Method for calculating three-dimensional relative orientation between collagenous fibers and cells based on vector operation

Abstract

The invention discloses a method for calculating three-dimensional relative orientation between collagenous fibers and cells based on vector operation. Three-dimensional relative orientation parameters are used for quantitatively representing relative positions and spatial distribution characteristics of the collagenous fibers and the cells. According to the method, spatial distribution information can be described by calculating the three-dimensional space direction of collagenous fibers and the three-dimensional space direction of cell outlines, and spatial relative position distribution of the collagenous fibers and the cell outlines is described by calculating three-dimensional relative orientation, so that the morphological and structural characteristics of extracellular matrixes and cells are combined for analysis; the method has the advantages of rapidness, high precision, noninvasive property, simplicity, high applicability and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of quantitative characterization and image analysis of biological tissues, and in particular 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 is an imaging technology based on the nonlinear optical property of second harmonics. It can achieve high-resolution, deep penetration, non-invasive and low-damage label-free imaging of collagen fibers with high nonlinear polarizability and asymmetric central structure, so it has great advantages in collagen fiber imaging. Two-photon excited fluorescence (TPEF) is a microscopy technology based on the nonlinear optical property of the two-photon absorption process. It uses ultrashort laser pulses to quickly scan samples to obtain three-dimensional structural image information of the sample to be tested. It has the advantages of low damage, high imaging depth, low interference, and low photobleaching, and can be used to perform three-dimensional imaging of cells.

[0003] Fibrous structure is a basic structural form of biological tissues and plays an important role in life activities. Collagen fibers and other fibers exist in organisms 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 cancer are often closely related to the disturbance of the interaction between cells and extracellular matrix (mainly collagen fibers).

[0004] The second harmonic generation microscopy results of collagen fibers contain rich information about the spatial morphology, structure and distribution of collagen fibers. At present, some parameters have been used to describe the spatial characteristics of collagen fibers, such as orientation order, curvature characteristics, local density, etc., and have been 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, the analysis of redox rates, etc. However, these quantitative characteristics are only for single collagen fibers or cells, lacking quantitative analysis that combines the spatial distribution characteristics of the two, ignoring their relative changes, and especially difficult to reflect the detailed information of the relative spatial distribution of collagen fibers and cells, and unable to fully reveal the interaction between cells and extracellular matrix.

[0005] At present, the analysis of the relative position of collagen fibers and cells mainly relies on pathologists to perform qualitative evaluation manually based on experience. The results lack sufficient detail identification and are more accidental. Some researchers also use the calculation of the relative direction of collagen fibers on two-dimensional pathological tissue slice images to replace the description of the relative distribution between collagen fibers and cells. The results have a certain reference value, but they cannot fully represent the relative distribution between the two in detail and lack the revelation of the three-dimensional structure. In summary, there is an urgent need for a method that can quantitatively describe the spatial distribution characteristics of the relative position of collagen fibers and cells, that is, a method for 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. The 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, concise, 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 position and spatial distribution 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 extracellular matrix, including the following steps:

[0008] 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;

[0009] 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;

[0010] 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

[0011] 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

[0012] 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;

[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 by the following mathematical derivation expression:

[0021] 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).

[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 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:

[0023]

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

[0025]

[0026] 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°];

[0027] 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:

[0028]

[0029] 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, 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 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 the collagen fiber image, the pixel on the corresponding cell contour closest to it is found, and the method is: 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.

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

[0032] 1. The present invention analyzes and extracts structural features from the three-dimensional image stack obtained by second harmonic generation microscopy. Compared with existing tissue pathology methods, the present invention has the advantages of high precision, rapidity, non-invasiveness, and saving of manpower and material resources, and can also realize the imaging of small lesions.

[0033] 2. The method proposed in the present invention can process three-dimensional images. Compared with the background technology which is limited to the calculation of the two-dimensional relative direction between collagen fibers, the method proposed in the present invention can more completely analyze the three-dimensional direction of fibrous tissue in three-dimensional images, and further calculate the three-dimensional relative orientation between it and cells, reflecting the three-dimensional relative position distribution characteristics between it and cells, rather than being limited to the relative position distribution characteristics between collagen fibers, and has a wide range of application scenarios. 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 changes in physiological characteristics.

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

[0035] 4. The three-dimensional relative orientation average value calculated by the present invention can quantitatively compare the changes in the overall spatial relative position of collagen fibers and cells during physiological changes. This value has clear scientific significance and can help researchers quickly grasp the trends and characteristics of the changes, which helps to improve the efficiency of subsequent research and determine the research plan.

[0036] 5. The three-dimensional relative orientation distribution characteristics obtained by the present invention can be visualized to 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, making it more vivid and making this information easier for users to obtain. Compared with the background technology, it has stronger information readability. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 The flowchart of the calculation of the spatial distribution characteristics of the three-dimensional relative orientation 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 hormone-sensitive three-dimensional breast engineering tissue model culture, imaging, image reconstruction process and three-dimensional relative orientation calculation results. DETAILED DESCRIPTION

[0040] In order to describe the present invention more specifically, the specific implementation modes of the present invention are described in detail below with reference to the accompanying drawings and examples, 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 follows Figure 1 As shown:

[0042] 1) Cultivate hormone-sensitive three-dimensional breast engineered tissues and treat them with estrogen (E2) and estrogen + prolactin (E2 + prol), such as Figure 3 (A)

[0043] 2) Perform three-dimensional imaging of the collagen fibers surrounding the cells using second harmonic generation microscopy to obtain a series of original three-dimensional image stacks;

[0044] 3) performing pixel intensity threshold filtering on the original three-dimensional image stack to obtain a three-dimensional array of collagen fiber images composed of binary images, with a value of 1 representing pixels containing collagen fiber spatial distribution information that require subsequent feature extraction and calculation, and a value of 0 representing background pixels;

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

[0046]

[0047] 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. The value range of is [0°, 180°].

[0048] 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:

[0049]

[0050] Here 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 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 of each point on the collagen fiber can be obtained. fiber and

[0051] 5) Use two-photon fluorescence microscopy to image cells, perform pixel intensity threshold filtering on each two-dimensional cell image in the obtained three-dimensional data, and use 1 value to represent pixels containing cell spatial information and 0 value to represent background pixels; extract cell contours through dilation, hole filling, maximum connected domain (cell area screening) and skeletonization operations, such as Figure 3 As shown in (B), the cell image binarization matrix is ​​obtained;

[0052] 6) Based on each image of the extracted cell contour, a three-dimensional array of cell contour images is obtained, and three-dimensional fitting is performed to obtain a 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, the ellipsoid equation is used for fitting, and the coordinates of the center of the sphere obtained by fitting are (x center ,y center ,z center ), the semi-axis lengths of the x, y, and z axes are a, b, and c respectively, and the fitting equation is ((xx center ) / a) 2 +((yy center ) / b) 2 +((zz center ) / c) 2 =1;

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

[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 positive direction pointing outward from the contour. The normal vector at point (x0, y0, z0) is:

[0055]

[0056] 8) Based on the normal vector at this point, we take the given pixel point (x0, y0, z0) on the contour as the origin of the spatial coordinate system at this point, and the θ and The definition is the same as Figure 2 As shown in (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 According to the vector angle calculation formula, cosθ is obtained normal as follows:

[0057]

[0058] θ is calculated by the arccosine normal value. Similarly, It is defined as the angle between the normal vector and the -z direction, where the -z direction vector is (0,0,-1).

[0059]

[0060] Calculated from the arccosine The true value range is as follows Figure 2 (C) shown.

[0061] 9) Based on a given point on the collagen fiber, find the pixel closest to the corresponding cell contour. Method: 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 for each point. Take the corresponding point on the cell contour corresponding to the minimum value of D.

[0062] 10) Based on the three-dimensional spatial direction θ at a given point on the collagen fiber fiber and And the three-dimensional space direction θ of the normal vector of the pixel at the minimum value of D on the corresponding cell contour normal and 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 ° ], the corresponding definition is as follows Figure 2 As shown in (E), the final three-dimensional relative orientation is 90-δ, and the value 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°.

[0065] 11) After calculation, the average three-dimensional relative orientation of the group treated with estrogen (E2) was 12.78°, and the average three-dimensional relative orientation of the group treated with estrogen + prolactin (E2+prol) was 22.66°, which indicates that on average, the use of estrogen and prolactin treatment on three-dimensional breast engineered tissue will induce collagen fibers to be more perpendicular to the cells than treatment with estrogen alone.

[0066] 12) Pseudo-color coding is performed on the image according to the calculated three-dimensional relative orientation value to more clearly and vividly represent the three-dimensional relative orientation value, thereby revealing the overall information of the spatial relative position of collagen fibers and cells in the image, such as Figure 3 (B) shown.

[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 shown in Figure 3 (C) Figure 3 (D) Figure 3 (B) The 3D relative orientation distribution histogram of the area pointed by the arrow shows that the 3D relative orientation can not only quantitatively describe the spatial relative position of collagen fibers and cells from an average and overall perspective, but also has high sensitivity and can reveal detailed position information in the image.

[0068] The above examples show that the present invention quantitatively characterizes the spatial position and spatial relative position of collagen fibers and cells by performing second harmonic generation microscopy and two-photon fluorescence microscopy on the collagen fibers and cells of the hormone-sensitive three-dimensional breast engineering tissue model, and calculates the three-dimensional relative orientation parameters, providing complementary and comprehensive spatial distribution information, and can analyze the spatial distribution characteristics of collagen fibers and cells in a more comprehensive manner with high sensitivity. At the same time, a pseudo-color image of three-dimensional relative orientation is provided with a resolution of pixel level, and the spatial distribution information is converted into a more vivid color image for presentation, which has strong information readability.

[0069] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. 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 work. Therefore, the present invention is not limited to the above embodiments, and improvements and modifications made to the present invention by those skilled in the art based on the disclosure of the present invention should be within the scope of protection 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.

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 ), the value range of δ is [0 ° , 90 ° ], the three-dimensional relative orientation is 90-δ, and the value 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 of collagen fibers and cells based on vector calculation according to claim 1 or 2, characterized in that: 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 b=(1,0,0), and cosθ is obtained according to the vector angle calculation formula 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.

4. The method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector calculation according to claim 3, 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:

5. The method for calculating the three-dimensional relative orientation between collagen fibers and cells based on vector calculation according to claim 4, characterized in that: 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 can be obtained.

6. The method for calculating the three-dimensional relative orientation of collagen fibers and cells based on vector calculation according to claim 1, 2, 4 or 5, 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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