WO2021098617A1

WO2021098617A1 - Method for generating tumor in digital blood vessel model, system, and electronic device

Info

Publication number: WO2021098617A1
Application number: PCT/CN2020/128855
Authority: WO
Inventors: 吴剑煌; 王浩宇; 步文瑜
Original assignee: 中国科学院深圳先进技术研究院
Priority date: 2019-11-21
Filing date: 2020-11-13
Publication date: 2021-05-27
Also published as: CN110956698A; CN110956698B

Abstract

A method for generating a tumor in a digital blood vessel model, a system, and an electronic device. The method comprises: step a: selecting a tumor position on a digital blood vessel model; step b: calculating the approximate radius of the digital blood vessel model at the tumor position; step c: constructing a smooth and regular tumor grid model; step d: editing a surface of the tumor grid model, and constructing an irregular deformation on a surface of the tumor grid; step e: performing fairing on a connection portion of the tumor grid model and the digital blood vessel model; and step f: performing strict boundary-preserving grid simplification on the tumor grid model to obtain a generation result of a tumor in the digital blood vessel model. The problem in which case data sources are limited does not exist, and the present invention may be used almost without any learning costs; in addition, a tumor may be constructed at almost any position in a normal digital blood vessel model, the degree of freedom is relatively high, and operation is simple and efficient.

Description

Method, system and electronic equipment for generating tumor in blood vessel digital model

Technical field

This application belongs to the technical field of virtual surgery, and in particular relates to a method, system and electronic equipment for generating tumors in a blood vessel digital model.

Background technique

Studies have shown that 80% of errors in surgical teaching and training are caused by human factors, so it is extremely important for doctors to train surgical skills. The use of virtual surgery system for surgical skills training is a new and efficient way.

The virtual surgery system is a typical application of virtual reality technology in the medical field. Virtual surgery is a surgical system that starts from medical image data, uses computer graphics to reconstruct a virtual human soft tissue model, simulates a virtual medical environment, and uses tactile interactive devices to interact with it. The doctor can observe the expert's operation process on the virtual operation system, and can also repeat the exercise. Virtual surgery greatly shortens the time for surgical training, reduces the need for expensive experimental subjects, and can avoid the shortcomings of traditional surgery such as high risk, high patient pain, and unsatisfactory postoperative results.

One of the current technical difficulties of the virtual surgery system is how to obtain the case model needed in the virtual surgery system. In the intracranial aneurysm surgery simulation training system, the case model refers to the digital model of the diseased blood vessel. At present, there are three main technical solutions for obtaining the digital model of the diseased blood vessel:

(1) Three-dimensional reconstruction

This method performs blood vessel segmentation based on CT/MRI/DSA scan images of actual cases, and then uses three-dimensional reconstruction technology to obtain a three-dimensional digital blood vessel model with tumor lesions. However, in the 3D reconstruction method, due to various factors, there is often a large amount of noise in the scanned image, and the automatic segmentation and recognition of blood vessels is difficult, and it is difficult to find a universal method. Therefore, the blood vessel model obtained by this method is often rough and requires manual intervention and post-processing before it can be used for virtual surgery. The prerequisite for this method to obtain the case model is to have the image of the case. Due to the issue of patient privacy, it is difficult to obtain, and it is necessary to master the post-processing method of the rough model obtained by 3D reconstruction.

(2) Edit through 3D editing software

This method is based on the three-dimensional blood vessel digital model that has been acquired and undergoes three-dimensional reconstruction and post-processing. The three-dimensional blood vessel digital model is edited through 3ds Max or Maya and other three-dimensional editing software to obtain different types of diseased blood vessel models. This method can obtain a case model with a rich variety of pathological characteristics. However, the method of editing through 3D software requires the operator to learn the use of 3Ds Max or Maya and other 3D editing software, and also need to understand the structure of the blood vessel digital model. Learning costs.

(3) Direct editing

This method is also based on the three-dimensional blood vessel digital model that has been acquired and undergoes three-dimensional reconstruction and post-processing. Through the steps of tumor location selection, tumor hole cutting and tumor grid generation, the vascular tumor lesions can be constructed simply and quickly. Although the direct editing method can quickly and conveniently generate digital models of tumor lesions, this method cannot adapt to digital models of blood vessels with different radii. The transition between the generated tumor and the digital model of blood vessels is unnatural, which is quite different from the real tumor. In addition, the operation process of direct editing will reduce the mesh quality of the blood vessel digital model.

Summary of the invention

This application provides a method, system, and electronic device for generating tumors in a digital blood vessel model, and aims to solve one of the above-mentioned technical problems in the prior art at least to a certain extent.

In order to solve the above problems, this application provides the following technical solutions:

A method for generating a tumor in a digital blood vessel model, including the following steps:

Step a: Select the tumor position on the blood vessel digital model;

Step b: Calculate the approximate radius of the blood vessel digital model at the tumor location based on the point method equation of the plane;

Step c: Generate a virtual sphere with the selected tumor position as the center of the sphere. After the virtual sphere collides with the blood vessel digital model, the collision triangle is deleted, and a cavity is generated by growing toward the center of the virtual sphere, and is refined by iterative triangles Method to construct a smooth and regular tumor grid model;

Step d: Edit the surface of the tumor mesh model, select a certain number of control points, and construct irregular deformations on the surface of the tumor mesh by maintaining rigid deformation;

Step e: smoothing the connection between the tumor mesh model and the blood vessel digital model;

Step f: Perform a strict boundary-preserving mesh simplification on the tumor mesh model to obtain the result of tumor generation in the blood vessel digital model.

The technical solution adopted in the embodiment of the application further includes: in the step a, the method for selecting the tumor position is specifically: selecting a point on the blood vessel digital model, and using the position information of the point as the screen coordinate information; The coordinate information is converted into world coordinate information, and the world coordinate information and the position of the virtual camera are connected to form a ray; the triangle patch on the digital model of the blood vessel that intersects with the ray is calculated, and the geometric center points of the three vertices of the triangle are calculated Position T _c , this position T _c is the tumor position selected on the blood vessel digital model.

The technical solution adopted in the embodiment of the present application further includes: in the step b, the approximate radius calculation method specifically includes:

Step b1: Take the tumor position selected on the blood vessel digital model as the center, obtain m triangle faces whose surrounding radius is R, calculate the normal vector of the first triangle face and the normal vector of the second triangle face Vector product of

Calculate the vector product of the normal vector of the second triangular facet and the normal vector of the third triangular facet

By analogy, m-1 vector products can be calculated

Then calculate their mean

_{Step b2: Take the triangle f 0} where the tumor position coordinates selected on the blood vessel digital model are located, calculate the coordinates G ₀ (x ₀ , y ₀ , z ₀ ) of its center of gravity, and pass

And G ₀ , we get a pass through G ₀ and perpendicular to

The point French equation of the plane, namely:

A(xx ₀ )+B(yy ₀ )+C(zz ₀ )=0

Step b3: Set a positive real number α, and find all the barycentric coordinates G _i (x _i , y _i , z _i ) in all triangles that make up the blood vessel digital model to meet the inequality -α≤A(xx _i )+B (yy _i )+C(zz _i )≤α and form a set F, calculate the average of the barycentric coordinates of all triangles in F, and get a point O ₀ ;

Step b4: Calculate the linear distance between the center of gravity of all triangles in the set F and the point O ₀ and then calculate the average value R ₀ , and the average value R ₀ is the approximate radius of the blood vessel digital model at the selected tumor position.

The technical solution adopted in the embodiment of the present application further includes: in the step c, the constructing a smooth and regular tumor grid model specifically includes:

Step c1: Taking the tumor position T _c selected on the blood vessel digital model as the center of the sphere, a virtual sphere with a radius of r is generated, r=αR ₀ , and α is a value between 0 and 1;

Step c2: Perform collision detection between the virtual sphere and the blood vessel digital model to obtain all triangle sets S that intersect the virtual sphere, and find the average normal vector D _t of all triangle faces in the set S, which is the growth direction of the tumor;

Step c3: Delete all the triangular faces in the set S from the blood vessel digital model to obtain an irregular boundary. The set of all vertices on the boundary is S _bd ;

Step c4: _{Connect each vertex on the vertex set S bd} with the center of the sphere T _c _{, and obtain the intersection set S int of} the corresponding link and the virtual sphere respectively;

Step c5: _{Triangulate the vertices on the vertex set S bd} and the intersection set S _int to form a circle of triangle meshes, and use _{the vertices in the intersection set S int} as the vertices where the tumor and the blood vessel intersect;

Step c6: Calculate the tumor sphere center position P _T and the tumor highest point position P _H :

P _T ＝T _c +(R ² -r ² )D _t

P _H ＝P _T +RD _t

In the above formula, R is the radius of the tumor, R=μr, μ is a constant greater than 1, r=αR ₀ , R ₀ is the approximate radius of the blood vessel digital model at the selected tumor position;

Step c7: _{Connect the vertices in the intersection set S int} and the highest point position P _{H of the} tumor to form a cone-shaped grid. The triangle set that composes the grid is S ₀ , and each triangle in the set S _{0 is performed} Subdivision operation, a new triangle set S _{1 is obtained} , and then the _{same subdivision operation is performed on each triangle in the set S 1.} This operation is performed for N rounds, and the final triangle set S _{N is} the regular tumor mesh model .

The technical solution adopted in the embodiment of the present application further includes: the subdivision operation of each triangle specifically includes: for each triangle in the set, if two vertices A and B of the three vertices belong to the intersection set S _int , then Take the midpoints X and Y of the other two sides except the side composed of vertices A and B, and take any one of the midpoints X and Y to connect with any one of the vertices A and B, and divide the original triangle into 3, X and Y are newly added vertices; if none of the three vertices of the triangle belong to the vertex set S _int , then take the midpoints X, Y, Z of the three sides and connect them in pairs to divide the original triangle Into 4 triangles, X, Y and Z are the new vertices; move the new vertices X and Y or X, Y and Z to the rays P _T X and P _T Y or P _T X, P _T Y and At _{the intersection of P T} Z and the virtual sphere, get its final position.

The technical solution adopted in the embodiment of the present application further includes: in the step d, the constructing an irregular deformation on the surface of the tumor grid specifically includes:

Step d1: Use the generated tumor mesh model as the input mesh S of the mesh deformation operation;

Step d2: Divide the tumor grid into m parts, randomly select q control points in each part; for each control point, select triangles within a certain range around the tumor grid, and divide these triangles The vertex of the slice is used as the free point set corresponding to the control point;

Step d3: Set the position constraint information of the control point as: the position of the current control point after moving λR along the normal direction or the normal direction of the point; where λ is a constant between greater than 0 and less than 1, and R is the radius of the tumor ；

Step d4: Combine input grid information, control points and their corresponding free point set information, and fixed position constraint information to perform rigidity-preserving grid deformation.

The technical solutions adopted in the embodiments of the present application also include: the rigidity-preserving grid deformation specifically includes:

Step 1: Obtain the adjacency information of the input mesh S, and make the vertex v _i and its 1-neighboring triangle patch form a unit C _i ;

Step 2: Define the rigid energy of each unit, and sum to obtain the overall rigid energy:

In the above formula, S is the input mesh, S′ is the deformed input mesh; E(S′) is the rigid energy of the entire mesh; n is the number of vertices in the input mesh S, and C _i is the vertex v _i and its 1-neighbor triangular facet constitute a unit, C _i ′ is the deformed unit, E(C′) is the rigid energy of a unit, N(i) is the vertex adjacent _{to vertex v i} collection, p _i is a vertex v _i coordinates, coordinates of p _i deformed p _i ', p _j is a vertex v _j of the coordinates, the coordinates of the p _j deformed p _j', w _ij is the weight of the edge e _ij weight , Using cotangent weights

α _ij and β _ij are the two opposite corners of the edge e _ij _{; R i} is the rotation matrix before and after the transformation of the unit C _i;

Step 3: Determine the initial guess of the vertex coordinates after deformation; for the selected control point, its initial guess is the fixed position constraint set before; for free points, determine the initial guess ^{by minimizing ||Lp′-δ|| 2,} Where δ=Lp, p is the coordinates of the vertices in the initial grid input by the user, and p′ is the coordinates of the vertices in the grid after the control point coordinates have been changed according to the above fixed position constraints; ||Lp′-δ|| ² Realize the smallest, then Lp′=Lp, where the matrix L is defined as follows:

In the above formula, w _ij is the weight of edge e _ij , and the weight of cotangent is used

N(i) is the _{set of vertices adjacent to the vertex v i} ; through further calculation and simplification, it can be obtained: A ^T AX _free =A ^T (Lp-BX _fixed _{), and X free} can be obtained by solving the equations, namely Is the initial guess of the free point;

The fourth step: use the post-deformation vertex coordinates p _i ′ and use the singular value decomposition to calculate the optimal rotation matrix of all deformed units;

Step 5: Use the current optimal rotation matrix to solve the linear equations to obtain the new vertex coordinates; when R _{i is} determined, solve the linear equations

Obtain p′ that minimizes E(S′). For each p _i ′, the following equation can be obtained:

The linear combination on the left side of the above equation is the discrete Laplacian-Beltrami operator of p′, so the system of equations can be written as: Lp′=b; p′ can be obtained by solving the system of equations;

The sixth step: iteratively execute the fourth and fifth steps until the overall rigidity energy is less than the set threshold.

The technical solution adopted in the embodiment of the present application further includes: in the step e, the smoothing process includes:

Step e1: Select the triangle surface of the tumor hole boundary and its n-neighboring triangle surface on the vascular mesh model, and use the digital mesh model composed of the above triangle surface as the input of the first mesh smoothing operation:

Get the adjacency information of the digital grid model, and record the set of adjacency points of each vertex i as N(i);

Calculate the weight of each adjacent point of each vertex:

In the above formula,

α _ij and β _ij are the two opposite corners of the edge (i, j);

Calculate the Laplacian coordinate L(i) of each point in the digital grid model according to the adjacency information and w _ij:

In the above formula, p _i is the coordinate of vertex i, and p _j is the coordinate of the adjacent point j of vertex i;

The original coordinate p _i is updated to λL _(i) + p i; where λ is a positive real number less than 1;

Perform the above grid smoothing step iteratively m ₁ times;

Step e2: Select again all the triangles on the tumor and the triangles of the tumor hole boundary on the vascular mesh model and its n-neighbor triangles, and use the digital mesh model composed of the above triangles as the mesh light For smooth input, perform the above mesh smoothing operation iteratively m ₂ times, where m ₁ should be much larger than m ₂ .

The technical solution adopted in the embodiment of the present application further includes: in the step f, the strict boundary-preserving mesh simplification of the tumor mesh model specifically includes:

Step f1: Calculate the error matrix Q for all initial vertices to obtain all valid edges (v ₁ , v ₂ );

Step f2: For each valid edge (v ₁ , v ₂ ), calculate the optimal extraction target v and the cost of extracting this edge;

Step f3: Store all edges in a heap according to the extraction cost cost;

Step f4: Remove the edge with the least extraction cost each time, and merge the vertices v ₁ and v ₂ into

And update all

The extraction cost of the connected effective edges and the optimal extraction position, and calculate the number of triangles in the tumor mesh after the least cost edge is removed;

Step f5: Repeat steps f1 to f4 until the number of existing faces is small to set a threshold.

Another technical solution adopted in the embodiment of the present application is: a system for generating tumors in a digital blood vessel model, including:

Tumor location selection module: used to select the tumor location on the blood vessel digital model;

Approximate radius calculation module: used to calculate the approximate radius of the blood vessel digital model at the tumor location based on the point method equation of the plane;

Tumor grid building module: used to generate a virtual sphere with the selected tumor position as the center of the sphere, collide the virtual sphere with the blood vessel digital model and delete the collision triangle, generate a cavity by growing toward the center of the virtual sphere, and pass Iterative triangle refinement method builds a smooth and regular tumor mesh model;

Tumor grid deformation module: used to edit the surface of the tumor grid model, select a certain number of control points, and construct irregular deformations on the tumor grid surface by maintaining rigid deformation;

Grid smoothing processing module: used for smoothing the connection between the tumor grid model and the blood vessel digital model;

Grid simplification module: used to perform grid simplification with strict boundary preserving on the tumor grid model to obtain the result of tumor generation in the blood vessel digital model.

Another technical solution adopted in the embodiments of the present application is: an electronic device, including:

At least one processor; and

A memory communicatively connected with the at least one processor; wherein,

The memory stores instructions executable by the one processor, and the instructions are executed by the at least one processor, so that the at least one processor can execute the above-mentioned method for generating a tumor in a blood vessel digital model. The following operations:

Step a: Select the tumor position on the blood vessel digital model;

Compared with the prior art, the beneficial effects produced by the embodiments of the present application are that the method, system and electronic device for generating tumors in the digital blood vessel model of the embodiments of the present application design an automatic generation and optimization method of the vascular tumor model. It is used to enrich the available case models in the field of virtual surgery, and make the operation simple and efficient. Compared with the prior art, this application has the following advantages:

1. This application does not have the problem of limited source of case data, and it can be used without any learning cost. It can construct tumors at almost any position in the digital model of normal blood vessels, and has a high degree of freedom;

2. In this application, the approximate radius of any position of the blood vessel digital model can be calculated, and the tumor radius and hole radius can be set adaptively according to the radius of the blood vessel model at the selected position when generating the tumor, instead of manually setting each time;

3. After the tumor grid is generated by sampling the latitude and longitude in this application, a certain number of control points are randomly selected on the tumor grid, and by maintaining rigid deformation, irregular deformations are constructed on the tumor surface, which can simulate more abundant tumor morphologies ；

4. After the tumor grid is generated in this application, the transition between the tumor and the blood vessel model is made smoother through the two-step grid smoothing, which is more in line with the morphology of the real tumor and the blood vessel connection;

5. After the tumor grid is generated in this application, the grid simplification with strict boundary preservation is carried out, so that there will be no excessive difference between the grid density of the tumor grid and the blood vessel grid.

Description of the drawings

Fig. 1 is a flowchart of a method for generating a tumor in a blood vessel digital model according to an embodiment of the present application;

Figure 2 is a schematic diagram of the relationship between R and r in the generated tumor grid model;

Figure 3(a) is a schematic diagram of the grid between two arcs on the tumor grid, and Figure 3(b) is a schematic diagram of a part of the tumor grid when the tumor grid is divided into three parts;

Fig. 4 is a flow chart of grid deformation to maintain rigidity;

Figure 5 is a schematic diagram _{of a vertex v i} and its corresponding unit C _i;

Figure 6 is a schematic diagram of the process of rigidity-preserving deformation of the tumor mesh;

Figure 7 is a schematic diagram of the first step grid smoothing operation process;

Figure 8 is a schematic diagram of the smoothing process of the grid at the junction of the tumor grid and the blood vessel digital model;

Figure 9 is a simplified flow chart of the grid;

Figure 10 is a schematic diagram of the final effect of generating a tumor in a blood vessel digital model;

FIG. 11 is a schematic structural diagram of a system for generating a tumor in a digital blood vessel model according to an embodiment of the present application;

FIG. 12 is a schematic diagram of the hardware device structure of the method for generating a tumor in a blood vessel digital model provided by an embodiment of the present application.

Detailed ways

In order to make the purpose, technical solutions, and advantages of this application clearer, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described here are only used to explain the present application, and are not used to limit the present application.

Please refer to FIG. 1, which is a flowchart of a method for generating a tumor in a blood vessel digital model according to an embodiment of the present application. The method for generating a tumor in a digital blood vessel model of the embodiment of the present application includes the following steps:

Step 100: Select the tumor position on the blood vessel digital model;

In step 100, the specific method for selecting the tumor position is: click on a point on the blood vessel digital model, and use the position information of the point as the screen coordinate information; convert the screen coordinate information into world coordinate information, and combine the world coordinate information with the virtual The position of the camera is connected to form a ray; calculate the triangular facet on the blood vessel digital model that intersects the ray, calculate the position T _c of the geometric center point of the three vertices of the triangle, the position T _c is selected on the blood vessel digital model Tumor location.

Step 200: Calculate the approximate radius of the blood vessel digital model at the tumor location based on the point method equation of the plane;

In step 200, through a series of simple calculations based on a plane-based French equation, the approximate radius of the blood vessel digital model at any position can be obtained, and the tumor radius and the hole radius can be adaptively set according to the approximate radius when the tumor is generated subsequently. The approximate radius calculation methods include:

Step 201: Take the tumor position selected on the blood vessel digital model as the center, obtain m triangle faces whose surrounding radius is R, calculate the normal vector of the first triangle face and the normal vector of the second triangle face Vector product of

By analogy, m-1 vector products can be calculated

Then calculate their mean

_{Step 202: Take the triangle f 0} where the tumor position coordinates selected on the blood vessel digital model are located, calculate the coordinates G ₀ (x ₀ , y ₀ , z ₀ ) of its center of gravity, and pass

And G ₀ , we get a pass through G ₀ and perpendicular to

The point French equation of the plane, namely:

A(xx ₀ )+B(yy ₀ )+C(zz ₀ )=0 (1)

The plane is considered to be approximately perpendicular to the direction in which the blood vessel extends.

Step 203: Set an appropriate positive real number α, and find all the barycentric coordinates G _i (x _i , y _i , z _i ) conform to the inequality-α ≤ A (xx _i ) among all the triangular faces constituting the blood vessel digital model +B(yy _i )+C(zz _i )≤α and form a set F. Calculate the average value of the barycentric coordinates of all triangles in F to obtain a point O ₀ ;

Step 204: Calculate the linear distance between the center of gravity of all triangles in the set F and the point O ₀ and then calculate the average value R _0. The average value R ₀ is the approximate radius of the blood vessel digital model at the selected tumor position.

Step 300: Generate a virtual sphere with the selected tumor position as the center of the sphere. After the virtual sphere collides with the blood vessel digital model, the collision triangle is deleted, and a cavity is generated by growing toward the center of the virtual sphere, and constructed by an iterative triangle refinement method Smooth and regular tumor grid model;

In step 300, the method for constructing a tumor grid model specifically includes:

Step 301: Taking the tumor position T _c selected on the blood vessel digital model as the center of the sphere, a virtual sphere with a radius r is generated, r=αR ₀ , and α is a value between 0 and 1;

Step 302: Perform collision detection between the virtual sphere and the blood vessel digital model to obtain all the triangle sets S that intersect the virtual sphere, and find the average normal vector D _t of all triangle faces in the set S, where the normal vector is the growth direction of the tumor;

Step 303: Delete all the triangular patches in the set S from the blood vessel digital model to obtain an irregular boundary, and the set of all vertices on the boundary is S _bd ;

Step 304: _{Connect each vertex on the vertex set S bd} to the center of the sphere T _c _{, and obtain the intersection set S int of} the corresponding link and the virtual sphere respectively;

Step 305: _{Triangulate the vertices on the vertex set S bd} and the intersection set S _int to form a circle of triangle meshes, and use _{the vertices in the intersection set S int} as the vertices where the tumor and the blood vessel intersect;

Step 306: Calculate the tumor sphere center position P _T and the tumor highest point position P _H :

P _T ＝T _c +(R ² -r ² )D _t (2)

P _H ＝P _T +RD _t (3)

In the above formula, R is the radius of the tumor, R=μr, μ is a constant greater than 1, r=αR ₀ , R ₀ is the approximate radius of the blood vessel digital model at the selected tumor position. In the generated tumor grid model, R is equal to The relationship of r is shown in Figure 2.

Step 307: the highest point of intersection of the tumor and the position of the vertex in the set of P _H S _int are connected to form a tapered grid, composed of triangles of the grid set S _0, set S ₀ of each of the triangles, Subdivision operation, a new triangle set S _{1 is obtained} , and then the _{same subdivision operation is performed on each triangle in the set S 1.} This operation is performed for N rounds, and the final triangle set S _{N is} the regular tumor mesh model .

Furthermore, the present application triangle set _{S i (i∈ [0, N} ]) operating segments comprises:

(1) For each triangle in the set, if two of the three vertices (assuming vertices A and B) belong to the intersection set S _int , then take the other two except the edge composed of vertices A and B The midpoints of the sides (assuming X and Y) are connected, and any one of the midpoints X and Y is connected to any one of the vertices A and B, and the original triangle is divided into three, X and Y are the new vertices ; If none of the three vertices of the triangle belong to the set of vertices S _int , then take the midpoints of the three sides (assuming X, Y, Z) and connect them in pairs to divide the original triangle into 4 triangles, X, Y and Z are the newly added vertices.

(2) Move the newly added vertices X and Y or X, Y and Z to _{the intersection of the ray P T} X and P _T Y or P _T X, P _T Y and P _T Z and the virtual sphere respectively, and obtain its final s position.

Step 400: Edit the surface of the tumor mesh model, select a certain number of control points, and construct irregular deformations on the surface of the tumor mesh by maintaining rigid deformation;

In step 400, the irregular deformation can simulate a more abundant tumor shape. Specific construction methods include:

Step 401: Set the input grid, select the control points and set the free point set corresponding to each control point, set the fixed position constraints of the control points, and perform the rigidity-preserving grid deformation;

Step 402: Use the generated tumor mesh model as the input mesh S of the mesh deformation operation;

Step 403: Select control points; combined with the method of latitude and longitude sampling to construct the tumor grid, it is easy to obtain the strip grid M _i (i=1, 2, ..., n, n number of sets of vertices P), and further, it can be set by a plurality of strip-shaped grid composed of M _i. According to this method, divide the tumor grid into m parts, each part has

One of the above strip grids, the last part has

The above strip grids. As shown in Fig. 3, Fig. 3(a) is a schematic diagram of the grid between two arcs on the tumor grid, and Fig. 3(b) is a schematic diagram of a part of the tumor grid when the tumor grid is divided into three parts. Divide the tumor mesh into m parts, randomly select q control points in each part; for each control point, select triangles within a certain range around the tumor mesh, and divide the vertices of these triangles As the free point set corresponding to this control point.

Step 404: Set fixed position constraint information; set the position of the control point as: the position of the current control point after moving λR along the normal direction or the reverse of the normal direction of the point; where λ is a constant between greater than 0 and less than 1, R is the radius of the tumor; the user can customize λ, the larger the λ, the greater the degree of irregular deformation of the tumor surface.

Step 405: Combine the input grid information, control points and their corresponding free point set information, and fixed position constraint information to perform rigidity-preserving grid deformation. The deformation process of the rigid mesh is shown in Figure 4, which specifically includes the following steps:

Step 1: Obtain the adjacency information of the input mesh S, and make the vertex v _i and its 1-neighbor triangle patch form a unit C _i , as shown in Figure 5; if the unit C _i undergoes a rigid transformation, then the before and after transformation The position relationship of the vertices can be represented by a rotation matrix, that is, it satisfies: p _i ′-p _j ′=R _i (p _i -p _j ),

Wherein p _i is the position of the vertex v _i; p _i the position modification as p _{_i} ', R _i is a rotation matrix before and after conversion cell C _i, N (i) is the set of vertices adjacent to vertex v _i. When the deformation is not rigid, you can still find the optimum rotation matrix R _i, so that the equation p _i '-p _j' = about R _{_i} (p _i -p _j) on both sides of the minimum difference.

α _ij and β _ij are the two opposite corners of the edge e _ij _{; R i} is the rotation matrix before and after the transformation of the unit C _i.

By minimizing the rigid energy E(S'), the mesh can be deformed as rigidly as possible. In the E(S') formula, only the coordinates p _i ′ and the rotation matrix R _i after the vertex are deformed are unknown quantities.

Step 3: Determine the initial guess of the vertex coordinates after deformation; for the selected control point, the initial guess is the fixed position constraint set before. For free points, the initial guess is determined by minimizing ||Lp′-δ|| ² , where δ=Lp, p is the coordinate of the vertex in the initial grid input by the user, and p′ is the coordinate of the control point which has been constrained according to the above fixed position The coordinates of the vertices in the changed mesh. ||Lp′-δ|| ² To achieve the minimum, then Lp′=Lp, where the matrix L is defined as follows:

In formula (5), w _ij is the weight of edge e _ij , and the weight of cotangent is used

N (i) is the set of vertices adjacent to vertex v _i.

According to Lp′=Lp, the initial guess of the free point coordinates in the grid S is obtained, and the equation can be rewritten as: AX _free +BX _fixed =Lp. Where A is the matrix composed of columns corresponding to the free vertex subscripts in matrix L, X _free is the coordinates of the free vertex, which is an unknown quantity, B is the matrix composed of columns corresponding to the fixed vertex subscripts in matrix L, and X _fixed is the fixed vertex The coordinates of, including the control points and the remaining vertices in mesh S.

Through further calculation and simplification, it can be obtained: A ^T AX _free =A ^T (Lp-BX _fixed _{), and X free} can be obtained by solving the equations, which is the initial guess of the free point.

Finally, iteratively updated rotation matrix R _i and the vertex coordinates of the vertices modifications p _i '.

The fourth step: use the post-deformation vertex coordinates p _i ′ and use the singular value decomposition to calculate the optimal rotation matrix of all the deformed elements; for a certain element C _i , mark e _ij = p _i -p _j , correspondingly, in the deformation after cell C _i ', note _{_{e ij' = p i '-p}} j', represents a collection of j∈N (i) with j simplified. Then the rigid energy E(C′) of a certain unit can be written as:

The term that does not include R _i in the formula can be regarded as a constant in the process of finding the optimal rotation matrix, so it can be deleted without discussion. At this time, the above formula can be written as:

make

It is known that when R _{_i} S _i is a semi-definite symmetric matrix, Tr (R _i S ') can be the maximum, can be from the decomposition of singular value S _i _{_{_{S i = U i Σ i V}}} i T R _i deduced :

R _i ＝V _i U _i ^T (8)

_{Calculate the rotation matrix R i} of each unit according to the above method.

The linear combination on the left side of the above equation is the discrete Laplacian-Beltrami operator of p′, so the system of equations can be written as: Lp′=b; p′ can be obtained by solving the system of equations.

Step 6: Iteratively execute the fourth and fifth steps until the overall rigidity energy is less than the set threshold; in the next iteration, use the newly obtained p′ as a known quantity to solve for the new R and p′, and repeat , Until the grid rigidity energy is less than the threshold specified by the user.

The process of the tumor mesh for rigidity-preserving deformation is shown in Figure 6, where (a) is the fixed position constraint, (b) is the initial guess of the mesh model deformation, and (c) is the iterative update of p and R for a certain number of times. Grid model. It should be noted that in the process of selecting control points in this application, in addition to randomly selecting control points in a certain way, control points can also be selected through human-computer interaction with the user's mouse clicking; the fixed position constraint process can be set in addition to In addition to the fixed offset λR, the offset can be set by recording the distance the user controls the mouse to move.

Step 500: Smoothing the connection between the tumor mesh model and the blood vessel digital model;

In step 500, the smoothing process is divided into the following two steps:

The first step is to smooth the grid: after the above-mentioned longitude and latitude sampling method is used to construct the tumor, it is easy to obtain the triangle surface near the bottom of the tumor grid (that is, the triangle surface where the tumor and the digital model of blood vessels are connected). In addition, select the triangle surface of the tumor hole boundary and its n-neighboring triangle surface on the vascular mesh model. The digital mesh model composed of the above-mentioned triangular faces is used as the input of the first mesh smoothing operation.

The first step of grid smoothing operation process is shown in Figure 7, which specifically includes the following steps:

Step 501: Obtain the adjacency information of the digital grid model, and record the set of adjacency points of each vertex i as N(i);

Step 502: Calculate the weight of each neighboring point of each vertex:

In formula (10),

α _ij and β _ij are two opposite corners of the edge (i, j).

Step 503: Calculate the Laplacian coordinate L(i) of each point in the digital grid model according to the adjacency information and w _ij:

In formula (11), p _i is the coordinate of vertex i, and p _j is the coordinate of point j adjacent to vertex i.

Step 504: the original coordinates p _i is updated to λL _(i) + p i; where λ is a positive real number less than 1;

Step 505: Iterate the mesh smoothing step m ₁ times, and then perform the second smoothing operation.

The second step is to smooth the mesh: select again all the triangles on the tumor and the triangles of the tumor hole boundary on the vascular mesh model and its n-neighboring triangles, and the digital grid composed of the above triangles The model is used as the input of mesh smoothing, and the above mesh smoothing operation is iteratively performed m ₂ times, where m ₁ should be much larger than m ₂ . The smoothing process of the grid at the junction of the tumor grid and the blood vessel digital model is shown in Figure 8. Figure 8 (a) the original tumor grid, Figure 8 (b) is the tumor grid after the first step of smoothing, Figure 8 (c) The tumor grid after smoothing in the second step.

Step 600: Perform a strict boundary-preserving mesh simplification on the tumor mesh model, and obtain the result of generating the tumor in the blood vessel digital model.

In step 600, after the tumor grid is generated, a grid simplification with strict boundary preservation is performed, so that there will be no excessive difference between the grid density of the tumor grid and the blood vessel grid. The entire tumor grid is used as the input grid to perform strict boundary-preserving QEM (secondary error metric) grid simplification. The process is shown in Figure 9, which specifically includes the following steps:

Step 601: Calculate the error matrix Q for all initial vertices to obtain all valid edges (v ₁ , v ₂ ) (valid edges refer to the edges of China Unicom);

In step 601, specifically, it is necessary to calculate the plane equations ax+by+cz+d=0 and a ₂ + b ₂ + c ₂ =1 of all planes adjacent to a vertex, and save the parameters a, b, c, d , Construct a vector p = (a, b, c, d) ^T , calculate the quadratic basic error matrix K _{p of} each face:

Summing all K _{p of} a vertex constitutes the error matrix Q of that point.

Step 602: For each valid edge (v ₁ , v ₂ ), calculate the optimal extraction target v and the cost of extracting this edge;

In step 602, if the edge (v ₁ , v ₂ ) is a boundary edge, the extraction cost is set to infinite. For the non-boundary effective edges (v ₁ , v ₂ ), suppose it shrinks to a point v, and mark

Where Q ₁ and Q ₂ are the error matrices of v ₁ and v ₂ , respectively, and the extraction cost of this edge should be

Differentiate cost and calculate the value of v when its derivative is 0

That is to solve the equation:

In formula (13), q _ij is the corresponding element in matrix Q. _{If the coefficient matrix is invertible, the coordinates of the optimal extraction target v 0} can be obtained by solving the above equation. If the coefficient matrix is not invertible, then let

Take the midpoint of _{v 1} and v _2.

Step 603: Store all edges in a heap according to the extraction cost cost;

Step 604: Remove the edge with the least extraction cost each time, and merge the vertices v ₁ and v ₂ into

And update all

The extraction cost of the connected effective edges and the optimal extraction position are calculated to calculate the number of triangles in the tumor mesh after the least cost edge is removed.

Step 605: Repeat the above steps until the number of existing faces is small to set a threshold.

After all the above steps, the final effect of generating a tumor in the blood vessel digital model is shown in Figure 10.

Please refer to FIG. 11, which is a schematic structural diagram of a system for generating a tumor in a blood vessel digital model according to an embodiment of the present application. The system for generating a tumor in a blood vessel digital model in an embodiment of the present application includes a tumor position selection module, an approximate radius calculation module, a tumor grid construction module, a tumor grid deformation module, a grid smoothing processing module, and a grid simplification module.

Tumor position selection module: used to select the tumor position on the blood vessel digital model; the specific method of tumor position selection is: click on a point on the blood vessel digital model, and use the position information of the point as the screen coordinate information; this screen coordinate information Convert it into world coordinate information, and connect the world coordinate information and the position of the virtual camera into a ray; calculate the triangle face on the digital model of the blood vessel that intersects the ray, and calculate the position T of the geometric center point of the three vertices of the triangle _c , the position T _c is the tumor position selected on the blood vessel digital model.

Approximate radius calculation module: used to calculate the approximate radius of the blood vessel digital model at the tumor location based on the point method equation of the plane; the approximate radius calculation method is specifically:

1. Take the tumor position selected on the blood vessel digital model as the center, get m triangle faces whose surrounding radius is R, and calculate the normal vector of the first triangle face and the normal vector of the second triangle face. Vector product

By analogy, m-1 vector products can be calculated

Then calculate their mean

_{2. Take the triangle f 0} where the tumor position coordinates selected on the blood vessel digital model are located, calculate the coordinates G ₀ (x ₀ , y ₀ , z ₀ ) of its center of gravity, and pass

And G ₀ , we get a pass through G ₀ and perpendicular to

The point French equation of the plane, namely:

A(xx ₀ )+B(yy ₀ )+C(zz ₀ )=0 (1)

3. Set a suitable positive real number α, and find all the barycentric coordinates G _i (x _i , y _i , z _i ) in all the triangles that constitute the blood vessel digital model to conform to the inequality -α≤A(xx _i )+ B(yy _i )+C(zz _i )≤α triangular faces are combined to form a set F, and the average value of the barycentric coordinates of all triangular faces in F is calculated to obtain a point O ₀ ;

4. Calculate the linear distance between the center of gravity of all triangles in the set F and the point O ₀ and then calculate the average value R _0. The average value R ₀ is the approximate radius of the blood vessel digital model at the selected tumor position.

Tumor mesh building module: used to generate a virtual sphere with the selected tumor position as the center of the sphere, collide the virtual sphere with the blood vessel digital model and delete the collision triangle, generate a cavity in a way that grows toward the center of the virtual sphere, and iteratively The triangle refinement method constructs a smooth and regular tumor mesh model; the specific method for constructing the tumor mesh model is as follows:

_{1. Using the tumor position T c} selected on the blood vessel digital model as the center of the sphere, a virtual sphere with a radius of r is generated, r=αR ₀ , and α is a value between 0 and 1;

2. Perform collision detection between the virtual sphere and the blood vessel digital model, and obtain all triangle sets S that intersect with the virtual sphere, and find the average normal vector D _t of all triangle faces in the set S, which is the growth direction of the tumor;

3. Delete all the triangular patches in the set S from the blood vessel digital model to obtain an irregular boundary. The set of all vertices on the boundary is S _bd ;

4. Connect each vertex on the vertex set S _bd to the center of the sphere T _c _{, and obtain the intersection set S int of} the corresponding link and the virtual sphere respectively;

5. Triangulate the vertices on the vertex set S _bd and the intersection set S _int to form a circle of triangle meshes, and use _{the vertices in the intersection set S int} as the vertices where the tumor and the blood vessel intersect;

6. Calculate the tumor sphere center position P _T and the tumor highest point position P _H :

P _T ＝T _c +(R ² -r ² )D _t (2)

P _H ＝P _T +RD _t (3)

7. Connect the vertices in the intersection set S _int and the highest point position P _{H of the} tumor to form a cone-shaped grid. The triangle set that composes the grid is S ₀ , and each triangle in the set S _{0 is refined.} _{A new triangle set S 1 is} obtained by sub-operation, and then the _{same subdivision operation is performed on each triangle in the set S 1.} This operation is performed for N rounds, and the finally obtained triangle set S _{N is a} regular tumor mesh model.

Tumor grid deformation module: used to edit the surface of the tumor grid model, select a certain number of control points, and construct irregular deformations on the tumor grid surface by maintaining rigid deformation; specific construction methods include:

1. Set the input grid, select the control points and set the free point set corresponding to each control point, set the fixed position constraints of the control points, and carry out the rigidity-preserving grid deformation;

2. Use the generated tumor mesh model as the input mesh S of the mesh deformation operation;

3. Select the control points; combined with the method of longitude and latitude sampling to construct the tumor grid, it is easy to obtain the strip grid M _i (i=1, 2) composed of triangles between two adjacent arcs on the tumor grid. , ..., n, n number of sets of vertices P), and further, it can be set by a plurality of strip-shaped grid composed of M _i. According to this method, the tumor grid is divided into m parts, each part has

One of the above strip grids, the last part has

The above strip grids. As shown in Fig. 3, Fig. 3(a) is a schematic diagram of the grid between two arcs on the tumor grid, and Fig. 3(b) is a schematic diagram of a part of the tumor grid when the tumor grid is divided into three parts. Divide the tumor grid into m parts, randomly select q control points in each part; for each control point, select triangles within a certain range around the tumor grid, and divide the vertices of these triangles As the free point set corresponding to this control point.

4. Set the fixed position constraint information; set the position of the control point as: the position of the current control point after moving λR along the normal direction or the reverse of the normal direction of the point; where λ is a constant between greater than 0 and less than 1, R It is the radius of the tumor; the user can customize λ, the larger the λ, the greater the degree of irregular deformation of the tumor surface.

5. Combine input grid information, control points and their corresponding free point set information, and fixed position constraint information to perform rigid grid deformation. The rigid mesh deformation process includes:

Step 1: Obtain the adjacency information of the input mesh S, and make the vertex v _i and its 1-neighbor triangle patch form a unit C _i , as shown in Figure 5; if the unit C _i undergoes a rigid transformation, then the before and after transformation The positional relationship of the vertices can be represented by a rotation matrix, that is, it satisfies: p _i ′-p _j ′=R _i (p _i -p _j )

N (i) is the set of vertices adjacent to vertex v _i.

make

R _i ＝V _i U _i ^T (8)

The process of the tumor mesh for rigidity-preserving deformation is shown in Figure 6, where (a) is the setting of fixed position constraints, (b) is the initial guess of the deformation of the mesh model, and (c) is the iterative update of p and R for a certain number of times. Grid model. It should be noted that in the process of selecting control points in this application, in addition to randomly selecting control points in a certain way, control points can also be selected through human-computer interaction with the user's mouse click; the fixed position constraint process can be set in addition to In addition to the fixed offset λR, the offset can be set by recording the distance the user controls the mouse to move.

Grid smoothing processing module: used to smooth the connection between the tumor grid model and the blood vessel digital model; the smoothing processing process is divided into the following two steps:

The first step of grid smoothing operation includes:

1. Obtain the adjacency information of the digital grid model, and record the set of adjacency points of each vertex i as N(i);

2. Calculate the weight of each adjacent point of each vertex:

In formula (10),

α _ij and β _ij are two opposite corners of the edge (i, j).

3. Calculate the Laplacian coordinate L(i) of each point in the digital grid model according to the adjacency information and w _ij:

4, the original coordinate of p _i is updated to λL _(i) + p i; where λ is a positive real number less than 1;

5. Iterate the mesh smoothing step m ₁ times, and then perform the second smoothing operation.

Mesh simplification module: used to simplify the tumor mesh model with strict boundary preservation, and obtain the result of tumor generation in the blood vessel digital model; after generating the tumor mesh, perform strict boundary preservation mesh simplification to make the tumor network There will not be too much difference between the grid density of the grid and the blood vessel grid. The entire tumor grid is used as the input grid, and the QEM (quadratic error metric) grid simplification with strict boundary preservation includes:

1. Calculate the error matrix Q for all initial vertices to obtain all effective edges (v ₁ , v ₂ ) (effective edges refer to connected edges); specifically, it is necessary to calculate the plane equation ax of all planes adjacent to a vertex +by+cz+d=0 and a ₂ +b ₂ +c ₂ =1, save the parameters a, b, c, d, construct the vector p=(a, b, c, d) ^T , calculate the Quadratic basic error matrix K _p :

Summing all K _{p of} a vertex constitutes the error matrix Q of that point.

2. For each valid edge (v ₁ , v ₂ ), calculate the optimal extraction target v and the cost of extracting this edge; if the edge (v ₁ , v ₂ ) is a boundary edge, set its extraction cost to infinite Big. For the non-boundary effective edges (v ₁ , v ₂ ), suppose it shrinks to a point v, and mark

Differentiate cost and calculate the value of v when its derivative is 0

That is to solve the equation:

Take the midpoint of _{v 1} and v _2.

3. Store all edges in a heap according to the extraction cost cost;

4. Each time the edge with the least extraction cost is removed, the vertices v ₁ and v _{2 are} merged into

And update all

5. Repeat the above steps until the number of existing faces is small and set the threshold;

This application is proved to be feasible through experiments, and the efficiency is high, and the time for generating tumor lesions on the blood vessel digital model is within 1s.

FIG. 12 is a schematic diagram of the hardware device structure of the method for generating a tumor in a blood vessel digital model provided by an embodiment of the present application. As shown in Figure 12, the device includes one or more processors and memory. Taking a processor as an example, the device may also include: an input system and an output system.

The processor, the memory, the input system, and the output system may be connected by a bus or in other ways. In FIG. 12, the connection by a bus is taken as an example.

As a non-transitory computer-readable storage medium, the memory can be used to store non-transitory software programs, non-transitory computer executable programs, and modules. The processor executes various functional applications and data processing of the electronic device by running non-transitory software programs, instructions, and modules stored in the memory, that is, realizing the processing methods of the foregoing method embodiments.

The memory may include a program storage area and a data storage area, where the program storage area can store an operating system and an application program required by at least one function; the data storage area can store data and the like. In addition, the memory may include a high-speed random access memory, and may also include a non-transitory memory, such as at least one magnetic disk storage device, a flash memory device, or other non-transitory solid-state storage devices. In some embodiments, the memory may optionally include a memory remotely provided with respect to the processor, and these remote memories may be connected to the processing system through a network. Examples of the aforementioned networks include, but are not limited to, the Internet, corporate intranets, local area networks, mobile communication networks, and combinations thereof.

The input system can receive input digital or character information, and generate signal input. The output system may include display devices such as a display screen.

The one or more modules are stored in the memory, and when executed by the one or more processors, the following operations of any of the foregoing method embodiments are performed:

Step a: Select the tumor position on the blood vessel digital model;

The above-mentioned products can execute the methods provided in the embodiments of the present application, and have functional modules and beneficial effects corresponding to the execution methods. For technical details that are not described in detail in this embodiment, please refer to the method provided in the embodiment of this application.

The embodiment of the present application provides a non-transitory (non-volatile) computer storage medium, the computer storage medium stores computer executable instructions, and the computer executable instructions can perform the following operations:

Step a: Select the tumor position on the blood vessel digital model;

The embodiment of the present application provides a computer program product, the computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program includes program instructions, when the program instructions are executed by a computer To make the computer do the following:

Step a: Select the tumor position on the blood vessel digital model;

The method, system and electronic device for generating tumors in digital blood vessel models in the embodiments of this application design an automatic generation and optimization method of blood vessel tumor models to enrich the available case models in the field of virtual surgery and make the operation simple Efficient. Compared with the prior art, this application has the following advantages:

1. This application does not have the problem of limited source of case data, and it can be used without any learning costs.

The tumor can be constructed at almost any position in the digital model of normal blood vessels, with a high degree of freedom;

The foregoing description of the disclosed embodiments enables those skilled in the art to implement or use this application. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined in this application can be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application will not be limited to the embodiments shown in this application, but should conform to the widest scope consistent with the principles and novel features disclosed in this application.

Claims

A method for generating a tumor in a digital blood vessel model, which is characterized in that it comprises the following steps:

Step a: Select the tumor position on the blood vessel digital model;

Step b: Calculate the approximate radius of the blood vessel digital model at the tumor location based on the point method equation of the plane;

Step c: Generate a virtual sphere with the selected tumor position as the center of the sphere. After the virtual sphere collides with the blood vessel digital model, the collision triangle is deleted, and a cavity is generated by growing toward the center of the virtual sphere, and is refined by iterative triangles Method to construct a smooth and regular tumor grid model;

Step d: Edit the surface of the tumor mesh model, select a certain number of control points, and construct irregular deformations on the surface of the tumor mesh by maintaining rigid deformation;

Step e: smoothing the connection between the tumor mesh model and the blood vessel digital model;

Step f: Perform a strict boundary-preserving mesh simplification on the tumor mesh model to obtain the result of tumor generation in the blood vessel digital model.
The method for generating a tumor in a blood vessel digital model according to claim 1, wherein, in the step a, the method of selecting the tumor position is specifically: clicking on a point on the blood vessel digital model, and then selecting a point on the blood vessel digital model. The position information is used as the screen coordinate information; the screen coordinate information is converted into world coordinate information, and the world coordinate information is connected with the position of the virtual camera to form a ray; the triangle patch on the digital model of the blood vessel that intersects the ray is calculated, and the calculation the geometric center position of the three vertices of the triangle T c, T c, ie the position selected on the digital model of the vascular tumor site.
The method for generating a tumor in a digital blood vessel model according to claim 2, wherein, in the step b, the approximate radius calculation method specifically includes:

Step b1: Take the tumor position selected on the blood vessel digital model as the center, obtain m triangle faces whose surrounding radius is R, calculate the normal vector of the first triangle face and the normal vector of the second triangle face Vector product of
Calculate the vector product of the normal vector of the second triangular face and the normal vector of the third triangular face
By analogy, m-1 vector products can be calculated
Then calculate their mean

Step b2: Take the triangle f 0 where the tumor position coordinates selected on the blood vessel digital model are located, calculate the coordinates G 0 (x 0 , y 0 , z 0 ) of its center of gravity, and pass
And G 0 , we get a pass through G 0 and perpendicular to
The point French equation of the plane, namely:

A(xx 0 )+B(yy 0 )+C(zz 0 )=0

Step b3: Set a positive real number α, and find all the barycentric coordinates G i (x i , y i , z i ) in all triangles that make up the blood vessel digital model to meet the inequality -α≤A(xx i )+B (yy i )+C(zz i )≤α and form a set F, calculate the average of the barycentric coordinates of all triangles in F, and get a point O 0 ;

Step b4: Calculate the linear distance between the center of gravity of all triangles in the set F and the point O 0 and then calculate the average value R 0 , and the average value R 0 is the approximate radius of the blood vessel digital model at the selected tumor position.
The method for generating a tumor in a digital blood vessel model according to claim 3, wherein, in the step c, the constructing a smooth and regular tumor grid model specifically includes:

Step c1: Taking the tumor position T c selected on the blood vessel digital model as the center of the sphere, a virtual sphere with a radius of r is generated, r=αR 0 , and α is a value between 0 and 1;

Step c2: Perform collision detection between the virtual sphere and the blood vessel digital model to obtain all triangle sets S that intersect the virtual sphere, and find the average normal vector D t of all triangle faces in the set S, which is the growth direction of the tumor;

Step c3: Delete all the triangular faces in the set S from the blood vessel digital model to obtain an irregular boundary. The set of all vertices on the boundary is S bd ;

Step c4: Connect each vertex on the vertex set S bd with the center of the sphere T c , and obtain the intersection set S int of the corresponding link and the virtual sphere respectively;

Step c5: Triangulate the vertices on the vertex set S bd and the intersection set S int to form a circle of triangle meshes, and use the vertices in the intersection set S int as the vertices where the tumor and the blood vessel intersect;

Step c6: Calculate the tumor sphere center position P T and the tumor highest point position P H :

P T ＝T c +(R 2 -r 2 )D t

P H ＝P T +RD t

In the above formula, R is the radius of the tumor, R=μr, μ is a constant greater than 1, r=αR 0 , R 0 is the approximate radius of the blood vessel digital model at the selected tumor position;

Step c7: Connect the vertices in the intersection set S int and the highest point position P H of the tumor to form a cone-shaped grid. The triangle set that composes the grid is S 0 , and each triangle in the set S 0 is performed Subdivision operation, a new triangle set S 1 is obtained , and then the same subdivision operation is performed on each triangle in the set S 1. This operation is performed for N rounds, and the final triangle set S N is the regular tumor mesh model .
The method for generating a tumor in a blood vessel digital model according to claim 4, wherein the subdivision operation for each triangle specifically includes: for each triangle in the set, if there are two vertices in the three vertices A and B belong to the intersection set S int , then take the midpoints X and Y of the other two edges except the edge composed of vertices A and B to connect, and take any one of the midpoints X and Y and vertices A and B If any of the three vertices of the triangle are connected, divide the original triangle into three, and X and Y are the new vertices; if none of the three vertices of the triangle belong to the vertex set S int , then take the midpoints X, Y, Z of the three sides , And connect two by two, divide the original triangle into 4 triangles, X, Y and Z are the new vertices; move the new vertices X and Y or X, Y and Z to the rays P T X and P T respectively At the intersection of Y or P T X, P T Y and P T Z with the virtual sphere, the final position is obtained.
The method for generating a tumor in a digital blood vessel model according to claim 4, wherein in the step d, the constructing an irregular deformation on the surface of the tumor grid specifically comprises:

Step d1: Use the generated tumor mesh model as the input mesh S of the mesh deformation operation;

Step d2: Divide the tumor grid into m parts, randomly select q control points in each part; for each control point, select triangles within a certain range around the tumor grid, and divide these triangles The vertex of the slice is used as the free point set corresponding to the control point;

Step d3: Set the position constraint information of the control point as: the position of the current control point after moving λR along the normal direction or the normal direction of the point; where λ is a constant between greater than 0 and less than 1, and R is the radius of the tumor ；

Step d4: Combine input grid information, control points and their corresponding free point set information, and fixed position constraint information to perform rigidity-preserving grid deformation.
The method for generating a tumor in a digital blood vessel model according to claim 6, wherein the rigidity-preserving mesh deformation specifically includes:

Step 1: Obtain the adjacency information of the input mesh S, and make the vertex v i and its 1-neighboring triangle patch form a unit C i ;

Step 2: Define the rigid energy of each unit, and sum to obtain the overall rigid energy:

In the above formula, S is the input mesh, S′ is the deformed input mesh; E(S′) is the rigid energy of the entire mesh; n is the number of vertices in the input mesh S, and C i is the vertex v i and its 1-neighbor triangular facet constitute a unit, C i ′ is the deformed unit, E(C′) is the rigid energy of a unit, N(i) is the vertex adjacent to vertex v i collection, p i is a vertex v i coordinates, coordinates of p i deformed p i ', p j is a vertex v j of the coordinates, the coordinates of the p j deformed p j', w ij is the weight of the edge e ij weight , Using cotangent weights
α ij and β ij are the two opposite corners of the edge e ij ; R i is the rotation matrix before and after the transformation of the unit C i;

Step 3: Determine the initial guess of the vertex coordinates after deformation; for the selected control point, its initial guess is the fixed position constraint set before; for free points, determine the initial guess by minimizing ||Lp′-δ|| 2, Where δ=Lp, p is the coordinates of the vertices in the initial grid input by the user, and p′ is the coordinates of the vertices in the grid after the control point coordinates have been changed according to the above fixed position constraints; ||Lp′-δ|| 2 Realize the smallest, then Lp′=Lp, where the matrix L is defined as follows:

In the above formula, w ij is the weight of edge e ij , and the weight of cotangent is used
N(i) is the set of vertices adjacent to the vertex v i ; through further calculation and simplification, it can be obtained: A T AX free =A T (Lp-BX fixed ), and X free can be obtained by solving the equations, namely Is the initial guess of the free point;

The fourth step: use the post-deformation vertex coordinates p i ′ and use the singular value decomposition to calculate the optimal rotation matrix of all deformed units;

Step 5: Use the current optimal rotation matrix to solve the linear equations to obtain the new vertex coordinates; when R i is determined, solve the linear equations
Obtain p′ that minimizes E(S′). For each p i ′, the following equation can be obtained:

The linear combination on the left side of the above equation is the discrete Laplacian-Beltrami operator of p′, so the system of equations can be written as: Lp′=b; p′ can be obtained by solving the system of equations;

The sixth step: iteratively execute the fourth and fifth steps until the overall rigidity energy is less than the set threshold.
The method for generating a tumor in a digital blood vessel model according to claim 6, wherein, in the step e, the smoothing process includes:

Step e1: Select the triangle surface of the tumor hole boundary and its n-neighboring triangle surface on the vascular mesh model, and use the digital mesh model composed of the above triangle surface as the input of the first mesh smoothing operation:

Get the adjacency information of the digital grid model, and record the set of adjacency points of each vertex i as N(i);

Calculate the weight of each adjacent point of each vertex:

In the above formula,
α ij and β ij are the two opposite corners of the edge (i, j);

Calculate the Laplacian coordinate L(i) of each point in the digital grid model according to the adjacency information and w ij:

In the above formula, p i is the coordinate of vertex i, and p j is the coordinate of the adjacent point j of vertex i;

The original coordinate p i is updated to λL (i) + p i; where λ is a positive real number less than 1;

Perform the above grid smoothing step iteratively m 1 times;

Step e2: Select again all the triangles on the tumor and the triangles of the tumor hole boundary on the vascular mesh model and its n-neighbor triangles, and use the digital mesh model composed of the above triangles as the mesh light For smooth input, perform the above mesh smoothing operation iteratively m 2 times, where m 1 should be much larger than m 2 .
The method for generating a tumor in a digital blood vessel model according to claim 8, wherein, in the step f, the strict boundary-preserving mesh simplification of the tumor mesh model specifically comprises:

Step f1: Calculate the error matrix Q for all initial vertices to obtain all valid edges (v 1 , v 2 );

Step f2: For each valid edge (v 1 , v 2 ), calculate the optimal extraction target v and the cost of extracting this edge;

Step f3: Store all edges in a heap according to the extraction cost cost;

Step f4: Remove the edge with the least extraction cost each time, and merge the vertices v 1 and v 2 into
And update all
The extraction cost of the connected effective edges and the optimal extraction position, and calculate the number of triangles in the tumor mesh after the least cost edge is removed;

Step f5: Repeat steps f1 to f4 until the number of existing faces is small to set a threshold.
A system for generating a tumor in a digital blood vessel model, which is characterized in that it comprises:

Tumor location selection module: used to select the tumor location on the blood vessel digital model;

Approximate radius calculation module: used to calculate the approximate radius of the blood vessel digital model at the tumor location based on the point method equation of the plane;

Tumor grid building module: used to generate a virtual sphere with the selected tumor position as the center of the sphere, collide the virtual sphere with the blood vessel digital model and delete the collision triangle, generate a cavity by growing toward the center of the virtual sphere, and pass Iterative triangle refinement method builds a smooth and regular tumor mesh model;

Tumor grid deformation module: used to edit the surface of the tumor grid model, select a certain number of control points, and construct irregular deformations on the tumor grid surface by maintaining rigid deformation;

Grid smoothing processing module: used for smoothing the connection between the tumor grid model and the blood vessel digital model;

Grid simplification module: used to perform grid simplification with strict boundary preserving on the tumor grid model to obtain the result of tumor generation in the blood vessel digital model.
An electronic device including:

At least one processor; and

A memory communicatively connected with the at least one processor; wherein,

The memory stores instructions that can be executed by the one processor, and the instructions are executed by the at least one processor, so that the at least one processor can execute any one of 1 to 9 above. The following operations of the method of generating tumors in the digital model:

Step a: Select the tumor position on the blood vessel digital model;

Step b: Calculate the approximate radius of the blood vessel digital model at the tumor location based on the point method equation of the plane;

Step c: Generate a virtual sphere with the selected tumor position as the center of the sphere. After the virtual sphere collides with the blood vessel digital model, the collision triangle is deleted, and a cavity is generated by growing toward the center of the virtual sphere, and is refined by iterative triangles Method to construct a smooth and regular tumor grid model;

Step d: Edit the surface of the tumor mesh model, select a certain number of control points, and construct irregular deformations on the surface of the tumor mesh by maintaining rigid deformation;

Step e: smoothing the connection between the tumor mesh model and the blood vessel digital model;

Step f: Perform a strict boundary-preserving mesh simplification on the tumor mesh model to obtain the result of tumor generation in the blood vessel digital model.