Agent model of vascular network exit boundary condition and construction method

Abstract

The invention provides an agent model of a vascular network exit boundary condition and a construction method, and is applied to the technical field of data processing. According to the method, data compression and space-time normalization processing are carried out on multi-scale blood vessel feature data, compressed and normalized data are generated, and the compressed and normalized data are composed of an automatic encoder dimension reduction result, a space-time normalization relation and a data mixing and enhancing result; processing the compressed and normalized data, and generating target agent model parameters based on DeepONet; processing the target proxy model parameters to generate proxy model output data; the proxy model output data and the pipe network high-dimensional changeable data are processed, an exit boundary condition proxy model is generated based on symbolic regression, and the exit boundary condition proxy model is used for representing a vascular network exit boundary condition; and processing the exit boundary condition proxy model, the fitness evaluation and the genetic manipulation strategy based on a genetic algorithm to generate a target exit boundary condition proxy model and a verification result.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly to a surrogate model for the outlet boundary condition of a vascular network and a construction method thereof. Background Art

[0002] Since the pulmonary capillary blood flow laminar flow model was introduced into the blood circulation problem, the hydrodynamic method has gradually become an important solution to hemodynamic problems. With the enhancement of computer 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 methods. However, the selection of boundary conditions in the computational model has a significant impact on the accuracy of its calculation results.

[0003] In the field of hemodynamics, the inlet boundary condition has been widely recognized and adopted the patient-specific physiological blood flow waveform, but there is no clear guideline for the setting of the outlet boundary condition. Traditional models such as zero-pressure outlet, constant-pressure outlet, Murray's law, Split method, and Windkessel model have obvious deficiencies. For example, the constant-pressure outlet has a large error, Murray's law and the Split method ignore the vascular geometric heterogeneity and dynamic regulation mechanism, and the Windkessel model has complex parameter calibration and relies on general values, resulting in low simulation accuracy. Therefore, there is an urgent need for a high-precision outlet boundary condition model to improve the credibility and practicality of hemodynamic simulation.

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

[0005] The purpose of this application is to provide a surrogate model for the outlet boundary condition of a vascular network and a construction method thereof, which can at least overcome the problems existing in the prior art to a certain extent. By multi-scale data fusion, DeepONet operator learning, and symbolic regression analysis, a multi-scale vascular feature database is constructed, and after dimensionality reduction, normalization, etc., compressed and normalized data is generated. The DeepONet is used to process the data to obtain the flow / pressure prediction value. After fusing the features, the symbolic regression is used for optimization to obtain a high-precision model, and the prediction speed is 1000 times faster than that of the full-order CFD.

[0006] Other features and advantages of this application will become apparent through the following detailed description, or will be partially learned through the practice of the present invention.

[0007] According to one aspect of the present application, a method for constructing a surrogate model of the outlet boundary condition of a blood vessel network is provided, including: constructing a multi-scale blood vessel feature database, where the multi-scale blood vessel feature database includes large / small blood vessel modeling data and capillary modeling data, the large / small blood vessel modeling data contains blood vessel diameter, bifurcation angle, wall shear stress and flow characteristic parameters, and the capillary modeling data contains inter-particle forces and red blood cell membrane flexibility characteristic information; performing data compression and spatio-temporal normalization processing on the multi-scale blood vessel feature data to generate compressed and normalized data, where the compressed and normalized data consists of the dimensionality reduction results of an autoencoder, spatio-temporal normalization relationships, data mixing and enhancement results; processing the compressed and normalized data, and generating target surrogate model parameters based on DeepONet; processing the target surrogate model parameters to generate surrogate model output data; processing the surrogate model output data and the high-dimensional and variable data of the pipe network, and generating an outlet boundary condition surrogate model based on symbolic regression, where the outlet boundary condition surrogate model is used to characterize the outlet boundary condition of the blood vessel network; processing the outlet boundary condition surrogate model, fitness evaluation and genetic operation strategy based on a genetic algorithm to generate a target outlet boundary condition surrogate model and verification results.

[0008] In another aspect of the present application, a device for constructing a surrogate model of the outlet boundary condition of a blood vessel network is characterized by including: an acquisition module for constructing a multi-scale blood vessel feature database, where the multi-scale blood vessel feature database includes large / small blood vessel modeling data and capillary modeling data, the large / small blood vessel modeling data contains blood vessel diameter, bifurcation angle, wall shear stress and flow characteristic parameters, and the capillary modeling data contains inter-particle forces and red blood cell membrane flexibility characteristic information; a processing module for performing data compression and spatio-temporal normalization processing on the multi-scale blood vessel feature data to generate compressed and normalized data, where the compressed and normalized data consists of the dimensionality reduction results of an autoencoder, spatio-temporal normalization relationships, data mixing and enhancement results; processing the compressed and normalized data, and generating target surrogate model parameters based on DeepONet; processing the target surrogate model parameters to generate surrogate model output data; processing the surrogate model output data and the high-dimensional and variable data of the pipe network, and generating an outlet boundary condition surrogate model based on symbolic regression, where the outlet boundary condition surrogate model is used to characterize the outlet boundary condition of the blood vessel network; processing the outlet boundary condition surrogate model, fitness evaluation and genetic operation strategy based on a genetic algorithm to generate a target outlet boundary condition surrogate model and verification results.

[0009] A surrogate model and construction method for the outlet boundary condition of a vascular network provided by the present application solve the problems of insufficient accuracy and complex calculation of traditional models through multi-scale data fusion, DeepONet operator learning, and symbolic regression analysis by a server. A multi-scale vascular feature database is constructed by integrating CFD data (such as diameter, bifurcation angle, etc.) of large / small blood vessels and DPD data (such as inter-particle force, etc.) of capillaries, and generating compressed and normalized data through autoencoder dimensionality reduction, spatio-temporal normalization (such as Reynolds number Re = 7950 to characterize turbulent characteristics), and data augmentation, retaining 95% of the key features and reducing the data volume to 6.4%.

[0010] Use DeepONet to process the compressed data. The branch network extracts the high-dimensional vector of vascular features, and the backbone network generates the boundary condition parameters by combining physical conservation constraints. After anti-normalization and spatio-temporal interpolation, the flow rate / pressure prediction values are obtained, and the error is controlled within 10%. Then, by fusing hemodynamic features and pipe network topology coding features, candidate expressions are generated through symbolic regression driven by a genetic algorithm. After Pareto front optimization, a model with an error ≤ 10% and the fewest number of nodes is selected, and the clinical verification error is within 10%. This method breaks through the limitation of the traditional Windkessel model relying on fixed parameters, realizes efficient modeling under multi-scale physiological feature fusion and physical constraints, and the prediction speed is 1000 times faster than that of full-order CFD, providing a high-precision and interpretable model for hemodynamic simulation and clinical applications. Brief Description of the Drawings

[0011] Figure 1 The flowchart showing a method for constructing a surrogate model for the outlet boundary condition of a vascular network provided by an embodiment of the present application is shown; Figure 2 The basic framework diagram of the DeepONet model provided by an embodiment of the present application is shown; Figure 3 The structural schematic diagram of a device for constructing a surrogate model for the outlet boundary condition of a vascular network provided by an embodiment of the present application is shown. Detailed Embodiments

[0012] The following describes the preferred embodiments of the present invention with reference to 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 used to limit the present invention. The following combination of Figure 1 is used to describe the method for constructing a surrogate model for the outlet boundary condition of a vascular network according to an exemplary embodiment of the present application. In one embodiment, the present application also proposes a surrogate model and construction method for the outlet boundary condition of a vascular network, as Figure 1 shown, including: S101, construct a multi-scale vascular feature database.

[0013] The multi-scale vascular feature database includes large / small blood vessel modeling data and capillary modeling data. The large / small blood vessel modeling data contains vascular diameter, bifurcation angle, wall shear stress, and flow characteristic parameters, while the capillary modeling data contains inter-particle forces and red blood cell membrane flexibility characteristic information.

[0014] In one implementation, an example of calculating vascular diameter and hemodynamic parameters is as follows. For the aortic diameter: take the diameter D = 8 mm of a certain segment of the descending aorta, and the diameter d = 3 mm of the branch artery (which is within the physiological range of aortic branches in the human body). For the calculation of blood flow velocity, according to the continuity equation , where is the cross-sectional area of the blood vessel. Assume the aortic flow rate Q = 500 ml / min, the aortic flow velocity , and the flow velocity in the branch artery . It can be seen that the decrease in diameter leads to a significant increase in flow velocity.

[0015] Regarding the influence of pressure distribution, based on Bernoulli's equation , the aortic pressure and the branch artery pressure satisfy: . Substituting ρ = 1050 kg / m³, the pressure difference can be obtained as approximately , indicating that the change in diameter directly affects the local pressure gradient. An example of calculating the bifurcation angle and blood flow distribution is as follows. For the blood flow distribution at a bifurcation angle θ = 60°, using Murray's law , with the main blood vessel diameter D = 8 mm and the diameters of the two branches being d1 = 5 mm and d2 = 3 mm respectively, the flow distribution ratio is . That is, when the main flow rate Q = 500 ml / min, the branch flow rates are approximately Q1 ≈ 398 ml / min and Q2 ≈ 102 ml / min.

[0016] Calculation of wall shear stress (WSS). The formula for WSS is: , where μ is the blood viscosity (taking ), and is the wall velocity gradient. In the near-wall region with a bifurcation angle of 60°, assuming the velocity gradient is , then: . WSS < 1 Pa is related to the susceptibility to atherosclerosis, and 2.5 Pa is within the normal physiological range (1 - 4 Pa).

[0017] Flow characteristic parameters and pulsatile blood flow modeling. An example of flow pulsation during the cardiac cycle is as follows. Set a cardiac cycle T = 0.8 s, the maximum flow rate = 500 ml / min (systole), the minimum flow rate (diastole), and the flow pulsation coefficient , reflecting the pulsation intensity of blood flow. The Reynolds number (Re) is calculated as follows: the characteristic length L = D = 8 mm, and the average flow velocity . Then , and the result shows that the aortic blood flow is in the turbulent transition region (Re > 2000), and the unsteady flow effect needs to be considered. Examples of control equations and sampling strategies are as follows. The Navier - Stokes equations are applied as follows. The incompressible continuity equation is , and the momentum equation is . For spatial sampling, velocity and pressure data are extracted at equal intervals of Δx = 0.1D = 0.8 mm along the blood vessel axis to ensure capturing the details of boundary layer flow. For the time sampling strategy, 20 phase points (Δt = T / 20 = 0.04 s) are taken within the pulsation period to record transient field data, such as the flow field parameters at the systolic peak (t = 0.2 s) and diastolic trough (t = 0.6 s), which are used to construct dynamic boundary conditions.

[0018] The force between particles: The red blood cell membrane is modeled by a spring network, and the plasma particles adopt the DPD force field. The dissipative particle dynamics (DPD) model defines the resultant force between particles: , where the conservative force , the dissipative force , and the random force , is the weight function, , are the force coefficients. For red blood cell modeling, the flexible characteristics of the red blood cell membrane are constructed through the bond potential energy and the angle potential energy . Among them, 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 elastic stiffness when the actual length of the bond deviates from the equilibrium length of the bond , is the actual angle, is the equilibrium angle, is the angle potential energy parameter, which is used to describe the degree of rigidity when the actual angle deviates from the equilibrium angle . For spatial statistics, the average velocity and pressure drop of each micro - element (10×10×10 μm3) are calculated. For time statistics, data are collected every 104 DPD time steps (Δt = 0.1τ), covering the red blood cell deformation period.

[0019] S102, perform data compression and spatio - temporal normalization on the multi - scale vascular feature data to generate compressed and normalized data.

[0020] In one implementation, perform dimensionality reduction on the multi - scale vascular feature data using an auto - encoder to generate the dimensionality reduction result of the auto - encoder. The original multi - scale vascular feature data contains a 5 - dimensional feature vector , where is the velocity component, p is the pressure, is the wall shear stress, and Q is the flow rate. An encoder structure is used to reduce its dimension to 32 dimensions: the input layer of the encoder network has 128 neurons, the hidden layer has 32 neurons, and the weight matrices , . The activation function is ReLU. After encoding a certain section of aortic data, the high-dimensional feature vector can be expressed as , where is the activation function. More than 95% of the key features (such as the correlation features between flow velocity and pressure) are retained after dimensionality reduction, and the data volume is compressed to 6.4% of the original size.

[0021] Construct the spatio-temporal normalization relationship for the multi-scale vascular feature data to generate the spatio-temporal normalization relationship; for the construction of the spatio-temporal normalization relationship and the calculation of the Reynolds number (Re): for large blood vessels (characteristic length , average flow velocity , blood density , viscosity . This value indicates that the blood flow is in the turbulent transition zone, and the unsteady effect needs to be considered. Perform data mixing and enhancement processing on the multi-scale vascular feature data to generate the data mixing and enhancement results. Construct the trapezoidal mixing weights and define the time normalization parameter . When , the macroscopic dominant weight , and the CFD data accounts for a higher proportion; when , the weight linearly transitions to 0.5; when , the microscopic dominant weight , and the DPD data accounts for a higher proportion.

[0022] Apply a +10% perturbation to the blood vessel diameter D = 8mm to generate virtual samples; apply a -5% perturbation to the bifurcation angle to generate samples. The final dataset is expanded from 10,000 samples to 100,000 samples, covering the physiological range of blood vessel diameters from 3 to 10 mm and bifurcation angles from 30° to 90°. Based on the dimensionality reduction results of the autoencoder, the spatio-temporal normalization relationship, and the data mixing and enhancement results, perform comprehensive processing to generate the compressed and normalized data. Fuse the 32-dimensional features after dimensionality reduction, the spatio-temporal normalization parameter and the enhanced samples: feature splicing, and each sample is expressed as to form a new feature vector. Perform consistency verification, and verify the physical rationality of the normalized data through the mass conservation equation . For example, the flow rate of a bifurcated blood vessel needs to satisfy , with the error controlled within 10%. The finally generated compressed and normalized data not only retains the key features of hemodynamics (such as the flow velocity-pressure coupling relationship), but also eliminates the scale differences through spatio-temporal normalization, providing a unified input format for subsequent DeepONet modeling.

[0023] S103, process the compressed and normalized data, and generate the target surrogate model parameters based on DeepONet.

[0024] In one implementation, perform branch network processing on the discrete sampling values of the vascular feature function in the compressed and normalized data to generate high-dimensional vascular feature vectors and network weight parameters. The compressed and normalized data includes the discrete sampling values of the vascular diameter distribution and the bifurcation angle sequence (such as 100 sampling points along the vascular axis), and input them into the branch network (BranchNet): network architecture, the input layer is 32-dimensional (the result of autoencoder dimensionality reduction), the hidden layer is 128-dimensional, and the output layer is a 64-dimensional feature vector b. The weight matrix , and the activation function is LeakyReLU. After the diameter distribution sampling values of a certain section of blood vessel are processed by the branch network, the output feature vector , where represents the coupling feature of diameter and flow rate (such as 's normalized value), represents the correlation feature of bifurcation angle and wall shear stress (such as 's normalized value).

[0025] Based on the high-dimensional vascular feature vectors and spatial basis function vectors, fuse the physical conservation constraints and network prediction errors to generate boundary condition parameters; generation of spatial basis function vectors, the main network (TrunkNet) inputs the spatial coordinate y (such as the position of the outlet section) and outputs a 64-dimensional basis function vector , where is a polynomial basis function (such as ). Physical conservation constraint fusion, the mass conservation equation is converted into a loss function constraint term: , where is the weight coefficient. The predicted flow field Q(x,y) of a certain bifurcated blood vessel does not satisfy the conservation condition, and by adjusting the network weights, is minimized. For example, the initial predicted flow rate difference is , and after optimization, it drops to . Generation of boundary condition parameters, generate the pressure boundary parameter and the flow rate boundary parameter through inner product operation: , where is the bias term. For example, at the outlet cross-section where y = 10 mm, it is calculated that , .

[0026] Based on the anti-normalization parameters and the physical quantity restoration formula, the flow prediction value and the pressure prediction value are fused to generate the physical quantity prediction result. The application of the anti-normalization parameter, the flow anti-normalization formula , where the characteristic flow velocity , the characteristic length (typical value of large blood vessels). If the normalized flow , then the actual flow after restoration is: . The pressure anti-normalization formula is , the blood density . The normalized pressure , the actual pressure after restoration is: .

[0027] Spatio-temporal coordinate mapping processing, the flow prediction value Q(t, y) and the pressure prediction value p(t, y) need to be mapped to the spatio-temporal coordinates (t, y). Taking a certain cardiac cycle T = 0.8 as an example, at the outlet cross-section where y = 10 mm, a dynamic distribution is generated through cubic spline interpolation: Systolic peak t = 0.2 s: Q = 500 ml / min, p = 120 Pa; Diastolic trough t = 0.6 s: Q = 100 ml / min, p = 80 Pa. Adaptive threshold processing and physical consistency verification, based on the physiological range (flow 50 - 600, ml / min, pressure 50 - 60 Pa), convert the predicted physical quantity distribution into an effective region marker. For example, if the predicted pressure at a certain point is 250 Pa (exceeding the threshold), it is marked as an invalid point and corrected through neighborhood interpolation. Mass conservation check, for bifurcated blood vessels, verify . The inlet flow , the initial predicted branch flow (error 6%), is adjusted to (error < 5%) through the projection method.

[0028] Analyze and process the boundary condition parameters and the physical quantity prediction results to generate the target surrogate model parameters, which are used to characterize the pressure and flow at the outlet boundary conditions of the blood vessel network. Perform weighted fusion on the pressure boundary parameter , the flow boundary parameter and the physical quantity prediction results p(t, y), Q(t, y): , , and the weights are dynamically adjusted according to the training set error (for example, the pressure weight is determined by minimizing the MSE of the validation set). Such as Figure 2As shown in the figure, DeepONet belongs to the operator learning network, and its core consists of two parts: the BranchNet and the 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 BranchNet, whose input layer is used to receive the compressed and normalized data, includes discrete sampling values such as the vascular diameter distribution D(x) and the bifurcation angle sequence θ(x) (e.g., 100 sampling points along the vascular axis), and the input dimension is 32 dimensions (the result of dimensionality reduction by the autoencoder). 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 geometry and hemodynamics (such as the coupling feature of diameter and flow 、the correlation feature between the bifurcation angle and the wall shear stress .

[0029] The TrunkNet, whose input layer receives the spatio-temporal coordinates y (such as the position of the outlet section). It outputs a 64-dimensional basis function vector t(y), which contains polynomial basis functions (such as ), and is used to characterize the spatial distribution features. The mass conservation equation is used as a constraint term in the loss function , and by adjusting the network weights, the predicted flow field is made to satisfy the conservation condition (such as the initial flow difference is optimized from 8% to <5%).

[0030] The parameter generation mechanism is as follows. By taking the inner product of the output vector b of the BranchNet and the basis function t(y) of the TrunkNet, the boundary condition parameters are generated: Pressure boundary parameter: ; Flow boundary parameter: (Example: At y = 10 mm, = 120×10³ Pa, = 450 ml / min. The DeepONet operator , where b is the output of the BranchNet and t(y) is the basis function of the TrunkNet, is the bias term.

[0031] maps the input function u(x) (such as diameter, bifurcation angle) to the physical quantity distribution at the outlet boundary (such as pressure 、flow . Feature extraction: ; Basis function generation: .

[0032] The non - stacked DeepONet has the core feature of processing a single feature with a single branch (such as only the diameter D, only dealing with simple vascular geometric features, with a simple structure, but unable to fuse multi - scale features. The stacked DeepONet has the core feature of processing multiple features in parallel with multiple branches (such as D, ) to handle the fusion requirements of the "multi - scale vascular feature database", capture the feature cross - effect, and improve the accuracy.

[0033] The parameters of the target surrogate model, and the finally generated parameter vector can be expressed as: , taking t = 0.2s, y = 10mm as an example, the parameter values are: pressure , flow rate , pressure gradient , flow rate change rate . Among them, characterizes the dynamic pressure distribution at the outlet boundary and directly affects blood flow resistance; reflects the pulsatile characteristics of the outlet flow rate and is related to the flow rate distribution at the vascular bifurcation; is used to evaluate the pressure wave propagation effect and is associated with arterial compliance; : characterizes the blood flow acceleration / deceleration characteristics and affects the instantaneous change of wall shear stress. Through the above processing, the parameters of the target surrogate model can 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 the dynamic simulation of complex vascular networks.

[0034] S104, process the parameters of the target surrogate model to generate the output data of the surrogate model.

[0035] In one implementation, perform flow rate restoration processing on the boundary condition parameters in the parameters of the target surrogate model to generate a flow rate prediction value. Among them, the flow rate prediction value is calculated by the boundary condition parameters through the flow rate restoration formula , where the characteristic flow velocity , and the characteristic length (typical value of large blood vessels). If the normalized flow rate parameter output by DeepONet, then the actual flow rate is: , and this value 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).

[0036] Perform pressure restoration processing on the boundary condition parameters in the parameters of the target surrogate model to generate a pressure prediction value. Among them, the pressure prediction value is calculated by the pressure component in the boundary condition parameters through the pressure restoration formula , where the blood density . If the normalized pressure parameter = 2.72, then the actual pressure is: , the pressure value conforms to the aortic systolic pressure range (100 - 150 mmHg, 1 mmHg ≈ 133 Pa).

[0037] Perform spatio - temporal coordinate mapping processing on the flow prediction value and the pressure prediction value to generate the physical quantity distribution in the spatio - temporal coordinates. Among them, the physical quantity distribution in the spatio - temporal coordinates is composed of the flow prediction value, the pressure prediction value, the spatial coordinate y, and the time t through an interpolation algorithm. In a certain vascular network, the discrete sampling points of the flow prediction value at the outlet section y = 10 mm within the cardiac cycle T = 0.8 s are: t = 0.2 s (systolic peak): Q = 500 mL / min, p = 120 Pa; t = 0.6 s (diastolic trough): Q = 100 mL / min, p = 80 Pa. Cubic spline interpolation is used to generate a continuous distribution: ; Similarly for the pressure distribution to ensure spatio - temporal continuity. Perform adaptive threshold processing on the physical quantity distribution in the spatio - temporal coordinates to generate the initial surrogate model output data. Among them, the adaptive threshold processing converts the physical quantity distribution into a preliminary result by setting a dynamic threshold based on the physiological range of blood flow. The spatio - temporal distribution generated by visualizing the physical quantity distribution can be represented as a matrix , where , y is the vascular axial coordinate. For example, at y = 5 mm, the pressure wave propagation delay is about 0.1 s, which conforms to the hemodynamic characteristics.

[0038] Perform physical consistency verification processing on the initial surrogate model output data to generate the final surrogate model output data. Among them, the physical consistency verification processing checks and corrects the initial result through the mass conservation equation Set thresholds based on the physiological range: flow threshold: [50, 600] mL / min; pressure threshold: [50, 150] Pa. If the predicted flow at a certain point is 700 mL / min (exceeding the upper limit), it is corrected to 580 mL / min through neighborhood interpolation to ensure data validity.

[0039] Mass conservation verification. Taking a bifurcated blood vessel as an example, the inlet flow , the initial predicted branch flow is , the flow difference (error rate 6%). It is corrected by the projection method: , substituting into the calculation gives , , the error rate is reduced to <10%, satisfying the mass conservation equation .

[0040] The final surrogate model output data is processed through a physical consistency correction algorithm, error localization, and the flow error at each outlet section is calculated , marked The cross-section is an outlier. Weight assignment: Corrective weights are assigned to outliers according to the flow ratio to ensure that branches with large flows are adjusted first. Iterative correction: Repeatedly execute the projection method correction until all cross-section errors... are met. Taking a complex vascular network as an example, the initial global error is 8.7%, which is reduced to 5.8% after 3 iterations.

[0041] The output data of the surrogate model after correcting the data structure finally contains: Spatiotemporal distribution matrix: , time resolution , spatial resolution ; Physical verification report: Mass conservation error <5%, pressure wave propagation speed c = 5 m / s (in line with arterial elasticity characteristics); Outlier marking table: Records all points corrected by the threshold and the basis for neighborhood interpolation, such as at t = 0.1 s and y = 8 mm, the pressure p = 250 Pa is corrected to 130 Pa.

[0042] S105: Process the output data of the surrogate model and the high-dimensional and variable data of the pipe network, and generate a surrogate model for the outlet boundary conditions based on symbolic regression.

[0043] In one implementation, feature extraction processing is performed on the output data of the surrogate model to generate hemodynamic features. Among them, the hemodynamic features are composed of the flow prediction value and the pressure prediction value in the output data of the surrogate model through spatiotemporal distribution feature extraction. The surrogate model outputs the flow and pressure spatiotemporal distribution of a certain section of blood vessel during the cardiac cycle: Flow prediction value: systolic peak , diastolic trough , pulsation coefficient ; Pressure prediction value: systolic pressure , diastolic pressure , pressure gradient . Through spatiotemporal distribution feature extraction, a hemodynamic feature vector is generated: , where is the flow rate change rate, reflecting the blood flow acceleration characteristic.

[0044] Encode the high-dimensional and variable data of the pipe network to generate pipe network topology encoding features. Among them, the pipe network topology encoding features are generated by mapping the pipe diameter, bifurcation angle, and wall shear stress in the high-dimensional and variable data of the pipe network through topological structure features. Taking a bifurcating blood vessel as an example, the high-dimensional data of the pipe network includes: main blood vessel diameter D = 8 mm, branch diameter ; Bifurcation angle , wall shear stress . Through topological structure feature mapping, encoding features are generated: , where corresponds to the flow distribution ratio of Murray's law.

[0045] Fuse the hemodynamic features and the network topology coding features to generate fused features. Among them, the fused features are composed of the hemodynamic features and the network topology coding features through multi-dimensional parameter space discretization and feature correlation mechanism. Correlate the hemodynamic features and the topology coding features through multi-dimensional parameter space discretization: Discretization processing: Divide the diameter ratio into three intervals [0.3, 0.6), [0.6, 0.8), [0.8, 1], and the pressure gradient into [0, 3), [3, 7), [7, 10] Pa / mm; Feature correlation: Construct cross features to capture the coupling effect of geometry and dynamics. The final fused feature vector is: .

[0046] Perform symbolic regression on the fused features to generate candidate mathematical expressions. Among them, the symbolic regression process includes genetic algorithm optimization to generate expression trees and fitness evaluation to screen target expressions. Randomly generate an initial population of expression trees, such as: Expression 1: ; Expression 2: , where is a constant randomly generated within the range of [-1, 1], and the initial population size is 100 expressions. Calculate the prediction error and complexity penalty term: ; Taking Expression 1 as an example, the MSE on the test set is 0.03 (corresponding to a flow 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: .

[0047] Genetic operation strategy, tournament selection: Randomly select 5 individuals from the population and retain the top 30% of the fitness (such as Top30); Subtree crossover (probability 0.7): Exchange the sub-structures of the expression trees. For example, exchange of Expression 1 with of Expression 2 to generate a new expression: ; Node mutation (probability 0.2): Replace the operator sin with cos, or perturb the constant by ±10%; Elite retention: Retain the top 5 individuals with the highest fitness in each generation. For example, Expression 1 always remains in the Top5 during iteration.

[0048] Perform multi-objective optimization on the candidate mathematical expressions to generate an outlet boundary condition surrogate model. Among them, the multi-objective optimization is composed of optimizing the prediction error and model complexity through Pareto front search, and selecting the expression of the target node number in the model with an error ≤ 10%. The outlet boundary condition surrogate model is used to characterize the outlet boundary conditions of the vascular network. The Pareto front search is optimized through 200 generations of iteration to find the optimal balance between the prediction error (MSE) and the model complexity (number of nodes). The typical Pareto solutions are as follows:

[0049] Final model selection and verification, selection criterion: select the expression with the fewest number of nodes in the model with an error ≤ 10% (MSE ≤ 0.01), and preferentially select the M-12 model: Clinical data fitting parameters: ( ; After unit adaptation, the expression: .

[0050] In a case of a bifurcated blood vessel, the diameter of the main blood vessel D = 8mm, the diameter of the branch , the pressure gradient : Model predicted flow rate: ; Measured flow rate: 40.2 mL / min, error rate < 10%, meeting the clinical accuracy requirements.

[0051] S106, process the outlet boundary condition surrogate model, fitness evaluation, and genetic operation strategy based on the genetic algorithm to generate the target outlet boundary condition surrogate model and verification results.

[0052] In one implementation, perform initialization population processing on the outlet boundary condition surrogate model to generate an initial model population. Among them, the initial model population is composed of randomly generating diverse expression trees by the outlet boundary condition surrogate model; taking a binary bifurcated blood vessel as an example, randomly generate 100 initial expression trees, and some examples are as follows: Expression A: ; Expression B: ; Expression C: , where is a constant randomly generated within the range of [-2, 2], and the depth limit of the expression tree is ≤ 5 to ensure the diversity of the initial population.

[0053] Perform encoding processing on the fitness evaluation to generate fitness evaluation indicators. Among them, the fitness evaluation indicators are generated by calculating 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 squared error MSE of flow prediction = 0.028 (corresponding to an error rate of approximately 4.2%); Complexity Penalty: Depth Penalty Coefficient , the tree depth of Expression A is 4; Node Penalty Coefficient , Expression A contains 7 operation nodes; Total Penalty Term: ; Fitness Value: .

[0054] Genetic operations are performed on the initial model population and fitness evaluation metrics to generate an evolutionary model population. Among them, the genetic operations consist of tournament selection, subtree crossover, node mutation, and elitist retention strategy. Tournament selection randomly selects 5 individuals from the population, and 30% (30 individuals) with the highest fitness are retained for the next generation. For example, Expression A (Fitness = 0.71), Expression B (Fitness = 0.65), etc. are retained. Subtree Crossover (probability 0.7): Exchange the subtree of Expression A with the subtree of Expression B to generate a new expression: ; Node Mutation (probability 0.2): Replace the division operator in Expression C with multiplication, or apply a +10% perturbation to the constant (such as ). Elitist Retention retains the 5 individuals with the highest fitness in each generation to ensure that the optimal solution is not lost.

[0055] Multi-objective optimization is performed on the evolutionary model population to generate candidate optimized models. Among them, the multi-objective optimization includes Pareto front search to optimize prediction error and model complexity. After 200 generations of iterative optimization, a Pareto optimal solution set is formed between prediction error (MSE) and model complexity (number of nodes). Typical solutions are as follows:

[0056] The horizontal axis represents the number of model nodes. The number of nodes 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 , which contains operation nodes such as multiplication and addition, and the total number of nodes is 8. The expression of the M-12 model is , with 5 nodes and a more concise structure. The fewer the number of nodes, the simpler the model, 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, which can fit more complex relationships, but may overfit.

[0057] The vertical axis represents the MSE value ( ), and MSE (mean squared 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× , corresponding to a flow prediction error of about 2.2%, with relatively high accuracy. The MSE of M-12 is 3.1× , with an error rate of 3.1%, slightly lower in accuracy than M-5, but still meeting the clinical requirements (error ≤ 10%).

[0058] M-5 (high accuracy - high complexity): Incorporates multi-dimensional features such as the cube of the pipe diameter, bifurcation angle, and wall shear stress (e.g., D³×sinθ) through more nodes (8), enabling a more comprehensive characterization of the coupling relationship between hemodynamics and vascular geometry. Therefore, the MSE is lower (2.2× ), but the computational cost is higher.

[0059] M-12 (low accuracy - low complexity): Using only 5 nodes, based on Murray's law (flow distribution ratio ) and pressure gradient to construct a linear combination, with a simple structure and high computational efficiency, but sacrificing some accuracy ( ).

[0060] Among the models with limited number of nodes (≤5), M-12, through key feature screening (such as the flow distribution ratio of Murray's law) and linear combination, simplifies the model while retaining the main physical mechanisms, thus achieving the optimal accuracy (3.1% error) under low complexity conditions. While other models with ≤5 nodes (such as M-45, with 4 nodes and MSE = 4.5× ) have higher errors due to a simpler feature correlation mechanism (only a linear model of the branch diameter ratio).

[0061] The candidate optimization model is verified, generating a target outlet boundary condition surrogate model and verification results. Among them, the verification process consists of selecting an expression with the target number of nodes from models with an error ≤ 10% and verifying the model accuracy based on clinical data. For the final model selection, the selection criterion is: select the expression with the fewest number of nodes from models with an error ≤ 10% (MSE ≤ 0.1), and give priority to the M-12 model: ; Parameter fitting: Obtained through least squares fitting of the clinical dataset (n = 500) , , and the expression after unit adaptation is: .

[0062] The following is a clinical verification case. Case conditions: The diameter of the main blood vessel D = 8mm, the diameter of the branch , and the pressure gradient ; The model prediction is: ; The branch flow measured by ultrasonic Doppler is 40.2 mL / min, and the error rate , meeting the clinical accuracy requirements (error ≤ 10%).

[0063] Through multi-scale data fusion, DeepONet operator learning, and symbolic regression analysis, the present invention solves the problems of insufficient accuracy and complex calculation of traditional models. The specific steps are as follows: First, construct a multi-scale vascular feature database, integrating CFD data (such as diameter, bifurcation angle, etc.) of large / small blood vessels and DPD data (such as inter-particle forces, etc.) of capillaries. Through autoencoder dimensionality reduction, spatio-temporal normalization (such as Reynolds number Re = 7950 to characterize turbulent characteristics), and data augmentation, generate compressed and normalized data, retaining 95% of the key features and reducing the data volume to 6.4%.

[0064] Secondly, use DeepONet to process the compressed data. The branch network extracts the high-dimensional vector of vascular features, and the backbone network generates boundary condition parameters in combination with physical conservation constraints. After anti-normalization and spatio-temporal interpolation, the flow rate / pressure prediction values are obtained, with the error controlled within 10%. Then, fuse hemodynamic features and pipe network topology coding features, generate candidate expressions through symbolic regression driven by a genetic algorithm, and through Pareto front optimization, select the model with an error ≤ 10% and the fewest number of nodes. The clinical verification error is only 10%. This method breaks through the limitation of the traditional Windkessel model relying on fixed parameters, realizes multi-scale physiological feature fusion and efficient modeling under physical constraints, and the prediction speed is 1000 times faster than that of full-order CFD, providing a high-precision and interpretable model for hemodynamic simulation and clinical applications.

[0065] In one implementation, as Figure 3 shown, the present application also provides a proxy model construction device for the outlet boundary conditions of a vascular network, including: An acquisition module 301, configured to construct a multi-scale vascular feature database, where 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 rate characteristic parameters, and the capillary modeling data includes inter-particle forces and red blood cell membrane flexibility characteristic information; A processing module 302, configured to perform data compression and spatio-temporal normalization processing on the multi-scale vascular feature data to generate compressed and normalized data, where the compressed and normalized data consists of the dimensionality reduction result of the autoencoder, the spatio-temporal normalization relationship, the data mixing and augmentation result; process the compressed and normalized data to generate 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 pipe network to generate an outlet boundary condition proxy model based on symbolic regression, where 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.

[0066] Although the present application is disclosed as above, the present application is not limited thereto. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application. Therefore, the protection scope of the present application shall be subject to the scope defined by the claims.

Claims

1. A method for constructing a surrogate model of the outlet boundary condition of a vascular network, characterized in that Including: Construct a multi-scale vascular feature database, where the multi-scale vascular feature database includes large / small vessel modeling data and capillary modeling data. The large / small vessel modeling data contains vascular diameter, bifurcation angle, wall shear stress, and flow characteristic parameters, and the capillary modeling data contains inter-particle forces and erythrocyte membrane flexibility characteristic information; Perform data compression and spatio-temporal normalization processing on the multi-scale vascular feature data to generate compressed and normalized data, where the compressed and normalized data consists of the dimensionality reduction result of the autoencoder, spatio-temporal normalization relationship, data mixing and enhancement result; Process the compressed and normalized data and generate target surrogate model parameters based on DeepONet; Process the target surrogate model parameters to generate surrogate model output data; Process the surrogate model output data and the high-dimensional and variable pipe network data, and generate an outlet boundary condition surrogate model based on symbolic regression, where the outlet boundary condition surrogate model is used to characterize the outlet boundary conditions of the vascular network; Process the outlet boundary condition surrogate model, fitness evaluation, and genetic operation strategy based on the genetic algorithm to generate a target outlet boundary condition surrogate model and verification results.

2. The method according to claim 1, wherein Perform data compression and spatio-temporal normalization processing on the multi-scale vascular feature data to generate compressed and normalized data, including: Perform dimensionality reduction processing on the multi-scale vascular feature data using an autoencoder to generate the dimensionality reduction result of the autoencoder; Construct a spatio-temporal normalization relationship for the multi-scale vascular feature data to generate a spatio-temporal normalization relationship; Perform data mixing and enhancement processing on the multi-scale vascular feature data to generate a data mixing and enhancement result; Perform comprehensive processing based on the dimensionality reduction result of the autoencoder, spatio-temporal normalization relationship, and data mixing and enhancement result to generate compressed and normalized data.

3. The method according to claim 1, characterized in that Process the compressed and normalized data and generate target surrogate model parameters based on DeepONet, including: Perform branch network processing on the discrete sampling values of the vascular feature function in the compressed and normalized data to generate high-dimensional vascular feature vectors and network weight parameters; Fuse the physical conservation constraints and network prediction errors based on the high-dimensional vascular feature vectors and spatial basis function vectors to generate boundary condition parameters; Fuse the flow prediction value and pressure prediction value based on the inverse normalization parameters and physical quantity reduction formula to generate a physical quantity prediction result; Analyze and process the boundary condition parameters and physical quantity prediction results to generate target surrogate model parameters, which are used to characterize the pressure and flow of the outlet boundary conditions of the vascular network.

4. The method according to claim 3, wherein Process the target surrogate model parameters to generate surrogate model output data, including: Perform traffic restoration processing on the boundary condition parameters in the target proxy model parameters to generate traffic prediction values, where the traffic prediction values are calculated by the boundary condition parameters through the traffic restoration formula Constitute the calculation; Perform pressure restoration processing on the boundary condition parameters in the target proxy model parameters to generate a pressure prediction value, where the pressure prediction value is composed of the pressure components in the boundary condition parameters through the pressure restoration formula Calculated composition; Perform spatio-temporal coordinate mapping processing on the flow prediction value and pressure prediction value to generate the physical quantity distribution in spatio-temporal coordinates, where the physical quantity distribution in spatio-temporal coordinates is composed of the flow prediction value, pressure prediction value, spatial coordinate y, and time t through an interpolation algorithm; Perform adaptive threshold processing on the physical quantity distribution in spatio-temporal coordinates to generate initial surrogate model output data, where the adaptive threshold processing converts the physical quantity distribution into a preliminary result by setting a dynamic threshold based on the physiological range of blood flow; Perform physical consistency verification processing on the output data of the initial surrogate model to generate the output data of the final surrogate model. Among them, the physical consistency verification processing is carried out through the mass conservation equation Check and correct the initial results.

5. The method according to claim 1, characterized in that Process the output data of the surrogate model and the high-dimensional and variable data of the pipe network, and generate a surrogate model for the outlet boundary conditions based on symbolic regression, including: Perform feature extraction processing on the output data of the surrogate model to generate hemodynamic features. Among them, the hemodynamic features are composed of the flow prediction value and the pressure prediction value in the output data of the surrogate model through spatio-temporal distribution feature extraction; Perform encoding processing on the high-dimensional and variable data of the pipe network to generate pipe network topology encoding features. Among them, the pipe network topology encoding features are generated by mapping the pipe diameter, bifurcation angle, and wall shear stress in the high-dimensional and variable data of the pipe network through topological structure features; Perform fusion processing on the hemodynamic features and the pipe network topology encoding features to generate fusion features. Among them, the fusion features are composed of the hemodynamic features and the pipe network topology encoding features through multi-dimensional parameter space discretization and feature association mechanism; Perform symbolic regression processing on the fusion features to generate candidate mathematical expressions. Among them, the symbolic regression processing includes genetic algorithm optimization to generate expression trees and fitness evaluation to screen target expressions; Perform multi-objective optimization processing on the candidate mathematical expressions to generate a surrogate model for the outlet boundary conditions. Among them, the multi-objective optimization processing is composed of Pareto front search to optimize the prediction error and the model complexity, and selecting the expression of the target number of nodes in the model with an error ≤ 10%. The surrogate model for the outlet boundary conditions is used to characterize the outlet boundary conditions of the vascular network.

6. The method according to claim 1, characterized in that, Process the surrogate model for the outlet boundary conditions, fitness evaluation, and genetic operation strategy based on the genetic algorithm to generate the target surrogate model for the outlet boundary conditions and the verification result, including: Perform initialization population processing on the surrogate model for the outlet boundary conditions to generate an initial model population. Among them, the initial model population is composed of the surrogate model for the outlet boundary conditions through randomly generating diverse expression trees; Perform encoding processing on the fitness evaluation to generate fitness evaluation indicators. Among them, the fitness evaluation indicators are generated by calculating the prediction error and the complexity penalty term through the fitness function; Perform genetic operation processing on the initial model population and the fitness evaluation indicators to generate an evolutionary model population. Among them, the genetic operation processing is composed of tournament selection, subtree crossover, node mutation, and elite retention strategy; Perform multi-objective optimization processing on the evolutionary model population to generate a candidate optimization model. Among them, the multi-objective optimization processing includes Pareto front search to optimize the prediction error and the model complexity; Perform verification processing on the candidate optimization model to generate the target surrogate model for the outlet boundary conditions and the verification result. Among them, the verification processing is composed of selecting the expression of the target number of nodes in the model with an error ≤ 10% and verifying the model accuracy based on clinical data.

7. An apparatus for constructing a surrogate model of the outlet boundary condition of a vascular network, characterized in that, The device includes: An acquisition module for constructing a multi-scale vascular feature database. Among them, the multi-scale vascular feature database includes large / small vessel modeling data and capillary modeling data. The large / small vessel modeling data contains vascular diameter, bifurcation angle, wall shear stress, and flow characteristic parameters. The capillary modeling data contains inter-particle force and erythrocyte membrane flexibility characteristic information; A processing module for performing data compression and spatio-temporal normalization processing on multi-scale vascular feature data to generate compressed and normalized data, where the compressed and normalized data consists of the dimensionality reduction result of the autoencoder, the spatio-temporal normalization relationship, and the data mixing and enhancement result; processing the compressed and normalized data to generate target surrogate model parameters based on DeepONet; processing the target surrogate model parameters to generate surrogate model output data; processing the surrogate model output data and the high-dimensional and variable data of the pipe network to generate an outlet boundary condition surrogate model based on symbolic regression, where the outlet boundary condition surrogate model is used to characterize the outlet boundary condition of the vascular network; processing the outlet boundary condition surrogate model, the fitness evaluation, and the genetic operation strategy based on the genetic algorithm to generate a target outlet boundary condition surrogate model and a verification result.

8. An electronic device, characterized in that, Comprising: A first processor; And a memory for storing executable instructions of the first processor; Wherein, the first processor is configured to execute the proxy model construction method for the outlet boundary condition of the vascular network according to any one of claims 1 to 6 by executing the executable instructions.

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