A SPH-based fluid-structure interaction simulation method for blood and aneurysm

Abstract

The application discloses a blood and aneurysm fluid-solid coupling simulation method based on SPH, which comprises the following steps: step 1, simulating blood fluid flowing in a blood vessel; step 2, simulating aneurysm rupture; step 3, simulating aneurysm growth and bulging; and step 4, establishing a bifurcated artery blood vessel model and optimizing simulation effect. On the basis of fluid simulation, the application combines an existing medical model, so that the fluid simulation can simulate real physiological characteristics of blood, realize simulation of aneurysm growth and rupture, dynamic fluid-solid coupling simulation of blood and solid substances in the body, interaction between blood and thrombus in thrombosis, interaction between blood and an artery wall in aneurysm growth and rupture, and restore real physiological phenomena and pathological processes; and the blood vessel blood-related pathological types are various, so that, on the basis of fluid simulation, in combination with blood characteristics and simulation of physical characteristics of blood vessels in various pathologies, clinical medical analysis, prediction and diagnosis of blood vessel blood diseases can be facilitated.

Description

Technical Field

[0001] This invention relates to the field of computer simulation and model building technology, and in particular to a fluid-structure interaction simulation method for blood and aneurysms based on SPH. Background Technology

[0002] Fluids are composed of a large number of molecules that are constantly in random motion, with gaps between them. Therefore, from a microscopic perspective, the spatial distribution of fluid molecules is discontinuous. Furthermore, due to the randomness of molecular motion, the temporal distribution of fluids is also discontinuous.

[0003] However, fluid mechanics studies the macroscopic motion of fluids under external forces, which are statistical average properties of a large number of molecules, such as fluid density, temperature, and pressure. These are very small compared to the typical physical scale of the problems studied in fluid mechanics.

[0004] Therefore, in the study of fluid mechanics, it can be assumed that fluid particles (fluid within a micro-volume that is macroscopically small and microscopically large) are composed of a sufficient number of molecules, with no gaps between them, continuously filling the space they occupy. This is the continuous medium assumption of fluids.

[0005] Fluid simulation is of great importance and necessity in the field of computer graphics physics simulation. Fluid simulation technology refers to the simulation of scenes such as water and smoke by combining fluid physics phenomena, equations, and computer graphics, thus recreating realistic physical environments. Currently, fluid simulation methods are mainly divided into mesh-based Eulerian methods, particle-based Lagrangian methods, and hybrid methods. Among them, Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method that tracks fluids based on particles. It has wide applications in various materials in nature. Its simulation results can provide realistic scene effects for movie and game production and virtual surgery, and can also be used as visualization results for scientific analysis in related fields. French scientist C.-L.-M.-H. Navier proposed the kinematic equations for viscous fluids, but only considered the flow of incompressible fluids. In the UK, physicist G.G. Stokes independently proposed a form where the viscosity coefficient is a constant. The research of these two scientists led to the famous Navier-Stokes equations, or NS equations for short, which laid the foundation for subsequent fluid mechanics research. The essence of the Navier-Stokes equations is to solve for the physical quantities of each fluid particle at different locations and times in the entire flow field. These physical quantities can be used to describe the physical state of the entire flow field.

[0006] Aneurysms are among the most common vascular diseases causing disability and death, primarily affecting the elderly and often accompanied by conditions such as hypertension and coronary heart disease. As aneurysms expand, they carry the risk of rupture. The consequences of aneurysm rupture are unimaginable. Therefore, computer simulations of aneurysm growth and rupture play a crucial role in virtual surgery, physiological simulation, science education, and disease prevention. Aneurysm growth and rupture mainly involve two processes: expansion and bulging of the diseased arterial wall due to blood flow impact, and rupture of the aneurysm wall leading to blood leakage. Both growth and rupture are primarily the result of fluid-structure interaction between blood and the diseased arterial wall. In the interaction between blood and blood vessels, the influence of blood on the vessel wall mainly includes plastic bulging and rupture, while the influence of blood vessels on blood is mainly the turbulence phenomenon caused by the rebound of blood from the vessel.

[0007] Regarding the mechanisms of aneurysm growth and rupture, existing research focuses on constructing elastic models for ideal, spherical aneurysms with uniform wall thickness. These models investigate rupture mechanisms under pressure alone, employing a nonlinear model based on Laplace's law to describe the growth and rupture of saccular aneurysms, relating tension within the aneurysm wall to its radius. Other models consider the potential for stress exceeding the aneurysm's yield limit before rupture, leading to plastic deformation, and the material's internal porosity, resulting in material failure. These models utilize a nonlinear model expressing the relationship between stress and porosity, deriving the critical radius for aneurysm rupture by combining the Laplace equation and Poisson's relation. The Laplace-based aneurysm model represents a static, linear elastic sphere. In contrast, a nonlinear constitutive quasi-static model has been proposed, deriving an expression for the critical size of the aneurysm and solving it numerically using a system of differential equations, which has been applied to clinical data.

[0008] For blood flow in aneurysms within aneurysms, existing techniques use numerical methods to study the flow patterns and fluid particle paths of saccular aneurysms at bifurcation points. The finite element method is used to solve the governing equations for incompressible Newtonian fluid flow, analyzing the flow characteristics of blood within the aneurysm. It is proposed that blood particles can circulate and rotate within the aneurysm for a sufficiently long time to allow for cell aggregation or blood clot formation. A nonlinear mathematical model is used to simulate blood flow within the aneurysm, studying important factors in aneurysm evolution and providing results that contribute to understanding certain medical aspects of Willis's circle aneurysms. A nonlinear mathematical model of blood flow is also established for an ideal cylindrical aneurysm of the human common carotid artery, using normal arteries and tandem aneurysms, and the model equations are numerically solved and analyzed using nonlinear dynamics methods. Regarding the impact of variations in the diameter of the bifurcation-bearing artery on hemodynamics, modeling aneurysms of different diameters and performing computational fluid dynamics (CFD) analysis is conducted, and morphological features related to aneurysm formation are used to assess aneurysm rupture. The preceding analyses share a common characteristic: they are all numerical studies and analyses concerning aneurysm hemodynamics and aneurysm rupture mechanisms.

[0009] For aneurysm growth, a novel mathematical model of the interaction between blood flow and the arterial wall surrounded by cerebrospinal fluid has been applied to intracranial saccular aneurysms to analyze the aneurysm growth and remodeling process. This method models blood pressure using Fourier series, employs compressible Euler equations to model cerebrospinal fluid, and models the arterial wall as a spring-mass system. It analyzes the nonlinear fluid-structure interaction problem and derives a first-order approximate solution using perturbation techniques, while also deriving a linearized analytical solution using Laplace transform. The results validate its biological significance; however, the model is complex and would incur significant computational costs for computer simulations.

[0010] The SPH method was first proposed in the field of astrophysics. As early as 2003, it was applied to the Navier-Stokes equations, using summation functions to solve fluid simulation problems. Consequently, the SPH model has gradually been widely used in computer graphics, becoming one of the mainstream fluid models. To improve the incompressibility of fluid simulations, the weakly compressible SPH method (WCSPH) was proposed. By changing a coefficient in the ideal gas equation of state, the incompressibility of the fluid is strengthened. Without increasing the computational load, the simulated fluid exhibits better incompressibility characteristics. However, when used for large-scale fluid particle simulations, the computational load increases dramatically, making real-time simulation difficult; it can only meet the needs of small to medium-scale fluid simulations.

[0011] Existing techniques for analyzing aneurysm growth and rupture rely on numerical simulations, focusing on specific aspects of aneurysm growth, rupture, or blood flow within the aneurysm. Current hematologic modeling methods are complex, and computer-based solutions and simulations incur significant computational costs. Integrating aneurysm growth and rupture processes further reduces the efficiency of computer fluid simulations. Therefore, simplifying the model and leveraging hardware advantages to improve simulation efficiency, while considering vascular blood flow characteristics to ensure realistic simulation results, is crucial. Summary of the Invention

[0012] The technical problem to be solved by this invention is to provide a fluid-structure interaction simulation method for blood and aneurysms based on SPH (Self-Structured Phosphorescence). Based on the aneurysm rupture mechanism, a model relating the critical rupture pressure to the aneurysm wall thickness and radius is established based on the plasticity of the aneurysm wall, and the SPH method is used to simulate aneurysm rupture. The interaction between blood fluid, vascular wall proteins, and tissue fluid is utilized, and the expansion of the aneurysm is simulated by solving the aneurysm expansion amount through motion control equations using fluid particle properties. A bifurcation artery model is established based on Murray's law, and improvements are made to the simulation results.

[0013] To address the aforementioned technical problems, this invention provides a blood-aneurysm fluid-structure interaction simulation method based on SPH, comprising the following steps: Step 1: Simulate the flow of blood in blood vessels; Step 2: Simulate aneurysm rupture; Step 3: Simulate aneurysm growth and bulging; Step 4: Establish a bifurcation artery model and optimize the simulation results.

[0014] Furthermore, the Navier-Stokes equation for the blood fluid in step 1 is: , in, The density of blood particles in the blood fluid. For acceleration, It is the acceleration due to gravity. The viscosity coefficient is... For the Laplace operator, For blood particle velocity, The opposite direction of the gradient. , and These are the forces of gravity, viscosity, and pressure acting on blood particles, respectively.

[0015] Furthermore, the continuity equation for the blood fluid in step 1 is: , The physical properties are: , in, Physical properties and These represent the current position of the blood particle in the blood fluid and the position of the next blood particle in its neighborhood. The location of each blood particle. and These are the mass and density of blood particles, respectively. For kernel function, denoted as the effective radius of the kernel function.

[0016] Furthermore, in step 1, the physical properties of the blood particles in each frame of the blood fluid include density, pressure, and viscosity. ,pressure Adhesion They are respectively: , , , in, For blood particle mass, The location of blood particles, For pressure, The viscosity coefficient of blood fluid is given by the equation of state. Calculated, The stiffness coefficient is set to 1. For constant density, subscript They represent the current number. The blood particle and the first The first blood particle nucleus within the radius of the neighborhood A blood particle.

[0017] Furthermore, the Laplace's law equation for aneurysm rupture in step 2 is: , The Poisson's ratio of aneurysm radius to aneurysm wall thickness is: , in, For pressure, The radius of the aneurysm. This refers to the thickness of the aneurysm wall. The stress on the tumor wall, Poisson's ratio; The relationship between the internal space of an aneurysm and the thickness of the aneurysm wall is as follows: , , Aneurysm wall stress With porosity The non-linear relationship is constructed as follows: , in, Porosity This refers to the volume of the aneurysm wall. This represents the yield strength of the stress on the aneurysm wall. The relationship between the aneurysm radius and the pressure on the aneurysm wall is as follows: , Pressure critical conditions for aneurysm rupture for: .

[0018] Furthermore, the impact force of the blood particles on the arterial wall is: , , The pressure of the blood fluid on the aneurysm wall is: , in, For the collection of blood particles participating in the pressure calculation, when the pressure on the aneurysm wall exceeds the critical condition, i.e. At that time, the aneurysm ruptured.

[0019] Furthermore, the resultant force on the aneurysm wall in step 3 for: , in, , , These are respectively represented as the force exerted by the blood fluid flow, the force exerted by the tissue fluid flow, and the resistance force exerted by elastin and collagen; The force exerted by the blood flow is approximated by the pressure of the blood flow on the aneurysm wall, i.e. .

[0020] The force of tissue fluid flow for: , in, The density of the tissue fluid, The cross-sectional area of ​​the fluid acting on the aneurysm. Let be the propagation speed in the wave equation. The speed at which the aneurysm wall bulges outward; The resistance between the elastin and collagen is as follows: , , , in, The scaling factor. For cross-sectional area, For stress, subscript , They represent elastin and collagen, respectively. In response, , These are the aneurysm radius and the radius increment, respectively. aneurysm radius increment for: , in, For the quality of the aneurysm wall, This represents the time step for each frame in the simulation.

[0021] Furthermore, in step 3, the updated aneurysm wall thickness is calculated based on the Poisson relationship between the aneurysm radius and the aneurysm wall thickness, combined with the passage of time: , in, for The thickness of the aneurysm wall at any given time. Poisson's ratio, Not exceeding 0.001, An intensity coefficient representing the relationship between aneurysm wall thickness and aneurysm radius.

[0022] Furthermore, the radius of the artery in step 4 is: , in, The main radius of the artery. , These are the radii of the two branch pipes, respectively.

[0023] Implementing this invention has the following beneficial effects: Based on the plasticity of the aneurysm wall, and combined with Laplace's law, Poisson's ratio and differential properties, a model is established to establish the relationship between the aneurysm rupture pressure and the aneurysm wall thickness and volume radius, so as to obtain the critical condition for aneurysm rupture and realize the simulation of aneurysm rupture. The simulation of aneurysm growth combines the interactions of blood, vascular elastin, collagen, and tissue fluid, and utilizes the physical properties of fluid particles to solve for the aneurysm expansion amount through motion control equations, thereby simulating the expansion and bulging of the arterial wall. The growth rate and rupture probability of aneurysms are affected by many factors. In order to reflect the process of aneurysm growth and rupture, this invention can simulate the interaction between blood and arterial walls by controlling the growth rate and rupture threshold of aneurysms through parameters. The simulation of blood fluids, based on fluid simulation and integrating existing medical models, enables the fluid to simulate the real physiological characteristics of blood. This allows for the simulation of aneurysm growth and rupture, dynamic simulation of fluid-structure interaction between blood and solid substances in the body, the interaction between blood and thrombus in thrombus formation, and the interaction between blood and arterial wall in aneurysm growth and rupture. It can recreate real physiological phenomena and pathological processes. Vascular and blood-related diseases are diverse. By combining fluid simulation with the simulation of blood characteristics and the physical properties of blood vessels in various diseases, it can help in the clinical medical analysis, prediction, and diagnosis of blood and vascular diseases. Attached Figure Description

[0024] Figure 1 This is a flowchart of the aneurysm growth simulation technology of the present invention; Figure 2 This invention presents a collision processing diagram of blood particles that extend beyond the aneurysm boundary within the aneurysm. Figure (a) shows the position and velocity direction of the blood particles before processing, Figure (b) shows the updated position of the blood particles, and Figure (c) shows the position and velocity direction of the blood particles after processing. Figure 3 This invention is different The effect of the selected value on the variation of aneurysm wall thickness and rupture threshold; Figure 4 This is a schematic diagram of the blood flow, tissue fluid, aneurysm environment, and stress analysis of the present invention, where the left and right sides represent blood flow. Force, tissue fluid flow force Elastin and collagen resistance The diagram shows the environment on the right where an aneurysm is surrounded by blood and tissue fluid. Figure 5 These are comparison images of blood particles filling blood vessels before (a) and after (b) the process of this invention. Figure 6 These are simulation results of aneurysm growth and rupture according to the present invention. Figures (a), (b), and (c) show the particle state presented online, while figures (d), (e), and (f) show the fluid state presented online. Figures (a) and (d) show the normal state of arterial bifurcation at frame 400, figures (b) and (e) show the growth state of aneurysm at frame 2200, and figures (c) and (f) show the rupture state at frame 2400. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings.

[0026] like Figure 1 As shown, a blood-aneurysm fluid-structure interaction simulation method based on SPH includes the following steps: Step 1: Simulate the flow of blood in blood vessels; Blood fluid obeys the Navier-Stokes equations and satisfies the law of conservation of mass. The Navier-Stokes equations are: , in, The density of blood particles in the blood fluid. For acceleration, It is the acceleration due to gravity. The viscosity coefficient is... For the Laplace operator, For blood particle velocity, The opposite direction of the gradient. , and These represent the forces acting on blood particles: gravity, viscosity, and pressure. The Navier-Stokes equations are well-known to those skilled in the art and will not be elaborated upon here.

[0027] The law of conservation of mass that blood fluid satisfies is expressed by the continuity equation as follows: , For the calculation of each physical property, SPH is solved using the kernel method, and the formula is: , in, Physical properties and These represent the current position of the blood particle in the blood fluid and the position of the next blood particle in its neighborhood. The location of each blood particle. and These are the mass and density of blood particles, respectively. For kernel function, The effective radius of the kernel function is 0.025, and the value is determined when the blood particle position is... The function value is 0 if it exceeds the kernel range; the search for neighboring blood particles first divides the space of blood particles into regions using a grid spatial partitioning method. Then, it traverses the region to which the current blood particle belongs and calculates the distance to the current blood particle. When the distance is less than the kernel radius, it is included in the calculation of the physical quantities of the current blood particle. The grid size is set to [value missing]. That is, a spatial domain includes 27 blood particles.

[0028] The physical properties of blood particles in each frame of blood fluid include density, pressure, and viscosity. ,pressure Adhesion They are respectively: , , , in, For blood particle mass, The location of blood particles, For pressure, The viscosity coefficient of blood fluid is given by the equation of state. Calculated, The stiffness coefficient is set to 1. For constant density, subscript They represent the current number. The blood particle and the first The first blood particle nucleus within the radius of the neighborhood A blood particle.

[0029] Treating blood as an incompressible fluid with density that does not change with time and location, and discretizing the blood fluid into blood particles, the SPH method is used for solving. Incompressibility requires that the following condition be met: , Therefore, a method based on constant coupling density and divergence-free conditions is first employed to correct the physical quantities of the incompressible blood fluid simulated by SPH. The fluid viscosity coefficient is then adjusted. The value is 4.0, and the density is... Values Blood particle mass The value is 0.0002 To better match the properties of blood.

[0030] Step 2: Simulate aneurysm rupture; The arterial wall is divided into the intima, media, and adventitia. The media and adventitia give arteries their elasticity and are composed of elastin and collagen, respectively. When an aneurysm develops, the function of elastin and collagen weakens, and the arterial wall loses some elasticity, causing the aneurysm to become plastic. Over time, the radius of the aneurysm increases within a certain range, while the wall thickness gradually thins. When the aneurysm wall ages to a certain extent or is subjected to external shocks such as abnormal blood pressure, the aneurysm can rupture, leading to bleeding.

[0031] The Laplace's law equation for aneurysm rupture is: , Based on the Poisson relationship of material deformation, the Poisson ratio of the aneurysm radius to the aneurysm wall thickness is obtained as follows: , in, For pressure, The radius of the aneurysm. This refers to the thickness of the aneurysm wall. The stress on the tumor wall, Poisson's ratio; The relationship between the internal space of an aneurysm and the thickness of the aneurysm wall is as follows: , Aneurysms are spherical, so they can be approximated as: , Aneurysm wall stress With porosity The non-linear relationship is constructed as follows: , in, Porosity This refers to the volume of the aneurysm wall. This represents the yield strength of the stress on the aneurysm wall. Applying Laplace's law and Poisson's relation, and combining the properties of derivatives, the relationship between the radius and the pressure on the aneurysm wall is as follows: , According to the properties of derivatives, when When it approaches infinity, it means that under pressure If the aneurysm radius increases rapidly and instantaneously, it indicates aneurysm rupture. Therefore, when the denominator on the right is set to 0, the critical pressure condition for aneurysm rupture can be obtained. for: , Because porosity changes relatively little, and because the aneurysm radius and thickness dynamically change during aneurysm growth, this paper will focus on porosity. Treating these as constants, we can obtain the mathematical relationship between the critical pressure value for aneurysm rupture and the aneurysm radius and wall thickness.

[0032] like Figure 2As shown, in aneurysm-bearing arteries containing blood flow, the wall pressure causing aneurysm rupture mainly originates from the blood fluid. The SPH method discretizes the fluid into the flow of blood particles, and the impact force of blood on the aneurysm is approximated by the blood particles located on the aneurysm wall, i.e., the pressure, to reduce the complexity of pressure calculation. The blood particles on the aneurysm wall participate in the blood pressure calculation, and these blood particles are more specifically defined as those that exceed the boundary range before collision processing in each frame during the simulation.

[0033] According to the impulse calculation formula: , Combined with the simulation process, the duration of action Take the time step of each frame in the simulation. , Let and represent the mass and velocity of the blood particle, respectively. Therefore, the expression for the impact force of the blood particle on the arterial wall is: Since the velocity of blood particles is obtained by multiplying acceleration by the time step, the impact force of blood particles on the arterial wall is: , acceleration The SPH method, which combines the Navier-Stokes equations with the forces in blood simulation, is as follows: , like Figure 3 As shown, the maximum impact force exerted on the aneurysm wall by all blood particles involved in the calculation is taken as the pressure of the blood fluid on the aneurysm wall: , in, For the collection of blood particles participating in the pressure calculation, when the pressure on the aneurysm wall exceeds the critical condition, i.e. At that time, the aneurysm ruptured.

[0034] In the simulation, blood flow within a closed blood vessel is controlled by processing blood particle collisions at the vessel boundary. When simulating aneurysm rupture, the blood particle collision processing is masked at the rupture site to simulate blood overflow due to aneurysm rupture. The default parameter values ​​for the aneurysm rupture simulation are... .

[0035] Step 3: Simulate aneurysm growth and bulging; The blood vessel wall is influenced by the interaction of blood and tissue fluid flow, and these two factors are often combined in stress analysis of the blood vessel wall. The blood vessel wall contains elastin and collagen, and an aneurysm is a bulging portion of the arterial wall caused by a localized lesion; it is a type of soft tissue. In the artery containing the aneurysm, elastin has the function of resisting aneurysm growth, while collagen can prevent aneurysm rupture. Even though the properties of elastin and collagen weaken with aneurysm growth and time, a comprehensive analysis of the resistance of these proteins to aneurysm bulging, in conjunction with the effects of blood and tissue fluid, can yield a more specific biological model of aneurysm growth.

[0036] like Figure 4 As shown, the net force on the aneurysm wall is due to the forces generated by the flow of blood and tissue fluid, as well as the resistance of elastin and collagen. for: , in, , , These represent the forces acting on the blood, the forces acting on the tissue fluid, and the resisting forces acting on the elastin and collagen, respectively. Since aneurysms tend to bulge due to the combined forces acting outwards during their growth, the positive and negative signs of the forces in the expressions also indicate the direction of the forces.

[0037] The force exerted by blood flow is approximated by the pressure of the blood flow on the aneurysm wall, i.e. In the simulation of blood circulation, the blood particle pressure calculated by the SPH method itself has an approximately periodic characteristic.

[0038] Forces of tissue fluid flow for: , in, The density of the tissue fluid, The cross-sectional area of ​​the fluid acting on the aneurysm. Let be the propagation speed in the wave equation. This refers to the rate at which the aneurysm wall bulges outward; The interaction between elastin and collagen in the arterial wall is modeled using a spring-mass system. The resistive forces between elastin and collagen are as follows: , , , in, The scaling factor. For cross-sectional area, For stress, subscript , They represent elastin and collagen, respectively. In response, , These are the aneurysm radius and the radius increment, respectively. Combination speed acceleration aneurysm radius increment for: , in, For the quality of the aneurysm wall, This represents the time step for each frame in the simulation. (Through...) The calculations can simulate the growth process of aneurysms under the interaction of blood flow, tissue fluid and arterial wall.

[0039] Since the risk of aneurysm rupture is related to the aneurysm radius and the duration of lesion accumulation, and the aneurysm wall thickness decreases accordingly as the aneurysm radius increases, the updated aneurysm wall thickness is calculated based on the Poisson relationship between aneurysm radius and aneurysm wall thickness, combined with the passage of time: , in, for The thickness of the aneurysm wall at any given time. Poisson's ratio, Not exceeding 0.001, An intensity coefficient representing the relationship between aneurysm wall thickness and aneurysm radius. It obtains the dynamic changes in aneurysm radius and wall thickness during aneurysm growth and bulging. After aneurysm develops to a certain extent, its growth rate slows down or even stops; a maximum limit for the aneurysm volume is set to represent complete aneurysm development, and this is defined when the aneurysm reaches its maximum volume.

[0040] In each frame of the simulation calculation, the aneurysm radius increment is calculated. The growth rate is obtained, and the growth of the aneurysm is controlled by this growth rate, which in turn controls the deformation of the geometric boundary of the artery, thereby achieving a fluid-structure interaction simulation of blood and the aneurysm. For the simulation of aneurysm growth, the main parameters involved are set to default values. .

[0041] Step 4: Establish a bifurcation artery model and optimize the simulation results; In arteries, the blood flow in bifurcated vessels is complex, which is why aneurysms usually occur at the bifurcation points of bifurcated vessels. The blood flow simulation in this embodiment is mainly based on bifurcated vessels. In order to ensure the realism of the simulation effect, this embodiment addresses the issue from two aspects: the vessel model and the blood flow control. In terms of the vessel model, the bifurcated branches of the vessel are symmetrical, that is, the angle of deviation between the branch and the main tube is the same and the radii of the two branches are equal.

[0042] The radius of the blood vessel is adjusted to satisfy Murray's law: , in, The main radius of the artery. , These are the radii of the two branch pipes, respectively. Murray's Law is a well-known technique in this field and will not be elaborated upon here.

[0043] like Figure 5 As shown, due to the inconsistent radii of the main and branch vessels in the vascular model, this embodiment also performs appropriate smoothing on the vessel walls at the bifurcation points. The computational efficiency of the SPH method used for fluid simulation is highly correlated with the number of particles set; generally, the more particles, the lower the simulation efficiency. To meet the real-time requirements of the simulation, the number of particles needs to be controlled within a certain range. Since the blood simulation in the tumor-bearing artery is only a small part of the human circulatory system, directly allowing blood particles to flow in the vessel without processing will result in particles not being able to distribute throughout the entire vascular space, which does not conform to the fact that blood fills the vessel, leading to unsatisfactory simulation results. The effect of blood not filling the vessel is as follows: Figure 5 As shown in (a) above. This phenomenon can be alleviated by controlling the blood flow at the vessel inlet and outlet. However, due to the limitation on the number of blood particles and the fact that flow calculation is related to many physical quantities, this method presents certain inconveniences. Since the images captured in the simulation only occupy a portion of the simulation environment, and particles exceeding a certain range do not affect the simulation of blood flow characteristics and aneurysm lesion processes, this embodiment, in terms of blood flow control, batches of particles outside the effective range are reset and given a relatively stable blood flow velocity. These batches of particles are placed at the vessel inlet to achieve full blood flow within the vessel. The simulated effect after processing is shown below. Figure 5 As shown in (b) in the figure. This simulation method not only alleviates the phenomenon of blood particles not filling the blood vessels, but also provides a blood pressure change with approximately periodicity and relative stability, which effectively matches the pressure calculation required for blood flow on aneurysms. At the same time, the number of particles used in the SPH method simulation can be appropriately reduced without affecting the simulation effect, thus improving the simulation efficiency to a certain extent.

[0044] The specific steps in this embodiment are as follows: Initialize particle positions and parameters: Set the initial blood vessel state, generate blood particles, and distribute the blood particles in a blood vessel pattern. Initialize the parameters required for the aneurysm growth simulation process. The parameter values ​​involved are shown in Table 1: Table 1. Parameter list for aneurysm growth simulation

[0045] SPH method: The mesh size is set to... Each particle has 26 nearest neighbor particles. Based on the particle's position, the particle is inserted into the corresponding grid. Then, the pressure of the particle is calculated based on the nearest neighbor particles, and then the net force on the particle is calculated. In order to satisfy the incompressibility of blood, the particle's properties need to be modified before collision processing to update the particle's position. After obtaining the latest position of the particle through collision processing, the particles located outside the effective range are recorded. When a certain number are reached, these particles are reset.

[0046] Aneurysm growth controller: Calculates whether the pressure on the aneurysm at this moment has reached the critical value of rupture pressure. If it does not meet the critical value, it controls the aneurysm to continue growing and performs a new round of SPH calculation; otherwise, the aneurysm ruptures.

[0047] The above description is merely a preferred embodiment of the present invention and should not be construed as limiting the scope of the invention. Therefore, any equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A fluid-structure interaction simulation method for blood and aneurysms based on SPH, characterized in that, Includes the following steps: Step 1: Simulate the flow of blood in blood vessels; Step 2: Simulate aneurysm rupture; the Laplace's law equation for aneurysm rupture is: ， The Poisson's ratio of aneurysm radius to aneurysm wall thickness is: ， in, For pressure, The radius of the aneurysm. This refers to the thickness of the aneurysm wall. The stress on the tumor wall, Poisson's ratio; The relationship between the internal space of an aneurysm and the thickness of the aneurysm wall is as follows: ， ， Aneurysm wall stress With porosity The non-linear relationship is constructed as follows: ， in, Porosity This refers to the volume of the aneurysm wall. This represents the yield strength of the stress on the aneurysm wall. The relationship between the aneurysm radius and the pressure on the aneurysm wall is as follows: ， Pressure critical conditions for aneurysm rupture for: ； Step 3: Simulate aneurysm growth and bulging; Step 4: Establish a bifurcation artery model and optimize the simulation results; the radius of the artery is: ， in, The main radius of the artery. , These are the radii of the two branch pipes, respectively.

2. The method for simulating blood-aneurysm fluid-structure interaction based on SPH according to claim 1, characterized in that, The Navier-Stokes equation for the blood fluid in step 1 is: ， in, The density of blood particles in the blood fluid. For acceleration, It is the acceleration due to gravity. The viscosity coefficient is... For the Laplace operator, For blood particle velocity, The opposite direction of the gradient. , and These are the forces of gravity, viscosity, and pressure acting on blood particles, respectively.

3. The method for simulating blood-aneurysm fluid-structure interaction based on SPH according to claim 2, characterized in that, The continuity equation for the blood fluid in step 1 is: ， The physical properties are: ， in, Physical properties and These represent the current position of the blood particle in the blood fluid and the position of the next blood particle in its neighborhood. The location of each blood particle and These are the mass and density of blood particles, respectively. For kernel function, denoted as the effective radius of the kernel function.

4. The method for simulating blood-aneurysm fluid-structure interaction based on SPH according to claim 3, characterized in that, In step 1, the physical properties of the blood particles in each frame of the blood fluid include density, pressure, and viscosity. ,pressure Adhesion They are respectively: ， ， ， in, For blood particle mass, The location of blood particles, For pressure, The viscosity coefficient of blood fluid is given by the equation of state. Calculated, The stiffness coefficient is set to 1. For constant density, subscript They represent the current number. The first blood particle and the first The first blood particle nucleus within the radius of the neighborhood A blood particle.

5. The method for simulating blood-aneurysm fluid-structure interaction based on SPH according to claim 2, characterized in that, Step 2 further includes calculating the impact force of the blood particles on the arterial wall: ， ， The pressure of the blood fluid on the aneurysm wall is: ， in, For the collection of blood particles participating in the pressure calculation, when the pressure on the aneurysm wall exceeds the critical condition, i.e. At that time, the aneurysm ruptured.

6. The method for simulating blood-aneurysm fluid-structure interaction based on SPH according to claim 5, characterized in that, The resultant force on the aneurysm wall in step 3 for: ， in, , , These are respectively represented as the force exerted by the blood fluid flow, the force exerted by the tissue fluid flow, and the resistance force exerted by elastin and collagen; The force exerted by the blood flow is taken as the pressure of the blood flow on the aneurysm wall: ; The force of tissue fluid flow for: ， in, The density of the tissue fluid, The cross-sectional area of ​​the fluid acting on the aneurysm. Let be the propagation speed in the wave equation. The speed at which the aneurysm wall bulges outward; The resistance between the elastin and collagen is as follows: ， ， ， in, The scaling factor. For cross-sectional area, For stress, subscript , They represent elastin and collagen, respectively. In response, , These are the aneurysm radius and the radius increment, respectively. aneurysm radius increment for: ， in, For the quality of the aneurysm wall, This represents the time step for each frame in the simulation.

7. The method for simulating blood-aneurysm fluid-structure interaction based on SPH according to claim 1, characterized in that, Step 3 includes calculating the updated aneurysm wall thickness based on the Poisson relationship between the aneurysm radius and the aneurysm wall thickness, combined with the passage of time: ， in, for The thickness of the aneurysm wall at any given time. Poisson's ratio, Not exceeding 0.001, An intensity coefficient representing the relationship between aneurysm wall thickness and aneurysm radius.

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