Non-invasive assessment method of coronary flow reserve fraction fusing hemodynamics
By constructing a neural network that integrates hemodynamics and combining the Navier-Stokes equations and Murray's law, the problems of high computational complexity and poor model interpretability of the CT-FFR assessment method are solved, realizing non-invasive, rapid, and accurate coronary artery FFR assessment to meet clinical application needs.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- THE SECOND AFFILIATED HOSPITAL ARMY MEDICAL UNIV
- Filing Date
- 2025-05-14
- Publication Date
- 2026-08-04
AI Technical Summary
Existing CT-FFR assessment methods are computationally complex and difficult to apply widely in clinical practice. Furthermore, deep learning models lack the ability to interpret the physical laws of hemodynamic systems, resulting in poor non-invasive FFR assessment results.
A neural network integrating hemodynamics was constructed. By adding residual terms of the Navier-Stokes equation and Murray's law to the loss function, and combining deep learning with the basic laws of hemodynamics, the neural network was trained to achieve non-invasive FFR assessment. Coronary artery CT image data was used for preprocessing and training. A fully connected neural network was constructed using a multilayer perceptron, and the model was optimized through transfer learning and adaptive weight adjustment.
It enables non-invasive, rapid, and accurate coronary artery FFR assessment, avoiding the pain and risks of invasive measurements, improving the accuracy and computational efficiency of the assessment, and meeting the needs of clinical practice.
Smart Images
Figure CN120495248B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of medical testing technology and relates to a non-invasive assessment method for coronary artery blood flow reserve that integrates hemodynamics. Background Technology
[0002] Fractional flow reserve (FFR) is an important indicator for assessing the physiological function of coronary artery stenosis. It reflects the ratio of blood flow to the myocardium supplied by the distal coronary artery under maximal congestion to the maximum blood flow that the area can normally receive. Traditional FFR measurement requires invasive coronary angiography, where a pressure guidewire is inserted into the coronary artery. This procedure not only causes pain and risks to the patient but also has a certain incidence of complications and is costly.
[0003] To avoid the drawbacks of invasive measurements, non-invasive FFR assessment techniques based on CT images (computedtomography-derived fractional flow reserve, CT-FFR) have emerged. However, existing CT-FFR assessment methods primarily rely on numerically solving the Navier-Stokes equations through computational fluid dynamics. Due to their high computational complexity, these methods require significant computational resources and time, hindering their widespread application in clinical practice. In recent years, the rapid development of deep learning has brought new opportunities for FFR assessment. Utilizing deep learning technology to learn from training sets generated by computational fluid dynamics and then automatically generating coronary artery FFR can effectively reduce computation time and manual operation. However, training deep learning models requires large-scale data support, and the models have poor interpretability, mainly due to the lack of application of the hidden physical laws within the hemodynamic system.
[0004] Therefore, by combining the advantages of deep learning with the fundamental laws of hemodynamics, an interpretable deep learning algorithm can be constructed to achieve non-invasive, rapid, and accurate assessment of coronary artery FFR. This provides reliable functional evidence for early screening of coronary artery stenosis, optimization of revascularization strategies, and prognostic assessment, and has significant clinical application value and socio-economic benefits. Summary of the Invention
[0005] In view of this, the purpose of the present invention is to provide a non-invasive method for assessing coronary artery fractional flow reserve by incorporating hemodynamics.
[0006] To achieve the above objectives, the present invention provides the following technical solution:
[0007] A non-invasive method for assessing coronary artery fractional flow reserve by incorporating hemodynamics, comprising the following steps:
[0008] S1: Acquire coronary artery CT image data and preprocess it to extract the three-dimensional geometric model of the coronary artery;
[0009] S2: Construct a neural network that integrates hemodynamics, and add residual terms of the Navier-Stokes equation and Murray's law to the network's loss function;
[0010] S3: Collect coronary CT image data and corresponding invasive FFR measurements as training samples, and use computational fluid dynamics to generate numerical simulation data of CT-FFR as training dataset.
[0011] S4: The neural network fused with hemodynamics is trained and optimized using the training samples and training dataset to minimize the error between the network output and the FFR training value, while satisfying the constraints of the Navier-Stokes equation and Murray's law.
[0012] S5: The coronary artery CT image data is processed using a trained network model that integrates hemodynamics to obtain the predicted FFR value.
[0013] Furthermore, step S1 specifically includes:
[0014] The patient's coronary arteries were scanned using a CT scanner to obtain CT image sequences containing information on the morphology and structure of the coronary arteries. The CT images were preprocessed, including noise reduction using a Gaussian filtering algorithm. Histogram equalization was used to enhance the contrast of the images and make the boundaries of the coronary arteries clear. The coronary arteries were segmented using a threshold-based segmentation and morphological manipulation method to extract the three-dimensional geometric model of the coronary arteries.
[0015] Furthermore, step S2 specifically includes:
[0016] A fully connected neural network consisting of an input layer, multiple hidden layers, and an output layer is constructed using a multilayer perceptron as the basic network structure.
[0017] The input layer receives the geometric parameters and boundary conditions of the coronary arteries;
[0018] The hidden layer uses multiple neurons and employs the tanh activation function for nonlinear transformation;
[0019] The output layer outputs the blood flow velocity and pressure within the coronary arteries;
[0020] The residual terms of the Navier-Stokes equation and Murray's law are added to the network's loss function.
[0021] Furthermore, the loss function of the neural network model that integrates hemodynamics consists of a data-driven term and a physical consistency loss term.
[0022] The data-driven item Measuring the difference between the model output and the observed data:
[0023]
[0024] Among them, u obs and p obs These represent the actual values of the measured flow velocity and pressure, respectively.
[0025] The physical consistency loss term ensures that the model output satisfies the basic hemodynamic equations, including the Navier-Stokes equations, the continuity equation, Murray's law, initial conditions, and boundary conditions.
[0026] The loss function of a neural network is expressed as the sum of a data-driven term and a physical consistency term:
[0027]
[0028] Where, {λ pde ,λ Mu ,λ data ,λ BC ,λ IC} represents the weighting coefficient of the corresponding loss term, used to adjust the relative importance of the loss term.
[0029] Furthermore, the blood flow in the coronary arteries satisfies the three-dimensional Navier-Stokes equation and the continuity equation:
[0030]
[0031] Where t represents time, u and p represent blood flow velocity and blood pressure, respectively, and ρ and μ represent blood density and viscosity, respectively;
[0032] In neural networks that integrate hemodynamics, deep neural networks are defined. To approximate the velocity u and pressure p, we use x = (x, y, z) as spatial coordinates and t as time. Substituting the output of the neural network into the Navier-Stokes equations, we obtain the loss term of the hemodynamic equations.
[0033]
[0034] in, and These represent the speed and pressure output by the neural network, respectively, and the symbol ‖·‖ represents the L2 norm.
[0035] Furthermore, the boundary conditions include inlet boundary conditions, outlet boundary conditions, and wall boundary conditions; the inlet boundary condition provides a given velocity distribution, the outlet boundary condition uses either pressure or flow boundary conditions, and the wall boundary condition uses a no-slip condition u = 0; the boundary condition loss is defined as:
[0036]
[0037] Among them, u BC and p BC It refers to the known velocity and pressure at the boundary.
[0038] Furthermore, the initial condition loss is:
[0039]
[0040] Where u0 represents the initial flow velocity within the blood vessel.
[0041] Furthermore, Murray's law states that at the bifurcation of a blood vessel, the cube of the diameter d0 of the main branch is equal to the sum of the cubes of the diameters d1 and d2 of the branch vessels:
[0042]
[0043] Traffic allocation also follows these rules:
[0044] Q1 / Q2 = (d1 / d2) 7 / 3
[0045] Therefore, the loss term related to Murray's law at the coronary artery bifurcation is... Represented as:
[0046]
[0047] Q1 and Q2 are the flow rates of the branch vessels, respectively, calculated using the velocity and diameter output by the neural network.
[0048] Assuming the number of branches in the coronary artery tree is N, then the total loss term in Murray's law is expressed as the sum of the loss terms at each branch location:
[0049]
[0050] Furthermore, in step S4, a gradient-based adaptive weight adjustment method is used to dynamically adjust the weights of the loss term, specifically including:
[0051] First, calculate each loss term separately. Gradient of the neural network parameter θ
[0052] Then, the weights of each loss term are adjusted based on the magnitude of the gradient norm:
[0053]
[0054] in Gradient The L2 norm;
[0055] Finally, the Adam algorithm is used to minimize the loss function. To optimize the parameters of the neural network model:
[0056]
[0057] Using transfer learning, the pre-training stage trains a neural network model that integrates hemodynamics with simulated data to learn the physical laws of hemodynamics; the fine-tuning stage fine-tunes the model on a small amount of clinical data to adapt it to the anatomical structure and noise distribution of real-world scenarios.
[0058] Furthermore, after training, sensitivity, specificity, and area under the curve are calculated based on the predicted FFR value and invasive blood flow reserve score; receiver operating characteristic (ROC) curves are plotted to visually demonstrate the model's performance; sensitivity, specificity, and AUC indices are analyzed to determine if the model meets the usage requirements; false positive and false negative cases are analyzed to identify problems and deficiencies in the model; based on the analysis conclusions, the model is improved and optimized, including adjusting model parameters and increasing training data; the model validation process is repeated until the model's performance meets the target requirements.
[0059] The beneficial effects of this invention are as follows:
[0060] Non-invasive: This invention uses coronary CT image data for FFR assessment, avoiding the pain and risks associated with invasive measurements and improving patient acceptance.
[0061] Speed: The neural network that integrates hemodynamics has high computational efficiency and can complete the assessment of CT-FFR in a short time, meeting the needs of clinical practice.
[0062] Accuracy: By using the Navier-Stokes equation and Murray's law, the hemodynamic physical laws within the coronary arteries and the blood flow distribution at the vascular branches are fully considered, making the assessment results more accurate and reliable.
[0063] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description
[0064] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:
[0065] Figure 1 This is a schematic diagram of the non-invasive assessment process for coronary artery FFR.
[0066] Figure 2 It is a neural network framework for non-invasive assessment of coronary artery FFR that integrates hemodynamics; where (a) is the input variable of the neural network: the geometry of the coronary artery, (b) is a fully connected neural network, and (c) is the output variable of the neural network: flow velocity and pressure;
[0067] Figure 3 This is a schematic diagram of Murray's law at the bifurcation point of the coronary artery. Detailed Implementation
[0068] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.
[0069] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.
[0070] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.
[0071] Example 1:
[0072] like Figure 1 As shown, this invention provides a non-invasive method for assessing coronary artery fractional flow reserve by incorporating hemodynamics, comprising the following steps:
[0073] (1) Acquiring coronary artery CT image data: The patient's coronary arteries are scanned using a CT scanner to obtain CT image sequences containing information on the morphology and structure of the coronary arteries. The CT images are preprocessed, including image noise reduction, enhancement, and segmentation, to extract the three-dimensional geometric model of the coronary arteries.
[0074] (2) Constructing a neural network integrating hemodynamics: A multilayer perceptron is used as the basic network structure. The input layer receives the geometric parameters of the coronary arteries (such as vessel diameter and length) and boundary conditions (such as inlet pressure and outlet pressure). The hidden layer performs nonlinear transformations through multiple neurons, and the output layer outputs physical quantities such as blood flow velocity and pressure within the coronary arteries. Residual terms of the Navier-Stokes equation and Murray's law are added to the network's loss function.
[0075] (3) Collect and generate training datasets: Collect coronary CT image data and corresponding invasive FFR measurements as training samples, and use computational fluid dynamics to generate numerical simulation data of CT-FFR as training datasets.
[0076] (4) Training the neural network that integrates hemodynamics: The network is trained using the stochastic gradient descent algorithm. Combined with adaptive weight coefficients and transfer learning, the network parameters are continuously adjusted to minimize the error between the network output and the FFR training value, while satisfying the constraints of the Navier-Stokes equation and Murray's law.
[0077] (5) Non-invasive FFR assessment and verification: The coronary artery CT image data of the patient to be assessed is preprocessed and input into the trained neural network. The network outputs physical quantities such as blood flow velocity and pressure in the coronary artery. The FFR value is calculated based on these physical quantities, and appropriate adjustments and optimizations are made based on the model evaluation effect.
[0078] Example 2:
[0079] This embodiment provides detailed steps of a non-invasive method for assessing coronary artery fractional flow reserve by incorporating hemodynamics, including:
[0080] (1) Data Acquisition and Preprocessing
[0081] Coronary CT angiography was performed on the patient using a multi-slice spiral CT scanner. Scanning parameters were adjusted based on the patient's specific condition and the scanner's performance. The scan area should cover the entire coronary artery tree, and the acquired image data was stored in DICOM format.
[0082] The CT image data is transferred to a computer and preprocessed using specialized image processing software. First, a Gaussian filtering algorithm is used to reduce noise in the image, removing interference. Then, a histogram equalization algorithm is used to enhance the image contrast, making the boundaries of the coronary arteries clearer. Finally, a threshold-based segmentation and morphological manipulation method is used to segment the coronary arteries and extract their three-dimensional geometric model.
[0083] (2) Construction of a neural network integrating hemodynamics
[0084] Construct a fully connected neural network consisting of an input layer, multiple hidden layers, and an output layer. The input layer has 10 neurons, which receive geometric parameters and boundary conditions such as the diameter, length, inlet pressure, and outlet pressure of the coronary artery. Each hidden layer has 50 neurons, which are activated by the tanh activation function for nonlinear transformation. The output layer has 2 neurons, which output the blood flow velocity and pressure within the coronary artery.
[0085] In hemodynamics, the Navier-Stokes equations describe the motion of fluids. By combining these equations with the geometric information of the coronary arteries, the PINN framework is constructed. Assuming blood is an incompressible laminar Newtonian fluid and the vessel wall is simplified to a linearly elastic material, the blood flow in the coronary arteries satisfies the three-dimensional Navier-Stokes equations and the continuity equation:
[0086]
[0087] Where t represents time, u and p represent blood flow velocity and blood pressure, respectively, and ρ and μ represent blood density and viscosity, respectively.
[0088] like Figure 2 As shown in (a)-(c), a deep neural network is defined in a neural network that integrates hemodynamics. We approximate the velocity u and pressure p using a method where x = (x, y, z) are spatial coordinates and t is time. Substituting the neural network output into the Navier-Stokes equations yields the loss term of the hemodynamic equations.
[0089]
[0090] in, and These represent the speed and pressure output by the neural network, respectively, and the symbol ‖·‖ represents the L2 norm.
[0091] Boundary conditions include inlet boundary conditions, outlet boundary conditions, and wall boundary conditions. Inlet boundary conditions typically specify the velocity distribution, outlet boundary conditions can be pressure or flow boundary conditions, and wall boundary conditions typically use no-slip conditions (u = 0). Boundary condition losses can be defined as:
[0092]
[0093] Among them, u BC and p BC It refers to the known velocity and pressure at the boundary.
[0094] Considering initial conditions, such as the initial velocity distribution, the initial condition loss can be defined as:
[0095]
[0096] Where u0 represents the initial flow velocity within the blood vessel.
[0097] We designed a Murray's law fusion mechanism and embedded it into a neural network model to improve the model's computational accuracy for complex anatomical structures (such as bifurcation and lateral branches).
[0098] like Figure 3 As shown, Murray's law states that at the bifurcation of a blood vessel, the cube of the diameter d0 of the main branch is equal to the sum of the cubes of the diameters d1 and d2 of the branch vessels:
[0099]
[0100] At the same time, traffic allocation also follows these rules:
[0101] Q1 / Q2 = (d1 / d2) 7 / 3
[0102] Therefore, the loss term related to Murray's law at the coronary bifurcation... Represented as:
[0103]
[0104] Q1 and Q2 are the flow rates of the branch vessels, which can be calculated using the velocity and diameter output by the neural network.
[0105] Assuming the number of branches in the coronary artery tree is N, then the total loss term in Murray's law is expressed as the sum of the loss terms at each branch location:
[0106]
[0107] The loss function of the neural network model incorporating hemodynamics consists of a data-driven term and a physical consistency loss term. Data-driven term Measuring the difference between model output and observed data (such as CFD blood flow velocity field and pressure field):
[0108]
[0109] Among them, u obs and p obs These represent the actual values of the measured flow rate and pressure, respectively.
[0110] The physical consistency loss term ensures that the model output satisfies the fundamental hemodynamic equations, including the Navier-Stokes equations, the continuity equation, Murray's law, initial conditions, and boundary conditions. Therefore, the loss function of the neural network can be expressed as the sum of the data-driven term and the physical consistency term:
[0111]
[0112] Where, {λ pde ,λ Mu ,λ data ,λ BC ,λ IC} represents the weighting coefficient of the corresponding loss term, used to adjust the relative importance of the loss term.
[0113] (3) Collect and generate training datasets
[0114] Coronary CT image data and corresponding invasive FFR measurements were collected as training samples, while numerical simulation data of CT-FFR generated by computational fluid dynamics were used as the training dataset.
[0115] (4) Training a neural network that integrates hemodynamics
[0116] Since different loss terms (such as boundary conditions, governing equations, etc.) usually have different scales and importance, a gradient-based adaptive weight adjustment method is used to dynamically adjust the weights of these loss terms in order to improve the training effect and convergence speed of the model.
[0117] First, calculate each loss term separately. Gradient with respect to the neural network parameters θ (including weights and biases) Then, the weights of each loss term are adjusted according to the magnitude of the gradient norm:
[0118]
[0119] in Gradient The L2 norm.
[0120] Finally, the Adam algorithm is used to minimize the loss function. To optimize the parameters of the neural network model:
[0121]
[0122] Transfer learning is employed to enhance the generalization performance of the model.
[0123] Clinical data (CT-FFR paired data) is typically sparse and costly to acquire, while simulation data (hemodynamic simulations based on computational fluid dynamics) can be generated on a large scale. The core idea of transfer learning is to train a neural network model incorporating hemodynamics using abundant simulation data during the pre-training phase, learning the physical laws of hemodynamics. The fine-tuning phase then fine-tunes the model on a small amount of clinical data to adapt it to the anatomical structures and noise distribution of real-world scenarios. Through a physical data co-optimization strategy and transfer learning methods, high-precision FFR assessment can be achieved with sparse clinical data, while ensuring that the model output conforms to the physical laws of hemodynamics.
[0124] (5) Non-invasive FFR assessment and verification
[0125] Based on the predicted FFR value and invasive blood flow reserve score, performance metrics such as sensitivity, specificity, and area under the curve (AUC) are calculated. Receiver operating characteristic (ROC) curves are plotted to visually demonstrate the model's performance. Sensitivity, specificity, and AUC are analyzed to determine if the model meets the usage requirements. False positive and false negative cases are analyzed to identify model problems and limitations. Based on the results analysis, the model is improved and optimized, including adjusting model parameters and increasing training data. The model validation process is repeated until the model's performance meets the target requirements. The trained hemodynamic fusion network model is used to predict the preprocessed image data to obtain the predicted FFR value for each patient.
[0126] In the above embodiments, the reference to "this embodiment" in the specification indicates that a specific feature, structure, or characteristic described in connection with the embodiment is included in at least some embodiments, but not necessarily all embodiments. Multiple appearances of "this embodiment" do not necessarily refer to the same embodiment.
[0127] In the above embodiments, although the invention has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory structures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed. The embodiments of the invention are intended to cover all such substitutions, modifications, and variations falling within the broad scope of the appended claims.
[0128] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements any of the methods in this embodiment.
[0129] This embodiment also provides an electronic terminal, including: a processor and a memory;
[0130] The memory is used to store computer programs, and the processor is used to execute the computer programs stored in the memory to cause the terminal to perform any of the methods in this embodiment.
[0131] As will be understood by those skilled in the art, the computer-readable storage medium described in this embodiment allows for the implementation of all or part of the steps in the above method embodiments by computer program-related hardware. The aforementioned computer program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.
[0132] The electronic terminal provided in this embodiment includes a processor, a memory, a transceiver, and a communication interface. The memory and the communication interface are connected to the processor and the transceiver and complete communication between them. The memory is used to store computer programs, the communication interface is used to perform communication, and the processor and the transceiver are used to run the computer programs, so that the electronic terminal performs the steps of the above method.
[0133] In this embodiment, the memory may include random access memory (RAM) and may also include non-volatile memory, such as at least one disk storage device.
[0134] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.
[0135] This invention can be used in a wide range of general-purpose or special-purpose computing system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices, etc.
[0136] This invention can be described in the general context of computer-executable instructions, such as program modules, that are executed by a computer. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform a specific task or implement a specific abstract data type. This invention can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.
[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A non-invasive method for assessing coronary artery fractional flow reserve by incorporating hemodynamics, characterized in that: Includes the following steps: S1: Acquire coronary artery CT image data and preprocess it to extract the three-dimensional geometric model of the coronary artery; S2: Construct a neural network that integrates hemodynamics, and add residual terms of the Navier-Stokes equation and Murray's law to the network's loss function; S3: Collect coronary CT image data and corresponding invasive FFR measurements as training samples, and use computational fluid dynamics to generate numerical simulation data of CT-FFR as training dataset. S4: The neural network fused with hemodynamics is trained and optimized using the training samples and training dataset to minimize the error between the network output and the FFR training value, while satisfying the constraints of the Navier-Stokes equation and Murray's law. S5: The coronary CT image data is processed using a trained network model that integrates hemodynamics to obtain the predicted FFR value; Step S2 specifically includes: A fully connected neural network consisting of an input layer, multiple hidden layers, and an output layer is constructed using a multilayer perceptron as the basic network structure. The input layer receives the geometric parameters and boundary conditions of the coronary arteries; The hidden layer uses multiple neurons and employs the tanh activation function for nonlinear transformation; The output layer outputs the blood flow velocity and pressure within the coronary arteries; Add the residual terms of the Navier-Stokes equation and Murray's law to the network's loss function; The loss function of the neural network model that integrates hemodynamics consists of a data-driven term and a physical consistency loss term. The data-driven item Measuring the difference between the model output and the observed data: in, and These represent the actual values of the measured flow velocity and pressure, respectively. The physical consistency loss term ensures that the model output satisfies the basic hemodynamic equations, including the Navier-Stokes equations, the continuity equation, Murray's law, initial conditions, and boundary conditions. The loss function of a neural network is expressed as the sum of a data-driven term and a physical consistency term: in, These are the weighting coefficients for the corresponding loss terms, used to adjust the relative importance of the loss terms; Murray's Law states that at the bifurcation of a blood vessel, the diameter of the main branch vessel... The cube of the branch vessel diameter is equal to the diameter of the branch vessel. and The sum of the cubes of: Traffic allocation also follows these rules: Therefore, the loss term related to Murray's law at the coronary artery bifurcation is... Represented as: in and These are the flow rates of the branch vessels, calculated using the velocity and diameter output by the neural network; Assuming the number of branches in the coronary artery tree is Then the total loss term of Murray's law can be expressed as the sum of the loss terms at each bifurcation point: 。 2. The non-invasive method for assessing coronary artery fractional flow reserve based on hemodynamics according to claim 1, characterized in that: Step S1 specifically includes: The patient's coronary arteries were scanned using a CT scanner to obtain CT image sequences containing information on the morphology and structure of the coronary arteries. The CT images were preprocessed, including noise reduction using a Gaussian filtering algorithm. Histogram equalization was used to enhance the contrast of the images and make the boundaries of the coronary arteries clear. The coronary arteries were segmented using a threshold-based segmentation and morphological manipulation method to extract the three-dimensional geometric model of the coronary arteries.
3. The non-invasive method for assessing coronary artery fractional flow reserve based on hemodynamics according to claim 1, characterized in that: Blood flow in the coronary arteries satisfies the three-dimensional Navier-Stokes equation and the continuity equation: in, Indicates time, and These represent blood flow velocity and blood pressure, respectively. and These are blood density and viscosity, respectively. In neural networks that integrate hemodynamics, deep neural networks are defined. To approximate the solution for velocity and pressure ,in These are spatial coordinates. It is time; substituting the output of the neural network into the Navier-Stokes equation, we obtain the loss term of the hemodynamic equation. : in, and These represent the speed and pressure output by the neural network, respectively, with symbols... This represents the L2 norm.
4. The non-invasive method for assessing coronary artery fractional flow reserve based on hemodynamics according to claim 1, characterized in that: The boundary conditions include inlet boundary conditions, outlet boundary conditions, and wall boundary conditions; the inlet boundary conditions specify a velocity distribution, the outlet boundary conditions use either pressure or flow boundary conditions, and the wall boundary conditions use no-slip conditions. Boundary condition loss is defined as: in, and It refers to the known velocity and pressure at the boundary.
5. The non-invasive method for assessing coronary artery fractional flow reserve based on hemodynamics according to claim 1, characterized in that: The initial conditional loss is: in, This indicates the initial flow velocity within the blood vessel.
6. The non-invasive method for assessing coronary artery fractional flow reserve based on hemodynamics according to claim 1, characterized in that: In step S4, the weights of the loss term are dynamically adjusted using a gradient-based adaptive weight adjustment method, specifically including: First, calculate each loss term separately. About neural network parameters gradient ; Then, the weights of each loss term are adjusted based on the magnitude of the gradient norm: in Gradient of Norm; Finally, the Adam algorithm is used to minimize the loss function. To optimize the parameters of the neural network model: Using transfer learning, the pre-training stage trains a neural network model that integrates hemodynamics with simulated data to learn the physical laws of hemodynamics; the fine-tuning stage fine-tunes the model on a small amount of clinical data to adapt it to the anatomical structure and noise distribution of real-world scenarios.
7. The non-invasive method for assessing coronary artery fractional flow reserve based on hemodynamics according to claim 1, characterized in that: After training, sensitivity, specificity, and area under the curve are calculated based on the predicted FFR value and the invasive blood flow reserve fraction. Plot receiver operating characteristic (ROC) curves to visually demonstrate the model's performance; analyze sensitivity, specificity, and AUC metrics to determine if the model meets the usage requirements; analyze false positive and false negative cases to identify model problems and shortcomings; and improve and optimize the model based on the analysis results, including adjusting model parameters and increasing training data. Repeat the model validation process until the model's performance meets the target requirements.