CN110634572B - Vascular blood flow simulation method and related device based on mechanical equation - Google Patents
Vascular blood flow simulation method and related device based on mechanical equation Download PDFInfo
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Abstract
The application discloses a blood vessel blood flow simulation method and a related device based on a mechanical equation, wherein the method comprises the steps of obtaining characteristic data of a blood vessel; constructing a three-dimensional cavity model and a blood vessel wall model of the blood vessel according to the characteristic data, and defining a calculation region; discretizing the calculation region to generate an initial grid for describing the calculation region; encrypting the initial grid to generate a fine grid computing area; coarsening the initial grid to generate a coarse grid calculation area; calculating the coarse grid calculation area to obtain the final blood flow parameter of each coarse grid point in the coarse grid calculation area; generating initial blood flow parameters of each fine grid point in the fine grid computing area according to the final blood flow parameters of each coarse grid point; and calculating the fine grid calculation region based on the initial blood flow parameters of each fine grid point to obtain the final blood flow parameters of each fine grid point in the fine grid calculation region. Accurate and efficient simulation of blood flow in a blood vessel can be achieved.
Description
Technical Field
The present application relates to the field of blood flow numerical simulation, and in particular, to a blood vessel blood flow simulation method based on a mechanical equation and a related device.
Background
The characteristics of blood flow can reflect to some extent whether a blood vessel is ill or not and whether a patient is ill or not due to hemodynamic changes, for example Fractional Flow Reserve (FFR) may reflect the risk of ischemia, blood flow velocity may reflect the degree of vascular occlusion, etc. Therefore, the simulation analysis of blood flow has become a research hotspot in the current vascular disease prevention and diagnosis field
Early days, due to the limitation of computer capability, many simplifications were performed in simulating blood flow, such as physical model simplification and discretized grid simplification; although the simplified calculation has high calculation timeliness, some important characteristics of blood flow cannot be obtained, and the simulation accuracy is not high. However, after the current computer hardware level is developed, the simulation method matched with the computer capability is not available, and the improvement of the efficiency and the precision of the blood flow simulation cannot be ensured at the same time, namely, the precision and the efficiency of the current blood flow simulation are still not high.
Disclosure of Invention
The application provides a blood vessel blood flow simulation method and a related device based on a mechanical equation, which are used for solving the problems of low accuracy and efficiency of blood flow simulation in the prior art.
In order to solve the above technical problems, the present application proposes a blood vessel blood flow simulation method based on a mechanical equation, the method comprising: acquiring characteristic data of the blood vessel; constructing a three-dimensional cavity model and a blood vessel wall model of the blood vessel according to the characteristic data, wherein a calculation area is defined by the three-dimensional cavity model and the blood vessel wall model; discretizing the calculation region based on unstructured stabilized finite elements to generate an unstructured tetrahedron initial grid for describing the calculation region; encrypting the initial grid to generate a fine grid computing area, and keeping the shapes of the fine grid units and the initial grid units consistent; coarsening the initial grid to generate a coarse grid calculation area, keeping the number of coarse grid points which characterize the edge of the calculation area shape of the three-dimensional cavity model consistent with that of the initial grid points, and keeping the number of coarse grid points which characterize the edge of the calculation area shape of the blood vessel wall model consistent with that of the initial grid points; constructing a physical mathematical model of the calculation region, wherein the physical mathematical model comprises a fully-coupled fluid mechanics control equation, a solid mechanics control equation, a grid movement equation and a fluid-solid interface equation; calculating the physical mathematical model based on the coarse grid to obtain a final blood flow parameter, a final blood vessel parameter and a final grid variation parameter; calculating an initial blood flow parameter, an initial blood vessel parameter and an initial grid variation parameter of the fine grid calculation region based on the final blood flow parameter, the final blood vessel parameter and the final grid variation parameter of the coarse grid calculation region; and calculating the physical mathematical model based on the fine grid so as to obtain a final blood flow parameter, a final blood vessel parameter and a final grid change parameter.
In order to solve the above technical problems, the present application provides a blood flow simulation device, which includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor implements the steps of the above method when executing the computer program.
To solve the above technical problem, the present application proposes a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of the above method.
The blood vessel blood flow simulation method comprises the following steps: acquiring characteristic data of a blood vessel; constructing a three-dimensional cavity model and a blood vessel wall model of a blood vessel according to the characteristic data, wherein a calculation area is defined between the three-dimensional cavity model and the blood vessel wall model; discretizing the calculation region to generate a grid for describing the calculation region; constructing a physical mathematical model of a calculation region, wherein the physical mathematical model comprises a fully-coupled fluid mechanics control equation, a solid mechanics control equation, a grid movement equation and a fluid-solid interface equation; calculating a physical mathematical model based on the grid to obtain blood flow parameters and blood vessel parameters of a calculation area; the change parameters of the mesh are calculated from the vessel parameters, thereby updating the calculation region. In the method, a physical mathematical model of fluid-solid full coupling is established in the embodiment, full coupling calculation is performed, namely interaction between blood flow and blood vessels is considered when blood flow simulation is performed, and a calculation area is updated, so that the simulation calculation accuracy is improved.
Drawings
FIG. 1 is a schematic diagram of a blood flow simulation system;
FIG. 2 is a flow chart of a blood flow simulation method;
FIG. 3 is a flow chart of an embodiment of a blood vessel flow simulation method of the present application;
FIG. 4 is a schematic diagram of the partitioning of the calculation region in the embodiment shown in FIG. 3;
FIG. 5 is a flow chart of another embodiment of a vascular flow simulation method of the present application;
FIG. 6 is a schematic diagram of an embodiment of a blood flow simulator of the present application;
FIG. 7 is a schematic diagram of an embodiment of a computer-readable storage medium of the present application.
Detailed Description
For better understanding of the technical solutions of the present application by those skilled in the art, a vascular blood flow simulation method, a blood flow simulation device and a computer readable storage medium based on mechanical equations provided by the present invention are described in further detail below with reference to the accompanying drawings and detailed description.
The simulation of blood flow in a blood vessel is to simulate the flow of blood by using a hydrodynamic method to obtain blood flow parameters including the mechanical characteristics of blood flow. Referring to fig. 1, fig. 1 is a schematic structural diagram of a blood flow simulation system, and a blood flow simulation system 100 includes the following modules.
The data is imported into the module 11.
For obtaining characteristic data of a blood vessel, for example, when the blood flow simulation system 100 is applied to disease diagnosis of a patient, the characteristic data of the blood vessel of the patient, including image data, physiological data, etc., may be imported through the data importing module 11.
The image data can be obtained based on nuclear magnetic resonance imaging (MRA), computed Tomography (CTA), digital subtraction imaging (DSA) or ultrasonic elastography. That is, the image data or the physiological data of the blood vessel is obtained by other devices or techniques, and then the blood flow simulation system 100 performs the blood flow simulation according to the image data or the physiological data.
A three-dimensional modeling module 12.
For constructing a three-dimensional model of the blood vessel from the blood vessel characteristic data acquired by the data import module 11. Specifically, a three-dimensional model of the blood vessel is constructed from the image data of the blood vessel. In the process of constructing the three-dimensional model, the three-dimensional model can be subjected to smoothing treatment, so that the three-dimensional model is more in line with the shape of the blood vessel; the three-dimensional model may also be trimmed, for example, when modeling the vessels of the heart, only the portion of the aorta is left, and other vessels in the three-dimensional model are trimmed.
When the user uses the present blood flow simulation system 100, the three-dimensional modeling module 12 may present the constructed three-dimensional model to the user, who determines whether the three-dimensional model is viable or not, and if not, reconstruct the three-dimensional model, such as a blood vessel model including a blood vessel wall.
After the three-dimensional model is built, a calculation area, namely a target area needing blood flow simulation, is defined on the three-dimensional model, wherein the calculation area can be the whole three-dimensional model or a part of the area in the three-dimensional model, for example, the three-dimensional model can be built for the whole blood vessel of the heart of a patient, but only the blood flow in the aorta is simulated, and the calculation area is the aorta.
A grid generation module 13.
The method is used for discretizing the calculation region and generating a grid for describing the calculation region. The generated mesh can embody the entire shape of the computing area.
Because the calculation process of blood flow simulation is to solve the hemodynamic control equation in the physical mathematical sense, and the solution of the hemodynamic control equation is to solve the partial differential problem, a discretization processing method such as a finite element method, a finite volume method, a discontinuous finite element method and the like is generally adopted when the partial differential problem is solved. Therefore, it is necessary to divide the calculation region into discrete grids for numerical simulation.
The mesh generation module 13 may divide the calculation region into a structured mesh or an unstructured mesh, which is used in the present application due to the complexity of the vessel geometry. For the calculation region of the three-dimensional structure, a Delaunay criterion, a front edge propulsion algorithm (Advancing Front Method) or a shepherd-Yery algorithm can be adopted to divide the tetrahedral grid units; hexahedral mesh cells may also be partitioned using a mapping method, a sub-mapping method, a scan method, a grid-based method, a medial axis method, a plasmterning method, or a Whisker Weaving method.
The boundary conditions module 14.
The method is used for determining boundary conditions when the calculation area is subjected to analog calculation, wherein the boundary conditions can be set by people or can be determined according to physiological data of blood vessels.
Based on the generated grid and the determined boundary conditions, the calculation region is solved, namely, the hemodynamic control equation with a certain boundary condition is solved, and when the hemodynamic control equation is solved, discretization is needed to be performed on the hemodynamic control equation, and then the discrete equation is solved through an algorithm. Finally, blood flow parameters in the calculation region are acquired, including blood flow speed, blood pressure, shearing force, blood vessel wall deformation and other information.
The connection relationship between the above modules is already shown in the functional description of the modules, and will not be described herein. The blood flow simulation system 100 can simulate blood flow, finally obtain parameters of blood flow in a calculation region, perform disease diagnosis according to the blood flow parameters, analyze pathological changes for pathological research, guide related operations of heart and cerebral vessels, such as vascular bypass operation and stent placement operation, simulate and evaluate postoperative conditions, and optimize the optimal design of stent structures in the vascular bypass operation by using bridges and stents.
To facilitate user interaction, the following modules are also included in the blood flow simulation system 100.
A visualization module 16.
The method is used for displaying the blood flow parameters after blood flow simulation, can be combined with a three-dimensional model for simulation display, for example, for the FFR value or the pressure value of the blood flow parameters, and can display different color distribution diagrams to a user based on the three-dimensional model, so that the blood flow simulation result is more visual.
The report generation module 17.
And generating a report according to the blood flow simulation result, and giving out disease diagnosis or treatment advice. Before report generation, the blood flow simulation result can be presented to the user, the user judges whether the blood flow simulation result is normal or not, if not, for example, a doctor considers that the result has large difference with other diagnostic results, grid generation can be performed again, and simulation calculation can be performed; if so, continuing to generate a report.
In the actual application of the blood flow simulation system 100, the application of the blood flow simulation system to a doctor is taken as an example.
The doctor can operate on the web interface or application interface of the blood flow simulation system 100, input the characteristic information of the blood vessel of the patient, and the characteristic information is imported into the system by the data importing module 11.
The three-dimensional modeling module 12 in the system generates a three-dimensional model of the blood vessel according to the characteristic information and performs visual presentation on an interface.
At this time, the doctor judges whether the three-dimensional model is feasible or not, and feeds back the judging result to the system; if feasible, the system grid generation module 13 performs discretization processing on the calculation region, and generates a grid for describing the calculation region.
The model solving module 15 solves the calculation region based on the grid, and boundary conditions and parameters of the calculation region are determined by the boundary condition module 14 in the solving process; and finally obtaining the blood flow parameters of the calculation region.
The visualization module 16 visually presents the blood flow parameters.
At this time, the doctor judges whether the simulation result is abnormal in blood flow parameters or not, and feeds back the judgment result to the system; if there is no abnormality, the report generation module 17 of the system generates a disease diagnosis report or a treatment plan report based on the simulation result.
The above-described respective modules constitute a system for realizing blood flow simulation, and from the viewpoint of the method, the blood flow simulation is realized mainly by the following steps. Referring to fig. 2, fig. 2 is a flow chart of a blood flow simulation method.
S11: feature data of the blood vessel is acquired.
S12: and constructing a three-dimensional model of the blood vessel according to the characteristic data, and defining a calculation region on the three-dimensional model.
S13: discretizing the calculation region to generate a grid for describing the calculation region.
S14: based on the grid, the calculation region is calculated, and thus the blood flow parameters of the calculation region are obtained.
The above steps correspond to each module in the blood flow simulation system 100, and specific processes in the steps are not repeated, where step S11 corresponds to the data importing module 11, step S12 corresponds to the three-dimensional modeling module 12, step S13 corresponds to the grid generating module 13, step S14 corresponds to the model solving module 15, and the boundary condition module 14.
The steps S11-S14 are basic steps for implementing the blood flow simulation, that is, the embodiments of the blood flow simulation method in the present application are all implemented based on the steps S11-S14. In order to improve the accuracy and efficiency of blood flow simulation, the application proposes optimizing the blood flow simulation process from multiple aspects. For example, the embodiment shown in fig. 3 and 5, the embodiment shown in fig. 3 introduces region decomposition in the discretization process of step S13 above; and based on the region decomposition, parallel computation is introduced in the above step S14 to improve the simulation efficiency. The embodiment shown in fig. 5 introduces fluid-solid full-coupling calculation in the above step S14 to improve the simulation accuracy.
The following describes two embodiments of the present application in detail. Referring first to fig. 3, fig. 3 is a flow chart illustrating an embodiment of a blood vessel blood flow simulation method of the present application. In the embodiment, the calculation area is decomposed, and the large-scale calculation area is decomposed into a plurality of small-scale calculation areas to be calculated independently, so that the calculation efficiency is improved, and the calculation accuracy is ensured by adopting a parallel algorithm. The present embodiment is a blood vessel blood flow simulation method based on regional decomposition, and the blood flow simulation method includes the following steps.
S21: feature data of the blood vessel is acquired.
In this embodiment, the feature data of the blood vessel may be acquired by receiving the feature data of the blood vessel transmitted from the external device (storage device, scanner, test instrument).
In other embodiments, the system for blood vessel flow simulation may be directly connected to a feature database of blood vessels (the feature database of blood vessels stores the latest feature data of blood vessels for each person). Before acquiring characteristic data of a blood vessel, the identity of the person to whom the blood vessel is to be simulated is determined. And acquiring the latest blood vessel characteristic data of the affiliated person from a characteristic database of the blood vessel according to the identity of the affiliated person.
The characteristic data of the blood vessel can be image data of the blood vessel and physiological characteristic data of the blood vessel.
S22: and constructing a three-dimensional model of the blood vessel according to the characteristic data. Wherein the three-dimensional model defines a calculation region.
The three-dimensional model of the blood vessel can be directly constructed through the characteristic data of the blood vessel. In other embodiments, the three-dimensional structure of the blood vessel may be determined through the feature data of the blood vessel, and then a three-dimensional model of the blood vessel may be constructed according to the three-dimensional structure of the blood vessel.
After the three-dimensional model of the blood vessel is built, the blood vessel area to be simulated (namely, a calculation area is defined on the three-dimensional model) can be determined according to the actual situation.
S23: discretizing the calculation region to generate a grid for describing the calculation region.
In this embodiment, the initial grid depicting the calculation region may be generated by performing a non-structurally stabilized finite element discretization process on the calculation region. The initial mesh may be an unstructured triangular mesh or an unstructured tetrahedral mesh, or an unstructured hexahedral mesh. Of course, the initial grid may also be a structured grid, or a semi-structured grid.
S24: and (3) carrying out encryption processing on the initial grid to generate a fine grid computing area, and keeping the fine grid units consistent with the shapes of the initial grid units.
The initial grid can be encrypted by adopting a consistent encryption algorithm, so that the grid can be encrypted rapidly under the condition of not changing the quality of the grid, for example, for a triangular grid unit, the midpoints of the sides of the triangular grid unit are connected, and one triangular grid unit is divided into four triangular grid units; for a three-dimensional tetrahedral mesh unit, it can be divided into eight tetrahedral units in the same way.
In the process of encrypting the initial grid, coarsening treatment can be carried out on the initial grid, so that the geometric information of part of grid units in the initial grid is reserved in the generated fine grid, namely, the geometric information in the initial grid is reserved. Firstly, selecting and reserving some geometrically important grid cells, such as all points on a curved surface, two end points on the plane edge and equidistant points inside; and deleting the grid cells which are not selected to be reserved, wherein the specific process adopts an Edge-connection algorithm to carry out iterative screening. After deleting the grid cells, the entire grid is optimized to ensure grid quality.
S25: and performing rough processing on the initial grid to generate a rough grid computing area, and keeping the number of rough grid points of the edge which characterizes the shape of the computing area consistent with the number of initial grid points of the edge which characterizes the shape of the computing area.
Coarsening the initial mesh may be a series of processes that merge the initial mesh. Merging the initial grid may be embodied as: the two adjacent initial meshes are merged into one coarse mesh by eliminating the common edges or common faces of the two adjacent initial meshes, for example by eliminating the common edges of the two adjacent triangular initial meshes.
In the course of coarsening the initial grids, a different priority may be assigned to each initial grid. By assigning priority to the initial grids, the undesired initial grids and the desired initial grids (the desired initial grids can be understood as initial grids containing more information, such as joints between blood vessels and/or the user is only a desired feature) are distinguished, the desired initial grids are kept as much as possible, the undesired initial grids are combined into coarse grids, so that the calculated vascular dynamics data of the desired region is finer, the calculation unit can be reduced, the calculation amount can be reduced, and the calculation efficiency can be improved.
In this embodiment, in the process of coarsening the initial grid, the number of coarse grid points of the edge that characterizes the shape of the calculation region and the number of initial grid points of the edge that characterizes the shape of the calculation region can be kept consistent, and the calculation accuracy can be improved.
S26: and calculating the coarse grid calculation area to obtain the final blood flow parameter of each coarse grid point in the coarse grid calculation area.
In this embodiment, iterative convergence calculation may be performed on the coarse mesh calculation region, to obtain the final blood flow parameter of each coarse mesh point in the coarse mesh calculation region.
The boundary conditions of the coarse mesh computing area may be acquired before the coarse mesh computing area is computed. The coarse mesh calculation region is then calculated based on the boundary conditions to obtain final blood flow parameters for each coarse mesh point.
The boundary conditions include one or more of a blood flow inlet boundary condition, a blood flow outlet boundary condition, and a vessel wall boundary condition.
The inlet boundary conditions include one or more of a coupled analog circuit inlet boundary condition, a blood flow pressure inlet boundary condition, and a blood flow velocity inlet boundary condition.
The outlet boundary conditions include one or more of an analog circuit outlet boundary condition, a blood flow resistance outlet boundary condition, and a small vessel tree boundary condition.
The wall boundary conditions include non-slip wall boundary conditions; according to whether the wall surface is rigid, the wall surface is divided into a rigid wall surface boundary condition, a unidirectional fluid-solid coupling wall surface boundary condition and a bidirectional fluid-solid coupling wall surface boundary condition.
S27: an initial blood flow parameter is generated for each fine mesh point in the fine mesh calculation region based on the final blood flow parameter for each coarse mesh point.
In this embodiment, the final blood flow parameter of the coarse mesh point may be converted into the initial blood flow parameter of the fine mesh point, so that the numerical conversion of the blood flow parameter between the coarse mesh and the fine mesh can be directly performed, so that the final blood flow parameter of the fine mesh point can be calculated by the initial blood flow parameter of the fine mesh point. Specifically, the numerical conversion of the blood flow parameter between the coarse and fine meshes may be performed by an interpolation calculation method.
S28: and calculating the fine grid calculation region based on the initial blood flow parameters of each fine grid point to obtain the final blood flow parameters of each fine grid point in the fine grid calculation region.
In this embodiment, the iterative convergence calculation may be performed on the fine mesh calculation area based on the initial blood flow parameter of each fine mesh point, to obtain the final blood flow parameter of each fine mesh point. Therefore, the efficiency and the accuracy of blood flow parameter calculation can be improved through a multi-level calculation mode of the coarse grid and the fine grid.
In practical application, the blood flow simulation calculation scale of the embodiment is larger, and the blood flow simulation calculation scale is generally uploaded to a super calculation center for calculation, so that when the blood flow simulation system is applied to a local computer to realize the blood flow simulation method, a set of initial grids can be firstly generated on the local computer, and then the initial grids are uploaded to the super calculation center for grid encryption, coarsening and other treatments. The process can obtain the initial grid with better depicting calculation area on the local computer, encrypt and thicken the initial grid based on the initial grid with better quality, and further ensure the quality of the subsequent grid, thereby improving the calculation precision.
In this embodiment, an initial grid is obtained by performing discretization processing on a calculation area, coarse grid calculation is obtained on the basis of the initial grid, then coarse grid calculation area is obtained by coarsening the initial grid, fine grid calculation area is obtained by encrypting the initial grid, coarse grid calculation area is calculated, fine grid calculation area is calculated according to coarse grid calculation result, and final blood flow parameter is obtained by calculating fine grid calculation area based on calculation result of coarse grid calculation area obtained by coarsening the initial grid, so that not only the calculation amount (the number of grid units of the coarse grid is less, and the calculation complexity is reduced) is reduced, but also calculation result can be obtained by multi-level calculation, and calculation efficiency and accuracy are improved.
In addition, the optimization of the above steps is further proposed in this embodiment, so as to improve the calculation efficiency and accuracy.
For example, step S26 may include the following S261 and S262.
S261: the coarse mesh calculation region is divided into a plurality of first sub-calculation regions, and the number of mesh points of each first sub-calculation region is identical.
Before actual calculation, the coarse grid calculation region can be divided into a first sub calculation region, namely, a large-scale calculation region is divided into a plurality of small-scale calculation regions, so that the calculation scale is reduced, and the calculation efficiency is improved.
In addition, the number of grid points in each first sub-calculation area obtained through division is consistent, so that coarse grid calculation areas can be equally divided, the calculation scale of each sub-calculation area is ensured to be consistent, and the overall calculation efficiency is improved.
S262: and simultaneously calculating the plurality of first sub-calculation areas to obtain the final blood flow parameters of each coarse grid point in the coarse grid calculation area.
After the coarse grid computing area is divided into areas, the computing areas are independent. And simultaneously, the plurality of first sub-calculation areas are calculated, namely the plurality of first sub-calculation areas are calculated in parallel, so that the final blood flow parameter of each coarse grid point in the plurality of first sub-calculation areas can be obtained at one time, and the calculation efficiency is improved. Of course, it is also possible to perform parallel computation on all the first sub-computation regions simultaneously.
In this embodiment, there may be a first overlap region between every adjacent two first sub-calculation regions. Accordingly, when the first sub-calculation regions are calculated, iterative convergence calculation can be performed on the plurality of first sub-calculation regions at the same time, and parameter exchange synchronization is performed in the first overlapping region, so that the consistency of the calculation precision of the plurality of first sub-calculation regions can be ensured.
As with the region decomposition and parallel computation of coarse meshes, the region decomposition and parallel computation may also be performed on fine meshes. Specifically, step S28 may include two steps S281 and S282.
S281: the fine grid computing area is divided into a plurality of second sub-computing areas, and the grid points of each second sub-computing area are identical in number.
The first sub-calculation areas are in one-to-one correspondence with the second sub-calculation areas, or one first sub-calculation area is a combination of at least two second sub-calculation areas. Therefore, the fine grid points in each second sub-calculation region can be ensured to fall in the same first sub-calculation region, the calculation result of the second sub-calculation region can be calculated based on the calculation result of the first sub-calculation region, and the calculation efficiency and accuracy are improved.
S282: and simultaneously calculating a plurality of second sub-calculation areas based on the initial blood flow parameters of each fine grid point to obtain the final blood flow parameters of each fine grid point in the fine grid calculation areas.
After the fine-grid computing regions are divided into regions, the computation between the sub-computing regions is independent of each other. And simultaneously, the plurality of second sub-calculation areas are calculated, namely the plurality of second sub-calculation areas are calculated in parallel, so that the final blood flow parameter of each fine grid point in the plurality of second sub-calculation areas can be obtained at one time, and the calculation efficiency is improved.
In this embodiment, the calculation region is divided into a plurality of second sub-calculation regions, and a first overlap region is provided between every two adjacent second sub-calculation regions. And simultaneously, carrying out iterative convergence calculation on the plurality of second sub-calculation areas, and carrying out parameter exchange synchronization on the second overlapping areas, so that the consistency of the calculation precision of the plurality of first sub-calculation areas can be ensured.
With continued reference to fig. 5, fig. 5 is a schematic flow chart of another embodiment of the blood vessel blood flow simulation method of the present application, in which a fluid-solid full-coupling physical mathematical model is built to perform full-coupling calculation, that is, interactions between blood flow and blood vessels are considered when performing blood flow simulation, so that the simulation calculation accuracy is improved in the present embodiment; and the calculation efficiency is ensured by combining a nonlinear system solving algorithm. The embodiment is a blood vessel blood flow simulation method based on a mechanical equation, and the blood flow simulation method in the embodiment comprises the following steps.
S31: feature data of the blood vessel is acquired.
S32: and constructing a three-dimensional cavity model and a blood vessel wall model of the blood vessel according to the characteristic data. Wherein the three-dimensional cavity model and the vessel wall model define a calculation region.
And constructing a three-dimensional cavity model of the blood vessel according to the characteristic data, constructing a blood vessel wall model by expanding 10% of the diameter of the blood vessel at the position of the external normal direction of the surface of the blood vessel, and defining a calculation area for the three-dimensional cavity model and the blood vessel wall model.
S33: discretizing the calculation region based on the unstructured stabilized finite element to generate an unstructured tetrahedron initial grid for describing the calculation region.
In order to improve the calculation efficiency and accuracy, step S43 may include the following two steps:
s331: and (3) carrying out encryption processing on the initial grid to generate a fine grid computing area, and keeping the fine grid units consistent with the shapes of the initial grid units.
The initial grid can be encrypted by adopting a consistent encryption algorithm, so that the grid can be encrypted rapidly under the condition of not changing the quality of the grid, for example, for a triangular grid unit, the midpoints of the sides of the triangular grid unit are connected, and one triangular grid unit is divided into four triangular grid units; for a three-dimensional tetrahedral mesh unit, it can be divided into eight tetrahedral units in the same way.
In the process of encrypting the initial grid, coarsening treatment can be carried out on the initial grid, so that the geometric information of part of grid units in the initial grid is reserved in the generated fine grid, namely, the geometric information in the initial grid is reserved. Firstly, selecting and reserving some geometrically important grid cells, such as all points on a curved surface, two end points on the plane edge and equidistant points inside; and deleting the grid cells which are not selected to be reserved, wherein the specific process adopts an Edge-connection algorithm to carry out iterative screening. After deleting the grid cells, the entire grid is optimized to ensure grid quality.
S332: and performing rough processing on the initial grid to generate a rough grid calculation region, keeping the number of rough grid points of the edge of the calculation region shape of the three-dimensional cavity model consistent with that of the initial grid points, and keeping the number of rough grid points of the edge of the calculation region shape of the blood vessel wall model consistent with that of the initial grid points.
Coarsening the initial mesh may be a series of processes that merge the initial mesh. Merging the initial grid may be embodied as: the two adjacent initial meshes are merged into one coarse mesh by eliminating the common edges or common faces of the two adjacent initial meshes, for example by eliminating the common edges of the two adjacent triangular initial meshes.
In the course of coarsening the initial grids, a different priority may be assigned to each initial grid. By assigning priority to the initial grids, the undesired initial grids and the desired initial grids (the desired initial grids can be understood as initial grids containing more information, such as joints between blood vessels and/or the user is only a desired feature) are distinguished, the desired initial grids are kept as much as possible, the undesired initial grids are combined into coarse grids, so that the calculated vascular dynamics data of the desired region is finer, the calculation unit can be reduced, the calculation amount can be reduced, and the calculation efficiency can be improved.
In this embodiment, in the process of coarsening the initial grid, the number of coarse grid points of the edge that characterizes the shape of the calculation region and the number of initial grid points of the edge that characterizes the shape of the calculation region can be kept consistent, and the calculation accuracy can be improved.
S34: and constructing a physical mathematical model of the calculation region.
The physical mathematical model can describe the physical phenomena of blood flow, vessel wall deformation and the influence of interaction forces between the two on blood flow parameters. The physical mathematical model is solved, and the obtained blood flow parameters represent blood flow characteristics. The physical mathematical model describes a physical phenomenon control equation, and the physical mathematical model constructed in the embodiment comprises a fully-coupled fluid mechanical control equation, a solid mechanical control equation, a grid movement equation and a fluid-solid interface equation.
Blood flow rate, pressure, etc. can be obtained from the fluid mechanics control equation including: compressible and incompressible navier-storage equations and their corresponding various turbulence models, such as, for example, reynolds average, large vortex simulation, etc.
Vessel wall displacement and the like can be obtained according to a solid mechanics control equation, which comprises: solid constitutive equations for linear and nonlinear elasticity, and models for viscoelastic, elastoplastic, porous media, and the like.
Fluid-solid full coupling in the constructed physical mathematical model, and thus the physical mathematical model further comprises: fluid-solid interface conditions.
The physical mathematical model also comprises the following components corresponding to the boundary in the calculation region: the sliding or non-sliding wall fixing boundary condition, the damping outflow boundary condition, the non-pressure boundary condition or the physiological boundary condition of the three-element elastic cavity and the like, and different boundary conditions correspond to different physical phenomena and directly influence the calculation complexity and the adaptability of the problem.
S35: and carrying out iterative convergence calculation on the physical mathematical model based on the grid to obtain the blood flow parameters and the blood vessel parameters of the calculation region.
In this embodiment, based on the grid, performing iterative convergence calculation on the physical mathematical model may include: performing iterative convergence calculation on the physical mathematical model based on the coarse grid, and simultaneously obtaining blood flow parameters, blood vessel parameters and grid change parameters of a coarse grid calculation area; updating the calculation area according to the grid change parameters; to obtain final blood flow parameters, final vascular parameters and final grid variation parameters.
And generating the initial blood flow parameters, the initial blood vessel parameters and the initial grid change parameters of the fine grid calculation region by interpolation algorithm from the final blood flow parameters, the final blood vessel parameters and the final grid change parameters of the coarse grid calculation region.
Performing iterative convergence calculation on the physical mathematical model based on the fine grid, and simultaneously obtaining blood flow parameters, blood vessel parameters and grid change parameters of a fine grid calculation area; updating the calculation area according to the grid change parameters; to obtain final blood flow parameters, final vascular parameters and final grid variation parameters.
The physical mathematical model constructed in the above step S34 couples the fluid mechanical control equation, the solid mechanical control equation, the mesh movement equation, and the fluid-solid interface equation to one equation. In the step S35, the solution is carried out in the equation, iteration among a plurality of equations is not needed in the calculation process, one-time solution is realized, and the solution precision is ensured.
Specifically, the method is based on grids, and is used for solving a fluid mechanics control equation, a solid mechanics control equation, a grid movement equation and a fluid-solid interface equation simultaneously, and the grid point information of the blood flow grid at the fluid-solid interface in the region and the grid point information of the blood vessel grid are uniformly calculated during solving.
The interaction of the fluid-solid interface and the acting force are opposite to each other, for example, the parameters such as shearing force, displacement and the like have a certain relation. Therefore, the fluid-solid interface condition is adopted in the physical mathematical model to simulate the interface condition; unifying grid point information of the fluid-solid interface in a network of the calculation region, specifically, unifying the grid point information through point-to-point information conversion if the blood flow grid at the interface is matched with the blood vessel grid; if the blood flow grid and the blood vessel grid at the interface are not matched, the interpolation method is utilized to unify grid point information, and a linear and quadratic interpolation method based on a finite element basis function, a radial basis function interpolation method, a Mortar element method and the like can be adopted.
The above steps create a fluid-solid coupled physical mathematical model that is calculated to more accurately simulate blood flow in a blood vessel.
When the fluid-solid full-coupling one-time solution is carried out, the problem scale is very large, so the embodiment also provides that a nonlinear system solution algorithm is utilized to calculate a physical mathematical model, and a Newton-gram Lei Luofu-Schwarz (Newton-Krylov-Schwarz) algorithm can be adopted specifically, and the method comprises the following steps.
S351: discretizing the physical mathematical model to obtain a nonlinear equation set.
First, discretizing a physical mathematical model, namely discretizing a partial differential equation into a nonlinear equation set. Wherein, for the hydrodynamic control equation, methods such as stabilized P1-P1 element, classical Taylor-Hood P2-P1 element and the like can be adopted; for a solid mechanical control equation, PEERS elements are adopted for a mixed form of a given weak symmetrical stress tensor, and uncoordinated P1 elements are adopted for displacement; for the fluid-solid interface conditions, the discrete format adopts a Mortar or hybridization technique and a novel method based on Lagrange multipliers.
S352: and solving a nonlinear equation set by using a non-precise Newton method.
In the solving process of the step, the searching direction and the step length can be determined by adopting the linear searching and the feasible domain technology, and the linear searching is carried out in the feasible domain; in the iteration process of solving by a non-precise Newton method, a grid sequence method and a non-linear preprocessing technology can be adopted, so that the non-linear iteration process of the step has grid-independent convergence; and for Jacobian matrix in the inaccurate Newton method, the method adopts a multi-color sorting finite difference method, an automatic differentiation technology, a Jacobian-free method or explicit generation and other strategy construction generation.
S353: and solving a linear equation set in the non-accurate Newton method by using a Kranolav subspace iteration method.
Specifically, a linear equation set with an asymmetric matrix in the non-precise newton method is solved in this step by using GMRES, or Lanczos double orthogonalization method of Short-repetition (Short-Recurrence).
S354: and constructing preconditions in the linear equation set by using a regional decomposition method.
Constructing preconditions accelerates the linear solution in step S353, in this embodiment, an overlapping Schwarz (Schwarz) algorithm is adopted, and specifically, the preconditions may be constructed by using an adjusting extended additive Schwarz algorithm or a limiting additive Schwarz algorithm.
If the calculation region is divided into a plurality of overlapping sub-calculation regions in this embodiment, a calculation method for the sub-calculation regions needs to be introduced, and in this embodiment, a direct method or an iterative method is adopted, including an LU decomposition algorithm, an incomplete LU decomposition algorithm, a Gauss-Seidel iterative method, and the like. The matrix of sub-regions is sparse and its non-zero elements can be stored and accessed in a point-block (point-block) fashion, i.e., a direct method or an iterative method can simultaneously store and access multiple variables on a node in the order of the grid node. When the direct method is adopted to solve the subarea problem, different subarea matrix ordering modes can be adopted, including methods of Nested Dissection, one-way discovery, reverse cuethill-McKee, quotient Minimum Degree and the like.
And solving the physical mathematical model by using a nonlinear system solving algorithm to obtain blood flow parameters and blood vessel parameters. The vessel parameters include the moving value of the vessel wall, the moving of the vessel wall has a certain influence on the grid, and the change of the grid needs to be considered in the next calculation. The following steps are also performed in this embodiment.
S36: the change parameters of the mesh are calculated from the vessel parameters, thereby updating the calculation region.
In the step S36, a moving grid equation is constructed to describe the movement of the grid, and the moving grid equation is calculated to obtain the change parameters of the grid, and because the calculation process involves the blood vessel parameters, the moving grid equation can be integrated into the physical mathematical model constructed in the step S34 to perform simultaneous solution, i.e. the step S36 and the step S35 have no strict precedence relationship, and can be performed simultaneously.
The physical mathematical model constructed in this embodiment may take the following form.
Fluid dynamics equation:
fluid-solid interface equation:
σ f ·n f ＝-σ s ·n s on Γ interface ,
d＝x on Γ interface ,
solid dynamics control equation:
grid movement equation:
the damping type outflow boundary conditions are as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,
is the Cauchy stress tensor of the flow field, u represents the blood flow velocity, p f Is the blood flow pressure ρ f For the blood density, μ is the viscosity coefficient of blood (μ is a constant when blood is considered as newtonian fluid and a complex function when it is considered as non-newtonian fluid).
d represents the displacement of the vessel wall, sigma s Let =λtrace (ε) i+2με be the stress tensor of the vessel wall, where λ and μ s Is the coefficient of the Lame and,
x represents the displacement of the grid movement, sigma m Is the stress tensor, form and sigma of the grid model s The same, but the corresponding Lame coefficients take different values.
The choice of the stress tensor in the above equation, the construction of the viscosity coefficient and the choice of the boundary conditions, and the choice of the stress tensor in the fluid and solid equations all need to be dependent on the specific properties of the blood and the vessel wall, and in practical clinical applications, the values are different for each case.
The method of the embodiment constructs a fluid-solid full-coupling physical mathematical model, and updates the grid change of the calculation area, so that the blood flow simulation is more accurate; a nonlinear system solving algorithm is introduced in the analog calculation to ensure the calculation efficiency.
The embodiment shown in FIG. 3 involves performing a region decomposition of the computation region after grid generation and performing parallel computation based on the region decomposition; the embodiment shown in fig. 5 involves establishing a physical mathematical model of fluid-solid full coupling to perform fluid-solid full coupling calculation and setting up a solution algorithm in a targeted manner; the techniques involved in both may be applied in combination.
For example, the mesh generation module in the blood flow simulation system adopts the mesh generation technology and the region decomposition technology of the embodiment shown in fig. 3, and the model solving module introduces the construction of the fluid-solid full-coupling model shown in fig. 5 and the adoption of the corresponding algorithm. For the blood flow simulation process, great improvement of simulation efficiency and accuracy is realized.
The above blood flow simulation methods can be implemented based on the software architecture shown in fig. 1, and in terms of hardware structure, please refer to fig. 6, fig. 6 is a schematic structural diagram of an embodiment of a blood flow simulation device in the present application.
The blood flow simulation device 200 of the present embodiment includes a processor 21 and a memory 22, where the memory 22 stores a computer program executable on the processor 21, and the processor 21 can implement the blood flow simulation method when executing the computer program.
The processor 21 in this embodiment is a broad-sense processor, and may include a plurality of processors, may be processors disposed in different devices, and may include a processor in a local computer and a processor group of a supercomputer. In this embodiment, when parallel computation is performed for blood flow simulation, how many sub-computation areas are provided, and how many processors are correspondingly provided to respectively compute the sub-computation areas.
In this embodiment, the processor 21 may adopt a heterogeneous architecture, and when the processor 21 of this embodiment is used to perform parallel computation of large-scale data, a series of parallel acceleration techniques are adopted, that is, according to the characteristics of different computations, the computing process is placed on different processors, so as to implement maximum utilization of the processor capacity.
For example, in terms of solution, core computing modules such as computation of nonlinear discrete functions, sparse matrix vector multiplication, sparse matrix fast decomposition, and the like, which are more time-consuming in nonlinear solution and linear solution, are transplanted to a GPU, MIC, or other many-core processor. The multi-color or multi-scheduling strategy is adopted to improve the decomposition and backtracking solution of the sparse matrix, so that on one hand, the algorithm parallelism is improved, and on the other hand, the convergence efficiency of the solver is maintained. The parts of boundary conditions and the like which relate to a large number of branch operations are independent from the inside of the region, and the parts with high logic processing capacity are used for calculating so that tasks are distributed more reasonably.
In the aspect of instruction calculation of a processor, the instruction level parallelism, the thread level parallelism and the process level parallelism are optimized, and the operation on the many-core processor is optimized by adopting the technologies of data reuse, calculation and memory access overlapping, data fusion and boundary access, data merging transmission, vectorization, scientific operation function optimization and the like, so that the floating point efficiency in actual running is improved.
Instructions of the processor implement programming language aspects, for GPU, MIC or other many-core processors, are executed on the GPU using CUDA, openACC, openCL language; executing on the MIC using OpenMP language; the pthread or other function packages are used to execute on other many-core processors.
When a plurality of processors process large-scale data in parallel, it is necessary to improve efficiency not only in terms of computation but also in terms of data transmission. For example, a series of large-scale discrete data parallel processing techniques are employed in this embodiment.
Blocking parallel I/O technology: and establishing a partitioned data structure to balance loads among the processors. That is, discrete data representing physical quantities of blood vessels and blood are read from or output to one or a plurality of data files in parallel by dividing the data into blocks in the calculation region, and the number of the divided blocks is equal to the number of processors used. The blocking parallel I/O technology in the embodiment is realized by adopting a mode of designating an explicit offset, an independent file pointer or a shared file pointer based on an MPI-2 (and the versions above) function library. The data file includes HDF5, VTK, etc. formats.
Coarsening or encrypting output technology, i.e. coarsening or encrypting grids representing blood vessels and blood, interpolating physical quantities on the original grids onto new grids, and outputting by using the block parallel I/O technology.
The vector compression technology or the MPI_pack data packing technology is adopted to reduce data traffic and I/O data traffic, and an overlapping mechanism of I/O and calculation is designed to solve the I/O bottleneck of large-scale discrete data.
The blood flow simulation device of the embodiment realizes the full utilization of an advanced computer with thousands of calculation cores, fully invokes calculation resources through the cooperation of software and an algorithm, improves the accuracy and the efficiency of blood flow dynamics analysis, realizes the parallel extensible efficiency of more than 60 percent, improves the blood flow dynamics simulation accuracy and reduces the calculation time.
When the blood flow simulation method is implemented in software and sold or used as a separate product, the blood flow simulation method may be stored in an electronic device readable storage medium, that is, the invention further provides a computer readable storage medium, please refer to fig. 7, fig. 7 is a schematic structural diagram of an embodiment of the computer readable storage medium of the present application, and the computer readable storage medium 300 stores a computer program, where the computer program when executed by a processor implements the steps of the method. The computer readable storage medium may be a usb disk, an optical disk, a server, etc.
The foregoing description is only of embodiments of the present application, and is not intended to limit the scope of the patent application, and all equivalent structures or equivalent processes using the descriptions and the contents of the present application or other related technical fields are included in the scope of the patent application.
Claims (9)
1. A vascular flow simulation method based on a mechanical equation, the method comprising:
acquiring characteristic data of the blood vessel;
constructing a three-dimensional cavity model and a blood vessel wall model of the blood vessel according to the characteristic data, wherein a calculation area is defined by the three-dimensional cavity model and the blood vessel wall model;
discretizing the calculation region based on unstructured stabilized finite elements to generate an unstructured tetrahedron initial grid for describing the calculation region;
encrypting the initial grid to generate a fine grid computing area, and keeping the shapes of the fine grid units and the initial grid units consistent; the fine grid computing area comprises a plurality of second sub-computing areas, and the number of fine grid units of each second sub-computing area is consistent;
coarsening the initial grid to generate a coarse grid calculation area, keeping the number of coarse grid points which characterize the edge of the calculation area shape of the three-dimensional cavity model consistent with that of the initial grid points, and keeping the number of coarse grid points which characterize the edge of the calculation area shape of the blood vessel wall model consistent with that of the initial grid points; in the process of coarsening the initial grids, assigning a priority to each initial grid, and coarsening the initial grids based on the priority, wherein the coarse grid computing area comprises a plurality of first sub-computing areas, and the number of coarse grid units of each first sub-computing area is consistent, wherein one first sub-computing area is a combination of at least two second sub-computing areas;
Constructing a physical mathematical model of the calculation region, wherein the physical mathematical model comprises a fully-coupled fluid mechanics control equation, a solid mechanics control equation, a grid movement equation and a fluid-solid interface equation;
calculating the physical mathematical model based on the plurality of first sub-calculation regions to obtain a final blood flow parameter, a final blood vessel parameter and a final grid variation parameter of each coarse grid unit in the coarse grid calculation region;
calculating an initial blood flow parameter, an initial blood vessel parameter and an initial grid variation parameter of the fine grid calculation region based on the final blood flow parameter, the final blood vessel parameter and the final grid variation parameter of the coarse grid calculation region;
and calculating the physical mathematical model based on the plurality of second sub-calculation regions to obtain a final blood flow parameter, a final blood vessel parameter and a final grid variation parameter of each fine grid unit in the fine grid calculation region.
2. The method of claim 1, wherein the vessel wall model is constructed by expanding 10% of the vessel diameter at the location in the outward normal direction of the vessel surface.
3. The vascular blood flow simulation method of claim 1, wherein the computing the physical mathematical model based on the plurality of the first sub-computation regions comprises:
Performing iterative convergence calculation on the physical mathematical model based on the plurality of first sub-calculation areas, and simultaneously obtaining blood flow parameters, blood vessel parameters and grid variation parameters of the coarse grid calculation area; and updating the calculation area according to the grid change parameters.
4. The method of claim 3, wherein calculating the initial blood flow parameters of the fine mesh computing region based on the final blood flow parameters of the coarse mesh computing region, the final blood flow parameters, and the final mesh variation parameters, the initial blood flow parameters, and the initial mesh variation parameters comprise:
and generating an initial blood flow parameter, an initial blood vessel parameter and an initial grid change parameter of the calculation fine grid calculation region by interpolation algorithm from the final blood flow parameter, the final blood vessel parameter and the final grid change parameter of the coarse grid calculation region.
5. The vascular blood flow simulation method of claim 4, wherein the computing the physical mathematical model based on the plurality of the second sub-computation regions includes:
performing iterative convergence calculation on the physical mathematical model based on the plurality of second sub-calculation areas, and simultaneously obtaining blood flow parameters, blood vessel parameters and grid change parameters of the fine grid calculation area; and updating the calculation area according to the grid change parameters.
6. The vascular blood flow simulation method of claim 1, wherein the performing iterative convergence computation on the physical mathematical model includes: discretizing the physical mathematical model to obtain a nonlinear equation set; solving a nonlinear equation set by using a non-precise Newton method; constructing preconditions in a linear equation set which appear when the non-accurate Newton method is solved by utilizing a limiting Schwarz algorithm; and solving the linear equation set by using a Kranolav subspace iteration method based on the preconditioner.
7. The vascular blood flow simulation method of claim 6, wherein the physical mathematical model includes a sliding or non-sliding solid wall boundary condition, a damped outflow boundary condition, a non-pressure boundary condition, or a three element elasto-luminal physiological boundary condition.
8. A blood flow simulation device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of claims 1-7 when the computer program is executed by the processor.
9. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method according to any of claims 1-7.
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