Liver blood vessel one-dimensional hemodynamic analysis method based on graph neural network

Abstract

The invention provides a hepatic blood vessel one-dimensional hemodynamic analysis method based on a graph neural network, which comprises the following steps: processing an acquired medical contrast image to obtain a geometric model of a central line of a hepatic blood vessel; determining a blood vessel grid according to the center line geometric model, and performing blood flow simulation according to the blood vessel grid to obtain a blood flow simulation result; constructing graph data according to the blood flow simulation result; constructing a GCN network structure fused with edge aggregation according to the graph data; and carrying out hemodynamic analysis according to the GCN network structure. According to the method, a mode of converting the hepatic vessel center line structure into the graph data is provided, compared with a traditional data format, the graph data has higher expression ability, more complex relations and connection modes can be expressed, and the graph data has higher flexibility and expansibility for hepatic vessels with complex vessel structures.

Description

Technical Field

[0001] The present invention relates to the field of deep learning technology, and in particular to a method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural networks. Background Art

[0002] Hepatic hemangioma is a common benign mesenchymal tumor in the liver. In most cases, it is asymptomatic. However, as the size of the tumor exceeds 5 cm and as the tumor size increases, patients will experience adverse reactions such as abdominal distension, indigestion, loss of appetite, nausea and vomiting. Giant hepatic hemangiomas may cause Kasabach-Merrit syndrome and be life-threatening. The lumen size, diameter ratio and curvature of the abdominal artery tree in patients with hepatic hemangioma are increased, which significantly increases the average avoided shear stress in the low time. The morphological changes caused by hepatic hemangioma will affect the hemodynamic distribution inside the hepatic blood vessels. Analysis of hemodynamics of hepatic vessels plays an important role in understanding the development of hepatic hemangioma.

[0003] The technologies currently used for hemodynamic analysis can be divided into two types: computational fluid dynamics (CFD) methods and deep learning methods. In the field of CFD, specific methods include finite difference method, finite element method, boundary element method, finite volume method and finite analysis method, all of which are based on the principles of discretization and algebraization. Hemodynamic problems conform to the Navier-Stokes equations. By setting relevant initial conditions, boundary conditions and adjusting the values ​​of various parameters, these methods can perform hemodynamic analysis on hepatic blood vessels. The CFD method will take up 75%-80% of the time for meshing. The quality of the mesh will directly affect the accuracy of the results, but the fineness of the mesh will directly affect the efficiency of the calculation. For CFD simulation of specific patients, it is necessary to consider the real boundary conditions and complex calculation domains, and the problem of computational cost is more serious. Therefore, many bottleneck problems have caused most simulations to remain at the research level and are difficult to fully promote to the clinical tool level.

[0004] Most deep learning methods use traditional neural networks, and the data format is represented as a matrix composed of multiple vectors. The matrix representation method lacks flexibility when processing data with complex connections and relationships. The vascular network in hemodynamics usually has complex features such as branching, circulation, and nonlinear connections. It is difficult to accurately capture these relationships using matrix representation. Matrix representation cannot intuitively reflect the connection relationship and topological structure between different blood vessels. The vascular network in hemodynamics often has an irregular structure, and the connections and relationships between different blood vessels are usually not in regular matrix form. It is difficult to directly represent irregular structures using matrix representation, and additional data structures or algorithms may be required to process and analyze irregular connections. Summary of the invention

[0005] In order to overcome the deficiencies of the prior art, the object of the present invention is to provide a method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural networks.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural network, comprising:

[0008] Processing the acquired medical angiography images to obtain a centerline geometric model of liver blood vessels;

[0009] Determine a blood vessel grid according to the centerline geometric model, and perform blood flow simulation according to the blood vessel grid to obtain a blood flow simulation result;

[0010] constructing graph data according to the blood flow simulation results;

[0011] Constructing a GCN network structure fused with edge aggregation according to the graph data;

[0012] Hemodynamic analysis was performed based on the GCN network structure.

[0013] Preferably, the acquired medical angiography image is processed to obtain a centerline geometric model of the liver blood vessels, including:

[0014] Obtaining the medical angiography image by means of multi-time series fusion;

[0015] A three-dimensional geometric model of liver blood vessels is extracted from the medical angiography image using a local value segmentation algorithm, and a target model is obtained after trimming, smoothing, and removing discrete points;

[0016] The centerline is extracted from the target model using the open source software library VMTK to obtain the centerline geometric model.

[0017] Preferably, determining a blood vessel grid according to the centerline geometric model, and performing blood flow simulation according to the blood vessel grid to obtain a blood flow simulation result includes:

[0018] Based on the spatial position of the centerline relative to the target model, the cross-sectional area corresponding to each point is calculated according to the section perpendicular to each point, a vascular mesh is defined according to the branch topology, and the corresponding cross-sectional area, vascular length and vascular wall properties are assigned to each vascular mesh;

[0019] A one-dimensional vascular network model is constructed based on the three-dimensional geometric data of the vascular mesh, and then the pressure-area relationship formula describing the viscoelastic properties of the vascular wall is introduced to couple the one-dimensional NS equation to obtain the final one-dimensional blood flow calculation equation.

[0020] By setting periodic inlet boundary conditions, ternary windkessel outlet boundary conditions, simulation time, time step, blood parameters, and material parameter information, the numerical discrete method is used for calculation to obtain the CFD simulation results of the one-dimensional vascular network. Then, the physical parameter information of the CFD simulation results is extracted, and the one-dimensional CFD simulation results are mapped back to the three-dimensional geometric model of the liver blood vessels to obtain the final blood flow simulation results.

[0021] Preferably, the graph data includes node features, edge indexes and edge features; the expression of the node features is: in, is the node feature, x i For each center point v i The x-axis coordinate value of the spatial position, y i For each center point v i The y-axis coordinate value of the spatial position, z i For each center point v i The z-axis coordinate value of the spatial position, A i For point v i The cross-sectional area perpendicular to the center line, k i For point v i The slope of the point tangent to the center line is C t and are boundary conditions, is the inlet velocity, α i is the node type, t is the time; the expression of the edge feature is: Among them, E ij is the characteristic of the edge, d ij is the true length of the side, z ij is the difference between the two endpoints of the edge in three dimensions in space, β ij The type of edge.

[0022] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0023] The present invention provides a method for one-dimensional hemodynamic analysis of liver blood vessels based on graph neural network, including: processing the acquired medical angiography images to obtain a centerline geometric model of liver blood vessels; determining a blood vessel grid according to the centerline geometric model, and performing blood flow simulation according to the blood vessel grid to obtain a blood flow simulation result; constructing graph data according to the blood flow simulation result; constructing a GCN network structure fused with edge aggregation according to the graph data; and performing hemodynamic analysis according to the GCN network structure. A method for converting the centerline structure of liver blood vessels into graph data is proposed. Compared with traditional data formats, graph data has stronger expression capabilities and can represent more complex relationships and connection methods. For liver blood vessels with complex vascular structures, graph data has higher flexibility and scalability. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0025] Figure 1 A flow chart of a method provided by an embodiment of the present invention;

[0026] Figure 2 A schematic diagram of a blood vessel centerline extraction process according to an embodiment of the present invention;

[0027] Figure 3 A schematic diagram of a periodic velocity curve at a hemodynamic inlet provided by an embodiment of the present invention;

[0028] Figure 4 A schematic diagram of a Windkessel circuit provided by an embodiment of the present invention;

[0029] Figure 5 A schematic diagram of the structure of hepatic vascular map data provided by an embodiment of the present invention;

[0030] Figure 6 A schematic diagram of a neural network structure provided by an embodiment of the present invention;

[0031] Figure 7 A comparison chart of the predicted results and the corresponding actual results provided by the embodiment of the present invention;

[0032] Figure 8 A schematic diagram of pressure and velocity provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0033] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0034] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0035] Figure 1 A flow chart of a method provided by an embodiment of the present invention, such as Figure 1 As shown, the present invention provides a method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural network, comprising:

[0036] Step 100: Processing the acquired medical angiography image to obtain a centerline geometric model of liver blood vessels;

[0037] Step 200: determining a blood vessel grid according to the centerline geometric model, and performing blood flow simulation according to the blood vessel grid to obtain a blood flow simulation result;

[0038] Step 300: constructing graph data according to the blood flow simulation result;

[0039] Step 400: constructing a GCN network structure integrated with edge aggregation according to the graph data;

[0040] Step 500: Perform hemodynamic analysis based on the GCN network structure.

[0041] Specifically, the blood vessel centerline extraction steps of this embodiment are as follows:

[0042] Read the medical angiography image of human liver blood vessels, use the local threshold segmentation of the open source medical software 3D Sclicer and the centerline extraction algorithm of VMTK to obtain the centerline geometric model of liver blood vessels. The steps are as follows: Figure 2 shown. Figure 2 The left side shows a more comprehensive angiography image obtained by fusion of multiple time series. Figure 2 In the figure, the local value segmentation algorithm is used to extract the three-dimensional geometric model of hepatic vessels from the hepatic angiography image. After trimming, smoothing, and removing discrete points, a suitable target model is obtained. Figure 2 On the right, the center line is extracted from the geometric model using the open source software library VMTK. The blue point is the entrance, the colored point is the exit, and the line segments of different colors represent different blood vessel branches.

[0043] Optionally, the steps of calculating the blood flow simulation results in this embodiment are as follows:

[0044] According to the spatial position of the centerline relative to the three-dimensional model of liver blood vessels, the cross-sectional area corresponding to each point is calculated according to the section perpendicular to each point, and the vascular grid is defined according to the branch topological structure, and the corresponding cross-sectional area, vascular length and vascular wall properties are assigned to each grid.

[0045] The results of CFD analysis of the one-dimensional vascular network model were obtained based on nektar++. First, a one-dimensional vascular network model was constructed based on the three-dimensional geometric data of the vascular network. Then, the pressure-area relationship formula describing the viscoelastic properties of the vascular wall was introduced to couple the one-dimensional NS equation to obtain the final one-dimensional blood flow calculation equation. By setting the periodic inlet boundary condition ( Figure 3 ), ternary Windkessel outlet boundary condition ( Figure 4 ) and simulation time, time step, blood parameters, material parameters and other information, use appropriate numerical discretization methods to calculate, get the CFD simulation results of the one-dimensional vascular network, then extract the physical parameter information of the simulation results, and map the one-dimensional simulation results back to the three-dimensional vascular geometry model (the one-dimensional simulation results are the values ​​of each point on the vertical section of the three-dimensional center line) to get the final visualization results. Figure 3 R p is the impedance element, P c is the internal pressure of the resistor, C is the capacitance element, R d is the reflection coefficient. 3. Graph data construction based on blood flow simulation results

[0046] Node features: For the centerline of the blood vessel, each center point v i The spatial position of At point v i The cross-sectional area perpendicular to the center line and the slope tangent to the center line The above are the geometric characteristics of the node. Windkessel Boundary Conditions (true value only at the exit, 0 at other locations), inlet velocity (True value at the entry, 0 elsewhere) Node Type Including internal nodes, entry nodes, exit nodes, one-hot encoding.

[0047]

[0048] Edge feature: True length of edge is the difference between the two endpoints of the edge in three dimensions in space. When the edge is from a node to an exit or from an entry to a node, d ij vi to v j The shortest path of the node is defined as: It is one-hot encoding. When constructing the edge from the entrance to the node, the entrance is connected to all nodes (including the exit). When constructing the edge from the internal node to the exit node, only the current node is established to the nearest exit node. The original topological result of the blood vessel is maintained by the edge type. Due to the field of view limitations of the graph neural network, adding edges from the node to the entrance and exit boundaries helps to learn the initial conditions of hemodynamics.

[0049]

[0050] like Figure 5 As shown in the figure, the graph structure consists of node features, edge indexes, and edge features. The graph structure can capture more complex relationships, convert unstructured vascular data into structured graph data, and help the neural network effectively learn the characteristics of the data itself. Converting vascular data in hepatic vascular hemodynamic analysis into graph data and applying deep learning methods can fully utilize the advantages of the graph structure to achieve comprehensive analysis and prediction of vascular relationships and functions.

[0051] This embodiment constructs a GCN network structure that integrates edge aggregation. The neural network structure is as follows: Figure 6 As shown in the figure, the first layer is the input layer, the second layer is the encoding layer, which encodes the node features and edge features, the third layer is the graph convolution layer, the fourth layer is the normalization and activation function, the fifth layer is the graph convolution layer, and the sixth layer is the output layer.

[0052] Node Features and edge features Mapped to The feature dimensions n after encoding edge features and node features may be different.

[0053] MeshGen:

[0054] Step 1: Calculate new edge features, where l is the number of layers, W is the linear layer, and E ij is the edge feature of the edge connecting node i and node j, V is the node feature, when the encoding dimension of the edge feature and the node feature is the same:

[0055]

[0056] When the dimensions of edge features and node features are different:

[0057]

[0058] Step 2: Calculate new node features:

[0059]

[0060] Step 3: Perform convolution operation. is the Laplacian matrix and W is the linear layer.

[0061]

[0062] After the above operations, this embodiment can update the edge features according to the nodes. While updating the node features according to the edges, the nodes can fuse the edge features. The edge features are very important in the process of solving hemodynamics. In the entire network architecture, this embodiment uses graph normalization and RELU activation function, and finally outputs a pressure field and a velocity field.

[0063] Optionally, this embodiment defines a loss function that combines the square error loss (MSE) and the absolute error loss (MAE) to calculate the loss of speed and pressure, θ i , α and β are weight parameters, where θ is the exit or entrance i =100, otherwise 1. (α+β)=1In this case, both α and β are 0.5. and are the predicted values ​​of pressure and velocity at point i, respectively, p i and q i are the true values ​​of pressure and velocity respectively.

[0064]

[0065] For p loss and q loss It is defined by a relative weight loss function, which weighs multiple loss functions by considering the uncertainty of the homoscedasticity of each task, where σ1 and σ2 are learnable parameters that will be adaptively adjusted during the learning process of the network.

[0066]

[0067] Graph data has stronger expressive power than ordinary data. It does not require a special network to learn the geometric features of the data. By adding an edge feature calculation layer to the graph neural network, a higher prediction accuracy can be obtained. By comparing multiple models, MeshGcn has better performance, as shown in Table 1 and Figure 7 and Figure 8 shown. Figure 7 The first column is the pressure (upper: error map, middle: true value, lower: predicted value), and the second column is the velocity (upper: error map, middle: true value, lower: predicted value).

[0068] Table 1 Comparison of various models

[0069] method MSE MAE R-squared MAPE GAT 0.0019 0.0283 0.9980 0.3197 GATv2 0.0006 0.0171 0.9993 0.1685 Transformer 0.0002 0.0099 0.9998 0.0948 MeshGcn 0.0001 0.0049 0.9999 0.0417

[0070] The beneficial effects of the present invention are as follows:

[0071] (1) The present invention proposes a method for converting the centerline structure of hepatic blood vessels into graph data. Compared with traditional data formats, graph data has stronger expression capabilities and can represent more complex relationships and connection methods. For hepatic blood vessels with complex vascular structures, graph data has higher flexibility and scalability.

[0072] (2) The present invention uses the MeshGcn architecture to construct an application example of hepatic vascular hemodynamics based on deep learning methods, which can obtain the corresponding hemodynamic prediction results in a short time. The graph data can be targeted at vascular structures with different numbers of nodes, so that MeshGcn has a powerful geometric shape generalization ability.

[0073] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0074] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural network, characterized in that: include: Processing the acquired medical angiography images to obtain a centerline geometric model of liver blood vessels; Determine a blood vessel grid according to the centerline geometric model, and perform blood flow simulation according to the blood vessel grid to obtain a blood flow simulation result; constructing graph data according to the blood flow simulation results; Constructing a GCN network structure fused with edge aggregation according to the graph data; Hemodynamic analysis was performed based on the GCN network structure.

2. The method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural network according to claim 1, characterized in that: The acquired medical angiography images are processed to obtain the centerline geometric model of the liver blood vessels, including: Obtaining the medical angiography image by means of multi-time series fusion; A three-dimensional geometric model of liver blood vessels is extracted from the medical angiography image using a local value segmentation algorithm, and a target model is obtained after trimming, smoothing, and removing discrete points; The centerline is extracted from the target model using the open source software library VMTK to obtain the centerline geometric model.

3. The method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural network according to claim 2, characterized in that: Determining a blood vessel grid according to the centerline geometric model, and performing blood flow simulation according to the blood vessel grid to obtain a blood flow simulation result, including: Based on the spatial position of the centerline relative to the target model, the cross-sectional area corresponding to each point is calculated according to the section perpendicular to each point, a vascular mesh is defined according to the branch topology, and the corresponding cross-sectional area, vascular length and vascular wall properties are assigned to each vascular mesh; A one-dimensional vascular network model is constructed based on the three-dimensional geometric data of the vascular mesh, and then the pressure-area relationship formula describing the viscoelastic properties of the vascular wall is introduced to couple the one-dimensional NS equation to obtain the final one-dimensional blood flow calculation equation. By setting periodic inlet boundary conditions, ternary windkessel outlet boundary conditions, simulation time, time step, blood parameters, and material parameter information, the numerical discrete method is used for calculation to obtain the CFD simulation results of the one-dimensional vascular network. Then, the physical parameter information of the CFD simulation results is extracted, and the one-dimensional CFD simulation results are mapped back to the three-dimensional geometric model of the liver blood vessels to obtain the final blood flow simulation results.

4. The method for one-dimensional hemodynamic analysis of hepatic vessels based on graph neural network according to claim 1, characterized in that: The graph data includes node features, edge indexes and edge features; the expression of the node features is: in, is the node feature, x i For each center point v i The x-axis coordinate value of the spatial position, y i For each center point v i The y-axis coordinate value of the spatial position, z i For each center point v i The z-axis coordinate value of the spatial position, A i For point v i The cross-sectional area perpendicular to the center line, k i For point v i The slope of the point tangent to the center line is C t and are boundary conditions, is the inlet velocity, α i is the node type, t is the time; the expression of the edge feature is: Among them, E ij is the characteristic of the edge, d ij is the true length of the side, z ij is the difference between the two endpoints of the edge in three dimensions in space, β ij The type of edge.

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