A method of tumor angiogenesis simulation and electronic device

Abstract

The application discloses a tumor angiogenesis simulation method and electronic equipment, and the method comprises the following steps: updating a morphological correction factor based on a blood vessel network topology graph; calculating the growth factor concentration of each blood vessel pixel point at simulation time t according to the morphological correction factor, the total number of endothelial cells of the blood vessel network and the current oxygen concentration of the blood vessel pixel point; calculating the endothelial cell density of the tip blood vessel segment at simulation time t according to the total number of endothelial cells of the blood vessel network at simulation time t and the length of the tip blood vessel segment; calculating the branch number of each tip and the elongation length of each branch according to the endothelial cell density of the tip blood vessel segment at simulation time t, the morphological correction factor and the growth factor concentration of the tip; and updating the blood vessel network topology graph based on the branch number of the tip and the elongation length of each branch. The application accurately depicts the spatial geometric structure and complexity of the blood vessel network through the morphological correction factor, and realizes tumor blood vessel simulation highly consistent with the pathological blood vessel network.

Description

Technical Field

[0001] This invention relates to the field of biological simulation technology, and in particular to a method and electronic device for simulating tumor angiogenesis. Background Technology

[0002] Blood vessels play a crucial role in tumor development and progression. They not only provide oxygen and nutrients to tumor cells and remove toxic metabolic products, but also provide blood pathways for tumor cell metastasis. Therefore, tumor angiogenesis simulation is essential for monitoring abnormal tumor vascular growth and for tumor treatment.

[0003] Currently, to more closely approximate the actual growth state of blood vessels, most angiogenesis simulations consider the influence of more scale factors on angiogenesis. However, the objectives of tumor angiogenesis simulation differ, and the emphasis of the constructed tumor angiogenesis schemes varies. In some application areas of tumor angiogenesis simulation, constructing tumor simulation schemes based on the complexity of vascular network morphology is crucial, for example: (1) Tumor angiogenesis and anti-angiogenic therapy research: It is very suitable for simulating the abnormal generation of tumor blood vessels, studying how parameters such as growth factors lead to the loss of control of vascular network structure, and evaluating whether anti-angiogenic drugs (such as bevacizumab) can "normalize" the vascular network. (2) Pathological state diagnosis and prognosis: It can be used to develop diagnostic indicators based on vascular morphology. For example, high complexity (morphological correction factor) can be directly used as a potential biomarker for tumor malignancy and poor prognosis. (3) Research on vascular malformations: Research on the abnormal spatial structure of vascular networks in diseases such as arteriovenous malformations and telangiectasia; (4) Tumor microenvironment heterogeneity study: Combined with hypoxia-related models, the vicious cycle of "high morphological correction factor M(t) in morphologically complex regions → hypoxia → upregulation of growth factor VEGF → more complex vascular network" can be simulated to reveal the heterogeneity inside the tumor.

[0004] Therefore, there is an urgent need for a scheme to simulate tumor angiogenesis based on the complexity of vascular network morphology. Summary of the Invention

[0005] To achieve the simulation of tumor blood vessels based on the complexity of vascular network morphology, embodiments of the present invention provide a method and electronic device for simulating tumor angiogenesis.

[0006] In a first aspect of the present invention, a method for simulating tumor angiogenesis is provided, comprising the following steps: Step S100: In a discrete coordinate system with pixels as coordinates, a binary tumor vascular network map including environmental pixels and vascular pixels is generated based on the patient's medical images. Undirected edges are constructed between two adjacent vascular pixels in the skeletonized tumor vascular network map to obtain a vascular network topology map. Step S200: Update the position coordinates of blood vessel pixels and the degree of each blood vessel pixel according to the blood vessel network topology map, and set the blood vessel pixels with a degree of 1 as the tip of the blood vessel; wherein, the degree of the blood vessel pixel is the number of blood vessel pixels among the 8 neighboring pixels of the blood vessel pixel; Step S300: Update the morphological correction factor according to the number of branch points in the vascular network topology diagram and the actual number of edges between each branch point and its adjacent branch points; wherein, the branch point is a vascular pixel with a degree greater than 2; Step S400: Calculate the total number of endothelial cells in the vascular network topology diagram at simulation time t based on the initial number of endothelial cells in the vascular network, the simulation time, and the endothelial cell proliferation model. Step S500: Calculate the VEGF concentration of each blood vessel pixel at simulation time t based on the morphological correction factor of the blood vessel network topology, the total number of endothelial cells in the blood vessel network, and the current oxygen concentration of the blood vessel pixel. Step S600: Calculate the endothelial cell density of the tip vessel segment of each tip in the vascular network topology at simulation time t based on the total number of endothelial cells in the vascular network at simulation time t and the elongation length of each branch at the tip and the position coordinates of the vessel pixel points obtained in each previous iteration; wherein, the tip vessel segment is all the edges connecting the tip to the branch point closest to the tip. Step S700: Based on the endothelial cell density of the vascular network topology diagram at simulation time t, obtain the number of branches of each tip bifurcation in this iteration, and calculate the elongation length of each branch of each tip based on the morphological correction factor, the growth factor concentration of the vascular pixel at each tip, and the endothelial cell density of the vascular segment corresponding to each tip at simulation time t. Step S800: Update the vascular network topology graph according to the number of branches at each tip and the elongation length of each branch in the vascular network topology graph at simulation time t, and increment the iteration count by 1; Step S900: Determine whether the simulation termination condition is met. If the condition is met, end the simulation and output the new vascular network topology and the relevant parameters selected by the user. If the condition is not met, proceed to step S200.

[0007] Preferably, step S100 includes the following steps: The patient's medical images were converted into grayscale images in BMP format, and a discrete coordinate system was constructed using the pixels of the grayscale image as coordinates. Then, the contrast between the vascular pixels and the environmental pixels was enhanced. The Otsu method is used to binarize the obtained grayscale image, and the pixels in the grayscale image are divided into vascular pixels and environmental pixels according to the definition of grayscale values ​​of vascular region and environmental region, so as to obtain the tumor vascular network map. The image skeletonization of the tumor vascular network map is performed using the median transformation and distance mapping matrix formula. The central skeleton of the tumor vascular network is extracted to obtain the skeletonized tumor vascular network map. By traversing the pixels in the skeletonized tumor vascular network graph, undirected edges are constructed between adjacent vascular pixels to obtain the vascular network topology graph.

[0008] Preferably, step S300 includes the following steps: The global clustering coefficient of the vascular network at simulation time t is calculated based on the number of branch points in the vascular network topology diagram and the actual number of edges between each branch point and its adjacent branch points. The fractal dimension of the vascular network is obtained using the Box-counting algorithm based on the vascular network topology diagram. The morphological correction factor at simulation time t is calculated based on the global clustering coefficient and the fractal dimension.

[0009] Preferably, the endothelial cell proliferation model is as follows: in: For simulation time; The total number of endothelial cells in the vascular network at simulation time t; The initial proliferation rate of endothelial cells (ECs) is denoted as , which is a constant. Let be the endothelial cell EC saturation coefficient, which is a constant; therefore This represents the maximum capacity of endothelial cells; This represents the initial total number of endothelial cells (ECs) in the vascular network, which is a preset value.

[0010] Preferably, step S500 includes the following steps: The oxygen concentration of the blood vessel pixels at simulation time t is predicted based on the morphological correction factor, the total number of endothelial cells in the vascular network, the current oxygen concentration of the blood vessel pixels, and the oxygen metabolism feedback equation. The hypoxia response coefficient at simulation time t is predicted based on the morphological correction factor described in the vascular network topology diagram. Based on the hypoxia response coefficient, oxygen concentration of blood vessel pixels, and growth factor secretion regulation equation at simulation time t, the growth factor secretion rate of each blood vessel pixel at simulation time t is predicted. The growth factor concentration of each blood vessel pixel at simulation time t is calculated based on the current growth factor concentration of the blood vessel pixel, the secretion rate of growth factor at simulation time t, and the kinetic equation of growth factor concentration.

[0011] Preferably, the oxygen metabolism feedback equation is: in: This represents the total number of endothelial cells in the vascular network at simulation time t. M(t) is the morphological correction factor of the vascular network at simulation time t; The current oxygen concentration of the blood vessel pixel. When the blood vessel pixel is first iterated, the initial oxygen concentration is a preset value. Let be the oxygen diffusion coefficient, and be a constant. Let be the cellular oxygen consumption rate, and be a constant. Here, is the oxygen transfer conversion coefficient, and is a constant. For blood oxygenation efficiency; The oxygen transport coefficient is denoted by , which is a constant. The formula for calculating the hypoxia response coefficient is as follows: in: The hypoxia response coefficient; The basic sensitivity is a constant. To adjust the intensity, it is a constant; The growth factor secretion regulation equation is as follows: in: S(x,y,t) represents the secretion rate of VEGF at the blood vessel pixel (x,y) at simulation time t. The normal oxygen concentration is a constant. is the scale for secretion attenuation, and is a constant. The maximum secretion rate at the tumor center is a constant. The oxygen concentration of the blood vessel pixel at the current location coordinates; The oxygen decay index; This is the straight-line distance from the current blood vessel pixel to the middle position of the blood vessel network; The straight-line distance to the center of the vascular network is obtained by taking the arithmetic mean of the coordinates of all pixels in the vascular network topology graph. The kinetic equation for the concentration of the growth factor is: in: The concentration of VEGF, the growth factor, at the vascular pixel (x,y); is the diffusion coefficient of growth factor at the blood vessel pixel, which is a constant; denoted as the degradation rate of growth factors in blood vessel pixels, and denoted as a constant.

[0012] Preferably, step S600 includes the following steps: Based on the total number of endothelial cells in the vascular network at simulation time t, the elongation length of each branch of the vascular pixel at the tip obtained from each previous iteration, and the coordinates of the vascular pixel, the number of endothelial cells in each vascular segment at the tip in the vascular network topology diagram at simulation time t is obtained; wherein, the formula for calculating the number of endothelial cells in the vascular segment at the tip is: in: The number of endothelial cells at the tip of the vascular network topology at simulation time t. The length of the tip blood vessel segment at the tip of the blood vessel network topology diagram at simulation time t is calculated based on the position coordinates of the blood vessel pixels on the tip blood vessel segment. This represents the number of branches at the blood vessel pixel where the tip is located during each iteration; Let K be the elongation length of the r-th branch of the blood vessel pixel i where the tip is located in the K-th iteration of the vascular network topology graph, where K is less than the current iteration number. ; The total number of endothelial cells in the vascular network at simulation time t; The volume of the tip of the vascular network topology at simulation time t is obtained by using the position coordinates of the vascular pixel points on the tip of the vascular segment and the average cross-sectional area of ​​the vascular segment. The number of endothelial cells and the volume of the corresponding endothelial segment in the vascular network topology diagram at simulation time t are calculated. The endothelial cell density of the corresponding endothelial segment in the vascular network topology diagram at simulation time t is calculated.

[0013] Preferably, step S700 includes the following steps: The number of branches at the tip bifurcation in this iteration is obtained based on the endothelial cell density and endothelial cell density bifurcation threshold of the vascular network topology diagram at simulation time t. The dynamic chemotaxis weights of the vascular network topology at simulation time t are calculated based on the morphological correction factor of the vascular network topology at simulation time t. The endothelial cell response function corresponding to the tip at simulation time t is obtained based on the endothelial cell density and endothelial cell density elongation threshold of the tip vascular segment corresponding to the tip in the vascular network topology diagram at simulation time t. The elongation length of each branch at each tip in the vascular network topology at simulation time t is calculated based on the dynamic chemotaxis weights at simulation time t, the growth factor concentration at each tip in the vascular network topology, and the endothelial cell response function.

[0014] Preferably, the formula for calculating the dynamic chemotaxis weight is: in: The dynamic chemiluminescence weights of the vascular network topology at simulation time t; The basic chemotaxis weight is a constant; Here, is the morphological inhibition coefficient, and is a constant; The morphological correction factor for the vascular network topology at simulation time t; The endothelial cell response function is: in: This is the endothelial cell response function at the tip during simulation time t; The endothelial cell density of the corresponding tip blood vessel segment at simulation time t; is the endothelial cell density bifurcation threshold, and is a constant; The equation for the evolution of blood vessel length is: in: For the first connection to the tip of this iteration The elongation length of the r-th branch of the blood vessel pixel i where the tip is located in the next iteration; The step size adjustment factor coefficient is a constant. The dynamic chemiluminescence weights of the vascular network topology at simulation time t; This represents the gradient of the current VEGF concentration. This is the reference concentration of the growth factor VEGF, used for gradient normalization; The unit vector representing the direction of blood vessel growth; The threshold for numerical stability; It is a random unit vector.

[0015] In a second aspect of the invention, an electronic device is provided, comprising a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the tumor angiogenesis simulation method as described in the first aspect. The method and electronic device for simulating tumor angiogenesis provided in this invention have the following technical effects: 1. The simulation scheme emphasizes morphological complexity. Its core advantage lies in accurately characterizing the spatial geometry and complexity of the vascular network through morphological correction factors. Furthermore, the fractal dimension used to calculate the morphological correction factors can quantify the tortuosity, space-filling ability, and self-similarity of the vascular network. 2. It has excellent pathological characterization ability. Pathological blood vessels (especially tumor blood vessels) are usually characterized by extreme disorder, tortuosity and abnormal morphology. The increase in fractal dimension used in the morphological correction factor calculation of this application is a direct mathematical description of this pathological disorder, which is highly consistent with clinical imaging observation, thus making the simulation of pathological vascular network closer to the actual situation. 3. It has powerful spatial analysis capabilities. Fractal dimension is essentially a spatial metric, which can better describe the uniformity of vascular network distribution, invasion range and microscopic heterogeneity in three-dimensional tissues, which is crucial for understanding tumor invasion and metastasis. 4. Integration with clinical diagnostic tools: Medical imaging (such as DSA, CT perfusion, pathological section analysis, etc.) has widely used fractal dimension as a radiomics feature to quantify tumor vascular morphology. The vascular network and related parameters obtained by morphological correction factor simulation using fractal dimension can be directly compared and verified with clinical imaging data.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 A schematic flowchart of a method for simulating tumor angiogenesis provided by an embodiment of the present invention; Figure 2 This is a schematic diagram of the structure of an electronic device according to an embodiment of this application. Detailed Implementation

[0018] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0019] like Figure 1 As shown in the figure, this application provides a method for simulating tumor angiogenesis, which includes the following steps: Step S100: In a discrete coordinate system with pixels as coordinates, a tumor vascular network map including environmental pixels and vascular pixels is generated based on the patient's medical images and the definitions of gray values ​​of vascular and environmental regions. An undirected edge is constructed between two adjacent vascular pixels (each pixel has 8 neighborhoods, i.e., pixels in the upper, lower, left, right, and 4 diagonal directions; the adjacent area in this application involves 8 neighborhoods) in the skeletonized tumor vascular network map, transforming the tumor vascular network map into a vascular network topology map with a graph data structure. This achieves specific initialization of the tumor vascular network map for each patient, which is closer to the actual situation of the patient's current tumor vessels. The tumor vascular network map is a binary map, with one gray value for each vascular pixel and one gray value for each environmental pixel. For example, in a tumor vascular network diagram, the grayscale value of the pixel corresponding to the blood vessel is 1, and the grayscale value of the pixel corresponding to the environment is 0. In other embodiments, the grayscale value of the pixel corresponding to the blood vessel in the tumor vascular network diagram may also be 0, and the grayscale value of the pixel corresponding to the environment may be 1. This application does not impose any restrictions. The specific method of defining and setting the grayscale values ​​of the blood vessel pixels and the environment pixels in the binarized tumor vascular network diagram is selected based on the grayscale value of the blood vessel in the patient's medical image.

[0020] In this embodiment, step S100 includes the following steps: Step S101: After acquiring medical images of the patient's tumor vessels, preprocess the image data by converting the patient's medical images into BMP format grayscale images, constructing a discrete coordinate system using the pixels of the grayscale image as coordinates, and then enhancing the contrast between the vessel pixels and the environment pixels; specifically including the following steps: Acquire DICOM format files of patient CT / MRI images, convert DICOM format files to BMP format images, and convert the generated BMP format images to grayscale images; If a discrete coordinate system is constructed using the pixels of a grayscale image as coordinates, then the grayscale value of each pixel in the grayscale image is... For example, in a discrete coordinate system, the horizontal coordinates are x = 0, 1, 2, ..., M-1, and the vertical coordinates are y = 0, 1, 2, ..., N-1; M is the number of rows of pixels in the grayscale image, and N is the number of columns of pixels in the grayscale image. Then, the grayscale image can be represented as a two-dimensional array F(x, y) consisting of the grayscale values ​​of each pixel in the grayscale image, i.e.: ; The equivalent gray value I is calculated using the formula for calculating the equivalent gray value I. The equivalent gray value I_(x,y) is:

[0021] in, θ represents the dividing line between red and black. (The default value is 0.2989). ω represents the dividing line between green and black. (The default value is 0.5870). φ represents the dividing line between blue and black. (Default value is 0.1140); R represents the red primary color component; G represents the green primary color component; B represents the blue primary color component; Brightness adjustment changes the image's brightness by linearly transforming the grayscale matrix and shifting the overall pixel values. In practice, the user inputs a brightness adjustment parameter. (The range is typically from -100 to 100). The system calculates the output matrix based on the original grayscale matrix (a two-dimensional array F(x,y)); each element of the output matrix is ​​calculated using the following formula: in, It is the normalization factor, usually taken as... =2.55, used to adjust the brightness parameter. This is converted into an actual change in grayscale value; this operation is equivalent to synchronously increasing or decreasing the grayscale value of all pixels by a fixed amount, thereby achieving overall brightness adjustment, i.e., taking... =2.55 is the standardization based on the grayscale value of 255 corresponding to 100% brightness.

[0022] The equivalent gray value of the pixel at position (x,y) in the original matrix represents the initial gray value of the grayscale image at coordinates (x,y). The grayscale value of the pixel at position (x,y) in the output matrix represents the grayscale value of the grayscale image after adjustment at coordinates (x,y). These are the brightness adjustment parameters.

[0023] Step S102: The Otsu method is used to binarize the grayscale image obtained in step S101. Based on the definitions of grayscale values ​​for the blood vessel region and the environment region, the pixels in the grayscale image are divided into blood vessel pixels and environment pixels, achieving segmentation of blood vessels and the environment. Most of the blood vessels within the grayscale image data are extracted, thus obtaining the tumor vascular network map. In other words, the goal of the Otsu method is to find a formula that minimizes the inter-class variance between the blood vessel and environment regions. Maximum optimal grayscale threshold The pixels of a grayscale image are divided into environmental regions based on the optimal grayscale threshold T. and vascular area Two regions (e.g., blood pixels with grayscale values ​​> T are blood vessel pixels, and pixels with grayscale values ​​≤ T are environment pixels) ensure optimal separation between blood vessels and the environment.

[0024] Step S103: Use median transformation and distance mapping matrix formula to skeletonize the tumor vascular network image and extract the central skeleton of the tumor vascular network. For each point z in region Z, if it has multiple nearest neighbor boundary points (i.e., points close to the boundary W), then z belongs to the skeleton; calculate the Manhattan distance from point z to the boundary W using the distance mapping matrix formula, and then determine the skeleton point based on the multiple nearest neighbor or local maximum conditions. After skeletonization, subsequent processing such as vascular network analysis is facilitated.

[0025] In this embodiment, the formula for defining the central axis transformation (MAT) skeleton is: In this embodiment, the distance mapping matrix formula is: in: The skeleton point set is the set of all points in region Z that belong to the skeleton. It is defined by the median transformation and is used to represent the central axis of the object. z represents a pixel in region Z, i.e., a pixel in the image, which can be represented by coordinates (x, y, z). z ,y z )express; Z represents the region of interest in the image, specifically the tumor vascular network portion.

[0026] Z z (B) is the set of nearest neighbors of pixel z to boundary W, i.e., it includes all boundary points w. Minimum value is used to determine if a pixel z has multiple nearest neighbors. W is the set of boundary points, that is, the set of edge or contour points of region Z; This is the distance mapping value, i.e., the minimum distance from pixel z to boundary w, calculated using the following formula: dist(z,w) is the distance from pixel z to pixel w; w represents the pixel point belonging to the boundary W, usually expressed in coordinates (x, y). w ,y w )express; In this embodiment, "local maximum" is a conditional term, representing the distance value of pixel z. The fact that z is the largest in its 8 neighborhoods indicates that z is a skeleton point.

[0027] In this embodiment of the application, step S103 specifically includes: 1. Calculate the distance from each pixel z in region Z to the boundary W based on the median transformation and distance mapping matrix formula, and output the distance mapping matrix. For quick calculations, the Manhattan distance |x is used. w -x z |+|y w -y z |; 2. Determine the skeleton points; a pixel Z satisfies any of the following conditions to be considered a skeleton: Multiple nearest neighbors: There exist ≥ 2 boundary points w such that dist(z,w)=D(z); Local maxima: D(z) is the maximum distance within the 8-neighborhood of pixel z.

[0028] Step 104: Traverse the pixels in the skeletonized tumor vascular network graph, construct undirected edges between adjacent vascular pixels, and transform the tumor vascular network graph into a graph data structure vascular network topology graph to reflect the connection relationship of the real vascular network.

[0029] Step S200: Update the number of blood vessel pixels, the coordinates of blood vessel pixels, the degree of each blood vessel pixel, and other data directly obtained from the blood vessel network topology map according to the blood vessel network topology map, and set the blood vessel pixels with a degree (the number of adjacent pixels with a gray value of 1) of 1 as the tip of the blood vessel, and store the coordinates of the blood vessel tip as the blood vessel growth point; wherein, the degree of the blood vessel pixel is the number of blood vessel pixels among the 8 neighboring pixels of the blood vessel pixel.

[0030] Step S300: Update the morphological correction factor based on the number of branch points in the vascular network topology graph and the actual number of edges between each branch point and its adjacent branch points (i.e., vascular pixels that are branch points in their 8 neighborhoods); wherein, a branch point is a vascular pixel with a degree greater than 2; in this embodiment, step S300 includes the following steps: Step S301: Calculate the global clustering coefficient of the vascular network at simulation time t based on the number of branch points in the vascular network topology and the actual number of edges between each branch point and its adjacent branch points. The global clustering coefficient measures the tightness of connection between adjacent branch points in the vascular network topology. The formula for calculating the global clustering coefficient is: in: The global clustering coefficient (unitless) of the vascular network at simulation time t; The number of branch points; The actual number of connecting edges between neighboring branch points that are directly connected to the blood vessel pixel i corresponding to the branch point; Let i be the degree of the blood vessel pixel. Step S302: Based on the vascular network topology diagram, the Box-counting algorithm is used to obtain the fractal dimension of the vascular network. The fractal dimension describes the geometric complexity and self-similarity of the vascular network. A high value indicates a more complex network, which may affect the material diffusion efficiency. The fractal dimension calculation formula in this embodiment is as follows: in: The fractal dimension (unitless) of the vascular network at simulation time t; The number of boxes required to cover the vascular network (the vascular network topology graph of vascular pixels and the edges between vascular pixels); The dimensions of the box are a scaling factor, which can be 0.1 × the average length of the blood vessels. No restrictions are imposed here.

[0031] Step S303: Calculate the morphological correction factor at simulation time t based on the global clustering coefficient and fractal dimension. In this embodiment, the formula for calculating the morphological correction factor is: in: M(t) is the morphological correction factor (unitless) of the vascular network at simulation time t; The global clustering coefficient of the vascular network at simulation time t; The fractal dimension of the vascular network at simulation time t; For example, weighting coefficients , .

[0032] Step S400: Calculate the total number of endothelial cells in the vascular network topology at simulation time t based on the initial number of endothelial cells in the vascular network, the simulation time, and the endothelial cell proliferation model. In this embodiment, to describe the logical growth of endothelial cells and simulate cell expansion during angiogenesis, the endothelial cell EC proliferation model is as follows: in: The simulation time is t; the simulation time t is the time step of each iteration. The sum of; The total number of endothelial cells in the vascular network at simulation time t; The initial proliferation rate of endothelial cells (ECs) is generally taken as 1.05 h. -1 No restrictions are imposed here; The EC saturation coefficient for endothelial cells is generally taken as 1.05 × 10⁻⁶. -4 cell -1 h -1 No restrictions are imposed here; in the formula This is the maximum capacity of endothelial cells; This represents the total number of initial endothelial cells (ECs) in the vascular network, which can generally be taken as 50, and there is no restriction here.

[0033] Step S500: Calculate the VEGF concentration of each blood vessel pixel at simulation time t based on the morphological correction factor of the vascular network topology, the total number of endothelial cells in the vascular network, and the current oxygen concentration of the blood vessel pixels. In this embodiment, step S500 includes the following steps: Step S501: Predict the oxygen concentration of the blood vessel pixels at simulation time t based on the morphological correction factor, the total number of endothelial cells in the vascular network, the current oxygen concentration of the blood vessel pixels, and the oxygen metabolism feedback equation. The oxygen metabolism feedback equation is an equation that simulates the relationship between oxygen delivery and consumption. In this embodiment, the oxygen delivery efficiency is negatively correlated with the morphological correction factor. A high value of the morphological correction factor (indicating high complexity of the vascular network) will lead to low oxygen delivery. Therefore, the oxygen metabolism feedback equation in this embodiment is: in: This represents the total number of endothelial cells in the vascular network at simulation time t. M(t) is the morphological correction factor of the vascular network at simulation time t; The current oxygen concentration of the blood vessel pixel. When the blood vessel pixel is first iterated, the initial oxygen concentration is a preset value. The oxygen diffusion coefficient is typically taken as 1.0 × 10⁻⁶. -5 cm 2 / s, there is no limit to this specific value, and this parameter can be optimized as the simulation scheme is optimized; The cellular oxygen consumption rate is generally taken as 3.5 × 10⁻⁶. -10 mol / cell / s, there is no specific limit to this value, and this parameter can be optimized as the simulation scheme is optimized; This is the oxygen transport conversion coefficient, which can generally be taken as 0.1. There is no restriction on the specific value here. This parameter can be optimized as the simulation scheme is optimized. For blood oxygenation efficiency; The oxygen delivery coefficient is generally taken as 0.8 mmHg / s, and there is no limit to this value. This parameter can be optimized as the simulation scheme is optimized.

[0034] Step S502: Predict the hypoxia response coefficient at simulation time t based on the morphological correction factor of the vascular network topology; enhance VEGF secretion in inefficient regions to promote angiogenesis and reduce the hypoxia response coefficient. The calculation formula is: in: The basic sensitivity is typically set to 0.3. To adjust the intensity, a value of 0.15 is generally used.

[0035] Step S503: Based on the hypoxia response coefficient at simulation time t, the oxygen concentration of the vascular pixel, and the VEGF secretion regulation equation, the VEGF secretion rate of each vascular pixel at simulation time t is predicted. To achieve the pathological positive feedback of "HIF-1α activation during hypoxia, leading to an increase in VEGF in vascular cells," the VEGF secretion regulation equation (hypoxia response) in this embodiment is as follows: in: S(x,y,t) represents the secretion rate of VEGF at the blood vessel pixel (x,y) at simulation time t. Normal oxygen concentration; As a measure of secretion attenuation; The maximum secretion rate at the tumor center (unit: ng / mL / s); The current oxygen concentration of the blood vessel pixel; The oxygen decay index; This is the straight-line distance from the current blood vessel pixel to the middle position of the blood vessel network; The straight-line distance to the center of the vascular network is obtained by taking the arithmetic mean of the coordinates of all pixels in the vascular network topology graph.

[0036] Step S504: Calculate the VEGF concentration of each blood vessel pixel at simulation time t based on the current VEGF concentration, the VEGF secretion rate of the blood vessel pixel at simulation time t, and the kinetic equation of VEGF concentration. To quantify the spatiotemporal distribution of VEGF, simulate tumor growth factor secretion. diffusion In this embodiment, the kinetic equation for the concentration of the growth factor VEGF during the degradation process is as follows: in: The concentration of VEGF (vessel growth factor) at the vascular pixel (x, y) (unit: ng / mL). This represents the diffusion coefficient of growth factors at the blood vessel pixel, which is typically taken as 1.2 × 10⁻⁶. -3 mm 2 / s; The degradation rate of growth factor in blood vessel pixels is typically taken as 0.05 s.-1 ; Step S600: Calculate the endothelial cell density of the tip vessel segment in the vascular network topology at simulation time t based on the total number of endothelial cells in the vascular network at simulation time t, the elongation length of each branch of the vascular pixel at the tip obtained from each previous iteration, and the position coordinates of the vascular pixel. The tip vessel segment is defined as all edges connecting the tip to the nearest branch point to the tip. Therefore, the tip vessel segment includes at least the edge between the tip and the nearest branch point. If there are other vascular pixels besides the tip and the nearest branch point on the tip vessel segment, for example, two more vascular pixels, vascular pixel 1 and vascular pixel 2, then the tip vessel segment includes the edge from the tip to the nearest vascular pixel 1 on the tip vessel segment, the edge from vascular pixel 1 to vascular pixel 2, and the edge from vascular pixel 2 to the nearest branch point. In this embodiment, step S600 includes the following steps: Step S601: Based on the total number of endothelial cells in the vascular network at simulation time t, and the elongation length of each branch of the vascular pixel at the tip location and the coordinates of the vascular pixel position obtained in each previous iteration, the number of endothelial cells in each tip vascular segment in the vascular network topology diagram at simulation time t is obtained. To ensure mass conservation, in this embodiment, the endothelial cells (ECs) of the vascular network are distributed to the tip vascular segment and the branch point vascular segment according to the vascular length ratio. The branch point vascular segment is defined as all edges connecting the branch point to the nearest branch point (there are no branch points between the two branch points). Therefore, the formula for calculating the number of endothelial cells at the tip in this embodiment is: in: The number of endothelial cells at the tip of the vascular network topology at simulation time t. The length of the tip vessel segment in the vascular network topology diagram at simulation time t is calculated based on the position coordinates of the vessel pixels on the tip vessel segment (including the tip and the vessel pixels where the nearest branch point to the tip is located). This represents the number of branches at the blood vessel pixel where the tip is located during each iteration; Let K be the elongation length of the r-th branch of the blood vessel pixel i where the tip is located in the K-th iteration of the vascular network topology graph, where K is less than the current iteration number. Since the simulated vascular network is composed of the elongation length of each branch of the tip elongation bifurcation in each iteration (i.e., the length of the edge between the tip and a certain environmental pixel), therefore... The calculated value is the length of the entire vascular network in the vascular network topology diagram.

[0037] Step S602: Obtain the volume of the tip blood vessel segment in the vascular network topology diagram at simulation time t based on the position coordinates of the blood vessel pixel points on the tip blood vessel segment corresponding to the tip and the average cross-sectional area of ​​the blood vessel; the volume of the blood vessel segment is determined by the cross-sectional area and the length of the blood vessel segment, so the calculation formula for the tip blood vessel segment in this embodiment is: in: This represents the volume of the tip of the vascular network topology at simulation time t. The average cross-sectional area of ​​the blood vessel is denoted as . Since the variation of the blood vessel radius is not explicitly modeled in this model, the average cross-sectional area in this embodiment is a preset constant.

[0038] Step S603: Calculate the endothelial cell density of each apex-corresponding apex segment in the vascular network topology diagram at simulation time t, based on the number of endothelial cells and the volume of the corresponding apex segment. In this embodiment, the endothelial cell density calculated for each apex-corresponding apex segment is the local endothelial cell density, and the apex segment reflects vascular maturity. The formula for calculating the endothelial cell density of the apex segment in this embodiment is: in: This represents the endothelial cell density of the tip of the blood vessel at simulation time t.

[0039] Step S700: Based on the endothelial cell density of the vascular network topology at simulation time t, the number of branches obtained by each tip bifurcation in this iteration is obtained. Then, based on the morphological correction factor of the vascular network at simulation time t, the growth factor concentration of the vascular pixel at each tip, and the endothelial cell density of the vascular segment corresponding to each tip, the elongation length of each branch at each tip is calculated. In this embodiment, step S700 includes the following steps: Step S701: Based on the endothelial cell density and endothelial cell density bifurcation threshold of the vascular network topology graph corresponding to the tip in the current iteration, obtain the number of branches of the tip bifurcation in this iteration; in order to realize density-dependent bifurcation events and generate a vascular network topology graph, in some embodiments step S701 includes: Determine the relationship between the endothelial cell density of the apex vessel segment and the endothelial cell density bifurcation threshold. If the endothelial cell density of the apex vessel segment corresponding to the tip is less than the endothelial cell density bifurcation threshold, it means that there is no bifurcation, and the number of branches of the pixel point of the vessel where the tip is located is 1. If the endothelial cell density of the corresponding apex vessel segment is greater than or equal to the endothelial cell density bifurcation threshold, it indicates a probability of bifurcation. The bifurcation probability of the apex is generated based on the endothelial cell density of the corresponding apex vessel segment and the endothelial cell density bifurcation threshold, and the number of branches of the apex is obtained based on the bifurcation probability. In this embodiment, the formula for calculating the bifurcation probability of the apex based on the endothelial cell density of the corresponding apex vessel segment and the endothelial cell density bifurcation threshold is as follows: in: The probability of bifurcation; The basic bifurcation probability is a constant, for example, 0.8; This is the endothelial cell density bifurcation threshold, which is a constant, such as 3 cells / μm. 3 .

[0040] In this embodiment, the branch of the fork at the tip, obtained based on the fork probability, can be: A random number is generated within the interval [0,1]. If this number is less than or equal to the bifurcation probability... This indicates that a branching process is being performed, and the number of branches is specified. The preset number of branches is set. If it is greater than the bifurcation probability, it means that there is no bifurcation and the number of branches is 1. The preset number of branches does not exceed the maximum number of branches that a blood vessel can bifurcate. It is greater than 1. The specific number is set according to the device environment in which the program implementing this method is deployed. If the device hardware configuration is high, the preset number of branches can be set larger. If it is low, it can be set directly to 2.

[0041] Step S702: Calculate the dynamic chemotaxis weight of the vascular network topology at simulation time t based on the morphological correction factor of the vascular network topology at simulation time t. This step converts the morphological correction factor into an explicit relationship of chemotaxis sensitivity, simulating signal response attenuation under complex structures. The dynamic chemotaxis weight calculation formula in this embodiment is as follows: in: The dynamic chemoattracting weights (unitless) of the vascular network topology at simulation time t; The basic chemotaxis weight is a constant and can be taken as 1.0; The morphological inhibition coefficient is a constant and can be taken as 0.3; This is the morphological correction factor for the vascular network topology at simulation time t.

[0042] Step S703: Based on the endothelial cell density and endothelial cell elongation threshold of the apex vessel segment corresponding to the apex in the vascular network topology diagram at simulation time t, obtain the endothelial cell response function corresponding to the apex at simulation time t. In this embodiment, the endothelial cell response function is used to control whether branches elongate and to reflect the degree of influence of endothelial cell density on elongation length, thereby simulating the cell crowding effect. Therefore, the endothelial cell response function in this embodiment is: in: This is the endothelial cell response function at the tip during simulation time t; The endothelial cell density bifurcation threshold is a constant, which can be taken as 2 cells / μm³.

[0043] Step S704: Calculate the elongation length of each branch at each tip at simulation time t based on the dynamic chemotaxis weight at simulation time t, the growth factor concentration at each tip in the vascular network topology diagram, and the endothelial cell response function. In this embodiment, to quantify the directional growth rate of blood vessels, the microenvironment signal (VEGF concentration gradient) and endothelial cell density state are integrated. The vascular length evolution equation used in this embodiment to calculate the elongation length of each branch at the tip is as follows: in: In order to be consistent with this iteration (the first iteration) (nth iteration) tip connection The elongation length (μm) of the r-th branch at the blood vessel pixel i where the tip is located in the nth iteration, that is, the length of the r-th branch at the nth iteration. In the next iteration, the r-th branch of the blood vessel pixel i containing the tip grows and elongates by... After that, arrive at the first The pixel where the tip is located in the nth iteration; if in the nth iteration... The elongation length of the r-th branch at the blood vessel pixel i where the tip is located in the next iteration It is 0, and in the first If the blood vessel pixel i is still a tip in the +1 iteration, then in the +1 iteration... +1 When iterating through the calculation of the elongation length of each branch at pixel i of the blood vessel containing the tip, another equal Used for calculation, stored in the first In the next iteration, the elongation length of the r-th branch of the blood vessel pixel i is still 0.

[0044] This is the step size adjustment factor coefficient, a constant, with a value of 0.1 μm / h; The dynamic chemiluminescence weights of the vascular network topology at simulation time t This represents the gradient of the current VEGF concentration. The reference concentration for the growth factor VEGF, used for gradient normalization, can be 0.1 ng / mL; The unit vector representing the direction of blood vessel growth; The numerical stability threshold is generally set to 1% or 0.1% of the gradient value of normal angiogenesis factor concentration.

[0045] It is a random unit vector.

[0046] Step S800: Update the vascular network topology based on the number of branches of each vascular pixel at each tip and the elongation length of each branch in the vascular network topology at simulation time t, and set the iteration number. Increment by 1, the initial iteration count is 1. In this embodiment, the morphological correction factor, growth factor concentration, coordinates of the blood vessel pixel where the tip is located, number of branches of the blood vessel pixel where the tip is located, elongation length of each branch, degree of the blood vessel pixel, and coordinates of the position of each blood vessel pixel generated in each iteration are stored according to the iteration count; wherein, the elongation length of each branch of the blood vessel pixel where the tip is located includes at least the coordinates of the position of the blood vessel pixel where the tip is located, the coordinates of the pixels through which the elongation length from the tip grows, and the elongation length value.

[0047] Step S900: Determine whether the simulation termination condition is met. If the condition is met, end the simulation and output a new vascular network topology and the relevant parameters selected by the user. If not, execute step S200 until the simulation termination condition is met. In this embodiment, the simulation termination condition may be that time or other parameters reach a set threshold (such as endothelial cell concentration gradient, average path length representing transport efficiency, etc.), and is not limited here.

[0048] This application provides a method for simulating tumor angiogenesis. By using morphological correction factors to accurately characterize the spatial geometry and complexity of the vascular network, it achieves a mathematical description of the extremely chaotic, tortuous, and morphologically abnormal features of pathological blood vessels, thus enabling highly consistent simulation of the pathological vascular network. Furthermore, the introduction of fractal dimensions in calculating the morphological correction factors better describes the uniformity of vascular network distribution, invasion range, and microscopic heterogeneity in three-dimensional tissues. This is crucial for understanding tumor invasion and metastasis. Moreover, fractal dimensions are widely used in medical imaging as a radiomics feature to quantify tumor vascular morphology. The vascular network and related parameters obtained from fractal dimension simulation can be directly compared and verified with clinical imaging data, effectively improving work efficiency.

[0049] This application provides an electronic device, such as... Figure 2 As shown, Figure 2 The illustrated electronic device 800 includes a processor 801 and a memory 803. The processor 801 and the memory 803 are connected, for example, via a bus 802. Optionally, the electronic device 800 may also include a transceiver 804. It should be noted that in practical applications, the transceiver 804 is not limited to one type, and the structure of this electronic device 800 does not constitute a limitation on the embodiments of this application.

[0050] Processor 801 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 801 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0051] Bus 802 may include a pathway for transmitting information between the aforementioned components. Bus 802 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 802 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 2The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0052] The memory 803 may be ROM (Read Only Memory) or other types of static storage devices capable of storing static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices capable of storing information and instructions, or EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0053] The memory 803 stores the application code that executes the scheme of this application, and its execution is controlled by the processor 801. The processor 801 executes the application code stored in the memory 803 to implement the content shown in the aforementioned embodiment of a method for simulating tumor angiogenesis.

[0054] Among them, electronic devices include, but are not limited to: mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (such as in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 2 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0055] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for simulating tumor angiogenesis, characterized in that, Includes the following steps: Step S100: In a discrete coordinate system with pixels as coordinates, a binary tumor vascular network map including environmental pixels and vascular pixels is generated based on the patient's medical images. Undirected edges are constructed between two adjacent vascular pixels in the skeletonized tumor vascular network map to obtain a vascular network topology map. Step S200: Update the position coordinates of blood vessel pixels and the degree of each blood vessel pixel according to the blood vessel network topology map, and set the blood vessel pixels with a degree of 1 as the tip of the blood vessel; wherein, the degree of the blood vessel pixel is the number of blood vessel pixels among the 8 neighboring pixels of the blood vessel pixel; Step S300: Update the morphological correction factor according to the number of branch points in the vascular network topology diagram and the actual number of edges between each branch point and its adjacent branch points; wherein, the branch point is a vascular pixel with a degree greater than 2; Step S400: Calculate the total number of endothelial cells in the vascular network topology diagram at simulation time t based on the initial number of endothelial cells in the vascular network, the simulation time, and the endothelial cell proliferation model. Step S500: Calculate the VEGF concentration of each blood vessel pixel at simulation time t based on the morphological correction factor of the blood vessel network topology, the total number of endothelial cells in the blood vessel network, and the current oxygen concentration of the blood vessel pixel. Step S600: Calculate the endothelial cell density of the tip vessel segment of each tip in the vascular network topology at simulation time t based on the total number of endothelial cells in the vascular network at simulation time t and the elongation length of each branch at the tip and the position coordinates of the vessel pixel points obtained in each previous iteration; wherein, the tip vessel segment is all the edges connecting the tip to the branch point closest to the tip. Step S700: Based on the endothelial cell density of the vascular network topology diagram at simulation time t, obtain the number of branches of each tip bifurcation in this iteration, and calculate the elongation length of each branch of each tip based on the morphological correction factor, the growth factor concentration of the vascular pixel at each tip, and the endothelial cell density of the vascular segment corresponding to each tip at simulation time t. Step S800: Update the vascular network topology graph according to the number of branches at each tip and the elongation length of each branch in the vascular network topology graph at simulation time t, and increment the iteration count by 1; Step S900: Determine whether the simulation termination condition is met. If the condition is met, end the simulation and output the new vascular network topology and the relevant parameters selected by the user. If the condition is not met, proceed to step S200.

2. The method according to claim 1, characterized in that, Step S100 includes the following steps: The patient's medical images were converted into grayscale images in BMP format, and a discrete coordinate system was constructed using the pixels of the grayscale image as coordinates. Then, the contrast between the vascular pixels and the environmental pixels was enhanced. The Otsu method is used to binarize the obtained grayscale image, and the pixels in the grayscale image are divided into vascular pixels and environmental pixels according to the definition of grayscale values ​​of vascular region and environmental region, so as to obtain the tumor vascular network map. The image skeletonization of the tumor vascular network map is performed using the median transformation and distance mapping matrix formula. The central skeleton of the tumor vascular network is extracted to obtain the skeletonized tumor vascular network map. By traversing the pixels in the skeletonized tumor vascular network graph, undirected edges are constructed between adjacent vascular pixels to obtain the vascular network topology graph.

3. The method according to claim 1, characterized in that, Step S300 includes the following steps: The global clustering coefficient of the vascular network at simulation time t is calculated based on the number of branch points in the vascular network topology diagram and the actual number of edges between each branch point and its adjacent branch points. The fractal dimension of the vascular network is obtained using the Box-counting algorithm based on the vascular network topology diagram. The morphological correction factor at simulation time t is calculated based on the global clustering coefficient and the fractal dimension.

4. The method according to claim 1, characterized in that, The endothelial cell proliferation model: in: For simulation time; The total number of endothelial cells in the vascular network at simulation time t; The initial proliferation rate of endothelial cells (ECs) is denoted as , which is a constant. Let be the endothelial cell EC saturation coefficient, which is a constant; therefore This represents the maximum capacity of endothelial cells; This represents the initial total number of endothelial cells (ECs) in the vascular network, which is a preset value.

5. The method according to claim 1, characterized in that, Step S500 includes the following steps: The oxygen concentration of the blood vessel pixels at simulation time t is predicted based on the morphological correction factor, the total number of endothelial cells in the vascular network, the current oxygen concentration of the blood vessel pixels, and the oxygen metabolism feedback equation. The hypoxia response coefficient at simulation time t is predicted based on the morphological correction factor described in the vascular network topology diagram. Based on the hypoxia response coefficient, oxygen concentration of blood vessel pixels, and growth factor secretion regulation equation at simulation time t, the growth factor secretion rate of each blood vessel pixel at simulation time t is predicted. The growth factor concentration of each blood vessel pixel at simulation time t is calculated based on the current growth factor concentration of the blood vessel pixel, the secretion rate of growth factor at simulation time t, and the kinetic equation of growth factor concentration.

6. The method according to claim 5, characterized in that, The oxygen metabolism feedback equation is: in: The total number of endothelial cells in the vascular network at simulation time t; M(t) is the morphological correction factor of the vascular network at simulation time t; The current oxygen concentration of the blood vessel pixel. When the blood vessel pixel is first iterated, the initial oxygen concentration is a preset value. Let be the oxygen diffusion coefficient, and be a constant. Let be the cellular oxygen consumption rate, and be a constant. Here, is the oxygen transfer conversion coefficient, and is a constant. For blood oxygenation efficiency; The oxygen transport coefficient is denoted by , which is a constant. The formula for calculating the hypoxia response coefficient is as follows: in: The hypoxia response coefficient; The basic sensitivity is a constant. To adjust the intensity, it is a constant; The growth factor secretion regulation equation is as follows: in: S(x,y,t) represents the secretion rate of VEGF at the blood vessel pixel (x,y) at simulation time t. The normal oxygen concentration is a constant. is the scale for secretion attenuation, and is a constant. The maximum secretion rate at the tumor center is denoted as , which is a constant. The oxygen concentration of the blood vessel pixel at the current location coordinates; The oxygen decay index; This is the straight-line distance from the current blood vessel pixel to the middle position of the blood vessel network; The straight-line distance to the center of the vascular network is obtained by taking the arithmetic mean of the coordinates of all pixels in the vascular network topology graph. The kinetic equation for the concentration of the growth factor is: in: The concentration of VEGF, the growth factor, at the vascular pixel (x,y); is the diffusion coefficient of growth factor at the blood vessel pixel, which is a constant; denoted as the degradation rate of growth factors in blood vessel pixels, and denoted as a constant.

7. The method according to claim 1, characterized in that, Step S600 includes the following steps: Based on the total number of endothelial cells in the vascular network at simulation time t, the elongation length of each branch of the vascular pixel at the tip obtained from each previous iteration, and the coordinates of the vascular pixel, the number of endothelial cells in each vascular segment at the tip in the vascular network topology diagram at simulation time t is obtained; wherein, the formula for calculating the number of endothelial cells in the vascular segment at the tip is: in: The number of endothelial cells at the tip of the vascular network topology at simulation time t. The length of the tip blood vessel segment at the tip of the blood vessel network topology diagram at simulation time t is calculated based on the position coordinates of the blood vessel pixels on the tip blood vessel segment. This represents the number of branches at the blood vessel pixel where the tip is located during each iteration; Let K be the elongation length of the r-th branch of the blood vessel pixel i where the tip is located in the K-th iteration of the vascular network topology graph, where K is less than the current iteration number. ; The total number of endothelial cells in the vascular network at simulation time t; The volume of the tip of the vascular network topology at simulation time t is obtained by using the coordinates of the vascular pixel points on the tip of the vascular segment and the average cross-sectional area of ​​the vascular segment. The number of endothelial cells and the volume of the corresponding endothelial segment in the vascular network topology diagram at simulation time t are calculated. The endothelial cell density of the corresponding endothelial segment in the vascular network topology diagram at simulation time t is calculated.

8. The method according to claim 1, characterized in that, Step S700 includes the following steps: The number of branches at the tip bifurcation in this iteration is obtained based on the endothelial cell density and endothelial cell density bifurcation threshold of the vascular network topology diagram at simulation time t. The dynamic chemotaxis weights of the vascular network topology at simulation time t are calculated based on the morphological correction factor of the vascular network topology at simulation time t. The endothelial cell response function corresponding to the tip at simulation time t is obtained based on the endothelial cell density and endothelial cell density elongation threshold of the tip vascular segment corresponding to the tip in the vascular network topology diagram at simulation time t. The elongation length of each branch at each tip in the vascular network topology at simulation time t is calculated based on the dynamic chemotaxis weights at simulation time t, the growth factor concentration at each tip in the vascular network topology, and the endothelial cell response function.

9. The method according to claim 8, characterized in that, The formula for calculating the dynamic chemotaxis weight is as follows: in: The dynamic chemiluminescence weights of the vascular network topology at simulation time t; The basic chemotaxis weight is a constant; Here, is the morphological inhibition coefficient, and is a constant; The morphological correction factor for the vascular network topology at simulation time t; The endothelial cell response function is: in: This is the endothelial cell response function at the tip during simulation time t; The endothelial cell density of the corresponding tip blood vessel segment at simulation time t; is the endothelial cell density bifurcation threshold, and is a constant; The equation for the evolution of blood vessel length is: in: For the first connection to the tip of this iteration The elongation length of the r-th branch of the blood vessel pixel i where the tip is located in the next iteration; The step size adjustment factor coefficient is a constant. The dynamic chemiluminescence weights of the vascular network topology at simulation time t; This represents the gradient of the current VEGF concentration. The reference concentration of the growth factor VEGF is used for gradient normalization. The unit vector representing the direction of blood vessel growth; The threshold for numerical stability; It is a random unit vector.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method for simulating tumor angiogenesis as described in any one of claims 1 to 9.

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