CN110801203B - Human cranial nerve fiber tracking method based on local features - Google Patents

Abstract

The invention discloses a human brain nerve fiber tracking method based on local features, which is used to solve the problem that the singular point cannot be correctly tracked in the process of human brain nerve fiber tracking. It mainly includes the following steps: Step 1, use the singular point localization method to find all the grids with singular points from the human brain tensor field; Step 2, judge whether the midpoint of the grid falls on the bisector of the four quadrant angles or the center, if Yes, during eigenvector interpolation, remove the edge corresponding to the less anisotropic tensor, otherwise remove the edge with the farthest distance; Step 3, tensor field interpolation, use the scalar bilinear interpolation method to calculate the grid midpoint The eigenvalues of , use tensor interpolation to calculate the eigenvectors of the points in the grid; step 4, render the interpolation results. The human brain nerve fiber tracking method of the present invention can not only accurately find the singular point existing in the human brain tensor field, but also overcome the problem of inaccurate tracking around the singular point, thereby improving the tracking accuracy.

Description

Human brain nerve fiber tracking method based on local features

technical field

The invention relates to the technical field of human brain nerve fiber tracking, in particular to a method for solving the problem of inability to correctly track around singular points in the process of human brain nerve fiber tracking.

Background technique

There are many nerve fibers in the human brain, and these intricate neurons are intertwined to form a network. This network of neurons controls different levels of consciousness such as thinking, action, and sleep. For example, the human brain coordinates our perception, thinking, and actions through its neuronal activity. Therefore, the tracking of human brain nerve fibers can help human brain researchers to draw a detailed human brain neural circuit map, and further promote neuroscientists' cognition of the human brain. However, due to the large number of human brain nerve fibers, intricate and random movement, human tracking of human brain nerve fibers has not been very ideal.

At present, the main methods of tracing human brain nerve fibers include electrical probes, chemical reagents, genetic modification and tensor field interpolation. Mathematically, the human brain can be represented as a diffusion tensor field, and neurons are tensors in the tensor field, so tracing the nerve fibers of the human brain is the tracing of the streamlines in the tensor field. In general, the tensor field interpolation method can accurately track the motion trajectory, but when there are tensor points (singular points) with zero anisotropy, Brownian motion has almost no direction around the singular points. Therefore, it is difficult for the prior art to accurately track around the singularity.

Therefore, neuroscientists need a method that can both accurately find singularities existing in the tensor fields of the human brain and overcome the inaccurate tracking around singularities.

SUMMARY OF THE INVENTION

In view of the above-mentioned prior art, the present invention proposes a method for tracking human brain nerve fibers based on local features, which overcomes the problem that the existing human brain nerve fiber tracking technology cannot accurately track around singular points.

In order to solve the above technical problems, a method for tracking human brain nerve fibers based on local features proposed by the present invention includes the following steps:

Step 1: Use the singular point localization method to find all the grids with singular points from the human brain tensor field;

Step 2: Determine whether the singular point in the grid falls on the four-quadrant angle bisector or the center. If so, during the eigenvector interpolation, remove the edge corresponding to the smaller anisotropic FA tensor, otherwise remove the edge with the farthest distance ;

Step 3, tensor field interpolation, using the scalar bilinear interpolation method to calculate the eigenvalue λ of the interpolation point in the grid, and using the tensor interpolation to calculate the eigenvector e of the interpolation point in the grid;

Step 4: Render the interpolation result.

Further, in step 1 of the method of the present invention, the steps of the singular point positioning method are as follows:

First determine the main directions of the four vertices of the grid, and the eigenvector corresponding to the largest eigenvalue is the main direction of the tensor; then determine whether the cosα of the tensor rotation angle of any two adjacent vertices is less than zero; finally, calculate the number of cosα less than zero n, if n is odd, there is a singularity in the grid, otherwise, there is no singularity.

In the second step of the inventive method, the expression of the anisotropic FA is as follows:

λ₁，λ₂，λ₃是矩阵的特征值。in,

λ ₁ , λ ₂ , λ ₃ are the eigenvalues of the matrix.

In step 3 of the method of the present invention, the eigenvalue λ of the interpolation point in the grid is expressed as follows:

和

是R₁和R₂两张量点的特征值。in,

and

are the eigenvalues _of the _two measurement points R1 and R2.

In step 3 of the method of the present invention, the feature vector e of the interpolation point in the grid is represented as follows:

分别为R₁和R₂两点的特征向量，

为旋转矩阵。where the coefficient S _y is

are the _{eigenvectors of} R1 and R2, respectively,

is the rotation matrix.

Compared with the prior art, the beneficial effects of the present invention are:

First, the present invention provides a method for locating singular points in step 1, by which all grids with singular points can be accurately found in the tensor field of the human brain.

Second, in the second step, the present invention provides a method to eliminate the interference of the singular point in the tensor field to the tracking, and overcome the problem that the singular point cannot be accurately tracked.

Thirdly, in the present invention, when the tensor field is interpolated in step 3, the eigenvalues and eigenvectors are respectively interpolated, and the result preserves the anisotropy of the tensor field as much as possible.

In conclusion, the present invention provides a method for solving the problem of inability to correctly track around singular points in the process of tracing human brain nerve fibers. This method improves the accuracy of human brain nerve fiber tracking, and further promotes human brain researchers' understanding of human brain neural circuits.

Description of drawings

FIG. 1 is a flow chart of the method for tracing human brain nerve fibers based on local features of the present invention.

FIG. 2 is a schematic diagram of locating singular points in the present invention.

FIG. 3 is a schematic diagram of tensor field interpolation in the present invention.

FIG. 4 is a partial code diagram of feature value interpolation in the present invention.

FIG. 5 is a partial code diagram of feature vector interpolation in the present invention.

FIG. 6 is a diagram showing the middle point of the present invention falling on the first quadrant angle bisector, and the left part of the code diagram is removed by comparing the anisotropy size of the tensors corresponding to the two vertices.

FIG. 7 is a diagram of the tracking effect near the trisection singular point in the present invention.

FIG. 8 is a diagram of the tracking effect near the wedge-shaped singular point in the present invention.

Detailed ways

The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but the following embodiments do not limit the present invention by any means.

The method for tracing human brain nerve fibers based on local features provided by the present invention mainly includes the following steps: finding all grids with singular points in the human brain tensor field by using the singular point localization method; judging whether the singular points in the grid are not It falls on the bisector or center of the four quadrant angles. If so, in the eigenvector interpolation, remove the edge corresponding to the smaller tensor of the anisotropic FA, otherwise remove the edge with the farthest distance; tensor field interpolation, using the double scalar The linear interpolation method calculates the eigenvalue λ of the interpolation point in the grid, and uses the tensor interpolation to calculate the eigenvector e of the interpolation point in the grid; renders the interpolation result and accurately tracks the singular point in the tensor field of the human brain. The nerve fibers are distributed evenly and accurately around the singularity.

As shown in Figure 1, the specific process is as follows:

Step 101, using the singular point localization method to find all grids with singular points from the human brain volume field;

In terms of data representation, a singularity is a tensor with zero anisotropy, which has two or more equal eigenvalues. For a tensor, the general eigenvector e represents the direction of the tensor, and its size is represented by the eigenvalue λ, so the eigenvector corresponding to the largest eigenvalue is the main direction of the tensor. Since Brownian motion has almost no direction of motion around singularities, it is difficult to track accurately around singularities.

The steps of the singular point location method are as follows: First, determine the main directions of the four vertices of the grid, and the eigenvector corresponding to the largest eigenvalue is the main direction of the tensor; then determine whether the cosα of the tensor rotation angle of any two adjacent vertices is less than zero. Finally, the number n of which cosα is less than zero is calculated. If n is an odd number, there is a singular point in the grid, otherwise, there is no singular point.

FIG. 2 is a schematic diagram of locating singular points in the present invention. The four vertices of each rectangle in the figure are four tensor samples, and the arrows point in the main direction of the tensor. The cosα of the main direction rotation angle of the two vertex tensors corresponding to the thick edges in the graph is less than zero. Then there is one thick edge in a, which is an odd number, and there is a singularity in the grid; if there are two thick edges in b, which is an even number, there is no singularity in the grid.

Step 102, determine whether the singular point in the grid falls on the four-quadrant angle bisector or the center, if so, go to Step 103, during the feature vector interpolation, remove the edge corresponding to the smaller anisotropic FA tensor; otherwise, execute Step 104, remove the edge with the farthest distance.

Anisotropy is an important indicator for studying tensor fields. At present, there are various anisotropy calculation methods, such as anisotropy index, fractional anisotropy, relative anisotropy and volume fraction, etc. However, the present invention uses the fractional anisotropy calculation method to calculate the anisotropy of the tensor. Then the calculation formula of anisotropic FA is:

λ₁，λ₂，λ₃是矩阵的特征值。in,

λ ₁ , λ ₂ , λ ₃ are the eigenvalues of the matrix.

There is a subtle difference in the comparison of anisotropy when the tensor points in the grid fall on the four-quadrant bisector and center. When the tensor point falls on the four-quadrant angle bisector, compare the magnitude of the tensor anisotropy corresponding to the two vertices; when the tensor point falls on the center, the two tensor anisotropies corresponding to each edge should be calculated and then compare the size. FIG. 6 is a diagram of the present invention where the middle point falls on the bisector of the first quadrant angle, and the left part of the code is removed by comparing the magnitude of anisotropy.

Step 105, tensor field interpolation, using the scalar bilinear interpolation method to calculate the eigenvalue λ of the interpolation point in the grid, and using the tensor interpolation to calculate the eigenvector e of the interpolation point in the grid.

即In order to preserve the anisotropy of the tensor field as much as possible, the eigenvalues and eigenvectors are separated during the tensor field interpolation, and the scalar bilinear interpolation method shown in Figure 4 and the tensor interpolation method shown in Figure 5 are used respectively. method calculation. The eigenvalue λ of the interpolation point, as shown in Figure 3, R ₁ and R ₂ are two measurement points, and the eigenvalue of R ₁ point

which is

即Then the eigenvalues of R ₂ points

which is

Then the eigenvalue λ of point P, namely

即The eigenvector of the interpolation point is e. As shown in Figure 3, first, the eigenvector of R ₁ point

which is

即Then the eigenvectors of R ₂ points

which is

Then the eigenvector e of point P, namely

为旋转矩阵，系数S_x和S_y分别为

in

is the rotation matrix, and the coefficients S _x and S _y are respectively

Step 106, rendering the interpolation result.

There are mainly two types of singularities in the tensor field of the human brain, which are Trisector and wedge. Many existing tracking technologies are difficult to accurately track streamlines near these two singularities. , the tracking results always have problems such as infinite approach, intersection and so on. In order to verify the effectiveness of our proposed local feature-based tracking method for human brain nerve fibers, we choose to track near these two singularities respectively. Figures 7 and 8 are the tracking effect diagrams around the trisate and wedge-shaped singularities, respectively. The point circled by the box in the figure is the seed point, that is, the starting point of each streamline tracing. Obviously, the streamlines tracked by each seed point are evenly distributed near the singular point, and there is no infinite approach or intersection between them.

Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments. The above-mentioned specific embodiments are only illustrative rather than restrictive. Under the inspiration of the present invention, many modifications can be made without departing from the spirit of the present invention, which all belong to the protection of the present invention.

Claims (4)

1. a human brain nerve fiber tracing method based on local feature, is characterized in that, comprises the steps: Step 1: Use the singular point localization method to find all the grids with singular points from the tensor field of the human brain; the specific steps are: first determine the main directions of the four vertices of the grid, and the eigenvector corresponding to the largest eigenvalue is the tensor. Main direction; then judge whether the cosα of the rotation angle of the tensor of any two adjacent vertices is less than zero; finally calculate the number n of which cosα is less than zero, if n is an odd number, there is a singular point in the grid, otherwise, there is no singular point; Step 2: Determine whether the singular point in the grid falls on the four-quadrant angle bisector or the center. If so, during the eigenvector interpolation, remove the edge corresponding to the smaller anisotropic FA tensor, otherwise remove the edge with the farthest distance ; Step 3, tensor field interpolation, using the scalar bilinear interpolation method to calculate the eigenvalue λ of the interpolation point in the grid, and using the tensor interpolation to calculate the eigenvector e of the interpolation point in the grid; Step 4: Render the interpolation result. 2. the human brain nerve fiber tracing method based on local feature according to claim 1, is characterized in that, in described step 2, the expression of anisotropy FA is as follows:

in,

λ ₁ , λ ₂ , λ ₃ are the eigenvalues of the matrix. 3. The human brain nerve fiber tracking method based on local features according to claim 1, wherein in the step 3, the eigenvalue λ of the interpolation point in the grid is represented as follows:

in,

and

are the _{eigenvalues of} R1 and R2, respectively. 4. The method for tracing human brain nerve fibers based on local features according to claim 1, wherein in the step 3, the feature vector e of the interpolation point in the grid is represented as follows:

where the coefficient S _y is

are the eigenvectors of R ₁ and R ₂ , respectively,

is the rotation matrix.

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