithms can effectively utilize large datasets for training, improving the model's generalization ability and enabling it to perform better in real-world applications. Post-processing and optimization: Many algorithms include post-processing steps to enhance the coherence and naturalness of the segmentation results through smoothing and optimization algorithms, reducing noise and artifacts.

[0083] Furthermore, during the 3D reconstruction of the abdominal aorta, the accuracy of the reconstruction was verified by comparing simulations with the physical model. The specific comparison steps and the process for verifying accuracy are as follows:

[0084] 1. Solid model construction: Based on medical imaging data, a solid model is created. Typically, 3D printing or other manufacturing techniques can be used to generate a realistic abdominal aorta model.

[0085] 2. Implementation of 3D Reconstruction: Computer-generated 3D model; Image preprocessing: Denoising, filtering, and enhancement operations are performed on the acquired image data. Segmentation: Advanced image segmentation algorithms are used to separate the abdominal aorta from the surrounding structures. Reconstruction: Using the segmented data, 3D reconstruction algorithms (such as voxel reconstruction, surface reconstruction, etc.) are employed to generate a 3D model of the abdominal aorta.

[0086] 3. Compare the simulation and the physical model, simultaneously setting comparison standards and standardizing comparison points: Determine comparison indicators, such as diameter, length, curvature, volume, and structural details. These indicators can be directly measured in the corresponding parts of the simulation and physical models. Alignment and registration: Ensure the alignment of the two models, typically through feature point matching, rigidity transformation, or other methods. This step is crucial for ensuring the accuracy of the comparison. Dimensional measurement: Use 3D spatial measurement tools to measure the models, comparing the differences in dimensions, shape, volume, and other dimensions between the simulation and physical models.

[0087] 4. Accuracy Verification and Bias Analysis: Compare the differences between the physical model and the simulation model across various measurement indicators, calculate their percentage errors, and analyze their reasonableness. Verification of Clinical Importance: Consider clinical needs and assess whether the differences in the simulation model are within medically acceptable limits. For example, for preoperative assessment, the tolerance for certain parameters may be small. Feedback and Implementation: Based on the comparison results, evaluate the accuracy of the reconstruction algorithm and model construction, and optimize and adjust parameters as necessary.

[0088] like Figure 4 As shown, Part A is the global mesh generation of the 3D model of the abdominal aorta, Γ IIndicates the entrance. Indicates export, Γ W The image represents the blood vessel wall. Sections B and D are magnified views of the local mesh and volume mesh, respectively. Sections C and E are magnified views of the surface mesh and boundary layer mesh at the outlet, respectively.

[0089] This application uses a specific numerical method (second-order implicit difference scheme) to discretize the ternary Windkessel equation. This method has higher computational accuracy than the backward Euler method used in previous studies, and has little impact on computational efficiency. Furthermore, this application uses the output of one cardiac cycle as the ingress boundary condition. By using the changes in output and pressure within one cardiac cycle to obtain the initial conditions for solving the ternary Windkessel equation and to calculate each parameter, this approach also helps to improve the approximation of the final analytical solution.

[0090] Furthermore, this application employs a ternary Windkessel model with parameters that can be used to simulate blood flow within blood vessels, including blood flow velocity and blood pressure changes. Using the output volume of the cardiac cycle as the inlet boundary condition allows for a more realistic simulation of the changes and magnitude of the outlet pressure within a cardiac cycle.

[0091] Example 2:

[0092] On the other hand, this application also provides a storage medium storing a program file capable of implementing the above-described method for calculating blood flow simulation boundary conditions with second-order accuracy.

[0093] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as ROM / RAM, disk, optical disk, etc.

[0094] Example 3:

[0095] On the other hand, this application also provides a processor for running a program, wherein the program executes the above-described method for calculating blood flow simulation boundary conditions with second-order accuracy.

[0096] In the embodiments of this application, the blood flow simulation boundary condition calculation method with second-order accuracy can be implemented by corresponding hardware or software units. Each unit can be an independent hardware or software unit, or it can be integrated into a single hardware or software unit, which is not intended to limit this application. The specific implementation of each unit can be referred to the description of Embodiment 1, and will not be repeated here.

[0097] Example 4:

[0098] In practical implementation, the blood flow simulation boundary condition calculation method of this application, with second-order accuracy, solves the technical problem of insufficient first-order accuracy. The following detailed comparison and verification process will illustrate this in detail.

[0099] As attached Figure 3 As shown, in order to verify the effectiveness of the blood flow simulation boundary condition calculation method with second-order accuracy proposed in this application, the effectiveness of the proposed method is verified by combining several sets of comparative simulation results.

[0100] Appendix Figure 3 In the diagram, Part A contains the three-dimensional geometric model and detailed parameters of the experiment; Part B contains the inlet boundary conditions of the experiment; and Parts C and D contain the experimental results, namely the inlet pressure and outlet pressure, respectively. Analytical represents the analytical solution, BDF2 represents the result of the second-order implicit difference scheme, and Euler represents the result of the backward Euler method. The magnified views in C and D show that the result of the second-order implicit difference scheme is closer to the analytical solution than the backward Euler method.

[0101] In the simulation experiment, this application simulated a blood vessel segment 200mm long and 20mm in diameter, with a blood density set to 1056kg / m³. 3 The viscosity is set to 0.0035 Pa·s, the inlet boundary condition is a mass flow of one cardiac cycle, the outlet boundary condition is a ternary Windkessel boundary condition, the wall boundary condition is no slip, rigid wall, and the velocity is 0.

[0102] The simulation results of this invention are compared with the analytical solutions of previous published literature. The results show that the overall and local distributions conform to the corresponding laws, and the corresponding values ​​are also within the reference range of existing literature.

[0103] This invention uses two different discretization methods (backward Euler scheme and second-order implicit difference scheme) for simulation, and compares and calculates the errors with analytical solutions published in previous literature. The results show (as shown in the table below): the errors are all less than 5%, and the results obtained by the second-order implicit difference scheme with second-order accuracy used in this invention have even smaller errors, all less than 1.5%, which are closer to the analytical solution.

[0104] The results of the relative error calculation are as follows:

[0105]

[0106] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for calculating boundary conditions in blood flow simulation with second-order accuracy, comprising: reconstructing the abdominal aorta three-dimensionally using medical computed tomography (CT) imaging data; then meshing the reconstructed model to discretize the continuous intravascular environment into a finite number of elements; characterized in that... The method further includes the following steps: s1. When performing fluid dynamics simulations, a second-order implicit difference scheme is used to discretize the ternary Windkessel equations; s2. Solve the discretized ternary Windkessel equation to obtain the inlet and outlet boundary conditions of the discretized unit, so as to simulate the blood flow environment in a real blood vessel; s3. Based on the calculation results of the fluid dynamics simulation, the hemodynamic parameters of the model are calculated using Paravierw, including: blood flow velocity, pressure, shear stress, shear oscillation index and relative residence time; In practical implementation, the ternary Windkessel equation is as follows: Where t represents time, and at the exit of the blood vessel, C i This indicates the overall compliance of each export. This represents the near-end resistance of each exit. Q represents the far-end resistance of each outlet. i P represents the flow rate at each outlet. i This indicates the pressure on each export channel; After discretization, we can obtain: Where Δt represents the time step, P i n and P represents the pressure and flow rate at each outlet at the current time step. i n-1 and P represents the pressure and flow rate at each outlet in the previous time step. i n-2 and These represent the pressure and flow rate at each outlet in the first two time steps, respectively, and P... i n As a pressure boundary condition for exports.

2. The method as described in claim 1, characterized in that, In step s2, the output of one cardiac cycle is used as the inlet boundary condition, and the output and pressure changes within one cardiac cycle are used to obtain the initial conditions and various calculation parameters for solving the ternary Windkessel equation.

3. The method as described in claim 2, characterized in that, In step s2, for the unit with a complex geometry having multiple outlets, the boundary conditions of the ternary Windkessel equation are applied to each outlet, and the simulated pressure is made to be at the normal physiological value of a human by adjusting the values ​​of total drag and total compliance.

4. The method as described in claim 3, characterized in that, In step s2, when implementing the Windkessel model using ANSYS CFX, four additional variables are defined to temporarily store the pressure and flow rate of each outlet in the previous time step, as well as the pressure and flow rate of each outlet in the previous two time steps, so that these four data are passed to the next time step in ANSYS CFX.

5. The method as described in claim 1, characterized in that, In step s3, the various hemodynamic parameters of Paravierw are calculated using a numerical integration method.

6. The method as described in claim 1, characterized in that, The medical computed tomography (CT) imaging data includes data on normal abdominal aortas and data on abdominal aortas with aneurysms.

7. The method as described in claim 1, characterized in that, In the process of three-dimensional reconstruction of the abdominal aorta, real-time processing and multimodal fusion are adopted to achieve rapid processing and integration of various imaging data.

8. The method as described in claim 7, characterized in that, In the process of 3D reconstruction of the abdominal aorta, advanced image segmentation algorithms are used to ensure clear model boundaries, and post-processing is performed on the model to remove noise and increase details.

9. The method as described in claim 8, characterized in that, During the three-dimensional reconstruction of the abdominal aorta, the accuracy of the reconstruction was verified by comparing simulation with the physical model.

10. The method as described in claim 9, characterized in that, During the three-dimensional reconstruction of the abdominal aorta, the model is updated regularly with the latest clinical data to improve its accuracy and reliability.

11. A storage medium, characterized in that, The storage medium stores a program file capable of implementing the blood flow simulation boundary condition calculation method with second-order accuracy as described in any one of claims 1 to 10.

12. A processor, characterized in that, The processor is used to run a program, wherein the program executes the blood flow simulation boundary condition calculation method with second-order accuracy as described in any one of claims 1 to 10.

Images