Method for simulating tumor blood vessel growth process

Abstract

The invention discloses a method for simulating a tumor blood vessel growth process. The method comprises the following steps: constructing a two-dimensional discrete coordinate system based on a tumor two-dimensional model, and defining a blood vessel index function for describing unit grid attributes of unit grids; updating the cell number, the oxygen concentration, the fibronectin concentration and the growth factor concentration of each unit grid every preset time t; predicting the movement direction of the blood vessel tip in the t time period according to the fibronectin concentration and the growth factor concentration; calculating a first predicted extension distance and a second predicted extension distance according to the motion direction in the current t time period and the motion direction in the last t time period; and updating the unit grid attribute of each unit grid in the two-dimensional discrete coordinate system according to the movement direction in the t time period, the blood vessel existence time of the blood vessel tip and the movement extension distance calculated by the blood vessel tip. The oxygen concentration and the number of cells are incorporated into the tumor blood vessel growth model, and accurate simulation prediction of the tumor blood vessel growth process is achieved.

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 one of the core processes in the occurrence and development of cancer, and its progression is closely related to the oxygen supply and the formation of new blood vessels in the tumor microenvironment. Tumors consume a large amount of oxygen and nutrients through rapid proliferation, resulting in a state of hypoxia (low oxygen) in local tissues. The hypoxic environment induces tumor cells to secrete vascular endothelial growth factor (VEGF), promotes the formation of new blood vessels (angiogenesis), provides more oxygen and nutritional support for tumors, and further promotes tumor growth and invasion.

[0003] Studies have shown that the rapid growth of tumors not only depends on their intrinsic proliferation ability, but is also closely related to the dynamic regulation of oxygen concentration and VEGF in the tumor microenvironment. Although new blood vessels can temporarily improve the oxygen supply in the tumor, they are often abnormal, showing characteristics such as disordered vascular structure, increased permeability, and unstable blood flow. This immature vascular network will further aggravate the local hypoxia state, forming a vicious circle. It can be seen that the role of oxygen concentration and VEGF regulation in tumor growth is a decisive factor.

[0004] Currently, a large number of studies have been devoted to analyzing the pathological mechanisms of tumor growth and its microenvironment. Among them, VEGF, as a key angiogenic factor, has been widely studied for its role in abnormal blood vessel formation in tumors. However, most studies only focus on one aspect of the tumor microenvironment, such as oxygen concentration or VEGF secretion dynamics, and fail to fully combine multiple key processes such as oxygen diffusion, VEGF secretion, and tumor cell dynamic balance. Therefore, the existing models may deviate significantly from the actual situation when predicting the tumor growth process and evaluating the treatment effect. 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] The 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 blood vessel 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 environment;

[0009] Step S200, initializing the unit grid properties, cell number, Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration, fibronectin concentration and growth factor concentration of each unit 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 according to the current Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, oxygen concentration and cell number control model of the unit grid;

[0011] Step S400, predicting the oxygen concentration, p53 concentration, fibronectin concentration, and growth factor VEGF concentration of each unit grid in the two-dimensional discrete coordinate system after a preset time t according to the current oxygen concentration of the unit grid, unit grid properties, cell number, p53 concentration, fibronectin concentration, and growth factor VEGF concentration, as well as the oxygen concentration control equation, the p53 concentration control equation, the fibronectin concentration control equation, and the growth factor 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 according to the fibronectin concentration of the unit grid after t time, the growth factor concentration after t time, and the blood vessel tip movement direction control equation;

[0013] Step S600, predicting the first movement speed of each blood vessel tip in the two-dimensional discrete coordinate system when it moves in the first movement direction according to the control equation of the fibronectin concentration at the blood vessel tip after t time, the first movement direction and the movement speed of the blood vessel tip, and predicting the second movement speed of each blood vessel tip in the two-dimensional discrete coordinate system when it moves in the second movement direction according to the control equation of the fibronectin concentration at the blood vessel tip after t time, the second movement direction and the movement speed of the blood vessel tip; wherein the first movement direction is the movement direction of the blood vessel tip in the current t time period of the blood vessel tip; and the second movement direction is the movement direction of the blood vessel tip in the last t time period of the blood vessel tip;

[0014] Step S700: According to the discrete coordinates (x 0 ,y 0) and the first movement speed to calculate the first predicted extension distance of each blood vessel tip in the first movement direction in the two-dimensional discrete coordinate system, and the discrete coordinates (x 0 ,y 0 ) and the second movement speed to calculate the second predicted extension distance of each blood vessel tip in the two-dimensional discrete coordinate system in the second movement direction; wherein the first predicted extension distance or the second predicted extension distance is the distance from the blood vessel tip to the discrete coordinate (x) of the unit grid to which the blood vessel tip belongs in the first movement direction or the second movement direction at the first movement speed or the second movement speed. 0 ,y 0 ) starts moving and reaches the end coordinate (x 1 ,y 1 ) passes through all the unit grids;

[0015] Step S800, performing extension simulation on each blood vessel tip in the two-dimensional discrete coordinate system within this time period t according to 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, and updating the unit grid attributes and the blood vessel tip existence time of each unit grid in the two-dimensional discrete coordinate system with the extension simulation of each blood vessel tip, and updating the simulation time when all blood vessel tips in the two-dimensional discrete coordinate system complete the extension simulation; wherein the extension simulation includes blood vessel extension, blood vessel branching occurring during blood vessel extension and blood vessel fusion occurring during blood vessel extension.

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

[0017] Predict the Cdh1 concentration of the unit grid after a preset time t according to the current Cdh1 concentration of the unit grid, the current cycCDK concentration, the current npRB concentration and the Cdh1 concentration control equation;

[0018] Predict the cycCDK concentration of the unit grid after a preset time t according to 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 according to 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 prediction, the Cdh1 concentration, cycCDK concentration, and p27 concentration of the cell grid after the preset time t are obtained, 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 number of cells in the unit grid is less than the maximum number of cells, 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 selected from the eight unit grids adjacent to the unit grid, and the number of cells in the unit grid with the highest current oxygen concentration among the selected unit grids is increased by one unit, and the p27 concentration is reset to the initial value; if the unit grid with a current number of cells less than the maximum number of cells is not selected, the number of cells remains unchanged;

[0023] When it is predicted that the p27 concentration of the cell grid is 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] J 2 , J 3 is the correction factor;

[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] J 4 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 control equation of 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 constant coefficient;

[0072] J 1 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 is the permeability of VEGF in blood vessels;

[0076] δ V is the degradation rate of VEGF, 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 chemotaxis parameter of growth factor VEGF;

[0082] is the fibrin chemotaxis parameter;

[0083] K is the anisotropic tensor matrix of the extracellular 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, which 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 control 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 are the components of the unit vector v that describes the orientation of the extracellular matrix at the cell grid (x, y). is a regular equation, randomly generating v x and v y , and is 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 of the blood vessel tip movement speed 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 vRelated;

[0093]

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

[0095] t c is the cell division cycle, which is determined by the concentration of growth factor VEGF cν, and the control 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 divided by the total number of unit grids, calculated once in each time period t;

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

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

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

[0102] According to the velocity of the blood vessel tip in the x and y directions, the vector (x p ,y p ) and the discrete coordinates of the blood vessel tip (x 0 ,y 0 ) Calculate the end point coordinates (x 1 ,y 1 ), where x 1 =x 0 +x p ,y 1 =y 0 +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 (x 0 ,y 0 ) to the end point coordinate (x 1 ,y 1 ) and the discrete coordinates of the unit grids passed by the straight line are taken as the vascular tip (x 0 ,y 0) is a predicted extension distance within this 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 occurrence of vascular branching when the vascular tip is extended 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 in 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 of vascular branching are met at the same time, the process of simulating vascular branching at the vascular tip includes:

[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 is extended include:

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

[0111] When the vascular fusion conditions are met, the vascular fusion process of simulating the vascular tip includes:

[0112] According to the order from the discrete coordinates of the blood vessel tip to the corresponding end point coordinates on the predicted extension distance, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips 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 is completed;

[0113] The blood vessel tip performing blood vessel extension comprises:

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

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

[0116] If the vascular tip does not branch, determine whether the vascular tip has vascular fusion at the first predicted extension distance. If vascular fusion does not occur, set the actual extension distance of the vascular tip to the unit grid to which the vascular tip belongs and all unit grids at the first predicted extension distance, use the current vascular tip existence time of the vascular tip as the initial value of the last unit grid timer at the actual extension distance, reset the vascular tip existence time of the vascular tip to zero and stop timing, change the unit grid attribute of the last unit grid at the actual extension distance to the vascular tip, start the timer to record the vascular tip existence time from the initial value, and change the unit grid attributes of the remaining unit grids at the actual extension distance to the blood vessel, and end the extension simulation of the vascular tip in this t time period. If vascular fusion occurs, the vascular tip is sequentially fused with the blood vessel and the vascular tip at the first predicted extension distance in the order from the discrete coordinates of the vascular tip to the end point coordinates at the first predicted extension distance, and is extended according to the actual extension distance of the vascular tip after the vascular fusion, until the extension simulation of the vascular tip in this t time period is ended.

[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 the vascular fusion does not occur, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all the unit grids on the first predicted extension distance, and the vascular tip existence time of the vascular tip 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 zero, and 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 vascular tip in this time period t is ended;

[0121] If blood vessel fusion occurs, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the first predicted extension distance in the order from the discrete coordinates of the blood vessel tip to the end point coordinates on the first predicted extension distance, and the blood vessel tip is extended 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 terminated;

[0122] The second movement direction of the blood vessel tip extending 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 the vascular fusion does not occur, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all the unit grids on the second predicted extension distance, and the vascular tip existence time of the vascular tip 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 zero, and 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 vascular tip in this time period t is ended;

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

[0126] Optionally, the vascular tip is fused with the blood vessel and the vascular tip at the predicted extension distance, and the vascular tip is extended according to the actual extension distance of the vascular tip after the vascular fusion, including:

[0127] If the vessel fused with the blood vessel tip is on 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 fused with the blood vessel tip belongs on the predicted extension distance, the blood vessel tip existence time of the blood vessel tip is cleared and the timing is stopped, and the unit grid attributes of all 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;

[0128] If the blood vessel tip that undergoes blood vessel fusion is the blood vessel tip at the predicted extension distance, 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 moving direction of the blood vessel tip and the moving 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, and the blood vessel tip existence time of the blood vessel tip and the blood vessel tip at the predicted extension distance is cleared and the timing is stopped, and 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 Record the existence time of the blood vessel tip and change the unit grid attributes of the remaining unit grids on the actual extension distance to blood vessels, and end the extension simulation of the blood vessel tip in this t time period; when there are still blood vessels and / or blood vessel tips after the blood vessel tip on the predicted extension distance that merges with the blood vessel tip on the corresponding predicted extension distance, the blood vessel tip continues to merge with the blood vessel and blood vessel tip on the predicted extension distance, and extends 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 t time period is ended; wherein, the initial value of the timer of the last unit grid on the actual extension distance is the existence time of the blood vessel tip before the blood vessel tip is cleared when no blood vessel branch occurs, and the initial value is zero if a blood vessel branch occurs;

[0131] If the blood vessel tip is randomly selected to stop extending, the blood vessel tip is extended at the predicted extension distance where the blood vessel fusion occurs; 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 at the predicted extension distance where the blood vessel fusion occurs on the corresponding predicted extension distance, and the blood vessel tip existence time of the blood vessel tip is cleared and the timing is stopped, and the attributes of all unit grids on the actual extension distance are changed to blood vessels, ending the extension simulation of the blood vessel tip within this time period t.

[0132] The method for simulating the growth process of tumor blood vessels provided by the embodiment of the present invention 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 blood vessel growth process at different stages through this application, it is possible to predict disease progression and the effects of different treatments, optimize treatment strategies at different stages, and improve treatment effects;

[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 the growth process of tumor blood vessels provided by an embodiment of the present invention;

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

[0140] The preferred embodiments of the present invention are described below in conjunction with 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, the method comprising 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 or 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) is 2, indicating 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 capture grid information more accurately 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 for simulating blood vessel growth. The unit grid with the unit grid attribute of the environment may become a blood vessel or a blood vessel tip as the blood vessel tip extends, branches and merges. 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 two-dimensional tumor 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, initializing the unit grid properties, cell number, Cdh1 (cadherin 1) concentration, cycCDK (complex of cyclin and cyclin-dependent kinase CDK) concentration, npRB concentration (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 unit grid in the two-dimensional discrete coordinate system according to the patient's examination results. In order to be closer to the actual situation of patients and ensure that the simulation 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 value is to directly obtain the patient's most recent test result. The initial values ​​of fibronectin concentration and growth factor concentration are steady-state values ​​under normal conditions; the initial values ​​of 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 change individually. There are differences in Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration and fibronectin concentration between each unit grid.

[0144] In an embodiment of the present application, when initializing the attribute of each unit grid in the two-dimensional discrete coordinate system, the unit grid attribute of the unit grid in the tumor two-dimensional model area is the blood vessel tip or the blood vessel, the unit grid attribute of at least one unit grid among all the unit grids in the tumor two-dimensional model area is the blood vessel tip, and the remaining unit grid attributes are blood vessels. The position of the unit grid whose unit grid attribute is the blood vessel tip is not restricted here; the unit grid attribute of the unit grid not in the tumor two-dimensional model area is the environment, but in order to better express the tumor blood vessel growth process over time, in this embodiment, the number of unit grids whose unit grid attributes are blood vessel tips and blood vessels is much smaller than the number of unit grids whose unit grid attributes are 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, predicting the number of cells in each unit grid in the two-dimensional discrete coordinate system after a preset time t according to the current Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, oxygen concentration and cell number control model of the unit grid, and saving it under the information of the corresponding unit grid.

[0147] Cells mainly achieve the process of cell proliferation and cell apoptosis through the dynamic changes of key regulatory proteins of cells, and the key regulatory proteins of cells mainly include Cdh1, cycCDK, npRB, and p27. Therefore, in this embodiment, the cell number control model includes:

[0148] The Cdh1 concentration of the unit grid after the preset time t is predicted based on the current Cdh1 concentration of the unit grid, the current cycCDK concentration, the current npRB concentration and the Cdh1 concentration control equation; since the Cdh1 concentration is affected by the npRB concentration and the 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 correlation constant; J 2 , J 3 is the correction factor;

[0151] The cycCDK concentration of the cell grid after the preset time t is predicted based on the current Cdh1 concentration, the current cycCDK concentration, the 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 the 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 the 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, so the p27 concentration control equation is as follows:

[0155]

[0156] Where: k p27 , k′ p27 is a constant coefficient; J 4 is the oxygen effect correction factor; c o is the current oxygen concentration of the unit grid;

[0157] The npRB concentration of the cell grid after the 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, so 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 prediction, the Cdh1 concentration, cycCDK concentration, and p27 concentration of the cell grid after the preset time t are obtained, the number of cells in the cell grid is increased or decreased; specifically:

[0161] When it is predicted that the Cdh1 concentration of the cell 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 cell grid is less than the maximum number of cells (generally 4 units), the number of cells in the cell grid is increased by one unit, and the p27 concentration is reset to the initial value; if the current number of cells in the cell grid is equal to the maximum number of cells, the cell grid whose current number of cells is less than the maximum number of cells is selected from the eight cell grids adjacent to the cell grid where the cells divide and proliferate, and the number of cells in the cell grid with the highest current oxygen concentration among the selected cell grids is increased by one unit, and the p27 concentration is reset to the initial value; if the cell grid whose current number of cells is less than the maximum number of cells is not selected, it means that there is no position for division and the division fails, and the number of cells remains unchanged.

[0162] When it is predicted that the p27 concentration of the cell grid is 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 start counting the quiescent state holding time, and then increases in each preset time step of the cell quiescent state holding time; when the cell quiescent state holding time exceeds a quiescent state holding time threshold, the cell will undergo apoptosis, the cell number will be reset to zero, and the p27 concentration will be reset to the initial state.

[0163] Step S400, predict the oxygen concentration, p53 concentration, fibronectin concentration, and growth factor VEGF concentration of each unit grid in the two-dimensional discrete coordinate system after a preset time t according to the current oxygen concentration of the unit grid, the current unit grid attributes, the current number of cells, the oxygen concentration control equation, the current p53 concentration, the p53 concentration control equation, the current fibronectin concentration, the fibronectin concentration control equation, the current growth factor VEGF concentration, and the growth factor VEGF diffusion reaction equation, and save them under the information of the corresponding unit grid. In the embodiment of the present application, oxygen diffuses in space, the unit grid with blood vessels releases oxygen according to the permeability, and the 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 present application example, 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 the formation of blood vessels. The increase in fibronectin concentration depends on the presence of endothelial cells, and the decrease in fibronectin concentration depends on the uptake of fibronectin by endothelial cells. It can be seen that whether it increases or decreases, it depends on the unit grid whose attribute is a blood vessel, that is, it is related to the value of the blood vessel index function n(x, y, t) (that is, n in the formula), that is, t = t 0When the cell grid property of the cell grid (x, y), the control equation of the fibronectin concentration without the diffusion term in the embodiment of the present application 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 constant coefficient; J 1 k' is the correction coefficient for the relationship between p53 and growth factor VEGF; v is the oxygen inhibition constant coefficient; D V is the diffusion coefficient of VEGF; 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, predicting the movement direction of the blood vessel tip in the two-dimensional discrete coordinate system within this time period t according to 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 saving 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 motion of the vascular tip u 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 chemotaxis parameter of growth factor VEGF; is the fibrin chemotaxis parameter; K is the extracellular matrix anisotropy tensor matrix, which is an inherent property of the unit grid (x, y)∈Ω matrix space outside each cell and is independent of time. It is non-uniform and anisotropic in space, which means that the extension direction of the tip cell (blood vessel tip) is not necessarily consistent with the direction of the growth factor concentration gradient or the fibronectin concentration gradient; the control equation is:

[0180]

[0181] k a is the anisotropy parameter, representing the resistance to movement in a certain direction; k cond Heterogeneity parameter; v x and v y are the components of the unit vector v that describes the orientation of the extracellular matrix at the cell 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 it moves in the first movement direction according to the control equation of the fibronectin concentration, the first movement direction and the movement speed of the blood vessel tip after t time at the blood vessel tip, and predict the second movement speed of each blood vessel tip in the two-dimensional discrete coordinate system when it moves in the second movement direction according to the control equation of the fibronectin concentration, the second movement direction and the movement speed of the blood vessel tip after t time at the blood vessel tip, and save it under the information of the corresponding unit grid; wherein the first movement direction is the movement direction of the blood vessel tip in this t time period of the blood vessel tip; the second movement direction is the movement direction of the blood vessel tip in the last t time period of the blood vessel tip. In the embodiment of the present application, the control equation of the movement speed of the blood vessel tip 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 divided by the total number of unit grids, calculated once in each time period t;

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

[0194] c vlim is the threshold concentration of growth factor. When the VEGF concentration is higher than this value, the equation starts to work. represents the critical time t c Depends on the current VEGF concentration c v and the average concentration When 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: According to the discrete coordinates (x 0 ,y 0 ) and the first movement speed to calculate the first predicted extension distance of each blood vessel tip in the first movement direction in the two-dimensional discrete coordinate system, and, according to the discrete coordinates (x 0 ,y 0 ) and the second movement speed are used to calculate the second predicted extension distance of each blood vessel tip in the two-dimensional discrete coordinate system in the second movement direction, and the predicted extension distance is saved in the information of the corresponding unit grid; wherein the predicted extension distance is the distance of the blood vessel tip in the corresponding movement direction and at the corresponding movement speed from the discrete coordinate (x 0 ,y 0 ) starts to move and reaches the end point coordinate (x 1 ,y 1 ) passes through all unit grids. In the 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 of the cell grid corresponding to the blood vessel tip (x 0 ,y 0 ) Calculate the end point coordinates (x 1 ,y 1 ), where x 1 =x 0 +x p ,y 1 =y 0 +y p ;

[0197] The Bresenham algorithm is used to calculate the discrete coordinates (x 0 ,y 0 ) to the end point coordinate (x 1 ,y 1 ) and use the discrete coordinates of the cell grids that pass through the straight line connected to the blood vessel tip (x 0 ,y 0 ) is a predicted extension distance in the corresponding movement direction (a first predicted extension distance when the movement speed is the first movement speed, and a second predicted extension distance when the movement speed is the second movement speed).

[0198] Step S800: Perform extension simulation on each blood vessel tip in the two-dimensional discrete coordinate system within the current time period t according to 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, and update the unit grid attributes and the existence time of each unit grid in the two-dimensional discrete coordinate system with the extension simulation of each blood vessel tip, and update the simulation time when all blood vessel tips in the two-dimensional discrete coordinate system have completed the extension simulation. The extension simulation includes blood vessel extension, blood vessel branching that occurs when the blood vessel is extended, and blood vessel fusion that occurs when the blood vessel is extended.

[0199] Blood vessel branching refers to the splitting of a blood vessel tip into two new blood vessel tips. This is an important mechanism for the formation of new blood vessels during angiogenesis. When branching occurs, a blood vessel tip (sprout tip) will become two blood vessel tips. In the embodiment of the present application, in order to simulate this process, the embodiment of the present application is defined as follows:

[0200] (I) 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 angle between the unit velocity vector of the blood vessel tip (i.e. the original movement 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] (II) When the two conditions of vascular branching are met at the same time, the vascular branching at the vascular tip is simulated as follows:

[0204] A new blood vessel tip is generated from an existing blood vessel tip, that is, the unit grid with the blood vessel tip attribute has two extension attributes of the blood vessel tips, that is, the movement direction of the blood vessel tip corresponding to the unit grid in this time period t is set to the first movement direction and the second movement direction, and starting from the blood vessel tip where the blood vessel 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 refers to the meeting and fusion of two vascular tips or one vascular tip with another vascular tip. In the fusion of vascular tip to vascular tip, both vascular tips may disappear, or only one vascular tip may disappear, depending on the specific situation; in the fusion of vascular tip to vascular tip, the vascular tip becomes part of the ring and disappears, no longer extending, that is, the tip no longer exists. In order to simulate this process, the embodiment of the present application is defined as follows:

[0206] (I) 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] (II) When the vascular fusion conditions are met, vascular fusion is simulated at the vascular tip as follows:

[0209] According to the order from the discrete coordinates where the blood vessel tip is located 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 implementation 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 is completed, wherein the actual extension distance is all the 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 the blood vessel branching and / or blood vessel fusion occurs during the movement of the blood vessel tip in the corresponding movement direction and at the corresponding movement speed according to the corresponding predicted extension distance. In the 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 blood vessel fused with the blood vessel tip is on the predicted extension distance (the first predicted extension distance and / or the second predicted extension distance), it means that the blood vessel tip needs to disappear at the unit grid where the blood vessel is located, and the extension of the blood vessel tip will also stop at the unit grid where the blood vessel is located, that is, 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 on the predicted extension distance (including the unit grid to which the blood vessel belongs), and the blood vessel tip existence time of the blood vessel tip is cleared and the timing is stopped, and the unit grid attributes of all unit grids on the actual extension distance are changed to blood vessels, and the extension simulation of the blood vessel tip in this t time period is ended.

[0211] 2. If the blood vessel tip that undergoes blood vessel fusion is the blood vessel tip at the predicted extension distance (the first predicted extension distance and / or the second predicted extension distance), 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:

[0212] (1) If the angle between the movement direction of the vascular tip (which may 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 may 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, and 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, and 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 terminated.

[0213] (2) If the angle between the moving direction of the blood vessel tip and the moving direction of the blood vessel tip at the corresponding predicted extension distance is less than 90 degrees, it is considered that only one of the two blood vessel tips that have fused has become inactive, and one blood vessel tip is randomly selected to continue extending at the corresponding predicted extension distance, and the other blood vessel tip stops extending at the unit grid where the two blood vessel tips have fused, and no longer extends. Since the two tips are at the same position in the model (i.e., the unit grid where the two blood vessel tips have fused), the selection of which tip becomes inactive will not affect the determinism of the model;

[0214] If the blood vessel tip is randomly selected for extension, the blood vessel tip on the predicted extension distance stops extending; when there is no blood vessel or blood vessel tip after the blood vessel tip on the predicted extension distance that merges with the blood vessel tip on 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 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 blood vessel tip, and the timer is started to record the blood vessel tip existence time from the initial value, and the other unit grids on the actual extension distance are reset to zero. The unit grid attributes of the remaining unit grids are changed to blood vessels; the extension simulation of the blood vessel tip in this t time period is ended; when there are still blood vessels and / or blood vessel tips after the blood vessel tip in the predicted extension distance that is fused 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 the blood vessel fusion, until the extension simulation of the blood vessel tip in this t time period 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 when no blood vessel branch occurs, and the initial value is zero if a blood vessel branch occurs;

[0215] If the blood vessel tip is randomly selected to stop extending, the blood vessel tip is extended at the predicted extension distance where the blood vessel fusion occurs; 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 at the predicted extension distance where the blood vessel fusion occurs (excluding the unit grid to which the blood vessel tip belongs at the predicted extension distance), and the blood vessel tip existence time of the blood vessel 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, and the extension simulation of the blood vessel tip within this t time period is ended; regardless of whether the blood vessel tip at the predicted extension distance where the blood vessel fusion occurs completes the extension simulation within this t time period, the blood vessel 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 definition is as follows:

[0217] Each blood vessel tip in the two-dimensional discrete coordinate system is sequentially extended in the current time period t by simulation, and the blood vessel tip is extended in the current time period t by simulation including:

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

[0219] If the vascular tip does not branch, determine whether the vascular tip has vascular fusion at the first predicted extension distance. If vascular fusion does not occur, set the actual extension distance of the vascular tip to the unit grid to which the vascular tip belongs and all unit grids at the first predicted extension distance, use the current vascular tip existence time of the vascular tip as the initial value of the last unit grid timer at the actual extension distance, reset the vascular tip existence time of the vascular tip to zero and stop timing, change the unit grid attribute of the last unit grid at the actual extension distance to the vascular tip, start the timer to record the vascular tip existence time from the initial value, and change the unit grid attributes of the remaining unit grids at the actual extension distance to the blood vessel, and end the extension simulation of the vascular tip in this t time period. If vascular fusion occurs, the vascular tip is sequentially fused with the blood vessel and the vascular tip at the first predicted extension distance in the order from the discrete coordinates of the vascular tip to the end point coordinates at the first predicted extension distance, and is extended according to the actual extension distance of the vascular tip after the vascular fusion, until the extension simulation of the vascular tip in this t time period is ended.

[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 the vascular fusion does not occur, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all the unit grids on the first predicted extension distance, and the vascular tip existence time of the vascular tip 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 zero, and 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 vascular tip in this time period t is ended;

[0224] If blood vessel fusion occurs, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the first predicted extension distance in the order from the discrete coordinates of the blood vessel tip to the end point coordinates on the first predicted extension distance, and the blood vessel tip is extended 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 terminated;

[0225] The second movement direction of the blood vessel tip extending 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 the vascular fusion does not occur, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all the unit grids on the second predicted extension distance, and the vascular tip existence time of the vascular tip 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 zero, and 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 vascular tip in this time period t is ended;

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

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

[0230] Step S801, judging whether a blood vessel branch occurs in the extension simulation of the blood vessel tip within this time period t according to 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 branch 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, judging whether vascular fusion occurs when the vascular tip is extended according to the first predicted extension distance according to the unit grid attributes of each unit grid on the first predicted extension distance and the vascular fusion condition; if vascular fusion occurs, executing step S814; otherwise, executing step S815;

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

[0234] Step S814: in the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point on the first predicted extension distance, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the first predicted extension distance, and the blood vessel tip is 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 is completed; then step S802 is executed;

[0235] Step S815, setting the actual extension distance of the blood vessel tip to the unit grid to which the blood vessel tip belongs and all the unit grids on the first predicted extension distance, clearing the blood vessel tip existence time of the blood vessel tip and stopping the timing, changing the unit grid attribute of the last unit grid on the actual extension distance to the blood vessel tip and starting the timer to record the blood vessel tip existence time from zero, and changing the unit grid attributes of the remaining unit grids on the actual extension distance to blood vessels, and ending the extension simulation of the blood vessel tip in this time period t; then executing step S802;

[0236] Step S816, in the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point on the second predicted extension distance, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the second predicted extension distance, and the blood vessel tip is 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 is completed; then step S802 is executed;

[0237] Step S817, setting the actual extension distance of the blood vessel tip to the unit grid to which the blood vessel tip belongs and all the unit grids on the second predicted extension distance, clearing the blood vessel tip existence time of the blood vessel tip and stopping the timing, changing the unit grid attribute of the last unit grid on the actual extension distance to the blood vessel tip and starting the timer to record the blood vessel tip existence time from zero, and changing the unit grid attributes of the remaining unit grids on the actual extension distance to blood vessels, and ending the extension simulation of the blood vessel tip in this time period t; then executing step S802;

[0238] Step S821, determining whether blood vessel fusion occurs at the tip of the blood vessel at the first predicted extension distance, if blood vessel fusion does not occur, executing step S822; otherwise, executing step S823;

[0239] Step S822: In the order from the discrete coordinates of the blood vessel tip to the coordinates of the end point on the first predicted extension distance, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the first predicted extension distance, and the blood vessel tip is 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 is completed; then step S802 is executed;

[0240] Step S823, setting the actual extension distance of the blood vessel tip to the unit grid to which the blood vessel tip belongs and all the unit grids on the first predicted extension distance, and using the current blood vessel tip existence time of the blood vessel tip as the initial value of the last unit grid timer on the actual extension distance, clearing the blood vessel tip existence time of the blood vessel tip and stopping the timing, changing the unit grid attribute of the last unit grid on the actual extension distance to the blood vessel tip and starting the timer to record the blood vessel tip existence time from the initial value, and changing the unit grid attributes of the remaining unit grids on the actual extension distance to blood vessels, ending the extension simulation of the blood vessel tip in this time period t, and then executing step S802;

[0241] Step S802, determine whether all blood vessel tips in the two-dimensional discrete coordinate system have completed the extension simulation within the current time period t. If all have completed, execute step S803; otherwise, extend the next blood vessel 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 plus the preset time t, and save the unit grid properties of each unit grid in the two-dimensional discrete coordinate system after time t, and then execute step S804.

[0243] Step S804, determine whether the simulation end condition is met, if the simulation end condition is met, output the simulation result and end, otherwise, enter the next extended simulation of the time period t, and repeat the above process from step S300; wherein the simulation result includes but is 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 in the time period t, and the unit grid attributes of each unit grid in the two-dimensional discrete coordinate system after each extension in the time period t. The simulation end condition can be a preset simulation time threshold, or it can be the simulation time T input by the user according to the needs, or the percentage of the 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 embodiment of the present application does not limit this.

[0244] The embodiment of the present application provides a method for simulating the tumor blood vessel growth process, and establishes a mathematical model including oxygen concentration, VEGF dynamics, and tumor cell proliferation, death, and competition. It can not only describe the tumor blood vessel growth process more comprehensively and accurately, but also provide important and reliable theoretical support and technical means for the study of tumor blood vessel growth mechanism, revealing the root cause of the disease and anti-angiogenic treatment; and through the dynamic simulation of the tumor blood vessel growth process at different stages of the present application, it is possible to predict the progression of the disease and the effects of different treatment methods, optimize the treatment strategies at different stages, and improve the treatment effect; 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 for different patients is established to achieve personalized disease prediction and treatment plan optimization.

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

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 blood vessel 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 environment; Step S200, initializing the unit grid properties, cell number, Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, p53 concentration, oxygen concentration, fibronectin concentration and growth factor concentration of each unit 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 according to the current Cdh1 concentration, cycCDK concentration, npRB concentration, p27 concentration, oxygen concentration and cell number control model of the unit grid; Step S400, predicting the oxygen concentration, p53 concentration, fibronectin concentration, and growth factor VEGF concentration of each unit grid in the two-dimensional discrete coordinate system after a preset time t according to the current oxygen concentration of the unit grid, unit grid properties, cell number, p53 concentration, fibronectin concentration, and growth factor VEGF concentration, as well as the oxygen concentration control equation, the p53 concentration control equation, the fibronectin concentration control equation, and the growth factor 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 according to the fibronectin concentration of the unit grid after t time, the growth factor concentration after t time, and the blood vessel tip movement direction control equation; Step S600, predicting the first movement speed of each blood vessel tip in the two-dimensional discrete coordinate system when it moves in the first movement direction according to the control equation of the fibronectin concentration at the blood vessel tip after t time, the first movement direction and the movement speed of the blood vessel tip, and predicting the second movement speed of each blood vessel tip in the two-dimensional discrete coordinate system when it moves in the second movement direction according to the control equation of the fibronectin concentration at the blood vessel tip after t time, the second movement direction and the movement speed of the blood vessel tip; wherein the first movement direction is the movement direction of the blood vessel tip in the current t time period of the blood vessel tip; and the second movement direction is the movement direction of the blood vessel tip in the last t time period of the blood vessel tip; Step S700, calculating a first predicted extension distance of each blood vessel tip in a two-dimensional discrete coordinate system in a first movement direction according to the discrete coordinates (x0, y0) of the blood vessel tip and a first movement speed, and calculating a second predicted extension distance of each blood vessel tip in a second movement direction according to the discrete coordinates (x0, y0) of the blood vessel tip and a second movement speed; wherein the first predicted extension distance or the second predicted extension distance is all unit grids through which the blood vessel tip moves in the first movement direction or the second movement direction at the first movement speed or the second movement speed 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; Step S800, performing extension simulation on each blood vessel tip in the two-dimensional discrete coordinate system within this time period t according to 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, and updating the unit grid attributes and the blood vessel tip existence time of each unit grid in the two-dimensional discrete coordinate system with the extension simulation of each blood vessel tip, and updating the simulation time when all blood vessel tips in the two-dimensional discrete coordinate system complete the extension simulation; wherein the extension simulation includes blood vessel extension, blood vessel branching occurring during blood vessel extension and blood vessel fusion occurring during blood vessel extension.

2. The method according to claim 1, characterized in that The cell number control model comprises: Predict the Cdh1 concentration of the unit grid after a preset time t according to the current Cdh1 concentration of the unit grid, the current cycCDK concentration, the current npRB concentration and the Cdh1 concentration control equation; Predict the cycCDK concentration of the unit grid after a preset time t according to 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 according to 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 prediction, the Cdh1 concentration, cycCDK concentration, and p27 concentration of the cell grid after the preset time t are obtained, 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 number of cells in the unit grid is less than the maximum number of cells, 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 selected from the eight unit grids adjacent to the unit grid, and the number of cells in the unit grid with the highest current oxygen concentration among the selected unit grids is increased by one unit, and the p27 concentration is reset to the initial value; if the unit grid with a current number of cells less than the maximum number of cells is not selected, the number of cells remains unchanged; When it is predicted that the p27 concentration of the cell grid is 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: 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 correlation constant; J2, J3 are correction coefficients; The cycCDK concentration control equation is as follows: in: 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; The p27 concentration control equation is as follows: in: k p27 , k′ p27 is a constant coefficient; J4 is the oxygen effect correction factor; c o is the current oxygen concentration of the unit grid; The npRB concentration control equation is as follows: Among them, k n1 , k n2 , k n3 is a constant coefficient.

4. The method according to claim 3, characterized in that The oxygen concentration control equation is as follows: in: D o is the oxygen diffusion coefficient; c o is the current oxygen concentration of the unit grid; P o is 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 cell grid attribute of the cell grid; The p53 concentration control equation is as follows: in: k p53 is the initial constant coefficient of p53; k′p53 is the constant coefficient of oxygen influence; C p53 is the oxygen effect correction factor; The control equation of the fibronectin concentration is: in: c f is the current fibronectin concentration of the cell grid; 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; The growth factor VEGF diffusion reaction equation is: in: c v is the current VEGF concentration of the unit grid; k v is the p53 promotion constant coefficient; J1 is the correction coefficient for 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 is the permeability of VEGF in blood vessels; δ V is the degradation rate of VEGF, which is a fixed constant; C v1 Corrected normal coefficients for oxygen effects.

5. The method according to claim 4, characterized in that The control equation for the movement direction of the blood vessel tip is as follows: in: is the chemotaxis parameter of growth factor VEGF; is the fibrin chemotaxis parameter; K is the anisotropic tensor matrix of the extracellular 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, which 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 control equation is: k a is the anisotropy parameter, representing the resistance to movement along a certain direction; k cond Heterogeneity parameters; v x and v y are the components of the unit vector v that describes the orientation of the extracellular matrix at the cell grid (x, y). is a regular equation, randomly generating v x and v y , and is fixed at all times t; for each unit grid (x, y) ∈ Ω, k cond and k a 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; k p is the rate of vascular tip division, which is related to the concentration of growth factor VEGF c v Related; l e is a constant, the length of the endothelial cell; 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: T 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 divided by the total number of unit grids, calculated once in each time period t; c v is the current growth factor VEGF concentration; c vlim is the threshold concentration of growth factor.

7. The method according to claim 4, characterized in that The step S700 includes the following steps: According to the velocity of the blood vessel tip in the x and y directions, the vector (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 current extension of the unit grid; where x1 = x0 + x p , y1=y0+y p ; The movement speed is the first movement speed or the second movement speed; The Bresenham algorithm is used to calculate the discrete coordinates of the unit grids 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 all the discrete coordinates of the unit grids passed are used as the predicted extension distance of the blood vessel tip (x0, y0) in 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 occurrence of vascular branching when the vascular tip extends include: The blood vessel existence time of the blood vessel tip is greater than a preset blood vessel tip existence time threshold τ a ; The unit velocity vector of the blood vessel tip in 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 ; When the two conditions of vascular branching are met at the same time, the process of simulating vascular branching at the vascular tip includes: 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 is extended include: Among the unit grids included in the blood vessel tip prediction extension distance, there are unit grids whose unit grid attributes are blood vessels and / or blood vessel tips; When the vascular fusion conditions are met, the vascular fusion process of simulating the vascular tip includes: According to the order from the discrete coordinates of the blood vessel tip to the corresponding end point coordinates on the predicted extension distance, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips 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 is completed; The blood vessel tip performing blood vessel extension comprises: Each blood vessel tip in the two-dimensional discrete coordinate system is sequentially extended in the current time period t for simulation, wherein the blood vessel tip is extended in the current time period t for simulation as follows: Determine whether vascular branching occurs at the vascular tip; If the vascular tip does not branch, determine whether the vascular tip has vascular fusion at the first predicted extension distance. If vascular fusion does not occur, set the actual extension distance of the vascular tip to the unit grid to which the vascular tip belongs and all unit grids at the first predicted extension distance, use the current vascular tip existence time of the vascular tip as the initial value of the last unit grid timer at the actual extension distance, reset the vascular tip existence time of the vascular tip to zero and stop timing, change the unit grid attribute of the last unit grid at the actual extension distance to the vascular tip, start the timer to record the vascular tip existence time from the initial value, and change the unit grid attributes of the remaining unit grids at the actual extension distance to the blood vessel, and end the extension simulation of the vascular tip in this t time period. If vascular fusion occurs, the vascular tip is sequentially fused with the blood vessel and the vascular tip at the first predicted extension distance in the order from the discrete coordinates of the vascular tip to the end point coordinates at the first predicted extension distance, and is extended according to the actual extension distance of the vascular tip after the vascular fusion, until the extension simulation of the vascular tip in this t time period is ended. 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 the vascular fusion does not occur, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all the unit grids on the first predicted extension distance, and the vascular tip existence time of the vascular tip 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 zero, and 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 vascular tip in this time period t is ended; If blood vessel fusion occurs, the blood vessel tip is sequentially fused with the blood vessels and blood vessel tips on the first predicted extension distance in the order from the discrete coordinates of the blood vessel tip to the end point coordinates on the first predicted extension distance, and the blood vessel tip is extended 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 terminated; The second movement direction of the blood vessel tip extending 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 the vascular fusion does not occur, the actual extension distance of the vascular tip is set to the unit grid to which the vascular tip belongs and all the unit grids on the second predicted extension distance, and the vascular tip existence time of the vascular tip 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 zero, and 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 vascular tip in this time period t is ended; If vascular fusion occurs, the vascular tip is fused with the blood vessels and vascular tips on the second predicted extension distance in sequence from the discrete coordinates of the vascular tip to the end point coordinates on the second predicted extension distance, and is extended according to the actual extension distance of the vascular tip after vascular fusion until the extension simulation of the vascular tip in this time period t is terminated.

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 the vascular tip is 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 on 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 fused with the blood vessel tip belongs on the predicted extension distance, the blood vessel tip existence time of the blood vessel tip is cleared and the timing is stopped, and the unit grid attributes of all 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 the blood vessel tip that undergoes blood vessel fusion is the blood vessel tip at the predicted extension distance, 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 moving direction of the blood vessel tip and the moving 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, and the blood vessel tip existence time of the blood vessel tip and the blood vessel tip at the predicted extension distance is cleared and the timing is stopped, and 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 Record the existence time of the blood vessel tip and change the unit grid attributes of the remaining unit grids on the actual extension distance to blood vessels, and end the extension simulation of the blood vessel tip in this t time period; when there are still blood vessels and / or blood vessel tips after the blood vessel tip on the predicted extension distance that merges with the blood vessel tip on the corresponding predicted extension distance, the blood vessel tip continues to merge with the blood vessel and blood vessel tip on the predicted extension distance, and extends 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 t time period is ended; wherein, the initial value of the timer of the last unit grid on the actual extension distance is the existence time of the blood vessel tip before the blood vessel tip is cleared when no blood vessel branch occurs, and the initial value is zero if a blood vessel branch occurs; If the blood vessel tip is randomly selected to stop extending, the blood vessel tip is extended at the predicted extension distance where the blood vessel fusion occurs; 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 at the predicted extension distance where the blood vessel fusion occurs on the corresponding predicted extension distance, and the blood vessel tip existence time of the blood vessel tip is cleared and the timing is stopped, and the attributes of all unit grids on the actual extension distance are changed to blood vessels, ending the extension simulation of the blood vessel tip within this time period t.

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