CN103247073B - Three-dimensional brain blood vessel model construction method based on tree structure - Google Patents

Abstract

The invention provides a three-dimensional cerebral vessel model construction method based on a tree structure, which comprises the following steps of firstly, obtaining a three-dimensional cerebral vessel body data field from CT or MRA equipment; separating cerebral vessels from background noise by adopting a segmentation algorithm; secondly, calculating a skeleton line of the cerebral vessels; constructing a tree-shaped cerebrovascular topological structure according to the skeleton line; thirdly, calculating the radius of each control point cerebral vessel by adopting an elastic sphere algorithm according to the skeleton line; and finally, displaying the constructed tree-structure cerebral vessels in three dimensions. The construction method provided by the invention conforms to the spatial topological structure information of the cerebral vessels, and has the advantages of high blood vessel display precision and small result error. The method can detect the cerebrovascular disease region and draw the display windows with different sizes in a multi-scale mode.

Description

Three-dimensional brain blood vessel model construction method based on tree structure

Technical Field

The invention belongs to the field of medicine, and particularly relates to a three-dimensional blood vessel model construction method based on a tree structure.

Background

Existing vascular modeling techniques can be broadly divided into two categories: a model-free (model-free) method and a model-based (model-based) method.

The most typical and common surface reconstruction method in the free model method is the mc (marching cubes) algorithm. The method is characterized in that a proper threshold value is selected, and an isosurface is calculated by a linear interpolation method, so that the space is divided into two parts to achieve the purpose of reconstruction. However, the use of linear interpolation and thresholding of the space into two parts is also too simple and the reconstruction is not optimal. After reconstruction, the aliasing effect of the surface needs to be removed by smoothing, and a simple laplacian smoothing method can destroy small branches. Taubin proposes a low-pass filtering method, and Vollmer improves Laplace smoothing, so that better effects are achieved. Constrained Elastic Surface Networks (CESNs) achieve the desired result of better balancing accuracy and smoothness by constraining the vertices of the smooth original surfaces within the cell to which they belong.

The method based on the model assumes that the blood vessel is a tubular structure, and approaches the cross section of the blood vessel by utilizing various geometric shapes and construction methods to achieve the purpose of reconstructing the blood vessel, wherein the method usually adopts a tubular or spherical representation blood vessel model, not only defines all points in a three-dimensional solid model, but also precisely defines the central line (skeleton) of the three-dimensional solid model, is very beneficial to real-time control, deformation and evolution of the model, and is a construction method which is very suitable for expressing tubular objects such as the constructed blood vessel.

Disclosure of Invention

Aiming at the defects that the topological structure of blood vessels is not considered and tiny branches are damaged in the processing process in the existing method, the invention provides a method for constructing a three-dimensional brain blood vessel model based on a tree structure, the tree structure is adopted by the model to accord with the topological characteristic of the brain blood vessels, a ball-combined central line mode is adopted to represent a single blood vessel, the description method can detect the diseased region of the brain blood vessels, and multi-scale mode drawing can be adopted for display windows with different sizes.

In order to achieve the purpose, the invention adopts the following technical scheme:

the three-dimensional blood vessel model construction method based on the tree structure comprises the following steps:

(1) acquiring a three-dimensional cerebral vascular body data field from a CT or MRA device;

(2) separating cerebral vessels from background noise by adopting a segmentation algorithm;

(3) calculating a skeleton line of the cerebral vessels;

(4) constructing a tree-shaped cerebrovascular topological structure according to the skeleton line;

(5) calculating the radius of the cerebral blood vessel of each node by adopting an elastic sphere algorithm according to the skeleton line;

(6) and displaying the constructed brain blood vessel with the tree structure in three dimensions.

Preferably, the step (2) includes:

(2.1) smoothing the three-dimensional cerebral vascular body data field by adopting Gaussian filtering, obtaining an MIP image through MIP projection, and obtaining three-dimensional vascular seed points by adopting a two-dimensional OTSU algorithm and the MIP image;

(2.2) defining a region growing rule combining global information and local information, and carrying out rough segmentation on the blood vessel through a region growing algorithm to obtain a region growing blood vessel outline;

and (2.3) performing anisotropic filtering on the three-dimensional cerebral vessel body data field by adopting a Catt diffusion model, and performing secondary segmentation by taking the primary segmentation result as an initial contour line of the adaptive active contour model by adopting a local adaptive C-V model.

Preferably, the cerebrovascular trend is calculated in step (3) by using a Hessian matrix method.

Preferably, the step (5) is to find the elastic ball center line through the construction of the elastic ball motion force equation.

Preferably, said step (2.3) is implemented by the following formula:

$E^{\mathrm{LCV}}(c_1,c_2,c_1^{\′},c_2^{\′},\mathrm{\φ})=\mathrm{\μ}{\∫}_{\mathrm{\Ω}}\mathrm{\δ}\left(\mathrm{\φ}(x,y)\right)|\▿\mathrm{\φ}(x,y)|\mathrm{dxdy}+V{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+$

${\mathrm{\λ}}_1{\∫}_{\mathrm{\Ω}}|u_0(x,y)-c_1{|}^{2}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+{\mathrm{\λ}}_2{\∫}_{\mathrm{\Ω}}{|u_0(x,y)-c_2|}^2(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}+$

${\mathrm{\λ}}_1^{\′}{\∫}_{\mathrm{\Ω}}{|u_0(x,y)-c_1^{\′}|}^{2}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+{\mathrm{\λ}}_2^{\′}{\∫}_{\mathrm{\Ω}}{|u_0(x,y)-c_2^{\′}|}^2(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}---\left(1\right)$

in the formula (1) and the formula (2),

$c_1=\frac{{\∫}_{{\mathrm{\Ω}}_1}{u}_0(x,y)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_1}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}$ $c_2=\frac{{\∫}_{{\mathrm{\Ω}}_2}{u}_0(x,y)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_2}(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}$

$c_1^{\′}=\frac{{\∫}_{{\mathrm{\Ω}}_1^{\′}}{u}_0(x,y)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_1^{\′}}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}$ $c_2^{\′}=\frac{{\∫}_{{\mathrm{\Ω}}_2^{\′}}{u}_0(x,y)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_2^{\′}}(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}.$

preferably, the specific process of obtaining the cerebrovascular centerline and radius information in the step (3) is as follows:

setting an elastic force equation to determine the center trend of the elastic ball:

$F(i,j,k)=\underset{m=i-r}{\overset{i+r}{\mathrm{\Σ}}}\underset{n=j-r}{\overset{j+r}{\mathrm{\Σ}}}\underset{p=k-r}{\overset{k+r}{\mathrm{\Σ}}}\mathrm{Seg}(m,n,k)---\left(3\right)$

in formula (3):

in equation (4), V (m, n, k) represents the segmentation result, Position (i, j, k) represents the vector Position of the pixel at the (i, j, k) Position, and r represents the currently calculated radius of the blood vessel, and the calculation process is as follows:

step1: setting r =1 for the current centerline point location endpoint;

step 2: calculating the elastic force;

step 3: if the elastic force is zero, setting r = r +1, and repeating Step2, otherwise, carrying out the next Step;

step 4: moving the central point along the vector direction of the force, and recalculating the elastic force;

step 5: if the elastic force is zero and double tangency occurs, the search is finished, otherwise, the next step is carried out;

step 6: the newly revised centerline and radius information is recorded, returning to Step 3.

Preferably, the method for constructing the cerebrovascular tree topology is as follows:

each branch vessel structure is represented in a node mode, and the data structure is defined as follows:

Struct Node

{

the node of the parent is a node of the parent,

{ center line position, radius, circular plane normal vector },

the left child node of the left child node,

right child node

}

The classification strategy of the nodes on the framework is as follows:

end point: the neighborhood relationship of the end points of the positions where the skeleton lines start or stop is as follows: there is only one adjacency point;

common points are as follows: forming basic points of the skeleton line, wherein two adjacent points exist around the common point;

a bifurcation point: the branch point of the skeleton line is of a bipartite structure, and three adjacent points are arranged around the branch point;

constructing a tree topology structure:

on the basis of the node classification, a blood vessel tree-shaped topological structure is constructed by adopting a depth-first side rate, and the algorithm is as follows:

step1, taking the current observation node as the starting point, directly establishing a new tree structure, and storing the current point as the root node;

step 2: entering the next node to be observed;

step 3: adding the current observation point which is a common point into the node structure being processed, and returning to Step 2; otherwise, go to Step 4;

step 4: if the observation point is a bifurcation point, establishing two new nodes respectively as a left child node and a right child node of the node, and respectively entering Step2 in a recursion mode aiming at the left child node and the right child node;

step 5: and after all the nodes are processed, the topological structure of the vessel tree is constructed.

The three-dimensional cerebral vessel model construction method based on the tree structure can effectively segment the thick branches of the cerebral vessels and can accurately extract the fine structures of the cerebral vessels. The three-dimensional cerebral blood vessel model constructed by the invention adopts a tree structure to accord with the topological characteristic of a cerebral blood vessel, adopts a sphere combined central line mode to represent a single blood vessel, can detect a cerebral blood vessel pathological change area, and can draw display windows with different sizes in a multi-scale mode.

Drawings

FIG. 1 is a flow chart of a three-dimensional brain blood vessel model construction method based on a tree structure according to the present invention;

FIG. 2 is a flow chart of a segmentation algorithm to separate cerebral vessels from background noise;

FIG. 3 results of extracted cerebrovascular skeleton lines;

FIG. 4 is a diagram illustrating an elastic sphere algorithm for obtaining a radius corresponding to a point on a centerline;

FIG. 5 structural design of data of each node in tree-like cerebral blood vessel;

fig. 6 shows the results of the three-dimensional brain blood vessel model construction.

Detailed Description

Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention is not limited to only these embodiments. The invention is intended to cover alternatives, modifications, equivalents, and alternatives that may be included within the spirit and scope of the invention. In the following description of the preferred embodiments of the present invention, specific details are set forth in order to provide a thorough understanding of the present invention, and it will be apparent to those skilled in the art that the present invention may be practiced without these specific details.

As shown in fig. 1, the present invention provides a method of construction comprising the steps of:

step S601: acquiring original data of a medical image, and acquiring a three-dimensional cerebral vascular body data field from CT or MRA equipment;

step S602: and separating the blood vessel data from the background by adopting a segmentation algorithm. As shown in fig. 2, the specific implementation method of step S602 is to firstly perform smoothing processing on the three-dimensional cerebral vascular body data field by using gaussian filtering, obtain an MIP image through MIP projection, and obtain three-dimensional vascular seed points by using a two-dimensional OTSU algorithm and using the MIP image; then, roughly dividing the blood vessel by a region growing algorithm by adopting a region growing rule combining self-defined global information and local information to obtain a region growing blood vessel outline; and finally, performing anisotropic filtering on the three-dimensional cerebral vessel body data field by adopting a Catt diffusion model, performing secondary segmentation by adopting a local self-adaptive C-V model and taking the primary segmentation result as an initial contour line of the self-adaptive active contour model to obtain a cerebral vessel skeleton line as shown in fig. 3. The parameter setting of the local self-adaptive C-V model is shown as a formula (1) and a formula (2),

$E^{\mathrm{LCV}}(c_1,c_2,c_1^{\′},c_2^{\′},\mathrm{\φ})=\mathrm{\μ}{\∫}_{\mathrm{\Ω}}\mathrm{\δ}\left(\mathrm{\φ}(x,y)\right)|\▿\mathrm{\φ}(x,y)|\mathrm{dxdy}+V{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+$

${\mathrm{\λ}}_1{\∫}_{\mathrm{\Ω}}|u_0(x,y)-c_1{|}^{2}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+{\mathrm{\λ}}_2{\∫}_{\mathrm{\Ω}}{|u_0(x,y)-c_2|}^2(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}+$

${\mathrm{\λ}}_1^{\′}{\∫}_{\mathrm{\Ω}}{|u_0(x,y)-c_1^{\′}|}^{2}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+{\mathrm{\λ}}_2^{\′}{\∫}_{\mathrm{\Ω}}{|u_0(x,y)-c_2^{\′}|}^2(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}---\left(1\right)$

wherein,

$c_1=\frac{{\∫}_{{\mathrm{\Ω}}_1}{u}_0(x,y)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_1}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}$ $c_2=\frac{{\∫}_{{\mathrm{\Ω}}_2}{u}_0(x,y)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_2}(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}$

$c_1^{\′}=\frac{{\∫}_{{\mathrm{\Ω}}_1^{\′}}{u}_0(x,y)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_1^{\′}}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}$ $c_2^{\′}=\frac{{\∫}_{{\mathrm{\Ω}}_2^{\′}}{u}_0(x,y)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}{{\∫}_{{\mathrm{\Ω}}_2^{\′}}(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}$

the profile curve C divides the image into an inner region omega_inAnd an outer region omega_out(ii) a Taking the pixel position of the current evolution observation as a circular point, a sphere with radius r will be omega_inIs divided into omega₁,Ω'₁Will be omega_outIs divided into omega₂,Ω'₂。C₁、C₁'、C₂、C'₂Respectively represent the region omega₁、Ω'₁、Ω₂、Ω'₂Is measured. U shape₀(x, y) represents the mean of the points (x, y).

A variant function definition of H (φ):

$\mathrm{H\ϵ}=\frac{1}{2}(1+\frac{2}{\mathrm{\π}}\arctan \left(\frac{\mathrm{\φ}}{\mathrm{\ϵ}}\right))---(3-16)$

experimental results show that the algorithm of the invention not only can effectively segment the large branches of the cerebral vessels, but also can accurately extract the small structures of the cerebral vessels.

Step S603: calculating a skeleton line of the cerebral vessels, obtaining information of a central line and a radius of the cerebral vessels, obtaining the radius corresponding to the central line, wherein the radius corresponding to the central line is shown in figure 4, and the used elastic sphere algorithm specifically comprises the following steps:

setting an elastic force equation of the elastic ball to determine the center trend of the elastic ball:

$F(i,j,k)=\underset{m=i-r}{\overset{i+r}{\mathrm{\Σ}}}\underset{n=j-r}{\overset{j+r}{\mathrm{\Σ}}}\underset{p=k-r}{\overset{k+r}{\mathrm{\Σ}}}\mathrm{Seg}(m,n,k)---\left(3\right)$

in the formula (3), the reaction mixture is,

r represents the currently calculated radius of the vessel,

in the formula (4), V (m, n, k) represents the division result, and Position (i, j, k) represents the vector Position of the pixel at the (i, j, k) Position; the calculation process is as follows:

step1: setting r =1 for the current centerline point location endpoint;

step 2: calculating the elastic force;

step 3: if the elastic force is zero, setting r = r +1, and repeating Step2, otherwise, carrying out the next Step;

step 4: moving the central point along the vector direction of the force, and recalculating the elastic force;

step 5: if the elastic force is zero and double tangency occurs, the search is finished, otherwise, the next step is carried out;

step 6: the newly revised centerline and radius information is recorded, returning to Step 3.

Step S604: and constructing a tree-shaped cerebrovascular topological structure according to the skeleton line. Specifically, the structure of each branch vessel is represented in a node manner, and as shown in fig. 5, the data structure is defined as follows:

Struct Node

{

the node of the parent is a node of the parent,

{ center line position, radius, circular plane normal vector },

the left child node of the left child node,

right child node

}

Nodes of blood vessels are classified into three categories: end points, common points, and bifurcation points, defined as follows:

end point: the neighborhood relation of the end points is as follows: there is only one point of adjacency.

Common points are as follows: the basic points of the skeleton line are formed, and two adjacent points are arranged around the common point.

A bifurcation point: since there are few multi-branch structures in the cerebral vessels, the branch point of the skeleton line is generally a bifurcate structure, and there are three adjacent points at the branch point.

On the basis of the node classification, a blood vessel tree-shaped topological structure is constructed by adopting a depth-first side rate, and the algorithm is as follows:

step1, taking the current observation node as the starting point, directly establishing a new tree structure, and storing the current point as the root node;

step 2: entering the next node to be observed;

step 3: adding the current observation point which is a common point into the node structure being processed, and returning to Step 2; otherwise, go to Step 4;

step 4: if the observation point is a bifurcation point, establishing two new nodes respectively as a left child node and a right child node of the node, and respectively entering Step2 in a recursion mode aiming at the left child node and the right child node;

step 5: and after all the nodes are processed, the topological structure of the vessel tree is constructed.

Step S605: and (5) calculating the radius of the cerebral blood vessel of each node according to the skeleton line by adopting an elastic sphere algorithm, and referring to the detailed description of the specific step (5).

Step S606: the constructed vessel model is visualized in a computer and the results are displayed as shown in fig. 6.

The preferred embodiments of the present invention are provided for illustration only, and not for the purpose of exhaustive description of all embodiments, the present invention is not limited to the specific embodiments described. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims (5)

1. The three-dimensional brain blood vessel model construction method based on the tree structure is characterized by comprising the following steps:

(1) acquiring a three-dimensional cerebral vascular body data field from a CT or MRA device;

(2) separating cerebral vessels from background noise by adopting a segmentation algorithm;

(3) calculating a cerebrovascular skeleton line to obtain cerebrovascular central line and radius information;

(4) constructing a tree-shaped cerebrovascular topological structure according to the skeleton line, wherein the construction method of the tree-shaped cerebrovascular topological structure comprises the following steps:

each branch vessel structure is represented in a node mode, and the data structure is organized as follows:

the nodes on the skeleton are classified as follows:

end point: the neighborhood relationship of the end points of the positions where the skeleton lines start or stop is as follows: there is only one adjacency point;

common points are as follows: forming basic points of the skeleton line, wherein two adjacent points exist around the common point;

a bifurcation point: the branch point of the skeleton line is of a bipartite structure, and three adjacent points are arranged around the branch point;

constructing a tree topology structure:

on the basis of the node classification, a blood vessel tree-shaped topological structure is constructed by adopting a depth-first side rate, and the algorithm is as follows:

step1: directly establishing a new tree structure by taking the current observation node as a starting point, and storing the current point as a root node;

step 2: entering the next node to be observed;

step 3: adding the current observation point which is a common point into the node structure being processed, and returning to Step 2; otherwise, go to Step 4;

step 4: if the observation point is a bifurcation point, establishing two new nodes as a left child node and a right child node of the node respectively, and recursively entering Step2 aiming at the left child node and the right child node respectively;

step 5: after all the nodes are processed, the topological structure of the vessel tree is constructed;

(5) calculating the radius of the cerebral blood vessel of each node by adopting an elastic sphere algorithm according to the skeleton line;

(6) and displaying the constructed brain blood vessel with the tree structure in three dimensions.

2. The method of claim 1, wherein step (2) comprises:

(2.1) smoothing the three-dimensional cerebral vascular body data field by adopting Gaussian filtering, obtaining an MIP image through MIP projection, and obtaining three-dimensional vascular seed points by adopting a two-dimensional OTSU algorithm and the MIP image;

(2.2) defining a region growing rule combining global information and local information, and carrying out rough segmentation on the blood vessel through a region growing algorithm to obtain a region growing blood vessel outline;

and (2.3) performing anisotropic filtering on the three-dimensional cerebral vessel body data field by adopting a Catt diffusion model, and performing secondary segmentation by taking the primary segmentation result as an initial contour line of the adaptive active contour model by adopting a local adaptive C-V model.

3. The method of claim 1, wherein the step (3) is to calculate the cerebrovascular trend by using a Hessian matrix method.

4. The method of claim 1, wherein step (5) is a step of finding the centerline of the elastic ball by constructing an elastic ball motion force equation.

5. A construction method as set forth in claim 3, characterized in that the specific process of obtaining the information of the centerline and radius of the cerebral blood vessel in the step (3) is as follows:

setting an elastic force vector equation to determine the center trend of the elastic ball:

$F(i,j,k)=\underset{m=i-r}{\overset{i+r}{\Σ}}\underset{n=j-r}{\overset{j+r}{\Σ}}\underset{p=k-r}{\overset{k+r}{\Σ}}Seg(m,n,k)---\left(3\right)$

in formula (3):

r represents the currently calculated radius of the vessel,

in equation (4), V (m, n, k) represents the segmentation result, and Position (i, j, k) represents the vector Position of the pixel at the (i, j, k) Position, and the calculation process is as follows:

step1: setting r to be 1 for the current central line point position endpoint;

step 2: calculating the elastic force;

step 3: if the elastic force is zero, setting r to r +1, and repeating Step2, otherwise, carrying out the next Step;

step 4: moving the central point along the vector direction of the elastic force, and recalculating the elastic force;

step 5: if the elastic force is zero and double tangency occurs, the search is finished, otherwise, the next step is carried out;

step 6: the newly revised centerline and radius information is recorded, returning to Step 3.