CN106709902B - Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation - Google Patents

Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation Download PDF

Info

Publication number
CN106709902B
CN106709902B CN201611003438.0A CN201611003438A CN106709902B CN 106709902 B CN106709902 B CN 106709902B CN 201611003438 A CN201611003438 A CN 201611003438A CN 106709902 B CN106709902 B CN 106709902B
Authority
CN
China
Prior art keywords
blood vessel
guide wire
blood
vessel
flow
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201611003438.0A
Other languages
Chinese (zh)
Other versions
CN106709902A (en
Inventor
顾力栩
蔡佳音
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Shanghai Jiaotong University
Original Assignee
Shanghai Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Shanghai Jiaotong University filed Critical Shanghai Jiaotong University
Priority to CN201611003438.0A priority Critical patent/CN106709902B/en
Publication of CN106709902A publication Critical patent/CN106709902A/en
Application granted granted Critical
Publication of CN106709902B publication Critical patent/CN106709902B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/0002—Inspection of images, e.g. flaw detection
    • G06T7/0012—Biomedical image inspection
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T15/00—3D [Three Dimensional] image rendering
    • G06T15/005—General purpose rendering architectures
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/10—Image acquisition modality
    • G06T2207/10072—Tomographic images
    • G06T2207/10081—Computed x-ray tomography [CT]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/30—Subject of image; Context of image processing
    • G06T2207/30004—Biomedical image processing
    • G06T2207/30101—Blood vessel; Artery; Vein; Vascular

Abstract

The invention relates to a real-time motion simulation method for a guide wire under the action of blood flow in a minimally invasive vascular interventional operation, which comprises the following steps of: firstly, segmenting data of a blood vessel part in advance, and modeling the blood vessel by adopting a triangular surface mesh; secondly, obtaining a central line of the blood vessel grid, representing the continuous blood vessel grid model in a discretization manner into a group of combinations of small cylindrical blood vessels according to the central line, and abstracting to be a directed graph; thirdly, establishing a fluid model for each section of small blood vessel; fourthly, establishing a fluid calculation matrix for the whole blood vessel model abstracted into the directed graph, and calculating the flow and pressure distribution in the blood vessel; fifthly, modeling the guide wire, calculating the acting force of blood flow on the guide wire according to the relative position of the guide wire in the blood vessel, applying the acting force to the guide wire to a simulation model of the guide wire, and updating the form of the guide wire; and sixthly, performing three-dimensional rendering on the guide wire. Compared with the prior art, the method has the advantages of stable calculation, good real-time performance, strong sense of reality, flexible application and the like.

Description

Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation
Technical Field
The invention relates to a simulation method of a virtual operation, in particular to a real-time motion simulation method of a guide wire under the action of blood flow in a minimally invasive vascular interventional operation.
Background
With the rapid development of scientific technology, the application of virtual surgery provides more and more help for the modernization of medical treatment. The virtual minimally invasive vascular surgery training system can quickly and effectively help interns to improve surgical skills, so that more patients with cardiovascular and cerebrovascular diseases can receive minimally invasive interventional therapy. The real-time motion simulation of the guide wire is the most important part of a minimally invasive vascular interventional operation system and is also the subject of research of a plurality of scholars.
In the research process of the real-time motion simulation of the guide wire, early learners are limited by that a non-physical geometric model, such as a B-spline curve, is adopted at the calculation level of hardware at that time, the non-physical model describes the form of the guide wire from the geometric angle, although the calculation speed is high, the physical characteristics of the guide wire are completely ignored, and the stress condition of the guide wire cannot be described, so the reality is poor; other students model the motion Simulation of the guide wire by using a physical mass spring model, an elastic rod model and the like, the physical model considers the physical characteristics of the guide wire, is easy to physically model the interaction between the guide wire and the blood vessel, can meet the requirement of real-time calculation after the continuous development of the hardware level, and has a larger improvement in the sense of reality compared with a non-physical model, and is widely used, for example, the mass spring model adopted by Basdogan and other students in the Virtual environment for medical Training, the physical and historical understanding of the spatial Common double expansion, and the elastic rod model adopted by Tatang and other students in the A relative elastic model for real-time Simulation of minor innovation.
However, although the guide wire moves in the blood stream during the operation, most scholars do not consider the effect of the blood stream manually when the guide wire moves in the blood stream; the minimally invasive vascular interventional operation training system provides a highly restored virtual training environment with immersion for a user, which requires that a simulated guide wire has high physical reliability, so that blood flow in a blood vessel needs to be calculated on the basis of considering the physical attributes of the guide wire, and the blood flow action condition received by the guide wire in motion is analyzed.
The main challenges to real-time simulation of blood-affected guidewires are the following:
1) due to the complexity of the fluid equations themselves, fluid calculations are typically computationally complex and time consuming;
2) the blood vessel is an irregular three-dimensional model, and the fluid model is difficult to establish in the irregular model, and the complexity of fluid calculation is increased;
3) the physical simulation of the guide wire requires higher real-time performance, and the integration of fluid calculation inevitably causes the reduction of simulation efficiency and even is difficult to achieve real-time performance;
disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a real-time motion simulation method for the guide wire under the blood flow effect in the minimally invasive vascular interventional surgery, which has stable calculation, good real-time performance, strong sense of reality and flexible application by means of simplifying a fluid equation, discretizing description of irregular blood vessels, hardware acceleration and the like.
The purpose of the invention can be realized by the following technical scheme:
a real-time motion simulation method for a guide wire under the action of blood flow in a minimally invasive vascular interventional operation comprises the following steps:
firstly, segmenting data of a blood vessel part in advance according to a CT scanning image of a patient, and modeling the blood vessel by adopting a triangular surface mesh;
secondly, obtaining a central line of the blood vessel grid, representing the continuous blood vessel grid model in a discretization manner into a group of combinations of small cylindrical blood vessels according to the central line, and abstracting to be a directed graph;
thirdly, establishing a fluid model for each section of small blood vessel according to Poisson's leaf rule, wherein the fluid model is used for describing the relationship between the flow in each section of small blood vessel and the pressure difference between the two ends of each section of small blood vessel;
fourthly, according to the conditions of the position relation among the small blood vessels, the consistency of the inlet flow and the outlet flow and the pressure difference between two ends of the small blood vessels, a fluid calculation matrix is integrally established for the blood vessel model abstracted as a directed graph, and the flow and the pressure distribution in the blood vessel are calculated;
fifthly, modeling the guide wire by using an elastic rod model, calculating the acting force of blood flow on the guide wire according to the relative position of the guide wire in the blood vessel, applying the acting force to a simulation model of the guide wire, and updating the shape of the guide wire;
and sixthly, performing three-dimensional rendering on the guide wire.
Discretizing the continuous mesh model into a set of circular tubes from the centerline and abstracting into a directed graph denoted G (N)n，Ne) Therein contains NnA node and NeThe edges are discrete points, the nodes are round tubes.
In the third step, the fluid in each segment of cylindrical small blood vessel is modeled according to Poisson leaf rule as follows:
Figure BDA0001151965780000031
wherein Q represents the flow in the segment of the vessel, Δ p represents the pressure difference across the vessel, L represents the length of the segment of the vessel, R represents the radius of the vessel, η represents the viscosity coefficient of the blood, R represents the resistance of the segment of the vessel, described by L, R, η;
the blood vessel whole fluid calculation process in the fourth step is as follows:
41) the topology of the vessel after abstraction as a directed graph is described using a node-edge matrix:
Figure BDA0001151965780000032
wherein if the jth edge starts from the ith node, then Ai,j1, if the jth edge ends up to the ith node, ai,j＝-1；
42) Since each node's incoming and outgoing traffic is equal, it is denoted as
AQ＝0
Wherein Q represents the flow in the segment of the vessel and A is a node-edge matrix describing the topology of the vessel;
43) and because there are 3 models shown for the fluid in each small vessel, the overall fluid calculation for the entire vessel is represented as:
CQ＝ΔP
wherein C is diagonal matrix
Figure BDA0001151965780000033
RiRepresenting the resistance of the ith segment of blood vessel, wherein i is 1. n, and Δ P is a column vector including the pressure difference of each side;
44) using a sine function to represent the variation p between systolic and diastolic blood pressuresource(t)
Figure BDA0001151965780000034
Wherein, P1And P2Systolic and diastolic pressures, respectively, ω being used to control the period of the output pressure;
45) integrating the equations listed above, the overall blood vessel overall flow calculation process is expressed as:
Figure BDA0001151965780000041
wherein the content of the first and second substances,
Figure BDA0001151965780000042
is a sparse, invertible matrix, P represents the pressure of the cardiac output, and the equation is solved as follows
Figure BDA0001151965780000043
Since the value of the matrix K is only related to the topological structure of the blood vessel, and the structure of the blood vessel is fixed, the inverse of K is solved in advance before the simulation is started, so as to improve the speed of the simulation.
In the fifth step, the step of calculating the acting force of the blood flow on the guide wire and applying the acting force to the simulation model of the guide wire is as follows:
51) searching the relative position of guide wire particles in the blood vessel and determining the small blood vessel to which the guide wire particles belong; describing the discretized vessel as V1～nAll guide wire particles are described as m1～nTo speed up the search, instead of searching all vessels for each particle, only the first particle m is searched1Search all vessels and find the corresponding vessel V1′For any subsequent particle miOnly the vessel V to which the previous particle belongs needs to be searched(i-1)′A neighborhood of V(i-1)′±nThe blood vessel where each particle is located is quickly found; the speed of simulation is effectively improved by using the searching method;
52) the force of the blood flow on the particle is obtained from the position of the particle in the blood vessel, and is expressed as follows
Figure BDA0001151965780000044
x represents the distance of the particle in the axial direction of the blood vessel, d represents the distance of the particle in the radial direction of the blood vessel, Q represents the flow rate in the section of the blood vessel, Δ P represents the pressure difference across the blood vessel, r represents the radius of the blood vessel, and η represents the viscosity coefficient of blood;
53) the blood flow effect is integrated into the physical simulation of the guide wire, and the calculation of each frame of the guide wire based on the elastic rod model is as follows
Figure BDA0001151965780000045
Where Δ x and Δ v represent the position and velocity changes of each particle, respectively, Δ t is the time interval, f represents the jacobian matrix of the force conditions of each particle, including the forces of push-pull, rotation and collision experienced by the guide wire, M is a diagonal matrix dependent on the position information of each particle of the guide wire, v is the diagonal matrix, andt,xtrespectively representing the velocity and position of the particle at time t;
the effect of adding blood flow to each particle is as follows, and a guide wire simulation calculation model influenced by the blood flow effect is obtained:
Figure BDA0001151965780000051
compared with the prior art, the method integrates the acting force of the blood flow into the motion simulation of the guide wire, and has the advantages of stable calculation, good real-time performance, strong sense of reality, flexible application and the like.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
The embodiment is realized on a PC, the CPU is Intel to Strong E3-1230, the memory 4G, the video card is Yingvian GTX760, and the realization mode is realized by C + + programming language.
The flow of this example is shown in FIG. 1.
Firstly, segmenting data of a blood vessel part by using a region growing and manual adjusting method according to a CT scanning image of a patient, and modeling the blood vessel by adopting a triangular surface mesh through a Marching cube algorithm;
secondly, obtaining a central line of the blood vessel grid, discretizing the continuous blood vessel grid model according to the central line to represent the combination of a group of cylindrical small blood vessels, wherein 2477 cylindrical small blood vessels exist after the blood vessels are discretized in the embodiment, and then, using a directed graph for abstract description;
thirdly, establishing a fluid model for each section of small blood vessel according to Poisson's leaf rule, and describing the relationship between the flow in each section of small blood vessel and the pressure difference between the two ends;
fourthly, according to the conditions of the position relation among the small blood vessels, the consistency of the inlet flow and the outlet flow and the pressure difference between two ends of the small blood vessels, a fluid calculation matrix is integrally established for the blood vessel model abstracted as a directed graph, and the flow and the pressure distribution in the blood vessel are calculated; the blood flow calculation is accelerated by adopting an Intel mathematical core operation library (Intel MKL).
Fifthly, calculating the acting force of the blood flow on the guide wire according to the relative position of the guide wire in the blood vessel and applying the acting force to the guide wire on a simulation model of the guide wire;
and sixthly, performing three-dimensional rendering on the guide wire by using OpenGL.

Claims (4)

1. A real-time motion simulation method for a guide wire under the action of blood flow in a minimally invasive vascular interventional operation comprises the following steps:
firstly, segmenting data of a blood vessel part in advance according to a CT scanning image of a patient, and modeling the blood vessel by adopting a triangular surface mesh;
secondly, obtaining a central line of the blood vessel grid, representing the continuous blood vessel grid model in a discretization manner into a group of combinations of small cylindrical blood vessels according to the central line, and abstracting to be a directed graph;
thirdly, establishing a fluid model for each section of small blood vessel according to the Poisson's rule, wherein the fluid model is used for describing the relationship between the flow in each section of small blood vessel and the pressure difference between the two ends of each section of small blood vessel;
fourthly, according to the conditions of the position relation among the small blood vessels, the consistency of the inlet flow and the outlet flow and the pressure difference between two ends of the small blood vessels, a fluid calculation matrix is integrally established for the blood vessel model abstracted as a directed graph, and the flow and the pressure distribution in the blood vessel are calculated;
fifthly, modeling the guide wire by using an elastic rod model, calculating the acting force of blood flow on the guide wire according to the relative position of the guide wire in the blood vessel, applying the acting force to a simulation model of the guide wire, and updating the shape of the guide wire;
sixthly, conducting three-dimensional rendering on the guide wire;
in the fifth step, the step of calculating the acting force of the blood flow on the guide wire and applying the acting force to the simulation model of the guide wire is as follows:
51) searching the relative position of guide wire particles in the blood vessel and determining the small blood vessel to which the guide wire particles belong; describing the discretized vessel as V1～nAll guide wire particles are described as m1～nTo speed up the search, instead of searching all vessels for each particle, only the first particle m is searched1Search all vessels and find the corresponding vessel V1′For any subsequent particle miOnly the vessel V to which the previous particle belongs needs to be searched(i-1)′A neighborhood of V(i-1)N, quickly finding the blood vessel where each particle is located; the speed of simulation is effectively improved by using the searching method;
52) the force of the blood flow on the particle is obtained from the position of the particle in the blood vessel, and is expressed as follows
Figure FDA0002458427700000011
x represents the distance of the particle in the axial direction of the blood vessel, d represents the distance of the particle in the radial direction of the blood vessel, Q represents the flow rate in the section of the blood vessel, Δ P represents the pressure difference across the blood vessel, r represents the radius of the blood vessel, and η represents the viscosity coefficient of blood;
53) the blood flow effect is integrated into the physical simulation of the guide wire, and the calculation of each frame of the guide wire based on the elastic rod model is as follows
Figure FDA0002458427700000021
Where Δ x and Δ v represent the position and velocity changes of each particle, respectively, Δ t is the time interval, f represents the jacobian matrix of the force conditions of each particle, including the forces of push-pull, rotation and collision experienced by the guide wire, M is a diagonal matrix dependent on the position information of each particle of the guide wire, v is the diagonal matrix, andt,xtrespectively representing the velocity and position of the particle at time t;
the effect of adding blood flow to each particle is as follows, and a guide wire simulation calculation model influenced by the blood flow effect is obtained:
Figure FDA0002458427700000022
2. the method for simulating real-time motion of a guidewire under the influence of blood flow in minimally invasive vascular interventional surgery as recited in claim 1, wherein the continuous mesh model is discretized according to a central line and represented as a set of circular tubes, and abstracted as a directed graph represented as G (N)n,Ne) Therein contains NnA node and NeThe edges are discrete points, the nodes are round tubes.
3. The method for simulating the real-time motion of the guidewire under the effect of blood flow in the minimally invasive vascular interventional operation according to claim 1, wherein a fluid model is established for each segment of small blood vessel according to Poisson's law as follows:
Figure FDA0002458427700000023
where Q represents the flow in the segment of the vessel, Δ p represents the pressure difference across the vessel, L represents the length of the segment of the vessel, R represents the radius of the vessel, η represents the viscosity coefficient of the blood, and R represents the resistance of the segment of the vessel, described by L, R, η.
4. The method for simulating the real-time motion of the guide wire under the action of the blood flow in the minimally invasive vascular interventional surgery according to claim 1, wherein a fluid calculation matrix is integrally established for the blood vessel model abstracted as a directed graph as follows:
41) the topology of the vessel after abstraction as a directed graph is described using a node-edge matrix:
Figure FDA0002458427700000024
wherein if the jth edge starts from the ith node, then Ai,j1, if the jth edge ends up to the ith node, ai,j＝-1；
42) Since each node's incoming and outgoing traffic is equal, it is denoted as
AQ＝0
Wherein Q represents the flow in the segment of the vessel and A is a node-edge matrix describing the topology of the vessel;
43) and because the fluid in each small blood vessel section has the model, the overall fluid calculation of the whole blood vessel is represented as:
CQ＝ΔP
wherein C is diagonal matrix
Figure FDA0002458427700000031
RiRepresenting the resistance of the ith segment of blood vessel, wherein i is 1 … n, and Δ P is a column vector including the pressure difference of each side;
44) using a sine function to represent the variation p between systolic and diastolic blood pressuresource(t)
Figure FDA0002458427700000032
Wherein, P1And P2Systolic and diastolic pressures, respectively, ω being used to control the period of the output pressure;
45) integrating the equations listed above, the overall blood vessel overall flow calculation process is expressed as:
Figure FDA0002458427700000033
wherein the content of the first and second substances,
Figure FDA0002458427700000034
is a sparse, invertible matrix, P represents the pressure of the cardiac output, and the equation is solved as follows
Figure FDA0002458427700000035
Since the value of the matrix K is only related to the topological structure of the blood vessel, and the structure of the blood vessel is fixed, the inverse of K is solved in advance before the simulation is started, so as to improve the speed of the simulation.
CN201611003438.0A 2016-11-14 2016-11-14 Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation Active CN106709902B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201611003438.0A CN106709902B (en) 2016-11-14 2016-11-14 Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201611003438.0A CN106709902B (en) 2016-11-14 2016-11-14 Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation

Publications (2)

Publication Number Publication Date
CN106709902A CN106709902A (en) 2017-05-24
CN106709902B true CN106709902B (en) 2020-06-19

Family

ID=58940480

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201611003438.0A Active CN106709902B (en) 2016-11-14 2016-11-14 Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation

Country Status (1)

Country Link
CN (1) CN106709902B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107978372A (en) * 2017-12-07 2018-05-01 北京理工大学 Analogy method, device and the electronic equipment that virtual bracket is expanded in the blood vessels
CN111798451B (en) * 2020-06-16 2023-08-08 北京理工大学 3D guide wire tracking method and device based on blood vessel 3D/2D matching

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102968811A (en) * 2012-10-25 2013-03-13 上海交通大学 Real-time motion simulation method for guide wire in minimally invasive vessel interventional operation
US8830234B2 (en) * 2009-08-17 2014-09-09 Mistretta Medical, Llc System and method for four dimensional angiography and fluoroscopy
CN104837407A (en) * 2012-12-07 2015-08-12 株式会社东芝 Blood vessel analysis device, medical diagnostic imaging apparatus, and blood vessel analysis method
CN106067269A (en) * 2016-05-13 2016-11-02 中国科学院自动化研究所 The determination method and system of feedback force in virtual cardiovascular interventional operation training system

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8830234B2 (en) * 2009-08-17 2014-09-09 Mistretta Medical, Llc System and method for four dimensional angiography and fluoroscopy
CN102968811A (en) * 2012-10-25 2013-03-13 上海交通大学 Real-time motion simulation method for guide wire in minimally invasive vessel interventional operation
CN104837407A (en) * 2012-12-07 2015-08-12 株式会社东芝 Blood vessel analysis device, medical diagnostic imaging apparatus, and blood vessel analysis method
CN106067269A (en) * 2016-05-13 2016-11-02 中国科学院自动化研究所 The determination method and system of feedback force in virtual cardiovascular interventional operation training system

Also Published As

Publication number Publication date
CN106709902A (en) 2017-05-24

Similar Documents

Publication Publication Date Title
Fedele et al. Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function
Takizawa et al. Space–time and ALE-VMS techniques for patient-specific cardiovascular fluid–structure interaction modeling
EP3166032B1 (en) Biometric simulation device, method for controlling biometric simulation device, and program for controlling biometric simulation device
Qian et al. Virtual reality based laparoscopic surgery simulation
Sasaki et al. Aorta zero-stress state modeling with T-spline discretization
France et al. A layered model of a virtual human intestine for surgery simulation
Li et al. A catheterization-training simulator based on a fast multigrid solver
CN106709902B (en) Real-time motion simulation method for blood flow effect of guide wire in minimally invasive vascular interventional operation
Saalfeld et al. Semi-Immersive 3D Sketching of Vascular Structures for Medical Education.
Fetita et al. An image-based computational model of oscillatory flow in the proximal part of tracheobronchial trees
Qian et al. Essential techniques for laparoscopic surgery simulation
Banihani et al. POD for real-time simulation of hyperelastic soft biological tissue using the point collocation method of finite spheres
Nürnberger et al. Using recurrent neuro-fuzzy techniques for the identification and simulation of dynamic systems
Pham et al. svMorph: interactive geometry-editing tools for virtual patient-specific vascular anatomies
Wu et al. A preliminary real-time and realistic simulation environment for percutaneous coronary intervention
Mi et al. A collision response algorithm for 3D virtual reality minimally invasive surgery simulator
Kulp et al. Practical patient-specific cardiac blood flow simulations using SPH
Erkoç et al. An observation based muscle model for simulation of facial expressions
Santhanam Modeling, Simulation, and Visualization of 3D Lung Dynamics
Mukai et al. Particle-based simulation on aortic valve behavior with CG model generated from CT
Bychkov et al. Construction of a Mathematical Model of the Heart Muscle.
Qiu et al. An improved matrix‐based endovascular guidewire position simulation using fusiform ternary tree
Himeno Blood flow simulation toward actual application at hospital
Hieber Particle methods for flow-structure interactions
Gao et al. Blood flow simulation of virtual simulation system for vascular interventional surgery

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant