Three-dimensional relative orientation calculation method between collagen fibers and cells based on vector operations

Abstract

The present invention discloses a method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector operations, which uses three-dimensional relative orientation parameters to quantitatively characterize the relative positions and spatial distribution characteristics of collagen fibers and cells. This method can describe the spatial distribution information by calculating the three-dimensional spatial directions of collagen fibers and the three-dimensional spatial directions of cell contours, and describe the spatial relative position distribution of the two by calculating the three-dimensional relative orientation, which helps to combine and analyze the morphological and structural characteristics of the extracellular matrix and cells, and has the advantages of being fast, highly accurate, non-invasive, concise, and highly applicable.

Description

Technical Field

[0001] The present invention belongs to the technical field of quantitative characterization and image analysis of biological tissues, and particularly relates to a method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector operations. Background Art

[0002] Second harmonic generation (SHG) microscopy imaging technology is an imaging technology based on the nonlinear optical property of second harmonic. It can achieve high-resolution, deep-penetrating, non-invasive, and low-damage label-free imaging of collagen fibers with high nonlinear susceptibility and non-centrosymmetric structures. Therefore, it has great advantages in collagen fiber imaging. Two-photon excited fluorescence (TPEF) is a microscopy imaging technology based on the nonlinear optical property of two-photon absorption. It uses ultrashort laser pulses to rapidly scan samples to obtain three-dimensional structural image information of the samples to be measured, and has the advantages of low damage, high imaging depth, low interference, and low photobleaching. It can be used for three-dimensional imaging of cells.

[0003] The fibrous structure is a basic structural form of biological tissues and plays an important role in life activities. Collagen fibers and the like exist in the body in the form of fibrous structures. The damage and healing of biological tissues, the occurrence and development of diseases, and the occurrence and metastasis of cancers are often closely related to the perturbation of the interaction between cells and the extracellular matrix (mainly collagen fibers).

[0004] The second harmonic generation microscopy imaging results of collagen fibers contain rich information about the spatial morphology, structure, and distribution of collagen fibers. Currently, some parameters have been used to describe the spatial characteristics such as the orientation order, curvature characteristics, and local density of collagen fibers, and are currently widely used in the fields of biomedicine and life sciences. At the same time, there are also analyses of cell characteristics in many physiological changes, such as the characteristic analysis of mitochondrial clusters and the analysis of redox rates. However, these quantitative characteristics only target single collagen fibers or cells, lack quantitative analysis combining the spatial distribution characteristics of both, ignore their relative changes, and are particularly difficult to reflect the detailed information of the relative spatial distribution of collagen fibers and cells, and cannot fully reveal the interaction between cells and the extracellular matrix.

[0005] Currently, the analysis of the relative positions of collagen fibers and cells mainly relies on pathologists to qualitatively evaluate manually according to experience. The results lack sufficient detail discrimination and have a large degree of contingency. Some researchers also use the relative directions between collagen fibers calculated on two-dimensional pathological tissue section images to replace the description of the relative distribution between collagen fibers and cells. The results have certain reference value, but in terms of details, they cannot fully represent the relative distribution between the two and lack the revelation of three-dimensional structures. To sum up, there is an urgent need for a method that can quantitatively describe the spatial distribution characteristics of the relative positions of collagen fibers and cells, that is, the three-dimensional relative orientation. Summary of the Invention

[0006] In view of the above, the present invention proposes a method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector operations. This method can reflect the spatial distribution characteristics of the three-dimensional relative positions of collagen fibers and cells, and has the advantages of being fast, simple, accurate, and highly applicable.

[0007] A method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector operations uses three-dimensional relative orientation parameters to quantitatively characterize the relative positions and spatial distributions of collagen fibers and cells, combines the morphological and structural characteristics of collagen fibers and cells for analysis, and expands the description of the spatial characteristics of cells and the extracellular matrix, including the following steps:

[0008] 1) Perform thresholding on each two-dimensional collagen fiber image in the obtained three-dimensional data to obtain a binary matrix of the collagen fiber image, and form a three-dimensional array of the collagen fiber image;

[0009] 2) Perform thresholding on each two-dimensional cell image in the obtained three-dimensional data, extract the cell contour through operations such as dilation, hole filling, finding the largest connected domain, and skeletonization, obtain a binary matrix of the cell image, and form a three-dimensional array of the cell image;

[0010] 3) Use the three-dimensional array of the collagen fiber image to calculate the pixel-level three-dimensional spatial orientation of the collagen fiber image, and obtain the three-dimensional spatial directions θ of all pixels in the image fiber and

[0011] 4) Based on the three-dimensional array of the cell image, perform three-dimensional fitting of the cell contour, obtain a three-dimensional fitting equation, and calculate the three-dimensional spatial directions θ of the normal vectors at each point on the cell contour normal and

[0012] 5) For each pixel point in the three-dimensional array of the collagen fiber image, find the pixel on the corresponding cell contour that is the closest to it, and based on the three-dimensional spatial directions θ fiber 、 θ normal and Calculate the difference between the two three-dimensional spatial directions, and take the remaining angle as the corresponding three-dimensional relative orientation;

[0013] 6) Calculate the average value of the three-dimensional relative orientation to quantitatively describe the overall characteristics of the spatial relative position between collagen fibers and cells, and perform pseudo-color coding on the image according to the calculated three-dimensional relative orientation value to visualize the spatial relative position distribution characteristics of collagen fibers and cells.

[0014] As a further improvement, in step 5) of the present invention, based on the three-dimensional space direction θ fiber , θ normal and The method for calculating the difference between the two three-dimensional spatial directions is as follows:

[0015]

[0016] Where Δθ=cos(θ fiber -θ normal )=cos(θ normal -θ fiber ), δ ranges from [0°, 90°]. The three-dimensional relative orientation is 90-δ, ranging from [0°, 90°]. When the collagen fibers are arranged more perpendicular to the cell outline, the three-dimensional relative orientation value is closer to 90°, and when the collagen fibers are arranged more parallel to the cell outline, the three-dimensional relative orientation value is closer to 0°.

[0017] As a further improvement, in step 4) of the present invention, the three-dimensional spatial direction θ of the normal vector at each point is calculated. normal and Specifically, the given pixel point (x0, y0, z0) on the contour is taken as the origin of the spatial coordinate system at that point, and the θ and The definition is the same, θ is defined as the angle between its projection on the xy plane and the +x direction, and the projection vector is +x axis direction vector is According to the vector angle calculation formula, cosθ is obtained normal as follows:

[0018]

[0019] θ is calculated by the arccosine normal Value, similarly, The normal vector is defined as The angle with the -z direction, the -z axis direction vector is (0,0,-1), and the final calculation is value.

[0020] As a further improvement, in step 4) of the present invention, the normal vector is obtained through the following mathematical derivation expression:

[0021] The spatial coordinates (x0, y0, z0) of each point are known. After directly taking the partial derivatives of the fitting equation f(x, y, z) = 0, the partial derivative of x is calculated as: f x '(x0, y0, z0), the partial derivative of y is: f y '(x0, y0, z0), and the partial derivative of z is: f z '(x0, y0, z0).

[0022] In three-dimensional space, the normal vector of a surface is a vector perpendicular to the tangent plane of the surface at that point. For the surface f(x, y, z) = 0, with the direction pointing outside the contour as the positive direction, the normal vector at the point (x0, y0, z0) is:

[0023]

[0024] As a further improvement, in step 3) of the present invention, the three-dimensional direction of the collagen fiber image is defined by the azimuth angle θ and the polar angle , both of which vary from 0° to 180°. The polar angle is further obtained from the equation:

[0025]

[0026] where β and γ are two introduced azimuth angles to characterize the polar angle For any fiber in three-dimensional space, its azimuth angle θ is defined as the angle between its projection on the xy plane and the +x direction, while the polar angle is defined as the angle between the fiber and the -z direction. Among them, the value ranges of θ and are both [0°, 180°];

[0027] Specifically, to obtain the three-dimensional direction of a given pixel, first create an n×n×n three-dimensional evaluation window around the pixel, generate all vectors passing through the central pixel of the window, and these vectors are weighted by W1 and W2:

[0028]

[0029] W1 weights the vector with the reciprocal of the vector length L, and W2 weights the vector according to the intensity change. Among them, a1, a2, a3 are the intensities of the central pixel and the two pixels symmetric to the central pixel along the vector direction, and is the average value of the intensities of these three pixels. The azimuth angle direction of the central pixel is defined as the direction of the sum of all weighted vectors. After determining these three azimuth angles, the three-dimensional direction can be obtained.

[0030] As a further improvement, in step 5) of the present invention, for each pixel point in the three-dimensional array of collagen fiber images, the pixel on the corresponding cell contour that is closest to it is found. The method is as follows: for the point (x1, y1, z1) on the collagen fiber, each point (x, y, z) on the cell contour is traversed and the distance calculation formula is used. The distance Take the pixel point on the cell contour corresponding to the minimum D.

[0031] Compared with the prior art solutions, the present invention has the following advantages:

[0032] 1. By analyzing and extracting structural features from the three-dimensional image stack obtained using second harmonic generation microscopy, the present invention has the advantages of high precision, fast non-invasive, and saving manpower and material resources compared with the existing histopathology methods. At the same time, it can achieve imaging of small lesions.

[0033] 2. The method proposed by the present invention can process three-dimensional images. Compared with the calculation of the two-dimensional relative directions limited between collagen fibers in the background art, the method proposed by the present invention can more comprehensively analyze the three-dimensional directions of fibrous tissues in three-dimensional images, and further calculate their three-dimensional relative orientations with cells, reflecting their three-dimensional relative position distribution characteristics with cells, rather than being limited to the relative position distribution characteristics between collagen fibers. The application scenarios are very extensive. The method of the present invention can achieve a more comprehensive and complete understanding of biological tissues, and has far-reaching significance for the research and analysis of physiological feature changes.

[0034] 3. Compared with the technology in the background art that only describes the three-dimensional space characteristics of collagen fibers, the present invention not only calculates the spatial directions of collagen fibers to describe their spatial distribution characteristics, but also introduces the feature extraction of the spatial directions of each point on the cell contour. By calculation, the relative positions of collagen fibers and cells in three-dimensional space are obtained, which is beneficial to simultaneously analyze the changes in the spatial distribution characteristics of collagen fibers and cells during physiological changes.

[0035] 4. The average value of the three-dimensional relative orientation calculated by the present invention can quantitatively compare the changes in the overall spatial relative positions between collagen fibers and cells during physiological changes. This value has clear scientific significance, can help researchers quickly grasp the trends and characteristics of the changes, and is helpful for improving the efficiency of subsequent research and determining research plans.

[0036] 5. The three-dimensional relative orientation distribution characteristics obtained by the present invention visually provide quantitative information with pixel-level resolution. The pseudo-color coding technology used can more clearly display different spatial relative position distribution characteristics through different colors, which is more vivid and makes this information more easily obtained by users, having stronger information readability compared with the background art. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Flow chart for calculating the three-dimensional relative orientation spatial distribution characteristics of collagen fibers and cells based on vector operations;

[0038] Figure 2 Schematic diagram of the calculation principle of three-dimensional relative orientation;

[0039] Figure 3 Pseudo-color schematic diagram of the culture, imaging, image reconstruction process of a hormone-sensitive three-dimensional breast engineering tissue model and the calculation results of three-dimensional relative orientation. Detailed implementation manners

[0040] To describe the present invention more specifically, the following combines the accompanying drawings and examples to elaborate on the detailed implementation manners of the present invention, but the application of the present invention is not limited thereto.

[0041] A method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector operations, the steps are as follows, and the overall calculation flow chart is as Figure 1 shown:

[0042] 1) Cultivate a hormone-sensitive three-dimensional breast engineering tissue, and treat it with estrogen (E2) and estrogen + prolactin (E2+prol) respectively, as Figure 3 (A) shown;

[0043] 2) Use second harmonic generation microscopy to perform three-dimensional imaging on the collagen fibers around the cells to obtain a series of original three-dimensional image stacks;

[0044] 3) Perform pixel intensity threshold filtering on the original three-dimensional image stacks to obtain a three-dimensional array of collagen fiber images composed of binary images. The value 1 represents the pixels containing the spatial distribution information of collagen fibers that need to be subjected to subsequent feature extraction and calculation, and the value 0 represents the background pixels;

[0045] 4) Use vector operations to calculate the three-dimensional direction of the collagen fibers. The three-dimensional direction is defined by the azimuth angle θ and the polar angle as Figure 2 (D) shown, and the true value range is as Figure 2 (F) shown, and both change from 0° to 180°. The polar angle can be further obtained from the equation:

[0046]

[0047] where β and γ are two introduced azimuth angles to characterize the polar angle For any fiber in three-dimensional space, its azimuth angle θ is defined as the angle between its projection on the xy plane and the +x direction, and the polar angle is defined as the angle between the fiber and the -z direction. Where, θ and both range from [0°, 180°].

[0048] Specifically, to obtain the three-dimensional direction of a given pixel, first create a three-dimensional evaluation window of n×n×n around the pixel, and generate all vectors passing through the central pixel of the window. These vectors are weighted by W1 and W2:

[0049]

[0050] Here, W1 weights the vector with the reciprocal of the vector length L, and W2 weights the vector according to the intensity change. Where a1, a2, a3 are the intensities of the central pixel and two pixels symmetric to the central pixel along the vector direction, and is the average value of the intensities of these three pixels. The azimuth direction of the central pixel is defined as the direction of the sum of all weighted vectors. After determining these three azimuths, the three-dimensional direction θ of each point on the collagen fiber can be obtained fiber and

[0051] 5) Use two-photon fluorescence microscopy to image the cells, perform pixel intensity threshold filtering on each two-dimensional cell image in the obtained three-dimensional data, where the value 1 represents the pixels containing cell spatial information, and the value 0 represents the background pixels; perform operations such as dilation, hole filling, finding the largest connected component (screening the cell area), and skeletonization to extract the cell contour, as shown in Figure 3 (B), to obtain the binary matrix of the cell image;

[0052] 6) Based on each image with the cell contour extracted, re-obtain a three-dimensional array of cell contour images and perform three-dimensional fitting to obtain the three-dimensional fitting equation of the cell contour. Considering that the three-dimensional breast engineering tissue in this specific embodiment can be approximately fitted as an ellipsoid, an ellipsoid equation is used for fitting. The coordinates at the center of the sphere obtained by fitting are (x center , y center , z center ), and the semi-axis lengths of the x, y, and z axes are a, b, c respectively. The fitting equation is ((x - x center ) / a) 2 + ((y - y center ) / b) 2 + ((z - z center ) / c) 2 = 1;

[0053] 7) Based on the fitting equation, mathematically derive the expression of the normal vector of each point on the cell contour:

[0054] In three-dimensional space, the normal vector of a surface is a vector perpendicular to the tangent plane of the surface at that point. With the direction pointing outside the contour as the positive direction, the normal vector at the point (x0, y0, z0) is:

[0055]

[0056] 8) Based on the normal vector at that point, we take the given pixel point (x0, y0, z0) on the contour as the origin of the spatial coordinate system at that point, and the θ and are defined in the same way as the three-dimensional direction of the collagen fiber. As shown in Figure 2 (B), θ is defined as the angle between its projection on the xy plane and the +x direction, and the projection vector is The +x direction vector is cosθ is obtained according to the vector angle calculation formula normal as follows:

[0057]

[0058] θ is obtained by inverse cosine calculation normal value. Similarly, is defined as the angle between the normal vector and the -z direction, and the -z direction vector is (0, 0, -1).

[0059]

[0060] is obtained by inverse cosine calculation value, and the range of the true value is as shown in Figure 2 (C).

[0061] 9) Method for finding the pixel of the point on the corresponding cell contour that is closest to a given point on the collagen fiber: For the point (x1, y1, z1) on the collagen fiber, traverse each point (x, y, z) on the cell contour, and each uses the distance calculation formula, and the distance Take the corresponding point on the cell contour corresponding to the minimum value of D.

[0062] 10) Based on the three-dimensional space direction θ fiber and and the three-dimensional space direction θ normal and of the normal vector at the pixel at the minimum value of D on the corresponding cell contour, the method for calculating the three-dimensional relative orientation is as follows:

[0063]

[0064] where Δθ = cos(θ fiber - θ normal ) = cos(θ normal - θ fiber), the value range of δ is [0 ° , 90 ° , corresponding to the definition as Figure 2 (E). Finally, the three-dimensional relative orientation is 90 - δ, and the value range is [0°, 90°]. When the collagen fibers are more perpendicular to the cell contour, the three-dimensional relative orientation value is closer to 90°. When the collagen fibers are more parallel to the cell contour, the three-dimensional relative orientation value is closer to 0°.

[0065] 11) After calculation, the average value of the three-dimensional relative orientation of the group treated with estrogen (E2) is 12.78°, and the average value of the three-dimensional relative orientation of the group treated with estrogen + prolactin (E2 + prol) is 22.66°. This indicates that, on average, treating three-dimensional breast engineering tissues with estrogen and prolactin will induce collagen fibers to be more perpendicular to the cells than treating with estrogen alone.

[0066] 12) Pseudo-color code the image according to the calculated three-dimensional relative orientation values to more clearly and vividly represent the three-dimensional relative orientation values, so as to reveal the overall information of the spatial relative positions of collagen fibers and cells in the image, as Figure 3 (B) shows.

[0067] 13) In the area 23 μm away from the edge of the epithelial structure, the distribution histogram of the three-dimensional relative orientation of collagen fibers within the corresponding pixel range is as Figure 3 (C) shows, Figure 3 (D) is Figure 3 the distribution histogram of the three-dimensional relative orientation of the area indicated by the arrow in (B). It can be seen that the three-dimensional relative orientation can not only quantitatively describe the spatial relative positions of collagen fibers and cells from the average level and overall, but also has high sensitivity and can reveal the detailed position information in the image.

[0068] The above examples show that the present invention performs second harmonic generation microscopy and two-photon fluorescence microscopy on the collagen fibers and cells of a hormone-sensitive three-dimensional breast engineering tissue model, and quantitatively characterizes the spatial positions and spatial relative positions of collagen fibers and cells by calculating the three-dimensional relative orientation parameter, providing complementary and comprehensive spatial distribution information, which can more comprehensively analyze the spatial distribution characteristics of collagen fibers and cells and has high sensitivity. At the same time, providing a pseudo-color image of the three-dimensional relative orientation with a resolution of pixel level, presenting the spatial distribution information as a more vivid color image, and having strong information readability.

[0069] The above description of the embodiments is to enable those of ordinary skill in the art to understand and apply the present invention. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative efforts. Therefore, the present invention is not limited to the above embodiments, and all improvements and modifications made by those skilled in the art based on the disclosure of the present invention should fall within the protection scope of the present invention.

Claims

1. A method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector calculation, characterized in that: The three-dimensional relative orientation parameters are used to quantitatively characterize the relative position and spatial distribution of collagen fibers and cells, and the morphological and structural characteristics of collagen fibers and cells are combined for analysis to expand the description of the spatial characteristics of cells and extracellular matrix, including the following steps: 1) performing threshold processing on each two-dimensional collagen fiber image in the obtained three-dimensional data to obtain a collagen fiber image binary matrix to form a three-dimensional array of collagen fiber images; 2) Perform threshold processing on each two-dimensional cell image in the obtained three-dimensional data, extract the cell contour through dilation, hole filling, maximum connected domain and skeletonization operations, obtain the cell image binary matrix, and form a three-dimensional array of cell images; 3) Using the three-dimensional array of collagen fiber images, calculate the pixel-level three-dimensional spatial orientation of the collagen fiber image and obtain the three-dimensional spatial orientation θ of all pixels in the image fiber and 4) Based on the three-dimensional array of cell images, perform three-dimensional fitting of the cell contour, obtain the three-dimensional fitting equation, and calculate the three-dimensional spatial direction θ of the normal vector at each point on the cell contour normal and 5) For each pixel point in the three-dimensional array of collagen fiber images, find the pixel closest to the corresponding cell contour, and based on the three-dimensional spatial direction θ of these two points fiber , θ normal and Calculate the difference between the two three-dimensional spatial directions, and take the remaining angle as the corresponding three-dimensional relative orientation; 6) Calculate the average value of the three-dimensional relative orientation to quantitatively describe the overall characteristics of the spatial relative position between collagen fibers and cells, and perform pseudo-color coding on the image according to the calculated three-dimensional relative orientation value to visualize the spatial relative position distribution characteristics of collagen fibers and cells; In step 3), the three-dimensional direction of the collagen fiber image is determined by the azimuth angle θ and the polar angle Definition, both vary from 0° to 180°, the polar angle Further from the equation: Among them, β and γ are two azimuth angles introduced to characterize the polar angle For any fiber in three-dimensional space, its azimuth angle θ is defined as the angle between its projection on the xy plane and the +x direction, while the polar angle is defined as the angle between the fiber and the -z direction, where θ and The value range of is [0°, 180°]; Specifically, to obtain the 3D direction of a given pixel, first create an n×n×n 3D evaluation window around the pixel and generate all vectors passing through the center pixel of the window, which are weighted by W1 and W2: The W1 weights the vector by the inverse of the vector length L, and W2 weights the vector according to the intensity change, where a1, a2, and a3 are the intensities of the center pixel and the two pixels symmetrical to the center pixel along the vector direction, and is the average value of the three pixel intensities. The azimuth direction of the central pixel is defined as the direction of the sum of all weighted vectors. After determining these three azimuths, the three-dimensional direction θ is obtained. fiber and In step 4), the three-dimensional space direction θ of the normal vector at each point is calculated. normal and Specifically, the given pixel point (x0, y0, z0) on the contour is taken as the origin of the spatial coordinate system at that point, and the θ and The definition is the same, θ is defined as the angle between its projection on the xy plane and the +x direction, and the projection vector is +x axis direction vector is According to the vector angle calculation formula, cosθ is obtained normal as follows: θ is calculated by the arccosine normal Value, similarly, The normal vector is defined as The angle with the -z direction, the -z axis direction vector is (0,0,-1), and the final calculation is value.

2. The method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector calculation according to claim 1, characterized in that: In the step 5), based on the three-dimensional space direction θ fiber , θ normal and The method for calculating the difference between the two three-dimensional spatial directions is as follows: Where Δθ=cos(θ fiber -θ normal )=cos(θ normal -θ fiber ), δ ranges from [0°, 90°], the three-dimensional relative orientation is 90-δ, and the range is [0°, 90°]. When the collagen fibers are arranged more perpendicular to the cell outline, the three-dimensional relative orientation value is closer to 90°, and when the collagen fibers are arranged more parallel to the cell outline, the three-dimensional relative orientation value is closer to 0°.

3. The method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector calculation according to claim 2, characterized in that: In step 4), the normal vector is obtained by the following mathematical derivation expression: The spatial coordinates of each point (x0, y0, z0) are known. After directly taking the partial derivative of the fitting equation f(x, y, z) = 0, the partial derivative of x is calculated: f' x (x0,y0,z0), partial derivative with respect to y: f' y (x0,y0,z0), partial derivative with respect to z: f' z (x0,y0,z0) In three-dimensional space, the normal vector of a surface is a vector perpendicular to the tangent plane of the surface at that point. For a surface f(x, y, z) = 0, with the direction pointing outside the contour as the positive direction, the normal vector at the point (x0, y0, z0) is:

4. The method for calculating the three-dimensional relative orientation of collagen fibers and cells based on vector calculation according to claim 1, 2 or 3, characterized in that: In step 5), for each pixel point in the three-dimensional array of the collagen fiber image, find the pixel on the corresponding cell contour that is closest to it, and the method is as follows: for a point (x1, y1, z1) on the collagen fiber, traverse each point (x, y, z) on the cell contour and use the distance calculation formula, the distance Take the pixel point on the cell contour that minimizes D.

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