Aorta central pressure non-invasive estimation method driven by a vascular tree network

Abstract

This invention discloses a non-invasive method for estimating central aortic pressure (PWV) driven by a vascular tree network, relating to the field of cardiovascular hemodynamic modeling. The method includes: collecting clinical data and scaling the vessel length and reference area; calculating the flow waveforms of the aorta and its branches based on the 4D-Flow MRI velocity field to determine the blood flow distribution ratio; constructing an eight-branch vascular tree network model based on the pressure propagation path from the aorta to the brachial artery; selecting a section on the descending aorta's central axis to calculate the flow waveform and inversely calculating PWV; constructing a dataset using sensitivity analysis and one-dimensional positive problem simulation to pre-train the neural network; performing PINN patient-specific fine-tuning on the model; extracting the aortic pressure waveform using the fine-tuned model, calculating the central aortic pressure value, and outputting patient-specific parameters and distribution results. The input waveform constructed based on non-invasive clinical data in this invention can adapt to different patient-specific differences, significantly improving the model's individualization and clinical compatibility.

Description

Technical Field

[0001] This invention relates to the field of cardiovascular hemodynamic modeling, and in particular to a non-invasive method for estimating central aortic pressure driven by a vascular tree network. Background Technology

[0002] Central aortic pressure and aortic pressure waveforms can reflect left ventricular afterload, aortic elasticity, wave reflection, and systemic arterial tree hemodynamics, and are of significant value in hypertension, aortic stenosis, arteriosclerosis, cardiovascular risk assessment, and individualized treatment planning. The brachial cuff blood pressure, including systolic, diastolic, and mean pressure, is readily available clinically. However, brachial artery pressure and central aortic pressure are influenced by factors such as vascular geometry, material properties, peripheral impedance, wave propagation, and wave reflection, and cannot be simply equated.

[0003] Existing methods for estimating central aortic pressure mainly include empirical transfer function methods, statistical regression methods, data-driven deep learning methods, and parameter optimization methods based on 0D / 1D vascular models. While empirical transfer function and purely data-driven methods are computationally fast, they typically rely on training data from specific populations and struggle to clearly reflect individual patient geometry, material properties, and blood flow distribution differences. Although traditional 1D vascular models have clear physical meaning, the complete arterial tree network has numerous parameters. If multi-parameter optimization is performed solely based on brachial artery blood pressure, problems such as unidentifiable parameters, local optima, and excessively long computation times can easily arise.

[0004] 4D-Flow MRI can acquire time-varying velocity fields and flow waveforms at the aorta and its branches, providing a non-invasive data foundation for estimating aortic branch flow distribution, local aortic pulse wave propagation time, and pulse wave velocity. Echocardiography can provide routine clinical parameters such as stroke volume, heart rate, aortic diameter, and left ventricular ejection fraction. If 4D-Flow MRI, echocardiography, and brachial artery blood pressure can be used together as constraint inputs and combined with 1D blood flow control equations and the PINN inverse problem solution framework, it is hoped that patient specificity can be maintained while reducing the model's degrees of freedom.

[0005] Given the current situation, there is a need for a method that can invert aortic pressure waveforms from brachial artery blood pressure, while simultaneously identifying vascular material properties and peripheral impedance parameters, provided clinically available data is available. This method should avoid complete reliance on invasive central pressure measurements, reduce the time cost of traditional high-dimensional parameter optimization, and output patient-specific aortic pressure waveforms suitable for clinical assessment.

[0006] Therefore, those skilled in the art are dedicated to developing a non-invasive method for estimating central aortic pressure driven by a vascular tree network. Summary of the Invention

[0007] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is that traditional lumped parameter models mainly rely on empirical values ​​or invasive measurements to obtain aortic pressure and flow. The former lacks individual variability, and the latter is not feasible in routine clinical diagnosis due to its invasiveness, resulting in the inability to obtain patient-specific input boundary waveforms.

[0008] To achieve the above objectives, the present invention provides a non-invasive method for estimating central aortic pressure driven by a vascular tree network, characterized in that the method includes the following steps: S101: Collect the patient's clinical multimodal data and scale the vessel length and vessel reference area according to the multimodal data; S103: Calculate the flow waveform of the aorta and major branches based on the velocity field of 4D-Flow MRI, and determine the blood flow distribution ratio of trunk / lower limb, head and neck, upper limb and distal upper limb branches based on the periodic average flow. S105: Based on the pressure propagation path from the aorta to the brachial artery, an eight-vessel tree network model is constructed, wherein the eight-vessel tree network model replaces the complete peripheral microcirculation network with a small number of boundary parameters. S107: Select two sections on the central line of the descending aorta, calculate the flow waveform of the two sections using 4D-Flow MRI velocity field, and calculate the propagation time difference using the cross-correlation method to inversely calculate the pulse wave velocity (PWV). S109: Generate multiple sets of combined parameters using sensitivity analysis, construct a pre-training dataset based on the combined parameters and the simulation results of a one-dimensional forward problem, and pre-train the neural network model using the pre-training dataset; S111: Perform PINN patient-specific fine-tuning on the pre-trained neural network model and output the fine-tuned neural network model; S113: Using the finely tuned neural network model, extract the aortic pressure waveform at the aortic root or proximal ascending aorta, calculate the central aortic pressure value, and output the patient-specific aortic pressure waveform, material property parameters, terminal impedance parameters, and branch flow distribution results.

[0009] Further, in step S101, the multimodal data includes brachial artery cuff blood pressure, echocardiographic parameters, 4D-Flow MRI velocity field, height and weight, and the cardiac cycle of the multimodal data is unified according to heart rate.

[0010] Furthermore, when scaling the vessel length and reference area, the following method is used:

[0011] in, For the first The length of the root vessel after expansion and contraction, For the first Average length of root vessels For the first Reference area of ​​root vessels For the first The average reference area of ​​root vessels Length factor, is the area scale factor.

[0012] Furthermore, in step S103, when calculating the cross-sectional flow waveform from the 4D-Flow velocity field, the following method is used:

[0013] The blood flow distribution ratio is calculated using the following method:

[0014] in, For the first Flow waveform of a section or branch For cross-sectional area, For 4D-FlowMRI velocity field, The normal vector of the cross section. For the first The proportion of blood flow shunt in each terminal branch This refers to the number of terminal exports. For the first One outlet flow waveform, For spatial coordinates, For time.

[0015] Further, in step S105, the eight-vessel tree network model includes the equivalent segments of the ascending aorta / proximal aorta, the aortic arch-descending aorta, the brachiocephalic trunk, the right common carotid artery, the right subclavian-axillary artery, the right brachial artery, the right radial artery, and the right ulnar artery. The eight-vessel tree network model preserves the main propagation path from the aorta to the brachial artery and equates the peripheral vascular beds of the trunk / lower limb, head and neck, and distal upper limb to the RCR terminal boundaries.

[0016] Furthermore, in step S107, the specific method for calculating the propagation time difference using the cross-correlation method is as follows:

[0017] Based on the distance between the two aortic cross sections along the aortic centerline and the time difference of propagation, the pulse wave velocity (PWV) is calculated inversely:

[0018] in, The propagation time difference between the two cross-sectional flow waveforms is given. This is the time lag. and The velocity integral of two aortic sections in 4D-Flow MRI. to The time period for waveform coherence. The pulse wave velocity is calculated inversely from 4D-FlowMRI. The distance between the two aortic sections along the aortic centerline.

[0019] Furthermore, in step S109, the pre-training dataset is generated through a process of "parameter sampling—forward problem simulation—output processing," specifically including the following steps: S1091: Determine the set of parameters to be sampled based on literature reference data, patient-scale scaling results, and reasonable physiological ranges; S1092: Set a wider sampling range for highly sensitive parameters and a narrower perturbation range for low-sensitive geometric parameters, or directly use scaled-down literature reference data; S1093: The combined parameters are generated using Latin hypercube sampling, Sobol sequence sampling, or single-factor perturbation methods; S1094: Input the combined parameters into a one-dimensional vascular tree positive problem model to calculate the aortic pressure waveform, brachial artery pressure waveform, flow waveforms of each branch, local PWV and terminal flow allocation results, forming the pre-training dataset; The pre-trained dataset is:

[0020] in, For the first Input features of the group of samples For the first Model parameters for the group of samples, The aortic pressure waveform. This is the brachial artery pressure waveform. For the first Branch flow waveforms For the first The wave velocity calculated from the material parameters The total number of samples.

[0021] Furthermore, in step S111, when performing PINN patient-specific fine-tuning on the pre-trained neural network model, patient-specific data is used to perform constraint correction based on the pre-trained neural network model, and the network weights and identifiable model parameters are fine-tuned within a small range to reduce the search space of multi-parameter global optimization and improve inversion stability and computational efficiency.

[0022] Furthermore, when performing PINN patient-specific fine-tuning on the pre-trained neural network model, the following steps are included: S1111: Combine the pre-trained network weights, initial material parameter values, and terminal... The initial parameter values ​​are used as initial values ​​for fine-tuning; S1112: Input patient-specific data, including heart rate, stroke volume, brachial cuff blood pressure, height and weight, aortic diameter, 4D-Flow shunt ratio, and 4D-Flow PWV; S1113: Randomly or uniformly select spatiotemporal points within eight blood vessel segments, output the blood vessel cross-sectional area, blood flow rate, and blood vessel pressure of the spatiotemporal points through the neural network model, and use automatic differentiation to calculate the residual of the one-dimensional equation; S1114: Calculate the systolic, diastolic, and mean pressure of the output pressure at the brachial artery observation location, and compare it with the patient's cuff blood pressure to construct peripheral pressure loss; S1115: Calculate the theoretical PWV determined by material parameters in two sections of the aorta or a specified aortic segment, and construct the material property loss by inversely calculating the PWV with 4D-Flow. S1116: Calculate the periodic average flow ratio at each terminal exit and construct the flow allocation loss with the 4D-Flow split ratio; S1117: Weighted sum of physical residual loss, brachial artery pressure loss, PWV loss, flow distribution loss, geometric prior loss, and bifurcation conservation loss; S1118: Use the L-BFGS optimizer to update network weights and high-sensitivity parameters, while keeping low-sensitivity geometric parameters at literature reference values ​​scaled down or allowing only small-scale corrections. S1119: When the total loss converges and the brachial artery pressure error, PWV error and shunt ratio error all meet the set thresholds, stop fine-tuning and output the aortic pressure waveform.

[0023] Furthermore, the total loss when performing PINN patient-specific fine-tuning on the pre-trained neural network model is:

[0024] in, For physical residual loss: For brachial artery pressure loss: For PWV loss: Distribute the loss to the traffic: for: For the fork conservation loss:

[0025] in, For the geometric prior loss of the quality-conserving residual, For momentum conservation residuals, For the cross-sectional area of ​​blood vessels, For blood flow, For vascular pressure, For momentum correction parameters, For density parameters, For friction parameters, For the number of spatiotemporal points, To find the derivative with respect to time, To find the derivative with respect to space; Brachial artery pressure, , , For cuff blood pressure indicators, For average pressure weighting; To predict PWV, For PWV images; For the first Individual terminal outbound traffic, For 4D-Flow splitting ratio, This refers to the number of terminal exports. This refers to the duration of the cardiac cycle; For the first The a priori length of the root vessel after expansion and contraction For the first Prior reference area after the root vessel is expanded or contracted; This represents the number of branching nodes in an octal tree network. For the first Flow at the parent vessel terminal at each bifurcation node and The first The inlet flow of the two sub-vessels at the bifurcation node For the first Pressure at the end of the parent vessel at each bifurcation node and The first Pressure at the inlet of two sub-vessels at a bifurcation node; Weights for physical residual loss, Weighting of brachial artery pressure loss For PWV loss weights, Assign loss weights to traffic, For geometric prior loss weights, The weight for the bifurcation conservation loss is determined.

[0026] In a preferred embodiment of the present invention, compared with the prior art, the present invention has the following beneficial effects: 1. This invention integrates multimodal non-invasive data such as brachial artery cuff blood pressure, echocardiography, and 4D-Flow MRI, which can construct patient-specific constraints without invasive aortic pressure measurement, thereby improving the clinical applicability of aortic central pressure estimation; 2. This invention constructs an eight-root vascular tree network model based on the pressure propagation path from the aorta to the brachial artery, and uses an equivalent peripheral vascular bed at the RCR boundary at the terminal, thereby reducing the parameter dimensionality and computational complexity of the complete arterial tree model while preserving the main wave propagation path. 3. The input waveform constructed by this invention can be adapted to the heart rate, blood pressure and ventricular pumping capacity of different patients, which significantly improves the individualization and clinical compatibility of the model.

[0027] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0028] Figure 1 This is a schematic diagram illustrating the implementation steps of a preferred embodiment of the present invention; Figure 2 This is a schematic diagram showing the correspondence between a vascular tree network model and human anatomical structures according to a preferred embodiment of the present invention; Figure 3 This is a schematic diagram of the average flow distribution ratio of the main branches in a preferred embodiment of the present invention; Figure 4 This is a preferred embodiment of the present invention, showing the aortic inlet flow waveform constructed based on HR=68 bpm and SV=74 mL; Figure 5This is a schematic diagram of the flow waveform and PWV inverse calculation of the aortic S1 / S2 cross sections according to a preferred embodiment of the present invention; Figure 6 This is a schematic diagram comparing the brachial artery pressure constraint and the inverted aortic central pressure waveform according to a preferred embodiment of the present invention. Detailed Implementation

[0029] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0030] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0031] like Figure 1 As shown, traditional lumped parameter models rely on empirical values ​​or invasive measurements to obtain aortic pressure and flow, resulting in the inability to obtain patient-specific input boundary waveforms. This invention uses an eight-vessel tree network model and a physical information neural network to invert aortic pressure waveform and vascular material properties from peripheral brachial artery blood pressure, achieving completely non-invasive parameter identification. Furthermore, the constructed input waveform can be adapted to the heart rate, blood pressure, and ventricular pumping capacity of different patients, improving the model's individualization and clinical compatibility.

[0032] Specifically, the non-invasive aortic central pressure estimation method driven by vascular tree network provided by the present invention includes the following steps: S101: Collect patient clinical multimodal data and scale the vessel length and reference area based on the multimodal data.

[0033] In this embodiment, the clinically collected multimodal data includes brachial artery cuff blood pressure, echocardiographic parameters, 4D-Flow MRI velocity field, height and weight, and the cardiac cycle of the multimodal data is unified according to heart rate.

[0034] When scaling the length and reference area of ​​blood vessels, the following method is used:

[0035] in, For the first The length of the root vessel after expansion and contraction, For the first Reference area of ​​root vessels For the first Average length of root vessels For the first The average reference area of ​​root vessels Length factor, is the area scale factor.

[0036] S103: Calculate the flow waveforms of the aorta and major branches based on the velocity field of 4D-Flow MRI, and determine the blood flow distribution ratio of the trunk / lower limb, head and neck, upper limb and distal upper limb branches based on the periodic average flow.

[0037] In this embodiment, the cross-sectional flow waveform is calculated from the 4D-Flow velocity field using the following method:

[0038] The blood flow distribution ratio is calculated using the following method:

[0039] in, For the first Flow waveform of a section or branch For cross-sectional area, For 4D-Flow MRI velocity field, The normal vector of the cross section. For the first The proportion of blood flow shunt in each terminal branch This refers to the number of terminal exports. For the first One outlet flow waveform, For spatial coordinates, For time.

[0040] S105: Based on the pressure propagation path from the aorta to the brachial artery, an eight-vessel tree network model is constructed. The eight-vessel tree network model replaces the complete peripheral microcirculation network with a small number of boundary parameters.

[0041] In this embodiment, the eight-vessel tree network model includes the equivalent segments of the ascending aorta / proximal aorta, the aortic arch-descending aorta, the brachiocephalic trunk, the right common carotid artery, the right subclavian-axillary artery, the right brachial artery, the right radial artery, and the right ulnar artery. The eight-vessel tree network model preserves the main propagation path from the aorta to the brachial artery and equates the peripheral vascular beds of the trunk / lower limb, head and neck, and distal upper limb to the RCR terminal boundaries.

[0042] S107: Select two sections on the central line of the descending aorta, calculate the flow waveforms of the two sections using 4D-Flow MRI velocity field, and calculate the propagation time difference using the cross-correlation method to inversely calculate the pulse wave velocity (PWV).

[0043] In this embodiment, the specific method for calculating the propagation time difference using the cross-correlation method is as follows:

[0044] Based on the distance between the two aortic cross sections along the aortic centerline and the time difference of propagation, the pulse wave velocity (PWV) is calculated inversely:

[0045] in, The propagation time difference between the two cross-sectional flow waveforms is given. This is the time lag. and The velocity integral of two aortic sections in 4D-Flow MRI. to To shorten the period of high waveform coherence in the early stages or within the complete cycle. The pulse wave velocity was calculated from 4D-Flow MRI. The distance between the two aortic sections along the aortic centerline.

[0046] S109: Generate multiple sets of combined parameters using sensitivity analysis, construct a pre-training dataset based on the combined parameters and simulation results of a one-dimensional positive problem, and pre-train the neural network model using the pre-training dataset.

[0047] In this embodiment, the pre-training dataset is generated through a process of "parameter sampling - forward problem simulation - output processing", specifically including the following steps: S1091: Determine the set of parameters to be sampled based on literature reference data, patient-scale scaling results, and reasonable physiological ranges; S1092: Set a wider sampling range for highly sensitive parameters and a narrower perturbation range for low-sensitive geometric parameters, or directly use scaled-down literature reference data; S1093: Combined parameters are generated using Latin hypercube sampling, Sobol sequence sampling, or single-factor perturbation methods; S1094: Input the combined parameters into a one-dimensional vascular tree positive problem model to calculate the aortic pressure waveform, brachial artery pressure waveform, flow waveforms of each branch, local PWV and terminal flow distribution results, forming a pre-training dataset; The pre-training dataset is:

[0048] in, For the first Input features of the group of samples For the first Model parameters for the group of samples, The aortic pressure waveform. This is the brachial artery pressure waveform. For the first Branch flow waveforms For the first The wave velocity calculated from the material parameters The total number of samples.

[0049] S111: Perform PINN patient-specific fine-tuning on the pre-trained neural network model and output the fine-tuned neural network model.

[0050] In this embodiment, when performing PINN patient-specific fine-tuning on the pre-trained neural network model, patient-specific data is used for constraint correction based on the pre-trained neural network model. The network weights and identifiable model parameters are fine-tuned within a small range, reducing the search space for multi-parameter global optimization and improving inversion stability and computational efficiency.

[0051] When performing PINN patient-specific fine-tuning on the pre-trained neural network model, the following steps are included: S1111: Combine the pre-trained network weights, initial material parameter values, and terminal... The initial parameter values ​​are used as initial values ​​for fine-tuning; S1112: Input patient-specific data, including heart rate, stroke volume, brachial cuff blood pressure, height and weight, aortic diameter, 4D-Flow shunt ratio, and 4D-Flow PWV; S1113: Randomly or uniformly select spatiotemporal points within eight blood vessel segments, output the blood vessel cross-sectional area, blood flow, and blood vessel pressure of the spatiotemporal points through a neural network model, and use automatic differentiation to calculate the residual of the one-dimensional equation. S1114: Calculate the systolic, diastolic, and mean pressure of the output pressure at the brachial artery observation location, and compare it with the patient's cuff blood pressure to construct peripheral pressure loss; S1115: Calculate the theoretical PWV determined by material parameters in two sections of the aorta or a specified aortic segment, and construct the material property loss by inversely calculating the PWV with 4D-Flow. S1116: Calculate the periodic average flow ratio at each terminal exit and construct the flow allocation loss with the 4D-Flow split ratio; S1117: Weighted sum of physical residual loss, brachial artery pressure loss, PWV loss, flow distribution loss, geometric prior loss, and bifurcation conservation loss; S1118: Use the L-BFGS optimizer to update network weights and high-sensitivity parameters, while keeping low-sensitivity geometric parameters at literature reference values ​​scaled down or allowing only small-scale corrections. S1119: When the total loss converges and the brachial artery pressure error, PWV error and shunt ratio error all meet the set thresholds, stop fine-tuning and output the aortic pressure waveform.

[0052] The total loss when performing PINN patient-specific fine-tuning on the pre-trained neural network model is:

[0053] in, For physical residual loss: For brachial artery pressure loss: For PWV loss: Distribute the loss to the traffic: For geometric prior loss: For the fork conservation loss:

[0054] in, For the geometric prior loss of the quality-conserving residual, For momentum conservation residuals, For the cross-sectional area of ​​blood vessels, For blood flow, For vascular pressure, For momentum correction parameters, For density parameters, For friction parameters, For the number of spatiotemporal points, To find the derivative with respect to time, To find the derivative with respect to space; Brachial artery pressure, , , For cuff blood pressure indicators, For average pressure weighting; To predict PWV, For PWV images; For the first Individual terminal outbound traffic, For 4D-Flow splitting ratio, The number of terminal exports (in the example) ), This refers to the duration of the cardiac cycle; For the first The a priori length of the root vessel after expansion and contraction For the first Prior reference area after the root vessel is expanded or contracted; In this embodiment, the number of branching nodes in the eight-vessel tree network is [number]. , For the first Flow at the parent vessel terminal at each bifurcation node and The first The inlet flow of the two sub-vessels at the bifurcation node For the first Pressure at the end of the parent vessel at each bifurcation node and The first Pressure at the inlet of two sub-vessels at a bifurcation node; Weights for physical residual loss, Weighting of brachial artery pressure loss For PWV loss weights, Assign loss weights to traffic, For geometric prior loss weights, The weight for the bifurcation conservation loss is determined.

[0055] S113: Using a finely tuned neural network model, the aortic pressure waveform is extracted at the aortic root or proximal ascending aorta, the central aortic pressure value is calculated, and the patient-specific aortic pressure waveform, material property parameters, terminal impedance parameters, and branch flow distribution results are output.

[0056] Compared with existing technologies, the non-invasive aortic central pressure estimation method driven by vascular tree network provided in this invention has the following beneficial technical effects: 1. This invention integrates multimodal non-invasive data such as brachial artery cuff blood pressure, echocardiography, and 4D-Flow MRI, which can construct patient-specific constraints without invasive aortic pressure measurement, thereby improving the clinical applicability of aortic central pressure estimation.

[0057] 2. This invention constructs an eight-vessel tree network model based on the pressure propagation path from the aorta to the brachial artery, and adopts an RCR boundary equivalent peripheral vascular bed at the terminal, thereby reducing the parameter dimension and computational complexity of the complete arterial tree model while preserving the main wave propagation path.

[0058] 3. This invention utilizes the two-section flow waveform of 4D-Flow MRI to calculate PWV and uses PWV as a constraint target for vascular material properties, reducing the problem of unidentifiable material parameters when relying solely on brachial artery blood pressure inversion, and improving the stability and interpretability of material parameter inversion.

[0059] 4. This invention utilizes sensitivity analysis and one-dimensional positive problem simulation to generate a pre-training dataset, enabling the neural network to obtain reasonable initial parameter values. Then, through PINN patient-specific fine-tuning, the aortic pressure waveform inversion is completed, which can reduce the multi-parameter global optimization search space and improve computational efficiency.

[0060] 5. This invention outputs patient-specific aortic pressure waveforms, central systolic pressure, central diastolic pressure, pulse pressure, material property parameters, and terminal impedance parameters, which can be used for aortic central pressure assessment, left ventricular afterload analysis, and hemodynamic assessment of valvular heart disease.

[0061] The present invention will now be described in detail with reference to preferred embodiments.

[0062] To address the shortcomings of existing technologies that rely on lumped parameter models to obtain aortic pressure and flow rates, which depend on empirical values ​​or invasive measurements and thus fail to capture patient-specific input boundary waveforms, this embodiment provides a non-invasive aortic central pressure estimation method driven by a vascular tree network. This method individualizes the classic aortic pressure / flow waveform based on clinical non-invasive data. The complete processing flow of this invention includes the following steps: Step 1: Collect multimodal clinical data from patients, including brachial artery cuff blood pressure, echocardiographic parameters, 4D-Flow MRI velocity field, and basic information such as patient height and weight; Step 2: Based on the heart rate, unify the cardiac cycle of each modality, and scale the blood vessel length and reference area in the literature according to height, weight, body surface area and aortic diameter to the patient scale. Step 3: Calculate the flow waveforms of the aorta and major branches based on the 4D-Flow MRI velocity field, and determine the blood flow distribution ratio of the trunk / lower limbs, head and neck, upper limbs and distal upper limb branches based on the periodic average flow. Step 4: Construct an eight-vessel tree network model based on the main pressure propagation path from the aorta to the brachial artery, and set equivalent boundaries for RCR at each terminal, replacing the complete peripheral microcirculation network with a small number of boundary parameters; Step 5: Select two sections on the centerline of the descending aorta, calculate the flow waveforms of the two sections using 4D-Flow MRI, calculate the propagation time difference using the cross-correlation method, and further calculate the pulse wave velocity (PWV). Step 6: Use PWV as a constraint on vascular material properties, brachial artery blood pressure as a constraint on peripheral pressure, 4D-Flow shunt ratio as a constraint on terminal flow rate, and ultrasound stroke volume as a constraint on inlet flow integral. Step 7: Construct a pre-training dataset using multiple parameter combinations generated by sensitivity analysis and one-dimensional forward problem simulation results, so that the neural network can obtain reasonable initial values ​​for vascular material properties, terminal impedance, and aortic pressure waveform; Step 8: Use the pre-trained network as the initial model, and perform PINN patient-specific fine-tuning by combining the residuals of the one-dimensional blood flow control equation, PWV loss, brachial artery pressure loss, flow distribution loss, geometric prior loss, and bifurcation conservation loss. Step 9: Extract the aortic pressure waveform from the fine-tuned network at the aortic root or proximal ascending aorta, and calculate the central aortic systolic pressure, diastolic pressure, mean pressure, and pulse pressure; Step 10: Output patient-specific aortic pressure waveform, material property parameters, terminal impedance parameters, and branch flow distribution results.

[0063] For ease of understanding, this embodiment follows the sequence of "first acquiring clinical input, then forming model constraints, then completing neural network inversion, and finally outputting aortic central pressure". Specifically, firstly, peripheral pressure constraints are provided by brachial cuff blood pressure, heart rate and stroke volume constraints are provided by echocardiography, and branch flow distribution ratio and descending aortic local PWV constraints are provided by 4D-Flow MRI; secondly, the vessel length and reference area are scaled according to the patient's height, weight, and aortic diameter, and an eight-vessel tree network from the aorta to the brachial artery is constructed; thirdly, the neural network is pre-trained using sensitivity analysis samples to obtain reasonable initial parameter values; finally, the multimodal data of patient A is input into the pre-trained network, and fine-tuned by PINN physical residuals and clinical observation losses to output patient-specific aortic pressure waveforms. Subsequent formulas (1) to (28) all serve this continuous process, rather than being independent calculation steps.

[0064] (a) Simulated patient input and correspondence between clinical indicators

[0065] Taking a simulated patient A as an example: height H = 172 cm, weight W = 70 kg, brachial cuff blood pressure SBP_br / DBP_br = 126 / 78 mmHg, heart rate HR = 68 bpm, estimated stroke volume SV from echocardiography = 74 mL, and proximal aortic diameter d_ao = 30 mm. 4D-Flow MRI was used to acquire the velocity field of the aorta and its major branches over one cardiac cycle, and two sections, S1 and S2, were selected on the centerline of the descending aorta, with a centerline distance D_{12} = 0.20 m. The one-to-one correspondence of the above indicators in this method is shown in Table 1.

[0066] Table 1 Correspondence between Patient Inputs and Clinical Indicators

[0067] (ii) Uniform cycle, mean blood pressure and patient-scale scaling

[0068] Formula (1): Determining the cardiac cycle from heart rate

[0069] (1)

[0070] Variable description: One cardiac cycle is measured in units of 10 ... HR stands for heart rate, in units of... .

[0071] Clinical indicator application: HR was obtained from echocardiography, electrocardiography, or vital sign monitoring. The 4D-Flow flow waveform, brachial artery pressure constraint, and neural network time input were periodically normalized based on T.

[0072] Its role in this method is to ensure that all modal data are on the same cardiac cycle coordinate, thus avoiding phase mismatch caused by differences in sampling frequency or heart rate.

[0073] Formula (2): Mean pressure estimated from brachial artery cuff blood pressure

[0074] (2)

[0075] Variable description: Mean pressure of the brachial artery; The systolic blood pressure of the brachial artery; This refers to the diastolic pressure of the brachial artery.

[0076] Application of clinical indicators: and Obtained from a cuff blood pressure monitor. This formula is used to construct a mean constraint for brachial artery pressure; when a continuous brachial artery waveform is available, the mean of the periodic integral can be used instead.

[0077] Its role in this method is to transform the most readily available clinical cuff blood pressure into a peripheral pressure constraint in neural network training.

[0078] Formula (3): Calculate body surface area based on height and weight

[0079] (3)

[0080] Variable description: The body surface area is expressed in units of 1000 ppm. ; Height, in units of ; Weight, in units of .

[0081] Application of clinical indicators: Height and weight are derived from basic clinical information. Used for patient-scale scaling of blood vessel length and area in literature.

[0082] Role in this method: To achieve geometric individualization using simple clinical indicators when complete patient vascular geometry reconstruction is lacking.

[0083] Formula (4): Scale of blood vessel length and reference area

[0084] (4)

[0085] Variable description: For the first The length of the root vessel after expansion and contraction; For reference cross-sectional area; and The geometric average value from literature or population data; and These are the length and area scale factors, respectively, which can be derived from height, And the diameter of the aorta is determined.

[0086] Application of clinical indicators: can be or Sure; can be or Sure. Obtained by echocardiography or imaging measurements.

[0087] Its role in this method is to fix the length and area parameters, which have a relatively small impact in the sensitivity analysis, to literature values ​​and scale them down, thereby reducing the inversion dimensionality.

[0088] (III) 4D-Flow MRI Flow Integration and Construction of Eight-Vessel Tree Network

[0089] In this embodiment, the eight-vessel tree network includes at least the following equivalent segments: ascending aorta / proximal aorta, aortic arch-descending aorta, brachiocephalic trunk, right common carotid artery, right subclavian-axillary artery, right brachial artery, right radial artery, and right ulnar artery. Figure 2 As shown in the figure, the model preserves the main propagation path from the aorta to the brachial artery and equates the peripheral vascular beds of the trunk / lower limb, head and neck, and distal upper limb to the RCR terminal boundaries.

[0090] Formula (5): Calculation of cross-sectional flow waveform from 4D-Flow velocity field

[0091] (5)

[0092] Variable description: For the first Periodic flow waveform of a section or branch; The cross-sectional area; For 4D-Flow MRI velocity field; This is the normal vector of the cross section.

[0093] Clinical application: 4D-Flow MRI provides a velocity field. By integrating the velocity across sections of the aorta, brachiocephalic trunk, descending aorta, or upper limb branches, the flow curves of each branch over time can be obtained.

[0094] Its role in this method is to convert image velocity data into flow constraints for vascular network ingress, branch, and terminal points.

[0095] Formula (6): Calculate the terminal diversion ratio by integrating the periodic flow rate.

[0096] (6)

[0097] Variable description: For the first The periodic traffic splitting ratio of each terminal branch; This refers to the quantity of terminal exports; For the first The waveform of the outflow.

[0098] Clinical application: 4D-Flow MRI can provide flow data for major branches such as the trunk / lower limbs, head and neck, and upper limbs. In the example, approximately 80% flow is observed in the trunk / lower limbs, 12% in the head and neck, and 8% in the upper limbs, with the distal upper limbs being redistributed to the radial and ulnar arteries.

[0099] Its role in this method: To set the RCR boundary based on the flow distribution ratio or as a PINN flow allocation loss, reducing the complexity of modeling the complete peripheral network; the average flow distribution ratio of the main branches is, for example... Figure 3 As shown.

[0100] Formula (7): Inlet flow is constrained by echocardiographic stroke volume.

[0101] (7)

[0102] Variable description: Aortic inlet flow or left ventricular ejection flow; This refers to the stroke volume.

[0103] Application of clinical indicators: It is estimated by the difference between the left ventricular end-diastolic volume and end-systolic volume as measured by echocardiography or by Doppler methods.

[0104] Its role in this method is to ensure that the total inflow in the model is consistent with the patient's true cardiac output capacity, avoiding erroneous flow rates obtained solely from pressure fitting. The aortic inlet flow waveform constructed based on HR=68 bpm and SV=74 mL is shown below. Figure 4 As shown.

[0105] (iv) One-dimensional blood vessel control equations, material relationships, and wave velocity relationships

[0106] Each blood vessel segment is described by a one-dimensional hemodynamic equation, and the neural network can output the cross-sectional area of ​​the blood vessel. ,flow and pressure .in, and Satisfying the laws of conservation of mass and momentum and Through pressure-area coupling, material properties are determined by... express.

[0107] In this embodiment, PINN employs a structure combining a shared backbone network and vessel number embedding. The neural network input is: spatial coordinates. ,time Blood vessel number Geometric features of blood vessels Patient-scale characteristics Clinical functional characteristics and 4D-Flow features .in, and Used to describe the spatiotemporal location within blood vessels, vessel numbering is used to distinguish different vessel segments, and clinical and imaging features are used to form patient-specific conditional inputs. The neural network output includes three categories: the first category is continuous field variables, namely the cross-sectional area within each blood vessel. ,flow and pressure The second category is material property parameters, including vascular equivalence. Or parameters related to the elastic modulus; the third category is terminal boundary parameters, including Near-end resistance in the boundary Distant resistance and adaptability A network can be represented as:

[0108] in, For having trainable parameters neural networks, Embedded vectors are assigned to blood vessel numbers. During training, automatic differentiation is used for calculation. , , The isoderm is used, and the physical residuals are formed by substituting them into the one-dimensional blood flow mass conservation equation and momentum conservation equation. This structure allows the same neural network to share the pressure propagation law across eight blood vessel segments, while preserving the geometric and boundary differences between different blood vessel segments.

[0109] Formula (8): One-dimensional blood flow mass conservation equation

[0110] (8)

[0111] Variable description: For the first Root vessels in location and time The cross-sectional area at that point; For the corresponding traffic volume.

[0112] Application of clinical indicators: The initial scale was obtained by scaling down ultrasound or literature values; Affected by heart rate And 4D-Flow split ratio constraints.

[0113] Its role in this method: as one of the PINN physical residuals, it restricts the neural network output to satisfy the volume conservation under the condition that blood is incompressible.

[0114] Formula (9): One-dimensional blood flow conservation equation

[0115] (9)

[0116] Variable description: For pressure; Blood density; This is the momentum correction factor; is the coefficient of viscous friction.

[0117] Clinical indicator application: Blood density and viscosity can be expressed using literature constants; pressure At the brachial artery end / The constraint is the output to be inverted at the aortic end.

[0118] Its role in this method is to link pressure gradient, flow rate change, and viscous resistance, which is the core physical constraint for inverting aortic pressure from brachial artery pressure.

[0119] Formula (10): Pressure-Area Relationship

[0120] (10)

[0121] Variable description: For reference pressure; For the first Material stiffness parameters of root vessels; For reference cross-sectional area.

[0122] Application of clinical indicators: Based on formula (4) and height, Or the diameter of the aorta may decrease or expand. The material properties to be inverted are constrained by 4D-Flow PWV.

[0123] The role of this method is to introduce the material properties of the blood vessel wall into the 1D model, so that the aortic pressure waveform is not only determined by the boundary fitting, but also by the elastic constraints of the blood vessel.

[0124] Formula (11): Local pulse wave velocity

[0125] (11)

[0126] Variable description: For the first Local wave velocity in root vessels; Represents the set of parameters to be identified, including and termination impedance, etc.

[0127] Clinical indicator application: PWV calculated by 4D-Flow MRI is used for correction. Or its spatial average; blood density Standard physiological values ​​were used.

[0128] Its role in this method: to establish material parameters. A bridge between PWV and imagery.

[0129] Formula (12): Reference wave velocity at the reference area

[0130] (12)

[0131] Variable description: for Reference wave velocity at that time; For material stiffness; Blood density.

[0132] Clinical indicator application: When the fluctuation of aortic cross-sectional area is relatively small or the implementation method needs to be simplified, this formula can be used to deduce PWV. The initial value of .

[0133] Its role in this method is to provide initial material property values ​​for PINN optimization and reduce instability caused by random initialization.

[0134] (v) Calculate PWV from two aortic flow waveforms

[0135] Pulse wave velocity (PWV) is the speed at which pressure or flow waves propagate along a blood vessel, and it is an important hemodynamic indicator reflecting the equivalent stiffness of the arterial wall. All other things being equal, the stiffer the blood vessel wall, the faster the pressure wave propagates, and the higher the PWV; conversely, the more compliant the blood vessel wall, the slower the pressure wave propagates, and the lower the PWV. This invention does not use PWV merely as a final evaluation indicator, but rather as an image-constrained target for inverting the material properties of the aorta.

[0136] In this method, 4D-Flow MRI can obtain flow waveforms from two cross-sections at different locations in the descending aorta. Because the flow wave propagates from proximal to distal, there is a time delay between the distal cross-section waveform and the proximal cross-section. The propagation time difference between the two flow waveforms is calculated. Then, combined with the distance between the two cross sections along the center line of the blood vessel This yields the local PWV. This PWV further constrains the material stiffness parameters in the pressure-area relationship. This reduces the problem of unidentifiable material parameters when relying solely on brachial artery pressure fitting.

[0137] In the 4D-Flow MRI data, two sections, S1 and S2, were selected along the centerline of the descending aorta, and samples were extracted from them. and After periodic registration, mean removal, normalization, and interpolation of the two flow waveforms, the propagation time difference can be calculated using the cross-correlation method, time-to-foot method, wavelet method, or Fourier phase method. This embodiment uses the cross-correlation method as an example.

[0138] Formula (13): Calculation of propagation time difference using the cross-correlation method

[0139] (13)

[0140] Variable description: The propagation time difference between the two cross-sectional flow waveforms; This represents the time lag.

[0141] Application of clinical indicators: and Velocity integrals from two aortic sections obtained from 4D-Flow MRI. to You can select a time period with high waveform coherence in the early stage of contraction or in the complete cycle.

[0142] Its role in this method is to obtain the local propagation time of the aorta using non-invasive imaging waveforms, avoiding reliance on invasive pressure sensors.

[0143] Formula (14): Calculate PWV from centerline distance and propagation time difference

[0144] (14)

[0145] Variable description: The pulse wave velocity was calculated from 4D-Flow MRI. The distance between the two cross sections along the centerline of the aorta.

[0146] Application of clinical indicators: Obtained by 4D-Flow MRI or vascular centerline reconstruction; It is obtained from formula (13). Example =0.20 m, =0.035 s, then It is approximately 5.71 m / s.

[0147] Its role in this method is to transform measurable image information into constrained targets for vascular material properties. The flow waveforms and PWV inverse calculation results for the aortic S1 / S2 cross-sections of patient A are shown below. Figure 5 As shown.

[0148] (vi) Discrete equations and bifurcation / terminal boundary conditions

[0149] To generate pre-training samples or discretize the PINN residuals, a finite volume scheme can be used for the one-dimensional equations. For each vessel segment, the conserved variables are written as follows: Numerical flux is written as Conservation conditions are applied at the bifurcation node and the terminal RCR boundary.

[0150] Formula (15): Finite volume discretization scheme for one-dimensional blood vessel segments

[0151] (15)

[0152] Variable description: For the first The grid in the first Conserved variables at each time step; For time step; For the first Root vessel grid length; For numerical flux; For source terms.

[0153] Application of clinical indicators: Determined based on cardiac cycle T and required time resolution; Based on blood vessel length It is obtained by discrete processing.

[0154] Its role in this method is to generate sensitivity analysis samples for positive problem simulation, and it can also be used as a discrete check method for neural network residuals.

[0155] Formula (16): Rusanov numerical flux

[0156] (16)

[0157] Variable description: and The physical flux for the left and right states of the mesh interface; and These are variables that are conserved on both sides. This represents the local maximum characteristic velocity.

[0158] Application of clinical indicators: Local flow velocity With wave speed jointly determined, wave speed Again received and constraint.

[0159] Its role in this method is to ensure the stability of the forward problem simulation and to provide a reliable numerical basis for the generation of pre-training data.

[0160] Formula (17): Flow conservation and pressure continuity at bifurcation nodes

[0161] (17)

[0162] Variable description: and For the flow and pressure at the distal end of the father's blood vessel; and For the first Individual blood vessel inlet flow and pressure; This represents the number of sub-branches.

[0163] Clinical indicator application: It can be used at the bifurcation of the brachiocephalic trunk, subclavian artery, and radial / ulnar artery. The overall flow of the branches must also meet the 4D-Flow shunt ratio.

[0164] Its role in this method is to ensure that the eight-vessel tree network satisfies basic blood flow conservation at the bifurcation points, thus avoiding discontinuities in the neural network output.

[0165] Formula (18): Terminal RCR Boundary Conditions

[0166] (18)

[0167] Variable description: For near-end resistance; For distant resistance; For terminal compliance; For resistance to pressure; This is the venous reference pressure.

[0168] Clinical indicator application: RCR boundary is used for terminal beds of trunk / lower limbs, head and neck, radial artery and ulnar artery. , , The parameters to be inverted or pre-trained are constrained by both the flow distribution ratio and brachial artery blood pressure.

[0169] Its role in this method is to replace the complete peripheral microcirculation network with a small number of terminal parameters, thereby reducing the computational load and inversion dimensionality.

[0170] (vii) Sensitivity analysis sample generation and data-driven pre-training

[0171] Pre-training samples are generated through a process of "parameter sampling - forward problem simulation - output processing".

[0172] First, based on literature values, patient-scale scaling results, and reasonable physiological ranges, the set of parameters to be sampled was determined, including the stiffness of the aortic and upper limb vascular materials. ,terminal parameter Inbound traffic amplitude, terminal diversion ratio And the necessary hemodynamic constants.

[0173] Secondly, a wider sampling range is set for highly sensitive parameters, and a narrower perturbation range is set for low-sensitivity geometric parameters, or the literature values ​​after scaling are directly used.

[0174] Furthermore, multiple parameter combinations are generated using Latin hypercube sampling, Sobol sequence sampling, or single-factor perturbation methods.

[0175] Finally, each set of parameters is input into a one-dimensional vascular tree forward problem model to calculate the aortic pressure waveform, brachial artery pressure waveform, flow waveforms of each branch, local PWV, and terminal flow allocation results, forming a pre-training dataset.

[0176] This dataset can be represented as:

[0177] in, For the first Input features of the group of samples For the corresponding model parameters, and These are the pressure waveforms of the aorta and brachial artery, respectively. For the first Branch flow waveforms The wave velocity is calculated from this set of material parameters. The total number of samples. The pre-training samples are not dependent on the invasive aortic pressure of real patients, but are generated in batches by a forward problem model constrained by physical equations.

[0178] Before making patient-specific adjustments, focus on material properties. Multiple parameter combinations are generated based on terminal RCR parameters, inlet flow amplitude, and shunt ratio. Aortic pressure, brachial artery pressure, and flow waveforms of each branch are obtained using a 1D forward problem model, forming a pre-training dataset. Sensitivity analysis results illustrate that vessel length and reference area have relatively small impacts on aortic pressure inversion within a certain range; therefore, baseline values ​​from literature can be used and scaled to the patient scale. Material properties, terminal impedance, and flow distribution have a significant impact on pressure propagation and must be included in the inversion.

[0179] In this embodiment, a one-dimensional blood flow forward problem model is used to generate pre-training samples in batches. Its basic governing equations, finite volume discretization scheme, bifurcation node conservation conditions, and RCR terminal boundary belong to the commonly used model framework in the field of hemodynamic modeling. In this embodiment, by combining this known forward problem model with 4D-Flow MRI shunt ratio, 4D-Flow PWV constraints, patient-scale scaling geometry, sensitivity analysis pre-training samples, and PINN patient-specific fine-tuning, a complete technical path is formed to invert aortic central pressure and material properties from brachial artery blood pressure.

[0180] In other words, the known one-dimensional model is mainly used as a physical constraint and a tool for generating pre-training samples in this invention; the focus of this invention is on how multimodal clinical data enters the model, which parameters are constrained by imaging and ultrasound, which parameters are mainly inverted by PINN, and how to use pre-training to shorten the patient-specific inversion time.

[0181] Formula (19): Data-driven pre-training loss

[0182] (19)

[0183] Variable description: For pre-training data loss; and These are the network-predicted aortic and brachial artery pressures, respectively. and Labels generated for the positive problem model; This represents the number of samples.

[0184] Clinical indicator application: The pre-training samples are derived from batch simulations of parameter sensitivity analysis, eliminating the need for invasive aortic pressure testing in real patients.

[0185] Its role in this method is to allow the network to learn the pressure propagation rules in a reasonable parameter space first, thereby shortening the subsequent patient-specific optimization time.

[0186] (viii) PINN patient-specific fine-tuning and total loss function

[0187] Patient-specific fine-tuning refers to further incorporating actual multimodal observation data from a specific patient into the pre-trained network parameters, and then making small-scale updates to the network weights and some identifiable model parameters. Specifically, it includes the following steps: S1, the pre-trained network weights Initial values ​​of material parameters and terminal Initial values ​​of parameters As initial values ​​for fine-tuning; S2, input patient A's heart rate, stroke volume, brachial cuff blood pressure, height and weight, aortic diameter, 4D-Flow shunt ratio, and 4D-Flow PWV; S3, randomly or uniformly select spatiotemporal points within the eight vascular segments. Output via network , , And use automatic differentiation to calculate the residuals of the one-dimensional equation; S4, calculate the systolic pressure, diastolic pressure, and mean pressure of the output pressure at the brachial artery observation position, and construct peripheral pressure loss with the patient's cuff blood pressure; S5, calculate the theoretical PWV determined by material parameters in two sections of the aorta or a specified aortic segment, and inversely calculate the PWV with 4D-Flow to construct the material property loss. S6 calculates the average flow ratio at each terminal exit and constructs the flow allocation loss with the 4D-Flow split ratio. S7, which is a weighted sum of physical residual loss, brachial artery pressure loss, PWV loss, flow distribution loss, geometric prior loss and bifurcation conservation loss; S8 uses the L-BFGS optimizer to update network weights and high-sensitivity parameters, while low-sensitivity geometric parameters are kept as scaled-down results from literature values ​​or only allowed to be modified within a small range. S9: When the total loss converges and the brachial artery pressure error, PWV error, and shunt ratio error all meet the set thresholds, stop fine-tuning and output the aortic pressure waveform.

[0188] Therefore, fine-tuning does not involve re-optimizing from random parameters, but rather using patient-specific data for constraint correction based on the pre-trained model. This approach reduces the search space for multi-parameter global optimization, improving inversion stability and computational efficiency.

[0189] After pre-training, fine-tuning is performed using patient A's clinical data as input. Network input includes time t, spatial location x, vessel number or geometric code, etc. Cuff blood pressure and 4D-Flow features; network output includes , , , And terminal RCR parameters. The loss function consists of the control equation residuals, brachial cuff pressure constraints, PWV constraints, flow distribution constraints, geometric prior constraints, and bifurcation conservation constraints.

[0190] Formula (20): PINN control equation residuals

[0191] (20)

[0192] Variable description: For quality conservation residuals; The residual is due to the conservation of momentum; , , For network output; , , For momentum correction, density, and friction parameters.

[0193] Application of clinical indicators: The scale is derived from formula (4). by and 4D-Flow splitting constraints, The blood pressure is constrained by the cuff at the brachial artery end.

[0194] The role of this method is to transform the neural network from a pure data fitter into a solver constrained by hemodynamic equations.

[0195] Formula (21): Residual loss of physical control equation

[0196] (twenty one)

[0197] Variable description: To control the loss of the equations; This represents the number of points allocated in space and time.

[0198] Clinical indicator application: Spatiotemporal allocation points cover the computational domain of eight vessel segments, and the cardiac cycle is... Sure.

[0199] Its role in this method is to ensure that the entire network output satisfies the 1D blood flow control equation along the aorta-brachial artery path.

[0200] Formula (22): Brachial artery cuff pressure restraint loss

[0201] (twenty two)

[0202] Variable description: The brachial artery pressure output by the network; , , This refers to cuff blood pressure indicators; The average pressure weight is used.

[0203] Application of clinical indicators: and Blood pressure is obtained directly from a brachial artery cuff monitor. It can be calculated by formula (2) or obtained by continuous waveform integration.

[0204] Its role in this method is to directly embed routine clinical cuff blood pressure into the inversion process, ensuring that the output brachial artery pressure is consistent with the actual measurement.

[0205] Formula (23): 4D-Flow PWV constraint loss

[0206] (twenty three)

[0207] Variable description: Wave velocity predicted by network material parameters and pressure-area relationship; The image PWV is calculated using formula (14).

[0208] Application of clinical indicators: The flow waveform obtained from two cross-sections of 4D-Flow MRI is an independent imaging constraint on the material properties of the aorta.

[0209] Its role in this method: to prevent the model from passing unreasonable... Fitting brachial artery pressure improves the interpretability of material parameters.

[0210] Formula (24): Terminal traffic allocation loss

[0211] (twenty four)

[0212] Variable description: The first output of the network Individual terminal outbound traffic; The 4D-Flow split ratio is obtained from formula (6).

[0213] Clinical indicator application: 4D-Flow MRI provides the proportion of bed flow in major branches or terminals, serving as a common constraint on RCR boundaries and network output.

[0214] Its role in this method is to align peripheral blood flow distribution with patient imaging data, thereby reducing peripheral network complexity from the source.

[0215] Formula (25): Geometric prior loss

[0216] (25)

[0217] Variable description: and The prior geometry of the literature values ​​after patient-scale scaling; and Used or fine-tuned geometric quantities for the model.

[0218] Clinical indicator application: Prior geometry based on height, And the diameter of the aorta is determined.

[0219] The role of this method is to embody the technical idea of ​​"using literature values ​​to scale down low-sensitivity geometric parameters and focusing on inversion of high-sensitivity material and boundary parameters".

[0220] Formula (26): Bifurcation conservation loss

[0221] Variable description: In this embodiment, the number of branching nodes in the eight-vessel tree network is [number]. , For the first Flow at the parent vessel terminal at each bifurcation node and The first The inlet flow of the two sub-vessels at the bifurcation node For the first Pressure at the end of the parent vessel at each bifurcation node and The first Pressure at the entrance of the two sub-vessels at the bifurcation node.

[0222] Formula (27): Total Loss Function

[0223] (27)

[0224] Variable description: , , , , , and Weights for each loss; The loss is the conserved loss at the fork node.

[0225] Application of clinical indicators: Clinical inputs correspond to different loss items: cuff blood pressure corresponds to 4D-Flow PWV corresponds to 4D-Flow splitting ratio corresponds to Xin Chao and Corresponding to time and flow constraints, the corresponding scale indicators .

[0226] Its role in this method is to achieve an integrated inversion of data-driven, physical equations and clinical multimodal observations.

[0227] Formula (28): Patient-specific parameter inversion

[0228] (28)

[0229] Variable description: The set of parameters to be identified includes RCR terminal parameters, necessary flow scale parameters, and neural network weights.

[0230] Application of clinical indicators: Taking patient A as an example , 4D-Flow split ratio and PWV were used as observation constraints.

[0231] Its role in this method is to obtain patient-specific material properties, terminal impedance, and aortic pressure waveforms.

[0232] (ix) Aortic pressure waveform output and simulated patient results

[0233] After completing the PINN fine-tuning, the aortic pressure waveform is extracted from the aortic root or the proximal node of the ascending aorta. And calculate the central aortic systolic pressure, diastolic pressure, mean pressure and pulse pressure.

[0234] Formula (29): Aortic central pressure index output

[0235] (29)

[0236] Variable description: The aortic pressure waveform obtained through inversion; and These are the aortic systolic pressure, diastolic pressure, mean pressure, and pulse pressure, respectively.

[0237] Clinical indicator applications: These indicators correspond to the final clinical output and can be used for aortic central pressure assessment, aortic stenosis transvalvular pressure gradient calculation, left ventricular afterload analysis, and individualized circulatory simulation.

[0238] Its role in this method is to transform the neural network output into stress indicators and complete waveforms that doctors can understand.

[0239] Taking patient A as an example, the cuff blood pressure was 126 / 78 mmHg, the heart rate was 68 bpm, the SV was 74 mL, and the terminal shunt ratio given by 4D-Flow MRI was approximately 80% for the trunk / lower limbs, 12% for the head and neck, and 8% for the upper limbs. The PWV calculated from the flow waveforms of the two descending aorta segments was approximately 5-7 m / s. After inputting the above indicators into this method, the network first obtains reasonable initial values ​​through pre-training, and then performs patient-specific fine-tuning using formulas (20)-(27). Figure 6 The waveform comparison between the brachial artery pressure constraint and the inverted central aortic pressure for patient A is shown in the example output. Under the condition of a brachial artery cuff blood pressure of 126 / 78 mmHg, the inverted central aortic pressure is approximately 114 / 80 mmHg. The mean pressure is close to the mean pressure of the brachial artery, and the pulse pressure is lower than the peripheral brachial artery pressure, which is consistent with the general hemodynamic law of pressure amplification from the aorta to the periphery.

[0240] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A non-invasive method for estimating central aortic pressure driven by a vascular tree network, characterized in that, The method includes the following steps: S101: Collect the patient's clinical multimodal data and scale the vessel length and vessel reference area according to the multimodal data; S103: Calculate the flow waveform of the aorta and major branches based on the velocity field of 4D-Flow MRI, and determine the blood flow distribution ratio of trunk / lower limb, head and neck, upper limb and distal upper limb branches based on the periodic average flow. S105: Based on the pressure propagation path from the aorta to the brachial artery, an eight-vessel tree network model is constructed, wherein the eight-vessel tree network model replaces the complete peripheral microcirculation network with a small number of boundary parameters. S107: Select two sections on the central line of the descending aorta, calculate the flow waveform of the two sections using 4D-Flow MRI velocity field, and calculate the propagation time difference using the cross-correlation method to inversely calculate the pulse wave velocity (PWV). S109: Generate multiple sets of combined parameters using sensitivity analysis, construct a pre-training dataset based on the combined parameters and the simulation results of a one-dimensional forward problem, and pre-train the neural network model using the pre-training dataset; S111: Perform PINN patient-specific fine-tuning on the pre-trained neural network model and output the fine-tuned neural network model; S113: Using the finely tuned neural network model, extract the aortic pressure waveform at the aortic root or proximal ascending aorta, calculate the central aortic pressure value, and output the patient-specific aortic pressure waveform, material property parameters, terminal impedance parameters, and branch flow distribution results.

2. The non-invasive aortic central pressure estimation method driven by vascular tree network as described in claim 1, wherein in step S101, the multimodal data includes brachial artery cuff blood pressure, echocardiographic parameters, 4D-Flow MRI velocity field, height and weight, and the cardiac cycle of the multimodal data is unified according to heart rate.

3. The non-invasive aortic central pressure estimation method driven by vascular tree network as described in claim 2, when scaling the vessel length and vessel reference area, employs the following method: in, For the first The length of the root vessel after expansion and contraction, For the first Average length of root vessels For the first Reference area of ​​root vessels For the first The average reference area of ​​root vessels Length factor, is the area scale factor.

4. The non-invasive aortic central pressure estimation method driven by vascular tree network as described in claim 3, in step S103, when calculating the cross-sectional flow waveform from the 4D-Flow velocity field, the following method is used for calculation: The blood flow distribution ratio is calculated using the following method: in, For the first Flow waveform of a section or branch For cross-sectional area, For 4D-Flow MRI velocity field, The normal vector of the cross section. For the first The proportion of blood flow shunt in each terminal branch This refers to the number of terminal exports. For the first One outlet flow waveform, For spatial coordinates, For time.

5. The non-invasive aortic central pressure estimation method driven by vascular tree network as described in claim 4, wherein in step S105, the eight-root vascular tree network model includes the equivalent segments of ascending aorta / proximal aorta, aortic arch-descending aorta, brachiocephalic trunk, right common carotid artery, right subclavian-axillary artery, right brachial artery, right radial artery, and right ulnar artery. The eight-root vascular tree network model preserves the main propagation path from the aorta to the brachial artery and equates the trunk / lower limb, head and neck, and distal upper limb peripheral vascular beds to RCR terminal boundaries.

6. In the non-invasive aortic central pressure estimation method driven by vascular tree network as described in claim 5, the specific method for calculating the propagation time difference using the cross-correlation method in step S107 is as follows: Based on the distance between the two aortic cross sections along the aortic centerline and the time difference of propagation, the pulse wave velocity (PWV) is calculated inversely: in, The propagation time difference between the two active cross-sectional flow waveforms is given. This is the time lag. and The velocity integral of two aortic sections in 4D-Flow MRI. to The time period for waveform coherence. The pulse wave velocity is calculated inversely from 4D-FlowMRI. The distance between the two aortic sections along the aortic centerline.

7. The non-invasive aortic central pressure estimation method driven by vascular tree network as described in claim 6, wherein in step S109, the pre-training dataset is generated through a "parameter sampling—forward problem simulation—output processing" method, specifically including the following steps: S1091: Determine the set of parameters to be sampled based on literature reference data, patient-scale scaling results, and reasonable physiological ranges; S1092: Set a wider sampling range for highly sensitive parameters and a narrower perturbation range for low-sensitive geometric parameters, or directly use scaled-down literature reference data; S1093: The combined parameters are generated using Latin hypercube sampling, Sobol sequence sampling, or single-factor perturbation methods; S1094: Input the combined parameters into a one-dimensional vascular tree positive problem model to calculate the aortic pressure waveform, brachial artery pressure waveform, flow waveforms of each branch, local PWV and terminal flow allocation results, forming the pre-training dataset; The pre-trained dataset is: in, For the pre-trained dataset, For the first Input features of the group of samples, For the first Model parameters for the group of samples, The aortic pressure waveform. This is the brachial artery pressure waveform. For the first Branch flow waveforms For the first The wave velocity calculated from the material parameters The total number of samples.

8. In the non-invasive aortic central pressure estimation method driven by vascular tree network as described in claim 7, in step S111, when performing PINN patient-specific fine-tuning on the pre-trained neural network model, patient-specific data is used for constraint correction based on the pre-trained neural network model to fine-tune the network weights and identifiable model parameters within a small range, thereby reducing the search space for multi-parameter global optimization and improving inversion stability and computational efficiency.

9. The non-invasive aortic central pressure estimation method driven by the vascular tree network as described in claim 8, when performing PINN patient-specific fine-tuning on the pre-trained neural network model, includes the following steps: S1111: Combine the pre-trained network weights, initial material parameter values, and terminal... The initial parameter values ​​are used as initial values ​​for fine-tuning; S1112: Input patient-specific data, including heart rate, stroke volume, brachial cuff blood pressure, height and weight, aortic diameter, 4D-Flow shunt ratio, and 4D-Flow PWV; S1113: Randomly or uniformly select spatiotemporal points within eight blood vessel segments, output the blood vessel cross-sectional area, blood flow rate, and blood vessel pressure of the spatiotemporal points through the neural network model, and use automatic differentiation to calculate the residual of the one-dimensional equation; S1114: Calculate the systolic, diastolic, and mean pressure of the output pressure at the brachial artery observation location, and compare it with the patient's cuff blood pressure to construct peripheral pressure loss; S1115: Calculate the theoretical PWV determined by material parameters in two sections of the aorta or a specified aortic segment, and construct the material property loss by inversely calculating the PWV with 4D-Flow. S1116: Calculate the periodic average flow ratio at each terminal exit and construct the flow allocation loss with the 4D-Flow split ratio; S1117: Weighted sum of physical residual loss, brachial artery pressure loss, PWV loss, flow distribution loss, geometric prior loss, and bifurcation conservation loss; S1118: Use the L-BFGS optimizer to update network weights and high-sensitivity parameters, while keeping low-sensitivity geometric parameters at literature reference values ​​scaled down or allowing only small-scale corrections. S1119: When the total loss converges and the brachial artery pressure error, PWV error and shunt ratio error all meet the set thresholds, stop fine-tuning and output the aortic pressure waveform.

10. The non-invasive aortic central pressure estimation method driven by the vascular tree network as described in claim 9, wherein the total loss when performing PINN patient-specific fine-tuning on the pre-trained neural network model is: in, For physical residual loss: For brachial artery pressure loss: For PWV loss: Assigning losses to traffic: For geometric prior loss: For the fork conservation loss: in, For the geometric prior loss of the quality-conserving residual, For momentum conservation residuals, This represents the cross-sectional area of ​​the blood vessel. For blood flow, For vascular pressure, For momentum correction parameters, For density parameters, For friction parameters, For the number of spatiotemporal points, To find the derivative with respect to time, To find the derivative with respect to space; Brachial artery pressure, , , For cuff blood pressure indicators, For average pressure weighting; To predict PWV, For PWV images; For the first Individual terminal outbound traffic, For 4D-Flow splitting ratio, This refers to the number of terminal exports. This refers to the duration of the cardiac cycle; For the first The a priori length of the root vessel after expansion and contraction. For the first Prior reference area after the root vessel is expanded or contracted; This represents the number of branching nodes in an octal tree network. For the first Flow at the parent vessel terminal at each bifurcation node and The first The inlet flow of the two sub-vessels at the bifurcation node For the first Pressure at the end of the parent vessel at each bifurcation node and The first Pressure at the inlet of two sub-vessels at a bifurcation node; Weights for physical residual loss, Weighting of brachial artery pressure loss For PWV loss weights, Assign loss weights to traffic, For geometric prior loss weights, The weight for the bifurcation conservation loss is determined.

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