CN110634572A - Blood vessel blood flow simulation method based on mechanical equation and related device - Google Patents
Blood vessel blood flow simulation method based on mechanical equation and related device Download PDFInfo
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- CN110634572A CN110634572A CN201910907673.8A CN201910907673A CN110634572A CN 110634572 A CN110634572 A CN 110634572A CN 201910907673 A CN201910907673 A CN 201910907673A CN 110634572 A CN110634572 A CN 110634572A
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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 vessel wall model of the vessel according to the characteristic data, and defining a calculation area; discretizing the calculation area to generate an initial grid depicting the calculation area; carrying out encryption processing on the initial grid to generate a fine grid computing area; carrying out coarse processing on the initial grid to generate a coarse grid calculation area; calculating the coarse grid calculation region to obtain the final blood flow parameter of each coarse grid point in the coarse grid calculation region; generating an initial blood flow parameter of each fine grid point in a fine grid calculation region according to the final blood flow parameter 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. An accurate and efficient simulation of blood flow in a blood vessel is achievable.
Description
Technical Field
The present application relates to the field of blood flow numerical simulation, and in particular, to a method and related apparatus for simulating blood flow in a blood vessel based on a mechanical equation.
Background
The characteristics of blood flow may reflect, to some extent, the presence of disease in the blood vessels and the presence of disease resulting from alterations in hemodynamics in the patient, e.g., Fractional Flow Reserve (FFR) may reflect the risk of ischemia, the rate of blood flow may reflect the degree of vascular occlusion, etc. Therefore, the simulation analysis of blood flow has become a research hotspot in the field of prevention and diagnosis of vascular diseases
In the early days, due to the limitation of computer capability, a lot of simplifications are carried out when the blood flow is simulated, such as the simplification of a physical model and the simplification of a discretization grid; although the calculation is time-efficient, some important characteristics of the blood flow cannot be obtained, and the simulation accuracy is not high. However, after the hardware level of the current computer is developed, there is no simulation method matching with the computer capability, and the efficiency and precision of blood flow simulation cannot be simultaneously improved, that is, the precision and efficiency of the current blood flow simulation are still not high.
Disclosure of Invention
The application provides a vascular blood flow simulation method and a related device based on a mechanical equation, which aim to solve the problems of low precision and low efficiency of blood flow simulation in the prior art.
In order to solve the above technical problem, the present application provides a method for simulating blood flow of a blood vessel 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; carrying out discretization processing based on an unstructured stabilized finite element on the calculation region to generate an unstructured tetrahedral initial grid for describing the calculation region; encrypting the initial grid to generate a fine grid calculation region, and keeping the shape of the fine grid unit consistent with that of the initial grid unit; performing rough treatment on the initial grid to generate a rough grid calculation region, keeping the number of rough grid points depicting 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 the rough grid points depicting the edge of the calculation region 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 mesh to obtain a final blood flow parameter, a final blood vessel parameter and a final mesh change parameter; calculating initial blood flow parameters, initial blood vessel parameters and initial grid change parameters of the fine grid calculation region based on the final blood flow parameters, the final blood vessel parameters and the final grid change parameters of the coarse grid calculation region; and calculating the physical mathematical model based on the fine mesh to obtain a final blood flow parameter, a final blood vessel parameter and a final mesh change parameter.
In order to solve the above technical problem, the present application provides a blood flow simulation apparatus, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method when executing the computer program.
To solve the above technical problem, the present application provides a computer-readable storage medium, on which a computer program is stored, and the computer program, 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 blood vessels; 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 area to generate a grid depicting the calculation area; constructing a physical mathematical model of a calculation area, 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 grid to obtain blood flow parameters and blood vessel parameters of a calculation region; and calculating the change parameters of the grid according to the blood vessel parameters, thereby updating the calculation area. In the method, the physical mathematical model of the fluid-solid total coupling is established to perform the total coupling calculation, namely, the interaction between the blood flow and the blood vessel is considered during the blood flow simulation, and the calculation area is updated, so that the simulation calculation precision is improved.
Drawings
FIG. 1 is a schematic diagram of a blood flow simulation system;
FIG. 2 is a schematic flow diagram of a blood flow simulation method;
FIG. 3 is a schematic flow chart diagram illustrating an embodiment of a method for simulating vascular blood flow according to the present application;
FIG. 4 is a schematic illustration of the partitioning of the computation regions in the embodiment shown in FIG. 3;
FIG. 5 is a schematic flow chart diagram illustrating another embodiment of a method for simulating vascular blood flow according to the present application;
FIG. 6 is a schematic structural diagram of an embodiment of a blood flow simulator of the present application;
FIG. 7 is a schematic structural diagram of an embodiment of a computer-readable storage medium of the present application.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present application, the blood flow simulation method, the blood flow simulation apparatus and the computer readable storage medium based on mechanical equations provided by the present invention are further described in detail below with reference to the accompanying drawings and the detailed description.
The simulation of the blood flow in the blood vessel is to simulate the flow of the blood by using a fluid mechanics method, and obtain a mechanical characteristic blood flow parameter comprising the blood flow. Referring to fig. 1, fig. 1 is a schematic structural diagram of a blood flow simulation system, and the blood flow simulation system 100 includes the following modules.
And a data import module 11.
For obtaining the characteristic data of the 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 by the data import module 11.
The image data may be acquired based on techniques such as magnetic resonance imaging (MRA), Computed Tomography (CTA), Digital Subtraction Angiography (DSA), or ultrasound elastography. That is, first, other devices or techniques obtain image data or physiological data of a blood vessel, and then the blood flow simulation system 100 performs blood flow simulation according to the image data or 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 a blood vessel is constructed from 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 retained and the other vessels in the three-dimensional model are trimmed away.
When the user uses the blood flow simulation system 100, the three-dimensional modeling module 12 may present the constructed three-dimensional model to the user visually, and the user determines whether the three-dimensional model is feasible or not, and if not, reconstructs the three-dimensional model, for example, a blood vessel model including a blood vessel wall.
After the three-dimensional model is constructed, a calculation region, that is, a target region to be subjected to blood flow simulation, is defined on the three-dimensional model, and the calculation region may be the entire three-dimensional model or a certain region in the three-dimensional model, for example, the three-dimensional model may be established for the entire blood vessel of the heart of a patient, but only the blood flow in the aorta is simulated, and at this time, the calculation region is the aorta.
A mesh generation module 13.
The method is used for carrying out discretization processing on the calculation area to generate a grid depicting the calculation area. The generated mesh can embody the entire shape of the calculation region.
In the calculation process of blood flow simulation, the hemodynamic control equation is solved in the physical and mathematical sense, and the solution of the hemodynamic control equation is to solve the partial differential problem, and a discretization processing method, such as a finite element method, a finite volume method, an intermittent 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 structured meshes or unstructured meshes, which are used in the present application due to the complexity of the vessel geometry. For a calculation region of a three-dimensional structure, a tetrahedral mesh unit can be divided by adopting a Delaunay criterion, a leading edge pushing algorithm (Advancing Front Method) or a Shephard-Yerry algorithm; and the hexahedral grid cells can also be marked by adopting a mapping method, a sub-mapping method, a sweep method, a grid-based method, a medial surface method, a leveling method or a Whisserweaveing method.
A boundary condition module 14.
The method is used for determining the boundary conditions when the simulation calculation is carried out on the calculation area, wherein the boundary conditions can be set manually or determined according to the physiological data of the blood vessel.
A model solving module 15.
And solving the calculation region based on the generated grid and the determined boundary condition, namely solving a hemodynamic control equation applying a certain boundary condition, wherein in the solving, the hemodynamic control equation is discretized firstly, and then the discretized equation is solved through an algorithm. And finally, obtaining blood flow parameters in the calculation area, wherein the blood flow parameters comprise information such as blood flow velocity, blood pressure, shearing force, vessel wall deformation and the like.
The connection relationship between the modules is already embodied in the functional description of the modules, and is not described herein again. The blood flow simulation system 100 can simulate blood flow, finally obtain parameters of blood flow in a calculation area, diagnose diseases according to the blood flow parameters, analyze pathological changes and perform pathological research, guide related operations of cardiovascular and cerebrovascular, such as a vascular bypass operation and a vascular stent placement operation, simulate and evaluate postoperative conditions, and optimize the optimal design of a stent structure in the vascular bypass operation by using a bridge and placing the vascular stent in the operation.
For more convenient user interaction, the blood flow simulation system 100 further includes the following modules.
A visualization module 16.
The blood flow simulation system is used for displaying blood flow parameters after blood flow simulation, simulation display can be performed by combining the three-dimensional model, for example, for blood flow parameter FFR values or pressure values, different color distribution maps can be presented and displayed to a user based on the three-dimensional model, and blood flow simulation results are enabled to be more visual.
A report generation module 17.
And generating a report according to the blood flow simulation result, and giving disease diagnosis or treatment suggestions. Before the report is generated, a blood flow simulation result can be presented to a user, the user judges whether the blood flow simulation result is normal or not, if the result is abnormal, for example, a doctor considers that the result has a larger difference with diagnosis results of other modes, the grid generation and the simulation calculation can be carried out again; if the report is normal, the report continues to be generated.
When the blood flow simulation system 100 is actually used, the blood flow simulation system is applied to a doctor, for example.
The doctor can operate on the web interface or application interface of the blood flow simulation system 100 to input the characteristic information of the blood vessel of the patient, and the characteristic information is imported into the system by the data import 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 the moment, the doctor judges whether the three-dimensional model is feasible or not, and feeds back the judgment result to the system; if the calculation area is feasible, the system grid generating module 13 performs discretization processing on the calculation area to generate a grid depicting the calculation area.
The model solving module 15 solves the calculation area based on the grid, and the boundary condition module 14 determines the boundary condition and the parameter of the calculation area in the solving process; and finally obtaining the blood flow parameters of the calculation area.
The visualization module 16 visually presents the blood flow parameters.
At the moment, the doctor judges whether the simulation result and the blood flow parameter are abnormal 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 according to the simulation result.
The above modules constitute a system for realizing blood flow simulation, and from the viewpoint of the method, blood flow simulation is realized mainly by the following steps. Referring to fig. 2, fig. 2 is a schematic flow chart of a blood flow simulation method.
S11: characteristic 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: and carrying out discretization processing on the calculation area to generate a grid depicting the calculation area.
S14: and calculating the calculation region based on the grid so as to obtain the blood flow parameters of the calculation region.
The above steps all correspond to the modules in the blood flow simulation system 100, and the specific processes in the steps are not repeated, wherein 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 above steps S11-S14 are basic steps for implementing blood flow simulation, that is, the embodiments of the blood flow simulation method in the present application are implemented based on the above steps S11-S14. In order to improve the accuracy and efficiency of blood flow simulation, the blood flow simulation process is optimized from multiple aspects. Such as the embodiments shown in fig. 3 and 5, the embodiment shown in fig. 3 introduces region decomposition in the discretization process of the upper step S13; 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 the fluid-solid full coupling calculation in the above step S14 to improve the simulation accuracy.
Two embodiments of the present application will be described in detail below. Referring to fig. 3, fig. 3 is a schematic flow chart of an embodiment of a method for simulating blood vessel flow according to the present application. In the embodiment, the calculation area is decomposed, and a large-scale calculation area is decomposed into a plurality of small-scale calculation areas to be respectively and independently calculated, so that the calculation efficiency is improved, and the calculation precision is ensured by adopting a parallel algorithm. The embodiment is a blood vessel blood flow simulation method based on regional decomposition, and the blood flow simulation method comprises the following steps.
S21: characteristic data of the blood vessel is acquired.
In this embodiment, the characteristic data of the blood vessel may be acquired by receiving the characteristic data of the blood vessel transmitted from an external device (a storage device, a scanner, or a test instrument).
In other embodiments, the system for blood vessel blood flow simulation may be directly connected to a blood vessel feature database (the blood vessel feature database stores the latest blood vessel feature data of each person). Before the characteristic data of the blood vessel is acquired, 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 person from the blood vessel characteristic database according to the identity of the person.
The characteristic data of the blood vessel may be image data of the blood vessel, physiological characteristic data of the blood vessel.
S22: and constructing a three-dimensional model of the blood vessel according to the characteristic data. Wherein, a calculation area is defined on the three-dimensional model.
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 first by 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 constructed, the blood vessel region to be simulated can be determined according to the actual situation (namely, a calculation region is defined on the three-dimensional model).
S23: and carrying out discretization processing on the calculation area to generate a grid depicting the calculation area.
In this embodiment, an initial mesh depicting the calculation region may be generated by performing non-structural-stabilized finite-element discretization on the calculation region. The initial mesh may be an unstructured triangular mesh or an unstructured tetrahedral mesh, an unstructured hexahedral mesh. Of course, the initial grid may also be a structured grid, or a semi-structured grid.
S24: and encrypting the initial grid to generate a fine grid calculation area, and keeping the fine grid unit consistent with the initial grid unit in shape.
The initial mesh can be encrypted by adopting a consistent encryption algorithm, so that the mesh can be quickly encrypted under the condition of not changing the mesh quality, for example, for a triangular mesh unit, the middle points of all edges of the triangular mesh unit are connected, and one triangular mesh unit is divided into four triangular mesh units; for a three-dimensional tetrahedral mesh cell, it is equally possible to divide it into eight tetrahedral cells.
In the process of encrypting the initial grid, coarsening processing can be further performed on the initial grid, so that the generated fine grid keeps the geometric information of part of grid units in the initial grid, namely the geometric information in the initial grid. Firstly, selecting and reserving some grid units which are important in geometry, such as all points on a curved surface, two end points on a plane edge and equidistant points inside; and then deleting the grid units which are not selected and reserved, and carrying out iterative screening by adopting an Edge-connection algorithm in the specific process. After the grid cells are deleted, the whole grid is optimized to ensure the grid quality.
S25: and carrying out rough treatment on the initial grid to generate a rough grid calculation region, and keeping the number of the edge rough grid points describing the shape of the calculation region consistent with that of the edge initial grid points describing the shape of the calculation region.
The thickening of the initial mesh may be a series of processes that merge the initial mesh. Merging the initial mesh may be embodied as: merging at least two adjacent initial meshes into one coarse mesh by eliminating common edges or common planes of the two adjacent initial meshes, for example merging two triangular initial meshes into one coarse mesh by eliminating common edges of the two adjacent triangular initial meshes.
In the coarsening of the initial mesh, a different priority may be assigned to each initial mesh. By assigning priorities to the initial grids, the undesired initial grids are distinguished from the desired initial grids (the desired initial grids can be understood as initial grids containing more information, for example, the connections between blood vessels and/or the user is only a desired feature), the desired initial grids are retained as much as possible, and the undesired initial grids are combined into a coarse grid, so that the calculated vascular dynamics data of the desired region is more detailed, the calculation units can be reduced, the calculation amount can be reduced, and the calculation efficiency can be improved.
In this embodiment, in the process of thickening the initial grid, the number of the coarse edge grid points describing the shape of the calculation region may be maintained to be the same as the number of the initial edge grid points describing the shape of the calculation region, so that the calculation accuracy may be improved.
S26: and calculating the coarse grid calculation region to obtain the final blood flow parameter of each coarse grid point in the coarse grid calculation region.
In this embodiment, iterative convergence calculation may be performed on the coarse mesh calculation region to obtain a final blood flow parameter of each coarse mesh point in the coarse mesh calculation region.
Before the coarse mesh calculation region is calculated, the boundary conditions of the coarse mesh calculation region may be obtained. The coarse mesh calculation region is then calculated based on the boundary conditions to obtain the final blood flow parameters for each coarse mesh point.
The boundary conditions include one or more of blood flow inlet boundary conditions, blood flow outlet boundary conditions, and blood vessel wall boundary conditions.
The entry boundary conditions include one or more of coupling analog circuit entry boundary conditions, blood flow pressure entry boundary conditions, and blood flow velocity entry boundary conditions.
The exit boundary conditions include one or more of analog circuit exit boundary conditions, blood flow resistance exit boundary conditions, and small vessel tree boundary conditions.
The wall boundary conditions include non-slip wall boundary conditions; the method is divided into a rigid wall boundary condition, a unidirectional fluid-solid coupling wall boundary condition and a bidirectional fluid-solid coupling wall boundary condition according to whether the wall is rigid or not.
S27: and generating an initial blood flow parameter of each fine grid point in the fine grid calculation region according to the final blood flow parameter of each coarse grid point.
In this embodiment, the final blood flow parameters of the coarse grid points may be converted into the initial blood flow parameters of the fine grid points, so that the blood flow parameters between the coarse and fine grid points may be directly converted, so as to calculate the final blood flow parameters of the fine grid points through the initial blood flow parameters of the fine grid points. Specifically, the numerical conversion of the blood flow parameter between the coarse and fine grids 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, iterative convergence calculation may be performed on the fine mesh calculation region on the basis of the initial blood flow parameter of each fine mesh point, so as to obtain a final blood flow parameter of each fine mesh point. Therefore, the efficiency and the precision of blood flow parameter calculation can be improved through a multi-level calculation mode of the coarse grid and the fine grid.
Correspondingly, in practical application, the blood flow simulation calculation scale of the embodiment is large, and the blood flow simulation calculation scale is generally uploaded to a super-computing 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 generated on the local computer at first, and then the initial grids are uploaded to the super-computing center for processing such as grid encryption and grid expansion. The process can realize that the initial grid with better depicting calculation area is obtained on the local computer, and the subsequent grid quality can be further ensured based on the encryption and the thickening of the initial grid with better quality, thereby improving the calculation precision.
In this embodiment, an initial grid is obtained by discretizing a calculation region, a coarse grid calculation is performed on the basis of the initial grid, then the initial grid is coarsened to obtain a coarse grid calculation region, the initial grid is encrypted to obtain a fine grid calculation region, then the coarse grid is calculated, and then the fine grid is calculated according to the coarse grid calculation result.
In addition, optimization of the steps is further provided in the embodiment, so that the calculation efficiency and the calculation accuracy are improved.
For example, step S26 may include the following S261 and S262.
S261: and dividing the coarse grid computing area into a plurality of first sub-computing areas, wherein the grid points of each first sub-computing area are consistent in number.
Before actual calculation, the coarse grid calculation area can be divided into the first sub-calculation areas, namely, the large-scale calculation area is divided into a plurality of small-scale calculation areas, so that the calculation scale is reduced, and the calculation efficiency is improved.
In addition, the grid points in each first sub-calculation region obtained by division are consistent in number, so that the coarse grid calculation region can be divided equally, the calculation scale of each sub-calculation region is consistent, and the overall calculation efficiency is improved.
S262: and simultaneously calculating the plurality of first sub-calculation regions to obtain the final blood flow parameters of each coarse grid point in the coarse grid calculation region.
After the coarse grid computing area is divided into areas, the sub-computing areas are independent from each other in computing. Meanwhile, the plurality of first sub-calculation regions are calculated, namely the plurality of first sub-calculation regions are calculated in parallel, so that the final blood flow parameters of each coarse grid point in the plurality of first sub-calculation regions can be obtained at one time, and the calculation efficiency is improved. Of course, all the first sub-calculation regions may be simultaneously calculated in parallel.
In this embodiment, each two adjacent first sub-calculation regions may have a first overlap region therebetween. Correspondingly, when the first sub-calculation regions are calculated, iterative convergence calculation can be simultaneously performed on the plurality of first sub-calculation regions, and parameter exchange synchronization is performed in the first overlapping region, so that the consistency of the calculation accuracy of the plurality of first sub-calculation regions can be ensured.
As with the region decomposition and parallel computation of the coarse mesh, the region decomposition and parallel computation may be performed on the fine mesh. Specifically, step S28 may include two steps S281 and S282.
S281: and dividing the fine grid computing area into a plurality of second sub-computing areas, wherein the number of grid points of each second sub-computing area is consistent.
The first sub-calculation regions correspond to the second sub-calculation regions one by one, or one first sub-calculation region is a combination of at least two second sub-calculation regions. Therefore, the fine grid points in each second sub-calculation region can be ensured to fall in the same first sub-calculation region, so that the calculation result of the second sub-calculation region can be calculated on the basis of 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 regions 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.
After the fine grid computing area is divided into areas, the sub-computing areas are independent from each other in computing. And meanwhile, the plurality of second sub-calculation regions are calculated, namely the plurality of second sub-calculation regions are calculated in parallel, so that the final blood flow parameters of each fine grid point in the plurality of second sub-calculation regions can be obtained at one time, and the calculation efficiency is improved.
In the embodiment, the calculation region is divided into a plurality of second sub-calculation regions, and a first overlapping region is arranged between every two adjacent second sub-calculation regions. And meanwhile, iterative convergence calculation is carried out on the plurality of second sub-calculation areas, and parameter exchange synchronization is carried out in the second overlapping area, so that the consistency of the calculation accuracy of the plurality of first sub-calculation areas can be ensured.
With reference to fig. 5, fig. 5 is a schematic flow chart of another embodiment of the blood vessel blood flow simulation method according to the present application, in this embodiment, a physical mathematical model of fluid-solid total coupling is established, and total coupling calculation is performed, that is, interaction between blood flow and blood vessel is considered during blood flow simulation, so that the present embodiment improves the simulation calculation accuracy; 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 method for simulating blood flow in the embodiment comprises the following steps.
S31: characteristic 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 blood vessel wall model define a calculation region.
And constructing a three-dimensional cavity model of the blood vessel according to the characteristic data, expanding 10% of the diameter of the blood vessel at the position to the external normal direction of the surface of the blood vessel to construct a blood vessel wall model, and defining a calculation area for the three-dimensional cavity model and the blood vessel wall model.
S33: and carrying out discretization processing based on the non-structural stabilized finite element on the calculation region to generate a non-structural tetrahedral initial grid for describing the calculation region.
To improve the calculation efficiency and accuracy, step S43 may include the following two steps:
s331: and encrypting the initial grid to generate a fine grid calculation area, and keeping the fine grid unit consistent with the initial grid unit in shape.
The initial mesh can be encrypted by adopting a consistent encryption algorithm, so that the mesh can be quickly encrypted under the condition of not changing the mesh quality, for example, for a triangular mesh unit, the middle points of all edges of the triangular mesh unit are connected, and one triangular mesh unit is divided into four triangular mesh units; for a three-dimensional tetrahedral mesh cell, it is equally possible to divide it into eight tetrahedral cells.
In the process of encrypting the initial grid, coarsening processing can be further performed on the initial grid, so that the generated fine grid keeps the geometric information of part of grid units in the initial grid, namely the geometric information in the initial grid. Firstly, selecting and reserving some grid units which are important in geometry, such as all points on a curved surface, two end points on a plane edge and equidistant points inside; and then deleting the grid units which are not selected and reserved, and carrying out iterative screening by adopting an Edge-connection algorithm in the specific process. After the grid cells are deleted, the whole grid is optimized to ensure the grid quality.
S332: and performing rough treatment on the initial grid to generate a rough grid calculation region, keeping the number of rough grid points on the edge of the calculation region shape depicting the three-dimensional cavity model consistent with that of the initial grid points, and keeping the number of the rough grid points on the edge of the calculation region shape depicting the blood vessel wall model consistent with that of the initial grid points.
The thickening of the initial mesh may be a series of processes that merge the initial mesh. Merging the initial mesh may be embodied as: merging at least two adjacent initial meshes into one coarse mesh by eliminating common edges or common planes of the two adjacent initial meshes, for example merging two triangular initial meshes into one coarse mesh by eliminating common edges of the two adjacent triangular initial meshes.
In the coarsening of the initial mesh, a different priority may be assigned to each initial mesh. By assigning priorities to the initial grids, the undesired initial grids are distinguished from the desired initial grids (the desired initial grids can be understood as initial grids containing more information, for example, the connections between blood vessels and/or the user is only a desired feature), the desired initial grids are retained as much as possible, and the undesired initial grids are combined into a coarse grid, so that the calculated vascular dynamics data of the desired region is more detailed, the calculation units can be reduced, the calculation amount can be reduced, and the calculation efficiency can be improved.
In this embodiment, in the process of thickening the initial grid, the number of the coarse edge grid points describing the shape of the calculation region may be maintained to be the same as the number of the initial edge grid points describing the shape of the calculation region, so that the calculation accuracy may be improved.
S34: and constructing a physical mathematical model of the calculation area.
The physical mathematical model can describe the physical phenomena of the influence of blood flow, vessel wall deformation and interaction force 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 includes a fully-coupled fluid mechanics control equation, a solid mechanics control equation, a grid movement equation and a fluid-solid interface equation.
The blood flow rate, pressure, etc. can be obtained from the fluid mechanics governing equations, which include: compressible and incompressible navier-stocks equations and their corresponding various turbulence models, such as reno mean, large vortex simulation, etc.
The vessel wall displacement and the like can be obtained according to a solid mechanics control equation which comprises the following steps: the solid constitutive equation of linear elasticity and nonlinear elasticity, and models of viscoelasticity, elastoplasticity, porous media and the like.
The physical mathematical model is constructed by fluid-solid full coupling, so that the physical mathematical model also comprises the following components: fluid-solid interface conditions.
Corresponding to the boundary in the calculation area, the physical mathematical model further comprises: the method comprises the following steps of sliding or non-sliding fixed wall boundary conditions, damping type outflow boundary conditions, non-pressure boundary conditions or three-element elastic cavity physiological boundary conditions and the like, wherein different boundary conditions correspond to different physical phenomena and directly influence the calculation complexity and adaptability of the problem.
S35: and carrying out iterative convergence calculation on the physical mathematical model based on the grid to obtain blood flow parameters and blood vessel parameters of the calculation region.
In this embodiment, based on the mesh, the iterative convergence calculation on the physical mathematical model may include: based on the coarse grid, carrying out iterative convergence calculation on the physical mathematical model, and simultaneously obtaining blood flow parameters, blood vessel parameters and grid change parameters of a coarse grid calculation region; updating the calculation area according to the grid change parameters; so as to obtain the final blood flow parameter, the final blood vessel parameter and the final mesh change parameter.
And generating the initial blood flow parameter, the initial blood vessel parameter and the initial grid change parameter of the fine grid calculation region by the final blood flow parameter, the final blood vessel parameter and the final grid change parameter of the coarse grid calculation region through an interpolation algorithm.
Based on the fine grid, carrying out iterative convergence calculation on the physical mathematical model, and simultaneously obtaining blood flow parameters, blood vessel parameters and grid change parameters of a fine grid calculation region; updating the calculation area according to the grid change parameters; so as to obtain the final blood flow parameter, the final blood vessel parameter and the final mesh change parameter.
The physical mathematical model constructed in step S34 above couples the fluid mechanics governing equation, the solid mechanics governing equation, the grid movement equation, and the fluid-solid interface equation to one equation. In the step S35, the solution is performed in the equation, and the calculation process does not require iteration among multiple equations, so that one-time solution is realized and the solution accuracy is ensured.
Specifically, the step is to solve a fluid mechanics control equation, a solid mechanics control equation, a mesh movement equation and a fluid-solid interface equation simultaneously based on the mesh, and calculate mesh point information of the blood flow mesh and mesh point information of the blood vessel mesh at the fluid-solid interface in the region in a unified manner during the solution.
For blood flow and vessel wall, their fluid-solid interface interact and the forces have a certain relation to each other, for example, in terms of shear force, displacement, etc. Therefore, the condition of the fluid-solid interface is adopted in the physical mathematical model to simulate the condition of the interface; unifying the mesh point information of the fluid-solid interface in the network of the calculation area, specifically, if the blood flow mesh and the blood vessel mesh at the interface are matched, unifying the mesh point information by point-to-point information conversion; if the blood flow grid and the blood vessel grid at the interface are not matched, the grid point information is unified by using an interpolation method, and a linear and quadratic interpolation method, a radial basis function interpolation method, a Mortar method and the like based on finite element basis functions can be adopted.
The steps are used for establishing a fluid-solid coupling physical mathematical model and calculating the physical mathematical model to simulate the blood flow in the blood vessel more accurately.
When the fluid-solid full-coupling one-time solution is performed, the problem scale is very large, so that the embodiment also proposes that a non-linear system solution algorithm is used for calculating the physical mathematical model, specifically, a Newton-Krylov-Schwarz (Newton-Krylov-Schwarz) algorithm can be adopted, and the method comprises the following steps.
S351: and carrying out discretization treatment on the physical mathematical model to obtain a nonlinear equation set.
Firstly, discretizing the physical mathematical model, namely discretizing a partial differential equation into a nonlinear equation set. Wherein, for the fluid mechanics control equation, methods of stabilized P1-P1 element, classic Taylor-Hood P2-P1 element and the like can be adopted; for a solid mechanics control equation, a PERS element is adopted for a mixed form of a given weak symmetrical stress tensor, and an uncoordinated P1 element is adopted for displacement; for fluid-solid interface conditions, the discrete format employs mortar or hybrid technology and novel methods based on Lagrange multipliers.
S352: and solving the nonlinear equation system by using a non-precise Newton method.
In the solving process of the step, linear search and feasible domain technology can be adopted to determine the search direction and the step length, and linear search is carried out in the feasible domain; in the iterative process of solving by the non-precise Newton method, a grid sequence method and a non-linear preprocessing technology can be adopted, so that the non-linear iterative process of the step has grid-independent convergence; and for the Jacobian matrix in the non-precise Newton method, the method adopts strategies such as a multi-color sequencing finite difference method, an automatic differentiation technology, a Jacobian-free method or explicit generation and the like to construct and generate.
S353: and solving a linear equation set in the non-precise Newton method by using a Kronov subspace iteration method.
Specifically, a linear equation set having an asymmetric matrix in the non-precision newton method is solved in this step using GMRES, or Lanczos biarthogonalization method of Short-Recurrence formula (Short-Recurrence).
S354: and constructing preconditioners in the linear equation system by using a region decomposition method.
The constructing of the preconditioner accelerates the linear solution in step S353, and in this embodiment, an overlapped Schwarz (Schwarz) algorithm is adopted, and specifically, the preconditioner may be constructed by using an adjusted extended additive Schwarz algorithm or a restricted 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 a direct method or an iterative method, including an LU decomposition algorithm, an incomplete LU decomposition algorithm, a Gauss-Seidel iterative method, or the like, is adopted in this embodiment. The matrix of the sub-regions is sparse, and the storage and access of the non-zero elements of the sub-regions can be carried out in a point-block mode, namely, a direct method or an iterative method can simultaneously store and access a plurality of variables on nodes according to the sequence of grid nodes. When the direct method is adopted to solve the subregion problem, different subregion matrix sorting modes can be adopted, including NestedDisection, One-way Disection, Reverse Cuthill-McKee, Quotient Minimum Degreee and other methods.
And solving the physical mathematical model by using a nonlinear system solving algorithm to obtain blood flow parameters and blood vessel parameters. The blood vessel parameters include the moving value of the blood vessel wall, the moving of the blood vessel wall has certain influence on the grid, and the change of the grid needs to be considered when the next calculation is carried out. Therefore, the following steps are also performed in this embodiment.
S36: and calculating the change parameters of the grid according to the blood vessel parameters, thereby updating the calculation area.
In 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 variation 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 step S34 and solved simultaneously, that is, step S36 and step S35 do not have a strict precedence relationship and can be performed simultaneously.
The physical mathematical model constructed by the present embodiment may take the following form.
Fluid dynamic equation:
fluid-solid interface equation:
σf·nf＝-σs·ns on Γinterface,
d＝x on Γinterface,
solid kinetics control equation:
grid movement equation:
the damping type outflow boundary conditions are as follows:
wherein the content of the first and second substances,
cauchy stress tensor for flow field, u denotes blood flow velocity, pfAs the pressure of the blood flow, ρfMu is the viscosity coefficient of blood for blood density (when blood is considered a Newtonian fluid, corresponding to a constant for mu, when it is considered a non-Newtonian fluid, mu is a complex function).
d represents the displacement of the vessel wall, σsλ trace (ε) I +2 μ ε is the stress tensor of the vessel wall, where λ and μ ∈sIs the coefficient of the Lame, and is,
x denotes the displacement of the grid movement, σmStress tensor, form and sigma for a mesh modelsSame, but in pairsThe values of the corresponding Lame coefficients are different.
The selection of the stress tensor in the above equation, the selection of the structure and boundary conditions of the viscosity coefficient, and the selection of the stress tensor in the fluid and solid equations are all determined according to the specific properties of blood and blood vessel walls, and in practical clinical application, the numerical values are different for each case.
The method of the embodiment constructs a fluid-solid fully-coupled 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 into the simulation calculation to ensure the calculation efficiency.
The embodiment shown in FIG. 3 involves performing a region decomposition of the computed regions after grid generation and performing parallel computations based on the region decomposition; the embodiment shown in fig. 5 involves building a physical mathematical model of fluid-solid total coupling to perform fluid-solid total coupling calculations and setting a solution algorithm on a target; the techniques involved in both can be applied in combination.
For example, the mesh generation module in the blood flow simulation system adopts the mesh generation technique and the region decomposition technique of the embodiment shown in fig. 3, and the model solving module introduces the construction of the fluid-solid fully-coupled model shown in fig. 5 and the adoption of the corresponding algorithm. For the blood flow simulation process, the simulation efficiency and precision are greatly improved.
All 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, and fig. 6 is a schematic structural diagram of an embodiment of the blood flow simulation apparatus according to the present application.
The blood flow simulation apparatus 200 of the present embodiment includes a processor 21 and a memory 22, wherein a computer program operable on the processor 21 is stored in the memory 22, 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 processor, and may include a plurality of processors, and may be processors disposed in different devices, for example, a processor in a local computer and a processor cluster in a super computing center. In this embodiment, when performing parallel computation of blood flow simulation, how many sub-computation regions are provided, and how many processors are correspondingly provided to calculate the sub-computation regions respectively.
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 on large-scale data, a series of parallel acceleration techniques are adopted, that is, according to different computation characteristics, a computation process is placed on different processors, so as to achieve maximum utilization of processor capacity.
For example, in the aspect of solving, core calculation modules such as calculation of nonlinear discrete functions, sparse matrix vector multiplication, sparse matrix fast decomposition and the like which are time-consuming in nonlinear solving and linear solving are transplanted to a GPU (graphics processing Unit), a MIC (many core processor) or other many-core processors. And a multi-color or multi-scheduling strategy is adopted to improve the decomposition and backtracking solution of the sparse matrix, so that the algorithm parallelism is improved on one hand, and the convergence efficiency of a solver is kept on the other hand. The parts such as boundary conditions and the like which relate to a large number of branch operations are separated from the inside of the region and are calculated by a part with strong logic processing capacity, so that the tasks are more reasonably distributed.
In the aspect of processor instruction calculation, instruction level parallelism, thread level parallelism and process level parallelism are optimized, data reuse, calculation and memory access overlapping, data fusion and boundary access, data merging transmission, vectorization, scientific operation function optimization and other technologies are adopted to optimize operation on the many-core processor, and floating point efficiency in actual operation is improved.
The instruction of the processor realizes the aspect of programming language, and for a GPU, a MIC or other many-core processors, CUDA, OpenACC and openCL languages are used for executing on the GPU; executing on the MIC using OpenMP language; execute on other many-core processors using pthread, athread, or other packages of functions.
When a plurality of processors process large-scale data in parallel, it is necessary to improve not only efficiency in terms of computation but also efficiency in terms of transmission of data. For example, in the present embodiment, a series of large-scale discrete data parallel processing techniques are employed.
Block parallel I/O technique: and establishing a partitioned data structure to balance the load among the processors. That is, discrete data representing physical quantities of blood vessels and blood are divided into blocks for each calculation region and read in parallel from or output to one or more data files, and the number of the divided blocks is the same as the number of processors used. The block parallel I/O technology in this embodiment is implemented by specifying an explicit offset, an independent file pointer, or a shared file pointer based on the MPI-2 (and versions above) function library. The data file includes HDF5, VTK and the like.
And the coarse-scaling or encryption output technology is to perform coarse-scaling or encryption on the grids representing the blood vessels and the blood, interpolate the physical quantity on the original grid to a new grid, and then output the new grid by using the block parallel I/O technology.
The vector compression technology or the MPI _ pack-based data packing technology is adopted to reduce the data traffic and the I/O data volume, 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 a high-level computer with thousands of computing cores, fully calls computing resources through the cooperation of software and an algorithm, improves the precision and the efficiency of the blood flow dynamic analysis, realizes the parallel expandable efficiency of more than 60 percent, improves the blood flow dynamic simulation precision and reduces the computing time.
The blood flow simulation method may be implemented in software and may be stored in a storage medium readable by an electronic device when being sold or used as a standalone product, that is, the present 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 a computer program is stored in the computer readable storage medium 300, and when being executed by a processor, the computer program implements the steps of the method. The computer readable storage medium may be a usb disk, an optical disk, a server, etc.
The above description is only for the purpose of illustrating embodiments of the present application and is not intended to limit the scope of the present application, and all modifications of equivalent structures and equivalent processes, which are made by the contents of the specification and the drawings of the present application or are directly or indirectly applied to other related technical fields, are also included in the scope of the present application.
Claims (10)
1. A method for simulating blood flow in a blood vessel based on mechanical equations, 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;
carrying out discretization processing based on an unstructured stabilized finite element on the calculation region to generate an unstructured tetrahedral initial grid for describing the calculation region;
encrypting the initial grid to generate a fine grid calculation region, and keeping the shape of the fine grid unit consistent with that of the initial grid unit;
performing rough treatment on the initial grid to generate a rough grid calculation region, keeping the number of rough grid points depicting 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 the rough grid points depicting the edge of the calculation region 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 mesh to obtain a final blood flow parameter, a final blood vessel parameter and a final mesh change parameter;
calculating initial blood flow parameters, initial blood vessel parameters and initial grid change parameters of the fine grid calculation region based on the final blood flow parameters, the final blood vessel parameters and the final grid change parameters of the coarse grid calculation region;
and calculating the physical mathematical model based on the fine mesh to obtain a final blood flow parameter, a final blood vessel parameter and a final mesh change parameter.
2. The method of claim 1, wherein the vessel wall model is constructed by expanding 10% of the vessel diameter at the location of the vessel surface in an outward normal direction.
3. The method of claim 1, wherein the computing the physical mathematical model based on the coarse mesh comprises:
based on the coarse grid, carrying out iterative convergence calculation on the physical mathematical model, and simultaneously obtaining blood flow parameters, blood vessel parameters and grid change parameters of a calculation area of the coarse grid; and updating the calculation area according to the grid change parameter.
4. The method according to claim 3, wherein the calculating of the initial blood flow parameters of the fine-mesh calculation region based on the final blood flow parameters, the final blood vessel parameters and the final mesh variation parameters of the coarse-mesh calculation region comprises:
and generating the initial blood flow parameter, the initial blood vessel parameter and the initial grid change parameter of the calculation fine grid calculation region by the final blood flow parameter, the final blood vessel parameter and the final grid change parameter of the coarse grid calculation region through an interpolation algorithm.
5. The method of claim 4, wherein the computing the physical mathematical model based on the fine mesh comprises:
based on the fine mesh, carrying out iterative convergence calculation on the physical mathematical model, and simultaneously obtaining blood flow parameters, blood vessel parameters and mesh change parameters of a calculation area of the fine mesh; and updating the calculation area according to the grid change parameter.
6. The method of claim 1, wherein the iterative convergence calculation of the physical mathematical model comprises: discretizing the physical mathematical model to obtain a nonlinear equation set; solving the nonlinear equation set by using a non-precise Newton method; constructing preconditioners in a linear equation set appearing in the non-precise Newton method during solving by using a restricted Schwarz algorithm; and solving the linear equation set by utilizing a Kronov subspace iteration method based on a preconditioner.
7. The method of claim 6, wherein the physical mathematical model comprises a slip or slip-free wall-fixation boundary condition, a damped outflow boundary condition, a pressure-free boundary condition, or a three-element elastic lumen physiological boundary condition.
8. The method of claim 7, wherein the fluid dynamics control equation is:
the solid mechanics governing equation is:
the grid motion equation is:
the fluid-solid interface equation is as follows:
σf·nf＝-σs·ns on Γinterface,
d＝x on Γinterface,
the damping type outflow boundary conditions are as follows:
wherein the content of the first and second substances,
is the stress tensor of the flow field, u denotes the blood flow velocity, pfAs the pressure of the blood flow, ρfIs the blood density, μ is the viscosity coefficient of blood;
d represents bloodDisplacement of the pipe wall, σsλ trace (ε) I +2 μ ε is the stress tensor of the vessel wall, where λ and μ ∈sIs the coefficient of the Lame, and is,
x denotes the displacement of the grid movement, σmA stress tensor for the mesh model;
9. A blood flow simulation apparatus comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the method of any one of claims 1 to 8 when executing the computer program.
10. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 8.
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