Three-dimensional blood vessel generation and reconstruction method based on deep learning and implicit geometry fusion

Abstract

This invention discloses a method for 3D blood vessel generation and reconstruction based on the fusion of deep learning and implicit geometry, belonging to the fields of medical image processing, computer graphics, and digital healthcare. It employs a dual-engine decoupling strategy of spatial dimensionality reduction followed by temporal extrapolation. First, the one-dimensional centerline and radius sequence of blood vessels are converted into temporal inputs. A high-fidelity two-dimensional cross-section is generated using a conditional variational autoencoder (CVAE) with interval roundness penalty. Then, a lightweight pure encoder (Transformer) is used to perform latent spatial temporal extrapolation to predict the complete cross-sectional sequence. Finally, distortion is eliminated through parallel transmission frame (RMF), and topological watertight reconstruction is achieved by implicit fitting using radial basis functions (RBF). This addresses the problems of high computational cost, topological damage, geometric distortion, susceptibility to torsional distortion, and inability to be directly used in CFD fluid simulations in 3D blood vessel reconstruction.

Description

Technical Field

[0001] This invention relates to the fields of medical image processing, computer graphics and digital medical technology, and in particular to a method for three-dimensional angiogenesis and reconstruction based on deep learning and implicit geometry fusion. Background Technology

[0002] Accurate 3D reconstruction of blood vessels is crucial for computational hemodynamics (CFD) analysis, surgical planning, and medical education. Existing techniques mainly include traditional geometric stitching methods and deep learning-based generation methods directly based on 3D space, but they have significant limitations:

[0003] The curse of dimensionality and computational bottleneck: Generating high-resolution 3D meshes or voxels directly in 3D space consumes a great deal of computing resources and GPU memory, making it difficult to generate complete vascular networks with complex cascading branches.

[0004] Topological defects and inability to directly simulate: Pure data-driven models lack strict mathematical and physical topological constraints. Defects such as holes, surface self-intersections, and non-manifold edges are prone to appear at the bifurcation of blood vessels, causing the CFD volume mesh generation program to crash and lack simulation readiness.

[0005] Over-smoothing and geometric distortion: Traditional variational autoencoders (VAEs) use only mean squared error (MSE) as the loss function, lacking global topological awareness. Strong regularization will lose small local pathological features of blood vessels, resulting in geometric distortion.

[0006] Three-dimensional inverse mapping twisting singularity of cross section: When using the Fleur-Serrey frame for two-dimensional contour mapping, the normal vector of the straight pipe section changes abruptly, causing the three-dimensional solid to twist into a twisted shape.

[0007] Existing technologies cannot automatically generate three-dimensional vascular solid models that combine biological realism with 100% topological watertightness and can be directly used for CFD simulation with low computing power consumption and by utilizing extremely sparse geometric constraints. Summary of the Invention

[0008] This invention provides a method for three-dimensional blood vessel generation and reconstruction based on the fusion of deep learning and implicit geometry, in order to solve the technical problems of dimensionality curse, topological damage, geometric distortion and mapping distortion in existing technologies.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0010] This invention provides a method for three-dimensional angiogenesis and reconstruction based on deep learning and implicit geometry fusion, comprising:

[0011] S1: Obtain the one-dimensional centerline coordinate set and radius sequence of blood vessels. After denoising, B-spline fitting and uniform resampling, the three-dimensional spatial geometry generation task is transformed into a temporal contour evolution prediction task along the centerline.

[0012] S2: Construct a conditional variational autoencoder (CVAE) with interval roundness penalty. The 2D contour point set and normalized radius are used as inputs. The latent feature vector is obtained through encoding and reparameterization. The 2D blood vessel cross section is generated through two-stage training of coarse-fine tuning.

[0013] S3: Using the latent feature vector as the sequence input, a lightweight pure encoder autoregressive Transformer is used to autoregressively predict the complete cross-sectional feature sequence in the latent space and decode it into a continuous two-dimensional contour sequence.

[0014] S4: The two-dimensional contour sequence is inversely mapped to a three-dimensional point cloud without distortion using the parallel transmission frame RMF. A global implicit scalar field is constructed through the radial basis function RBF, and the zero isosurface is extracted to obtain a topologically watertight three-dimensional vascular mesh.

[0015] Furthermore, the method for constructing the interval roundness penalty in S2 is as follows: the contour area A is calculated using the tensor shoelace formula, and the contour perimeter P is calculated using the L2 norm, resulting in roundness C = 4πA / P. 2 Based on the prior interval of healthy blood vessel roundness [C] min C max Construct the geometric penalty loss term L geo The total loss function is L total =L CVAE +L geo , where L CVAE The loss is generated based on this.

[0016] Furthermore, the coarse-build-fine-tuning two-stage training includes:

[0017] Coarse-scale stage: The geometric penalty term is turned off, and the KL divergence of mean squared error (MSE) and β-VAE is used for joint training to converge the basic shape of the contour;

[0018] Fine-tuning stage: Activate the interval roundness penalty term and amplify the penalty coefficient to correct distortion with a small learning rate and output a high-fidelity smooth cross section.

[0019] Furthermore, the Transformer in S3 adopts a lightweight structure of encoding as prediction, integrates sinusoidal positional encoding to preserve temporal causality, and extracts the hidden layer representation in the last step to autoregressively predict the potential features of the next frame.

[0020] Furthermore, in S4, the RMF eliminates the rotation of the normal vector through the double reflection method, avoiding the occurrence of torsional singularities in the three-dimensional reconstruction; the RBF uses a triharmonic spline kernel function to generate internal and external constraint points to solve the linear equation system and obtain a continuous implicit field.

[0021] Furthermore, in S4, the three-dimensional vascular mesh is a simulation-ready model without holes, self-intersections, or manifold defects, which can be directly imported into computational fluid dynamics (CFD) software to complete fluid simulation calculations.

[0022] Compared with the prior art, the technical solution disclosed in this invention has the following beneficial effects:

[0023] A decoupling strategy of first reducing spatial dimensions and then extrapolating temporally transforms the complex angiogenesis problem in 3D space into a temporal evolution problem of 2D cross-sections along a 1D centerline. This significantly reduces computational dimensionality and resource consumption, effectively alleviating the curse of dimensionality and computational bottlenecks faced by traditional direct 3D generation methods. By constructing a conditional variational autoencoder (CVAE) with interval roundness penalty and combining it with a two-stage training strategy of coarse-build and fine-tuning, high-fidelity 2D vascular cross-sections are generated, overcoming the geometric distortion problem caused by simple MSE loss in traditional VAE models, while also ensuring the biological rationality of the cross-sectional morphology. A lightweight pure encoder autoregressive Transformer performs autoregressive prediction on the cross-sectional feature sequence in the latent space, efficiently generating continuous and temporally consistent 2D contour sequences, providing high-quality foundational data for subsequent 3D reconstruction. By using the parallel transport frame RMF for inverse mapping from 2D contours to 3D point clouds, the torsional singularities caused by the Fleur-Cere frame were successfully eliminated, ensuring the smoothness of the 3D structure. By combining the radial basis function (RBF) to construct a global implicit scalar field and extracting the zero isosurface, the resulting 3D vascular mesh has 100% topological watertightness, completely solving the topological damage problem and realizing the automated generation of a "simulation-ready" model that can be directly used for CFD simulation from sparse geometric constraints. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 This is a schematic diagram of the process of a three-dimensional angiogenesis and reconstruction method based on deep learning and implicit geometry fusion provided in an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] This invention provides a method for three-dimensional blood vessel generation and reconstruction based on the fusion of deep learning and implicit geometry, which can solve the technical problems of dimensionality curse, topological damage, geometric distortion, and mapping distortion in the prior art.

[0029] like Figure 1 As shown, embodiments of the present invention provide a method for three-dimensional angiogenesis and reconstruction based on deep learning and implicit geometry fusion, including:

[0030] S1: Obtain the one-dimensional centerline coordinate set and radius sequence of blood vessels. After denoising, B-spline fitting and uniform resampling, the three-dimensional spatial geometry generation task is transformed into a temporal contour evolution prediction task along the centerline.

[0031] In other words, skeletal data preprocessing and spatial-temporal transformation are performed. One-dimensional centerline spatial coordinates and one-dimensional radius sequences of blood vessels are obtained. The static three-dimensional centerline is treated as a trajectory extending over time, transforming the spatial dimension of three-dimensional geometry generation into temporal dimension contour sequence evolution prediction.

[0032] This step aims to acquire the extremely sparse geometric features of three-dimensional blood vessels and convert them into a temporal standard input that can be processed by deep learning networks. The specific implementation includes the following core components:

[0033] 1. Acquisition and Mathematical Definition of Raw Sparse Skeleton Data: Acquire the static one-dimensional centerline spatial coordinate set and corresponding one-dimensional radius sequence of the three-dimensional vascular network to be reconstructed (e.g., extracted from enhanced CT images of the liver). Mathematically, this is rigorously defined as a discrete set of spatial points. (in and the corresponding set of pipe diameter constraints. (in These data constitute the extremely sparse geometric priors for the generative reconstruction of this invention.

[0034] 2. Continuous and Uniform Temporal Resampling Based on B-Splines: Since the original centerline point set extracted clinically often has uneven spacing and local noise, directly using it as sequence input makes it difficult for deep learning models (such as Transformer) to capture stable temporal evolution patterns. Therefore, this invention first... Denoising was performed, and B-spline curves were used for smooth fitting to construct a continuous parameterized space curve. Subsequently, a fixed spatial step size is set, and uniform resampling is performed along the arc length of the curve to obtain the centerline nodes and interpolation radius at equal intervals.

[0035] Core Mechanism: Spatial-Temporal Transformation: To overcome the "curse of dimensionality" caused by directly generating high-resolution solid meshes in 3D space, this invention proposes to reduce the dimensionality of static geometric shapes in the spatial dimension into dynamic growth sequences in the temporal dimension. Specifically, this involves uniformly resampling the 3D blood vessel centerline... Equivalent to a period of virtual time The trajectory of unidirectional growth. Through this mapping, the complex task of evolving the three-dimensional spatial mesh is completely decoupled and transformed into: an ordered sequence... This approach is designed to drive the task of predicting the time-series features of vascular 2D cross-sectional morphology along the growth direction of the skeletal structure. This transformation not only significantly reduces the memory usage of the subsequent generative network but also lays the theoretical foundation for introducing an autoregressive sequence model.

[0036] S2: Construct a conditional variational autoencoder (CVAE) with interval roundness penalty. The CVAE takes a two-dimensional contour point set and a normalized radius as input, and obtains the latent feature vector through encoding and reparameterization. The CVAE is then trained through a two-stage coarse-build and fine-tuning process to generate a two-dimensional blood vessel cross section.

[0037] Specifically, a conditional variational autoencoder (CVAE) based on interval roundness penalty is constructed. A CVAE model is then built to extract the static micromorphology of blood vessel cross-sections. The encoder receives a two-dimensional contour point set and normalized radius features, mapping them to obtain a low-dimensional latent distribution vector. In this step, a range roundness penalty term is embedded into the deep learning loss function. The area of ​​the generated contour is calculated in real time using the tensor shoelace formula. ,use Perimeter calculation by norm accumulation ; Calculate roundness ; Define a priori range for healthy blood vessels, and for vessels exceeding this range... A second-order penalty gradient is applied. A two-stage "coarse-build-fine-tuning" strategy is adopted: the first stage closes... Based on mean square error and the introduction of - The KL divergence of the VAE mechanism achieves basic convergence; second-stage activation Fine-tune the contour with a small learning rate to avoid self-intersection and wrinkles.

[0038] Static shape feature extraction and micromorphological modeling (based on an improved CVAE end) utilizes a conditional variational autoencoder (CVAE) as a "shape expert" to map two-dimensional cross-sections to a low-dimensional continuous latent space.

[0039] Encoding and Reparameterization: The encoder of a CVAE receives a set of two-dimensional contour points. and normalized radius constraint As conditional input, the concatenated input is passed through a multilayer perceptron (MLP) network, which outputs the mean vector of the latent distribution. With log-variance vector To ensure the gradient is differentiable during backpropagation, standard normal distribution noise is introduced. Using reparameterization techniques Calculate the low-dimensional latent feature vector To construct an interval roundness penalty loss function that integrates global geometric priors and completely solve the problem of wrinkles and self-intersections in 2D contour generation caused by purely data-driven methods, this embodiment of the invention designs area and perimeter operators with physical meaning in the differentiable computational graph of deep learning. For the ordered contour point set generated by the decoder... The area of ​​the polygon is calculated using the tensor shoelace formula. Using adjacent point difference Norm calculation of perimeter Then, the roundness feature, which reflects geometric smoothness, is calculated. Statistical prior intervals based on real healthy blood vessels. (If set to) Construct a flexible interval penalty loss term. The loss term is expressed through dynamic coefficients. This forcibly punishes unnatural distortions with high perimeter and low area from a physical level. A two-stage training mechanism of "coarse-fine tuning" is implemented: the overall network loss function is defined as... .in Based on the generation loss, this invention introduces -VAE mechanism, applying dynamic weights (like To reduce the regularization penalty of KL divergence and avoid over-smoothing, thus preserving the microscopic pathological features of local blood vessels. The actual training consists of two phases: a data-driven coarse-scale phase where the geometric penalty term is disabled (set...). The network is trained solely on mean squared error (MSE) and KL divergence, employing a standard learning rate decay strategy to quickly capture the basic dimensions of the vascular contour. In the geometric prior fine-tuning stage, the optimal network weights from the coarse-scale stage are loaded, the interval roundness penalty term is activated, and the penalty is amplified (e.g., by setting...). With a very small fine-tuning learning rate, the model is guided to self-correct subtle jagged edges and non-manifold distortions based on a rough outline, ultimately outputting an absolutely smooth and self-intersecting high-fidelity cross-section.

[0040] S3: Using the latent feature vector as the sequence input, a lightweight pure encoder autoregressive Transformer is used to autoregressively predict the complete cross-sectional feature sequence in the latent space and decode it into a continuous two-dimensional contour sequence.

[0041] That is, temporal deduction of latent space sequences based on autoregressive Transformers. A lightweight pure encoder-only Transformer with a multi-head self-attention mechanism is constructed. The continuous latent space vectors extracted by S2 are then processed. As the input sequence, the model actively truncates redundant outputs within the sequence, extracting only the hidden layer representation of the last time step. It then predicts the feature distribution of the next frame's contour in the low-dimensional manifold space through mapping autoregression, and finally decodes it into a solid 2D contour using CVAE.

[0042] A lightweight, encoder-only autoregressive Transformer based on a multi-head self-attention mechanism is constructed as a "temporal expert" to deduce the morphological evolution of blood vessel cross-sections as they grow along the centerline. The specific implementation includes the following core components:

[0043] Cross-dimensional serialized input construction: To overcome the "curse of dimensionality" and memory bottleneck caused by directly generating point clouds or voxels in 3D space, this invention proposes a decoupled paradigm of "spatial dimensionality reduction first, followed by temporal derivation." This involves highly compressing the low-dimensional continuous latent feature vector output by the CVAE "shape expert" in S2. As the basic unit. In time step The model receives data containing past events. The latent feature window of the frame context as an input sequence .

[0044] Fusion of linear mapping and sinusoidal positional encoding: Since the self-attention mechanism itself does not have the ability to process sequence order, in order to preserve the spatial causal relationship of blood vessel cross-sections along the centerline, the input feature sequence is... First, linear mapping (Embedding) is applied, followed by element-wise fusion with sinusoidal positional encoding. The specific formula for calculating the positional encoding is as follows:

[0045]

[0046] in, This represents the position of the section in the sequence. Represents the feature dimension index. is the feature hidden layer dimension of the model.

[0047] Multi-head self-attention mechanism extracts long-range spatial dependencies: The feature matrix after fusing location information enters the core multi-head self-attention layer. A learnable weight matrix maps the features to a query matrix. Key matrix AND-value matrix Furthermore, the long-range spatial-temporal dependencies between upstream and downstream cross-sectional features of blood vessels are calculated using the scaled dot product:

[0048]

[0049] in is the dimension of the key vector. This mechanism enables the model to adaptively focus on the historical features most critical to downstream growth, based on the upstream blood vessel's trajectory and morphology.

[0050] A lightweight autoregressive output design based on "encoding as prediction": Addressing the causal relationship of vascular unidirectional extension along the skeleton "from front to back," this invention abandons the traditional bulky decoder module. At the output of the self-attention layer, redundant historical outputs within the sequence are actively truncated, extracting only the deep representation of the last time step. Subsequently, Through a fully connected projection matrix, it is directly and autoregressively mapped to the latent feature distribution vector of the next time step. This design significantly reduces model parameters, avoids future information leaks, and substantially reduces computational latency during the inference phase.

[0051] High-fidelity solid 2D contour reconstruction: This involves reconstructing the predicted latent space vector at the new time step. The data is then re-input into the pre-trained CVAE decoder in S2. The decoder inversely maps this data from the low-dimensional manifold space back to the high-dimensional physical space, generating a highly biologically realistic set of 2D entity contour coordinates for the next frame, providing high-quality data support for subsequent 3D surface assembly.

[0052] S4: The two-dimensional contour sequence is inversely mapped to a three-dimensional point cloud without distortion using the parallel transmission frame RMF. A global implicit scalar field is constructed through the radial basis function RBF, and the zero isosurface is extracted to obtain a topologically watertight three-dimensional vascular mesh.

[0053] That is, a fully watertight 3D solid assembly based on the parallel transport frame and implicit field. The parallel transport frame (RMF) of the vessel centerline is calculated, and the rotation of the normal vector is eliminated through a dual reflection algorithm, accurately inversely mapping the 2D contour sequence output by S3 into a 3D spatial point cloud. Using this point cloud as a constraint, a radial basis function (RBF) based on a triharmonic spline kernel function is constructed. A globally continuous implicit scalar field is obtained by solving a dense system of linear equations. Finally, an isosurface extraction algorithm is used to output a 100% self-intersecting, pore-free topological watertight triangular mesh model suitable for finite volume fluid simulation (FVM).

[0054] This step aims to transform the two-dimensional sequence generated by the deep learning engine into a fully watertight three-dimensional solid geometry that meets the stringent preprocessing requirements of computational fluid dynamics (CFD). The specific implementation includes the following core steps:

[0055] Twisted-Free 3D Inverse Mapping Based on Rotation-Minimizing Frame (RMF): This invention abandons the Frenet frame and innovatively introduces the Rotation-Minimizing Frame (RMF). For the current node on the centerline... and its tangent vector RMF forcibly removes the normal vector of the previous point through double reflection or orthogonalization. The projection component onto the current tangent vector. The specific calculation formula is as follows:

[0056]

[0057] After normalization, the normal vector of the current point is obtained. The binormal vector is obtained by the cross product. This mechanism mathematically ensures that the normal vector does not rotate around the tangent direction when moving along the curve. Finally, the two-dimensional contour sequence output by S3 is converted into polar coordinates (or local Cartesian coordinates). Robustly inversely map back to the global 3D space:

[0058]

[0059] By traversing all cross sections, a dense three-dimensional surface point cloud with high microscopic fidelity and no topological distortion is formed.

[0060] 3D Implicit Field Construction and Complete Watertightening Based on Radial Basis Functions (RBF): This invention introduces implicit surface fitting technology to construct a globally continuous 3D implicit scalar field using radial basis functions (RBF). To avoid trivial solutions to the equations (i.e., all zeros in the space), the point cloud on the blood vessel surface is offset by a minimum distance along the normal direction, both inward and outward, to generate corresponding internal constraint points (let...). ) and external constraint points (let) Triharmonic splines were selected as the kernel function. This is transformed into solving for a weight vector. With polynomial coefficients Large-scale block-dense linear equation systems:

[0061]

[0062] Where the matrix It consists of the RBF kernel function values ​​between each center point. Let be the polynomial basis function matrix.

[0063] Simulation-ready mesh extraction: Obtaining a continuous scalar field after equation solving. Then, the Marching Cubes algorithm is called to extract the zero isosurface in the spatial grid. Thanks to the mathematical continuity of the RBF analytical expression throughout the real number space, the extracted 3D triangular solid mesh... It inherently possesses 100% closure and non-self-intersection characteristics, completely eliminating the topological damage dead zones caused by traditional generation methods, achieving true simulation-ready, and can be directly imported into finite volume method (FVM) software for accurate mesh generation of hexahedral core and boundary layer meshes.

[0064] Furthermore, the construction method of the interval roundness penalty in S2 is simplified as follows: the contour area A is calculated using the tensor shoelace formula, and the contour perimeter P is calculated using the L2 norm, resulting in roundness C = 4πA / P²; based on the prior interval of healthy blood vessel roundness [C min C max Construct the geometric penalty loss term L geo The total loss function is L total =L CVA E+L ge o, where L CVAE The loss is generated based on this.

[0065] Furthermore, the coarse-build-fine-tuning two-stage training includes:

[0066] Coarse-scale stage: The geometric penalty term is turned off, and the KL divergence of mean squared error (MSE) and β-VAE is used for joint training to converge the basic shape of the contour;

[0067] Fine-tuning stage: Activate the interval roundness penalty term and amplify the penalty coefficient to correct distortion with a small learning rate and output a high-fidelity smooth cross section.

[0068] Furthermore, the Transformer in S3 adopts a lightweight structure of encoding as prediction, integrates sinusoidal positional encoding to preserve temporal causality, and extracts the hidden layer representation in the last step to autoregressively predict the potential features of the next frame.

[0069] Furthermore, in S4, the RMF eliminates the rotation of the normal vector through the double reflection method, avoiding the occurrence of torsional singularities in the three-dimensional reconstruction; the RBF uses a triharmonic spline kernel function to generate internal and external constraint points to solve the linear equation system and obtain a continuous implicit field.

[0070] Furthermore, in S4, the three-dimensional vascular mesh is a simulation-ready model without holes, self-intersections, or manifold defects, which can be directly imported into computational fluid dynamics (CFD) software to complete fluid simulation calculations.

[0071] Compared with the prior art, the key technical points to be protected by the embodiments of the present invention are reflected in the following aspects:

[0072] This patent pioneers a "range-based roundness penalty" physical fusion loss function: existing technologies rely solely on Euclidean distance (MSE) to calculate loss. This patent innovatively embeds the classic shoelace formula (for area calculation) into a tensorized deep learning differentiable computational graph, combining it with perimeter calculation to determine dynamic roundness. This innovative underlying loss function forces purely data-driven models to be constrained by physical laws, completely solving the problem of AI-generated polygon self-intersections.

[0073] The patented patent features a unique "cross-dimensional dual-engine decoupled generation" architecture. Unlike existing technologies that directly generate meshes in 3D space, this architecture protects a strategy for decoupling tasks: static features are compressed into a low-dimensional latent space by CVAE, and then temporal prediction is performed in the low-dimensional manifold space by an Encoder-only Transformer. This structure has extremely low computational requirements and solves the curse of dimensionality.

[0074] Torque-eliminating RMF and RBF combined pipeline reconstruction: The parallel transport frame (RMF) and implicit surface equation (RBF) in computer graphics are deeply integrated into the output of the AI ​​model, breaking through the technical barrier that traditional AI models cannot be directly used in fluid dynamics CFD software, and achieving 100% watertightness guarantee.

[0075] Compared with the prior art, the advantages of the embodiments of the present invention are reflected in the following aspects:

[0076] Extremely high topological integrity and CFD "simulation-ready" capability: The mesh is extracted through RBF analytical expressions, inherently possessing 100% topological watertightness and no self-intersection characteristics. Experimental data shows that the maximum skewness of the extracted volume mesh is strictly controlled below 0.8, meeting the stringent conditions for high-precision finite volume method (FVM) solutions. Importing into OpenFOAM enables stable convergence of the Navier-Stokes equations.

[0077] Excellent microscopic geometric fidelity: thanks to - The VAE mechanism and the "coarse-build-fine-adjust" strategy generate blood vessels that accurately reproduce the microscopic anatomical features of real compression, such as elliptical deformation and asymmetric expansion, avoiding the "over-smoothing" distortion caused by traditional Poisson reconstruction or standard VAE.

[0078] Computational resource consumption is reduced exponentially: By reducing the dimensionality of 3D generation to one-dimensional extrapolation in latent space, there is no need to explicitly construct high-resolution 3D convolutional kernels. The entire complex liver vascular tree can be automatically generated in batches on consumer-grade graphics cards (such as those with 8GB of video memory).

[0079] Specific Implementation Example: Reconstruction and CFD Flow Field Analysis of Complex Cascade Bifurcation of the Hepatic Portal Vein, the process is as follows:

[0080] 1. Data preparation: In a Windows 11 environment with an NVIDIA RTX 4060 GPU (8GB VRAM) and 32GB of memory, import the list of one-dimensional centerline coordinates and radii of the portal vein of the liver after clinical contrast-enhanced CT dissection.

[0081] 2. CVAE Training and Inference: Initial learning rate set to Perform a 50-epoch decay coarse-scale build; then set the penalty coefficient. The learning rate dropped to The optimal weights are applied to activate the roundness penalty for fine-tuning. The inference phase yields the features of the cross-section in the low-dimensional latent space.

[0082] 3. Temporal extrapolation: Using a trained lightweight Transformer (Batch Size set to 1024), all features of the terminal micro-branches are predicted by autoregression based on the centerline trajectory and decoded into a two-dimensional contour array.

[0083] 4. Reconstruction and Verification: RMF inverse mapping was performed to calculate 3D spatial points, and the RBF matrix equation was solved using the SciPy library to extract the STL mesh. The STL mesh was imported into the open-source fluid dynamics software OpenFOAM, and the body-fitted boundary layer mesh was successfully generated using snappyHexMesh. SimpleFoam (with blood density set to 1060 kg / m³ and viscosity to 0.0035 Pa·s) was then used to successfully complete the steady-state solution of wall shear stress (WSS) and blood flow velocity vector. No mesh breakage errors occurred throughout the process, proving that the model fully meets medical-grade simulation standards.

[0084] The basic principles of the present invention have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in the present invention are merely examples and not limitations, and should not be considered as essential features of each embodiment of the present invention. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the present invention to the necessity of employing the aforementioned specific details.

[0085] The block diagrams of devices, apparatuses, devices, and systems involved in this invention are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0086] It should also be noted that in the apparatus, device, and method of the present invention, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of the present invention.

[0087] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the invention. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of the invention. Therefore, the invention is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0088] It should be understood that the qualifying terms "first", "second", "third", "fourth", "fifth" and "sixth" used in the description of the embodiments of the present invention are only used to more clearly illustrate the technical solutions and are not intended to limit the scope of protection of the present invention.

[0089] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of the invention to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A method for three-dimensional angiogenesis and reconstruction based on deep learning and implicit geometry fusion, characterized in that, include: S1: Obtain the one-dimensional centerline coordinate set and radius sequence of blood vessels. After denoising, B-spline fitting and uniform resampling, the three-dimensional spatial geometry generation task is transformed into a temporal contour evolution prediction task along the centerline. S2: Construct a conditional variational autoencoder (CVAE) with interval roundness penalty. The 2D contour point set and normalized radius are used as inputs. The latent feature vector is obtained through encoding and reparameterization. The 2D blood vessel cross section is generated through two-stage training of coarse-fine tuning. S3: Using the latent feature vector as the sequence input, a lightweight pure encoder autoregressive Transformer is used to autoregressively predict the complete cross-sectional feature sequence in the latent space and decode it into a continuous two-dimensional contour sequence. S4: The two-dimensional contour sequence is inversely mapped to a three-dimensional point cloud without distortion using the parallel transmission frame RMF. A global implicit scalar field is constructed through the radial basis function RBF, and the zero isosurface is extracted to obtain a topologically watertight three-dimensional vascular mesh.

2. The three-dimensional angiogenesis and reconstruction method based on deep learning and implicit geometry fusion according to claim 1, characterized in that, The method for constructing the interval roundness penalty in S2 is as follows: the contour area A is calculated using the tensor shoelace formula, and the contour perimeter P is calculated using the L2 norm, resulting in roundness C = 4πA / P. 2 Based on the prior interval of healthy blood vessel roundness [C] min C max Construct the geometric penalty loss term L geo The total loss function is L total =L CVAE +L geo , where L CVAE The loss is generated based on this.

3. The three-dimensional angiogenesis and reconstruction method based on deep learning and implicit geometry fusion according to claim 2, characterized in that, The two-stage training process, coarse-scale and fine-tuning, includes: Coarse-scale stage: The geometric penalty term is turned off, and the KL divergence of mean squared error (MSE) and β-VAE is used for joint training to converge the basic shape of the contour; Fine-tuning stage: Activate the interval roundness penalty term and amplify the penalty coefficient to correct distortion with a small learning rate and output a high-fidelity smooth cross section.

4. The three-dimensional angiogenesis and reconstruction method based on deep learning and implicit geometry fusion according to claim 1, characterized in that, The Transformer in S3 adopts a lightweight structure of encoding as prediction, integrates sinusoidal positional encoding to preserve temporal causality, and extracts the hidden layer representation in the last step to autoregressively predict the potential features of the next frame.

5. The three-dimensional angiogenesis and reconstruction method based on deep learning and implicit geometry fusion according to claim 1, characterized in that, In S4, the RMF eliminates the rotation of the normal vector through the double reflection method, avoiding the occurrence of torsional singularities in the three-dimensional reconstruction; the RBF uses a triharmonic spline kernel function to generate internal and external constraint points to solve the linear equation system and obtain a continuous implicit field.

6. The three-dimensional angiogenesis and reconstruction method based on deep learning and implicit geometry fusion according to claim 1, characterized in that, In S4, the three-dimensional vascular mesh is a simulation-ready model without holes, self-intersections, or manifold defects, which can be directly imported into computational fluid dynamics (CFD) software to complete fluid simulation calculations.

Images