A method for constructing a viscoelastic blood flow simulation model in virtual surgery
By constructing a viscoelastic bleeding simulation model in virtual surgery, the problem of the lack of realism in bleeding simulation is solved, a more realistic bleeding simulation effect is achieved, and the realism of training and the operator's ability to deal with complex bleeding situations are improved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- BEIJING JIAOTONG UNIV
- Filing Date
- 2023-07-05
- Publication Date
- 2026-07-21
Smart Images
Figure CN116861757B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of virtual surgery technology in virtual reality, and specifically relates to a method for constructing a viscoelastic bleeding simulation model in virtual surgery. Background Technology
[0002] A virtual surgical simulation system is a virtual reality application system built on virtual reality technology. It can simulate various phenomena that may occur during surgery without distortion. It primarily works through visual, auditory, and tactile senses, providing the operator with an immersive simulation training experience while avoiding the risks of failure that may arise during actual surgical training. Bleeding is one of the most common phenomena in real surgery, often occurring frequently throughout the procedure. If the surgeon has not received sufficient prior training, it will be difficult to handle complex bleeding situations during surgery. Therefore, establishing a highly realistic and immersive bleeding simulation system within a virtual reality environment is crucial for improving the realism and completeness of the entire surgical simulation system and cultivating surgeons' ability to handle surgical bleeding situations.
[0003] Establishing a highly realistic and immersive bleeding simulation system in virtual surgery is crucial for enhancing the realism of the entire virtual surgical simulation system and improving operator training effectiveness. Current research on bleeding simulation in virtual surgery mainly falls into two categories: one focuses on depicting blood morphology, aiming to render realistic blood surface features; the other focuses on the dynamic simulation of bleeding changes, accurately describing the physical processes of real bleeding. However, most bleeding simulation research concentrates on rendering blood surface morphology, with very little research on simulating the actual flow of blood.
[0004] From a biological perspective, blood is a suspension composed of various red blood cells and plasma. During blood flow, red blood cells form long-chain polymer molecules that influence blood flow. When blood flow is slow, red blood cells connect to form aggregates, which in turn intertwine to form a network structure capable of transmitting elastic deformation. This elastic network structure, suspended in viscous plasma, gives blood its unique viscoelastic characteristics during flow. Furthermore, the unique composition of blood, the deformability and aggregation of red blood cells, all affect the macroscopic flow characteristics of blood, resulting in a dynamic process that differs from that of typical Newtonian fluids, ultimately exhibiting a velocity distribution distinctly different from Newtonian fluid flow. To meet the real-time requirements of bleeding simulation, current research on the dynamic changes in bleeding mostly relies on computer graphics technology to rigidly imitate the flow of blood as the motion process of ordinary Newtonian fluids (such as the Navier-Stokes equations), while ignoring the unique biological properties of blood itself. This makes it impossible to realistically simulate the actual flow of blood, which seriously affects the overall realism of the virtual surgery simulation system. Consequently, operators cannot understand the real blood flow and changes during simulation training, leading to incorrect judgments about bleeding and reducing the training effect of virtual surgery.
[0005] Therefore, in order to improve the realism of bleeding simulation in virtual surgery, this invention aims to establish a simulation model that can accurately describe the bleeding process. Summary of the Invention
[0006] To address the limitations of current traditional bleeding models in simulating bleeding during virtual surgery due to a lack of visual realism, this invention innovatively proposes a method for constructing a bleeding simulation model that incorporates the viscoelastic characteristics of blood. By adding an elastic stress term caused by the elasticity of red blood cells in the fluid model to the Navier-Stokes equations, a momentum equation that can characterize the viscoelastic effect of blood is constructed. Ultimately, a simulation model that can accurately describe the bleeding process is established, thereby improving the realism of bleeding simulation in virtual surgery.
[0007] The technical solution provided by this invention is as follows:
[0008] This invention provides a method for constructing a viscoelastic blood flow simulation model in virtual surgery, comprising the following steps:
[0009] Establish a bleeding particle system and generate initial bleeding particles;
[0010] An expression for blood elastic stress was constructed using viscoelastic blood viscosity and relaxation time. Based on this expression, a blood flow momentum equation was established that supplements the elastic stress term.
[0011] The pressure, viscous force, and elastic stress terms in the bleeding momentum equation were discretized and solved using the SPH method to obtain the acceleration of the bleeding particles.
[0012] The initial velocity and position information of the bleeding particles are updated based on the acceleration of the bleeding particles;
[0013] The updated bleeding particles were visualized to establish a viscoelastic bleeding simulation model.
[0014] Preferably, the method for establishing the elastic stress term in the blood flow momentum equation includes the following steps:
[0015] An expression for the elastic stress of blood is constructed using viscoelastic blood viscosity and relaxation time:
[0016] τ p =n(x,t)ρυ[f(λ,τ)C-δ] / λ
[0017] Where f(λ,τ) is the nonlinear stretching factor of the erythrocyte molecular chain in blood, n(x,t) is the blood concentration, ρ is the blood density, υ is the kinematic viscosity of blood, λ is the relaxation time of the erythrocyte polymer molecular chain, C is the erythrocyte deformability tensor in blood, δ is the Dirac function, and τ is the elastic stress tensor;
[0018] Based on the blood elastic stress expression established above, the elastic stress term in the blood flow momentum equation is obtained:
[0019]
[0020] Where μ is the dynamic viscosity of blood with viscoelastic properties; The spatial derivative of the velocity of the bleeding particles; G0 is the transpose of the spatial derivative of the velocity of blood particles; G0 is the linear relaxation modulus; λ is the relaxation time of the erythrocyte polymer molecular chain; δ is the Dirac function; and C is the erythrocyte deformability tensor in blood.
[0021] Preferably, assuming uniform blood concentration, then n(x,t) = 1, and the expression for the elastic stress of the blood simplifies to:
[0022] τ p =ρυ[f(λ,τ)C-δ] / λ.
[0023] Preferably, assuming that red blood cells are linearly stretched during bleeding, according to the Oldroyd-B model, f(λ,τ)=1, and the expression for the elastic stress of the blood simplifies to:
[0024] τ p =ρυ(C-δ) / λ.
[0025] Preferably, the blood flow momentum equation is:
[0026]
[0027] Where ρ represents the fluid density, v represents the fluid velocity, P represents the fluid pressure, t represents the fluid time; υ is the kinematic viscosity of blood, f is the external force, x is the spatial coordinate, and τ is the fluid velocity. p This refers to the elastic stress of blood.
[0028] Preferably, the pressure term in the bleeding momentum equation is discretely solved to obtain the acceleration of bleeding particles caused by pressure:
[0029]
[0030] Where m j Let p be the mass of the bleeding particle j. i For the pressure exerted on the bleeding particle i, p j ρ is the pressure exerted on the bleeding particle j. i Let ρ be the density of the bleeding particle i. j Where W(r) is the density of the bleeding particle j; i -r j (h) is the kernel function that influences the bleeding particle j on the bleeding particle i, r i -r j Let be the distance between bleeding particles, and h be the radius of influence of the kernel function.
[0031] Preferably, the viscous force term in the bleeding momentum equation is discretely solved to obtain the acceleration of bleeding particles caused by viscous force:
[0032]
[0033] Where μ is the dynamic viscosity of blood with viscoelastic properties, v i v is the velocity of the bleeding particle i. j Let be the velocity of the bleeding particle j.
[0034] Preferably, the elastic stress term in the bleeding momentum equation is discretely solved to obtain the acceleration of bleeding particles caused by elastic force:
[0035]
[0036] Where G0 is the linear relaxation modulus, C is the red blood cell deformability tensor in blood, and δ is the Dirac function.
[0037] Preferably, the bleeding particle velocity is updated:
[0038]
[0039] Bleeding particle location update:
[0040]
[0041] Where n is the nth time step, and Δt is the time step size. and Let be the velocity and displacement of particle i at time t, respectively.
[0042] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0043] 1. This invention analyzes the rheological properties of blood and, based on the viscoelastic physical characteristics of blood as a non-Newtonian fluid, adds an elastic stress term caused by the viscoelasticity of blood to the Navier-Stokes equation, thus constructing a momentum equation that can characterize the viscoelastic features of blood and more realistically restore the physical properties of blood flow.
[0044] 2. In the simulation of the viscoelastic bleeding model, the bleeding process no longer occurs as a central gushing, but rather as a seepage flow. In actual surgery, the vast majority of cases involve blood seepage caused by the cutting of soft tissues such as the liver or the rupture of capillaries. Blood gushing only occurs when arterial vessels rupture, which is something to be avoided during surgery. Therefore, the bleeding scenario simulated in this invention has wider applicability and eliminates the flow boundary between the bleeding center and the bleeding diffusion range, making the overall bleeding simulation process visually more continuous and further enhancing the realism of the bleeding simulation effect.
[0045] 3. The viscoelastic bleeding model increases the randomness of bleeding diffusion during the bleeding simulation process, so that the final blood shape is no longer a standard axisymmetric shape, but presents an irregular state that is closer to the real bleeding situation. This improves the operator's ability to respond to and handle complex bleeding situations during the simulation training process. Attached Figure Description
[0046] Figure 1 This is a flowchart illustrating the construction process of the viscoelastic bleeding simulation model in virtual surgery provided in this embodiment of the invention.
[0047] Figure 2 The simulation results of the bleeding process at different times are shown in the blood flow model without the introduction of elastic force (i.e., comparative model); A, simulation time is 8s; B, simulation time is 12s; C, simulation time is 16s.
[0048] Figure 3The simulation results of the bleeding process at different times are based on the bleeding model (i.e., the example) which introduces elastic force; A) Simulation time is 8s; B) Simulation time is 12s; C) Simulation time is 16s. Detailed Implementation
[0049] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.
[0050] Example
[0051] A method for constructing a viscoelastic blood flow simulation model in virtual surgery, such as... Figure 1 As shown, it includes the following steps:
[0052] a. Establish the bleeding particle system and generate initial bleeding particles;
[0053] b. Constructing an expression for the elastic stress of blood using viscoelastic blood viscosity and relaxation time:
[0054] τ p =n(x,t)ρυ[f(λ,τ)C-δ] / λ
[0055] Where f(λ,τ) is the nonlinear stretching factor of the erythrocyte molecular chain in blood, n(x,t) is the blood concentration, ρ is the blood density, υ is the kinematic viscosity of blood, λ is the relaxation time of the erythrocyte polymer molecular chain, C is the erythrocyte deformability tensor in blood, δ is the Dirac function, and τ is the elastic stress tensor.
[0056] Assuming uniform blood concentration, then n(x,t) = 1, and the elastic stress of the blood can be simplified as:
[0057] τ p =ρυ[f(λ,τ)C-δ] / λ
[0058] To improve the real-time performance of the bleeding simulation, the deformation process of red blood cells during bleeding is simplified, assuming that they are all linearly stretched. According to the Oldroyd-B model, f(λ,τ)=1. Equation (2) can be further simplified to:
[0059] τ p =ρυ(C-δ) / λ
[0060] Based on the blood elastic stress expression established above, the elastic stress term in the viscoelastic blood momentum equation is obtained:
[0061]
[0062] Where μ is the dynamic viscosity of blood with viscoelastic properties; The spatial derivative of the velocity of the bleeding particles; G0 is the transpose of the spatial derivative of the velocity of blood-flowing particles; G0 is the linear relaxation modulus; λ is the relaxation time of the erythrocyte polymer molecular chain; δ is the Dirac function; and C is the erythrocyte deformability tensor in blood.
[0063] c. Based on the Navier-Stokes (NS) equations, add the elastic stress term caused by viscoelastic fluid elasticity to construct the blood flow momentum equation:
[0064]
[0065] Where ρ represents the fluid density, v represents the fluid velocity, P represents the fluid pressure, t represents the fluid time; υ is the kinematic viscosity of blood, f is the external force, x is the spatial coordinate, and τ is the fluid velocity. p For the elastic stress of blood;
[0066] d. The SPH method is used to discretize and solve the pressure, viscous force, and elastic stress terms in the blood flow momentum equation. The specific implementation includes the following sub-steps:
[0067] (1) Discretely solve the pressure term of the blood flow particles in the viscoelastic blood momentum equation. To obtain more accurate results, integration by parts is used to make the discrete expression of the pressure term appear in the form of paired blood flow particles, maintaining the symmetrical interaction between the blood flow particles. The pressure term in the momentum equation causes the acceleration of the blood flow particles:
[0068]
[0069] Where m j Let p be the mass of the bleeding particle j. i For the pressure exerted on the bleeding particle i, p j ρ is the pressure exerted on the bleeding particle j. i Let ρ be the density of the bleeding particle i. j Where W(r) is the density of the bleeding particle j; i -r j (h) is the kernel function that influences the bleeding particle j on the bleeding particle i, r i -r j Let be the distance between bleeding particles, and h be the radius of influence of the kernel function.
[0070] (2) Discretely solve the viscous force term of the blood-flowing particles in the viscoelastic blood momentum equation. The viscous force between blood-flowing particles is based on their relative velocity rather than the absolute velocity of the blood-flowing particles. Therefore, the relative velocity between the blood-flowing particles is used to replace the velocity of individual particles in the solution process. The acceleration of the blood-flowing particles caused by the viscous force term in the momentum equation is:
[0071]
[0072] Where μ is the dynamic viscosity of blood with viscoelastic properties, v i v is the velocity of the bleeding particle i. j m is the velocity of the bleeding particle j; j ρ is the mass of the bleeding particle j; j Where W(r) is the density of the bleeding particle j; i -r j (h) is the kernel function that influences the bleeding particle j on the bleeding particle i, r i -r j Where is the distance between bleeding particles, and h is the radius of influence of the kernel function;
[0073] (3) Discretly solve the elastic stress term of the blood flow particles in the viscoelastic blood momentum equation, and the acceleration of the blood flow particles caused by the elastic stress term:
[0074]
[0075] Where m j ρ is the mass of the bleeding particle j; i and ρ j These are the densities of bleeding particle i and bleeding particle j, respectively; v i and v j Let W(r) be the velocity of bleeding particle i and bleeding particle j; i -r j (h) is the kernel function that influences the bleeding particle j on the bleeding particle i, r i -r j denoted as denoted as , h as denoted as , and G0 as , where is the distance between blood particles, is the radius of influence of the kernel function, G0 is the linear relaxation modulus, C is the red blood cell deformability tensor in blood, δ is the Dirac function, μ is the dynamic viscosity of blood, and λ is the relaxation time of the red blood cell polymer molecular chain.
[0076] e. Update the initial velocity and position information of the bleeding particles based on their acceleration and using the frog-jumping algorithm.
[0077]
[0078]
[0079] Where n is the nth time step, and Δt is the time step size. and Let be the velocity and displacement of particle i at time t, respectively. At the end of each time step, the velocity and position of the bleeding particle advance by one time step.
[0080] f. Visualize the bleeding particles after updating their velocity and position information, and re-render and display the bleeding particles.
[0081] Comparative Example
[0082] A method for constructing a viscoelastic bleeding simulation model in virtual surgery differs from Example 1 in that it does not introduce an elastic stress term.
[0083] The bleeding process was simulated using both the comparative model without elastic stress and the embodiment model with stress. The simulation results at different times are as follows: Figure 2 and Figure 3 As shown.
[0084] pass Figure 2 and Figure 3 The comparison shows that in the simulation of the bleeding model incorporating the elastic stress term, the overall diffusion range of the bleeding is significantly smaller. This is because the introduced elastic stress term causes the blood to exhibit viscoelasticity, which "restricts" the diffusion of blood. In actual bleeding, the aggregation of red blood cells at low shear rates slows down the diffusion process. Therefore, the viscoelasticity of blood acts as an internal barrier to the diffusion of blood.
[0085] Furthermore, a comparison of the final blood flow simulation results shows that the final shape of the simulated blood flow is no longer axially symmetric, but rather exhibits an irregular state that more closely resembles real blood flow. This is because the aggregation and entanglement of particles in the blood flow simulation increases the randomness of the blood flow diffusion process. Simultaneously, the blood flow simulation effect incorporating elastic stress eliminates the flow boundary formed between the central gushing point and the diffusion range, resulting in an overall seepage-like state of the blood flow process. This confirms that the method proposed in this invention has better visual continuity and further enhances the realism of the blood flow simulation effect.
[0086] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.
Claims
1. A method for constructing a viscoelastic bleeding simulation model in virtual surgery, characterized in that, Includes the following steps: Establish a bleeding particle system and generate initial bleeding particles; An expression for blood elastic stress was constructed using viscoelastic blood viscosity and relaxation time. Based on this expression, a blood flow momentum equation was established that supplements the elastic stress term. The pressure, viscous force, and elastic stress terms in the bleeding momentum equation were discretized and solved using the SPH method to obtain the acceleration of the bleeding particles. The initial velocity and position information of the bleeding particles are updated based on the acceleration of the bleeding particles; The updated bleeding particles were visualized to establish a viscoelastic bleeding simulation model. The method for establishing the elastic stress term in the blood flow momentum equation includes the following steps: Constructing an expression for blood elastic stress using viscoelastic blood viscosity and relaxation time: in, It is a nonlinear stretching factor for the molecular chains of red blood cells in the blood. Blood concentration; The density of blood; The kinematic viscosity of blood; The relaxation time of the red blood cell polymer molecular chains; The deformability tensor of red blood cells in blood; It is the Dirac function; It is the elastic stress tensor; Based on the blood elastic stress expression established above, the elastic stress term in the blood flow momentum equation is obtained: in The dynamic viscosity of blood exhibiting viscoelastic properties; The spatial derivative of the velocity of the bleeding particles; This is the transpose of the spatial derivative of the velocity of the bleeding particles; It is a linear relaxation modulus.
2. The construction method according to claim 1, characterized in that, Assuming the blood concentration is uniform, then... =1, the expression for the elastic stress of blood simplifies to: 。 3. The construction method according to claim 2, characterized in that, Assuming that red blood cells are linearly stretched during bleeding, according to the Oldroyd-B model, we have: The simplified expression for the elastic stress of blood is: 。 4. The construction method according to claim 3, characterized in that, The blood flow momentum equation is: in, t represents the fluid's time. For the kinematic viscosity of blood, As an external force, For spatial coordinates, This refers to the elastic stress of blood.
5. The construction method according to claim 1, characterized in that, Discretely solve the pressure term in the blood flow momentum equation to obtain the acceleration of blood flow particles caused by pressure: in Let the mass of the bleeding particle j be... The pressure experienced by the bleeding particle i The pressure experienced by the bleeding particle j Let i be the density of the bleeding particle. Let be the density of the bleeding particle j; Let be the kernel function that influences the bleeding particle j on the bleeding particle i. Let be the distance between bleeding particles, and h be the radius of influence of the kernel function.
6. The construction method according to claim 5, characterized in that, Discretely solve the viscous force term in the bleeding momentum equation to obtain the acceleration of bleeding particles caused by viscous force: in The dynamic viscosity of blood exhibiting viscoelastic properties. Let i be the velocity of the bleeding particle. Let be the velocity of the bleeding particle j.
7. The construction method according to claim 6, characterized in that, Discretely solve the elastic stress term in the bleeding momentum equation to obtain the acceleration of bleeding particles caused by elastic force: in For linear relaxation modulus, The deformability tensor of red blood cells in blood. This is the Dirac function.
8. The construction method according to claim 7, characterized in that, Bleeding particle speed update: Bleeding particle location update: ； Where n is the nth time step, For time step, and Let be the velocity and displacement of particle i at time t, respectively.