Cardiovascular fluid-structure interaction digital simulation method and system based on spce

Abstract

The present application belongs to the technical field of the intersection of computational biomechanics and artificial intelligence, and particularly relates to a cardiovascular fluid-structure coupling numerical simulation method and system based on SPCE. In the simulation stage, the sampling parameters are injected into the SPH fluid-structure coupling simulation, the fluid-structure coupling simulation containing non-Newtonian blood rheology, anisotropic hyperelasticity of the blood vessel wall and 3D-0D multi-scale coupling is executed, and the hemodynamic output is extracted to constitute a training data set; in the agent model construction stage, a candidate base is generated through hyperbolic truncation, a hierarchical genetic constraint reverse pruning algorithm is used to solve sparse polynomial chaos expansion coefficients, a warm start mechanism is used to inherit the model structure of the last round, convergence is judged based on leave-one-out cross-validation, and when the convergence is not achieved, adaptive hybrid sampling is used for iterative optimization; in the application stage, the agent model is deployed for rapid prediction and clinical decision support. The present application reduces the computational cost while maintaining high accuracy, and realizes the numerical integration and rapid application of cardiovascular fluid-structure coupling simulation.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of computational biomechanics and computational hematology, specifically involving an intelligent simulation method and system that deeply integrates numerical simulation of fluid-structure interaction (FSI) based on the Smoothed Particle Hydrodynamics (SPH) method with a surrogate model of Sparse Polynomial Chaos Expansion (SPCE), and in particular, a cardiovascular fluid-structure interaction numerical simulation method and system based on SPCE. Background Technology

[0002] Cardiovascular disease is one of the leading causes of death worldwide. Hemodynamic factors—such as wall shear stress (WSS), oscillatory shear index (OSI), and translesion pressure gradient—have been shown to be highly correlated with pathological processes such as atherosclerosis, aneurysm dilation, and plaque rupture. However, these hemodynamic parameters vary significantly between individuals, and their complete spatial distribution information cannot be directly obtained through clinical measurements; therefore, quantitative assessment using numerical simulations is essential.

[0003] Fluid-structure interaction (FSI) is a core physical process for understanding the pathophysiological mechanisms of cardiovascular diseases and evaluating the effectiveness of surgical interventions. Blood flow and the vessel wall form a bidirectional coupling system—pulsating blood flow exerts pressure and viscous shear force on the vessel wall, causing periodic deformation of the vessel wall; conversely, the deformation of the vessel wall alters the geometry of the blood flow channel, affecting the velocity and pressure distribution of the flow field. This coupling effect is particularly significant in lesions such as atherosclerotic plaques, aortic dissection, and aortic stenosis, directly determining the pathological characteristics of the local hemodynamic environment.

[0004] However, cardiovascular FSI simulation faces the following unique challenges: (1) The non-Newtonian rheological properties of blood (shear thinning, yield stress) deviate significantly from the Newtonian fluid assumption in low shear rate regions (such as aneurysm cavities and post-stenotic reflux zones); (2) The vessel wall has highly nonlinear hyperelastic / viscohyperelastic mechanical behavior and exhibits anisotropy (collagen fiber reinforcement) and layered structure (intima, media, and adventitia); (3) Blood flow and vessel wall undergo large deformation periodic motion driven by the cardiac cycle, which places extremely high demands on the robustness and accuracy of numerical methods; (4) The impedance effect of the peripheral vascular bed needs to be correctly described by coupling the lumped parameter model with the three-dimensional computational domain, while the lumped parameters themselves have significant inter-individual physiological variability.

[0005] Currently, the methods used for numerical simulation of cardiovascular fluid-structure interaction problems mainly include the following categories: (1) Mesh-based methods: Arbitrary Lagrange-Eulerian (ALE) finite element method or immersed boundary method is used to handle fluid-solid interfaces. These methods face difficulties in mesh distortion and reconstruction when dealing with complex geometries and large interface deformations, resulting in high computational costs. Especially in large deformation vascular motion driven by the cardiac cycle, the ALE method requires frequent mesh updates (remeshing), which seriously affects computational efficiency and numerical stability.

[0006] (2) Smooth Particle Hydrodynamics (SPH) Method: As a Lagrangian meshless particle method, SPH is suitable for handling large deformation and free surface flow problems, and can cope with large-amplitude periodic deformation of the blood vessel wall without mesh reconstruction. In the SPH framework, fluid-solid coupling is achieved through interparticle interaction forces, without the need for explicit interface tracking, which is particularly important for diseased blood vessels with complex geometries (such as stenosis, bifurcation, and aneurysm). The SPH method has been widely used in the field of cardiovascular hemodynamics, but there is still a lack of systematic solutions for SPH modeling of non-Newtonian rheology of blood and anisotropic hyperelastic constitutive structures of blood vessel walls. In addition, the SPH particle method provides a direct spatial interpolation framework for the calculation of key hemodynamic indicators (WSS, OSI, etc.).

[0007] (3) 3D-0D Coupled Model: In cardiovascular hemodynamic simulation, due to computational resource limitations, only local vascular segments of interest (such as coronary artery stenosis, aortic arch, abdominal aortic aneurysm segments, etc.) can be modeled in 3D detail. The remaining circulatory system downstream and upstream is equivalently represented by zero-dimensional (0D) lumped parameter models (such as the Windkessel RCR circuit model and the coronary microcirculation model). The core of 3D-0D coupling is: (a) extracting the driving signal of the 0D model from the instantaneous flow and pressure at the 3D outlet section; (b) feeding back the pressure obtained from the 0D model solution to the 3D outlet boundary. 0D modeling of coronary circulation is particularly complex, requiring consideration of the squeezing effect of intramyocardial pressure on coronary microvessels during systole, as well as the compensatory mechanism of coronary sinus pressure. This is a key multi-scale technique that combines local detail simulation with the systemic circulatory system.

[0008] (4) Surrogate Model / Uncertainty Quantification (UQ) Method: In cardiovascular clinical applications, significant uncertainties exist in parameters such as vascular geometry, tissue material properties, blood pressure level, cardiac output, and peripheral impedance of individual patients. Assessing these uncertainties for their impact on hemodynamic QoI (e.g., pressure gradient across stenosis) is crucial. The effects of factors such as WSS distribution and wall displacement are crucial for personalized treatment decisions. However, traditional Monte Carlo methods require thousands of high-fidelity SPH-FSI simulations, resulting in extremely high computational costs (a single cardiovascular SPH-FSI simulation can take hours to days). Surrogate model methods construct input-output mappings using a small number (tens to hundreds) of high-fidelity simulation samples to approximate expensive simulation calculations, enabling parameter uncertainty quantification and sensitivity analysis within a clinically acceptable timescale. Commonly used surrogate model methods include Gaussian process regression (Kriging), polynomial chaotic expansion (PCE), and neural networks. However, existing surrogate model methods lack a dedicated framework for multiphysics scenarios in cardiovascular SPH-FSI and cannot fully utilize prior knowledge of cardiovascular mechanics problems (such as physiological ranges of parameters and physical constraints) to guide the construction and optimization of surrogate models.

[0009] In summary, the existing technology has the following main shortcomings: The mechanical modeling of cardiovascular SPH-FSI is incomplete. Existing SPH hemodynamic simulations mostly use the Newtonian fluid assumption and linear elastic vessel wall model, which fail to fully characterize the non-Newtonian rheological properties of blood, the anisotropic hyperelastic behavior of the vessel wall, and the systolic squeezing effect of intramyocardial pressure unique to the coronary circulation.

[0010] Simulation and surrogate models are disconnected. High-fidelity simulation tools and surrogate model tools are usually developed and run independently, lacking a unified automated workflow orchestration mechanism. Users need to manually execute simulations, extract results, and train models, which is inefficient and makes it difficult to establish a standardized clinical evaluation process.

[0011] The surrogate model approach suffers from the "curse of dimensionality" and insufficient interpretability. The number of basis variables in traditional PCE increases exponentially with the input dimension and the order of the polynomial. The cardiovascular parameter space typically involves 10-30 variables, making it difficult to build a reliable model with limited samples. Existing sparse methods (such as LARS and OMP) do not guarantee the hierarchical inheritance relationship between basis terms, causing the model to violate the mathematical structure of polynomial expansion and lack physical interpretability.

[0012] Sampling strategies lack model awareness. Traditional sampling methods (such as LHS and Sobol sequences) do not consider feedback information from the constructed surrogate model, cannot be specifically encrypted in regions with high model uncertainty, and have low sampling efficiency.

[0013] There is a lack of dedicated proxy model frameworks for cardiovascular SPH-FSI. Existing tools lack deep integration with cardiovascular SPH simulation solvers—including automatic mapping of physiological parameters to simulation configurations, automatic extraction of cardiovascular-specific QoIs, and deployment schemes for clinical decision support. Summary of the Invention

[0014] The purpose of this invention is to overcome the shortcomings of the prior art and provide a cardiovascular fluid-structure interaction digital simulation method and system based on SPCE. It achieves rapid prediction of complex SPH-FSI simulation results by constructing a high-precision surrogate model, and significantly reduces the computational cost of multi-parameter uncertainty quantification analysis in a data-driven manner.

[0015] To address the aforementioned technical problems, this invention provides a cardiovascular fluid-structure interaction digital simulation method based on SPCE, comprising the following steps: (a) Simulation Phase: S1. Define the cardiovascular simulation workflow contract, determine the input parameter space and its probability distribution type, and determine the hemodynamic output type.

[0016] S2. Generate an initial sample set in the input parameter space. Automatically inject the parameter values ​​of each sample into the SPH fluid-structure interaction simulation input file through a cardiovascular-specific input parameter mapper. Perform SPH fluid-structure interaction simulation for cardiovascular applications, extract the hemodynamic output values ​​corresponding to each sample, and form a training dataset.

[0017] Preferably, in the simulation phase, in step S1, the input parameter space includes five types of parameters and their probability distribution types: (1) Blood rheological parameters, including the yield stress of the Casson model or the zero-shear viscosity and asymptotic viscosity, relaxation time, transition parameters and power law exponent of the Carreau-Yasuda model, are uniformly distributed and the range of values ​​is based on population statistics in the literature. Human blood exhibits significant shear thinning behavior in the low shear rate region. In the aneurysm sac, the reflux area after stenosis and other regions with slow blood flow, the Newtonian fluid hypothesis will seriously underestimate viscous dissipation.

[0018] (2) Material parameters of the blood vessel wall, including fiber stiffness and fiber angle of the HGO model or material constants of the Mooney-Rivlin model, are normally distributed, and the mean and standard deviation are taken from the biaxial tensile test data of human arterial wall in vitro. The arterial wall is composed of three layers, of which the media and adventitia contain two groups of collagen fibers arranged in a spiral along the circumferential and axial directions, which give the blood vessel wall significant direction-dependent stiffness.

[0019] (3) 3D-0D coupled lumped parameters, including proximal impedance, distal impedance and compliance of the RCR model, or intramyocardial pressure related parameters of the coronary artery model, are log-normally distributed to reflect the skewed distribution characteristics of peripheral impedance in the population.

[0020] (4) Cardiac cycle and blood flow parameters, including peak systolic flow, cardiac cycle and systolic percentage, are set according to the clinical measurement range.

[0021] (5) Vascular geometric parameters, including stenosis rate, stenosis offset, radius of curvature and bifurcation angle, are set according to the clinical measurement range.

[0022] Hemodynamic output includes: (1) Hemodynamic scalars: pressure step across stenosis, outlet flow distribution ratio, mean wall shear stress (WSS).

[0023] (2) Hemodynamic field variables: spatial distribution field of time-averaged wall shear stress (TAWSS), spatial distribution field of oscillating shear index (OSI), and spatial distribution field of relative residence time (RRT). The calculations for these three variables are shown in equations (1) to (3). (1), (2), (3), In the formula, T is the duration of a complete cardiac cycle.

[0024] (3) Displacement field of blood vessel wall: containing radial and circumferential components.

[0025] (4) Stress field of blood vessel wall: including von Mises equivalent stress field and first principal stress field.

[0026] (5) Velocity profile: Velocity distribution curve along the center line of the blood vessel.

[0027] (6) Pressure waveform: outlet pressure time history curve.

[0028] (7) Solid domain final state / transient snapshot field variables.

[0029] Preferably, in step S2, the cardiovascular-specific input parameter mapper supports at least one of the following types: (1) an inlet waveform amplitude mapper for scaling the inlet blood flow waveform amplitude; (2) a cardiac cycle mapper for setting cardiac cycle parameters and automatically calculating the simulation time steps; (3) an HGO anisotropic hyperelastic material parameter mapper for writing fiber stiffness, fiber nonlinearity, fiber angle, and dispersion parameters into the solid material property configuration; (4) a Mooney-Rivlin isotropic hyperelastic material parameter mapper for writing material constants into the solid material property configuration; and (5) a blood non-Newtonian rheology parameter mapper for writing Casson model parameters (yield stress) into the solid material property configuration. and asymptotic viscosity ) or Carreau-Yasuda model parameters (zero shear viscosity) asymptotic viscosity Relaxation time Transition parameters Power Law Index (6) A 3D-0D coupled lumped parameter mapper, used to write the lumped parameters of the RCR model or coronary artery model into the outlet boundary condition configuration; (7) A stenosis geometry parameter mapper, used to map the stenosis rate, eccentricity, and stenosis length to the vascular geometry generation script; (8) A general XML attribute mapper, which locates arbitrary simulation input parameters through the PATH element path and attribute name. Each mapper is declared through JSON configuration in the workflow contract, and the proxy model automatically completes the parameter injection without writing additional code.

[0030] Preferably, in step S2, the SPH fluid-structure interaction simulation includes: (1) non-Newtonian blood rheology modeling, where the apparent viscosity of blood is dynamically updated particle by particle according to the local shear rate using the Casson model or the Carreau-Yasuda model; (2) anisotropic hyperelastic solid mechanics modeling of the blood vessel wall, using the fully Lagrangian SPH solid mechanics framework, supporting the Holzapfel-Gasser-Ogden anisotropic hyperelastic constitutive model; (3) calculation of bidirectional coupling force between blood and the blood vessel wall, where the bidirectional coupling force includes viscous coupling force and pressure coupling force; (4) three-dimensional computational domain outlet coupling zero-dimensional lumped parameter boundary model, where the zero-dimensional lumped parameter boundary model includes the RCR three-element model and the coronary artery-specific model, where the coronary artery-specific model introduces time-varying intramyocardial pressure to characterize the squeezing effect of myocardial systole on coronary microvessels.

[0031] This invention constructs a cardiovascular SPH-FSI mechanical simulation method within a meshless framework of smooth particle hydrodynamics (SPH), integrating non-Newtonian blood rheology, anisotropic hyperelasticity of the vessel wall, and bidirectional fluid-structure interaction forces. Specifically: (1) Weakly Compressible SPH (WCSPH) Cardiovascular Flow Control Equation. Blood is considered a weakly compressible fluid within the SPH framework. For any fluid particle... Its motion is described by the Lagrangian form of the Navier-Stokes equations, and the density evolution, momentum equation, and Tait-Murnaghan state equations are shown in equations (4) to (6), respectively: Density evolution: (4), Momentum equation: (5), Tait-Murnaghan equations of state: (6), In the formula, Let be the current density of particle i; Let j be the mass of the neighboring particle. These are the velocity vectors of particles i and j, respectively; For the kernel function gradient, The Wendland C2 quintic smoothing kernel function was selected, with a smoothing length of [missing information]. Using 1.3 times the initial particle spacing to ensure a sufficient number of neighboring particles is crucial for numerical stability in complex vascular geometries such as narrow throats and bifurcation tips.

[0032] , The pressures of particle i and its neighboring particle j are respectively; This is the viscous force term; This is a fluid-structure interaction force term; The speed of sound is artificially determined, and is taken as 10 times the maximum blood flow velocity to ensure weak compressibility. ); For reference density (human blood density), the value is taken as follows. ; The multi-factor index, with a value of 7, represents the standard Tait-Murnaghan equation of state parameter for water.

[0033] Equations (4)-(6) constitute the complete set of governing equations for the Newtonian blood flow solver under the weakly compressible SPH framework: the density evolution equation tracks the spatiotemporal changes in particle density, the momentum equation describes the accelerated motion of fluid particles under pressure, viscosity, and fluid-structure interaction, and the state equation maps density changes to a pressure field. Solving these three equations together allows for the spatial distribution of the velocity, pressure, and density fields of blood flow at any given time within the Lagrange particle framework, providing fundamental physical field data for wall shear stress calculation and subsequent fluid-structure interaction analysis. The viscosity term in the above equations adopts the Newtonian fluid assumption, i.e., blood viscosity is considered constant. However, human blood exhibits significant shear thinning behavior in low shear rate regions (such as aneurysm sacs and post-stenotic reflux zones). The constant viscosity assumption will severely underestimate viscous dissipation, leading to WSS prediction bias. Therefore, this invention further embeds a non-Newtonian blood rheology model into the SPH framework, enabling the calculation of viscous force to be dynamically adjusted according to the local blood flow state.

[0034] (2) SPH modeling of non-Newtonian blood rheology This invention realizes the embedding of two non-Newtonian blood constitutive models in the SPH framework: the Casson model and the Carreau-Yasuda model.

[0035] Casson model: Introducing yield stress This describes the "thickness" characteristic of blood at extremely low shear rates (the minimum stress threshold required for blood to begin flowing; below this value, blood does not flow like a solid). Shear stress and apparent viscosity The calculations are shown in equations (7) and (8) respectively: (7), (8), In the formula, The yield stress (the minimum stress threshold required for blood to begin flowing) is positively correlated with fibrinogen concentration and hematocrit Hct. It is an asymptotic viscosity (infinite shear viscosity), with typical values ​​of 0.03-0.05 dyn·s / cm2; denoted as shear rate.

[0036] The Carreau-Yasuda model is suitable for a wider range of shear rates (covering the mainstream arterial region to the slow capillary region), has no mathematical singularities, and its apparent viscosity... The calculation is shown in equation (9): (9), In the formula, Zero shear viscosity, which is the limiting viscosity when the shear rate approaches zero; The relaxation time constant controls the position of the transition zone on the shear rate axis. The larger the value, the leftward shift of the transition zone; The Yasuda index controls the steepness of the transition zone; The power-law exponent controls the downslope that high shear rates tend to approach. <1 indicates shear thinning. =1 indicates a Newtonian fluid.

[0037] In the SPH framework, shear rate The particle-by-particle calculation is performed using the Frobenius norm of the particle velocity gradient, as shown in equation (10): (10) In the formula, For strain rate tensor; and It is the velocity gradient tensor at particle i. This is the velocity difference vector, reflecting the change in local velocity. The gradient of the kernel function.

[0038] The viscous force term uses the harmonic average viscosity of particle pairs: (11), In the formula, Let be the equivalent viscosity between particles i and j; Let be the apparent viscosity of particle i; Let be the apparent viscosity of neighboring particle j.

[0039] The discrete form of viscous force under the SPH framework is given by equation (12). (12), In the formula, Let be the viscous force acting on particle i; Let be the harmonic average viscosity of particles i and j; Spatial dimension; It is the velocity difference vector; The position difference vector; For smooth length; This is a stabilization term. This formula achieves a smooth transition in non-Newtonian viscosity fields, avoiding artificial viscosity jumps at the interface.

[0040] The aforementioned non-Newtonian blood rheology modeling provides the SPH fluid solver with two optional constitutive models: the Casson model, which introduces yield stress, is suitable for describing the flow characteristics of bulk flows at extremely low shear rates and is applicable to regions with slow blood flow, such as aneurysm sacs; the Carreau-Yasuda model, which has no mathematical singularities, is suitable for a wide range of shear rates and is applicable to complete flow scenarios from the main arterial flow region to the slow flow region. Both models share the same velocity gradient calculation and viscous force discretization scheme, allowing users to flexibly choose according to the blood flow environment of the simulated object.

[0041] (3) Anisotropic hyperelastic SPH solid mechanical modeling of blood vessel wall The arterial wall consists of three layers (intima, media, and adventitia). The media and adventitia contain two groups of collagen fibers arranged spirally in the circumferential and axial directions (at an angle with the circumferential direction). Typical value This imparts significant load-direction-dependent stiffness and nonlinear stress-strain response to the blood vessel wall.

[0042] This invention employs a fully Lagrangian SPH solid mechanics framework (based on an initial reference configuration, eliminating tensile instabilities) to support the following hyperelastic constitutive models: Mooney-Rivlin model: Isotropic approximation, suitable for vein walls or newly formed intimal tissue in diseased areas. (13) In the formula, Strain energy density; It is the first material constant; This is the second material constant; , They are respectively

[0043] Holzapfel-Gasser-Ogden (HGO) anisotropic hyperelastic model: applicable to arterial walls, explicitly modeling the strain-strengthening behavior of two families of dispersed collagen fibers.

[0044] (14)

[0045] In the formula, Let be the deformation gradient tensor of particle i; , Here, represents the mass of neighboring particle j and the reference density, respectively; This is the position difference vector under the current configuration; This is the gradient correction tensor for the reference configuration position. Wherein, The calculation is as shown in equation (17). (17) In the formula, The position difference vector under the reference configuration; The gradient of the kernel function under the reference configuration.

[0046] The core advantage of the full Lagrangian scheme is that the neighborhood search is performed in an invariant reference configuration, avoiding the computational overhead of frequent neighborhood updates in long-term (multiple cardiac cycles) cardiovascular simulations, while also eliminating the stretching instability caused by Euler kernel function updates.

[0047] The aforementioned anisotropic hyperelastic SPH modeling of the vascular wall establishes a complete mechanical description framework for the solid domain—the Mooney-Rivlin model describes the isotropic behavior of the venous wall or diseased neointimal tissue, the HGO model describes the anisotropic mechanical response of the arterial wall's fiber reinforcement, and the fully Lagrangian SPH scheme eliminates tensile instability under large deformation conditions, ensuring that the deformation gradient and stress calculations remain stable throughout the cardiac cycle. However, the solid and fluid domains are solved independently—blood flow affects the deformation of the vascular wall, and the deformation of the vascular wall, in turn, changes the geometry of the blood flow channel, resulting in a continuous mechanical interaction between the two. To fully describe this bidirectional coupling effect, a force transmission mechanism must be established between fluid and solid particles. Therefore, this invention further constructs a blood-vascular wall SPH-FSI bidirectional coupling force model, coupling the two physical fields at the interface through viscous and pressure coupling forces to form a closed cardiovascular fluid-structure interaction simulation system.

[0048] (4) Blood-vascular wall SPH-FSI bidirectional coupling force The bidirectional coupling between fluid particles (blood) and solid particles (blood vessel walls) consists of two physical components: viscous coupling force and pressure coupling force.

[0049] Among them, viscous coupling force The calculation of (the Morris formula adapted for non-Newtonian viscosity) is shown in equation (18): (18) In the formula, Let i be the volume of the solid particle. Let be the volume of fluid particle j; The average viscosity is determined by the particle pair harmonization. Spatial dimension; The position difference vector; Here, represents the densities of particle i and particle j, respectively. The square of the position difference modulus; To stabilize the terms and prevent the denominator from being zero; The virtual velocity of the solid particle (obtained from the solution of solid dynamics); This represents the relative velocity between fluid particles and wall particles. This relative velocity is the physical source of viscous forces—the greater the velocity difference, the stronger the viscous resistance exerted by the wall on the fluid (or the drag force exerted by the fluid on the wall), and the stronger the force between them. Establish quantitative relationships.

[0050] Pressure coupling force The calculation of (symmetric SPH scheme, ensuring conservation of interface momentum) is shown in equation (19): (19) In the formula, These are the pressures of fluid particle i and wall particle j, respectively. Let i be the volume of fluid particle i and wall particle j, respectively.

[0051] The fluid-structure interaction force is applied in the form of acceleration, as shown in equation (20): (20) In the formula, Let be the fluid-structure interaction acceleration of particle i; The viscous coupling force experienced by particle i; The pressure coupling force experienced by particle i; Let i be the mass of particle i. This meshless FSI scheme avoids the mesh reconstruction required by the ALE method when there is large deformation of the blood vessel wall (displacement can reach 10%-15% of the vessel diameter during the cardiac cycle), and the interface particles are automatically identified through the support domain overlap, without the need for explicit interface tracking.

[0052] Thus, this invention establishes a complete bidirectional fluid-structure interaction (SPH-FSI) simulation framework for cardiovascular SPH: a non-Newtonian blood rheology model describes the viscosity changes of blood over a wide shear rate range using Casson or Carreau-Yasuda constitutive models; an anisotropic hyperelastic model of the vessel wall describes the large deformation behavior of the arterial or venous wall under physiological loads using HGO or Mooney-Rivlin constitutive models; and the fluid-solid coupling force is bidirectionally transmitted at the interface through viscous and pressure coupling forces, and is converted into acceleration acting on the corresponding particles—thus forming a complete closed-loop simulation system of "blood flow → wall stress → wall deformation → flow channel change → blood flow adjustment".

[0053] The aforementioned mechanical simulation layer provides high-fidelity training data for the surrogate model. It needs to run under cardiac cycle boundary conditions and extract clinically relevant hemodynamic outputs (QoIs) from the simulation results. To this end, this invention further introduces a parameterized description method for cardiac cycle inlet / outlet boundary conditions and defines seven types of hemodynamic QoIs for clinical decision-making and their calculation methods within the SPH framework.

[0054] (5) Boundary conditions of cardiac cycle and calculation of hemodynamic QoI The inlet boundary is parameterized using clinical physiological waveforms. Typical aortic / coronary blood flow waveforms are described by the following family of parameters: (a) peak systolic flow. (b) Diastolic baseline flow (c) Proportion of contraction period (d) Cardiac cycle The inlet velocity profile can be obtained using the Womersley transient analytical solution or a flat profile plus an inlet development segment strategy.

[0055] This invention extracts the following hemodynamic parameters from the SPH particle field as core concerns (QoI) for the surrogate model. Their spatial distribution and temporal variations are key biomechanical markers for assessing vascular disease risk and surgical outcomes: wall shear stress ( Vector, time-averaged wall shear stress ), oscillatory shear index ( ), relative stay time ( The mechanical simulation layer supports the proxy model layer.

[0056] Among them, wall shear stress ( ) vector The calculation is performed by reconstructing the velocity gradient of the wall particles and projecting the normal vector, as shown in equation (21). (twenty one), In the formula, The apparent viscosity of blood. This represents the tangential velocity gradient along the normal direction of the wall.

[0057] Time-averaged wall shear stress The calculation is shown in equation (22). (twenty two), In the formula, This refers to the duration of the cardiac cycle.

[0058] Oscillatory shear index The calculation is shown in equation (23). (twenty three).

[0059] Relative stay time The calculation is shown in equation (24). (twenty four).

[0060] The mechanical simulation layer supports the surrogate model layer: the blood rheological parameters involved in the above SPH-FSI simulation ( ), vessel wall material constant ( ), Input waveform parameters ( The input parameter space of the surrogate model is composed of the surrogate model and geometric parameters (narrowing ratio, eccentricity, radius of curvature); TAWSS, OSI, RRT, and transnarrowing pressure step. The wall displacement field and other factors constitute the prediction target (QoI) of the surrogate model.

[0061] The above-mentioned cardiac cycle boundary conditions and hemodynamic QoI calculations establish a direct link between simulation and clinical indicators—by describing inlet blood flow through parameterized waveforms and extracting… , , Clinically relevant indicators enable SPH-FSI simulation results to be understood by cardiologists and used for clinical decision-making. However, all the above fluid dynamics calculations are limited to three-dimensional local vascular segments, while the actual blood circulation system is a complete closed loop—downstream of the local vascular segment are connected to distal vascular beds such as arterioles, capillaries, and venules, which exert significant impedance effects on local blood flow. If only the three-dimensional outlet is set as free outflow or constant pressure boundary, it will deviate significantly from physiological reality. To bridge the scale gap between local fine simulation and the systemic circulatory system, this invention further constructs a 3D-0D multi-scale coupled boundary model, achieving cross-scale unified simulation of "local fine-grained simulation and global equivalence" through real-time data exchange between the three-dimensional outlet and the zero-dimensional lumped parameter model.

[0062] (6) Cardiovascular 3D-0D multi-scale coupled boundary model This invention constructs a 3D-0D multi-scale coupled boundary model for the multi-level cardiovascular system. It bidirectionally couples the three-dimensional SPH fine simulation of local vascular segments with the zero-dimensional lumped parameter equivalent model of the whole system through the exit interface, realizing a cross-scale unified simulation of "local fine-scale simulation and global equivalence".

[0063] 1) RCR (Windkessel) three-element lumped parameter model At each exit boundary of the SPH three-dimensional computational domain, an RCR circuit analog model is coupled to simulate the lumped impedance effect of the downstream vascular bed (arterioles, capillaries, venules). Its governing equation is shown in equation (25): (25) In the formula, For vascular compliance (simulating the volumetric-pressure elasticity of the vascular bed); The instantaneous volumetric flow rate is extracted from the SPH outlet section; Capacitor branch pressure; The characteristic impedance of the proximal end (simulating wave reflection from a large blood vessel). The distal peripheral impedance (simulating the total resistance of microcirculation); This is the outlet pressure fed back to the SPH boundary particles.

[0064] 2) Coronary artery-specific lumped parameter model There are fundamental differences between coronary circulation and systemic circulation. During myocardial contraction, intramyocardial pressure... The compression of coronary microvessels penetrating the myocardium causes a significant reduction or even reversal of coronary blood flow during systole. This invention realizes a coronary artery OD model considering the myocardial compression effect, as shown in equation (26): (26) In the formula, For epicardial artery capacitive branch pressure, This refers to the capacitive branch pressure of microvessels within the myocardium; This refers to time-varying intramyocardial pressure. Volumetric flow rate; and These are epicardial artery compliance and intramyocardial microvascular compliance, respectively. and These are the microcirculatory impedances at the arterial and venous ends of the myocardium, respectively.

[0065] 3) 3D-0D Coupling Algorithm At each SPH time step, the coupling process is as follows: ① Extract the instantaneous volumetric flow rate at the SPH outlet section (Achieved through the SPH integral of the velocity field of the particles at the exit boundary); ② The input is passed to the 0D model as the driving input, using sub-stepping time integration. That is, the internal time step of the 0D model can be 1 / thrombus_factor of the SPH step size. Solving for the 0D state variables yields the results. ; ③ Feedback is applied to the particles at the SPH exit boundary, and the solution to the SPH momentum equation is affected by modifying the pressure value of the exit particles, thus establishing a two-way coupled closed loop.

[0066] 4) Flow distribution and parameter calibration of multi-branch outlets For vascular segments with multiple outlet branches (such as the three branches of the aortic arch, the bifurcation of the coronary artery, and the bifurcation of the abdominal aorta), the calibration of the RCR parameters of each branch outlet follows Murray's law to ensure the physiologically accurate flow distribution, as shown in equation (27): (27) In the formula, The total peripheral impedance of all branch outlets; For target pressure reduction; The inlet volumetric flow rate; For the first The peripheral impedance of each outlet branch; For the first The radius of each exit branch; For the first The near-end characteristic impedance of each exit branch; Blood density; Wave speed; For the first The cross-sectional area of ​​each exit branch; this calibration strategy enables the 3D-0D coupled system to achieve a given target pressure drop. (Clinically, the appropriate branch flow distribution can be automatically obtained from the brachial artery cuff pressure estimate.)

[0067] 5) Quantification requirements for the uncertainty of 3D-0D coupling parameters RCR parameters ( ) and coronary artery model parameters ( Peripheral impedance exhibits significant physiological variability among individuals and cannot be directly measured clinically, typically requiring indirect fitting. This inherent uncertainty forms the core driving force behind the surrogate model layer's parameter sensitivity analysis and uncertainty quantification. The surrogate model establishes a rapid mapping from "lumped parameters to hemodynamic QoI" within the multidimensional space spanned by these lumped parameters, enabling the assessment of the impact of peripheral impedance uncertainty on QoI prediction within a clinically acceptable timescale.

[0068] The aforementioned 3D-0D multi-scale coupled boundary model (RCR / coronary artery specific model) enables a physiologically correct connection between the local 3D SPH-FSI simulation and the systemic circulatory system through bidirectional real-time exchange of flow-pressure at the outlet section, completing a complete mechanical simulation chain "from blood microrheology to vascular wall macro deformation, and then to coupling with the systemic circulatory system." The mechanical simulation layer can now output corresponding hemodynamic QoIs (pressure step, WSS, OSI, etc.) for any set of input parameters (stenosis rate, blood pressure, vascular stiffness, peripheral impedance, blood viscosity, etc.). However, high-fidelity SPH-FSI simulation is computationally extremely expensive—a single simulation can take hours to days, making it unsuitable for direct application in clinical scenarios requiring rapid response, such as parameter sensitivity analysis, What-If scenario exploration, and personalized prediction. Therefore, this invention enters the surrogate model construction stage: utilizing the high-fidelity training data generated by the mechanical simulation layer, a fast approximate mapping from the input parameter space to the QoI output space is constructed using the Sparse Polynomial Chaotic Expansion (SPCE) method, enabling clinical prediction to be completed within milliseconds.

[0069] II. Agent Model Construction Phase: S3. Based on the input parameter dimension and the preset maximum polynomial order, a set of candidate polynomial basis is generated by combining the hyperbolic truncation strategy to construct the design matrix; the sparse polynomial chaotic expansion coefficients are solved by the hierarchical genetic constraint reverse pruning algorithm, and the surrogate model structure of the previous training round is inherited in the iteration using the warm start mechanism. S4. Determine the convergence of the surrogate model based on the relative change of the leave-one-out cross-validation error. If it does not converge, calculate the gradient score of the candidate point using the analytical gradient information of the polynomial chaotic expansion coefficients of the surrogate model. Combine the distance score between the candidate point and the existing samples, and obtain the comprehensive sampling score through adaptive weight mixing. Select the next batch of sampling points that meet the spatial diversity constraints from the candidate pool generated by the low difference sequence, and return to step S2 for a new round of simulation. S5. Continue until the surrogate model converges or reaches the maximum number of iterations, then output the trained surrogate model.

[0070] Based on the high-fidelity training data provided by the mechanics simulation layer, the surrogate model layer constructs a fast approximate mapping from the input parameter space to the QoI output space using the Sparse Polynomial Chaotic Expansion (SPCE) method. The surrogate model actively participates in and optimizes the simulation process through adaptive sampling, convergence determination, and warm-start mechanisms.

[0071] Preferably, in step S3, the truncation exponent of the hyperbolic truncation strategy is determined based on the range of values ​​for the input dimension, and the truncation exponent decreases as the input dimension increases. Specifically, (1) A method for constructing sparse PCE basis based on hyperbolic truncation 1) Mathematical framework for polynomial chaotic expansion.

[0072] for 3D random input vector and scalar output (in (Representing the expensive SPH-FSI simulation model), the polynomial chaotic expansion expresses it as equation (28): (28) In the formula, For multiple indicators, It forms a multivariate orthogonal polynomial basis. The coefficients to be determined are denoted as .

[0073] 2) Hyperbolic truncation sparsity strategy This invention introduces a hyperbolic cutoff index. The base space of the full-order PCE Cut off to equation (29): (29) In the formula, It is the order of the largest polynomial; The smaller the value, the stronger the suppression of higher-order interaction terms.

[0074] The hyperbolic truncation strategy significantly reduces the number of basis units, from all orders. Down to and It exhibits approximately linear growth, and different families of orthogonal polynomials are used for different types of input variables: Uniformly distributed variables ( ): Using Legendre polynomials, normalized to ; Normally distributed variables ( ): Using Hermite polynomials, normalized to the standard normal space.

[0075] The transformation from physical space to normalized space is given by equation (30): (30).

[0076] The hyperbolic truncation sparsity strategy described above introduces a truncation exponent. By compressing the basement space of the full-order PCE, the number of bases is reduced from exponential growth to approximately linear growth, effectively solving the "curse of dimensionality" problem in the high-dimensional parameter space (10-30 dimensions) of cardiovascular systems.

[0077] This invention proposes a Heredity-Constrained Backward Pruning (HCBP) algorithm. Based on the candidate base set generated by hyperbolic truncation, it uses a three-stage process of elastic net initial screening, hierarchical genetic ancestor supplementation, and importance-based backward pruning to forcibly retain all lower-order sub-terms of higher-order terms. This ensures that the final model satisfies both sparsity requirements and the mathematical completeness of polynomial expansion, guaranteeing the physical interpretability of the surrogate model in cardiovascular clinical applications.

[0078] (2) Algorithm for solving sparse PCE coefficients under hierarchical genetic constraints: 1) Mathematical definition of the hierarchical inheritance principle The principle of hierarchical inheritance requires that: if a certain If the order of interaction terms is included in the model, then all of them (obtained by reducing the order in any dimension) are considered. Subterms of order and below must also be retained. Formally, for the base terms... Its ancestor set is defined as shown in equation (31): (31), In the formula, For multiple indicators of the current basis term; Multiple indicators for candidate ancestor terms; Is the i-th variable in The number of times in; For the i-th variable in The number of times in; This means that it holds true for all dimensions i; If it is a positive integer, it represents a "leap reduction" by subtracting 2 / 4 / 6... from the original order; It indicates the exclusion of itself.

[0079] Hierarchical genetic constraints ensure the mathematical completeness of the surrogate model expansion and avoid the physically unreasonable sparse pattern of "having higher-order terms but no corresponding lower-order terms".

[0080] 2) The three-stage solution process of the Heredity-Constrained Backward Pruning (HCBP) algorithm.

[0081] Phase 1: Initial Screening of Elastic Net Paths: Run the regularized path of the elastic net under the standardized design matrix, solve for multiple regularization parameter values, and efficiently calculate the leave-one cross-validation error and information criterion value for the active set corresponding to each regularization parameter through singular value decomposition. Take the union of the active sets of the top several path points with the best information criterion as the initial screening set.

[0082] In the standardized design matrix (Containing only non-intercept columns) the elastic-net regularization path is run as shown in equation (32): (32), In the formula, To the regularization parameter The optimal coefficient vector is as follows; This represents the number of training samples; This is the output vector; For standardized design matrix; The square of the L2 norm of the residual; The L1 ratio; It is an L1 norm. For each... For the corresponding active set, calculate the leave-one-out cross-validation (LOOCV) error and information criterion value. use , Using EBIC), as shown in equations (33) and (34) respectively: (33), (34), In equation (33), The number of bases with non-zero coefficients in the model; This represents the number of training samples; To leave one variance of the cross-validation residuals; This is the logarithm of the residual variance; This is a small sample correction term. When the input dimension... At that time, adopt , exist Based on this, a small sample correction term was added to avoid the problem of model selection bias towards overfitting when the sample size is limited.

[0083] In equation (34), for Adjust parameters; The total number of candidate bases; It is the number of combinations; For high maintenance positive items. When input dimension When adopted . In the classics The total number of candidate bases was increased based on this. The penalty ensures that the correct sparse model can still be selected in high-dimensional scenarios.

[0084] On the regularized path of the elastic network, the LOOCV error and information criterion value are calculated for the active set of each path point. The union of the active sets of the top K path points with the best information criterion (K takes a smaller value in high dimensions) is taken as the initial screening set.

[0085] Contribution of the surrogate model: This stage leverages the computational efficiency of elastic nets to rapidly narrow down the candidate basis space. LOOCV is implemented through an efficient computational formula for SVD decomposition, utilizing... The diagonal element (i.e., the leverage value) and residuals Direct calculation As shown in equation (35): (35), In the formula, For ordinary residuals; This is the leverage value; This is the LOOCV residual.

[0086] The core contribution of this formula is that it eliminates the need to retrain the model for each sample, thus reducing the computational complexity of each model evaluation from... Down to This is one of the key reasons why the HCBP algorithm can operate efficiently in parameter spaces of tens to hundreds of dimensions.

[0087] Phase Two: Ancestor Completion Based on the base name resolution, a hierarchical genetic ancestor relationship graph is constructed. For each active base item in the initial screening set, all its ancestral items obtained by reducing any number of dimensions are added to the candidate set, so that the candidate set satisfies the hierarchical genetic principle - if a certain high-order interaction item is retained, then all its low-order children items are also retained at the same time.

[0088] Phase 3: Importance-based reverse pruning Starting from a hierarchically complete candidate set, the process iteratively identifies leaf bases with no active items, calculates the importance metric for each leaf base, removes the leaf bases with the lowest importance, refits using singular value decomposition and least squares, evaluates the information criterion, and tracks and records the optimal model. Specifically, this includes: Starting from a hierarchically complete candidate set, perform iterative reverse pruning: ① Identify the "pruning leaf bases" of the current active set, that is, the base items (excluding intercept items) whose children are not in the active set. ② Calculate the importance measure of each pruning leaf, as shown in equation (36): (36) In the formula, as base PCE coefficient estimates; as base The vector of values ​​in the design matrix; The standardized norm takes values ​​from the base.

[0089] ③ Remove the leaf basis with the lowest importance; refit the remaining basis using SVD least squares (OLS), and calculate the new LOOCV and information criterion; if the information criterion improves, record the current model as the best model; 6. Repeat steps 1-5 until only the intercept term remains.

[0090] The HCBP algorithm guarantees the mathematical hierarchy completeness and physical interpretability of the surrogate model expansion. Compared with common sparse solution methods such as LARS and OMP, the model obtained by HCBP not only has a lower generalization error (guaranteed by the information criterion), but also has a clear hierarchical structure. The "parent term" of each term in the model exists in the model, which conforms to the inherent mathematical logic of polynomial expansion.

[0091] (3) Warm-Start Model Inheritance Mechanism In iterative adaptive sampling, the surrogate model needs to be retrained after each round of new samples. The warm-start mechanism refers to this: in iterative adaptive sampling, the surrogate model needs to be retrained after each round of new samples. The surrogate model trained in the previous iteration is used as the warm-start model. Its coefficients are refitted onto a new design matrix, and the information criterion is calculated. If the information criterion of the warm-start model is better than the optimal model trained from scratch in the current round, then the warm-start model is adopted as the optimal model for this round, achieving knowledge inheritance across iterations.

[0092] The aforementioned Hierarchical Genetic Constraint Reverse Pruning (HCBP) algorithm, through a three-stage process of elastic net initial screening, ancestor supplementation, and reverse pruning, selects the optimal sparse PCE model that satisfies the hierarchical genetic principle from the candidate basis space generated by hyperbolic truncation—ensuring both the prediction accuracy of the surrogate model and the mathematical completeness and physical interpretability of the polynomial expansion. However, the accuracy of the surrogate model depends not only on the coefficient solving algorithm itself, but also fundamentally on the quality of the training samples and their distribution in the parameter space. The accuracy of the surrogate model depends on the quality of the distribution of training samples in the parameter space—if the samples are concentrated in regions with low information content, the model may produce large errors in critical regions. To address this, this invention further proposes a surrogate model-driven adaptive hybrid sampling strategy. This strategy utilizes the analytical gradient information of the constructed PCE model to actively identify critical regions where the model changes drastically and guide subsequent sampling, maximizing the improvement in model accuracy for each high-fidelity simulation.

[0093] This invention proposes an adaptive hybrid sampling strategy driven by a surrogate model. The hybrid sampling scoring function with adaptive weights consists of two parts: gradient scoring and distance scoring. The gradient scoring is based on the analytical gradient calculation of the polynomial chaotic expansion coefficients of the surrogate model, using the analytical derivative formula of orthogonal polynomials to map from the normalized space back to the physical space through the chain rule. The distance scoring is based on the spatial index structure to calculate the nearest neighbor distance between candidate points and existing training samples. The adaptive weights are dynamically adjusted with the number of iterations, biasing towards spatial exploration in early iterations and gradually increasing the weight of gradient information in later iterations. Specifically, it includes: (1) Hybrid scoring function: This invention proposes a hybrid sampling scoring function that integrates gradient information of the surrogate model and spatial exploration, as shown in equation (37): (37) In the formula, For gradient scoring, the gradient norm of the candidate point in the parameter space is calculated based on the PCE coefficients of the constructed surrogate model. For distance scoring, the nearest neighbor distance from the candidate point to the existing training sample is calculated based on the k-dimensional tree spatial index structure. Candidate points that are far away from the existing samples are selected first to ensure the uniformity of spatial coverage. These are weighting coefficients that are adaptively adjusted with each iteration. Gradient scoring. The gradient in the equation is calculated using the basis-wise analytical differentiation method. The analytical derivative formula of the Legendre / Hermite polynomial is used, combined with the chain rule to map from the normalized space back to the physical space, as shown in equation (38): (38) In the formula, The derivative with respect to the polynomial basis in the normalized space is used to reflect how fast the surrogate model changes in the normalized parameter space. As a chain factor, it maps the gradient of the normalized space back to the physical space. Together, they indicate which regions in the physical space surrogate model changes drastically and require priority sampling. It is the partial derivative with respect to the j-th parameter in the normalized space; This is the normalized value of the j-th parameter; Let j be the physical value of the j-th parameter; For the active base index set; base PCE coefficient; as base The corresponding polynomial; It is the analytic derivative of the polynomial basis with respect to the normalized variables.

[0094] The hybrid scoring function upgrades the sampling process from "blind uniform sampling" to "model-aware intelligent sampling," with the surrogate model directly guiding where to select the next sampling point to maximize information gain. This is the core manifestation of the surrogate model actively participating in and optimizing the mechanical simulation process.

[0095] (2) Batch sampling with diversity constraints Preferably, in step S4, the spatial diversity constraint is as follows: starting from the candidate point with the highest score, candidate points are selected sequentially. If the minimum distance between the candidate point and all selected points is greater than a preset threshold, the candidate point is accepted; otherwise, it is skipped. After accepting a new point, the minimum distance array of all remaining candidate points is updated until a preset batch size is selected.

[0096] When selecting multiple sampling points in batches, a sequential screening strategy is adopted to ensure spatial diversity among samples: 1) All candidate points are sorted in descending order of score; 2) The candidate points with the highest scores are selected sequentially, if their minimum distance to the already selected points is greater than a threshold. ( For the minimum distance ratio, If the distance is the average nearest neighbor distance of the training set, then accept the point; otherwise, skip it; 3) After accepting each new point, update the minimum distance array of all remaining candidate points; 4) Repeat until the batch size is sufficient. .

[0097] (3) Generation of Sobol sequence candidate pool The adaptive sampling candidate pool is generated using Sobol low-discrepancy sequences. Compared to purely random sampling, Sobol sequences have better uniform distribution characteristics (low discrepancy) in the parameter space, ensuring efficient coverage of the parameter space by the candidate pool. Candidate pool size. The number of bases is adaptively determined based on the input dimension and the number of bases.

[0098] Preferably, it also supports surrogate modeling of field variable outputs: For high-dimensional hemodynamic field variable outputs, dimensionality reduction to at least a few principal components is first performed using principal component analysis (PCA). An independent scalar polynomial chaotic expansion surrogate model is then established for each principal component score. During prediction, the prediction results of the surrogate models for each principal component are reconstructed using inverse principal component analysis to reconstruct the complete output field. Specifically, for high-dimensional hemodynamic field variable outputs (such as TAWSS spatial distribution field, OSI spatial distribution field, and vessel wall displacement field), dimensionality reduction to at least a few principal components is first performed using principal component analysis (PCA) (the first 20 are retained by default). (variance), and establish an independent scalar PCE surrogate model for each principal component score; during prediction, perform inverse PCA transformation on the PCE prediction results of each principal component. Reconstruct the complete output field.

[0099] III. Application Phase: S6. Deploy the trained surrogate model to perform rapid hemodynamic output prediction and uncertainty quantification for newly input cardiovascular physiological parameters.

[0100] Preferably, in the application phase, the trained surrogate model supports the following clinical decision support functions: analytically calculating the global sensitivity index of each input parameter to any hemodynamic output based on the polynomial chaotic expansion coefficients, obtaining parameter sensitivity ranking without additional simulation; supporting real-time interactive exploration of the parameter space, dynamically adjusting key parameters, and updating the output prediction in real time by the surrogate model; and providing point estimates and confidence intervals for the predicted output.

[0101] In another aspect, this invention also discloses a cardiovascular fluid-structure interaction digital simulation system based on SPCE, comprising, The workflow contract module is used to define the anatomical location, pathological type, physiological parameter space, hemodynamic output type, and surrogate model training configuration of cardiovascular simulation cases through configuration files; The simulation data generation module is used to generate a sample set in the parameter space. The sample values ​​are automatically injected into the SPH fluid-structure interaction simulation input file through the cardiovascular-specific input parameter mapper, and the simulation is executed to extract the hemodynamic output. The surrogate model training module is used to solve sparse polynomial chaotic expansion surrogate models through hyperbolic truncation basis generation and hierarchical genetic constraint reverse pruning algorithms, and supports warm-start cross-iteration knowledge inheritance. The convergence determination and adaptive sampling module is used to determine the convergence status of the surrogate model based on leave-one-out cross-validation error, and to schedule hybrid adaptive sampling to generate the next batch of sample points when the model has not converged. The clinical deployment module is used for rapid prediction of individualized hemodynamic output, parameter sensitivity analysis, and real-time scenario analysis of patients based on the trained surrogate model.

[0102] The beneficial effects of this invention are as follows: 1. Complete high-fidelity cardiovascular SPH-FSI mechanical simulation capability. This invention systematically integrates non-Newtonian blood rheology (Casson / Carreau-Yasuda model), anisotropic hyperelasticity of the vessel wall (HGO model), bidirectional coupling force between blood and vessel wall, and 3D-0D multi-scale coupled boundary model (RCR / coronary artery specific model) within the meshless SPH framework, realizing cross-scale cardiovascular FSI simulation from blood microrheology to vessel wall macro-deformation. Compared with the Newtonian fluid + linear elastic vessel wall assumptions commonly used in existing SPH hemodynamic simulations, this invention significantly improves the prediction accuracy of hemodynamic indicators such as WSS and OSI in the low shear rate region, while avoiding the mesh distortion and dynamic reconstruction difficulties of traditional mesh methods in large deformation problems. The mechanical simulation layer is executed in parallel on the GPU, and the proxy model layer is executed on the CPU. The GPU-CPU heterogeneous computing architecture fully leverages the computational advantages of each.

[0103] 2. Hyperbolic truncation and hierarchical genetic constraints solve the "curse of dimensionality" in high-dimensional parameter spaces. Addressing the problem of the exponential growth in the number of traditional PCE basis vectors in the cardiovascular parameter space (10-30 dimensions), this invention reduces the number of basis vectors from exponential growth to approximately linear growth through a hyperbolic truncation sparsity strategy. The hierarchical genetic constraint reverse pruning (HCBP) algorithm forcibly retains all lower-order sub-terms of higher-order terms, ensuring the model satisfies the mathematical structure of a polynomial expansion. This makes the surrogate model not only accurate in prediction but also physically interpretable, allowing physicians to understand the independent contributions and interaction effects of each physiological parameter on hemodynamic indicators. Simultaneously, a warm-start mechanism enables cross-iteration knowledge inheritance, accelerating convergence and ensuring model stability.

[0104] 3. Adaptive sampling driven by a surrogate model maximizes information gain. This invention establishes an intelligent sampling mechanism that "actively guides simulation using a surrogate model"—based on the analytical gradient of PCE coefficients, a hybrid sampling strategy automatically identifies and densifies key regions with drastic QoI changes, while also taking into account the overall coverage of the parameter space, significantly reducing the total number of simulations required to achieve the target accuracy.

[0105] 4. Deep Adaptation to Cardiovascular Scenarios and Closed-Loop Clinical Translation. Through eight cardiovascular-specific input parameter mappers and seven types of hemodynamic QoI automatic extractors, a complete closed-loop translation process is achieved, from "patient image data → simulation model construction → surrogate model training → rapid clinical QoI prediction," completing parameter injection and result extraction without manual coding. It supports breakpoint resume training and historical record tracking, adapting to real-world scenarios where simulation tasks may be interrupted in research and clinical settings. 5. Millisecond-level rapid clinical prediction and decision support. The deployed surrogate model achieves a prediction speedup of up to 10. 4 Up to 10 7It supports rapid single-shot prediction, global parameter sensitivity analysis, and real-time What-If interactive exploration, enabling high-fidelity cardiovascular simulations that originally required hours to days to be applied within the clinical decision-making time window.

[0106] 6. Full-field variable proxy modeling capability. Through PCA dimensionality reduction and multi-output PCE joint modeling, this invention is the first to possess the proxy modeling capability to handle full-field variables of cardiovascular SPH-FSI (such as TAWSS spatial distribution field, OSI spatial distribution field, vascular wall displacement field and stress field), which can answer "what is the WSS distribution of the entire vascular segment", which is crucial for assessing the spatial risk distribution of plaques. Attached Figure Description

[0107] Figure 1 This is a diagram of the architecture of the present invention. Detailed Implementation

[0108] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present application.

[0109] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0110] The present invention will now be further described with reference to the accompanying drawings. The following embodiments are only used to illustrate the structure of the present invention more clearly.

[0111] The computing system of the present invention can run on a computer device with the following hardware configuration, and the hardware environment is as follows: Processor: Intel / AMD multi-core CPU + NVIDIA GPU (supports CUDA architecture for SPH emulation acceleration); Storage: DDR4 / DDR5 system memory (≥32GB) and GPU video memory (≥16GB); Storage medium: SSD solid-state drive, used to store the operating system, simulation program, proxy model training data, and model files; Network interface: A network connection that supports remote data transmission and result visualization.

[0112] The training of the surrogate model (HCBP solution, elastic network path, SVD decomposition, etc.) is performed efficiently on the CPU using a numerical computing library, while the SPH simulation is accelerated on the GPU through CUDA parallel processing.

[0113] like Figure 1 As shown, a cardiovascular fluid-structure interaction digital simulation method based on SPCE includes the following steps: Simulation phase: S1. Define the cardiovascular simulation workflow contract, determine the input parameter space and its probability distribution type, and determine the hemodynamic output type; S2. Generate an initial sample set in the input parameter space. Automatically inject the parameter values ​​of each sample into the SPH fluid-structure interaction simulation input file through the cardiovascular-specific input parameter mapper. Perform SPH fluid-structure interaction simulation for cardiovascular applications. Extract the hemodynamic output values ​​corresponding to each sample to form a training dataset. Agent model construction phase: S3. Based on the input parameter dimension and the preset maximum polynomial order, a set of candidate polynomial basis is generated by combining the hyperbolic truncation strategy to construct the design matrix; the sparse polynomial chaotic expansion coefficients are solved by the hierarchical genetic constraint reverse pruning algorithm, and the surrogate model structure of the previous training round is inherited in the iteration using the warm start mechanism. S4. Determine the convergence of the surrogate model based on the relative change of the leave-one-out cross-validation error. If it does not converge, calculate the gradient score of the candidate point using the analytical gradient information of the polynomial chaotic expansion coefficients of the surrogate model. Combine the distance score between the candidate point and the existing samples, and obtain the comprehensive sampling score through adaptive weight mixing. Select the next batch of sampling points that meet the spatial diversity constraints from the candidate pool generated by the low difference sequence, and return to step S2 for a new round of simulation. S5. Continue until the surrogate model converges or reaches the maximum number of iterations, then output the trained surrogate model. Application phase: S6. Deploy the trained surrogate model to perform rapid hemodynamic output prediction and uncertainty quantification for newly input cardiovascular physiological parameters.

[0114] Example 1: Step S1: Workflow Contract Definition and Proxy Model Initialization S1.1 Create a workflow contract configuration file in the simulation case directory to define the cardiovascular simulation scenario: Case identification (simulation type is cardiovascular fluid-structure coupling, anatomical location is coronary artery / aortic arch, pathological type is stenosis / aneurysm / healthy); The input parameter list includes blood rheology parameters (Casson). / Carreau-Yasuda ), HGO hyperelasticity parameters of blood vessel walls ( ) or Mooney-Rivlin parameters ( ), RCR / coronary artery lumped parameters ( or ), cardiac cycle and blood flow parameters ( ), geometric parameters (stenosis rate, eccentricity), distribution type (uniform / normal / lognormal) and physiological range of each parameter (based on population statistics from the literature); Output hemodynamic QoI type (hemodynamic scalar type: Mean WSS, hemodynamic field variable types: TAWSS field, OSI field, vessel wall displacement type, vessel wall stress field type, etc. Default values ​​for hyperparameters used in surrogate model training (initial number of samples, maximum PCE order, hyperbolic truncation exponent) (e.g., PCA principal component count).

[0115] S1.2 Parse the WorkflowContract and construct the distribution matrix (dimension d×3), where each row contains [distribution type code, parameter 1, parameter 2].

[0116] S1.3 Initialize the HCBP solver and adaptive hybrid sampler for the surrogate model.

[0117] Step S2: Simulation Phase – Initial Sample Generation and SPH-FSI Simulation Execution.

[0118] The S2.1 surrogate model is generated in the parameter space via Latin hypercube sampling (LHS). 1 initial sample point.

[0119] For each sample point, the S2.2 proxy model calls the corresponding input parameter mapper (mutator) to automatically modify the SPH simulation input file (XML format) and write the sample values ​​into the corresponding configuration items.

[0120] S2.3 Perform cardiovascular SPH-FSI simulation. The calculation process is shown in formulas (4) to (27): (1) SPH fluid dynamics solution (blood domain): Density evolution is as shown in equation (4): ; The particle-by-particle shear rate is calculated as shown in equation (10): Approximated by the SPH velocity gradient get; Non-Newtonian apparent viscosity update: based on the selected blood rheology model (Casson or Carreau-Yasuda), by... calculate See equations (8)-(9); The momentum equation is solved (including non-Newtonian viscous forces, pressure gradient forces, and fluid-structure interaction forces), see formula (5); The Tait-Murnaghan equation of state updates the pressure, see formula (6).

[0121] (2) SPH solid mechanics solution (vascular wall domain): Fully Lagrangian Framework: Deformation Gradient The approximate calculation is performed using the reference configuration SPH, as shown in formula (16). Right Cauchy-Green deformable tensor and its invariants ( See formula (14); Calculate the strain energy based on the constitutive model of the blood vessel wall specified in the WorkflowContract (HGO anisotropic hyperelastic or Mooney-Rivlin isotropic hyperelastic). and PK2 stress See formula (13); The solution to the solid particle acceleration equation is shown in formula (15).

[0122] (3) Calculation of blood-vascular wall fluid-structure interaction force: Interface particle recognition (automatic determination through support for domain overlap). Morris viscous coupling force, using the non-Newtonian apparent viscosity of fluid particles. See formula (18); Symmetrical pressure coupling force ensures the conservation of interface momentum, see formula (19).

[0123] (4) 3D-0D multi-scale coupling (exit boundary): Instantaneous volumetric flow rate was extracted at each SPH outlet section. ; Based on the 0D model type (RCR, coronary artery, or pure resistance) specified in the WorkflowContract, Drive 0D state variable updates; For the coronary artery model, the current time-varying intramyocardial pressure is interpolated based on the cardiac cycle phase. ; The outlet pressure obtained by solving the 0D model Feedback to the particles at the SPH outlet boundary, see formula (26); Substep time integration (the step size inside the 0D model can be 1 / N of the SPH step size to ensure coupling stability).

[0124] (5) Online calculation of hemodynamic QoI: Calculate the WSS vector of the wall SPH particles at each SPH time step or a specified output step. See formula (21); Accumulated time integrals for TAWSS and OSI: and See formulas (22) and (23); Across narrow pressure gradient Real-time monitoring.

[0125] (6) Time progresses to steady state or preset number of cardiac cycles (cardiovascular simulation usually requires 3-5 cardiac cycles to eliminate the initial transient, approximately per cycle). (SPH time steps, adjusted according to specific cases).

[0126] The S2.4 surrogate model extracts the QoI values ​​of interest (scalar or principal component scores after PCA dimensionality reduction) from the simulation output file.

[0127] Step S3: Proxy Model Construction Phase – Hyperbolic Phase and HCBP Algorithm S3.1 Basis Generation: The surrogate model is based on the input dimension. and maximum order Combined with hyperbolic truncation index Generate a set of candidate polynomial basis functions. For high-dimensional inputs ( The proxy model automatically lowers the upper limit of the interaction order and reduces... The value controls the number of bases. Different families of orthogonal polynomials are used for different types of input variables: Legendre polynomials are used for uniform distributions; Hermite polynomials are used for normal distributions.

[0128] S3.2 Design Matrix Construction: For each sample, the surrogate model calculates the values ​​of each basis in the normalized input space to construct the design matrix. .

[0129] S3.3 HCBP Sparse Solution: Three-stage sparse coefficient solution for the surrogate model: Phase 1: Elastic Network Path ( 100 Candidate active set paths are generated on the standardized design matrix. The LOOCV and information criteria (AICc / EBIC) of each path point are efficiently calculated using SVD. The active set of the top K path points with the best information criteria is then taken as the union. Phase 2: Parse the base names to construct a hierarchical genetic ancestor relationship graph, and supplement all ancestor entries of each base in the initial screening set to the candidate set; Phase 3: Starting from the hierarchical candidate set, iteratively remove the leaf basis with the lowest importance. After each removal, refit the model using singular value decomposition least squares and evaluate the information criterion, and track and record the best model. If the current iteration has a warm-start model from the previous round, refit it on the new design matrix using OLS and participate in the information criterion comparison, and select the best one to retain.

[0130] Warm start mechanism: When there is a surrogate model that has been trained in the previous iteration, it is used as a warm start model. Its coefficients are refitted on the new design matrix and the information criterion is calculated. If it is better than the best model trained from scratch in the current round, it is selected and retained.

[0131] S3.4 Model Evaluation: The surrogate model records the LOOCV error, PCE mean and standard deviation, and number of active bases, and writes them into the history.

[0132] Step S4: Proxy Model Construction Phase – Convergence Determination and Adaptive Sampling S4.1 Convergence Criterion: The convergence of the surrogate model is determined by the relative change in the Leave-One-out Cross-Validation (LOOCV) error. If the historical record length is ≥11, the mean of the relative change of the most recent 10 LOOCVs is calculated. If it is less than tol ( ), marked as converged; If the maximum number of iterations is reached, mark it as having reached the maximum number of iterations; Otherwise, continue iterating.

[0133] S4.2 If convergence is not achieved, the surrogate model performs adaptive sampling: Update Mixed Weights ; For each candidate point in the candidate pool (generated by Sobol sequence), calculate the gradient score (analytical gradient of the PCE coefficients of the surrogate model) and the distance score (nearest neighbor distance of the k-dimensional tree space index structure). Calculate mixed score ; Sequential selection from high-scoring candidate points A point that satisfies the minimum distance constraint; Remove selected points from the candidate pool until the preset batch size is reached.

[0134] S4.3 The proxy model submits the new sampling points to step S2 for a new round of SPH simulation, and then returns to step S3.

[0135] Step S5: Agent Model Construction Phase -- Model Output The trained surrogate model (HCBP instance, containing key attributes such as coefficient vector, basis mapping table and distribution matrix) is persistently stored in serialized file format.

[0136] S5.2 Post-deployment agent model prediction process: Receive a new input parameter vector (physical space); Normalize to standard space; Construct the design matrix of the corresponding basis based on the basis mapping table (only construct the columns corresponding to the active basis); Calculate the predicted value ; For multi-output / field variable models, perform inverse PCA transformation to reconstruct the complete output.

[0137] The computational complexity of the S5.3 surrogate model prediction is... Compared to a complete SPH simulation ( Particle × (Time step), acceleration ratio can reach times.

[0138] Additionally, the multi-output field variable proxy modeling section is optional: For field variables QoI (such as displacement field and pressure field), the surrogate model first reduces the dimensionality of the output of the training set through PCA.

[0139] The surrogate model retains the number of principal components (20 by default) of the front-field variables in the PCA.

[0140] The surrogate model establishes an independent single-output PCE surrogate model for each principal component score.

[0141] During prediction, the surrogate model predicts each principal component separately, and then performs an inverse PCA transformation (PCA). Reconstruct the complete output field.

[0142] Step S6: Application Phase – Clinical Deployment and Decision Support S6.1 Proxy Model Serialization Storage: The trained proxy model is persistently stored in a serialized file format. A cardiovascular case library is established according to anatomical location (coronary artery / aortic arch, etc.) and pathological type (stenosis / aneurysm, etc.), supporting retrieval and reuse by patient characteristics.

[0143] S6.2 Single-shot rapid prediction: Clinical users input the patient's individualized physiological parameter vector. (e.g., stenosis rate = 70%, systolic blood pressure = 140 mmHg, heart rate = 72 bpm, HCT = 42%, etc.), the surrogate model returns the result in milliseconds: Scalar QoI point estimation and 95% confidence intervals (e.g., across narrow pressure steps) mmHg); Spatial distribution of field variable QoI (TAWSS field, OSI field, and wall displacement field reconstructed by PCA inverse transformation).

[0144] S6.3 Parameter Sensitivity Analysis: Directly Calculate the Total Sobol Index Using the Analytical Properties of the PCE Coefficients It generates a global sensitivity ranking without additional simulation, completing the process in seconds. Clinical significance: It visually demonstrates the impact of "vascular stiffness vs. peripheral impedance vs. degree of stenosis" on... The relative importance of (determining whether interventional treatment is necessary).

[0145] S6.4 What-If Scenario Analysis: The surrogate model supports real-time interactive exploration of the parameter space. Clinical users can adjust key parameters (such as simulating stenosis progression from 50% to 80%), and the surrogate model updates the QoI prediction in real time to assess the risk of disease progression and the timing of intervention.

[0146] S6.5 Surgical outcome prediction: By modifying geometric parameters (such as reducing the stenosis rate to 0% after stent implantation) and boundary conditions, the surrogate model can quickly predict the postoperative hemodynamic status and assist in the optimization decision-making of surgical plans (such as stent length / diameter selection and bypass anastomosis location).

[0147] Example 2: This invention also provides a cardiovascular fluid-structure interaction digital simulation system based on SPCE, comprising the following modules: Workflow Contract Module: Used to define the anatomical location, pathological type, physiological parameter space, hemodynamic output type, and surrogate model training configuration for cardiovascular simulation cases through configuration files; Simulation data generation module: used to generate sample sets in parameter space, automatically inject sample values ​​into SPH fluid-structure interaction simulation input file through cardiovascular-specific input parameter mapper, execute simulation and extract hemodynamic output; Proxy model training module: used to solve sparse polynomial chaotic expansion Proxy models through hyperbolic truncated basis generation and hierarchical genetic constraint reverse pruning algorithm, supporting warm-start cross-iteration knowledge inheritance; Convergence determination and adaptive sampling module: used to determine the convergence status of the surrogate model based on leave-one-out cross-validation error, and to schedule hybrid adaptive sampling to generate the next batch of sample points when convergence has not been achieved; Clinical deployment module: used for rapid prediction of individualized hemodynamic output, parameter sensitivity analysis, and real-time scenario analysis of patients based on the trained surrogate model.

[0148] Example 3: The present invention also provides a computer device, including a memory and a processor, wherein the processor is used to run a program stored in the memory, and the program executes the cardiovascular fluid-structure interaction digital simulation method described in any of the above embodiments. For the specific hardware configuration of the computer device, please refer to the description in Section 1 of this specific embodiment.

[0149] The present invention also provides a non-volatile storage medium storing a program, wherein the program controls the device containing the non-volatile storage medium to execute the cardiovascular fluid-structure interaction digital simulation method described in any of the above embodiments when the program is executed.

[0150] To facilitate understanding of this invention, the following explains the main English abbreviations that appear in the text and their meanings:

[0151] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A digital simulation method for cardiovascular fluid-structure interaction based on SPCE, characterized in that: Includes the following steps: Simulation phase: S1. Define the cardiovascular simulation workflow contract, determine the input parameter space and its probability distribution type, and determine the hemodynamic output type; S2. Generate an initial sample set in the input parameter space. Automatically inject the parameter values ​​of each sample into the SPH fluid-structure interaction simulation input file through the cardiovascular-specific input parameter mapper. Perform SPH fluid-structure interaction simulation for cardiovascular applications. Extract the hemodynamic output values ​​corresponding to each sample to form a training dataset. Agent model construction phase: S3. Based on the input parameter dimension and the preset maximum polynomial order, a set of candidate polynomial basis is generated by combining the hyperbolic truncation strategy to construct the design matrix; the sparse polynomial chaotic expansion coefficients are solved by the hierarchical genetic constraint reverse pruning algorithm, and the surrogate model structure of the previous training round is inherited in the iteration using the warm start mechanism. S4. Determine the convergence of the surrogate model based on the relative change of the leave-one-out cross-validation error. If it does not converge, calculate the gradient score of the candidate point using the analytical gradient information of the polynomial chaotic expansion coefficients of the surrogate model. Combine the distance score between the candidate point and the existing samples, obtain the comprehensive sampling score through adaptive weight mixing, select the next batch of sampling points that meet the spatial diversity constraints from the candidate pool generated by the low difference sequence, and return to step S2 for a new round of simulation. S5. Continue until the surrogate model converges or reaches the maximum number of iterations, then output the trained surrogate model. Application phase: S6. Deploy the trained surrogate model to perform rapid hemodynamic output prediction and uncertainty quantification for newly input cardiovascular physiological parameters.

2. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: In step S1, the input parameter space includes five types of parameters, and the output quantity type includes seven types: The five types of parameters in the input parameter space and their probability distribution types are as follows: (1) Blood rheological parameters, including Casson model yield stress and asymptotic viscosity, or Carreau-Yasuda model zero shear viscosity, asymptotic viscosity, relaxation time, transition parameters and power law exponent, are uniformly distributed and the range of values ​​is based on population statistics in the literature. (2) Blood vessel wall material parameters, including fiber stiffness and fiber angle of the HGO model, or material constants of the Mooney-Rivlin model, are normally distributed, and the mean and standard deviation are taken from the biaxial tensile test data of human arterial wall in vitro. (3) 3D-0D coupled lumped parameters, including proximal impedance, distal impedance and compliance of the RCR model, or intramyocardial pressure-related parameters of the coronary artery model, are log-normally distributed; (4) Cardiac cycle and blood flow parameters, including peak systolic flow, cardiac cycle and systolic percentage, are set according to the clinical measurement range; (5) Vascular geometric parameters, including stenosis rate, stenosis offset, radius of curvature and bifurcation angle, are set according to the clinical measurement range; The seven types of output quantities are: (1) hemodynamic scalar; (2) hemodynamic field variables; (3) vessel wall displacement field; (4) vessel wall stress field; (5) velocity profile; (6) pressure waveform; and (7) solid domain final / transient snapshot field variables.

3. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: In step S2, the cardiovascular-specific input parameter mapper supports at least one of the following types: (1) an inlet waveform amplitude mapper for scaling the inlet blood flow waveform amplitude; (2) a cardiac cycle mapper for setting cardiac cycle parameters and automatically calculating the simulation time steps; (3) an HGO anisotropic hyperelastic material parameter mapper for writing fiber stiffness, fiber nonlinearity, fiber angle, and dispersion parameters into the solid material property configuration; (4) a Mooney-Rivlin isotropic hyperelastic material parameter mapper for writing material constants into the solid material property configuration; (5) a blood non-Newtonian rheology parameter mapper for writing Casson model or Carreau-Yasuda model parameters into the fluid property configuration; (6) a 3D-0D coupled lumped parameter mapper for writing lumped parameters of the RCR model or coronary artery model into the outlet boundary condition configuration; (7) a stenosis geometry parameter mapper for mapping stenosis rate, eccentricity, and stenosis length to the vascular geometry generation script; and (8) a general XML attribute mapper for locating and modifying arbitrary simulation input parameters through element paths.

4. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: In step S2, the SPH fluid-structure interaction simulation includes: (1) non-Newtonian blood rheology modeling, where the apparent viscosity of blood is dynamically updated particle by particle according to the local shear rate using the Casson model or the Carreau-Yasuda model; (2) anisotropic hyperelastic solid mechanics modeling of the blood vessel wall, using the fully Lagrangian SPH solid mechanics framework, supporting the Holzapfel-Gasser-Ogden anisotropic hyperelastic constitutive model; (3) calculation of bidirectional coupling force between blood and blood vessel wall, where the bidirectional coupling force includes viscous coupling force and pressure coupling force; (4) three-dimensional computational domain outlet coupling zero-dimensional lumped parameter boundary model, where the zero-dimensional lumped parameter boundary model includes the RCR three-element model and the coronary artery-specific model, where the coronary artery-specific model introduces time-varying intramyocardial pressure to characterize the squeezing effect of myocardial systole on coronary microvessels.

5. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: In step S3, The truncation exponent of the hyperbolic truncation strategy is determined based on the range of values ​​for the input dimension, and the truncation exponent decreases as the input dimension increases. The process of the hierarchical genetic constraint reverse pruning algorithm is as follows: (1) Initial screening of elastic network paths: Run the elastic network regularized path on the standardized design matrix, solve on multiple regularization parameter values, efficiently calculate the leave-one cross-validation error and information criterion value for the active set corresponding to each regularization parameter through singular value decomposition, and take the union of the active sets of the top several path points with the best information criterion as the initial screening set; (2) Hierarchical genetic ancestor supplementation: Based on the base name resolution, a hierarchical genetic ancestor relationship graph is constructed. For each active base item in the initial screening set, all its ancestor items obtained by reducing any dimension number of times are supplemented to the candidate set so that the candidate set satisfies the hierarchical genetic principle - if a certain high-order interaction item is retained, then all its low-order sub-items are also retained at the same time. (3) Importance-based reverse pruning: Starting from a hierarchical candidate set, iteratively identify leaf bases without active sub-items, calculate the importance metric of each leaf base, remove the leaf base with the lowest importance, refit and evaluate the information criterion through singular value decomposition least squares, and track and record the optimal model. The warm-start mechanism refers to: using the surrogate model trained in the previous iteration as the warm-start model, refitting its coefficients on the new design matrix and calculating the information criterion; if the information criterion of the warm-start model is better than the optimal model trained from scratch in the current round, then the warm-start model is adopted as the optimal model for this round, thereby realizing knowledge inheritance across iterations.

6. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: In step S4 The criterion for convergence of the surrogate model is: the mean of the error variation is less than the preset tolerance; The adaptive weighted hybrid sampling scoring function consists of two parts: gradient scoring and distance scoring. The gradient scoring is based on the analytical gradient calculation of the polynomial chaotic expansion coefficients of the surrogate model. The analytical derivative formula of the orthogonal polynomial is used to map from the normalized space back to the physical space through the chain rule. The distance score is calculated based on the spatial index structure to determine the nearest neighbor distance between the candidate point and the existing training samples; the adaptive weight is dynamically adjusted with the number of iterations.

7. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: In step S4, the spatial diversity constraint is as follows: starting from the candidate point with the highest score, candidate points are selected sequentially. If the minimum distance between the candidate point and all selected points is greater than a preset threshold, the candidate point is accepted; otherwise, it is skipped. After accepting a new point, the minimum distance array of all remaining candidate points is updated until a preset batch size is selected.

8. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: It also supports proxy modeling of field variable outputs: for high-dimensional hemodynamic field variable outputs, the dimensionality is first reduced to at least a few principal components through principal component analysis, and an independent scalar polynomial chaotic expansion proxy model is established for each principal component score; during prediction, the prediction results of the proxy models of each principal component are reconstructed by principal component analysis inverse transformation to reconstruct the complete output field.

9. The cardiovascular fluid-structure interaction numerical simulation method based on SPCE according to claim 1, characterized in that: In the application phase, the trained surrogate model supports the following clinical decision support functions: it can analyze the global sensitivity index of each input parameter to any hemodynamic output based on the polynomial chaos expansion coefficients, and obtain the parameter sensitivity ranking without additional simulation. It supports real-time interactive exploration of the parameter space, dynamic adjustment of key parameters, and real-time updates of output predictions by the proxy model; Provides point estimates and confidence intervals for the predicted output.

10. A cardiovascular fluid-structure interaction digital simulation system based on SPCE, which utilizes the simulation method described in any of the preceding claims, characterized in that: include, The workflow contract module is used to define the anatomical location, pathological type, physiological parameter space, hemodynamic output type, and surrogate model training configuration of cardiovascular simulation cases through configuration files; The simulation data generation module is used to generate a sample set in the parameter space. The sample values ​​are automatically injected into the SPH fluid-structure interaction simulation input file through the cardiovascular-specific input parameter mapper, and the simulation is executed to extract the hemodynamic output. The surrogate model training module is used to solve sparse polynomial chaotic expansion surrogate models through hyperbolic truncation basis generation and hierarchical genetic constraint reverse pruning algorithms, and supports warm-start cross-iteration knowledge inheritance. The convergence determination and adaptive sampling module is used to determine the convergence status of the surrogate model based on leave-one-out cross-validation error, and to schedule hybrid adaptive sampling to generate the next batch of sample points when the model has not converged. The clinical deployment module is used for rapid prediction of individualized hemodynamic output, parameter sensitivity analysis, and real-time scenario analysis of patients based on the trained surrogate model.

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