A computer-implemented non-newtonian blood flow simulation method, system, and medium

Abstract

The application discloses a computer-implemented non-Newtonian blood flow simulation method, system and medium, and the method comprises the following steps: S1, receiving a particle graph representing blood in a blood vessel and a boundary; S2, constructing edge features based on particle relative positions, relative velocities, smooth particle fluid dynamics kernel function values and kernel function gradients; S3, determining the effective viscosity of each particle based on the local shear rate according to a non-Newtonian viscosity model, and incorporating the effective viscosity as an additional component into the edge features; S4, generating the acceleration of each fluid particle according to the particle graph and the edge features with the effective viscosity incorporated by using a graph neural network with an anti-symmetric message passing mechanism; and S5, applying a hard gating of the acceleration, velocity or position to the non-fluid boundary particles in the model output stage. The application directly involves the effective viscosity in the calculation of the pair interaction, strictly guarantees the total momentum conservation by using the anti-symmetric message passing, and fundamentally prevents the boundary condition from being violated.

Description

Technical Field

[0001] This invention relates to the fields of computational fluid dynamics, medical simulation, biomechanics, graph neural networks and computer-aided diagnosis and treatment, and in particular to a computer-implemented non-Newtonian blood flow simulation method, system and medium. Background Technology

[0002] Hemodynamic simulation has significant applications in cardiovascular disease diagnosis, surgical planning, stent and catheter design, drug delivery evaluation, and medical education. Traditional computational fluid dynamics (CFD) methods, such as the finite volume method or finite element method based on the Navier-Stokes equations, while highly accurate, typically require complex preprocessing (mesh generation, boundary layer setting) and lengthy computation time, making them unsuitable for intraoperative real-time simulation or large-scale parameter exploration.

[0003] Smoothed Particle Hydrodynamics (SPH) is a meshless Lagrangian method naturally suited for handling free surfaces, large deformations, and complex boundary problems, and has already been applied in blood flow simulation. However, traditional SPH methods often rely on penalty force models or virtual particles when dealing with wall boundary conditions, which can easily lead to particle penetration or boundary condition relaxation in complex geometries. Furthermore, blood, as a non-Newtonian fluid, exhibits viscosity variations with shear rate (shear thinning effect). In microvessels, narrow blood vessels, or low-shear-rate regions, using the Newtonian viscosity assumption can introduce significant errors.

[0004] Learning-based solvers based on graph neural networks (GNNs) have shown potential in solid mechanics and fluid mechanics. For example, graph neural network simulators, continuous convolutional networks, and message-passing networks can be used to accelerate traditional numerical simulations. However, applying graph neural networks to SPH blood flow simulations faces the following challenges: (1) SPH particle interactions have natural pairwise antisymmetry, that is, the force exerted by particle i on particle j is equal in magnitude and opposite in direction to the force exerted by particle j on particle i. However, the message passing of ordinary graph neural networks may not satisfy this condition. After training convergence, a force field with correct local energy gradient but non-conserved global momentum may be obtained. Existing methods usually only apply this constraint in the form of a penalty term in the loss function, without providing any guarantee in the inference stage. (2) The viscosity of non-Newtonian fluids depends on the local shear rate, and the model needs to dynamically determine the effective viscosity during inference. Existing learning-based SPH solvers mostly treat viscosity as a fixed global constant or only as a node scalar feature added to the network input, without making the effective viscosity directly participate in the calculation of pairwise interactions. Therefore, it is difficult to correctly reproduce shear thinning behavior in narrow sections and near-wall regions where the shear rate changes drastically. (3) The motion of boundary particles such as walls, entrances and exits in the simulation is subject to physical constraints. Relying solely on the loss function for soft constraints cannot strictly guarantee that the forward simulation meets the boundary conditions, and errors will continue to accumulate during long-term step progression.

[0005] Therefore, there is a need for a computer-implemented method, system, and medium for simulating non-Newtonian blood flow in order to achieve accurate, stable, and real-time simulation of non-Newtonian blood flow. Summary of the Invention

[0006] This invention proposes a computer-implemented non-Newtonian blood flow simulation method, system, and medium to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A computer-implemented method for simulating non-Newtonian blood flow includes the following steps: S1: Receive a particle map representing blood and boundaries within blood vessels, wherein the nodes of the particle map are smoothed particle hydrodynamic particles, and the edges of the particle map are generated by the particle neighborhood relations within a support radius, wherein the support radius is 2h, and h is the particle smoothing length; S2: Construct edge features e_ij for edge (i,j) based on particle relative position, particle relative velocity, smooth particle hydrodynamic kernel function value and kernel function gradient; S3: Based on the non-Newtonian viscosity model, the effective blood viscosity μ_eff,i of particle i is determined based on the local shear rate γd_i at particle i, and the effective viscosity μ_eff,i and μ_eff,j of particles at both ends of edge (i,j) are added as additional components to the edge feature e_ij; S4: Using a graph neural network with an antisymmetric message passing mechanism, the acceleration of each fluid particle is generated based on the particle graph and the edge features after incorporating effective viscosity. The antisymmetric message passing mechanism calculates the first message φ(h_i, h_j, e_ij) for edge (i, j) using a shared message function φ, and calculates the second message φ(h_j, h_i, e_ji) ​​for the edge feature e_ji after swapping endpoints. Then, the first message is subtracted from the second message to form the directional message m_ij = φ(h_i, h_j, e_ij) - φ(h_j, h_i, e_ji) ​​on edge (i, j), where e_ji is obtained from e_ij according to the following rules: the relative position, relative velocity, and kernel function gradient components are the opposites, the distance between particles and the kernel function value remain unchanged, and the effective viscosity components of the particles at both ends are swapped. Thus, for edge (j, i), m_ji = -m_ij is always true. The acceleration of particle i is obtained by summing the paired interactions acting on it and dividing by the particle mass: a_i = (1 / m_i)·Σ_(j∈N(i)) m_ij, and Σ_i m_i·a_i = 0; S5: Apply hard gating to non-fluid boundary particles during the model output phase, controlling their acceleration, velocity, or position. Where M_i is the type mask of particle i, The acceleration value specified for this particle type.

[0008] Preferably, in S1, the particle graph includes at least two types of particle labels from fluid, wall, inlet, and outlet. Each particle has physical properties of position, velocity, density, and pressure. The node features of the particle graph include position, velocity, density, pressure, and particle type. The edge features of the particle graph include three-dimensional relative position, distance, three-dimensional relative velocity, kernel function value, and three-dimensional kernel function gradient.

[0009] Preferably, in S2, the smooth particle hydrodynamic kernel function is the Wendland-C2 kernel function, a cubic spline kernel function, or a Gaussian kernel function; the Wendland-C2 kernel function is defined as follows: when 0 ≤ q ≤ 2, When q > 2, W(q) = 0; where q = ||r_ij|| / h, and α_d is a normalization constant related to the spatial dimension in the three-dimensional case. .

[0010] Preferably, in S3, the non-Newtonian viscosity model is a Carreau-Yasuda model, a Casson model, a power-law model, or a Quemada model; the Carreau-Yasuda model is... Local shear rate γd_i = √(2·D_i:D_i), .

[0011] Preferably, in step S5, in addition to applying the hard gating to the acceleration, a projection is also applied to the velocity or position of the particles on the wall, at the inlet, or at the outlet, so that the projection is onto a subspace that satisfies a no-slip boundary, an inlet velocity boundary, an outlet pressure boundary, or a periodic boundary.

[0012] Preferably, it further includes updating the fluid particle state using the Sinusoidal method, the Verlet method, the Runge-Kutta method, or the projective integral method, and updating the density and pressure based on the equation of state or the continuity equation; wherein the equation of state is... γ_T is the exponent of the Tait equation of state, and the artificial sound speed satisfies c_s≥10·U_max.

[0013] Preferably, in step S4, the graph neural network includes an encoder and L antisymmetric message passing layers, and the shared message function φ is a multilayer perceptron; the shared message function of the Lth antisymmetric message passing layer outputs three-dimensional pairwise interaction forces, and no decoder is set after aggregation.

[0014] This invention also proposes a computer-implemented non-Newtonian blood flow simulation system, including a medical image input module, a blood vessel segmentation and particleization module, a graph construction module, a material and boundary condition assignment module, a simulation module, and an output module.

[0015] The present invention also proposes a non-transitory computer-readable storage medium having instructions stored thereon, which, when executed by a processor, cause a computing device to perform the methods described above.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. By using the kernel function value and gradient of the smooth particle hydrodynamic kernel function as the edge features of the graph neural network, the particle interactions learned by the graph neural network are naturally built on the mathematical framework of smooth particle hydrodynamics, and the network does not need to learn the spatial decay law of neighborhood weights from zero. 2. An antisymmetric message passing mechanism is adopted to ensure that the messages after the endpoints are exchanged satisfy the algebraic identity m_ji=-m_ij. Thus, Σ_i m_i·a_i = 0 is strictly true in each forward propagation. Global momentum conservation is guaranteed by the network structure rather than by the soft constraints of the loss function. 3. The effective viscosity of blood is modeled as a function of the local shear rate, and the effective viscosity of particles at both ends of the edge is added as an additional component to the edge feature. This allows the effective viscosity to directly participate in the calculation of pairwise interactions, rather than just being added to the network input as a node scalar. This enables the simulation to correctly reproduce the shear thinning behavior of blood in narrow sections and near-wall regions where the shear rate changes drastically. 4. Apply hard gating directly to the wall, entrance and exit particles during the output stage of forward propagation, so that the acceleration, velocity or position of the boundary particles strictly meet the specified boundary conditions at each time step, fundamentally preventing boundary condition violations and error accumulation during long-term step propagation. 5. After training, the solution for a single time step is a forward graph propagation, without the need to assemble and solve the global linear system. In the verification of steady-state Poiseuille flow, the velocity profile error relative to the analytical solution is 0.1%. Attached Figure Description

[0017] Figure 1 This is a flowchart of a non-Newtonian blood flow simulation method implemented by a computer, as proposed in this invention. Figure 2 This is a schematic diagram of the structure of the graph neural network and the antisymmetric message passing mechanism in a non-Newtonian blood flow simulation method implemented by a computer proposed in this invention; Figure 3 This is a block diagram of a non-Newtonian blood flow simulation system implemented by a computer, as proposed in this invention. Detailed Implementation

[0018] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0019] Example 1 Reference Figure 1 and Figure 2 A computer-implemented method for simulating non-Newtonian blood flow includes the following steps: S1: Receive a particle map representing blood and boundaries within the blood vessel. The particle map includes at least two types of particle labels from fluid, wall, inlet, and outlet. Each particle has physical properties of position, velocity, density, and pressure. The node features of the particle map include position, velocity, density, pressure, and particle type. The specific construction of the particle map includes the following steps: S101: Receives a smoothed particle hydrodynamic particle set obtained by segmentation and particleization of medical vascular images; S102: Each particle is assigned a type label: fluid particle, wall particle, inlet particle, and outlet particle; the particle spacing Δx is set according to the blood vessel diameter and the required resolution, and the particle smoothing length h is 1.2Δx to 1.5Δx; S103: For each particle i, search for neighboring particles j within its support radius 2h and construct graph edges (i, j); S2: Construct edge features e_ij for edge (i, j) based on particle relative position, particle relative velocity, smooth particle hydrodynamic kernel function value, and kernel function gradient. Its components include: The three-dimensional relative position r_ij = x_j - x_i; The interparticle distance d_ij = ||r_ij||; The three-dimensional relative velocity v_ij = v_j - v_i; Kernel function value W(d_ij / h); 3D kernel function gradient ; The smooth particle hydrodynamic kernel function can be the Wendland-C2 kernel function, the cubic spline kernel function, or the Gaussian kernel function. This embodiment uses the Wendland-C2 kernel function, and its formula is as follows: When 0≤q≤2 ; When q > 2, W(q) = 0; Where q = ||r_ij|| / h, h is the smooth length of the particle, the supporting radius of the kernel function is 2h, and α_d is a normalization constant related to the spatial dimension in the three-dimensional case. ; S3: Based on the non-Newtonian viscosity model, the effective blood viscosity μ_eff,i of particle i is determined according to the local shear rate γd_i at particle i. The non-Newtonian viscosity model can be the Carreau-Yasuda model, Casson model, power-law model, or Quemada model. This embodiment uses the Carreau-Yasuda model, and its formula is as follows:

[0020] Where: μ_eff is the effective viscosity, μ_0 is the zero shear rate viscosity, μ_∞ is the infinite shear rate viscosity, λ is the relaxation time constant, representing the shear rate transitioning from the Newtonian region to the shear-thinning region, n is the power law exponent, a is the Yasuda parameter, and γd is the local shear rate; in a specific implementation, for human blood, μ_0 = 0.056 Pa·s, μ_∞ = 0.00345 Pa·s, λ = 3.313 s, n = 0.3568, and a = 2; The local shear rate γd is approximated by the particle velocity gradient in smoothed particle hydrodynamics, and its formula is as follows: γd_i = √(2·D_i:D_i),

[0021] Where D_i is the strain rate tensor at particle i, v_i and v_j are the velocities of particles i and j respectively, ρ_j is the density of particle j, m_j is the mass of particle j, ⊗ represents the tensor product, and “:” represents the double dot product of tensors; Then, the effective viscosities μ_eff,i and μ_eff,j of the particles at both ends of edge (i,j) are added as two additional components to the edge feature e_ij, that is, the expanded edge feature is: e_ij = [r_ij, d_ij, v_ij, W(d_ij / h), [,μ_eff,i,μ_eff,j]; It should be noted that this step allows the effective viscosity to directly participate in the calculation of subsequent pairwise interactions. Since viscous stress is essentially a pairwise momentum exchange, placing the effective viscosity in the edge features rather than just the node features allows the message function to obtain the viscosity information at both ends of the interaction in the same evaluation, thus providing the correct viscous action in narrow segments where viscosity changes drastically along space and in the near-wall region; S4: Using a graph neural network with an antisymmetric message passing mechanism, the acceleration of each fluid particle is generated based on the particle graph and the edge features after incorporating the effective viscosity. S5: Apply hard gating to non-fluid boundary particles during the model output phase, controlling their acceleration, velocity, or position.

[0022] Where M_i is the type mask for particle i, M_i = 1 for fluid particles, and M_i = 0 for wall, inlet, and outlet particles. This is the acceleration value specified for this particle type. ⊙ represents element-wise product. For stationary wall particles, take... ; In addition to applying the hard gating to the acceleration, the velocity or position of particles at the wall, entrance, or exit can also be projected onto a subspace that satisfies the no-slip boundary, entrance velocity boundary, exit pressure boundary, or periodic boundary. Since the gating is applied to the output of the network rather than the loss function, the boundary conditions are strictly satisfied at each time step and will not accumulate violations as time steps progress.

[0023] Reference Figure 2 The graph neural network includes an encoder and L antisymmetric message passing layers. The encoder maps node features and edge features to the hidden space, respectively, and can use multilayer perceptrons as the node encoder and edge encoder, respectively. The directional messages of the first L-1 antisymmetric message passing layers are used to update the hidden state of the nodes, and the shared message function of the Lth antisymmetric message passing layer directly outputs the three-dimensional pairwise interaction forces. It should be noted that no decoder is set after aggregation because any nonlinear mapping acting on the aggregation result will destroy Σ_i m_i·a_i = 0, causing the momentum conservation equation to degenerate from an algebraic identity to an approximate one. In a specific implementation, L is 6, the hidden dimension is 128, and both the encoder and the shared message function φ use two multilayer perceptrons. The antisymmetric message passing mechanism calculates the first message φ(h_i, h_j, e_ij) for edge (i, j) using the shared message function φ, and calculates the second message φ(h_j, h_i, e_ji) ​​for the edge feature e_ji after exchanging endpoints. Then, it subtracts the second message from the first message to form the directed message on edge (i, j): m_ij = φ(h_i, h_j, e_ij) - φ(h_j, h_i, e_ji); Where e_ji is obtained from e_ij according to the following rules: relative position r_ij, relative velocity v_ij, and kernel function gradient. Taking the opposite of the three components, the interparticle distance d_ij and the kernel function value W remain unchanged, while the effective viscosity components μ_eff,i and μ_eff,j of the particles at both ends are interchanged, i.e.: e_ji = [-r_ij, d_ij, -v_ij, W(d_ij / h), ,μ_eff,j,μ_eff,i]; From this definition, we can directly obtain that the message on the (j, i) endpoint after the exchange endpoint is: m_ji = φ(h_j, h_i, e_ji) ​​- φ(h_i, h_j, e_ij) = -m_ij; That is, m_ji=-m_ij is an algebraic identity that holds for any network parameters and any input, and does not need to be explicitly applied through a loss function; The acceleration of particle i is obtained by summing the paired interactions acting on it and dividing by the particle's mass: a_i = (1 / m_i)·Σ_(j∈N(i)) m_ij, Where N(i) is the set of neighbors of particle i within the support radius, and m_i is the mass of particle i; since m_ij + m_ji = 0 for each edge (i, j), summing over all particles yields: Σ_i m_i·a_i = Σ_i Σ_(j∈N(i)) m_ij = 0, That is, the total momentum of the system is strictly conserved in each forward propagation. This property is guaranteed by the network structure and is independent of whether the training converges.

[0024] This embodiment also includes updating the fluid particle state using the Sin-Euler method, the velocity Verlet method, the Runge-Kutta method, or the projective integral method, and updating the density and pressure based on the equation of state or the continuity equation; The formula for Szymborsaurus is as follows: v_i(t+Δt) = v_i(t)+a_i(t)·Δt, x_i(t+Δt) = x_i(t)+v_i(t+Δt)·Δt; The formula for the continuity equation is as follows:

[0025] The formula for the state equation is as follows:

[0026] Where c_s is the artificial sound velocity, ρ_0 is the reference density, and γ_T is the Tait equation of state exponent, which is usually taken as γ_T = 7 in weakly compressible smooth particle fluid dynamics; the selection of the artificial sound velocity should satisfy c_s ≥ 10·U_max, where U_max is the maximum value of the fluid particle velocity modulus in the simulation domain, so as to control the density fluctuation within 1%.

[0027] It should be noted that in this specification, γd represents the local shear rate and γ_T represents the exponent of the equation of state. These are different physical quantities and should not be confused.

[0028] Example 2 This embodiment provides a set of data verified according to the method described in Embodiment 1 to illustrate the technical effects of the present invention: A steady-state Poiseuille flow through a circular tube was used as a verification example. The tube radius and particle resolution were set according to S102 of Example 1. A constant driving force was applied at the inlet, and the wall particles were hard-gated with zero acceleration according to S5. After the simulation reached steady state, the cross-sectional velocity profile was compared with the analytical solution, and the relative error was 0.1%.

[0029] Throughout the simulation, the displacement of the wall particles remained zero, and the particle penetration phenomenon commonly seen in traditional penalty force models or virtual particle methods did not occur. The change in the total momentum Σ_i m_i·v_i was contributed only by the external driving force and boundary gating. The pairwise interactions within the network did not generate any net momentum, consistent with the theoretical conclusion of Σ_i m_i·a_i = 0 in S4.

[0030] Example 3 Reference Figure 3 This embodiment proposes a computer-implemented non-Newtonian blood flow simulation system, including: The medical image input module is used to receive CT angiography, MR angiography, Doppler ultrasound, digital subtraction angiography or intraoperative sensor data. The vessel segmentation and particleization module is used to extract vascular cavities from medical images and generate smooth particle fluid dynamics particle discretization, assigning fluid, wall, inlet or outlet labels to each particle. The graph construction module is used to generate particle graphs based on particle neighborhoods within the support radius. The Material and Boundary Condition Assignment Module is used to assign blood density, non-Newtonian viscosity model parameters, inlet velocity profile and outlet pressure conditions to particles. The Material and Boundary Condition Assignment Module also updates the model parameters online or offline based on patient blood viscosity measurement data, blood pressure measurement data, ultrasonic Doppler flow velocity data or a combination thereof. The simulation module is used to execute the method described in Embodiment 1. The simulation module runs on a graphics processor, neural network accelerator, server, edge device, medical imaging workstation, or surgical navigation platform. The output module is used to output blood flow velocity field, pressure field, wall shear stress, streamlines, particle trajectories, stenosis pressure gradient or a combination thereof. The output module also overlays the blood flow simulation results onto the patient's vascular image, three-dimensional anatomical model or augmented reality navigation interface. In addition, the output module is configured to generate stenosis pressure gradient, wall shear stress distribution, thrombosis risk assessment, vascular remodeling prediction or interventional treatment plan based on the blood flow simulation results.

[0031] Example 4 This embodiment proposes a non-transitory computer-readable storage medium storing instructions that, when executed by a processor, cause a computing device to perform the method described above.

[0032] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A computer-implemented non-Newtonian blood flow simulation method, characterized in that, Includes the following steps: S1: Receive a particle map representing blood and boundaries within blood vessels, wherein the nodes of the particle map are smoothed particle hydrodynamic particles, and the edges of the particle map are generated by the particle neighborhood relations within a support radius, wherein the support radius is 2h, and h is the particle smoothing length; S2: Construct edge features e_ij for edge (i,j) based on particle relative position, particle relative velocity, smooth particle hydrodynamic kernel function value and kernel function gradient; S3: Based on the non-Newtonian viscosity model, the effective blood viscosity μ_eff,i of particle i is determined based on the local shear rate γd_i at particle i, and the effective viscosity μ_eff,i and μ_eff,j of particles at both ends of edge (i,j) are added as additional components to the edge feature e_ij; S4: Using a graph neural network with an antisymmetric message passing mechanism, the acceleration of each fluid particle is generated based on the particle graph and the edge features after incorporating effective viscosity; the antisymmetric message passing mechanism calculates the first message φ(h_i, h_j, e_ij) for edge (i, j) using a shared message function φ, and calculates the second message φ(h_j, h_i, e_ji) ​​for the edge feature e_ji after swapping endpoints, and then subtracts the second message from the first message to form the directional message on edge (i, j): m_ij = φ(h_i, h_j, e_ij) - φ(h_j, h_i, e_ji), Where h_i and h_j are the hidden states of particles i and j, and e_ji is obtained from e_ij according to the following rules: the relative position, relative velocity and kernel function gradient components are reversed, the distance between particles and the kernel function value remain unchanged, and the effective viscosity components of the particles at both ends are interchanged; thus, for edge (j, i), m_ji = -m_ij always holds. The acceleration of particle i is obtained by summing the paired interactions acting on it and dividing by the particle's mass: a_i = (1 / m_i)·Σ_(j∈N(i)) m_ij, Where N(i) is the set of neighbors of particle i within the support radius, and m_i is the mass of particle i; from m_ji=-m_ij, we can get Σ_i m_i·a_i = 0, that is, the total momentum of the system is strictly conserved; S5: Apply hard gating to non-fluid boundary particles during the model output phase, controlling their acceleration, velocity, or position. Where M_i is the type mask for particle i, M_i = 1 for fluid particles, and M_i = 0 for wall, inlet, and outlet particles. The acceleration value is specified for this particle type, and ⊙ represents element-wise product.

2. The non-Newtonian blood flow simulation method implemented by a computer according to claim 1, characterized in that, In S1, the particle graph includes at least two types of particle labels from fluid, wall, inlet, and outlet. Each particle has physical properties of position, velocity, density, and pressure. The node features of the particle graph include position, velocity, density, pressure, and particle type. The edge features of the particle graph include three-dimensional relative position, distance, three-dimensional relative velocity, kernel function value, and three-dimensional kernel function gradient.

3. The non-Newtonian blood flow simulation method implemented by a computer according to claim 1, characterized in that, In S2, the smooth particle hydrodynamic kernel function is the Wendland-C2 kernel function, the cubic spline kernel function, or the Gaussian kernel function; The formula for the Wendland-C2 kernel function is as follows: When 0≤q≤2 ; When q > 2, W(q) = 0; Where q = ||r_ij|| / h, h is the smooth length of the particle, the supporting radius of the kernel function is 2h, and α_d is a normalization constant related to the spatial dimension in the three-dimensional case. .

4. The non-Newtonian blood flow simulation method implemented by a computer according to claim 1, characterized in that, In S3, the non-Newtonian viscosity model is the Carreau-Yasuda model, the Casson model, the power-law model, or the Quemada model. The formula for the Carreau-Yasuda model is as follows: Where μ_eff is the effective viscosity, μ_0 is the zero shear rate viscosity, μ_∞ is the infinite shear rate viscosity, λ is the relaxation time constant, which characterizes the transition shear rate from the Newton region to the shear-thinning region, n is the power law exponent, a is the Yasuda parameter, and γd is the local shear rate. The local shear rate γd is approximated by the particle velocity gradient in smoothed particle hydrodynamics, and its formula is as follows: γd_i = √(2·D_i:D_i), Where D_i is the strain rate tensor at particle i, v_i and v_j are the velocities of particles i and j, respectively, ρ_j is the density of particle j, and m_j is the mass of particle j. is the gradient of the kernel function, ⊗ represents the tensor product, and ":" represents the double dot product of the tensor.

5. A computer-implemented non-Newtonian blood flow simulation method according to claim 1, characterized in that, In S5, in addition to applying the hard gating to the acceleration, a projection is also applied to the velocity or position of the particles at the wall, entrance, or exit, so that the projection is onto a subspace that satisfies the no-slip boundary, the entrance velocity boundary, the exit pressure boundary, or the periodic boundary.

6. The computer-implemented non-Newtonian blood flow simulation method according to claim 1, characterized in that, It also includes updating the fluid particle state using the Sin-Euler method, the velocity Verlet method, the Runge-Kutta method, or the projective integral method, and updating density and pressure based on the equation of state or the continuity equation; The formula for Szymborsaurus is as follows: v_i(t+Δt) = v_i(t)+a_i(t)·Δt, x_i(t+Δt) = x_i(t)+v_i(t+Δt)·Δt; The formula for the continuity equation is as follows: The formula for the state equation is as follows: Where c_s is the artificial sound velocity, ρ_0 is the reference density, γ_T is the Tait equation of state exponent, and the artificial sound velocity satisfies c_s≥10·U_max, where U_max is the maximum value of the fluid particle velocity modulus in the simulation domain.

7. The non-Newtonian blood flow simulation method implemented by a computer according to claim 1, characterized in that, In step S4, the graph neural network includes an encoder and L antisymmetric message passing layers, where L is an integer greater than or equal to 1. The encoder maps node features and edge features to the hidden space, respectively. The shared message function φ is a multilayer perceptron. The directional messages of the first L-1 antisymmetric message passing layers are used to update the hidden state of the nodes. The shared message function of the Lth antisymmetric message passing layer outputs three-dimensional pairwise interaction forces. The particle acceleration is obtained by summing the three-dimensional pairwise interaction forces as described in step S4 and dividing by the particle mass. After aggregation, no decoder is set.

8. A computer-implemented non-Newtonian blood flow simulation system, characterized in that, include: The medical image input module is used to receive CT angiography, MR angiography, Doppler ultrasound, digital subtraction angiography or intraoperative sensor data. The vessel segmentation and particleization module is used to extract vascular cavities from medical images and generate smooth particle fluid dynamics particle discretization, assigning fluid, wall, inlet or outlet labels to each particle. The graph construction module is used to generate particle graphs based on particle neighborhoods within the support radius. The Material and Boundary Condition Assignment Module is used to assign blood density, non-Newtonian viscosity model parameters, inlet velocity profile, and outlet pressure conditions to particles. A simulation module for executing the method according to any one of claims 1 to 7; The output module is used to output blood flow velocity field, pressure field, wall shear stress, streamlines, particle trajectories, or stenosis pressure gradient.

9. A computer-implemented non-Newtonian blood flow simulation system according to claim 8, characterized in that, The material and boundary condition assignment module updates the model parameters online or offline based on patient blood viscosity measurement data, blood pressure measurement data, or ultrasound Doppler flow velocity data. The simulation module runs on a graphics processor, neural network accelerator, server, edge device, medical imaging workstation, or surgical navigation platform; The output module overlays the blood flow simulation results onto the patient's vascular images, three-dimensional anatomical models, or augmented reality navigation interface, and is configured to generate stenosis pressure gradients, wall shear stress distributions, thrombosis risk assessments, vascular remodeling predictions, or interventional treatment plans based on the blood flow simulation results.

10. A non-transitory computer-readable storage medium, characterized in that, It stores instructions that, when executed by a processor, cause the computing device to perform the method of any one of claims 1 to 7.

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