A method for reconstructing spatial and angular distribution of fluorescent molecules

Abstract

The application discloses a fluorescent molecule space and angle distribution reconstruction method based on a spherical domain continuity prior and a plug-and-play alternating direction minimization algorithm, which introduces the excitation light polarization state and the angle distribution two dimensions in the traditional alternating direction minimization algorithm, and introduces the spherical domain continuity prior to suppress noise, so that the fluorescent molecule space and angle distribution can be better reconstructed through the polarization fluorescence microscope data. The application can improve the spatial resolution of the reconstruction result and the accuracy of the angle distribution under the condition of suppressing noise, and only needs to preliminarily and roughly set an iteration number and a continuity prior weight, does not need to manually adjust parameters for many times additionally, simultaneously, converts the originally complex operation of the angle distribution in the spherical domain to the simple spherical harmonic domain to implement, and ensures reasonable operation cost.

Description

Technical Field

[0001] This invention belongs to the field of polarization fluorescence microscopy imaging technology, specifically relating to a method for reconstructing the spatial and angular distribution of fluorescent molecules based on spherical domain continuity priors and a plug-and-play alternating direction minimization algorithm. Background Technology

[0002] Most fluorescent molecules can be modeled using dipoles, which have different orientations. Several fluorescent molecules with arbitrary orientations at the same location can be considered a fluorophore. A fluorophore possesses characteristics such as spatial location and intensity at different orientations, i.e., spatial and angular distribution. Polarized fluorescence microscopy (PFM) is a highly effective imaging technique in the biological field. Using fluorescent protein labels or specific proteins within biological samples, the samples emit fluorescence of varying intensities under different polarized light excitations. This intensity is closely related to the spatial and angular distribution of the protein molecules, thus reflecting specific properties of the biological sample. Its applications extend from single-cell imaging to large tissue imaging. Polarization fluorescence microscopy offers submicron spatial resolution, high contrast, and molecular orientation sensitivity, allowing us to acquire microscopic images under different excitation light polarization states for indirect observation. However, to directly explore the structure and function of biological samples, it is necessary to recover the three-dimensional spatial and angular distribution of fluorescent molecules from these images. Furthermore, inherent blurring and noise degrade fluorescence data, all of which affect researchers' understanding of real biological samples. However, as long as the forward projection process of the imaging system can be described, sample information can be recovered using a linear inverse problem-solving algorithm to reconstruct the spatial and angular distribution of the sample.

[0003] To date, the algorithms for reconstructing the three-dimensional spatial and angular distribution of fluorescent molecules in polarized fluorescence microscopy are mainly based on the least squares algorithm of Singular Value Decomposition (SVD) [Richard W. Hendler, Richard I. Shrager. Deconvolutions based on singular value decomposition and the pseudoinverse: a guide for beginners. Journal of Biochemical and Biophysical Methods, Volume 28, Issue 1, 1994]. Although this method has been statistically proven to be a maximum likelihood estimator for data that has been corrupted by uncorrelated Gaussian noise, the small eigenvalues ​​obtained during SVD can amplify the noise to an unacceptable level during computation. Generally, it is necessary to add a Tikhonov regularization term to the optimization problem to suppress noise [Fuhry, M., Reichel, L. A new Tikhonov regularization method. Numerical Algorithm]. [59,433–445 (2012)], but the introduction of Tikhonov regularization inevitably introduces a bias into the final spatial and angular distribution reconstruction results. This bias manifests as a shift in a certain direction in the angular distribution and a reduction in resolution in the spatial distribution. Furthermore, this method requires a lot of manual debugging experience to select a reasonable regularization weight.

[0004] Therefore, improving the resolution and accuracy of spatial and angular distribution reconstruction results while ensuring noise suppression and minimizing the number of manual empirical parameter adjustments is a challenging and hot research topic in this field. Summary of the Invention

[0005] In view of the above, the present invention provides a method for reconstructing the spatial and angular distribution of fluorescent molecules based on spherical domain continuity prior and plug-and-play alternating direction minimization algorithm. This method can improve the spatial resolution and angular distribution accuracy of the reconstruction results while suppressing noise. Furthermore, it only requires a rough setting of one iteration number and one continuity prior weight beforehand, without the need for multiple manual parameter tunings. At the same time, it transforms the complex calculations of angular distribution in the spherical domain to be implemented in the simple spherical harmonic domain, ensuring reasonable computational costs.

[0006] A method for reconstructing the spatial and angular distributions of fluorescent molecules based on spherical domain continuity priors and a plug-and-play alternating direction minimization algorithm includes the following steps:

[0007] (1) In each viewpoint of the polarization fluorescence microscope system, multiple excitation lights with different polarization states are used to excite fluorescently labeled biological tissue samples, and fluorescence is collected by the probe objective, thereby acquiring fluorescence microscopic image data of biological tissue samples under different viewpoints and different excitation light polarization states.

[0008] (2) The dipole point diffusion function of fluorescent molecules under different viewpoints and different excitation light polarization states is obtained by simulation, and then normalized and the back projection operator is calculated.

[0009] (3) Preprocess the fluorescence microscopic image data of the collected biological tissue samples;

[0010] (4) The polarization state domain, which characterizes the polarization state of the excitation light, and the spherical domain, which characterizes the angular distribution, are introduced into the alternating direction minimization algorithm based on the continuity prior of the spherical domain and plug-and-play. The calculations that should have been performed in the three-dimensional spatial domain and the spherical domain are transferred to the frequency domain and the spherical harmonic domain, thereby iteratively reconstructing the spatial and angular distribution of fluorescent molecules in biological tissue samples.

[0011] Furthermore, the number of viewing angles and the number of excitation light polarization states can be single or multiple.

[0012] Furthermore, the fluorescence microscopic image data acquired in step (1) is a three-dimensional voxel image, which is composed of stacked two-dimensional slice pixel images; the fluorescence molecular dipole point spread function corresponding to each viewpoint and each excitation light polarization state has five dimensions, namely the three-dimensional spatial dimension, the excitation light polarization state dimension, and the spherical harmonic dimension.

[0013] Furthermore, the imaging equation of the polarization fluorescence microscope system is as follows:

[0014]

[0015] Wherein: g v,p (r d The symbol () represents the position r in the fluorescence micrograph data of a biological tissue sample acquired under the excitation light polarization state p at the viewing angle v. d grayscale at that location The distance per unit concentration is represented by r under the polarization state p of the excitation light at the viewing angle v. d -r o Orientation is The fluorescent molecular response is the dipole point diffusion function. The spatial location r of a biological tissue sample o The angle of orientation is The concentration of fluorescent molecules, Representing a three-dimensional spatial domain, Represents a spherical region.

[0016] Furthermore, the calculation expression for the backprojection operator in step (2) is as follows:

[0017]

[0018] in: The distance per unit concentration is -r, and the orientation is v, where v represents the polarization state p of the excitation light. The fluorescent molecular response is the dipole point diffusion function. Corresponding to The back projection operator, The distance per unit concentration is r, and the orientation is p, representing the polarization state of the excitation light at the viewpoint v. The fluorescent molecular response.

[0019] Furthermore, in step (4), for a certain viewpoint v, the spatial and angular distribution of fluorescent molecules in the biological tissue sample is iteratively reconstructed using the following matrix operation expression:

[0020]

[0021] Where: f k This represents the reconstructed spatial angular distribution of fluorescent molecules in a biological tissue sample after the k-th iteration, where I is the identity matrix, α is the given weighting coefficient, k is a positive integer, and H... v and These are the orthogonal projection operator and inverse projection operator corresponding to the point diffusion function of the fluorescent molecule dipole at a viewing angle v, respectively, g v The fluorescence micrographs of biological tissue samples after preprocessing at a viewing angle v, ψ and ψ -1 These are the transformation operators and inverse transformation operators from the spherically harmonic domain to the spherical domain, respectively, Fenoiser. η () denotes the denoiser for the continuity prior of the spherical domain, where η is the weight of the regularization term for the continuity prior of the spherical domain, u k and ξ k These are the auxiliary variables introduced after the k-th iteration.

[0022] Furthermore, regarding the prior knowledge of continuity in the spherical domain, in updating ξ... k At that time, ψ(f) in the spherical domain k +u k-1 The denoiser contains four dimensions: the three-dimensional spatial dimension and the spherical domain dimension. The denoiser applies Hessian smoothing constraints (second-order partial derivative smoothing constraints) or TV smoothing constraints (first-order partial derivative smoothing constraints) to the three-dimensional spatial dimension along the spherical domain dimension.

[0023] Furthermore, in the matrix operation expression and The expression for the back projection operation is as follows:

[0024]

[0025]

[0026] in: The distance per unit concentration at a viewing angle v is r. d -r o Orientation is The fluorescent molecular response, Corresponding to The back projection operator, The distance per unit concentration is represented by r under the polarization state p of the excitation light at the viewing angle v. d -r o Orientation is The fluorescent molecular response, g′ v,p (r d The symbol () represents the position r in the preprocessed fluorescence micrograph data of biological tissue samples under the excitation light polarization state p at the viewing angle v. d grayscale at that location Representing a three-dimensional spatial domain, Represents a spherical region.

[0027] Furthermore, to reduce computational cost, the back projection and spherical domain multiplication operations involved in the iteration process of step (4) are rewritten using spherical harmonic domain and Fourier domain respectively as follows:

[0028]

[0029]

[0030]

[0031] in: and These represent the Fourier transform and the spherical harmonic transform, respectively. and Corresponding to and inverse transform, g v,p The image data of the biological tissue sample under preprocessed fluorescence microscopy with excitation light polarization state p at viewing angle v is h. v,p The fluorescent molecular response under the excitation of light polarization state p at the viewpoint v. Corresponding to hv, p The back projection operator, * denotes the spherical domain multiplication operator, f0 and f1 represent two variables respectively, and the subscripts lm, l′m′ and l″m″ represent the index numbers of the spherical harmonic components obtained after the spherical harmonic transformation. This is the Gaunt coefficient.

[0032] Furthermore, the Gaunt coefficient The expression is as follows:

[0033]

[0034] in: and All are spherical harmonic functions, corresponding to the orientation on the spherical domain. The mapping relationship between a certain point and the spherical harmonic components lm, l′m′, and l″m″, respectively.

[0035] Furthermore, the initial value f for the spatial angular distribution of fluorescent molecules in biological tissue samples... 0 Then, back projection is performed on the preprocessed fluorescence micrograph data of biological tissue samples at a viewing angle v, that is, the biological tissue sample is set at a spatial position r. o The angle of orientation is Initial value of fluorescent molecule concentration

[0036] This invention presents a method for reconstructing the spatial and angular distributions of fluorescent molecules based on spherical domain continuity priors and a plug-and-play alternating direction minimization algorithm. By introducing two dimensions—excitation light polarization state and angular distribution—into the traditional alternating direction minimization algorithm, and by incorporating spherical domain continuity priors to suppress noise, it enables better reconstruction of the spatial and angular distributions of fluorescent molecules using polarized fluorescence microscopy data. This invention designs a spherically harmonic domain-based computational process for the plug-and-play alternating direction minimization algorithm, significantly reducing the computational cost of backprojection and spherical domain multiplication. With reasonable computational cost, it solves the problems of poor noise suppression, cumbersome manual parameter adjustment, low spatial resolution, and inaccurate angular distribution in the original SVD-based least squares method. Attached Figure Description

[0037] Figure 1 This is a flowchart illustrating the method for reconstructing the spatial and angular distribution of fluorescent molecules based on the spherical domain continuity prior and the plug-and-play alternating direction minimization algorithm of the present invention.

[0038] Figure 2(a) shows the spatial distribution of the simulation data after adding different levels of Gaussian noise to the data and the structural similarity curve of the actual value when reconstructing the data using the present invention. It is also compared with the least squares method based on SVD using the optimal regularization term parameter.

[0039] Figure 2(b) is a curve showing the variation of the average cosine value of the difference between the peak direction of the angle distribution and the true angle of the simulation data after adding different levels of Gaussian noise and reconstructing it using the present invention. It is also compared with the least squares method based on SVD using the optimal regularization term parameter.

[0040] Figure 3The image shows the angular distribution peak direction pattern of a partial region of the three-dimensional reconstruction results of the polarized fluorescence microscopy data of a giant monolayer vesicle (GUV) sample. The first and second rows are observation images of the reconstruction results of one iteration of this invention and the reconstruction results using the least squares method based on SVD from different perspectives, respectively. The first to third columns correspond to three different observation perspectives. Detailed Implementation

[0041] To describe the present invention in more detail, the technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0042] A polarized light-sheet fluorescence microscope emits excitation light of a specific polarization state in its illumination path, illuminating biological tissue samples labeled with fluorescent proteins or possessing their own fluorescent proteins, causing them to fluoresce. The detector path of the light-sheet fluorescence microscope collects the fluorescence. By continuously moving the focal plane of the illumination path, traversing the entire volume of the biological tissue sample, the acquired two-dimensional pixel images are stacked to form a three-dimensional voxel image. For data with multiple views and multiple excitation light polarization states, the excitation direction of the fluorescence microscope can be adjusted, or the sample and the polarization mode of the excitation light can be rotated to acquire multiple sets of volume data, obtaining biological sample data with multiple views and multiple polarization excitation modes.

[0043] like Figure 1 As shown, the present invention provides a method for reconstructing the spatial and angular distribution of fluorescent molecules based on spherical domain continuity priors and alternating direction minimization algorithms, comprising the following steps:

[0044] S1. Calculate the system matrix, including the dipole point spread function and its back projection operator; generate the dipole point spread function h for each viewpoint v and excitation light polarization state p through simulation. v,p And calculate its back projection operator. They are saved in the form of a multidimensional matrix for subsequent data processing.

[0045]

[0046] S2. Since the coordinate systems referenced by the acquired images are inconsistent, preprocessing is required first. A viewpoint and excitation light polarization state are selected as a reference, and data obtained from other viewpoints and excitation light polarization states are linearly interpolated and rotated by a certain angle to give them corresponding coordinate systems. This results in a coarsely registered image. For more accurate image fusion, an intensity-based registration method is used to generate a registration matrix. The data from each viewpoint and excitation mode are multiplied by the corresponding registration matrix to obtain registered multi-viewpoint, multi-polarization excitation mode image data.

[0047] S3. Iterative calculations are performed using a spherical domain-based algorithm that incorporates a polarization state domain characterizing the polarization state of the excitation light and a spherical domain characterizing the angular distribution. The corresponding estimated results of the reconstructed spatial angular distribution of the fluorescent molecules are obtained in each iteration.

[0048]

[0049] To reduce computational costs, the operations originally defined in the spatial and spherical domains are transformed into calculations in the Fourier and spherical harmonic domains. The back projection and spherical domain multiplication are changed to the following form to iteratively estimate the spatial and angular distribution of biological samples.

[0050]

[0051]

[0052]

[0053] S4. Determine whether the iteration stopping condition is met, i.e. whether the expected number of iterations has been reached. If the condition is not met, proceed to step S3. If the condition is met, the iteration stops, and the spatial angle distribution estimation result obtained from the last iteration is used as the final reconstruction result.

[0054] Example

[0055] Below, we will take the reconstruction of data obtained from a single viewpoint and multiple excitation light polarization states as an example to introduce a spherical domain continuity and plug-and-play alternating direction minimization algorithm that introduces the polarization state domain representing the excitation mode and the spherical domain representing the angular distribution.

[0056] This invention introduces the polarization state domain, which characterizes the polarization state of the excitation light, and the spherical domain, which characterizes the angular distribution, into a plug-and-play alternating direction minimization algorithm, and proposes the following new iterative formula:

[0057]

[0058] Operations such as back projection are defined as follows:

[0059]

[0060]

[0061]

[0062] Regarding the backprojection operator, we introduce more dimensions here, as follows:

[0063]

[0064] Because during the calculation process, the spherical domain dimension Typically, the data needs to be discretized into thousands of directional values, resulting in a huge computational burden. Therefore, spherical harmonic transformation can be used to transform the data into the spherical harmonic domain. In the spherical harmonic domain, only a few dozen lm values ​​are usually needed to represent the distribution that would require thousands of values ​​to describe in the spherical domain. Furthermore, the computational cost of performing multiplication in the Fourier domain is far less than that of performing convolution operations in the spatial domain.

[0065] Therefore, in this example, the definitions of each operator in the iteration structure are rewritten as follows:

[0066]

[0067]

[0068]

[0069] Similarly, for data obtained from multiple views, each with several excitation polarization states, the backprojection operator is:

[0070]

[0071] The iterative reconstruction formula is:

[0072]

[0073]

[0074] Below, we use simulated data to verify the effectiveness of this invention. A phantom with a certain spatial and angular distribution was randomly generated, and the excitation and detection process of polarization fluorescence microscopy was simulated by forward projection using the dipole point spread function, resulting in a set of simulated data. Poisson noise (SNR = 2dB) was added to the simulated data, and the invention was used for reconstruction. The results after each iteration were recorded and compared with the least squares method based on SVD using the optimal regularization term parameters. Figure 2(a) shows the difference between the spatial distribution of the reconstructed result and the true value, characterized by the structural similarity index. Figure 2(b) shows the difference between the peak direction of the angular distribution of the reconstructed result and the true value, characterized by the mean cosine value of the angle difference. These figures together demonstrate that, while ensuring a good angular distribution, the spatial distribution accuracy of the reconstructed result of this invention is better than the best result obtainable by manually adjusting the parameters of the least squares method based on SVD.

[0075] In addition, we used experimental data from giant monolayer vesicle samples to further verify the effectiveness of the present invention. Giant monolayer vesicles are commonly used biological tissue samples in biological polarization fluorescence imaging. According to current biological understanding, the angular distribution peak direction of fluorescent molecules on their vesicle membrane is perpendicular to the tangential direction of the membrane surface. The data were acquired by polarization dual-view inverted light sheet fluorescence microscopy (pol-diSPIM).

[0076] The spatial angular distribution reconstruction method of fluorescent molecules based on the continuity prior of the spherical domain and plug-and-play alternating direction minimization of this invention is compared with the reconstruction results of the traditional least squares algorithm based on SVD. The former has one iteration, while the latter's regularization parameter was set to 0.5 after multiple trials. Both methods process the same data, and the observation diagrams of the peak direction of the angular distribution of the processed results under different viewpoints are shown. Figure 3 It can be intuitively seen that, in terms of the angular distribution of fluorescent molecules, the reconstruction algorithm based on the continuity prior of the spherical domain and the plug-and-play alternating direction minimization of this invention can obtain a more accurate and biologically consistent sample fluorescent angular distribution compared with the traditional least squares algorithm based on SVD. Specifically, the peak directions of the angular distribution are almost perpendicular to the vesicle membrane, the overall change is more continuous, and there is higher signal-to-noise ratio and better discrimination in the region of interest.

[0077] The above description of the embodiments is provided to enable those skilled in the art to understand and apply the present invention. It will be apparent to those skilled in the art that various modifications can be made to the above embodiments, and the general principles described herein can be applied to other embodiments without inventive effort. Therefore, the present invention is not limited to the above embodiments, and any improvements and modifications made to the present invention by those skilled in the art based on the disclosure thereof should be within the scope of protection of the present invention.

Claims

1. A method for reconstructing the spatial and angular distribution of fluorescent molecules based on spherical domain continuity priors and a plug-and-play alternating direction minimization algorithm, comprising the following steps: (1) In each viewpoint of the polarization fluorescence microscope system, multiple excitation lights with different polarization states are used to excite the fluorescently labeled biological tissue samples, and the fluorescence is collected by the probe objective, thereby acquiring fluorescence microscopic image data of biological tissue samples under different viewpoints and different excitation light polarization states. (2) The dipole point diffusion function of fluorescent molecules under different viewpoints and different excitation light polarization states is obtained by simulation, and then normalized and the back projection operator is calculated. (3) Preprocess the fluorescence microscopic image data of the collected biological tissue samples; (4) The polarization state domain, which characterizes the polarization state of the excitation light, and the spherical domain, which characterizes the angular distribution, are introduced into the alternating direction minimization algorithm based on the continuity prior of the spherical domain and plug-and-play. The calculations that should have been performed in the three-dimensional spatial domain and the spherical domain are transferred to the frequency domain and the spherical harmonic domain, thereby iteratively reconstructing the spatial and angular distribution of fluorescent molecules in biological tissue samples. From a certain perspective v The spatial and angular distribution of fluorescent molecules in biological tissue samples can then be reconstructed iteratively using the following matrix operation expression: in: For the first The spatial angular distribution reconstruction results of fluorescent molecules in biological tissue samples after one iteration. I It is the identity matrix. α Given the weight coefficients, k It is a positive integer. and Each is a perspective v The forward and backward projection operators corresponding to the point diffusion function of the dipole of the fluorescent molecule. From the perspective v Fluorescence micrographs of preprocessed biological tissue samples. and These are the transformation operator and inverse transformation operator from the spherically harmonic domain to the spherical domain, respectively. A denoiser representing the continuity prior of the spherical domain. The weights of the prior regularization term for continuity in the spherical domain are given. and The first Auxiliary variables introduced after the next iteration; For the prior of continuity of the spherical domain, in updating At that time, within the spherical region It includes four dimensions: three-dimensional spatial dimension and spherical domain dimension. The denoiser described therein applies Hessian smoothing constraint or TV smoothing constraint to the three-dimensional spatial dimension along the spherical domain dimension.

2. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1, characterized in that: The fluorescence microscopic image data acquired in step (1) is a three-dimensional voxel image, which is composed of stacked two-dimensional slice pixel images; the diffusion function of the fluorescent molecule dipole point corresponding to each viewpoint and each excitation light polarization state has five dimensions, namely the three-dimensional spatial dimension, the excitation light polarization state dimension, and the spherical harmonic dimension.

3. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1, characterized in that: The imaging equation of the polarization fluorescence microscope system is as follows: in: Indicates perspective v Excitation light polarization state p Corresponding location in the fluorescence microscopic image data of the biological tissue samples collected below grayscale at that location Indicates perspective v Excitation light polarization state p The distance between lower unit concentrations is Orientation The fluorescent molecular response is the dipole point diffusion function. Indicates the spatial location of biological tissue samples The angle of the direction is The concentration of fluorescent molecules, Represents a three-dimensional spatial domain. Represents a spherical region.

4. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1, characterized in that: The calculation expression for the back projection operator in step (2) is as follows: in: Indicates perspective v Excitation light polarization state p The distance per unit concentration is - Orientation is - The fluorescent molecular response is the dipole point diffusion function. Corresponding to The back projection operator, Indicates perspective v Excitation light polarization state p The distance between lower unit concentrations is Orientation The fluorescent molecular response.

5. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1, characterized in that: In the matrix operation expression and The expression for the back projection operation is as follows: in: Indicates perspective v The distance between lower unit concentrations is Orientation The fluorescent molecular response, Corresponding to The back projection operator, Indicates perspective v Excitation light polarization state p The distance between lower unit concentrations is Orientation The fluorescent molecular response, Indicates perspective v Excitation light polarization state p Corresponding position in the preprocessed biological tissue sample fluorescence micrograph data grayscale at that location Represents a three-dimensional spatial domain. Represents a spherical region.

6. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 5, characterized in that: To reduce computational cost, the back projection and spherical multiplication operations involved in the iteration process of step (4) are rewritten using spherical harmonic domain and Fourier domain respectively: in: and These represent the Fourier transform and the spherical harmonic transform, respectively. and Corresponding to and inverse transform, From the perspective v Excitation light polarization state p Fluorescence micrographs of preprocessed biological tissue samples From the perspective v Excitation light polarization state p Fluorescent molecule response under the following conditions Corresponding to The back projection operator, This represents the spherical field multiplication operator. f 0 and f 1 represents two variables, and the subscript is... , and This indicates the index number of the spherical harmonic component obtained after the spherical harmonic transformation. This is the Gaunt coefficient.

7. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 6, characterized in that: The Gaunt coefficient The expression is as follows: in: , and All are spherical harmonic functions, corresponding to the orientation on the spherical domain. A point on the sphere is respectively related to the spherical harmonic components. , spherical harmonic component Harmonious components The mapping relationship.

8. The method for reconstructing the spatial and angular distribution of fluorescent molecules according to claim 1, characterized in that: Initial values ​​for the spatial angular distribution of fluorescent molecules in biological tissue samples Then, from the perspective of v Back projection is performed on the preprocessed fluorescence microscopic image data of biological tissue samples, i.e., the spatial location of the biological tissue samples is set. The angle of the direction is Initial value of fluorescent molecule concentration .

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