A method for simulating tumor blood vessel growth process

Abstract

The present invention discloses a method for simulating the tumor blood vessel growth process, comprising constructing a two-dimensional discrete coordinate system based on a two-dimensional tumor model and defining a blood vessel index function that describes the cell grid properties of the cell grid; updating the cell number, oxygen concentration, fibronectin concentration, and growth factor concentration of each cell grid at preset intervals t; predicting the movement direction of the blood vessel tip within the current time period t based on the fibronectin concentration and growth factor concentration; calculating a first predicted extension distance and a second predicted extension distance based on the movement direction within the current time period t and the movement direction within the previous time period t; and updating the cell grid properties of each cell grid in the two-dimensional discrete coordinate system based on the movement direction within the current time period t, the vessel tip's existence time, and the movement extension distance calculated from the vessel tip. The present invention incorporates oxygen concentration and cell number into the tumor blood vessel growth model to achieve accurate simulation and prediction of the tumor blood vessel growth process.

Description

Technical Field

[0001] The present invention relates to the technical field of biological simulation, and in particular to a method for simulating the growth process of tumor blood vessels. Background Art

[0002] Tumor growth is a core process in the development and progression of cancer, and its progression is closely linked to the oxygen supply and angiogenesis in the tumor microenvironment. Rapid tumor proliferation consumes large amounts of oxygen and nutrients, leading to a state of hypoxia (low oxygen) in local tissues. This hypoxic environment induces tumor cells to secrete vascular endothelial growth factor (VEGF), promoting angiogenesis (angiogenesis), providing the tumor with more oxygen and nutrients, further fueling tumor growth and invasion.

[0003] Research has shown that rapid tumor growth depends not only on its intrinsic proliferative capacity but also on the dynamic regulation of oxygen concentration and VEGF within the tumor microenvironment. While newly formed blood vessels can temporarily improve oxygen supply within a tumor, they are often abnormal, characterized by disordered vascular structure, increased permeability, and unstable blood flow. This immature vascular network further exacerbates local hypoxia, creating a vicious cycle. Therefore, oxygen concentration and VEGF regulation play a decisive role in tumor growth.

[0004] Numerous studies have been devoted to understanding the pathological mechanisms of tumor growth and its microenvironment. VEGF, a key angiogenic factor, has been extensively studied for its role in abnormal blood vessel formation within tumors. However, most studies focus solely on a single factor within the tumor microenvironment, such as oxygen concentration or the dynamics of VEGF secretion, failing to comprehensively integrate multiple key processes, including oxygen diffusion, VEGF secretion, and tumor cell homeostasis. Consequently, existing models may exhibit significant deviations from actual conditions when predicting tumor growth and assessing treatment efficacy. Summary of the Invention

[0005] In order to solve the above technical problems, an embodiment of the present invention provides a method for simulating the growth process of tumor blood vessels.

[0006] The specific technical solutions are as follows:

[0007] An embodiment of the present invention provides a method for simulating the growth process of tumor blood vessels, comprising the following steps:

[0008] Step S100: constructing a two-dimensional discrete coordinate system based on the two-dimensional model of the patient's tumor, and defining a vascular index function n(x, y, t) that describes and records the unit grid attributes of each unit grid in the two-dimensional discrete coordinate system at each preset time t; wherein the unit grid attributes include blood vessels, blood vessel tips, and the environment;

[0009] Step S200, initializing the cell grid properties, cell number, Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration, fibronectin concentration, and growth factor concentration of each cell grid in the two-dimensional discrete coordinate system according to the patient's examination results;

[0010] Step S300, predicting the number of cells in each unit grid in the two-dimensional discrete coordinate system after a preset time t based on the current Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, oxygen concentration of the unit grid and the cell number control model;

[0011] Step S400, predicting the oxygen concentration, p53 concentration, fibronectin concentration, and VEGF concentration of each unit grid in the two-dimensional discrete coordinate system after a preset time t based on the current oxygen concentration, unit grid properties, cell number, p53 concentration, fibronectin concentration, and VEGF concentration of the unit grid, as well as the oxygen concentration control equation, the p53 concentration control equation, the fibronectin concentration control equation, and the VEGF diffusion reaction equation;

[0012] Step S500, predicting the movement direction of each blood vessel tip in the two-dimensional discrete coordinate system within the current time period t based on the fibronectin concentration of the unit grid after time t, the growth factor concentration after time t, and the blood vessel tip movement direction control equation;

[0013] Step S600: Predicting a first motion velocity of each blood vessel tip in a two-dimensional discrete coordinate system when moving in a first motion direction based on a governing equation for the fibronectin concentration at the blood vessel tip after time t, the first motion direction, and the motion velocity of the blood vessel tip; and predicting a second motion velocity of each blood vessel tip in a two-dimensional discrete coordinate system when moving in a second motion direction based on a governing equation for the fibronectin concentration at the blood vessel tip after time t, the second motion direction, and the motion velocity of the blood vessel tip; wherein the first motion direction is the motion direction of the blood vessel tip during the current time period t; and the second motion direction is the motion direction of the blood vessel tip during the previous time period t.

[0014] Step S700: Calculate a first predicted extension distance of each blood vessel tip in a two-dimensional discrete coordinate system in a first direction of motion based on the discrete coordinates (x0, y0) of the blood vessel tip and a first motion velocity, and calculate a second predicted extension distance of each blood vessel tip in a second direction of motion based on the discrete coordinates (x0, y0) of the blood vessel tip and a second motion velocity; wherein the first predicted extension distance or the second predicted extension distance is the total number of unit grids that the blood vessel tip passes through when it starts moving in the first direction or the second direction at the first motion velocity or the second motion velocity from the unit grid discrete coordinates (x0, y0) to which the blood vessel tip belongs and reaches the end point coordinates (x1, y1) after a preset time t.

[0015] Step S800: Perform an extension simulation on each blood vessel tip in the two-dimensional discrete coordinate system within the current time period t based on the first movement direction of the blood vessel tip, the existence time of the blood vessel tip, the second movement direction of the blood vessel tip, the first movement speed, the second movement speed, the first predicted extension distance, and the second predicted extension distance. The unit grid attributes and the existence time of the blood vessel tip of each unit grid in the two-dimensional discrete coordinate system are updated as the extension simulation of each blood vessel tip is performed. The simulation time is updated when the extension simulation of all blood vessel tips in the two-dimensional discrete coordinate system is completed. The extension simulation includes blood vessel extension, blood vessel branching that occurs during blood vessel extension, and blood vessel fusion that occurs during blood vessel extension.

[0016] Optionally, the cell number control model includes:

[0017] Predicting the Cdh1 concentration of the unit grid after a preset time t based on the current Cdh1 concentration of the unit grid, the current cycCDK concentration, the current npRB concentration, and the Cdh1 concentration control equation;

[0018] Predicting the cycCDK concentration of the unit grid after a preset time t based on the current Cdh1 concentration, the current cycCDK concentration, the current p27 concentration and the cycCDK concentration control equation of the unit grid;

[0019] Predict the p27 concentration of the unit grid after a preset time t based on the current oxygen concentration of the unit grid, the current p27 concentration and the p27 concentration control equation;

[0020] Predict the npRB concentration of the unit grid after a preset time t based on the current npRB concentration of the unit grid, the current cycCDK and the npRB concentration control equation;

[0021] According to the predicted Cdh1 concentration, cycCDK concentration, and p27 concentration of the cell grid after the preset time t, the number of cells in the cell grid is increased or decreased; specifically:

[0022] When it is predicted that the Cdh1 concentration of the unit grid is less than the Cdh1 concentration threshold and the cycCDK concentration is greater than the cycCDK concentration threshold after the preset time t, if the current cell number of the unit grid is less than the maximum carrying cell number, the cell number of the unit grid is increased by one unit, and the p27 concentration is reset to the initial value; if the current cell number of the unit grid is equal to the maximum carrying cell number, the unit grid with a current cell number less than the maximum carrying cell number is screened out from the eight unit grids adjacent to the unit grid, and the cell number of the unit grid with the highest current oxygen concentration among the screened unit grids is increased by one unit, and the p27 concentration is reset to the initial value; if no unit grid with a current cell number less than the maximum carrying cell number is screened out, the cell number remains unchanged;

[0023] When the p27 concentration of the cell grid is predicted to be greater than the p27 concentration threshold after the preset time t, the cell grid starts the timer to start counting the static state maintenance time; when the static state maintenance time of the cell exceeds a static state maintenance time threshold, the cell number is cleared and the p27 concentration is reset to the initial state.

[0024] Optionally, the Cdh1 concentration control equation is as follows:

[0025]

[0026] in:

[0027] c Cdh1 is the current Cdh1 concentration of the cell grid;

[0028] c npRB is the current npRB concentration of the unit grid;

[0029] c cycCDK is the current cycCDK concentration of the cell grid;

[0030] k Cdh1 , k′ Cdh1 is the correlation constant;

[0031] J2, J3 are correction coefficients;

[0032] The cycCDK concentration control equation is as follows:

[0033]

[0034] in:

[0035] k c1 , k c2 , k c3 , k c4 is the correlation constant;

[0036] c cycCDK is the current cycCDK concentration of the cell grid;

[0037] c p27 is the current p27 concentration of the cell grid;

[0038] The p27 concentration control equation is as follows:

[0039]

[0040] in:

[0041] k p27 , k′ p27 is a constant coefficient;

[0042] J4 is the oxygen effect correction factor;

[0043] c o is the current oxygen concentration of the unit grid;

[0044] The npRB concentration control equation is as follows:

[0045]

[0046] Among them, k n1 , k n2 , k n3 is a constant coefficient.

[0047] Optionally, the oxygen concentration control equation is as follows:

[0048]

[0049] in:

[0050] D o is the oxygen diffusion coefficient;

[0051] c o is the current oxygen concentration of the unit grid;

[0052] P o is vascular permeability, which is a fixed coefficient;

[0053] k(x, y) is the current number of cells in the unit grid;

[0054] n(x,y) is the current cell grid attribute of the cell grid;

[0055] The p53 concentration control equation is as follows:

[0056]

[0057] in:

[0058] k p53 is the initial constant coefficient of p53;

[0059] k′ p53 is the oxygen influence constant coefficient;

[0060] C p53 is the oxygen effect correction factor;

[0061] The governing equation for the fibronectin concentration is:

[0062]

[0063] in:

[0064] c f is the current fibronectin concentration of the cell grid;

[0065] ω is the production rate of fibronectin in endothelial cells, which is a fixed constant;

[0066] μ is the uptake rate of fibronectin by endothelial cells, which is a fixed constant;

[0067] The growth factor VEGF diffusion reaction equation is:

[0068]

[0069] in:

[0070] c v is the current VEGF concentration of the unit grid;

[0071] k v is the p53 promotion coefficient;

[0072] J1 is the correction coefficient for the relationship between p53 and growth factor VEGF

[0073] k′ v is the oxygen inhibition constant coefficient;

[0074] D V is the VEGF diffusion coefficient;

[0075] P V The permeability of VEGF in blood vessels;

[0076] δ V is the VEGF degradation rate, which is a fixed constant;

[0077] C v1 Corrected normal coefficients for oxygen effects.

[0078] Optionally, the control equation for the movement direction of the blood vessel tip is as follows:

[0079]

[0080] in:

[0081] is the chemotactic parameter of growth factor VEGF;

[0082] is the fibrin chemotaxis parameter;

[0083] K is the extracellular matrix anisotropy tensor matrix, which is an intrinsic property of the matrix space of each cell grid (x, y)∈Ω and is independent of time. It is non-uniform and anisotropic in space. This property means that the extension direction of the tip cell is not necessarily consistent with the direction of the growth factor concentration gradient or the fibronectin concentration gradient; the governing equation is:

[0084]

[0085] k a is the anisotropy parameter, representing the resistance to movement along a certain direction;

[0086] k cond Heterogeneity parameters;

[0087] v x and v y is the component of the unit vector v that describes the orientation of the extracellular matrix at the unit grid (x, y). At each unit grid (x, y), is a regular equation, randomly generating v x and v y , and fixed at all times t; for each unit grid (x, y) ∈ Ω, k cond and k a Also randomly generated.

[0088] Optionally, the control equation for the velocity of the blood vessel tip is as follows:

[0089]

[0090] in:

[0091] P is the velocity of the blood vessel tip;

[0092] k p is the rate of vascular tip division, which is related to the concentration of growth factor VEGF c v Related;

[0093]

[0094] l e is a constant, the length of the endothelial cell;

[0095] tc is the cell division cycle, which is determined by the concentration of growth factor VEGF cν, and the governing equation is as follows:

[0096]

[0097] τ is a constant, the cell proliferation time coefficient;

[0098] is the average growth factor (VEGF) concentration; the sum of the growth factor concentrations of all unit grids in the two-dimensional discrete coordinate system at the current time is divided by the total number of unit grids, and is calculated once for each time period t;

[0099] c ν is the current concentration of growth factor VEGF;

[0100] c νlim is the threshold concentration of growth factors.

[0101] Optionally, step S700 includes the following steps:

[0102] According to the velocity of the blood vessel tip in the x and y directions (x p ,y p ) and the discrete coordinates (x0, y0) of the blood vessel tip to calculate the end point coordinates (x1, y1) of the cell grid this extension; where x1 = x0 + x p , y1=y0+y p ; The movement speed is the first movement speed or the second movement speed;

[0103] The Bresenham algorithm is used to calculate the discrete coordinates of the unit grids passed on the straight line connecting the discrete coordinates (x0, y0) of the blood vessel tip to the end point coordinates (x1, y1) of the current extension of the blood vessel tip, and the discrete coordinates of all the passed unit grids are used as the predicted extension distance of the blood vessel tip (x0, y0) within the current time period t; the predicted extension distance is the first predicted extension distance or the second predicted extension distance.

[0104] Optionally, the conditions for the blood vessel branching when the blood vessel tip extends include:

[0105] The blood vessel existence time of the blood vessel tip is greater than a preset blood vessel tip existence time threshold τ a ;

[0106] The unit velocity vector of the blood vessel tip during this time period t The angle change between the angle between the positive direction of the x-axis of the coordinate system and the angle between the unit velocity vector of the blood vessel tip and the positive direction of the x-axis of the coordinate system in the last time period t is greater than the preset angle threshold τ u ;

[0107] When the two conditions for vascular branching are met at the same time, the process of vascular branching at the vascular tip is simulated as follows:

[0108] Starting from the tip of the blood vessel where the blood vessel branch occurs, the blood vessel is extended in the second movement direction according to the second predicted extension distance and in the first movement direction according to the first predicted extension distance;

[0109] The conditions for vascular fusion to occur when the vascular tip extends include:

[0110] Among the cell grids included in the blood vessel tip prediction extension distance, there are cell grids whose cell grid attributes are blood vessels and / or blood vessel tips;

[0111] When the vascular fusion conditions are met, the vascular fusion process at the vascular tip is simulated including:

[0112] According to the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point on the corresponding predicted extension distance, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the predicted extension distance, and the blood vessel tip is extended according to the actual extension distance after the blood vessel fusion, until the extension simulation of the blood vessel tip in this time period t is completed;

[0113] The blood vessel tip extending the blood vessel comprises:

[0114] Each blood vessel tip in the two-dimensional discrete coordinate system is sequentially extended within the current time period t by simulation, wherein the blood vessel tip extension simulation within the current time period t is:

[0115] Determine whether vascular branching occurs at the vascular tip;

[0116] If no branching occurs at the vascular tip, it is determined whether vascular fusion occurs at the vascular tip within the first predicted extension distance. If no vascular fusion occurs, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids within the first predicted extension distance. The current vascular tip existence time of the vascular tip is used as the initial value of the timer for the last unit grid within the actual extension distance. The vascular tip existence time of the vascular tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid within the actual extension distance is changed to vascular tip, and the timer is started to record the vascular tip existence time from the initial value. The unit grid attributes of the remaining unit grids within the actual extension distance are changed to blood vessels, and the extension simulation of the vascular tip within the current time period t is terminated. If vascular fusion occurs, the vascular tip is sequentially fused with the blood vessels and the vascular tip within the first predicted extension distance in the order from the discrete coordinates of the vascular tip to the end point coordinates within the first predicted extension distance. The vascular tip is extended according to the actual extension distance of the vascular tip after vascular fusion until the extension simulation of the vascular tip within the current time period t is terminated.

[0117] If a blood vessel branch occurs at the tip of the blood vessel, the tip of the blood vessel is extended in the second movement direction according to the second predicted extension distance and the tip of the blood vessel is extended in the first movement direction according to the first predicted extension distance; wherein:

[0118] The extending of the blood vessel tip in the first movement direction according to the first predicted extension distance specifically includes:

[0119] determining whether vascular fusion occurs at the tip of the blood vessel at the first predicted extension distance;

[0120] If blood vessel fusion does not occur, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids in the first predicted extension distance, the blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped, the unit grid attribute of the last unit grid in the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero, and the unit grid attributes of the remaining unit grids in the actual extension distance are changed to blood vessel, and the extension simulation of the blood vessel tip in this time period t is ended;

[0121] If vessel fusion occurs, the vessel tip is sequentially fused with the vessels and vessel tips at the first predicted extension distance in the order from the discrete coordinates of the vessel tip to the coordinates of the end point at the first predicted extension distance, and the vessel tip is extended according to the actual extension distance of the vessel tip after vessel fusion until the extension simulation of the vessel tip in this time period t is completed;

[0122] The extending of the second movement direction of the blood vessel tip according to the second predicted extension distance specifically includes:

[0123] determining whether vascular fusion occurs at the tip of the blood vessel at the second predicted extension distance;

[0124] If blood vessel fusion does not occur, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids on the second predicted extension distance, and the blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid on the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero. The unit grid attributes of the remaining unit grids on the actual extension distance are changed to blood vessels, and the extension simulation of the blood vessel tip in this time period t is ended.

[0125] If vessel fusion occurs, the vessel tip is sequentially fused with the vessels and vessel tips on the second predicted extension distance in the order from the discrete coordinates of the vessel tip to the coordinates of the end point on the second predicted extension distance, and the vessel tip is extended according to the actual extension distance of the vessel tip after vessel fusion until the extension simulation of the vessel tip in this time period t is completed.

[0126] Optionally, fusing the blood vessel tip with the blood vessel and the blood vessel tip at the predicted extension distance, and extending the blood vessel tip according to the actual extension distance of the blood vessel tip after the blood vessel fusion includes:

[0127] If the vessel fused with the blood vessel tip is within the predicted extension distance, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids before the unit grid to which the blood vessel tip belongs within the predicted extension distance, the blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped, and the unit grid attributes of all unit grids within the actual extension distance are changed to blood vessels, thereby ending the extension simulation of the blood vessel tip within the current time period t.

[0128] If the blood vessel tip that undergoes vascular fusion is the blood vessel tip at the predicted extension distance, the blood vessel fusion is performed according to the movement direction of the blood vessel tip and the movement direction of the blood vessel tip at the predicted extension distance, specifically:

[0129] If the angle between the movement direction of the blood vessel tip and the movement direction of the blood vessel tip at the corresponding predicted extension distance is greater than or equal to 90 degrees, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids before the unit grid to which the blood vessel fusion occurs at the predicted extension distance. The blood vessel tip existence time of the blood vessel tip and the blood vessel tip at the predicted extension distance is reset to zero and the timing is stopped. The unit grid attributes of all unit grids at the actual extension distance are changed to blood vessels, and the extension simulation of the blood vessel tip in this time period t is terminated.

[0130] If the angle between the movement direction of the blood vessel tip and the movement direction of the blood vessel tip at the corresponding predicted extension distance is less than 90 degrees, if the blood vessel tip is randomly selected for extension, the blood vessel tip at the predicted extension distance stops extending; when there is no blood vessel or blood vessel tip after the blood vessel tip at the predicted extension distance that merges with the blood vessel tip at the corresponding predicted extension distance, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids included in the predicted extension distance of the blood vessel tip, and the blood vessel tip existence time of the blood vessel tip and the blood vessel tip at the predicted extension distance that merges with it is cleared and the timing is stopped, the unit grid attribute of the last unit grid at the actual extension distance is changed to the blood vessel tip and the timer is started to count from the initial value Recording the existence time of the blood vessel tip and changing the unit grid attributes of the remaining unit grids in the actual extension distance to blood vessels, ending the extension simulation of the blood vessel tip in this time period t; when there are still blood vessels and / or blood vessel tips after the blood vessel tip in the predicted extension distance that merges with the blood vessel tip in the corresponding predicted extension distance, the blood vessel tip continues to fuse with the blood vessel and blood vessel tip in the predicted extension distance, and extends according to the actual extension distance of the blood vessel tip after blood vessel fusion, until the extension simulation of the blood vessel tip in this time period t is ended; wherein, the initial value of the timer of the last unit grid in the actual extension distance is the existence time of the blood vessel tip before the blood vessel tip is cleared if no blood vessel branch occurs, and the initial value is zero if a blood vessel branch occurs;

[0131] If the vascular tip is randomly selected to stop extending, the vascular tip is extended at the predicted extension distance where the vascular tip merges with the vascular tip; the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids before the unit grid to which the vascular tip belongs at the predicted extension distance where the vascular tip merges with the vascular tip at the corresponding predicted extension distance, and the vascular tip existence time of the vascular tip is cleared and the timing is stopped, and the attributes of all unit grids at the actual extension distance are changed to blood vessels, ending the extension simulation of the vascular tip within this time period t.

[0132] The embodiment of the present invention provides a method for simulating the growth process of tumor blood vessels, which has the following technical effects:

[0133] (1) Establish a mathematical model (cell number control model) that includes oxygen concentration, VEGF dynamics, and tumor cell proliferation, death, and competition, which can more comprehensively and accurately describe the tumor blood vessel growth process and provide important and reliable theoretical support and technical means for tumor mechanism research and anti-angiogenic therapy;

[0134] (2) By dynamically simulating the tumor vascular growth process at different stages, the present invention can predict disease progression and the effects of different treatments, optimize treatment strategies at different stages, and improve treatment outcomes;

[0135] (3) Considering the different Cdh1 concentrations, cycCDK concentrations, npRB concentrations, p27 concentrations, p53 concentrations and oxygen supply status of individual patients, a personalized simulation model is established for different patients to achieve personalized disease prediction and treatment plan optimization.

[0136] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0137] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0138] Figure 1 A schematic flow chart of a method for simulating tumor blood vessel growth process provided by an embodiment of the present invention;

[0139] Figure 2 Flowchart of step S800 in an embodiment of the present invention. DETAILED DESCRIPTION

[0140] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0141] like Figure 1 As shown, the embodiment of the present application provides a method for simulating the growth process of tumor blood vessels, which includes the following steps:

[0142] Step S100: construct a two-dimensional discrete coordinate system (x, y) based on the two-dimensional model of the patient's tumor, and define a vascular index function n(x, y, t) that describes and records the attributes of each unit grid in the two-dimensional discrete coordinate system at each preset time t; the unit grid attributes include blood vessels, blood vessel tips, and environment; it can be seen that the vascular index function n(x, y, t) in the embodiment of the present application is actually a binary value function with a value of 0, 1, or 2, indicating the attribute of the unit grid (x, y) at time t. For example, n(x, y, t) is 0, indicating that the unit grid attribute at time t is the environment, and n(x, y, t) is 1, indicating that At time t, the unit grid attribute is a blood vessel; n(x, y, t) being 2 indicates that at time t, the unit grid attribute is a blood vessel tip. A binary value function is used as a vascular network morphology descriptor to more accurately capture grid information than the traditional endothelial cell density function. The blood vessel tip is a state before it becomes a blood vessel. The tumor blood vessel growth process is simulated through biological processes such as blood vessel tip extension, branching, and fusion. The unit grid attribute is the environment, which is a space where simulated blood vessels can grow. The unit grid with the unit grid attribute of the environment may become a unit grid attribute of a blood vessel or a blood vessel tip as the blood vessel tip extends, branches, and fuses. The patient tumor two-dimensional model can be a tumor two-dimensional model constructed based on the patient's most recent tumor imaging data, or it can be a system-preset tumor two-dimensional model. In addition, the two-dimensional discrete coordinate system constructed in the embodiment of the present application is much larger than the patient tumor two-dimensional model in both the x-direction and the y-direction, reserving more space for tumor blood vessel growth.

[0143] Step S200: Initialize the cell grid properties, cell number, Cdh1 (cadherin 1) concentration, cycCDK (a complex of cyclin and cyclin-dependent kinase CDK) concentration, npRB (natriuretic peptide receptor B), p27 concentration (cyclin-dependent kinase inhibitor), p53 concentration (tumor suppressor protein), oxygen concentration, fibronectin concentration, and growth factor concentration of each cell grid in the two-dimensional discrete coordinate system according to the patient's examination results. To ensure that the simulation results are closer to the actual patient situation and that the results are closer to the actual development, the Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, and oxygen concentration are set according to the patient's examination results. The initial values ​​are directly obtained from the patient's most recent test results. The initial values ​​of the fibronectin concentration and growth factor concentration are the steady-state values ​​under normal conditions. The initial values ​​of the Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration, and fibronectin concentration of each unit grid are the same. Over time, the Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration, and fibronectin concentration of each unit grid undergo personalized changes. The Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration, and fibronectin concentration of each unit grid are different.

[0144] In an embodiment of the present application, when initializing the attributes of each unit grid in the two-dimensional discrete coordinate system, the unit grid attributes of the unit grids in the tumor two-dimensional model area are blood vessel tips or blood vessels. Among all the unit grids in the tumor two-dimensional model area, at least one unit grid has a blood vessel tip attribute, and the remaining unit grid attributes are blood vessels. The positions of the unit grids with the unit grid attribute of the blood vessel tip are not restricted herein; the unit grid attributes of the unit grids not in the tumor two-dimensional model area are the environment. However, in order to better represent the tumor blood vessel growth process over time, in this embodiment, the number of unit grids with the unit grid attributes of the blood vessel tips and blood vessels is much smaller than the number of unit grids with the unit grid attribute of the environment.

[0145] In an embodiment of the present application, when initializing the number of cells in each unit grid in a two-dimensional discrete coordinate system, the initial value of the number of cells in each unit grid in the tumor two-dimensional model area is 2 units, and the initial value of the number of cells in each unit grid not in the tumor two-dimensional model area is zero.

[0146] Step S300: predict the number of cells in each unit grid in the two-dimensional discrete coordinate system after a preset time t based on the current Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, oxygen concentration and cell number control model of the unit grid, and save it under the information of the corresponding unit grid.

[0147] Cell proliferation and apoptosis are primarily achieved through dynamic changes in key regulatory proteins, including Cdh1, cycCDK, npRB, and p27. Therefore, the cell number control model in this embodiment includes:

[0148] The Cdh1 concentration of the unit grid after the preset time t is predicted based on the current Cdh1 concentration, current cycCDK concentration, current npRB concentration and the Cdh1 concentration control equation of the unit grid. Since the Cdh1 concentration is affected by the npRB concentration and cycCDK concentration, the Cdh1 concentration control equation is as follows:

[0149]

[0150] Where: c Cdh1 is the current Cdh1 concentration of the cell grid; c npRB is the current npRB concentration of the unit grid; c cycCDK is the current cycCDK concentration of the cell grid; k Cdh1 , k′ Cdh1 is the related constant; J2, J3 are correction coefficients;

[0151] The cycCDK concentration of the cell grid after the preset time t is predicted based on the current Cdh1 concentration, current cycCDK concentration, current p27 concentration and the cycCDK concentration control equation of the cell grid; cycCDK is a key driving factor of the cell cycle, and the cycCDK concentration is negatively regulated by the Cdh1 concentration and p27 concentration, so the cycCDK concentration control equation is as follows

[0152]

[0153] Where: k c1 , k c2 , k c3 , k c4 is the correlation constant; c cycCDK is the current cycCDK concentration of the cell grid; c p27 is the current p27 concentration of the cell grid;

[0154] The p27 concentration of the cell grid after a preset time t is predicted based on the current oxygen concentration of the cell grid, the current p27 concentration, and the p27 concentration control equation. p27 is an inhibitory factor of the cell cycle, and the p27 degradation rate is positively correlated with the oxygen concentration. Therefore, the p27 concentration control equation is as follows:

[0155]

[0156] Where: k p27 , k′ p27 is a constant coefficient; J4 is the oxygen effect correction coefficient; c o is the current oxygen concentration of the unit grid;

[0157] The npRB concentration of the cell grid after a preset time t is predicted based on the current npRB concentration of the cell grid, the current cycCDK, and the npRB concentration control equation. npRB regulates the cell cycle process, and the npRB concentration is regulated by the cycCDK concentration. Therefore, the npRB concentration control equation is as follows:

[0158]

[0159] Among them, k n1 , k n2 , k n3 is a constant coefficient;

[0160] According to the predicted Cdh1 concentration, cycCDK concentration, and p27 concentration of the cell grid after the preset time t, the number of cells in the cell grid is increased or decreased; specifically:

[0161] When it is predicted that the Cdh1 concentration of the unit grid is less than the Cdh1 concentration threshold and the cycCDK concentration is greater than the cycCDK concentration threshold after the preset time t, the cells begin to divide and proliferate. If the current number of cells in the unit grid is less than the maximum number of cells (generally 4 units), the number of cells in the unit grid is increased by one unit, and the p27 concentration is reset to the initial value; if the current number of cells in the unit grid is equal to the maximum number of cells, the unit grid with a current number of cells less than the maximum number of cells is screened out from the eight unit grids adjacent to the unit grid in which the cells divide and proliferate, and the number of cells in the unit grid with the highest current oxygen concentration among the screened out unit grids is increased by one unit, and the p27 concentration is reset to the initial value; if no unit grid with a current number of cells less than the maximum number of cells is screened out, it means that there is no position for division and the division fails, and the cell number remains unchanged.

[0162] When the p27 concentration of the cell grid is predicted to be greater than the p27 concentration threshold after a preset time t, the cell enters a quiescent state; when entering the quiescent state, the cell grid starts a timer to begin counting the quiescent state maintenance time, which is then increased in each preset time step of the cell quiescent state maintenance time; when the cell quiescent state maintenance time exceeds a quiescent state maintenance time threshold, the cell undergoes apoptosis, the cell number is reset to zero, and the p27 concentration is reset to the initial state.

[0163] Step S400: Predict the oxygen concentration, p53 concentration, fibronectin concentration, and VEGF concentration of each cell in the two-dimensional discrete coordinate system after a preset time t based on the cell's current oxygen concentration, current cell attributes, current cell number, oxygen concentration control equation, current p53 concentration, p53 concentration control equation, current fibronectin concentration, fibronectin concentration control equation, current VEGF concentration, and VEGF diffusion reaction equation, and save the predictions under the corresponding cell information. In this embodiment of the present application, oxygen diffuses in space, and cells with blood vessels release oxygen based on permeability, while cells consume oxygen. The oxygen concentration control equation is as follows:

[0164]

[0165] Where: D o is the oxygen diffusion coefficient; c o is the current oxygen concentration of the unit grid; P o is the vascular permeability, which is a fixed coefficient; k(x, y) is the current number of cells in the unit grid; n(x, y) is the current unit grid attribute of the unit grid.

[0166] In the embodiment of the present application, in a hypoxic environment, the p53 concentration increases, and the p53 concentration control equation is as follows:

[0167]

[0168] Where: k p53 is the initial constant coefficient of p53; k′ p53 is the oxygen influence constant coefficient; C p53 is the oxygen effect correction factor;

[0169] Fibronectin is attached to the extracellular matrix and is an important substance for angiogenesis. The increase in fibronectin concentration depends on the presence of endothelial cells, while the decrease in fibronectin concentration depends on the uptake of fibronectin by endothelial cells. It can be seen that whether it increases or decreases depends on the cell grid whose cell grid attribute is a blood vessel, that is, it is related to the value of the vascular index function n(x, y, t) (i.e., n in the formula), that is, the cell grid attribute of the cell grid (x, y) at t = t0. Therefore, the control equation for the fibronectin concentration in the embodiment of the present application, which does not include the diffusion term, is:

[0170]

[0171] Where: c f is the current fibronectin concentration of the unit grid; the initial value has been set in step S200; ω is the production rate of fibronectin in endothelial cells, which is a fixed constant; μ is the uptake rate of fibronectin by endothelial cells, which is a fixed constant.

[0172] The growth factor diffuses in space, is transported in blood vessels, degraded and consumed, and is synthesized by p53. Oxygen negative feedback causes the concentration of the growth factor VEGF to decrease. The diffusion reaction equation of the growth factor VEGF in the embodiment of the present application is as follows:

[0173]

[0174] Where: c v is the current VEGF concentration of the unit grid; k v is the p53 promotion coefficient; J1 is the correction coefficient of the relationship between p53 and growth factor VEGF; k' v is the oxygen inhibition constant coefficient; D V is the VEGF diffusion coefficient; P V δ is the permeability of VEGF in blood vessels; V is the degradation rate of VEGF, which is a fixed constant; C v1 Corrected normal coefficients for oxygen effects.

[0175] Step S500: predict the movement direction of the blood vessel tip in the two-dimensional discrete coordinate system within the current time period t based on the fibronectin concentration after the preset time t of the unit grid, the growth factor concentration after the preset time t, and the control equation of the movement direction of the blood vessel tip, and save it under the information of the corresponding unit grid.

[0176] The dynamics of the vascular tip are influenced by the structure and chemical properties of the extracellular matrix. The direction of movement u of the vascular tip is related to the growth factor concentration c after time t. v and fibronectin concentration c after time t f The gradient of K is proportional to the properties of the extracellular matrix defined by K.

[0177] According to the gradient of growth factor VEGF concentration and fibronectin concentration, the control equation of the direction of blood vessel tip movement is:

[0178]

[0179] in: is the chemotactic parameter of growth factor VEGF; is the fibrin chemotaxis parameter; K is the extracellular matrix anisotropy tensor matrix, which is an intrinsic property of the matrix space of each extracellular unit grid (x, y)∈Ω and is independent of time. It is non-uniform and anisotropic in space. This property means that the extension direction of the tip cell (vascular tip) is not necessarily consistent with the direction of the growth factor concentration gradient or the fibronectin concentration gradient; the governing equation is:

[0180]

[0181] k a is the anisotropy parameter, representing the resistance to movement along a certain direction; k cond Heterogeneity parameter; v x and v y is the component of the unit vector v that describes the orientation of the extracellular matrix at the unit grid (x, y). At each unit grid (x, y), is a regular equation, randomly generating v x and v y , and is fixed at all times. Similarly, for each position (x, y)∈Ω, k cond and k a Also randomly generated.

[0182] Step S600: Predict the first movement speed of each blood vessel tip in the two-dimensional discrete coordinate system when moving in the first movement direction based on the fibronectin concentration at the blood vessel tip after t time, the first movement direction, and the control equation for the blood vessel tip movement speed. Also, predict the second movement speed of each blood vessel tip in the two-dimensional discrete coordinate system when moving in the second movement direction based on the fibronectin concentration at the blood vessel tip after t time, the second movement direction, and the control equation for the blood vessel tip movement speed, and save the information under the corresponding unit grid; wherein the first movement direction is the movement direction of the blood vessel tip during the current t time period; and the second movement direction is the movement direction of the blood vessel tip during the previous t time period. In this embodiment of the present application, the control equation for the blood vessel tip movement speed is as follows:

[0183]

[0184] in:

[0185] P is the velocity of the blood vessel tip;

[0186] k p is the rate of vascular tip division, which is related to the concentration of growth factor VEGF c v Related.

[0187]

[0188] l e is a constant, the length of the endothelial cell;

[0189] t c The cell division cycle is determined by the concentration of growth factor VEGF c v Determine that the control equation is as follows:

[0190]

[0191] τ is a constant, the cell proliferation time coefficient;

[0192] is the average growth factor (VEGF) concentration; the sum of the growth factor concentrations of all unit grids in the two-dimensional discrete coordinate system at the current time is divided by the total number of unit grids, and is calculated once for each time period t;

[0193] c v is the current concentration of growth factor VEGF;

[0194] c vlim is the threshold concentration of growth factor. When the VEGF concentration is higher than this value, the equation begins to work. It represents the critical time t c Depends on the current VEGF concentration c v and average concentration When the VEGF concentration c v Greater than the threshold c vlim When the critical time t c It will be calculated according to this equation.

[0195] Step S700: Calculate a first predicted extension distance of each blood vessel tip in a two-dimensional discrete coordinate system in a first direction of motion based on the discrete coordinates (x0, y0) of the corresponding unit grid of the blood vessel tip and the first motion velocity, and calculate a second predicted extension distance of each blood vessel tip in a second direction of motion based on the discrete coordinates (x0, y0) of the corresponding unit grid of the blood vessel tip and the second motion velocity, and save the calculations in the corresponding unit grid information; wherein the predicted extension distance is the total number of unit grids that the blood vessel tip passes through when it starts moving from the discrete coordinates (x0, y0) of the blood vessel tip in the corresponding direction of motion at the corresponding motion velocity and reaches the end coordinates (x1, y1) after t time, under the premise that no blood vessel branching or fusion occurs during extension. In this embodiment of the present application, step S700 specifically includes:

[0196] According to the movement speed of the blood vessel tip (which can be the first movement speed or the second movement speed), the vector (x p ,y p ) and the discrete coordinates (x0, y0) of the cell grid corresponding to the blood vessel tip to calculate the end point coordinates (x1, y1) of the cell grid this extension; where x1 = x0 + x p , y1=y0+y p ;

[0197] The Bresenham algorithm is used to calculate the discrete coordinates of the unit grids passing through the straight line connecting the discrete coordinates (x0, y0) of the unit grid corresponding to the blood vessel tip to the end point coordinates (x1, y1) of the current extension of the blood vessel tip, and these passed discrete coordinates of the unit grids are used as the predicted extension distance of the blood vessel tip (x0, y0) in the corresponding movement direction (the first predicted extension distance when the movement speed is the first movement speed, and the second predicted extension distance when the movement speed is the second movement speed).

[0198] Step S800: Perform an extension simulation for each blood vessel tip in the two-dimensional discrete coordinate system within a current time period t based on the first movement direction of the blood vessel tip, the existence time of the blood vessel tip, the second movement direction of the blood vessel tip, the first movement speed, the second movement speed, the first predicted extension distance, and the second predicted extension distance. The unit cell attributes and the existence time of each unit cell in the two-dimensional discrete coordinate system are updated as the extension simulation of each blood vessel tip is performed. The simulation time is updated when the extension simulation of all blood vessel tips in the two-dimensional discrete coordinate system is completed. The extension simulation includes blood vessel extension, blood vessel branching that occurs during blood vessel extension, and blood vessel fusion that occurs during blood vessel extension.

[0199] Blood vessel branching occurs when a single blood vessel tip splits into two new ones. This is an important mechanism for the formation of new blood vessels during angiogenesis. When branching occurs, a single blood vessel tip becomes two new ones. In this example, to simulate this process, the following definitions are defined:

[0200] (1) The conditions for vascular branching are as follows:

[0201] 1. The existence time of the blood vessel tip is greater than a preset blood vessel tip existence time threshold τ a ;

[0202] 2. Unit velocity vector of the blood vessel tip during this time period t The angle change between the angle between the positive (or negative) direction of the x-axis of the coordinate system and the unit velocity vector of the blood vessel tip (i.e., the original motion direction of the blood vessel tip) and the positive (or negative) direction of the x-axis of the coordinate system in the last time period t is greater than the preset angle threshold τ u .

[0203] (2) When both conditions for vascular branching are met simultaneously, vascular branching at the vascular tip is simulated as follows:

[0204] A new vascular tip is generated from an existing vascular tip, that is, the same unit grid with the vascular tip attribute has two vascular tip extension attributes, that is, the movement direction of the vascular tip corresponding to the unit grid in the current time period t is set to the first movement direction and the second movement direction, and starting from the vascular tip where the vascular branch occurs, it is extended in the original movement direction (second movement direction) according to the second predicted extension distance; and it is extended in the newly predicted movement direction (first movement direction) according to the first predicted extension distance.

[0205] Vascular fusion occurs when two vascular tips, or one vascular tip, meet and fuse with another. In tip-to-tip fusion, both or only one of the vascular tips may disappear, depending on the specific circumstances. In tip-to-tip fusion, the vascular tip disappears as part of a ring, no longer extending, meaning the tip no longer exists. To simulate this process, the following definitions are defined in this embodiment:

[0206] (1) The conditions for vascular fusion are as follows:

[0207] Among the unit grids included in the predicted extension distance of the blood vessel tip (including the first predicted extension distance and / or the second predicted extension distance), there are unit grids whose unit grid attributes are blood vessels and / or blood vessel tips.

[0208] (2) When the vascular fusion conditions are met, vascular fusion occurs at the simulated vascular tip as follows:

[0209] In the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point on the corresponding predicted extension distance (the order of the unit grids and unit grid attributes on the predicted extension distance and the actual extension distance mentioned in this embodiment is in this order), the blood vessel tip is sequentially fused with the blood vessel and the blood vessel tip on the predicted extension distance, and extended according to the actual extension distance of the blood vessel tip after the blood vessel fusion, until the extension simulation of the blood vessel tip in this time period t ends. The actual extension distance is all unit grids (including the unit grid (x0, y0) to which the blood vessel tip belongs) passes from the discrete coordinates (x0, y0) of the blood vessel tip to the end of the extension simulation after blood vessel branching and / or blood vessel fusion occurs during the process of the blood vessel tip starting from the discrete coordinates (x0, y0) of the blood vessel tip in the corresponding movement direction and at the corresponding movement speed according to the corresponding predicted extension distance. In this embodiment of the present application, the blood vessel tip is fused with the blood vessel and the blood vessel tip on the predicted extension distance, and extended according to the actual extension distance of the blood vessel tip after the blood vessel fusion includes:

[0210] 1. If the vessel fused with the vessel tip is within the predicted extension distance (the first predicted extension distance and / or the second predicted extension distance), it means that the vessel tip needs to disappear at the unit grid where the vessel is located, and the extension of the vessel tip will also stop at the unit grid where the vessel is located. That is, the actual extension distance of the vessel tip is set to the unit grid to which the vessel tip belongs and all unit grids before the unit grid to which the vessel tip fused with the vessel tip within the predicted extension distance (including the unit grid to which the vessel belongs). The vessel tip existence time of the vessel tip is reset to zero and the timing is stopped. The unit grid attributes of all unit grids within the actual extension distance are changed to vessels, and the extension simulation of the vessel tip within this time period t is terminated.

[0211] 2. If the vessel tip that undergoes vascular fusion is the vessel tip at the predicted extension distance (the first predicted extension distance and / or the second predicted extension distance), vascular fusion is performed based on the movement direction of the vessel tip and the movement direction of the vessel tip at the predicted extension distance, specifically:

[0212] (1) If the angle between the movement direction of the vascular tip (which can be the first movement direction or the second movement direction) and the movement direction of the vascular tip at the corresponding predicted extension distance (which can be the first predicted extension distance or the second predicted extension distance) is greater than or equal to 90 degrees, it is considered that both tips become inactive. At this time, the vascular tip where the vascular fusion occurs and the vascular tip at its predicted extension distance will disappear, that is, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids before the unit grid to which the vascular tip belongs where the vascular fusion occurs at the predicted extension distance. The vascular tip existence time of the vascular tip and the vascular tip at the predicted extension distance is cleared and the timing is stopped. The unit grid attributes of all unit grids at the actual extension distance are changed to blood vessels, and the extension simulation of the vascular tip in this time period t is ended.

[0213] (2) If the angle between the movement direction of the vascular tip and the movement direction of the vascular tip at the corresponding predicted extension distance is less than 90 degrees, it is considered that only one of the two vascular tips that have fused has become inactive. One vascular tip is randomly selected to continue extending at the corresponding predicted extension distance, and the other vascular tip stops extending at the unit grid where the two vascular tips have fused. Since the two tips are in the same position in the model (i.e., the unit grid where the two vascular tips have fused), the choice of which tip becomes inactive will not affect the determinism of the model.

[0214] If the vascular tip is randomly selected for extension, the vascular tip on the predicted extension distance stops extending; when there is no more blood vessel or vascular tip after the vascular tip on the predicted extension distance that merges with the vascular tip on the corresponding predicted extension distance, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids included in the predicted extension distance of the vascular tip, and the vascular tip existence time of the vascular tip and the vascular tip on the predicted extension distance that merges with it is cleared and the timing is stopped, the unit grid attribute of the last unit grid on the actual extension distance is changed to the vascular tip and the timer is started to record the vascular tip existence time from the initial value and the other unit grids on the actual extension distance are reset. The cell mesh attributes of the remaining cell meshes are changed to blood vessels; the extension simulation of the blood vessel tip within the current time period t is terminated; when there are still blood vessels and / or blood vessel tips after the blood vessel tip at the predicted extension distance that is fused with the blood vessel tip at the corresponding predicted extension distance, the blood vessel tip continues to fuse with the blood vessel and blood vessel tip at the predicted extension distance, and extends according to the actual extension distance of the blood vessel tip after blood vessel fusion, until the extension simulation of the blood vessel tip within the current time period t is terminated; wherein, the initial value of the timer of the last cell mesh at the actual extension distance is the existence time of the blood vessel tip before the blood vessel tip is cleared if no blood vessel branching occurs, and the initial value is zero if a blood vessel branching occurs;

[0215] If the vascular tip is randomly selected to stop extending, the vascular tip is extended at the predicted extension distance where the vascular tip fuses; the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids before the unit grid to which the vascular tip belongs at the predicted extension distance where the vascular tip fuses (excluding the unit grid to which the vascular tip belongs at the predicted extension distance), and the vascular tip existence time of the vascular tip is cleared and the timing is stopped, and the attributes of all unit grids at the actual extension distance are changed to blood vessels, ending the extension simulation of the vascular tip within this t time period; regardless of whether the vascular tip at the predicted extension distance where the vascular tip fuses has completed the extension simulation within this t time period, the vascular tip extension simulation continues, and it has no effect on it.

[0216] In the embodiment of the present application, in order to simulate the process of blood vessel extension, the following definition is given:

[0217] Each blood vessel tip in the two-dimensional discrete coordinate system is sequentially extended within the current time period t by simulation. The extension simulation of the blood vessel tip within the current time period t includes:

[0218] Determine whether vascular branching occurs at the vascular tip;

[0219] If no branching occurs at the vascular tip, it is determined whether vascular fusion occurs at the vascular tip within the first predicted extension distance. If no vascular fusion occurs, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids within the first predicted extension distance. The current vascular tip existence time of the vascular tip is used as the initial value of the timer for the last unit grid within the actual extension distance. The vascular tip existence time of the vascular tip is reset and the timer is stopped. The unit grid attribute of the last unit grid within the actual extension distance is changed to vascular tip, and the timer is started to record the vascular tip existence time from the initial value. The unit grid attributes of the remaining unit grids within the actual extension distance are changed to blood vessels, and the extension simulation of the vascular tip within the current time period t is terminated. If vascular fusion occurs, the vascular tip is sequentially fused with the blood vessels and the vascular tip within the first predicted extension distance in the order from the discrete coordinates of the vascular tip to the end point coordinates within the first predicted extension distance. The vascular tip is then extended according to the actual extension distance of the vascular tip after vascular fusion, until the extension simulation of the vascular tip within the current time period t is terminated.

[0220] If a blood vessel branch occurs at the tip of the blood vessel, the tip of the blood vessel is extended in the second movement direction according to the second predicted extension distance and the tip of the blood vessel is extended in the first movement direction according to the first predicted extension distance; wherein:

[0221] The extending of the blood vessel tip in the first movement direction according to the first predicted extension distance specifically includes:

[0222] determining whether vascular fusion occurs at the tip of the blood vessel at the first predicted extension distance;

[0223] If blood vessel fusion does not occur, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids in the first predicted extension distance, the blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped, the unit grid attribute of the last unit grid in the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero, and the unit grid attributes of the remaining unit grids in the actual extension distance are changed to blood vessel, and the extension simulation of the blood vessel tip in this time period t is ended;

[0224] If vessel fusion occurs, the vessel tip is sequentially fused with the vessels and vessel tips at the first predicted extension distance in the order from the discrete coordinates of the vessel tip to the coordinates of the end point at the first predicted extension distance, and the vessel tip is extended according to the actual extension distance of the vessel tip after vessel fusion until the extension simulation of the vessel tip in this time period t is completed;

[0225] The extending of the second movement direction of the blood vessel tip according to the second predicted extension distance specifically includes:

[0226] determining whether vascular fusion occurs at the tip of the blood vessel at the second predicted extension distance;

[0227] If blood vessel fusion does not occur, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids within the second predicted extension distance. The blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid within the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero. The unit grid attributes of the remaining unit grids within the actual extension distance are changed to blood vessels, and the extension simulation of the blood vessel tip within the current time period t is terminated.

[0228] If vessel fusion occurs, the vessel tip is sequentially fused with the vessels and vessel tips on the second predicted extension distance in the order from the discrete coordinates of the vessel tip to the coordinates of the end point on the second predicted extension distance, and the vessel tip is extended according to the actual extension distance of the vessel tip after vessel fusion until the extension simulation of the vessel tip in this time period t is completed.

[0229] like Figure 2 As shown, in this embodiment, step S800 includes the following steps:

[0230] Step S801: Determine whether a blood vessel branch occurs during the extension simulation of the blood vessel tip within this time period t based on the first movement direction of the blood vessel tip, the existence time of the blood vessel tip, the second movement direction of the blood vessel tip, and the blood vessel branching condition. If a blood vessel branch occurs, execute step S811; otherwise, execute step S821.

[0231] Step S811, the blood vessel tip is extended according to the first predicted extension distance and the second predicted extension distance respectively, and then steps S812 and S813 are executed;

[0232] Step S812: determining whether vascular fusion occurs when the vascular tip extends according to the first predicted extension distance based on the unit grid attributes of each unit grid and the vascular fusion condition; if vascular fusion occurs, executing step S814; otherwise, executing step S815;

[0233] Step S813: determining whether vascular fusion occurs when extending according to the second predicted extension distance based on the unit grid attributes and the vascular fusion condition of each unit grid at the second predicted extension distance; if vascular fusion occurs, executing step S816; otherwise, executing step S817;

[0234] Step S814: The blood vessel tip is sequentially fused with the blood vessels and blood vessel tips within the first predicted extension distance in the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point within the first predicted extension distance. The blood vessel tip is then extended according to the actual extension distance of the blood vessel tip after fusion, until the extension simulation of the blood vessel tip within the current time period t is completed. Then, step S802 is executed.

[0235] Step S815: The actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids within the first predicted extension distance. The blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid within the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero. The unit grid attributes of the remaining unit grids within the actual extension distance are changed to blood vessel, and the extension simulation of the blood vessel tip within the current time period t is terminated. Then, step S802 is executed.

[0236] Step S816: The blood vessel tip is sequentially fused with the blood vessels and blood vessel tips within the second predicted extension distance in the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point within the second predicted extension distance. The blood vessel tip is extended according to the actual extension distance of the blood vessel tip after fusion, until the extension simulation of the blood vessel tip within the current time period t is completed; then, step S802 is executed.

[0237] Step S817: The actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids within the second predicted extension distance. The blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid within the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero. The unit grid attributes of the remaining unit grids within the actual extension distance are changed to blood vessel, and the extension simulation of the blood vessel tip within the current time period t is terminated. Then, step S802 is executed.

[0238] Step S821: Determine whether vascular fusion occurs at the tip of the blood vessel within the first predicted extension distance. If vascular fusion does not occur, execute step S822; otherwise, execute step S823.

[0239] Step S822: The blood vessel tip is sequentially fused with the blood vessels and blood vessel tips within the first predicted extension distance in the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point within the first predicted extension distance. The blood vessel tip is then extended according to the actual extension distance of the blood vessel tip after fusion, until the extension simulation of the blood vessel tip within the current time period t is completed. Then, step S802 is executed.

[0240] Step S823: The actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids within the first predicted extension distance. The current blood vessel tip existence time of the blood vessel tip is used as the initial value of the timer for the last unit grid within the actual extension distance. The blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid within the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from the initial value. The unit grid attributes of the remaining unit grids within the actual extension distance are changed to blood vessels. The extension simulation of the blood vessel tip within the current time period t is terminated, and then step S802 is executed.

[0241] Step S802: Determine whether all vascular tips in the two-dimensional discrete coordinate system have completed the extension simulation within the current time period t. If so, execute step S803; otherwise, extend the next vascular tip in the two-dimensional discrete coordinate system within the current time period t and execute step S801.

[0242] Step S803 , the simulation time T is added to the preset time t, and the unit grid properties of each unit grid in the two-dimensional discrete coordinate system after the time t are saved, and then step S804 is executed.

[0243] Step S804: Determine whether the simulation termination condition has been met. If the simulation termination condition has been met, output the simulation results and terminate; otherwise, enter the next extended simulation for a time period t, and repeat the above process starting from step S300; wherein the simulation results include but are not limited to the simulation time T, the initial values ​​of the patient, the initial value of the oxygen concentration, the unit grid attributes of each unit grid in the two-dimensional discrete coordinate system after the last extension within the time period t, and the unit grid attributes of each unit grid in the two-dimensional discrete coordinate system after each extension within the time period t. The simulation termination condition can be a preset simulation time threshold, or a simulation time T input by the user according to needs, or the percentage of unit grids in the two-dimensional discrete coordinate system that are blood vessels to the total number of unit grids in the two-dimensional discrete coordinate system, and the embodiments of the present application do not limit this.

[0244] The embodiments of the present application provide a method for simulating the tumor blood vessel growth process, establishing a mathematical model that includes oxygen concentration, VEGF dynamics, and tumor cell proliferation, death, and competition. This method not only can more comprehensively and accurately describe the tumor blood vessel growth process, but also provides important and reliable theoretical support and technical means for studying the mechanism of tumor blood vessel growth, revealing the root cause of the disease, and anti-angiogenic treatment. Moreover, by dynamically simulating the tumor blood vessel growth process at different stages, the present application can predict disease progression and the effects of different treatment methods, optimize treatment strategies at different stages, and improve treatment efficacy. In addition, considering the different Cdh1 concentrations, cycCDK concentrations, npRB concentrations, p27 concentrations, p53 concentrations, and oxygen supply status of individual patients, a personalized simulation model is established for different patients, realizing personalized disease prediction and treatment plan optimization.

[0245] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A method for simulating the growth process of tumor blood vessels, characterized in that: The following steps are involved: Step S100: constructing a two-dimensional discrete coordinate system based on the two-dimensional model of the patient's tumor, and defining a vascular index function n(x, y, t) that describes and records the unit grid attributes of each unit grid in the two-dimensional discrete coordinate system at each preset time t; wherein the unit grid attributes include blood vessels, blood vessel tips, and the environment; Step S200, initializing the cell grid properties, cell number, Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration, fibronectin concentration, and growth factor concentration of each cell grid in the two-dimensional discrete coordinate system according to the patient's examination results; Step S300, predicting the number of cells in each unit grid in the two-dimensional discrete coordinate system after a preset time t based on the current Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, oxygen concentration of the unit grid and the cell number control model; Step S400, predicting the oxygen concentration, p53 concentration, fibronectin concentration, and VEGF concentration of each unit grid in the two-dimensional discrete coordinate system after a preset time t based on the current oxygen concentration, unit grid properties, cell number, p53 concentration, fibronectin concentration, and VEGF concentration of the unit grid, as well as the oxygen concentration control equation, the p53 concentration control equation, the fibronectin concentration control equation, and the VEGF diffusion reaction equation; Step S500, predicting the movement direction of each blood vessel tip in the two-dimensional discrete coordinate system within the current time period t based on the fibronectin concentration of the unit grid after time t, the growth factor concentration after time t, and the blood vessel tip movement direction control equation; Step S600: Predicting a first motion velocity of each blood vessel tip in a two-dimensional discrete coordinate system when moving in a first motion direction based on a governing equation for the fibronectin concentration at the blood vessel tip after time t, the first motion direction, and the motion velocity of the blood vessel tip; and predicting a second motion velocity of each blood vessel tip in a two-dimensional discrete coordinate system when moving in a second motion direction based on a governing equation for the fibronectin concentration at the blood vessel tip after time t, the second motion direction, and the motion velocity of the blood vessel tip; wherein the first motion direction is the motion direction of the blood vessel tip during the current time period t; and the second motion direction is the motion direction of the blood vessel tip during the previous time period t. Step S700, calculating a first predicted extension distance of each blood vessel tip in a two-dimensional discrete coordinate system in a first motion direction based on the discrete coordinates (x0, y0) of the blood vessel tip and a first motion speed, and calculating a second predicted extension distance of each blood vessel tip in a second motion direction based on the discrete coordinates (x0, y0) of the blood vessel tip and a second motion speed; wherein the first predicted extension distance or the second predicted extension distance is the distance that the blood vessel tip moves in the first motion direction or the second motion direction at the first motion speed or the second motion speed starting from the discrete coordinates (x0, y0) of the unit grid to which the blood vessel tip belongs, and reaching the end coordinate after a preset time t. All cell grids passed; Step S800: Perform an extension simulation on each blood vessel tip in the two-dimensional discrete coordinate system within the current time period t based on the first movement direction of the blood vessel tip, the existence time of the blood vessel tip, the second movement direction of the blood vessel tip, the first movement speed, the second movement speed, the first predicted extension distance, and the second predicted extension distance. The unit grid attributes and the existence time of the blood vessel tip of each unit grid in the two-dimensional discrete coordinate system are updated as the extension simulation of each blood vessel tip is performed. The simulation time is updated when the extension simulation of all blood vessel tips in the two-dimensional discrete coordinate system is completed. The extension simulation includes blood vessel extension, blood vessel branching that occurs during blood vessel extension, and blood vessel fusion that occurs during blood vessel extension.

2. The method according to claim 1, characterized in that The cell number control model includes: Predicting the Cdh1 concentration of the unit grid after a preset time t based on the current Cdh1 concentration of the unit grid, the current cycCDK concentration, the current npRB concentration, and the Cdh1 concentration control equation; Predicting the cycCDK concentration of the unit grid after a preset time t based on the current Cdh1 concentration, the current cycCDK concentration, the current p27 concentration and the cycCDK concentration control equation of the unit grid; Predict the p27 concentration of the unit grid after a preset time t based on the current oxygen concentration of the unit grid, the current p27 concentration and the p27 concentration control equation; Predict the npRB concentration of the unit grid after a preset time t based on the current npRB concentration of the unit grid, the current cycCDK and the npRB concentration control equation; According to the predicted Cdh1 concentration, cycCDK concentration, and p27 concentration of the cell grid after the preset time t, the number of cells in the cell grid is increased or decreased; specifically: When it is predicted that the Cdh1 concentration of the unit grid is less than the Cdh1 concentration threshold and the cycCDK concentration is greater than the cycCDK concentration threshold after the preset time t, if the current cell number of the unit grid is less than the maximum carrying cell number, the cell number of the unit grid is increased by one unit, and the p27 concentration is reset to the initial value; if the current cell number of the unit grid is equal to the maximum carrying cell number, the unit grid with a current cell number less than the maximum carrying cell number is screened out from the eight unit grids adjacent to the unit grid, and the cell number of the unit grid with the highest current oxygen concentration among the screened unit grids is increased by one unit, and the p27 concentration is reset to the initial value; if no unit grid with a current cell number less than the maximum carrying cell number is screened out, the cell number remains unchanged; When the p27 concentration of the cell grid is predicted to be greater than the p27 concentration threshold after the preset time t, the cell grid starts the timer to start counting the static state maintenance time; when the static state maintenance time of the cell exceeds a static state maintenance time threshold, the cell number is cleared and the p27 concentration is reset to the initial state.

3. The method according to claim 2, characterized in that The Cdh1 concentration control equation is as follows: in: is the current Cdh1 concentration of the cell grid; is the current npRB concentration of the cell grid; is the current cycCDK concentration of the cell grid; is the correlation constant; is the correction factor; The cycCDK concentration control equation is as follows: in: is the correlation constant; is the current cycCDK concentration of the cell grid; is the current p27 concentration of the cell grid; The p27 concentration control equation is as follows: in: is a constant coefficient; is the oxygen effect correction factor; is the current oxygen concentration of the unit grid; The npRB concentration control equation is as follows: in, is a constant coefficient.

4. The method according to claim 3, characterized in that The oxygen concentration control equation is as follows: in: is the oxygen diffusion coefficient; is the current oxygen concentration of the unit grid; is vascular permeability, which is a fixed coefficient; is the current number of cells in the unit grid; The current cell grid properties of the cell grid; The p53 concentration control equation is as follows: in: is the initial constant coefficient of p53; is the oxygen influence constant coefficient; is the oxygen effect correction factor; The governing equation for the fibronectin concentration is: in: is the current fibronectin concentration of the cell grid; is the production rate of fibronectin in endothelial cells, which is a fixed constant; is the uptake rate of fibronectin by endothelial cells, which is a fixed constant; The growth factor VEGF diffusion reaction equation is: in: is the current VEGF concentration of the unit grid; is the p53 promotion coefficient; is the correction coefficient for the relationship between p53 and growth factor VEGF; is the oxygen inhibition constant coefficient; is the VEGF diffusion coefficient; The permeability of VEGF in blood vessels; is the VEGF degradation rate, which is a fixed constant; Corrected normal coefficients for oxygen effects.

5. The method according to claim 4, characterized in that The control equation for the direction of movement of the blood vessel tip is as follows: in: is the chemotactic parameter of growth factor VEGF; is the fibrin chemotaxis parameter; is the extracellular matrix anisotropy tensor matrix, which is an intrinsic property of the matrix space of each extracellular unit grid (x, y)∈Ω and is independent of time. It is non-uniform and anisotropic in space. This property means that the extension direction of the tip cell is not necessarily consistent with the direction of the growth factor concentration gradient or the fibronectin concentration gradient. The governing equation is: is the anisotropy parameter, representing the resistance to movement along a certain direction; Heterogeneity parameters; and is the description unit grid The unit vector of the extracellular matrix orientation at Component, in each unit grid ,by is a regular equation, randomly generated and , and at all times Fixed; for each unit grid ∈ Ω, and Also randomly generated.

6. The method according to claim 4, characterized in that The control equation of the blood vessel tip movement speed is as follows: in: P is the velocity of the blood vessel tip; is the rate of vascular tip division and is related to the concentration of growth factor VEGF Related; is the unit velocity vector of the blood vessel tip; is a constant, the length of the endothelial cell; For the cell division cycle, the concentration of growth factor VEGF Determine that the control equation is as follows: is a constant, the cell proliferation time coefficient; is the average growth factor (VEGF) concentration; the sum of the growth factor concentrations of all unit grids in the two-dimensional discrete coordinate system at the current time is divided by the total number of unit grids, and is calculated once for each time period t; is the current concentration of growth factor VEGF; is the threshold concentration of growth factors.

7. The method according to claim 4, characterized in that The step S700 includes the following steps: The vectors in the x and y directions according to the velocity of the blood vessel tip and the discrete coordinates of the vessel tip Calculate the coordinates of the end point of this extension of the cell grid ; where x1=x0+x p , y1=y0+y p ; The movement speed is the first movement speed or the second movement speed; Use Bresenham algorithm to calculate the discrete coordinates of the blood vessel tip The coordinates of the end point of this extension to the blood vessel tip The discrete coordinates of the unit grids passed by this straight line are used as the vascular tip. The predicted extension distance within this time period t; the predicted extension distance is the first predicted extension distance or the second predicted extension distance.

8. The method according to claim 7, characterized in that The conditions for the vascular tip to branch when extending include: The vessel existence time of the vessel tip is greater than a preset vessel tip existence time threshold ; The unit velocity vector of the blood vessel tip during this time period t The angle change between the angle between the positive direction of the x-axis of the coordinate system and the angle between the unit velocity vector of the blood vessel tip and the positive direction of the x-axis of the coordinate system in the last time period t is greater than the preset angle threshold ; When the two conditions for vascular branching are met at the same time, the process of vascular branching at the vascular tip is simulated as follows: Starting from the tip of the blood vessel where the blood vessel branch occurs, the blood vessel is extended in the second movement direction according to the second predicted extension distance and in the first movement direction according to the first predicted extension distance; The conditions for vascular fusion to occur when the vascular tip extends include: Among the cell grids included in the blood vessel tip prediction extension distance, there are cell grids whose cell grid attributes are blood vessels and / or blood vessel tips; When the vascular fusion conditions are met, the vascular fusion process at the vascular tip is simulated including: According to the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point on the corresponding predicted extension distance, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the predicted extension distance, and the blood vessel tip is extended according to the actual extension distance after the blood vessel fusion, until the extension simulation of the blood vessel tip in this time period t is completed; The blood vessel tip extending the blood vessel comprises: Each blood vessel tip in the two-dimensional discrete coordinate system is sequentially extended within the current time period t by simulation, wherein the blood vessel tip extension simulation within the current time period t is: Determine whether vascular branching occurs at the vascular tip; If no branching occurs at the vascular tip, it is determined whether vascular fusion occurs at the vascular tip within the first predicted extension distance. If no vascular fusion occurs, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids within the first predicted extension distance. The current vascular tip existence time of the vascular tip is used as the initial value of the timer for the last unit grid within the actual extension distance. The vascular tip existence time of the vascular tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid within the actual extension distance is changed to vascular tip, and the timer is started to record the vascular tip existence time from the initial value. The unit grid attributes of the remaining unit grids within the actual extension distance are changed to blood vessels, and the extension simulation of the vascular tip within the current time period t is terminated. If vascular fusion occurs, the vascular tip is sequentially fused with the blood vessels and the vascular tip within the first predicted extension distance in the order from the discrete coordinates of the vascular tip to the end point coordinates within the first predicted extension distance. The vascular tip is extended according to the actual extension distance of the vascular tip after vascular fusion until the extension simulation of the vascular tip within the current time period t is terminated. If a blood vessel branch occurs at the tip of the blood vessel, the tip of the blood vessel is extended in the second movement direction according to the second predicted extension distance and the tip of the blood vessel is extended in the first movement direction according to the first predicted extension distance; wherein: The extending of the blood vessel tip in the first movement direction according to the first predicted extension distance specifically includes: determining whether vascular fusion occurs at the tip of the blood vessel at the first predicted extension distance; If blood vessel fusion does not occur, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids in the first predicted extension distance, the blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped, the unit grid attribute of the last unit grid in the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero, and the unit grid attributes of the remaining unit grids in the actual extension distance are changed to blood vessel, and the extension simulation of the blood vessel tip in this time period t is ended; If vessel fusion occurs, the vessel tip is sequentially fused with the vessels and vessel tips at the first predicted extension distance in the order from the discrete coordinates of the vessel tip to the coordinates of the end point at the first predicted extension distance, and the vessel tip is extended according to the actual extension distance of the vessel tip after vessel fusion until the extension simulation of the vessel tip in this time period t is completed; The extending of the second movement direction of the blood vessel tip according to the second predicted extension distance specifically includes: determining whether vascular fusion occurs at the tip of the blood vessel at the second predicted extension distance; If blood vessel fusion does not occur, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids on the second predicted extension distance, and the blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped. The unit grid attribute of the last unit grid on the actual extension distance is changed to blood vessel tip, and the timer is started to record the blood vessel tip existence time from zero. The unit grid attributes of the remaining unit grids on the actual extension distance are changed to blood vessels, and the extension simulation of the blood vessel tip in this time period t is ended. If vessel fusion occurs, the vessel tip is sequentially fused with the vessels and vessel tips on the second predicted extension distance in the order from the discrete coordinates of the vessel tip to the coordinates of the end point on the second predicted extension distance, and the vessel tip is extended according to the actual extension distance of the vessel tip after vessel fusion until the extension simulation of the vessel tip in this time period t is completed.

9. The method according to claim 8, characterized in that The vascular tip is fused with the blood vessel and the vascular tip at the predicted extension distance, and extended according to the actual extension distance of the vascular tip after the vascular fusion, including: If the vessel fused with the blood vessel tip is within the predicted extension distance, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids before the unit grid to which the blood vessel tip belongs within the predicted extension distance, the blood vessel tip existence time of the blood vessel tip is reset to zero and the timer is stopped, and the unit grid attributes of all unit grids within the actual extension distance are changed to blood vessels, thereby ending the extension simulation of the blood vessel tip within the current time period t. If the blood vessel tip that undergoes vascular fusion is the blood vessel tip at the predicted extension distance, the blood vessel fusion is performed according to the movement direction of the blood vessel tip and the movement direction of the blood vessel tip at the predicted extension distance, specifically: If the angle between the movement direction of the blood vessel tip and the movement direction of the blood vessel tip at the corresponding predicted extension distance is greater than or equal to 90 degrees, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids before the unit grid to which the blood vessel fusion occurs at the predicted extension distance. The blood vessel tip existence time of the blood vessel tip and the blood vessel tip at the predicted extension distance is reset to zero and the timing is stopped. The unit grid attributes of all unit grids at the actual extension distance are changed to blood vessels, and the extension simulation of the blood vessel tip in this time period t is terminated. If the angle between the movement direction of the blood vessel tip and the movement direction of the blood vessel tip at the corresponding predicted extension distance is less than 90 degrees, if the blood vessel tip is randomly selected for extension, the blood vessel tip at the predicted extension distance stops extending; when there is no blood vessel or blood vessel tip after the blood vessel tip at the predicted extension distance that merges with the blood vessel tip at the corresponding predicted extension distance, the actual extension distance of the blood vessel tip is set to the unit grid to which the blood vessel tip belongs and all unit grids included in the predicted extension distance of the blood vessel tip, and the blood vessel tip existence time of the blood vessel tip and the blood vessel tip at the predicted extension distance that merges with it is cleared and the timing is stopped, the unit grid attribute of the last unit grid at the actual extension distance is changed to the blood vessel tip and the timer is started to count from the initial value Recording the existence time of the blood vessel tip and changing the unit grid attributes of the remaining unit grids in the actual extension distance to blood vessels, ending the extension simulation of the blood vessel tip in this time period t; when there are still blood vessels and / or blood vessel tips after the blood vessel tip in the predicted extension distance that merges with the blood vessel tip in the corresponding predicted extension distance, the blood vessel tip continues to fuse with the blood vessel and blood vessel tip in the predicted extension distance, and extends according to the actual extension distance of the blood vessel tip after blood vessel fusion, until the extension simulation of the blood vessel tip in this time period t is ended; wherein, the initial value of the timer of the last unit grid in the actual extension distance is the existence time of the blood vessel tip before the blood vessel tip is cleared if no blood vessel branch occurs, and the initial value is zero if a blood vessel branch occurs; If the vascular tip is randomly selected to stop extending, the vascular tip is extended at the predicted extension distance where the vascular tip merges with the vascular tip; the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all unit grids before the unit grid to which the vascular tip belongs at the predicted extension distance where the vascular tip merges with the vascular tip at the corresponding predicted extension distance, and the vascular tip existence time of the vascular tip is cleared and the timing is stopped, and the attributes of all unit grids at the actual extension distance are changed to blood vessels, ending the extension simulation of the vascular tip within this time period t.

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