A proxy model and construction method for vascular network outlet boundary conditions

Abstract

The present invention provides a proxy model and construction method for the outlet boundary conditions of a vascular network, which are applied to the field of data processing technology. The present application performs data compression and spatiotemporal normalization processing on multi-scale vascular feature data to generate compressed and normalized data, which is composed of the dimensionality reduction results of an autoencoder, spatiotemporal normalization relationships, and data mixing and enhancement results; processes the compressed and normalized data to generate target proxy model parameters based on DeepONet; processes the target proxy model parameters to generate proxy model output data; processes the proxy model output data and high-dimensional and variable data of the pipeline network to generate an outlet boundary condition proxy model based on symbolic regression, wherein the outlet boundary condition proxy model is used to characterize the outlet boundary conditions of the vascular network; and processes the outlet boundary condition proxy model, fitness evaluation, and genetic operation strategy based on a genetic algorithm to generate a target outlet boundary condition proxy model and verification results.

Description

Technical Field

[0001] The present invention relates to the field of data processing technology, and in particular to a proxy model of a vascular network outlet boundary condition and a construction method thereof. Background Art

[0002] Since the laminar flow model of pulmonary capillary blood flow was introduced to solve blood circulation problems, fluid dynamics methods have gradually become an important solution to hemodynamic problems. With the increase in computing power, computational fluid dynamics (CFD) has brought new development opportunities for the diagnosis and prevention of blood diseases, the design and optimization of medical devices, and the simulation and evaluation of surgical procedures. However, the choice of boundary conditions in the computational model has a significant impact on the accuracy of the results.

[0003] In the field of hemodynamics, inlet boundary conditions are widely accepted to utilize patient-specific physiological blood flow waveforms, but clear guidelines for setting outlet boundary conditions have yet to be established. Traditional models such as zero-pressure outlet, constant-pressure outlet, Murray's law, split method, and Windkessel model have significant shortcomings. For example, the constant-pressure outlet has large errors, Murray's law and split method ignore vascular geometric heterogeneity and dynamic regulatory mechanisms, and Windkessel model parameter calibration is complex and relies on universal values, resulting in low simulation accuracy. Therefore, high-precision outlet boundary condition models are urgently needed to improve the credibility and practicality of hemodynamic simulations.

[0004] It should be noted that the information disclosed in the above background technology section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute prior art known to ordinary technicians in the field. Summary of the Invention

[0005] The purpose of this application is to provide a proxy model and construction method for the boundary conditions of the vascular network outlet, which at least to some extent overcomes the problems existing in the prior art. Through multi-scale data fusion, DeepONet operator learning and symbolic regression analysis, a multi-scale vascular feature database is constructed, and compressed normalized data is generated through dimensionality reduction and normalization. The flow / pressure prediction value is obtained by DeepONet processing. After the features are fused, symbolic regression optimization is performed to obtain a high-precision model, and the prediction speed is increased by 1000 times compared with full-order CFD.

[0006] Other features and advantages of the present application will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0007] According to one aspect of the present application, a method for constructing an agent model of the boundary conditions of a vascular network outlet is provided, comprising: constructing a multi-scale vascular feature database, wherein the multi-scale vascular feature database includes large / small vessel modeling data and capillary modeling data, wherein the large / small vessel modeling data includes vessel diameter, bifurcation angle, wall shear stress and flow characteristic parameters, and the capillary modeling data includes inter-particle force and red blood cell membrane flexibility characteristic information; performing data compression and spatiotemporal normalization processing on the multi-scale vascular feature data to generate compressed normalized data, wherein the compressed normalized data is obtained by dimensionality reduction results of an automatic encoder, The spatiotemporal normalization relationship, data mixing and enhancement results are composed; the compressed and normalized data are processed to generate the target proxy model parameters based on DeepONet; the target proxy model parameters are processed to generate the proxy model output data; the proxy model output data and the high-dimensional and variable data of the pipeline network are processed to generate the outlet boundary condition proxy model based on symbolic regression, wherein the outlet boundary condition proxy model is used to characterize the outlet boundary conditions of the vascular network; the outlet boundary condition proxy model, fitness evaluation and genetic operation strategy are processed based on the genetic algorithm to generate the target outlet boundary condition proxy model and verification results.

[0008] Another aspect of the present application is a proxy model construction device for the boundary conditions of the vascular network outlet, characterized in that it includes: an acquisition module for constructing a multi-scale vascular feature database, wherein the multi-scale vascular feature database includes large / small vessel modeling data and capillary modeling data, the large / small vessel modeling data includes vessel diameter, bifurcation angle, wall shear stress and flow characteristic parameters, and the capillary modeling data includes inter-particle force and red blood cell membrane flexibility characteristic information; a processing module for compressing the multi-scale vascular feature data and performing spatiotemporal normalization processing to generate compressed normalized data, wherein the compressed normalized data is automatically The method is composed of the dimensionality reduction results of the dynamic encoder, the spatiotemporal normalization relationship, and the data mixing and enhancement results; the compressed and normalized data is processed to generate the target proxy model parameters based on DeepONet; the target proxy model parameters are processed to generate the proxy model output data; the proxy model output data and the high-dimensional and variable data of the pipeline network are processed to generate the outlet boundary condition proxy model based on symbolic regression, wherein the outlet boundary condition proxy model is used to characterize the outlet boundary conditions of the vascular network; the outlet boundary condition proxy model, fitness evaluation and genetic operation strategy are processed based on the genetic algorithm to generate the target outlet boundary condition proxy model and verification results.

[0009] This application provides a proxy model and construction method for vascular network outlet boundary conditions. The server uses multi-scale data fusion, DeepONet operator learning, and symbolic regression analysis to address the limited accuracy and computational complexity of traditional models. A multi-scale vascular feature database is constructed, integrating CFD data (diameter, bifurcation angle, etc.) of large and small vessels with DPD data (interparticle forces, etc.) of capillaries. Using autoencoder dimensionality reduction, spatiotemporal normalization (e.g., Reynolds number Re = 7950 to characterize turbulent flow characteristics), and data augmentation, compressed normalized data is generated, retaining 95% of key features while compressing the data size to 6.4%.

[0010] DeepONet is used to process compressed data. The branch network extracts high-dimensional vectors of vascular characteristics. The backbone network combines physical conservation constraints to generate boundary condition parameters. After denormalization and spatiotemporal interpolation, flow / pressure prediction values ​​are obtained with an error within 10%. Then, the hemodynamic characteristics are fused with the network topology encoding features, and a genetic algorithm-driven symbolic regression is used to generate candidate expressions. After Pareto front optimization, the model with an error ≤ 10% and the fewest nodes is selected. Clinical verification shows that the error is within 10%. This method breaks through the limitations of the traditional Windkessel model that relies on fixed parameters, achieving efficient modeling under the fusion of multi-scale physiological characteristics and physical constraints. The prediction speed is 1000 times faster than full-order CFD, providing a high-precision interpretable model for hemodynamic simulation and clinical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Figure 1 A flowchart showing a method for constructing a proxy model of a vascular network outlet boundary condition provided by an embodiment of the present application;

[0012] Figure 2 The figure shows the basic framework of the DeepONet model provided in one embodiment of the present application;

[0013] Figure 3 A schematic structural diagram of a proxy model construction device for a vascular network outlet boundary condition provided in one embodiment of the present application is shown. DETAILED DESCRIPTION

[0014] The preferred embodiments of the present invention are described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention and are not intended to limit the present invention. Figure 1 To describe the proxy model construction method of the vascular network outlet boundary condition according to the exemplary embodiment of the present application. In one embodiment, the present application also proposes a proxy model and construction method of the vascular network outlet boundary condition, such as Figure 1 Shown, including:

[0015] S101, construct a multi-scale vascular feature database.

[0016] The multi-scale vascular feature database includes large / small blood vessel modeling data and capillary modeling data. The large / small blood vessel modeling data includes blood vessel diameter, bifurcation angle, wall shear stress and flow characteristic parameters, and the capillary modeling data includes inter-particle force and red blood cell membrane flexibility characteristic information.

[0017] In one embodiment, the calculation of blood vessel diameter and hemodynamic parameters is as follows: aortic diameter: the diameter of a certain section of the descending aorta is D=8mm, and the diameter of the branch artery is d=3mm (which is consistent with the physiological range of the human aortic branch). Blood flow velocity is calculated according to the continuity equation ,in is the cross-sectional area of ​​the blood vessel. Assume that the aortic flow rate Q = 500 ml / min and the aortic flow velocity , branch artery flow , it can be seen that the reduction in diameter leads to a significant increase in flow velocity.

[0018] Pressure distribution effects, based on Bernoulli's equation , aortic pressure Branch artery pressure satisfy: , substituting ρ=1050kg / m³, we can get the pressure difference of approximately , indicating that the change in diameter directly affects the local pressure gradient. The following is an example of the calculation of bifurcation angle and blood flow distribution. The blood flow distribution at bifurcation angle θ = 60° is calculated using Murray's law. , the main blood vessel diameter D = 8mm, the two branches have diameters d1 = 5mm and d2 = 3mm respectively, and the flow distribution ratio is , that is, when the main flow Q=500ml / min, the branch flow is approximately Q1≈398ml / min and Q2≈102ml / min.

[0019] Wall shear stress (WSS) calculation, WSS calculation formula: , where μ is the blood viscosity (take ), is the wall velocity gradient. In the near-wall region with a bifurcation angle of 60°, the velocity gradient is assumed to be ,but: WSS < 1Pa is associated with the susceptibility of atherosclerosis, and 2.5Pa is within the normal physiological range (1~4Pa).

[0020] Flow characteristic parameters and pulsating blood flow modeling, the flow pulsation example within the cardiac cycle is as follows, setting a cardiac cycle T = 0.8s, the maximum flow =500ml / min (systolic period), minimum flow (Diastole), flow pulsation coefficient , reflecting the intensity of blood flow pulsation. The Reynolds number (Re) calculation process is as follows: characteristic length L = D = 8mm, average flow velocity .but The results show that the aortic blood flow is in the turbulent transition region (Re>2000), and the unsteady flow effect needs to be considered. The control equation and sampling strategy example, the Navier-Stokes equation is applied as follows, and the incompressible continuity equation is , the momentum equation is Spatial sampling extracts velocity and pressure data at equal intervals of Δx = 0.1D = 0.8 mm along the vascular axis to ensure that boundary layer flow details are captured. A temporal sampling strategy uses 20 phase points (Δt = T / 20 = 0.04 s) within the pulsation cycle to record transient field data, such as flow field parameters at the systolic peak (t = 0.2 s) and diastolic trough (t = 0.6 s), for constructing dynamic boundary conditions.

[0021] The interparticle forces are modeled using a spring network for the red blood cell membrane and a DPD force field for the plasma particles. The dissipative particle dynamics (DPD) model defines the interparticle force as: , where the conservative force , dissipative force , random force , is the weight function, 、 is the force coefficient. Red blood cell modeling, through the bond potential energy and angular potential energy Construct the red blood cell membrane flexibility feature, where r is the actual length of the bond, is the equilibrium length of the bond, is the bond potential energy parameter, which is used to describe the deviation of the actual length of the bond from the equilibrium length of the bond The elastic stiffness when is the actual angle, For the balance angle, is the angle potential energy parameter, which is used to describe the deviation of the actual angle from the equilibrium angle The degree of rigidity at the time of deformation was calculated. For spatial statistics, the average velocity and pressure drop of each microelement (10×10×10μm3) were calculated. For temporal statistics, data were collected every 104 DPD step (Δt=0.1τ), covering the entire red blood cell deformation cycle.

[0022] S102 , performing data compression and spatiotemporal normalization processing on the multi-scale vascular feature data to generate compressed and normalized data.

[0023] In one embodiment, the multi-scale vascular feature data is subjected to an autoencoder dimensionality reduction process to generate an autoencoder dimensionality reduction result. The original multi-scale vascular feature data contains a 5-dimensional feature vector ,in is the velocity component, p is the pressure, is the wall shear stress, Q is the flow rate. The encoder structure is used to reduce the dimension to 32 dimensions: the input layer of the encoder network is 128 neurons, the hidden layer is 32 neurons, and the weight matrix 、 , the activation function is ReLU. After encoding a certain section of aorta data, the high-dimensional feature vector can be expressed as ,in The activation function is . After dimensionality reduction, the data retains more than 95% of key features (such as the correlation between flow velocity and pressure), and the data size is compressed to 6.4% of the original size.

[0024] The spatiotemporal normalization relationship is constructed and processed for the multi-scale vascular feature data to generate the spatiotemporal normalization relationship; the spatiotemporal normalization relationship is constructed and the Reynolds number (Re) is calculated: for large blood vessels (characteristic length , average flow rate , blood density , viscosity . This value indicates that the blood flow is in the turbulent transition zone and the non-steady-state effect needs to be considered. The multi-scale vascular feature data is mixed and enhanced to generate data mixing and enhancement results. Trapezoidal mixing weights are constructed to define time normalization parameters. ,when When the macro-dominant weight , CFD data accounts for a higher proportion; when When , the weight transitions linearly to 0.5; when When the micro-dominant weight , DPD data accounts for a higher proportion.

[0025] Apply +10% perturbation to the blood vessel diameter D=8mm to generate Virtual sample of bifurcation angle Apply -5% perturbation, generating The final dataset was expanded from 10,000 samples to 100,000 samples, covering the physiological range of tube diameters 3-10 mm and bifurcation angles 30°-90°. Based on the dimensionality reduction results of the autoencoder, the spatiotemporal normalization relationship, and the data mixing and enhancement results, a comprehensive process was performed to generate compressed normalized data. The 32-dimensional features after dimensionality reduction and the spatiotemporal normalization parameters were used to generate the compressed normalized data. And the enhanced samples are fused: feature concatenation, each sample is represented as , forming a new eigenvector. Consistency check, through the mass conservation equation Verify the physical rationality of the normalized data. For example, the flow of a bifurcated vessel must meet the following requirements after normalization: , with the error controlled within 10%. The resulting compressed normalized data not only retains key hemodynamic features (such as the velocity-pressure coupling relationship), but also eliminates scale differences through spatiotemporal normalization, providing a unified input format for subsequent DeepONet modeling.

[0026] S103: Process the compressed and normalized data and generate target proxy model parameters based on DeepONet.

[0027] In one embodiment, the discrete sampling values ​​of the vascular characteristic function in the compressed and normalized data are processed by a branch network to generate a high-dimensional vector of vascular characteristics and network weight parameters. The compressed and normalized data contains the distribution of vascular diameters. and bifurcation angle sequence The discrete sampling values ​​(such as 100 sampling points along the vascular axis) are input into the branch network (BranchNet): the network architecture has a 32-dimensional input layer (the result of the automatic encoder dimensionality reduction), a 128-dimensional hidden layer, and a 64-dimensional feature vector b as the output layer. Weight matrix , the activation function is LeakyReLU. The diameter distribution sampling value of a certain section of blood vessels is processed by the branch network and the output feature vector is ,in Characterize the coupling characteristics of diameter and flow rate (such as ), Characterizing the correlation between bifurcation angle and wall shear stress (e.g. normalized value of ).

[0028] Based on the high-dimensional vector of vascular characteristics and the spatial basis function vector, the physical conservation constraints and network prediction errors are fused to generate boundary condition parameters; the spatial basis function vector is generated, and the trunk network (TrunkNet) inputs the spatial coordinate y (such as the outlet section position) and outputs a 64-dimensional basis function vector ,in is a polynomial basis function (such as ). Physical conservation constraint fusion, mass conservation equation Convert to loss function constraint: ,in The predicted flow field Q(x,y) of a bifurcated vessel does not meet the conservation condition. By adjusting the network weights, Minimize, for example, the initial predicted flow difference is , after optimization, it is reduced to . Boundary condition parameters are generated by inner product operation to generate pressure boundary parameters and flow boundary parameters : ,in is the offset term. For example, at the outlet section y=10mm, the calculation is , .

[0029] Based on the inverse normalization parameters and physical quantity restoration formula, the flow prediction value and pressure prediction value are fused to generate the physical quantity prediction result. , where the characteristic flow velocity , characteristic length (Typical value for large vessels). If normalized flow , then the actual flow after restoration is: The pressure denormalization formula is: , blood density Normalized pressure , the actual pressure after reduction is: .

[0030] Time-space coordinate mapping processing: The flow prediction value Q(t,y) and the pressure prediction value p(t,y) need to be mapped to the time-space coordinate (t,y). Taking a cardiac cycle T=0.8 as an example, at the outlet section y=10mm, the dynamic distribution is generated by cubic spline interpolation:

[0031] Peak systolic pressure t = 0.2 s: Q = 500 ml / min, p = 120 Pa;

[0032] Diastolic trough t=0.6s: Q=100ml / min, p=80Pa. Adaptive threshold processing and physical consistency verification, based on the physiological range (flow 50~600, ml / min, pressure 50~60Pa), convert the predicted physical quantity distribution into a valid area mark. For example, if the predicted pressure at a point is 250Pa (exceeding the threshold), it is marked as an invalid point and corrected by neighborhood interpolation. Mass conservation verification, for bifurcated vessels, verification Ingress traffic , initial predicted branch flow (error 6%), adjusted to (Error <5%).

[0033] The boundary condition parameters and physical quantity prediction results are analyzed and processed to generate target proxy model parameters, which are used to characterize the pressure and flow of the vascular network outlet boundary conditions. , flow boundary parameters Perform weighted fusion with the physical quantity prediction results p(t,y) and Q(t,y): , , the weight is dynamically adjusted according to the training set error (e.g., the pressure weight is determined by minimizing the MSE of the validation set). Figure 2 As shown, DeepONet belongs to the operator learning network, and its core consists of two parts: the branch network (BranchNet) and the trunk network (TrunkNet), which are used to process the compressed and normalized vascular feature data and generate the pressure and flow parameters of the outlet boundary conditions. Its framework features are as follows: The branch network (BranchNet), its input layer is used to receive compressed and normalized data, including discrete sampling values ​​such as vascular diameter distribution D(x), bifurcation angle sequence θ(x) (such as 100 sampling points along the vascular axis), and the input dimension is 32 dimensions (the result of automatic encoder dimensionality reduction). The hidden layer uses 128-dimensional neurons and the activation function is LeakyReLU to extract the high-dimensional representation of vascular features. The output layer generates a 64-dimensional feature vector b, which characterizes the coupling relationship between vascular geometric characteristics and hemodynamics (such as the coupling characteristics of diameter and flow). , the correlation characteristics between bifurcation angle and wall shear stress .

[0034] The trunk network (TrunkNet) receives the space-time coordinate y (such as the exit section position) as input layer and outputs a 64-dimensional basis function vector t(y), which contains polynomial basis functions (such as ), used to characterize the spatial distribution characteristics. Fusion mass conservation equation As a constraint term in the loss function , by adjusting the network weights, the predicted flow field meets the conservation conditions (such as optimizing the initial flow difference from 8% to <5%).

[0035] The parameter generation mechanism is as follows: the boundary condition parameters are generated by the inner product of the branch network output vector b and the backbone network basis function t(y): ;Flow boundary parameters: (Example: At y=10mm, =120×10³Pa, =450ml / min. DeepONet operator , where b is the output of the branch network, t(y) is the basis function of the main network, is the bias term.

[0036] Map the input function u(x) (such as diameter, bifurcation angle) to the physical quantity distribution of the outlet boundary (such as pressure ,flow Feature extraction: ; Basis function generation: .

[0037] The core feature of non-stacked DeepONet is that a single branch processes a single feature (such as diameter D, which only processes simple vascular geometric features). It has a simple structure but cannot fuse multi-scale features. The core feature of stacked DeepONet is that multiple branches process multiple features in parallel (such as D, ) Process the fusion requirements of the "multi-scale vascular feature database" to capture feature cross-effects and improve accuracy.

[0038] The target proxy model parameters, the final parameter vector can be expressed as: , taking t=0.2s,y=10mm as an example, the parameter value is: pressure ,flow , pressure gradient , flow rate change rate .in, Characterizes the dynamic pressure distribution at the outlet boundary, which directly affects blood flow resistance; Reflects the pulsating characteristics of the outlet flow and is related to the flow distribution at the vascular bifurcation; Used to evaluate the effect of pressure wave propagation and correlate with arterial compliance; : Characterizing the acceleration / deceleration characteristics of blood flow and influencing the instantaneous change of wall shear stress. Through the above processing, the target proxy model parameters not only retain the prediction accuracy of DeepONet (error <10%) but also satisfy the basic conservation laws of fluid mechanics, and can be directly used for dynamic simulation of complex vascular networks.

[0039] S104: Process the target proxy model parameters to generate proxy model output data.

[0040] In one embodiment, the boundary condition parameters in the target proxy model parameters are subjected to flow restoration processing to generate flow prediction values, wherein the flow prediction values ​​are obtained by converting the boundary condition parameters into flow restoration formulas. Calculation composition, where the characteristic flow rate , characteristic length (Typical value for large blood vessels). If the normalized flow parameter output by DeepONet is , the actual flow rate is: , which corresponds to the flow rate of the aortic branch at a certain phase point, and is consistent with the physiological range (50-600 mL / min).

[0041] The boundary condition parameters in the target proxy model parameters are subjected to pressure reduction processing to generate pressure prediction values, wherein the pressure prediction values ​​are obtained by the pressure components in the boundary condition parameters through the pressure reduction formula Calculate the composition, where blood density If the normalized pressure parameter =2.72, then the actual pressure is: , this pressure value is consistent with the aortic systolic pressure range (100~150mmHg, 1mmHg≈133Pa).

[0042] The predicted flow and pressure values ​​are mapped to time-space coordinates to generate a physical quantity distribution in time-space coordinates. The physical quantity distribution in time-space coordinates is composed of the predicted flow and pressure values, the spatial coordinates y, and the time t, fused through an interpolation algorithm. In a certain vascular network, the predicted flow value at the outlet section y = 10mm is sampled at discrete points within the cardiac cycle T = 0.8s: t = 0.2s (systolic peak): Q = 500mL / min, p = 120Pa; t = 0.6s (diastolic trough): Q = 100mL / min, p = 80Pa. Cubic spline interpolation is used to generate a continuous distribution: The pressure distribution is similar to that in order to ensure spatiotemporal continuity. Adaptive threshold processing is performed on the physical quantity distribution under spatiotemporal coordinates to generate the initial proxy model output data. The adaptive threshold processing converts the physical quantity distribution into preliminary results by setting a dynamic threshold based on the physiological range of blood flow. The spatiotemporal distribution generated by the visualization of the physical quantity distribution can be expressed as a matrix ,in , y is the axial coordinate of the blood vessel. For example, at y = 5 mm, the pressure wave propagation delay is about 0.1 s, which is consistent with the hemodynamic characteristics.

[0043] The physical consistency verification process is performed on the initial proxy model output data to generate the final proxy model output data. The physical consistency verification process is performed by the mass conservation equation Initial results were verified and corrected. Thresholds were set based on physiological ranges: flow threshold: [50, 600] mL / min; pressure threshold: [50, 150] Pa. If the predicted flow rate at a point was 700 mL / min (exceeding the upper limit), it was corrected to 580 mL / min through neighborhood interpolation to ensure data validity.

[0044] Verification of mass conservation, taking a bifurcated blood vessel as an example, the inlet flow , the initial predicted branch flow is , flow rate difference (Error rate 6%). Correction by projection method: , substitute into the calculation to get , , the error rate is reduced to <10%, satisfying the mass conservation equation .

[0045] The final proxy model output data is processed through the physical consistency correction algorithm to locate the error and calculate the flow error of each outlet section. ,mark The section is an outlier. Weight allocation, the outlier is allocated a correction weight according to the traffic ratio. , ensure that the large flow branch is adjusted first. Iterative correction, repeat the projection method correction until all cross-sectional errors are corrected. Taking a complex vascular network as an example, the initial global error was 8.7%, which was reduced to 5.8% after three iterations.

[0046] The final output data structure of the modified proxy model output data includes: spatiotemporal distribution matrix: , time resolution , spatial resolution ; Physical verification report: mass conservation error <5%, pressure wave propagation velocity c=5m / s (consistent with arterial elastic characteristics); Abnormal marking table: records all threshold-corrected points and their neighborhood interpolation basis, such as t=0.1s, y=8mm pressure p=250Pa corrected to 130Pa.

[0047] S105 , processing the proxy model output data and the high-dimensional and variable data of the pipe network, and generating an outlet boundary condition proxy model based on symbolic regression.

[0048] In one embodiment, feature extraction is performed on the proxy model output data to generate hemodynamic features, wherein the hemodynamic features are composed of the flow prediction value and pressure prediction value in the proxy model output data through spatiotemporal distribution feature extraction. The proxy model outputs the spatiotemporal distribution of flow and pressure in a certain section of blood vessels during the cardiac cycle: Flow prediction value: Systolic peak , diastolic trough , pulsation coefficient ;Pressure prediction value: systolic pressure , diastolic pressure , pressure gradient By extracting spatiotemporal distribution features, the hemodynamic feature vector is generated: ,in is the flow rate change rate, reflecting the blood flow acceleration characteristics.

[0049] The high-dimensional multi-variable data of the pipeline network is encoded and processed to generate the pipeline network topology encoding features, wherein the pipeline network topology encoding features are generated by the pipe diameter, bifurcation angle, and wall shear stress in the high-dimensional multi-variable data of the pipeline network through topological structure feature mapping. Taking the bifurcated blood vessels as an example, the high-dimensional data of the pipeline network includes: the main blood vessel diameter D=8mm, the branch diameter ; bifurcation angle , wall shear stress . Generate encoding features through topological structure feature mapping: ,in Flow distribution ratio corresponding to Murray's law.

[0050] The hemodynamic characteristics and the pipe network topology coding characteristics are fused to generate fusion characteristics, wherein the fusion characteristics are composed of the hemodynamic characteristics and the pipe network topology coding characteristics through the multi-dimensional parameter space discretization and feature association mechanism. The hemodynamic characteristics and the topology coding characteristics are associated through the multi-dimensional parameter space discretization: Discretization processing: The diameter ratio Divided into 3 intervals [0.3, 0.6), [0.6, 0.8), [0.8, 1], pressure gradient Divided into [0,3), [3,7), [7,10] Pa / mm; Feature association: Construct cross features , capturing the coupling effect of geometry and dynamics. The final fusion feature vector is: .

[0051] Perform symbolic regression on the fused features to generate candidate mathematical expressions. The symbolic regression process includes genetic algorithm optimization to generate expression trees and fitness evaluation to screen target expressions. Randomly generate the initial expression tree population, such as: Expression 1: ; Expression 2: ,in is a randomly generated constant in the range [-1,1], and the initial population size is 100 expressions. Calculate the prediction error and complexity penalty: Taking Expression 1 as an example, the prediction error on the test set has an MSE of 0.03 (corresponding to a traffic prediction error of about 3%). Complexity penalty: Depth penalty , the depth of expression 1 is 5, the number of nodes is 8, and the complexity penalty is: ;Fitness value: .

[0052] Genetic operation strategy, tournament selection: randomly select 5 individuals from the population and retain the 30% with the highest fitness (such as Top30); subtree crossover (probability 0.7): exchange the substructure of the expression tree, for example, replace the expression 1 With expression 2 Crossover to generate a new expression: Node mutation (probability 0.2): Replace the operator sin with cos, or a constant Perturbation ±10%; Elite retention: retain the 5 individuals with the highest fitness in each generation, such as Expression 1, which always maintains the Top 5 in the iteration.

[0053] A multi-objective optimization process was performed on the candidate mathematical expressions to generate a proxy model for the outlet boundary condition. This process involved optimizing the prediction error and model complexity through a Pareto front search, selecting an expression for the target number of nodes in models with an error ≤ 10%. The proxy model for the outlet boundary condition was used to characterize the outlet boundary condition of the vascular network. The Pareto front search, through 200 generations of iterative optimization, sought the optimal balance between prediction error (MSE) and model complexity (number of nodes). A typical Pareto solution was as follows:

[0054]

[0055] Final model selection and verification, selection criteria: select the expression with the least number of nodes among the models with error ≤ 10% (MSE ≤ 0.01), and give priority to the M-12 model: . Clinical data fitting parameters: ( ; Expression after unit adaptation: .

[0056] In a bifurcated vessel case, the main vessel diameter D=8mm and the branch diameter , pressure gradient : Model predicted traffic: ; Measured flow rate: 40.2mL / min, error rate <10%, meeting clinical accuracy requirements.

[0057] S106 , processing the outlet boundary condition proxy model, fitness evaluation, and genetic operation strategy based on a genetic algorithm to generate a target outlet boundary condition proxy model and a verification result.

[0058] In one embodiment, the outlet boundary condition proxy model is initialized to generate an initial model population. The initial model population is composed of the outlet boundary condition proxy model by randomly generating diverse expression trees. Taking a binary bifurcated blood vessel as an example, 100 initial expression trees are randomly generated. Some examples are as follows:

[0059] Expression A: ;

[0060] Expression B: ;

[0061] Expression C: ,in For constants randomly generated in the range [-2, 2], the depth of the expression tree is limited to ≤ 5 to ensure the diversity of the initial population.

[0062] The fitness evaluation is encoded and processed to generate a fitness evaluation index, where the fitness evaluation index is generated by the prediction error and the complexity penalty term through the fitness function. The fitness function is defined as: ; Prediction error (MSE): Taking expression A in the test set as an example, the mean square error MSE of traffic prediction is 0.028 (corresponding to an error rate of about 4.2%); Complexity penalty: depth penalty coefficient , the tree depth of expression A is 4; the node penalty coefficient , expression A contains 7 operation nodes; the total penalty term is: ;Fitness value: .

[0063] Genetic manipulation is performed on the initial model population and fitness evaluation indicators to generate an evolutionary model population. The genetic manipulation consists of tournament selection, subtree crossover, node mutation, and elite retention strategies. Tournament selection randomly selects 5 individuals from the population and retains the 30% (30 individuals) with the highest fitness to advance to the next generation, such as retaining expression A (Fitness = 0.71) and expression B (Fitness = 0.65). Subtree crossover (probability 0.7): Swap the subtrees of expression A. Subtree with expression B , generating a new expression: ; Node mutation (probability 0.2): Replace the division operator in expression C with multiplication, or change the constant Apply +10% perturbation (e.g. Elite retention: the five individuals with the highest fitness are retained in each generation to ensure that the optimal solution is not lost.

[0064] A multi-objective optimization process was performed on the population of evolved models to generate candidate optimized models. This multi-objective optimization process included a Pareto frontier search to optimize both prediction error and model complexity. After 200 generations of iterative optimization, a Pareto optimal solution set was formed between prediction error (MSE) and model complexity (number of nodes). Typical solutions are as follows:

[0065]

[0066] The horizontal axis is the number of model nodes, which represents the complexity of the model expression, that is, the total number of operators and variables in the expression. For example, the expression of the M-5 model is , including multiplication, addition and other operation nodes, the total number of nodes is 8. The expression of the M-12 model is , the number of nodes is 5, and the structure is simpler. The fewer the number of nodes, the simpler the model and the higher the computational efficiency, but it may not be able to capture complex features; the more the number of nodes, the more complex the model, and it can fit more complex relationships, but it may overfit.

[0067] The vertical axis is the MSE value ( ), MSE (mean square error) is used to quantify the deviation between the model prediction value and the true value. The smaller the MSE, the higher the model accuracy. For example: the MSE of M-5 is 2.2× , the corresponding flow prediction error is about 2.2%, which is relatively high accuracy. The MSE of M-12 is 3.1× The error rate is 3.1%, and the accuracy is slightly lower than that of M-5, but still meets the clinical requirements (error ≤ 10%).

[0068] M-5 (high precision - high complexity): By integrating more nodes (8) with multi-dimensional features such as diameter cube, bifurcation angle, and wall shear stress (such as D³×sinθ), it can more comprehensively characterize the coupling relationship between hemodynamics and vascular geometry, resulting in a lower MSE (2.2× ), but the computation is more intensive.

[0069] M-12 (low precision - low complexity): only 5 nodes are used, based on Murray's law (traffic distribution ratio ) and pressure gradient Constructing a linear combination has a simple structure and high computational efficiency, but sacrifices some accuracy ( ).

[0070] In models with a limited number of nodes (≤5), M-12 simplifies the model while retaining the main physical mechanisms through key feature screening (such as the flow distribution ratio of Murray's law) and linear combination, thus achieving the best accuracy (3.1% error) under low complexity conditions. For other models with a number of nodes ≤5 (such as M-45, with 4 nodes, MSE=4.5× ) has a higher error due to the simpler feature association mechanism (linear model with only branch diameter proportion).

[0071] The candidate optimization models were validated to generate the target export boundary condition proxy model and validation results. The validation process was performed by selecting the expression with the target number of nodes from the models with an error ≤ 10% and verifying the model accuracy based on clinical data. The final model selection criteria were: the expression with the least number of nodes from the models with an error ≤ 10% (MSE ≤ 0.1) was selected, with the M-12 model being the preferred choice: ; Parameter fitting: obtained by least square fitting of clinical data set (n=500) , , the expression after unit adaptation is: .

[0072] The clinical verification case is as follows: Case conditions: main vessel diameter D = 8mm, branch diameter , pressure gradient ; The model predicts: The branch flow rate was measured by ultrasound Doppler and was 40.2 mL / min, with an error rate of , meeting clinical accuracy requirements (error ≤ 10%).

[0073] This method addresses the limited accuracy and computational complexity of traditional models through multi-scale data fusion, DeepONet operator learning, and symbolic regression analysis. The specific steps are as follows: First, a multi-scale vascular feature database is constructed, integrating CFD data of large and small vessels (diameter, bifurcation angle, etc.) with DPD data of capillaries (interparticle forces, etc.). Using an autoencoder for dimensionality reduction, spatiotemporal normalization (e.g., Reynolds number Re = 7950 to characterize turbulence), and data enhancement, compressed normalized data is generated, retaining 95% of key features and compressing the data volume to 6.4%.

[0074] Secondly, DeepONet was used to process compressed data, and the branch network extracted high-dimensional vectors of vascular characteristics. The backbone network combined physical conservation constraints to generate boundary condition parameters. After denormalization and spatiotemporal interpolation, flow / pressure prediction values ​​were obtained with an error within 10%. Then, the hemodynamic characteristics and the network topology encoding features were fused, and candidate expressions were generated through symbolic regression driven by a genetic algorithm. After Pareto front optimization, the model with an error ≤ 10% and the fewest nodes was selected. Clinical verification showed that the error was only 10%. This method breaks through the limitations of the traditional Windkessel model that relies on fixed parameters, and achieves efficient modeling under the fusion of multi-scale physiological characteristics and physical constraints. The prediction speed is 1000 times faster than full-order CFD, providing a high-precision interpretable model for hemodynamic simulation and clinical applications.

[0075] In one embodiment, Figure 3 As shown, the present application also provides a proxy model construction device for the vascular network outlet boundary condition, comprising:

[0076] Acquisition module 301 is used to construct a multi-scale vascular feature database, wherein the multi-scale vascular feature database includes large / small vessel modeling data and capillary modeling data. The large / small vessel modeling data includes vessel diameter, bifurcation angle, wall shear stress, and flow characteristic parameters. The capillary modeling data includes inter-particle force and red blood cell membrane flexibility characteristic information.

[0077] Processing module 302 is used to perform data compression and spatiotemporal normalization on the multi-scale vascular feature data to generate compressed normalized data, wherein the compressed normalized data is composed of the dimensionality reduction results of the autoencoder, the spatiotemporal normalization relationship, and the data mixing and enhancement results; process the compressed normalized data to generate the target proxy model parameters based on DeepONet; process the target proxy model parameters to generate proxy model output data; process the proxy model output data and the high-dimensional and variable data of the pipeline network to generate an outlet boundary condition proxy model based on symbolic regression, wherein the outlet boundary condition proxy model is used to characterize the outlet boundary conditions of the vascular network; process the outlet boundary condition proxy model, fitness evaluation, and genetic operation strategy based on a genetic algorithm to generate a target outlet boundary condition proxy model and verification results.

[0078] Although the present application is disclosed as above, the present application is not limited thereto. Any person skilled in the art may make various changes and modifications without departing from the spirit and scope of the present application. Therefore, the scope of protection of the present application shall be based on the scope defined by the claims.

Claims

1. A method for constructing a proxy model of the boundary conditions of a vascular network outlet, characterized in that: include: Construct a multi-scale vascular feature database, which includes large / small vessel modeling data and capillary modeling data. The large / small vessel modeling data includes vessel diameter, bifurcation angle, wall shear stress, and flow characteristic parameters, while the capillary modeling data includes information on interparticle forces and red blood cell membrane flexibility. Performing data compression and spatiotemporal normalization on the multi-scale vascular feature data to generate compressed normalized data, where the compressed normalized data consists of the dimensionality reduction results of the autoencoder, the spatiotemporal normalization relationship, and the data mixing and enhancement results; Process the compressed and normalized data and generate the target proxy model parameters based on DeepONet; Processing the target proxy model parameters to generate proxy model output data; The proxy model output data and the high-dimensional multi-variable data of the pipeline network are processed, and the outlet boundary condition proxy model is generated based on symbolic regression, including: feature extraction processing of the proxy model output data to generate hemodynamic features, wherein the hemodynamic features are composed of the flow prediction value and the pressure prediction value in the proxy model output data through the spatiotemporal distribution feature extraction; encoding processing of the pipeline network high-dimensional multi-variable data to generate pipeline network topology encoding features, wherein the pipeline network topology encoding features are generated by the pipe diameter, bifurcation angle, and wall shear stress in the pipeline network high-dimensional multi-variable data through topological structure feature mapping; fusion processing of the hemodynamic features and the pipeline network topology encoding features to generate fusion features, wherein the fusion features are composed of the hemodynamic The vascular network topology encoding features and the vascular network topology encoding features are constructed through the discretization of multi-dimensional parameter space and the feature association mechanism; the fused features are subjected to symbolic regression processing to generate candidate mathematical expressions, wherein the symbolic regression processing includes genetic algorithm optimization to generate expression trees and fitness evaluation to screen target expressions; the candidate mathematical expressions are subjected to multi-objective optimization processing to generate an outlet boundary condition proxy model, wherein the multi-objective optimization processing optimizes the prediction error and model complexity through Pareto front search, and selects the expression of the target number of nodes in the model with an error ≤ 10%. The outlet boundary condition proxy model is used to characterize the outlet boundary conditions of the vascular network; The outlet boundary condition proxy model, fitness evaluation and genetic operation strategy are processed based on the genetic algorithm to generate the target outlet boundary condition proxy model and verification results.

2. The method according to claim 1, wherein Perform data compression and spatiotemporal normalization on the multi-scale vascular feature data to generate compressed and normalized data, including: Performing autoencoder dimensionality reduction processing on the multi-scale vascular feature data to generate autoencoder dimensionality reduction results; Performing spatiotemporal normalization relationship construction processing on multi-scale vascular feature data to generate spatiotemporal normalization relationship; Perform data mixing and enhancement processing on multi-scale vascular feature data to generate data mixing and enhancement results; Based on the dimensionality reduction results of the automatic encoder, the spatiotemporal normalization relationship, and the data mixing and enhancement results, comprehensive processing is performed to generate compressed normalized data.

3. The method according to claim 1, wherein The compressed and normalized data is processed to generate the target proxy model parameters based on DeepONet, including: Perform branch network processing on the discrete sampling values ​​of the vascular characteristic function in the compressed and normalized data to generate a high-dimensional vector of vascular characteristics and network weight parameters; Based on the high-dimensional vector of vascular characteristics and the spatial basis function vector, the physical conservation constraints and network prediction errors are fused to generate boundary condition parameters; Based on the inverse normalization parameters and physical quantity restoration formula, the flow prediction value and pressure prediction value are fused to generate the physical quantity prediction result; The boundary condition parameters and physical quantity prediction results are analyzed and processed to generate target proxy model parameters, which are used to characterize the pressure and flow of the boundary conditions at the outlet of the vascular network.

4. The method according to claim 3, wherein Process the target proxy model parameters to generate proxy model output data, including: The boundary condition parameters in the target proxy model parameters are processed for flow restoration to generate flow prediction values, where the flow prediction values ​​are obtained by converting the boundary condition parameters into flow restoration formulas. Calculation composition; The boundary condition parameters in the target proxy model parameters are subjected to pressure reduction processing to generate pressure prediction values, wherein the pressure prediction values ​​are obtained by the pressure components in the boundary condition parameters through the pressure reduction formula Calculation composition; The flow prediction value and the pressure prediction value are mapped to the space-time coordinate to generate the physical quantity distribution under the space-time coordinate. The physical quantity distribution under the space-time coordinate is formed by fusing the flow prediction value, the pressure prediction value with the spatial coordinate y and the time t through the interpolation algorithm. Adaptive threshold processing is performed on the physical quantity distribution under the spatiotemporal coordinates to generate initial proxy model output data, wherein the adaptive threshold processing converts the physical quantity distribution into preliminary results by setting a dynamic threshold based on the physiological range of blood flow; The physical consistency verification process is performed on the initial proxy model output data to generate the final proxy model output data. The physical consistency verification process is performed by the mass conservation equation Verify and correct the initial results.

5. The method according to claim 1, wherein The export boundary condition agent model, fitness evaluation and genetic operation strategy are processed based on the genetic algorithm to generate the target export boundary condition agent model and verification results, including: Performing population initialization processing on the outlet boundary condition proxy model to generate an initial model population, wherein the initial model population is composed of the outlet boundary condition proxy model through randomly generating diverse expression trees; Encoding the fitness evaluation to generate a fitness evaluation index, wherein the fitness evaluation index is generated by calculating the prediction error and the complexity penalty term through the fitness function; Genetic manipulation is performed on the initial model population and fitness evaluation indicators to generate an evolved model population. The genetic manipulation consists of tournament selection, subtree crossover, node mutation, and elite retention strategies. Performing multi-objective optimization on the population of evolved models to generate candidate optimized models, wherein the multi-objective optimization includes Pareto frontier search to optimize prediction error and model complexity; The candidate optimization model is verified to generate a proxy model of the target export boundary condition and the verification results. The verification process is performed by selecting an expression for the target number of nodes in the model with an error ≤ 10%, and verifying the accuracy of the model based on clinical data.

6. A proxy model construction device for the boundary conditions of a vascular network outlet, characterized in that: For implementing the method of claim 1, the apparatus comprises: An acquisition module is used to construct a multi-scale vascular feature database, wherein the multi-scale vascular feature database includes large / small vessel modeling data and capillary modeling data. The large / small vessel modeling data includes vessel diameter, bifurcation angle, wall shear stress, and flow characteristic parameters, and the capillary modeling data includes inter-particle force and red blood cell membrane flexibility characteristic information; The processing module is used to perform data compression and spatiotemporal normalization on multi-scale vascular feature data to generate compressed normalized data, wherein the compressed normalized data is composed of the dimensionality reduction results of the automatic encoder, the spatiotemporal normalization relationship, and the data mixing and enhancement results; the compressed normalized data is processed to generate the target proxy model parameters based on DeepONet; the target proxy model parameters are processed to generate the proxy model output data; the proxy model output data and the high-dimensional and variable data of the pipeline network are processed to generate the outlet boundary condition proxy model based on symbolic regression, wherein the outlet boundary condition proxy model is used to characterize the outlet boundary conditions of the vascular network; the outlet boundary condition proxy model, fitness evaluation and genetic operation strategy are processed based on the genetic algorithm to generate the target outlet boundary condition proxy model and verification results.

7. An electronic device, characterized in that: include: a first processor; and a memory for storing executable instructions of the first processor; wherein the first processor is configured to execute the agent model construction method of the vascular network outlet boundary condition of any one of claims 1 to 5 by executing the executable instructions.

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