CN109064559A - Vascular flow analogy method and relevant apparatus based on mechanical equation - Google Patents
Vascular flow analogy method and relevant apparatus based on mechanical equation Download PDFInfo
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Abstract
This application discloses a kind of vascular flow analogy method, blood flow simulator and computer readable storage medium based on mechanical equation, wherein method includes obtaining the characteristic of blood vessel；The threedimensional model of blood vessel is constructed according to characteristic, threedimensional model definition has zoning；Sliding-model control is carried out to zoning, generates the grid for portraying zoning；The Physics-mathematics model of zoning is constructed, Physics-mathematics model includes the hydrodynamics governing equation and Solid Mechanics governing equation of unity couping；Based on grid, Physics-mathematics model is calculated, obtains the blood flow parameter and blood vessel parameter of zoning；The running parameter that grid is calculated according to blood vessel parameter, to update zoning.The achievable accurate efficient simulation to blood flow in blood vessel of the application.
Description
Technical field
This application involves blood flow numerical simulation fields, more particularly to a kind of vascular flow simulation side based on mechanical equation
Method, blood flow simulator and computer readable storage medium.
Background technique
The feature of blood flow is being able to reflect out blood vessel with the presence or absence of disease and patient with the presence or absence of blood to a certain degree
Disease caused by hydromechanics changes, such as blood flow reserve score (FFR) can reflect that ischemic risk, blood flow velocity can reflect blood vessel
Chocking-up degree etc..Sunykatuib analysis thus is carried out to blood flow and has become blood vessels present disease prevention and the research of diagnostic field heat
Point
Early stage, due to the limitation of computer capacity, many simplification, such as physics were carried out when simulating to blood flow
The simplification of model, the simplification of discretization grid；Although this simplified computational valid time that calculates is high, some of blood flow can not be obtained
The precision of important feature, simulation is not high.And after current computer level of hardware is developed, it is not matched with computer capacity but
Analogy method, can not guarantee the raising of the efficiency and precision of Simulation of Blood, i.e., the precision currently simulated to blood flow simultaneously
It remains unchanged with efficiency not high.
Summary of the invention
The application provides a kind of vascular flow analogy method, blood flow simulator and computer based on mechanical equation can
Storage medium is read, to solve the problems, such as the precision simulated in the prior art to blood flow and inefficient.
In order to solve the above technical problems, the application proposes a kind of vascular flow analogy method based on mechanical equation, including
Obtain the characteristic of blood vessel；The threedimensional model of blood vessel is constructed according to characteristic, threedimensional model definition has zoning；To meter
It calculates region and carries out sliding-model control, generate the grid for portraying zoning；Construct the Physics-mathematics model of zoning, physics number
Learn the hydrodynamics governing equation and Solid Mechanics governing equation that model includes unity couping；Based on grid, to Physics-mathematics model
It is calculated, obtains the blood flow parameter and blood vessel parameter of zoning；The running parameter of grid is calculated according to blood vessel parameter, thus
Update zoning.
In order to solve the above technical problems, the application proposes a kind of blood flow simulator, including memory, processor and storage
On a memory and the computer program that can run on a processor, processor realize the above method when executing computer program
Step.
In order to solve the above technical problems, the application proposes a kind of computer readable storage medium, it is stored thereon with computer
Program, when computer program is executed by processor the step of the realization above method.
The application vascular flow analogy method includes: to obtain the characteristic of blood vessel；Blood vessel is constructed according to characteristic
Threedimensional model, threedimensional model definition have zoning；Sliding-model control is carried out to zoning, generates the net for portraying zoning
Lattice；The Physics-mathematics model of zoning is constructed, Physics-mathematics model includes the hydrodynamics governing equation and solid of unity couping
Mechanics governing equation；Based on grid, Physics-mathematics model is calculated, obtains the blood flow parameter and blood vessel ginseng of zoning
Number；The running parameter that grid is calculated according to blood vessel parameter, to update zoning.It is established in the present embodiment in the application method
The Physics-mathematics model for flowing solid unity couping, carries out unity couping calculating, i.e., considers between blood flow and blood vessel when carrying out Simulation of Blood
Interaction, and zoning is updated, thus embodiment improves simulation computational accuracies.
Detailed description of the invention
Fig. 1 is the structural schematic diagram of Simulation of Blood system；
Fig. 2 is the flow diagram of Simulation of Blood method；
Fig. 3 is the flow diagram of one embodiment of the application vascular flow analogy method；
Fig. 4 is the subregion schematic diagram of zoning in embodiment shown in Fig. 3；
Fig. 5 is the flow diagram of another embodiment of the application vascular flow analogy method；
Fig. 6 is the structural schematic diagram of one embodiment of the application blood flow simulator；
Fig. 7 is the structural schematic diagram of one embodiment of the application computer readable storage medium.
Specific embodiment
To make those skilled in the art more fully understand the technical solution of the application, with reference to the accompanying drawing and it is embodied
Mode can to a kind of vascular flow analogy method, blood flow simulator and computer based on mechanical equation provided by invention
Storage medium is read to be described in further detail.
Carrying out simulation to blood flow in blood vessel is the flowing that blood is simulated using hydromechanical method, and obtaining includes blood flow
Mechanical characteristics blood flow parameter.The computer system of Simulation of Blood is realized in building one in the application, referring to Fig. 1, Fig. 1 is blood flow
The structural schematic diagram of simulation system, the Simulation of Blood system 100 include following several big modules.
Data import modul 11.
For obtaining the characteristic of blood vessel, such as when the Simulation of Blood system 100 is applied to the medical diagnosis on disease of patient,
The characteristic, including image data, physiological data etc. of patient vessel can be imported by data import modul 11.
Wherein image data can be based on nuclear-magnetism radiography MRA, computer tomography CTA, digital subtraction angiography DSA or
The technologies such as ultrasonic elastograph imaging obtain.The image data or physiological data of blood vessel are obtained by other equipment or technology first, so
Simulation of Blood system 100 carries out Simulation of Blood further according to the image data or physiological data afterwards.
Three-dimensional modeling module 12.
For the threedimensional model according to the blood vessel characteristic building blood vessel obtained by data import modul 11.It is specific i.e. by
The image data of blood vessel constructs the threedimensional model of blood vessel.During constructing this threedimensional model, can to threedimensional model into
Row smoothing processing, so that threedimensional model more meets the shape of blood vessel itself；Pruning modes can also be carried out to threedimensional model, such as
When the blood vessel to heart models, only retains the part of aorta, trim other blood vessels in threedimensional model.
When user uses this Simulation of Blood system 100, three-dimensional modeling module 12 can be visual by constructed threedimensional model
Change and presented to user, judges whether the threedimensional model is feasible by user, if infeasible, rebuild threedimensional model, such as wrap
Include the vascular pattern including vascular wall.
After the building for completing threedimensional model, definition has zoning on threedimensional model, that is, needs to carry out Simulation of Blood
Target area, zoning can be entire threedimensional model, be also possible to certain partial region in threedimensional model, such as can be to patient
The entire blood vessel of heart establishes threedimensional model, but only simulates to the blood flow in aorta, at this time zoning, that is, aorta.
Grid generation module 13.
For carrying out sliding-model control to zoning, the grid for portraying zoning is generated.Grid generated can
Embody the entire shape of zoning.
Calculating process due to carrying out Simulation of Blood is to haemodynamics governing equation from physical mathematics meaning
It solves, and the solution for solving haemodynamics governing equation solves partial differential problem, generally adopts when solving partial differential problem
With sliding-model control method, such as finite element method, Finite Volume Method, Discontinuous Finite Element Method etc..Therefore, it is necessary to will calculate
Region division goes out to be used for the discrete grid block of numerical simulation.
Zoning can be divided into structured grid or unstructured grid by grid generation module 13, since blood vessel is several
The complexity of what form uses unstrctured grid in the application.For the zoning of three-dimensional structure, Delaunay standard can be used
Then, delaunay triangle algorithm (Advancing Front Method) or Shephard-Yerry algorithm partition go out tetrahedral grid list
Member；Reflection method, sub- reflection method can also be used, sweep fine jade method, based on Grid Method, middle axial plane method, Plastering method or Whisker
Weaving method marks off hexahedral mesh unit.
Boundary condition module 14.
For determine to zoning carry out simulation calculate when boundary condition, wherein boundary condition can taking human as setting,
It can also be determined according to the physiological data of blood vessel.
Model solution module 15.
Based on grid generated and identified boundary condition, zoning is solved, that is, solves and is applied with
The haemodynamics governing equation of certain boundary conditions, solve when, be also required to first to the haemodynamics governing equation into
Then row sliding-model control again solves the equation after discrete by algorithm.Finally obtain the blood flow in the zoning
The information such as parameter, including the deformation of blood flow velocity, blood pressure, shearing force, vascular wall.
Connection relationship between above-mentioned module has been embodied in the function description to module, and details are not described herein.Pass through
Simulation of Blood system 100 can be realized the simulation to blood flow, the final parameter for obtaining blood flow in zoning, according to blood flow parameter
Medical diagnosis on disease can be carried out, analysis lesion carries out pathological study, can also instruct the related surgical of cardiovascular and cerebrovascular, such as vascular bypass
Operation, intravascular stent is put into operation, and simulation assessment can be also carried out to post-surgical condition, optimize in vascular bypass surgery using bridge with
Intravascular stent is put into the optimization design of supporting structure in operation.
It further include with lower module in Simulation of Blood system 100 for more convenient realization user interaction.
Visualization model 16.
For showing the blood flow parameter after Simulation of Blood, simulative display is carried out in combination with threedimensional model, such as blood flow
Parameter FFR value or pressure value can be presented different colours distribution map based on threedimensional model and be shown to user, so that Simulation of Blood result
It is more intuitive.
Report generation module 17.
It is generated and is reported according to Simulation of Blood result, provide medical diagnosis on disease or treatment recommendations.Before report generation, Ke Yixian
Simulation of Blood is presented as a result, judging whether the Simulation of Blood result is normal, and for example doctor thinks if abnormal, by user to user
The diagnostic result of the result and other modes differs greatly, then can re-start grid generation, and simulation calculates；If normal, then after
It is continuous to generate report.
When Simulation of Blood system 100 carries out practical application, by taking the Simulation of Blood system is towards the application of doctor as an example.
Doctor can operate on the web interface or application interface of the Simulation of Blood system 100, input patient vessel
Characteristic information, characteristic information imported into system by data import modul 11.
Three-dimensional modeling module 12 generates the threedimensional model of blood vessel according to characteristic information in system, and carries out visually on interface
Change and presents.
Doctor judges whether the threedimensional model is feasible at this time, and judging result is fed back to system；If feasible, system network
Lattice generation module 13 carries out sliding-model control to zoning, generates the grid for portraying zoning.
Model solution module 15 is based on grid and solves to zoning, by boundary condition module 14 in solution procedure
Determine the boundary condition and parameter of zoning；The final blood flow parameter for obtaining zoning.
Blood flow parameter is carried out visualization presentation by visualization model 16.
Doctor judges the analog result at this time, and whether blood flow parameter has exception, and judging result is fed back to system；If nothing
Abnormal, then the report generation module 17 of system generates medical diagnosis on disease report or therapeutic scheme report according to analog result.
Above-mentioned modules constitute the system for realizing Simulation of Blood and then mainly pass through following step from the perspective of method
It is rapid to realize Simulation of Blood.Referring to Fig. 2, Fig. 2 is the flow diagram of Simulation of Blood method.
S11: the characteristic of blood vessel is obtained.
S12: the threedimensional model of blood vessel is constructed according to characteristic, zoning is defined on threedimensional model.
S13: sliding-model control is carried out to zoning, generates the grid for portraying zoning.
S14: it is based on grid, zoning is calculated, to obtain the blood flow parameter of zoning.
Above-mentioned steps both correspond to the modules in Simulation of Blood system 100, and the detailed process in step repeats no more,
Wherein, step S11 corresponding data import modul 11, step S12 corresponding three-dimensional modeling module 12, step S13 correspond to grid generation
Module 13, step S14 correspond to model solution module 15 and boundary condition module 14.
Above-mentioned steps S11-S14 is the basic step for realizing Simulation of Blood, i.e., Simulation of Blood embodiment of the method in the application
It is based on above-mentioned steps S11-S14 realization.The application proposes pair to improve the precision and efficiency of Simulation of Blood from many aspects
Simulation of Blood process is optimized.Such as Fig. 3 and embodiment shown in fig. 5, embodiment shown in Fig. 3 upper step S13 from
Introduce region is decomposed in dispersion processing；And it is based on Region Decomposition, parallel computation is introduced in above-mentioned steps S14, to improve simulation
Efficiency.Embodiment shown in fig. 5 introduces the solid unity couping of stream in above-mentioned steps S14 and calculates, to improve simulation precision.
Two embodiments of the application are specifically introduced individually below.It is the application blood vessel blood referring initially to Fig. 3, Fig. 3
The flow diagram of one embodiment of flow field simulation method.Zoning is decomposed in the present embodiment, area will be calculated on a large scale
Domain is decomposed into multiple small-scale zonings and is independently calculated, to improve computational efficiency, and is calculated using parallel
Method ensure that computational accuracy.The present embodiment is the vascular flow analogy method based on Region Decomposition, is simulated to blood flow
Method includes the following steps.
S21: the characteristic of blood vessel is obtained.
S22: the threedimensional model of blood vessel is constructed according to characteristic.Wherein, definition has zoning on threedimensional model.
S23: sliding-model control is carried out to zoning, generates the grid for portraying zoning.
S24: zoning is divided into multiple sub- zonings.
This step is understood in combination with Fig. 4, Fig. 4 is the subregion schematic diagram of zoning in embodiment shown in Fig. 3.It will
Zoning is divided into multiple sub- zonings, i.e., large-scale zoning is divided into multiple small-scale zonings, with
Reduce calculation scale, improves computational efficiency.
When carrying out the division of sub- zoning in this step S24, need to guarantee the mesh point quantity of every sub- zoning
Unanimously, since calculation scale is evaluated with mesh point quantity, in order to guarantee whole computational efficiency, to calculating in this step
The calculation scale in region carries out impartial division, i.e., the mesh point quantity of every sub- zoning is consistent.
Certainly in practical applications, be not can guarantee every sub- zoning mesh point quantity it is just the same, therefore this
Within an acceptable range, i.e., mesh point quantity is unanimously simultaneously for mesh point number differences in step between every sub- zoning
It is just the same to be not limited to mesh point quantity, guarantees almost the same.
S25: being based on grid, while calculating at least two sub- zonings, to obtain the blood flow ginseng of zoning
Number.
After zoning to be divided into multiple sub- zonings, the calculating between sub- zoning is mutually indepedent, thus
In this step S25, while at least two sub- zonings are calculated, thus obtain the blood flow parameter of zoning, i.e., it is more
A sub- zoning parallel computation, improves computational efficiency.It, can also be to all sub- zonings if computing capability is powerful enough
Parallel computation simultaneously.
Region division is carried out to zoning first in the present embodiment, parallel computation then is carried out to multiple regions again, is mentioned
High computational efficiency, and expand calculation scale.The present embodiment makes full use of high-performance computer to improve Hemodynamic analysis
Precision and efficiency, meet clinical medicine application accuracy and requirement of real-time.
In addition, it is further proposed that optimization to above-mentioned steps in the present embodiment, to improve computational efficiency and precision.
Such as step S23 may include following two step:
S231: sliding-model control is carried out to zoning, generates the coarse grid for portraying zoning；
S232: being encrypted coarse grid, generates the refined net for portraying zoning.
Above-mentioned steps S231-S232 indicates that multi-level realization grid generates, including following a variety of situations.
It can be and small-scale sliding-model control is carried out to zoning first, generate a set of coarse grid, and guarantee that this is thick
Grid can portray the shape of zoning；Then the coarse grid is encrypted again, then generates and portrays zoning
Refined net.
It corresponds in practical applications, the Simulation of Blood calculation scale of the present embodiment is larger, is generally uploaded to super meter
Calculation center is calculated, thus on the local computer using Simulation of Blood system realize Simulation of Blood method when, can exist first
A set of coarse grid is generated on local computer, and the coarse grid is then uploaded into the encryption etc. that supercomputing center carries out grid again
Processing.The process, which can be realized to obtain on the local computer, portrays the preferable coarse grid in zoning, preferable based on the quality
Coarse grid is encrypted, and can be further ensured that subsequent meshes quality.
It can also be and multiple encryption is carried out to coarse grid, such as initial coarse grid is carried out at first time encryption
Reason, obtains the first refined net；Then second of encryption is carried out to the first refined net, obtains the second refined net；First fine-structure mesh
Comparatively lattice and the second refined net are respectively the refined net in coarse grid and S232 in step S231.
Obtain multilevel coarse grid and refined net in this way, calculate when can by multilevel calculating come
Improve the efficiency and precision calculated.Specifically, i.e., calculate to zoning in step S25 may include following two step.
S251: being based on coarse grid, while calculating at least two sub- zonings, obtains at least two sons and calculates area
The coarse grid blood flow parameter in domain.
S252: it is based on refined net, and according to the coarse grid blood flow parameter of at least two sub- zonings, while at least two
A sub- zoning is calculated, to obtain the refined net blood flow parameter of at least two sub- zonings.
The multilevel calculating can be Waterfall type, and corresponding above-mentioned steps S251 and S252 first calculate coarse grid,
Then refined net is calculated according to coarse grid calculated result, i.e., coarse grid calculating-refined net calculates；It can also be that V is recycled
Type first calculates coarse grid, is then calculated according to coarse grid calculated result refined net, secondly according to refined net
Calculated result calculates coarse grid again, i.e., coarse grid calculating-refined net calculating-coarse grid calculates；It can also be that W is followed
Ring-like, i.e., coarse grid calculating-refined net calculating-coarse grid calculating-refined net calculating-coarse grid calculates.
The calculating process multilevel for coarse grid and fine grid has the step of numerical value exchange, i.e. interpolation calculation between coarse grid and fine grid
Process.In order to guarantee the precision of boundary interpolation, in the present embodiment when step S231-S234 constructs coarse grid and fine grid, guarantee institute
Boundary having the same mesh point quantity of the refined net and coarse grid of generation in zoning.
It is consistent Encryption Algorithm used by coarse grid is encrypted above, mesh quality can be not being changed
In the case of grid is quickly encrypted, such as the grid cell of triangle, the midpoint on its each side is connected, thus by one three
Hexagonal lattice dividing elements are four triangular mesh units；For three-dimensional tetrahedral grid unit, can similarly be given
For eight tetrahedron elements.
During encrypting to coarse grid, can also roughening treatment be carried out to it, so that in refined net generated
Remain with the geological information of subnetting lattice point in the middle part of coarse grid, i.e. geological information in reservation coarse grid.Selection retains first
In geometrically important mesh point, such as point all on curved surface, two-end-point and internal equidistant points in flat edge；Then will not have
The grid point deletion for having selection to retain, detailed process are iterated screening using Edge-contraction algorithm.Deleting net
After lattice point, entire grid is optimized to guarantee mesh quality.
For the subregion of step S24, the application also proposes multilevel partitioning technique, to obtain balanced multiple sons of rule
Zoning specifically includes following steps.
S241: carrying out first time region division to zoning, obtains multiple first sub- zonings, each first son meter
The mesh point quantity for calculating region is consistent.
S242: while second of region division is carried out at least two first sub- zonings, obtain multiple second son meters
Region is calculated, the mesh point quantity of each second sub- zoning is consistent.
Based on above-mentioned steps S241 and S242, can also multiple region division be carried out to zoning, until required for obtaining
Number of partitions.Multiple subregion may make the quantity of each institute's subregion little, guarantee between the sub- zoning of every subzone
The consistency of mesh point quantity.Subregion quality thus can be improved.
Sub- zoning is solved using parallel algorithm in step s 25, to obtain the meter of entire zoning
Calculate result.Sub- zoning is divided by zoning and is obtained, and can be overlapped also not be overlapped between sub- zoning, corresponding using not
Same parallel algorithm.
In the present embodiment, there is overlapping region between the sub- zoning of each adjacent two, it is corresponding using Overlapping region point
Resolving Algorithm.
In the present embodiment when calculating zoning, boundary condition can be artificial setting, can be according to neighbour
The calculating of nearly zoning is obtained, and is also possible to be determined according to acquired physiological data.This is not repeated them here again.
The present embodiment Simulation of Blood method is calculated using Region Decomposition technology integrating parallel, improves the efficiency of Simulation of Blood
And precision.
It is the flow diagram of another embodiment of the application vascular flow analogy method, this reality please continue to refer to Fig. 5, Fig. 5
The Physics-mathematics model established in example and flow solid unity couping is applied, unity couping calculating is carried out, i.e., considers blood flow when carrying out Simulation of Blood
Interaction between blood vessel, thus embodiment improves simulation computational accuracies；And it is calculated in conjunction with Nonlinear System Solving
Method ensure that the efficiency of calculating.The present embodiment is the vascular flow analogy method based on mechanical equation, the present embodiment to blood flow into
The method of row simulation includes the following steps.
S31: the characteristic of blood vessel is obtained.
S32: the threedimensional model of blood vessel is constructed according to characteristic.Wherein, definition has zoning in threedimensional model.
S33: sliding-model control is carried out to zoning, generates the grid for portraying zoning.
Step S31-S33 is similar with above-mentioned corresponding step in the present embodiment, specifically repeats no more.
S34: the Physics-mathematics model of zoning is constructed.
Physics-mathematics model, which can describe blood flow, vascular wall deformation and interaction force between the two, joins blood flow
The physical phenomenon of several influences.The Physics-mathematics model is solved, blood flow parameter obtained, that is, represents blood flow spy
Sign.Physics-mathematics model is the governing equation for describing physics objective phenomenon, constructed Physics-mathematics model packet in the present embodiment
Include the hydrodynamics governing equation and Solid Mechanics governing equation of unity couping.
It can get velocity of blood flow and pressure etc. according to hydrodynamics governing equation, hydrodynamics governing equation includes: that can press
Contracting and incompressible Navier-Stockes equation and its corresponding various turbulence models, such as equal, large eddy simulation when Reynolds.
It can get vascular wall displacement etc. according to Solid Mechanics governing equation, Solid Mechanics governing equation includes: linear elasticity
With the models such as the solid constitutive equation and viscoelasticity, elastoplasticity, porous media of nonlinear elasticity.
Solid unity couping is flowed in constructed Physics-mathematics model, thus in Physics-mathematics model further include: stream liquid/solid interface item
Part.
Boundary in corresponding zoning, in Physics-mathematics model further include: sliding or without sliding wall boundary condition, resistance
Buddhist nun's type Outlet boundary condition, no pressure boundary condition etc., various boundary corresponds to different physical phenomenons, and directly affects and ask
The computation complexity and adaptability of topic.
S35: it is based on grid, Physics-mathematics model is calculated, the blood flow parameter and blood vessel parameter of zoning are obtained.
Physics-mathematics model constructed by above-mentioned steps S34 is by hydrodynamics governing equation and Solid Mechanics governing equation coupling
It closes to an equation, this step S35 is solved in the equation, and calculating process is realized without the iteration between two equations
Estimate simultaneously guarantees solving precision.
Specifically, this step is based on grid, and Fluid Mechanics governing equation and Solid Mechanics governing equation carry out same
When solve, and flow the mesh point information of blood flow grid and the net of blood vessel grid at solid interface in unified calculation region when solving
Lattice point information.
For blood flow and vascular wall, the two is flowing solid interface interaction, and is opposing force, such as cutting
Shear force, displacement etc. have certain relationship in parameters.It is thus simulated and is handed over using stream liquid/solid interface condition in Physics-mathematics model
The case where interface；And the mesh point information that interface is consolidated in convection current in the network of zoning carries out unification, specifically, if handing over
Interface blood flow grid and blood vessel mesh fitting are then converted by point-to-point information to carry out the unification of mesh point information；If
Blood flow grid and blood vessel grid mismatch at interface, then carry out the unification of mesh point information using interpolation method, can use
Linear and quadratic interpolation method, Interpolation Property of Radial Basis Function method, Mortar member method based on finite element basic function etc..
Above-mentioned steps establish the Physics-mathematics model of fluid structurecoupling, calculate the Physics-mathematics model more accurately to blood
Blood flow in pipe is simulated.
When carrying out flowing solid unity couping estimate simultaneously, problem scale is very big, therefore the present embodiment is also proposed using non-thread
Property system solution algorithm calculates Physics-mathematics model, and newton-krylov-Schwarz (Newton- specifically can be used
Krylov-Schwarz) algorithm includes the following steps.
S351: sliding-model control is carried out to Physics-mathematics model, obtains Nonlinear System of Equations.
Sliding-model control is carried out to Physics-mathematics model first, i.e., turns to Nonlinear System of Equations for partial differential equation are discrete.
Wherein, for hydrodynamics governing equation, the side such as stabilized P1-P1 member, classics Taylor-Hood P2-P1 member can be used
Method；Solid Mechanics governing equation uses displacement to the mixed form for giving weak stress symmetric tensor using PEERS member
Non-coordinating P1 member；For flowing liquid/solid interface condition, discrete scheme is using mortar or hybridization technique and is based on Lagrange multiplier
Novel method.
S352: Nonlinear System of Equations is solved using Newton method.
In the solution procedure of this step, linear search can be used and feasible field technique determines the direction of search and step-length,
Linear search is carried out in feasible zone；In the iterative process of Newton Algorithm, grid sequence method and non-linear pretreatment can be used
Technology, so that the convergence that the nonlinear iteration process of this step has grid unrelated；And for the Jacobian in Newton method
Matrix, then using strategies such as multicolor ordering finite difference calculus, automatic differential technology, Jacobian-free method or explicit generations
Construction generates.
S353: the system of linear equations in Newton method is solved using Cray promise husband subspace iteration method.
Specifically, bis- using the Lanczos of GMRES or short reproduce-type (Short-Recurrence) in this step
Orthogonalization method solves the system of linear equations in Newton method with unsymmetrical matrix.
S354: fore condition in domain decomposition method construction system of linear equations is utilized.
Construction fore condition accelerates the linear solution in step S353, and Overlapping Schwarz is used in the present embodiment
(Schwarz) algorithm is specifically constructed using adjusting extension additive schwarz method or restricted type additive schwarz method pre-
Condition.
If zoning is divided into multiple sub- zonings of overlapping in the present embodiment, need to introduce antithetical phrase calculating at this time
The calculation method in region, uses direct method or iterative method in the present embodiment, including LU decomposition algorithm, incomplete factorization algorithm,
Gauss-Seidel iterative method etc..The matrix of subregion be it is sparse, storing and accessing for non-zero entry can be by a block (point-
Block) mode carries out, i.e., direct method or iterative method can store and access simultaneously multiple changes on node by the sequence of grid node
Amount.When solving subregion problem using direct method, different subregion matrix sort modes, including Nested can be used
Dissection, One-way Dissection, Reverse Cuthill-McKee and Quotient Minimum Degree
The methods of.
Physics-mathematics model is solved using Nonlinear System Solving algorithm, obtains blood flow parameter and blood vessel parameter.
It include the mobile numerical value of vascular wall in blood vessel parameter, the mobile of vascular wall can have a certain impact to grid, when calculating next time,
Need to consider the variation of grid.Therefore it is also followed the steps below in the present embodiment.
S36: the running parameter of grid is calculated according to blood vessel parameter, to update zoning.
When blood and vascular wall interaction are so that zoning changes, the grid of corresponding zoning is also required to
Corresponding to adjust, the movement for specifically capturing grid in this step using Dynamic mesh utilizes removable net according to blood vessel parameter
Lattice algorithm calculates the running parameter of grid, to construct new grid according to running parameter.
It using the calculating of removable trellis algorithm is based on removable grid framework, such as ALE frame, ALE in this step
Frame combines Lagrangian format and Euler scheme, and Lagrangian format grid in solid expression can deform with material and be become
Shape, Euler scheme grid in fluid expression, which does not move, to be unlikely to cause mesh torsion and interlocks.Specifically, when based on ALE
Frame is modeled when being calculated, to flow the fluid mass near liquid/solid interface using ALE referential, and the fluid far from stream liquid/solid interface
It is modeled using Euler's referential.Spring body method, partial differential equation method or interpolation method then specifically can be used in removable trellis algorithm.Example
Such as, spring body method assumes that calculating grid domain is elastic fluid, chooses appropriate elasticity modulus and utilizes displacement boundary conditions, passes through
Elastic equation linearly or nonlinearly is solved, obtains calculating grid with convenient and fast movement or deformation.
In order to improve grid updating quality, in calculating process, Young's modulus and Poisson's ratio are constructed to obtain high quality
New grid, i.e., when being calculated using removable trellis algorithm, in conjunction with the Young's modulus and Poisson's ratio constructed.In addition, right
In the problem that amount of movement is larger, when the mesh quality after movement is poor, net is adjusted by the method for mesh point local directed complete set
The distribution of lattice point is to improve mesh quality.Also, after constructing new grid according to running parameter, it can also be calculated based on grid optimization
Method, such as Delaunay algorithm optimize new grid.
A dynamic mesh equation is constructed in this step S36, and to describe the movement of grid, dynamic mesh equation is calculated
The running parameter that can get grid, since calculating process is related to blood vessel parameter, thus can be integrated in step for dynamic mesh equation
It in S34 in constructed Physics-mathematics model, carries out while solving, is i.e. there is no stringent successive by this step S36 and step S35
Relationship can carry out simultaneously.
Physics-mathematics model constructed by the present embodiment can use following form.
Hydrodynamic equations:
Flow liquid/solid interface condition:
σf·nf=-σs·ns on Γinterface,
D=x on Γinterface,
Dynamics of solids equation:
p0ns+σs·ns+ α d=0
Dynamic mesh equation:
inΩf,
X=0
Wherein,For the Cauchy stress tensor in flow field, u indicates blood flow velocity, pfFor blood
Flowing pressure, ρfFor density of blood, μ is that (when blood is considered as Newtonian fluid, corresponding μ is constant, is considered as non-for the viscosity of blood
When Newtonian fluid, μ is a complicated function).
D indicates the displacement of vascular wall, σs=λ trace (ε) I+2 μ ε is the stress tensor of vascular wall, wherein λ and μsFor Lame
Coefficient,
X indicates the displacement of Grid Mobile, σmFor the stress tensor of grid model, form and σsEqually, but corresponding Lame system
Number value is different.
For become a mandarin boundary and the Outlet boundary in fluid calculation domain,It is handed over for removing for solid (tube wall) with fluid
Boundary out-of-bounds, such as the outer wall of blood vessel, ΓinterfaceFor the interface (blood-vascular wall interface) of fluid and solid；α is steady
Surely change constant, specific value is set according to experimental data.ΩfFor fluid calculation region, ΩsFor solid zoning.
For the selection of the selection of the stress tensor in above-mentioned equation, the construction of viscosity and boundary condition, fluid and
The selection of stress tensor is required to depending on the specific nature of blood and vascular wall in solid equation, in practical clinical
In, for each case, numerical value is different.
The method of the present embodiment constructs the Physics-mathematics model for flowing solid unity couping, and to the grid of zoning change into
Row updates, so that Simulation of Blood is more accurate；Nonlinear System Solving algorithm is introduced in simulation calculates, to guarantee to calculate effect
Rate.
Embodiment illustrated in fig. 3 is related to after grid generates to the carry out Region Decomposition of zoning, and based on Region Decomposition into
Row parallel computation；Embodiment illustrated in fig. 5 involves setting up the Physics-mathematics model for flowing solid unity couping, is flowed in terms of solid unity couping by carrying out
It calculates, and derivation algorithm is arranged in specific aim；Technology involved by the two is in combination with application.
Such as grid generation module is divided using the grid generation technique of embodiment illustrated in fig. 3 and region in Simulation of Blood system
Solution technology, model solution module then introduce the building shown in fig. 5 for flowing solid fully-coupled model, and the use of corresponding algorithm.For
For Simulation of Blood process, being greatly improved for simulation precision and precision is realized.
Above-mentioned Simulation of Blood method can be realized based on software architecture shown in FIG. 1, in terms of hardware configuration, please refer to figure
6, Fig. 6 be the structural schematic diagram of one embodiment of the application blood flow simulator.
The present embodiment blood flow simulator 200 includes processor 21 and memory 22, is stored with and can locate in memory 22
The computer program run on reason device 21, processor 21 can be realized above-mentioned Simulation of Blood method when executing computer program.
Processor 21 is the processor of broad sense in the present embodiment, may include multiple processors, can be and is arranged not
It with the processor in equipment, such as may include the processor group of the processor and supercomputing center in local computer.This
In embodiment when carrying out the parallel computation of Simulation of Blood, how many sub- zoning is then correspondingly arranged how many a processors,
To calculate respectively sub- zoning.
Isomeric architecture can be used in processor 21 in the present embodiment, carries out on a large scale using the present embodiment processor 21
When the parallel computation of data, calculating process is placed into that is, according to the feature of different calculating using a series of parallel acceleration techniques
On different processors, maximally utilizing for processor ability is realized.
Such as in terms of solution, the meter of time-consuming more nonlinear discrete function when by non-linear solution and linear solution
It calculates, Sparse Matrix-Vector multiplies, the core calculation modules such as sparse matrix fast decoupled are transplanted to GPU, MIC or other many-core processors
On.Decomposition and Retrospect Solution using polychrome or more scheduling stragetic innovation sparse matrixes, one side boosting algorithm are parallel
On the other hand degree keeps the convergence efficiency of solver.Boundary condition etc. is related to the part of a large amount of branch operations inside region
It is independent, it is calculated by the strong component of logic processing capability, so that task is more reasonably distributed.
In terms of processor computations, optimization instruction level parallelism, Thread-Level Parallelism and process level are parallel, using data weight
With, calculate, data fusion overlapping with memory access and to boundary's access, data merging transmission, vectorization, the skills such as scientific calculation function optimization
Art optimizes the operation on many-core processor, improves floating-point efficiency when actual motion.
In terms of programming language is realized in the instruction of processor, for GPU, MIC or other many-core processors, using CUDA,
OpenACC, openCL language on GPU in executing；It is executed on MIC using OpenMP language；Using pthread, athread or
Other function packets execute on other many-core processors.
In multiple processor parallel processing large-scale datas, improved efficiency necessary not only in terms of calculating, it need to also be
It is improved efficiency in terms of the transmission of data.Such as a series of large-scale discrete data parallel processing techniques are used in the present embodiment.
Block parallel I/O technology: establishing the data structure of piecemeal, makes load balance between processor.It will indicate blood vessel
With the discrete data of the physical quantity of blood by zoning piecemeal and it is parallel read in from or be output in one or more data files,
Piecemeal number is identical as used processor number.Block parallel I/O technology is based on MPI-2 (and with adjustment of the printing plate in the present embodiment
This) function library, it is realized by the way of specifying explicit offset, unique file pointers or shared file pointer.Data file packet
Include the formats such as HDF5, VTK.
Thick or encryption export technique is put, i.e., the grid for indicating blood vessel and blood put thick or encryption, and by former grid
On physical quantity be interpolated on new grid, then use the block parallel I/O technology export.
Data traffic and I/O data volume are reduced using vector compression technology or based on MPI_pack packetizing techniques,
And design the I/O bottleneck that I/O solves large-scale discrete data with the overlapping mechanism of calculating.
The present embodiment blood flow simulator is realized to the abundant of the high level computer for configuring thousands of calculating cores up to ten thousand
It utilizes, computing resource is sufficiently had invoked by the cooperation of software and algorithm, improves the precision and efficiency of Hemodynamic analysis, it is real
The parallel expansible efficiency for having showed 60% or more decreases while improving haemodynamics simulation precision and calculates the time.
Above-mentioned Simulation of Blood method is realized and when sold or used as an independent product in a software form, is storable in one
A electronic device-readable takes in storage medium, that is, the present invention also provides a kind of computer readable storage mediums, referring to Fig. 7, figure
7 be the structural schematic diagram of one embodiment of the application computer readable storage medium, is stored in computer readable storage medium 300
Computer program, when which is executed by processor the step of the realization above method.Computer readable storage medium can
Think USB flash disk, CD, server etc..
The foregoing is merely presently filed embodiments, are not intended to limit the scope of the patents of the application, all to utilize this
Equivalent structure or equivalent flow shift made by application specification and accompanying drawing content, it is relevant to be applied directly or indirectly in other
Technical field similarly includes in the scope of patent protection of the application.
Claims (10)
1. a kind of vascular flow analogy method based on mechanical equation, which is characterized in that the described method includes:
Obtain the characteristic of the blood vessel；
The threedimensional model of the blood vessel is constructed according to the characteristic, the threedimensional model definition has zoning；
Sliding-model control is carried out to the zoning, generates the grid for portraying the zoning；
The Physics-mathematics model of the zoning is constructed, the Physics-mathematics model includes the hydrodynamics controlling party of unity couping
Journey and Solid Mechanics governing equation；
Based on the grid, the Physics-mathematics model is calculated, obtains the blood flow parameter and blood vessel of the zoning
Parameter；
The running parameter of the grid is calculated according to the blood vessel parameter, to update the zoning.
2. the method according to claim 1, wherein described be based on the grid, to the Physics-mathematics model
It is calculated, comprising:
Based on the grid, the hydrodynamics governing equation and the Solid Mechanics governing equation are carried out while being solved, and
The mesh point information of blood flow grid and the mesh point of blood vessel grid at solid interface are flowed in the unified zoning when solving
Information.
3. according to the method described in claim 2, it is characterized in that, flowing blood at solid interface in the unification zoning
The mesh point information of stream trellis and the mesh point information of blood vessel grid, comprising:
If blood flow grid and blood vessel mesh fitting at the interface, are converted by point-to-point information to carry out mesh point letter
The unification of breath；
If blood flow grid domain blood vessel grid mismatches at the interface, the system of mesh point information is carried out using interpolation method
One.
4. the method according to claim 1, wherein described calculate the Physics-mathematics model, comprising:
The Physics-mathematics model is calculated using Nonlinear System Solving algorithm.
5. according to the method described in claim 4, it is characterized in that, described utilize Nonlinear System Solving algorithm to the physics
Mathematical model is calculated, comprising:
Sliding-model control is carried out to the Physics-mathematics model, obtains Nonlinear System of Equations；
The Nonlinear System of Equations is solved using Newton method；
The system of linear equations in the Newton method is solved using Cray promise husband subspace iteration method；
Of the fore condition in the system of linear equations is constructed using domain decomposition method.
6. according to the method described in claim 5, it is characterized in that, described constructed in the system of linear equations using Region Decomposition
Fore condition, comprising:
Utilize of fore condition described in restricted type additivity Schwarz algorithm construction.
7. the method according to claim 1, wherein the change for calculating the grid according to the blood vessel parameter
Change parameter, comprising:
According to the blood vessel parameter, the running parameter of the grid is calculated using removable trellis algorithm, and according to the transformation
The new grid of parametric configuration.
8. the method according to the description of claim 7 is characterized in that described calculate the grid using removable trellis algorithm
Running parameter, and new grid is constructed according to the transformation parameter, comprising:
Construct Young's modulus and Poisson's ratio；
In conjunction with the Young's modulus and Poisson's ratio, the running parameter of the grid is calculated using removable trellis algorithm；
New grid is constructed according to the running parameter, and the new grid is optimized based on grid optimization algorithm.
9. a kind of blood flow simulator, including memory, processor and it is stored on the memory and can be in the processor
The computer program of upper operation, which is characterized in that the processor is realized in claim 1-8 when executing the computer program
The step of any one the method.
10. a kind of computer readable storage medium, is stored thereon with computer program, which is characterized in that the computer program
The step of any one of claim 1-8 the method is realized when being executed by processor.
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