A numerical method and system for solving coronary blood flow based on deformation inversion

Abstract

The application provides a numerical solution method of coronary blood flow based on deformation inversion, comprising the steps of: acquiring multi-phase coronary CTA images of a target to be evaluated, and extracting coronary vessel deformation waveform data from the multi-phase coronary CTA images; generating a time-varying flow waveform at the entrance of the coronary artery of the target to be evaluated according to the vessel deformation data and the basic law of fluid mechanics; and deriving an instantaneous volume flow curve of the whole coronary vessel segment of the target to be evaluated based on the time-varying flow waveform. The application only relies on the vessel deformation data of the multi-phase CTA to construct a solution model, without the need for three-dimensional geometric reconstruction, mesh processing or complex boundary condition setting, and has higher clinical implementability.

Description

Technical Field

[0001] This application relates to the technical field of coronary artery blood flow calculation, specifically to a numerical calculation method and system for coronary artery blood flow based on deformation inversion. Background Technology

[0002] Coronary artery blood flow is a core indicator for assessing the functional severity of coronary artery stenosis, directly reflecting vascular perfusion status and providing crucial information for clinical decisions regarding invasive angiography and revascularization. Coronary computed tomography (CTA), currently the most widely used non-invasive examination technique, can clearly present the three-dimensional anatomical structure of blood vessels. However, its biggest limitation is that it can hardly provide direct physiological information such as intraluminal blood flow and pressure, leading to insufficient specificity in identifying hemodynamically significant lesions and a tendency to misjudge the severity of stenosis.

[0003] To compensate for the shortcomings of CTA in functional assessment, existing technologies mostly rely on hemodynamic simulation or predictive models to estimate blood flow. Among them, fluid dynamic simulation methods based on one-dimensional / zero-dimensional models reconstruct vascular geometry through CTA and combine it with blood flow control equations (such as the Navier-Stokes equations) for numerical solution. However, these methods require discrete processing of time and space, rely on complex physical boundary conditions and a large number of empirical parameters, and have huge computational resource requirements, making it difficult to meet the requirements of clinical real-time performance and generalizability. Another type of prediction method is based on physically constrained neural networks (PINNs), which drives network training by embedding blood flow control equations in the loss function. However, its prediction results depend on the quality of training data and network structure design, lack strict mathematical uniqueness guarantees, and have poor transparency and verifiability, which is not conducive to clinical application.

[0004] It is worth noting that multi-temporal CTA technology can acquire images of multiple phases within a single cardiac cycle, capturing the periodic deformation information of the vessel cross-sectional area over time. This deformation information directly reflects the compliance and elasticity of the vessel wall, representing a direct physiological response to blood flow fluctuations and providing a novel data source for non-invasive inference of blood flow parameters. However, current technologies do not directly incorporate this multi-temporal deformation information into blood flow solution models, remaining limited to reliance on static geometry or complex simulation assumptions, thus failing to fully leverage the potential advantages of CTA technology. Therefore, how to fully utilize the vascular deformation information provided by multi-temporal CTA to develop a computationally efficient and stable method for calculating coronary blood flow without constructing complex simulation models or setting complex boundary conditions has become a pressing technical challenge. Summary of the Invention

[0005] In view of the aforementioned problems, this application is proposed to provide a method for numerically solving coronary blood flow based on deformation inversion to overcome or at least partially solve the aforementioned problems, comprising the following steps: Acquire multi-temporal coronary CTA images of the target to be evaluated, and extract coronary vessel deformation waveform data from the multi-temporal coronary CTA images; Based on the aforementioned vascular deformation data and fundamental principles of fluid mechanics, a time-varying flow waveform at the coronary artery inlet of the target to be evaluated is generated; Based on the time-varying flow waveform, the instantaneous volumetric flow curve of the entire coronary artery segment of the target to be evaluated is derived.

[0006] Furthermore, the step of acquiring multi-temporal coronary CTA images of the target to be evaluated and extracting coronary vessel deformation waveform data from the multi-temporal coronary CTA images specifically includes the following steps: The multi-temporal coronary CTA images were subjected to noise reduction, contrast enhancement, and edge sharpening. Using pre-defined phase coronary CTA images as a reference, non-rigid registration is performed on coronary CTA images of different time phases to compensate for the spatiotemporal shift caused by cardiac pulsation and respiratory motion. Coronary artery deformation waveform data are extracted from the registered coronary CTA image data.

[0007] Furthermore, the step of extracting coronary artery deformation waveform data from the registered coronary CTA image data specifically includes the following steps: The registered coronary CTA image data is segmented into coronary artery lumens to generate a 3D coronary artery vessel model; Extract the geometric center line of the 3D coronary artery model, and set uniformly distributed nodes along the geometric center line; The cross-sectional area of ​​the blood vessel at each node in each time phase is calculated, and a dynamic waveform of the cross-sectional area of ​​the blood vessel changing over time is generated as the blood vessel deformation data.

[0008] Furthermore, the step of generating a time-varying flow waveform at the coronary artery inlet of the target to be evaluated based on the vascular deformation data and fundamental principles of fluid mechanics specifically includes the following steps: Based on the aforementioned blood vessel deformation data and fundamental laws of fluid mechanics, a periodic ordinary differential equation containing only one unknown quantity—the inlet flow rate—is constructed. Solve the periodic ordinary differential equation to output the time-varying flow waveform at the coronary artery inlet.

[0009] Furthermore, the step of constructing a periodic ordinary differential equation containing only one unknown quantity, the inlet flow rate, based on the blood vessel deformation data and fundamental laws of fluid mechanics, specifically includes the following steps: The mass conservation equation is established based on the principle that the blood volume within a blood vessel segment remains constant, and the momentum conservation equation is established based on Newton's second law. Spatial variables are eliminated through integration, and a periodic ordinary differential equation containing only one unknown quantity, the inlet flow rate, is constructed by combining variable substitution. Based on the vascular deformation data, the coefficients of the periodic ordinary differential equation that change with time are calculated, and the solution equation is generated.

[0010] Furthermore, the step of solving the periodic ordinary differential equation and outputting the time-varying flow waveform at the coronary artery inlet specifically includes the following steps: Set the initial value of the inlet flow rate based on prior information about the average clinical flow rate. The periodic ordinary differential equation is integralized over time based on the initial inlet flow rate and the solution equation. Calculate the flow error between the end and the beginning of the cardiac cycle, and determine whether the flow error meets a preset threshold; The initial value of the inlet flow is iteratively optimized, and when the flow error converges within a preset threshold, the time-varying flow waveform at the inlet is output.

[0011] Furthermore, the step of deriving the instantaneous volumetric flow curve of the entire coronary artery segment based on the time-varying flow waveform at the inlet specifically includes the following steps: Based on the law of conservation of mass, a correlation is established between inlet flow and flow at any location in the blood vessel; The flow distribution is corrected by combining the dynamic changes in cross-sectional area at each location in the aforementioned vascular deformation data; Output the instantaneous volumetric flow curve of any node in the main coronary artery and its branches.

[0012] A numerical solution system for coronary blood flow based on deformation inversion, comprising: The data acquisition module is used to acquire multi-temporal coronary CTA images of the target to be evaluated, and extract coronary vessel deformation waveform data from the multi-temporal coronary CTA images; The inlet time-varying flow rate solution module is used to generate the time-varying flow rate waveform at the coronary artery inlet of the target to be evaluated based on the vascular deformation data and the basic laws of fluid mechanics. The whole-vessel flow derivation module is used to derive the instantaneous volumetric flow curve of the whole coronary artery segment of the target to be evaluated based on the time-varying flow waveform.

[0013] A computer electronic device includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor. When executed by the processor, the computer program implements the steps of a deformation inversion-based numerical solution method for coronary blood flow as described above.

[0014] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of a deformation inversion-based numerical solution method for coronary blood flow as described above.

[0015] This application has the following advantages: In the embodiments of this application, addressing the inherent drawbacks of existing technologies such as high computational complexity, reliance on numerous assumptions or training, and poor clinical reproducibility, this application provides a method for high-precision estimation of time-varying coronary flow based on cardiac cycle deformation information provided by multi-temporal CTA. This method transforms one-dimensional hemodynamic partial differential equations into periodic ordinary differential equations containing only a single variable. By numerically solving the periodic ordinary differential equations, a method for high-precision estimation of time-varying coronary flow is achieved. Specifically, this method is a numerical solution method for coronary blood flow based on deformation inversion, comprising the following steps: acquiring multi-temporal coronary CTA images of the target to be evaluated, and extracting coronary vessel deformation waveform data from the multi-temporal coronary CTA images; generating a time-varying flow waveform at the coronary artery inlet of the target to be evaluated based on the vessel deformation data and basic laws of fluid mechanics; and deriving the instantaneous volumetric flow curve of the entire coronary artery segment of the target to be evaluated based on the time-varying flow waveform. By transforming the one-dimensional hemodynamic partial differential equation into a periodic ordinary differential equation containing only the inlet flow rate as an unknown, complex spatial-temporal discretization and extensive empirical parameter calibration are avoided. This addresses the shortcomings of existing technologies, such as high computational complexity and difficulty in meeting real-time clinical requirements, achieving improved computational efficiency and rapid result output. Furthermore, by directly utilizing vascular periodic deformation data provided by multi-temporal CTA to construct the solution model, without relying on training data, neural network structures, or stringent physical assumptions, the shortcomings of existing technologies, such as lack of transparency and verifiability, and poor clinical reproducibility, are overcome. This achieves a rigorous solution logic and unique and transparent results. The technology achieves physiologically significant effects by extracting dynamic waveforms of coronary artery cross-sectional area changes with the cardiac cycle and deeply integrating them into the solution process. This fully explores the potential physiological information of multi-temporal CTA, overcoming the shortcomings of existing technologies in not fully utilizing CTA deformation data and insufficient specificity of functional assessment. This results in improved accuracy of blood flow parameter inversion and enhanced accuracy of clinical lesion identification. Furthermore, by extending the inlet time-varying flow waveform to the entire coronary artery segment based on the law of mass conservation, the technology overcomes the limitation of existing technologies in comprehensively assessing the impact of blood flow at different lesion locations. This provides clinicians with quantitative blood flow information for the entire vessel segment and assists in the precise formulation of revascularization plans. Attached Figure Description

[0016] To more clearly illustrate the technical solution of this application, the drawings used in the description of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of a numerical solution method for coronary blood flow based on deformation inversion provided in one embodiment of this application; Figure 2 This is a comparison diagram of the predicted blood flow waveform at the blood vessel inlet and the reference blood flow waveform provided in an embodiment of this application; Figure 3 This is a structural block diagram of a numerical solution system for coronary blood flow based on deformation inversion provided in one embodiment of this application; Figure 4 This is a schematic diagram of the structure of a computer electronic device provided in an embodiment of this application; 1. Computer electronic device; 2. External device; 3. Processing unit; 4. Bus; 5. Network adapter; 6. I / O interface; 7. Display; 8. Memory; 9. Random access memory; 10. Cache memory; 11. Storage system; 12. Program / utility; 13. Program module. Detailed Implementation

[0018] To make the objectives, features, and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0019] The inventors, through analysis of existing technologies, discovered the following: 1. Methods based on one-dimensional partial differential equations rely on time-space discretization and complex boundary condition settings, resulting in high computational costs and difficulty in guaranteeing model stability. 2. Physically constrained neural networks depend on training data and network construction processes, lacking strict mathematical uniqueness guarantees, and their prediction results lack transparency and verifiability. 3. Multi-temporal CTA can provide information on the periodic deformation of blood vessel cross-sectional area over time, but existing technologies do not incorporate this information into blood flow solution models.

[0020] Reference Figure 1 This paper illustrates a method for numerically solving coronary artery blood flow based on deformation inversion, according to an embodiment of this application, including the following steps: S110. Acquire multi-temporal coronary CTA images of the target to be evaluated, and extract coronary vessel deformation waveform data from the multi-temporal coronary CTA images; S120. Based on the vascular deformation data and the basic laws of fluid mechanics, generate a time-varying flow waveform at the coronary artery inlet of the target to be evaluated; S130. Based on the time-varying flow waveform, derive the instantaneous volumetric flow curve of the entire coronary artery segment of the target to be evaluated.

[0021] In the embodiments of this application, addressing the inherent shortcomings of existing technologies such as high computational complexity, reliance on numerous assumptions or training, and poor clinical reproducibility, this application provides a method for high-precision estimation of time-varying coronary flow based on cardiac cycle deformation information provided by multi-temporal CTA. This method transforms a one-dimensional hemodynamic partial differential equation into a periodic ordinary differential equation containing only a single variable. By numerically solving this periodic ordinary differential equation, a method for high-precision estimation of time-varying coronary flow is achieved. By transforming the one-dimensional hemodynamic partial differential equation into a periodic ordinary differential equation containing only the inlet flow as an unknown variable, complex spatial-temporal discretization processing and extensive empirical parameter calibration are avoided. This overcomes the shortcomings of existing technologies, such as high computational complexity and difficulty in meeting real-time clinical requirements, achieving improved computational efficiency and rapid result output. Furthermore, by directly utilizing the vascular periodic deformation data provided by multi-temporal CTA to construct the solution model, without relying on training data, neural network structures, or stringent physical assumptions, the shortcomings of existing technologies, such as lack of transparency and verifiability, and poor clinical reproducibility, are overcome. This achieves a rigorous solution logic and unique and transparent results. The technology achieves physiologically significant effects by extracting dynamic waveforms of coronary artery cross-sectional area changes with the cardiac cycle and deeply integrating them into the solution process. This fully explores the potential physiological information of multi-temporal CTA, overcoming the shortcomings of existing technologies in not fully utilizing CTA deformation data and insufficient specificity of functional assessment. This results in improved accuracy of blood flow parameter inversion and enhanced accuracy of clinical lesion identification. Furthermore, by extending the inlet time-varying flow waveform to the entire coronary artery segment based on the law of mass conservation, the technology overcomes the limitation of existing technologies in comprehensively assessing the impact of blood flow at different lesion locations. This provides clinicians with quantitative blood flow information for the entire vessel segment and assists in the precise formulation of revascularization plans.

[0022] The following will further explain a numerical solution method for coronary blood flow based on deformation inversion in this exemplary embodiment.

[0023] In one embodiment of this application, the specific process of "acquiring multi-temporal coronary CTA images of the target to be evaluated and extracting coronary vessel deformation waveform data from the multi-temporal coronary CTA images" described in step S110 can be further explained in conjunction with the following description.

[0024] As described in the following steps The multi-temporal coronary CTA images were subjected to noise reduction, contrast enhancement, and edge sharpening. Using pre-defined phase coronary CTA images as a reference, non-rigid registration is performed on coronary CTA images of different time phases to compensate for the spatiotemporal shift caused by cardiac pulsation and respiratory motion. Coronary artery deformation waveform data are extracted from the registered coronary CTA image data.

[0025] It should be noted that noise reduction can employ anisotropic diffusion filtering or nonlocal mean filtering to preserve the vessel edges while smoothing noise; contrast enhancement can use the CLAHE (Constrained Contrast Adaptive Histogram Equalization) algorithm to highlight the differences between the vessel lumen and the surrounding tissue; and edge sharpening can employ unsharp masking technology.

[0026] As an example, non-rigid registration can employ a B-spline-based free deformation model or the Demons algorithm. The similarity measure can be mutual information or normalized cross-correlation to handle potential grayscale differences between different time phases. The reference phase for registration is typically chosen as the end-diastolic phase of the heart (e.g., 75% phase), when the heart is relatively still and the image is clearest.

[0027] In one specific implementation, firstly, a CTA image sequence of 10 equally spaced phases (0%, 10%, ..., 90%) of the target coronary artery within a complete cardiac cycle is acquired. For each image, nonlocal mean filtering is applied for noise reduction, contrast-limited adaptive histogram equalization is applied for contrast enhancement, and the Laplacian operator is applied for edge sharpening. Next, using the end-diastolic image (typically 75% phase) as a spatial reference, a registration toolkit such as Elastix is ​​used, with the aforementioned other phase images as floating images. Through a multi-resolution optimization strategy, the mutual information between the reference image and the floating image, using the coronary artery trunk region as a mask, is minimized to solve for the non-rigid spatial transformation parameters. Subsequently, this transformation is applied to the floating image and its corresponding segmentation label (if any), achieving accurate alignment of all temporal images in three-dimensional space, compensating for motion artifacts, and laying a consistent coordinate foundation for subsequent deformation extraction.

[0028] In one embodiment of this application, the specific process of "extracting coronary artery deformation waveform data from registered coronary CTA image data" can be further explained in conjunction with the following description.

[0029] As described in the following steps The registered coronary CTA image data is segmented into coronary artery lumens to generate a 3D coronary artery vessel model; Extract the geometric center line of the 3D coronary artery model, and set uniformly distributed nodes along the geometric center line; The cross-sectional area of ​​the blood vessel at each node in each time phase is calculated, and a dynamic waveform of the cross-sectional area of ​​the blood vessel changing over time is generated as the blood vessel deformation data.

[0030] It should be noted that the purpose of the steps in this embodiment is to convert the aligned multi-temporal three-dimensional image into cross-sectional area data along the blood vessel axis that varies with time, i.e., the deformation waveform S(x,t).

[0031] As an example, coronary artery lumen segmentation can be automated using deep learning-based 3D segmentation networks (such as 3D U-Net, V-Net). Geometric centerline extraction can be performed using distance-transform-based topology thinning algorithms or fast traversal methods. Cross-sectional area calculation can be performed at each centerline node by extracting a cross-sectional image perpendicular to the centerline tangent, obtained through pixel counting or ellipse fitting.

[0032] In one specific implementation, a pre-trained 3D U-Net model is first used to perform preliminary lumen segmentation on the registered CTA images. The training process requires a dataset containing hundreds of cases of coronary artery lumens precisely annotated by physicians. During training, image patches and labels are input into the network. The predicted segmentation map is calculated via forward propagation, and the weighted sum of the Dice loss function and cross-entropy loss function between the predicted map and the ground truth label is minimized via backpropagation. The Adam optimizer is used to update the network weights until the model's segmentation Dice coefficient on the independent validation set stabilizes above 0.92. For the preliminary segmentation results, especially at vessel bifurcation, adjacent calcified plaques, or blurred boundaries, an active contour model can be used for iterative optimization. This model defines a parametric curve initially near the network's predicted boundary. By iteratively minimizing the energy function composed of image gradient force (external energy) and curve curvature constraint (internal energy), the curve gradually conforms to the actual lumen boundary, thereby obtaining a high-precision three-dimensional lumen surface model. Subsequently, the centerline of the 3D model was extracted using a centerline tracing algorithm, and sampling nodes were set along the centerline at intervals of 0.4 mm. For each node and each registration phase, the cross-sectional area of ​​the blood vessel perpendicular to the centerline at that node was calculated. Finally, these data were organized into a two-dimensional matrix. The matrix contains the row index i corresponding to the node position and the column index j corresponding to the time phase. This matrix is ​​the vascular deformation data required for subsequent solutions.

[0033] In one embodiment of this application, the specific process of "generating a time-varying flow waveform at the coronary artery inlet of the target to be evaluated based on the vascular deformation data and the basic laws of fluid mechanics" in step S120 can be further explained in conjunction with the following description.

[0034] As described in the following steps Based on the aforementioned blood vessel deformation data and fundamental laws of fluid mechanics, a periodic ordinary differential equation containing only one unknown quantity—the inlet flow rate—is constructed. Solve the periodic ordinary differential equation to output the time-varying flow waveform at the coronary artery inlet.

[0035] It should be noted that the fundamental laws of fluid mechanics mainly refer to the conservation of mass (continuity equation) and the conservation of momentum (equation of motion). The process of constructing the equations involves spatial integration of the partial differential equations along the vessel axis and constitutive substitution of the pressure gradient term using deformation data.

[0036] In a specific implementation, based on the assumptions that blood is incompressible and blood vessels are thin-walled elastic tubes, and based on the principle that the blood volume within a blood vessel segment remains constant:

[0037] The momentum conservation equation, based on Newton's second law, describes the mechanical equilibrium relationship during blood flow:

[0038] Where P, Q, and S represent pressure, flow rate, and cross-sectional area, respectively. x represents the axial coordinate of the container's centerline, and t is time. The blood density ρ is 1060 kg / m³. The blood flow viscosity is 0.0033 Pa·s. The core transformation lies in using the mass conservation equation to express the flow rate Q(x,t) at any position x as the sum of the inlet flow rate Q(t) and a spatial integral Φ(x,t) consisting only of the area-time derivative of the known deformation data.

[0039] To form a closed-form equation system, a constitutive relation of the blood vessel is required to describe the elastic response of the vessel wall. This application employs a nonlinear (Olufsen) model to accommodate different physiological conditions:

[0040] Where P0 is the reference pressure, r0 is the resting radius at t=0, S0 = πr0² is the resting cross-sectional area, E is Young's modulus, and h is the wall thickness. The constitutive relation directly relates deformation data and pressure, providing physical constraints for the inversion problem.

[0041] Next, substituting the nonlinear constitutive relation of the blood vessel into the pressure gradient term of the momentum equation, we obtain the term Ψ(x,t) explicitly expressed using the area S and its spatial derivative. Finally, integrating the momentum equation containing Q(t), Φ(x,t), Ψ(x,t), and S(x,t) along the blood vessel length L with respect to x, and after algebraic simplification and elimination of spatial variables, we finally obtain the form as follows: The ordinary differential equation is obtained by numerically integrating the time-varying coefficients α(t), β(t), and γ(t) from the deformation data S(x,t) and its spatiotemporal derivatives. The equation is then solved. Since both vascular deformation and blood flow exhibit cardiac periodicity, the solution must satisfy the periodic boundary condition Q(T) = Q(0). This is typically achieved using a numerical targeting method: first, an initial inlet flow rate Q(0) is guessed; then, Q(T) is obtained by numerically integrating the equation for one period T using the fourth-order Runge-Kutta method; the error between Q(0) and Q(0) is calculated; and finally, Q(0) is iteratively updated using an optimization algorithm (such as the Newton-Raphson method) until the error is less than a preset tolerance (e.g., 1e-4 mL / s). The obtained Q(t) is then the desired inlet time-varying flow rate waveform.

[0042] In one embodiment of this application, the specific process of "constructing a periodic ordinary differential equation containing only one unknown quantity, the inlet flow rate, based on the blood vessel deformation data and the basic laws of fluid mechanics" can be further explained in conjunction with the following description.

[0043] As described in the following steps The mass conservation equation is established based on the principle that the blood volume within a blood vessel segment remains constant, and the momentum conservation equation is established based on Newton's second law. Spatial variables are eliminated through integration, and a periodic ordinary differential equation containing only one unknown quantity, the inlet flow rate, is constructed by combining variable substitution. Based on the vascular deformation data, the coefficients of the periodic ordinary differential equation that change with time are calculated, and the solution equation is generated.

[0044] It should be noted that this application simplifies and calculuses the blood flow inversion problem by transforming the one-dimensional blood flow control equation into a periodic single-variable ordinary differential equation. Establishing mass and momentum conservation equations is a common starting point for fluid mechanics modeling, and variable substitution aims to separate known quantities (deformation) from unknown quantities (flow rate). Spatial integration is a key operation to eliminate the dependence of the equations on spatial coordinates, simplifying the distributed parameter system into a lumped parameter system.

[0045] In a specific implementation, based on the conservation of mass, formula (1) is obtained. According to Newton's second law (conservation of momentum), and combined with the one-dimensional blood flow assumption and Newtonian fluid stress relationship, the momentum equation shown in formula (2) is obtained, which includes convection terms, pressure gradient terms, and viscous drag terms. Expanding the derivative terms of the momentum conservation equation (2), and then... Substituting, we get:

[0046] Let x∈[0,L] represent the coordinates along the vessel axis, and t be time. The volumetric flow rate at the inlet is defined as... For the equation The spatial integral from the entry x=0 to any x can be written as:

[0047] According to the pressure gradient term in equation (3), define for:

[0048] Substituting the decomposed flow rate expression (5) and pressure gradient expression (6) into equation (4), and performing spatial integration over the interval [0,L], we obtain:

[0049] Each coefficient is obtained explicitly from S(x,t) and its derivative: , , .

[0050] In one embodiment of this application, the specific process of "solving the periodic ordinary differential equation and outputting the time-varying flow waveform at the coronary artery inlet" can be further explained in conjunction with the following description.

[0051] As described in the following steps Set the initial value of the inlet flow rate based on prior information about the average clinical flow rate. The periodic ordinary differential equation is integralized over time based on the initial inlet flow rate and the solution equation. Calculate the flow error between the end and the beginning of the cardiac cycle, and determine whether the flow error meets a preset threshold; The initial value of the inlet flow is iteratively optimized, and when the flow error converges within a preset threshold, the time-varying flow waveform at the inlet is output.

[0052] It should be noted that the target-shooting method is a classic numerical method for solving periodic boundary value problems. The fourth-order Runge-Kutta method is a commonly used method for solving initial value problems of ordinary differential equations with high accuracy and stability. Combining the two can effectively handle the periodic constraints of this problem, and optimization tools can be used to ensure the physiological rationality of the solution. The entire solution process is based on vascular deformation data, and approximates the periodic solution through numerical iteration, meeting the dual requirements of computational efficiency and reliability for clinical applications.

[0053] In one specific implementation, the core framework of the numerical solution is based on the shooting method. The periodic boundary condition Q(T) = Q(0) is forced by adjusting the initial value, where T is the cardiac cycle. This method avoids the uncertainty of the convergence rate during asymptotic convergence and the error caused by insufficient convergence in actual inversion. The specific steps are as follows: First, the initial value of the inlet flow rate Q(0) is set based on the average flow rate prior; second, the ordinary differential equation is solved using the RK4 algorithm; finally, the periodic error is calculated. The algorithm iteratively optimizes Q(0) until the error converges below a threshold, outputting a converged Q(t) that satisfies the periodic boundary conditions. The blood flow velocity Q(x,t) at all positions can be directly calculated based on the law of conservation of mass. Through this solution strategy, we can determine an initial value that satisfies the periodic conditions, thereby deriving the blood flow distribution Q(x,t) throughout the entire cardiac cycle and achieving a quantitative assessment of coronary hemodynamic parameters.

[0054] In one embodiment of this application, the specific process of "deriving the instantaneous volumetric flow curve of the entire coronary artery segment based on the time-varying flow waveform at the inlet" described in step S130 can be further explained in conjunction with the following description.

[0055] As described in the following steps Based on the law of conservation of mass, a correlation is established between inlet flow and flow at any location in the blood vessel; The flow distribution is corrected by combining the dynamic changes in cross-sectional area at each location in the aforementioned vascular deformation data; Output the instantaneous volumetric flow curve of any node in the main coronary artery and its branches.

[0056] It should be noted that, based on the law of conservation of mass, the flow rate at any point in a blood vessel can be obtained by subtracting the rate of change of blood volume in the upstream segment of the blood vessel at that point over time (i.e., the spatial integral of the area-time derivative) from the inlet flow rate. This is essentially an application of the one-dimensional continuity equation in space.

[0057] In a specific implementation, the first step is to establish the correlation. Based on the one-dimensional mass conservation equation, a spatial integral is performed from the blood vessel inlet (x=0) to any point of interest x, yielding... Where Q(t) is the inlet flow waveform obtained in step S120, This represents the rate of change of area at the axial coordinate y, over time t. Next, the spatial integral term is calculated. This is done for each pre-defined node position on the centerline. (i=1,2,…,M), at each discrete time point (j=1,2,…,N), perform the following calculations: 1) Calculate the deformed data matrix S(x, t) at each node using the central difference method. 1) Find the approximate value of the partial derivative with respect to time t. 2) Use numerical integration methods (e.g., the composite trapezoidal rule) to calculate the value from x=0 to x= The integral. Finally, the flow distribution is synthesized. The inflow flow Q( Subtracting the integral value calculated in the second step from the integral value yields the position. At any moment The instantaneous volume flow. Traverse all node positions. and all points in time This generates an M-row N-column matrix that fully describes the two-dimensional distribution of blood flow over time on the target coronary artery trunk and its branches, i.e., the "instantaneous volumetric flow curve of the entire vessel segment". This matrix can be directly used to visualize or calculate functional indicators such as the fractional flow reserve at specific locations.

[0058] To verify the accuracy and reliability of the time-varying flow waveform generated by this method, this application conducted a comparative analysis through simulation experiments. (Refer to...) Figure 2 This paper demonstrates a comparison between the blood flow waveform at the vascular inlet predicted using the method of this application (yellow curve in the figure) and the reference blood flow waveform obtained through high-fidelity computational fluid dynamics (CFD) simulation (blue curve in the figure) over a complete cardiac cycle. First, a set of known, physiologically plausible reference inlet flow waveforms (i.e., blue curves) is used as input. Combined with a one-dimensional hemodynamic forward model and preset vascular elastic parameters, simulated deformation data of the vascular cross-sectional area changing over time is generated. This process is equivalent to generating the "exam question" (deformation) from a known "answer" (flow rate). Then, this simulated deformation data is used as input to this application, and blood flow inversion calculations are performed strictly according to the steps S110 to S130 described above, ultimately obtaining the predicted inlet flow waveform (i.e., yellow curve). Figure 2 As shown, the predicted waveform (yellow) and the reference waveform (blue) are highly consistent in the time domain. Specifically, this is demonstrated by: 1. Morphological consistency: The predicted waveform accurately reproduces the main characteristics of the reference waveform, including the rapid rise peak during systole, the decay plateau during diastole, and key physiological features such as the dicrotic notch. 2. Amplitude accuracy: Throughout the entire cycle, the average relative deviation between the predicted flow rate and the reference flow rate is less than 5%, indicating that this method has high accuracy in quantitative estimation. 3. Periodicity satisfaction: The predicted waveform is continuous and smooth, satisfying the periodic boundary condition Q(T)=Q(0), proving the effectiveness of the numerical solution strategy (targeting method). The simulation results show that the numerical solution method based on deformation inversion described in this application can stably and accurately invert the core hemodynamic parameter—time-varying volumetric flow rate—from vascular periodic deformation data. This verifies the correctness of the core theory of this application (dimensionality reduction transformation from partial differential equations to periodic ordinary differential equations) and the robustness of the subsequent numerical solution process, providing feasibility support for the application of this method on real clinical CTA data.

[0059] As the device embodiment is basically similar to the method embodiment, the description is relatively simple, and relevant parts can be found in the description of the method embodiment.

[0060] Reference Figure 3 This paper illustrates a numerical solution system for coronary artery blood flow based on deformation inversion, according to an embodiment of this application. The system specifically includes the following modules: Specifically, it includes: The data acquisition module 310 is used to acquire multi-temporal coronary CTA images of the target to be evaluated, and extract coronary vessel deformation waveform data from the multi-temporal coronary CTA images; The inlet time-varying flow solution module 320 is used to generate a time-varying flow waveform at the coronary artery inlet of the target to be evaluated based on the vascular deformation data and the basic laws of fluid mechanics. The whole vessel segment flow derivation module 330 is used to derive the instantaneous volumetric flow curve of the whole coronary artery segment of the target to be evaluated based on the time-varying flow waveform.

[0061] In one embodiment of this application, the data acquisition module 310 includes: The first data acquisition submodule is used to perform noise reduction, contrast enhancement, and edge sharpening on the multi-temporal coronary CTA images; The second data acquisition submodule is used to perform non-rigid registration of coronary CTA images of different time phases based on the preset phase coronary CTA images to compensate for the spatiotemporal shift caused by heart pulsation and respiratory motion. The third data acquisition submodule is used to extract coronary artery deformation waveform data from the registered coronary CTA image data.

[0062] In one embodiment of this application, the third data acquisition submodule includes: The coronary artery 3D modeling unit is used to segment the coronary artery lumen from the registered coronary CTA image data and generate a 3D coronary artery model. The coronary artery centerline extraction unit is used to extract the geometric centerline of the 3D coronary artery model and set uniformly distributed nodes along the geometric centerline. The vascular deformation data generation unit is used to calculate the vascular cross-sectional area of ​​each node in each time phase and generate a dynamic waveform of the vascular cross-sectional area changing over time as the vascular deformation data.

[0063] In one embodiment of this application, the inlet time-varying flow rate solving module 320 includes: The first inlet time-varying flow rate solution submodule is used to construct a periodic ordinary differential equation containing only one unknown quantity, the inlet flow rate, based on the blood vessel deformation data and the basic laws of fluid mechanics. The second inlet time-varying flow solution submodule is used to solve the periodic ordinary differential equation and output the time-varying flow waveform at the coronary artery inlet.

[0064] In one embodiment of this application, the first inlet time-varying flow calculation submodule includes: The governing equation establishment unit is used to establish the mass conservation equation based on the principle that the blood volume in the blood vessel segment remains constant, and to establish the momentum conservation equation based on Newton's second law. Equation transformation and dimensionality reduction unit is used to eliminate spatial variables through integration operations and construct periodic ordinary differential equations containing only one unknown quantity, inlet flow rate, by combining variable substitution. The periodic coefficient calculation element is used to calculate the time-varying coefficient terms in the periodic ordinary differential equation based on the vascular deformation data, and generate the solution equation.

[0065] In one embodiment of this application, the second inlet time-varying flow rate solution submodule includes: The initial value setting unit is used to set the initial value of the inlet flow rate based on prior information of the clinical average flow rate; The time integration calculation unit is used to perform time integration calculation on the periodic ordinary differential equation based on the initial value of the inlet flow and the solution equation; The cycle error assessment unit is used to calculate the flow error between the end and the beginning of the cardiac cycle and to determine whether the flow error meets a preset threshold. The iterative optimization and solution output unit is used to iteratively optimize the initial value of the inlet flow rate, and outputs the time-varying flow waveform at the inlet when the flow error converges within a preset threshold.

[0066] In one embodiment of this application, the whole blood vessel segment flow estimation module 330 includes: The first whole-vessel flow derivation submodule is used to establish the correlation between inlet flow and flow at any location in the blood vessel based on the law of conservation of mass. The second whole-vessel flow derivation submodule is used to correct the flow distribution by combining the dynamic changes of cross-sectional area at each location in the vessel deformation data; The third whole-vessel flow derivation submodule is used to output the instantaneous volumetric flow curve of any node in the main coronary artery and its branches.

[0067] Reference Figure 4 The illustration shows a computer electronic device for implementing a non-invasive coronary blood flow assessment method based on multi-temporal CTA and Bayesian inference according to this application, which may specifically include the following: The aforementioned computer device 1 is in the form of a general-purpose computing device. The components of the computer device 1 may include, but are not limited to: one or more processors or processing units 3, memory 8, and a bus 4 connecting different system components (including memory 8 and processing unit 3).

[0068] Bus 4 represents one or more of several bus architectures, including memory buses or memory controllers, peripheral buses, graphics acceleration ports, processors, or local buses using any of the various bus architectures. For example, these architectures include, but are not limited to, the Industry Standard Architecture (ISA) bus, the Micro Channel Architecture (MAC) bus, the Enhanced ISA bus, the Audio / Video Electronics Standards Association (VESA) local bus, and the Peripheral Component Interconnect (PCI) bus.

[0069] Computer device 1 typically includes a variety of computer system readable media. These media can be any available media that can be accessed by computer device 1, including volatile and non-volatile media, removable and non-removable media.

[0070] Memory 8 may include computer system readable media in the form of volatile memory, such as random access memory 9 and / or cache memory 10. Computer device 1 may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, storage system 11 may be used to read and write non-removable, non-volatile magnetic media (commonly referred to as a "hard disk drive"). Although Figure 4 As not shown, a disk drive for reading and writing to a removable non-volatile disk (such as a "floppy disk") and an optical disk drive for reading and writing to a removable non-volatile optical disk (such as a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 4 via one or more data media interfaces. The memory may include at least one program product having a set (e.g., at least one) of program modules 13 configured to perform the functions of the embodiments of this application.

[0071] A program / utility 12 having a set (at least one) of program modules 13 may be stored, for example, in memory. Such program modules 13 include—but are not limited to—an operating system, one or more application programs, other program modules 13, and program data. Each or some combination of these examples may include an implementation of a network environment. Program modules 13 typically perform the functions and / or methods described in the embodiments of this application.

[0072] Computer device 1 can also communicate with one or more external devices 2 (e.g., keyboard, pointing device, monitor 7, camera, etc.), and with one or more devices that enable an operator to interact with computer device 1, and / or with any device that enables computer device 1 to communicate with one or more other computing devices (e.g., network card, modem, etc.). This communication can be performed through I / O interface 6. Furthermore, computer device 1 can also communicate with one or more networks (e.g., local area network (LAN)), wide area network (WAN), and / or public networks (e.g., the Internet) through network adapter 5. Figure 4 As shown, network adapter 5 communicates with other modules of computer device 1 via bus 4. It should be understood that, although... Figure 4 Not shown, it can be combined with computer device 1 to use other hardware and / or software modules, including but not limited to: microcode, device drivers, redundant processing unit 3, external disk drive array, RAID system, tape drive and data backup storage system 11, etc.

[0073] The processing unit 3 executes various functional applications and data processing by running programs stored in memory 8, such as implementing a numerical solution method for coronary blood flow based on deformation inversion provided in the embodiments of this application.

[0074] That is, when the processing unit 3 executes the above procedure, it achieves the following: acquiring multi-temporal coronary CTA images of the target to be evaluated, and extracting coronary vessel deformation waveform data from the multi-temporal coronary CTA images; generating a time-varying flow waveform at the coronary artery inlet of the target to be evaluated based on the vessel deformation data and the basic laws of fluid mechanics; and deriving the instantaneous volumetric flow curve of the entire coronary artery segment of the target to be evaluated based on the time-varying flow waveform.

[0075] In this application embodiment, this application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a method for numerically solving coronary artery blood flow based on deformation inversion as provided in all embodiments of this application.

[0076] That is, when the program is executed by the processor, it performs the following: acquiring multi-temporal coronary CTA images of the target to be evaluated, and extracting coronary vessel deformation waveform data from the multi-temporal coronary CTA images; generating a time-varying flow waveform at the inlet of the coronary artery of the target to be evaluated based on the vessel deformation data and the basic laws of fluid mechanics; and deriving the instantaneous volumetric flow curve of the entire coronary artery segment of the target to be evaluated based on the time-varying flow waveform.

[0077] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0078] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including—but not limited to—electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, capable of transmitting, propagating, or transmitting programs for use by or in connection with an instruction execution system, apparatus, or device.

[0079] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof. These programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on the operator's computer, partially on the operator's computer, as a standalone software package, partially on the operator's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the operator's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider). The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably.

[0080] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0081] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0082] The above provides a detailed description of the numerical solution method and system for coronary blood flow based on deformation inversion provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A numerical solution method for coronary artery blood flow based on deformation inversion, characterized in that, Including the following steps: Acquire multi-temporal coronary CTA images of the target to be evaluated, and extract coronary vessel deformation waveform data from the multi-temporal coronary CTA images; Based on the aforementioned vascular deformation data and fundamental principles of fluid mechanics, a time-varying flow waveform at the coronary artery inlet of the target to be evaluated is generated; Based on the time-varying flow waveform, the instantaneous volumetric flow curve of the entire coronary artery segment of the target to be evaluated is derived.

2. The numerical solution method for coronary artery blood flow based on deformation inversion according to claim 1, characterized in that, The steps of acquiring multi-temporal coronary CTA images of the target to be evaluated and extracting coronary vessel deformation waveform data from the multi-temporal coronary CTA images specifically include the following steps: The multi-temporal coronary CTA images were subjected to noise reduction, contrast enhancement, and edge sharpening. Using pre-defined phase coronary CTA images as a reference, non-rigid registration is performed on coronary CTA images of different time phases to compensate for the spatiotemporal shift caused by cardiac pulsation and respiratory motion. Coronary artery deformation waveform data are extracted from the registered coronary CTA image data.

3. The numerical solution method for coronary blood flow based on deformation inversion according to claim 2, characterized in that, The step of extracting coronary artery deformation waveform data from the registered coronary CTA image data specifically includes the following steps: The registered coronary CTA image data is segmented into coronary artery lumens to generate a 3D coronary artery vessel model; Extract the geometric center line of the 3D coronary artery model, and set uniformly distributed nodes along the geometric center line; The cross-sectional area of ​​the blood vessel at each node in each time phase is calculated, and a dynamic waveform of the cross-sectional area of ​​the blood vessel changing over time is generated as the blood vessel deformation data.

4. The numerical solution method for coronary artery blood flow based on deformation inversion according to claim 1, characterized in that, The step of generating a time-varying flow waveform at the coronary artery inlet of the target to be evaluated based on the vascular deformation data and basic principles of fluid mechanics specifically includes the following steps: Based on the aforementioned blood vessel deformation data and fundamental laws of fluid mechanics, a periodic ordinary differential equation containing only one unknown quantity—the inlet flow rate—is constructed. Solve the periodic ordinary differential equation to output the time-varying flow waveform at the coronary artery inlet.

5. The numerical solution method for coronary blood flow based on deformation inversion according to claim 4, characterized in that, The step of constructing a periodic ordinary differential equation containing only the inlet flow rate as an unknown quantity, based on the blood vessel deformation data and fundamental laws of fluid mechanics, specifically includes the following steps: The mass conservation equation is established based on the principle that the blood volume within a blood vessel segment remains constant, and the momentum conservation equation is established based on Newton's second law. Spatial variables are eliminated through integration, and a periodic ordinary differential equation containing only one unknown quantity, the inlet flow rate, is constructed by combining variable substitution. Based on the vascular deformation data, the coefficients of the periodic ordinary differential equation that change with time are calculated, and the solution equation is generated.

6. The numerical solution method for coronary blood flow based on deformation inversion according to claim 5, characterized in that, The steps of solving the periodic ordinary differential equation and outputting the time-varying flow waveform at the coronary artery inlet specifically include the following steps: Set the initial value of the inlet flow rate based on prior information about the average clinical flow rate. The periodic ordinary differential equation is integralized over time based on the initial inlet flow rate and the solution equation. Calculate the flow error between the end and the beginning of the cardiac cycle, and determine whether the flow error meets a preset threshold. The initial value of the inlet flow is iteratively optimized, and when the flow error converges within a preset threshold, the time-varying flow waveform at the inlet is output.

7. The numerical solution method for coronary blood flow based on deformation inversion according to claim 1, characterized in that, The step of deriving the instantaneous volumetric flow curve of the entire coronary artery segment based on the time-varying flow waveform at the inlet specifically includes the following steps: Based on the law of conservation of mass, a correlation is established between inlet flow rate and flow rate at any location in the blood vessel; The flow distribution is corrected by combining the dynamic changes in cross-sectional area at each location in the aforementioned vascular deformation data; Output the instantaneous volumetric flow curve of any node in the main coronary artery and its branches.

8. A numerical solution system for coronary artery blood flow based on deformation inversion, characterized in that, include: The data acquisition module is used to acquire multi-temporal coronary CTA images of the target to be evaluated, and extract coronary vessel deformation waveform data from the multi-temporal coronary CTA images; The inlet time-varying flow rate solution module is used to generate the time-varying flow rate waveform at the coronary artery inlet of the target to be evaluated based on the vascular deformation data and the basic laws of fluid mechanics. The whole-vessel flow derivation module is used to derive the instantaneous volumetric flow curve of the whole coronary artery segment of the target to be evaluated based on the time-varying flow waveform.

9. A computer electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and capable of running on the processor, wherein the computer program, when executed by the processor, implements the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, which, when executed by a processor, implements the method as described in any one of claims 1 to 7.

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