Three-dimensional reconstruction neural network algorithm for space transcriptome data

Abstract

The invention relates to the technical field of neural networks, and discloses a three-dimensional reconstruction neural network algorithm for space transcriptome data. According to the algorithm, firstly, multi-modal fusion preprocessing including coordinate alignment, noise filtering and sparsity correction is carried out on original space transcriptome data, and standardized data are generated; constructing a deep neural network model containing space graph embedding, multi-scale three-dimensional convolution and a dynamic attention fusion module, and optimizing the model based on an adversarial training strategy to generate three-dimensional probability distribution features; and converting into a three-dimensional geometric structure by utilizing a differentiable three-dimensional grid deformation algorithm, correcting abnormity, and finally, iteratively updating through an implicit field optimization algorithm, and outputting a high-resolution three-dimensional reconstruction result. According to the algorithm, the problems of data noise and sparsity are effectively solved, the relationship between gene expression and a three-dimensional structure is deeply mined, high-precision three-dimensional reconstruction is realized, and the algorithm has a wide application prospect in the field of biomedical research.

Description

Technical Field

[0001] The present invention relates to the field of neural network technology, and in particular to a neural network algorithm for three-dimensional reconstruction of spatial transcriptome data. Background Art

[0002] In biomedical research, a deep understanding of the spatial distribution of cells within tissues and their gene expression patterns is crucial for uncovering the mechanisms of disease progression and developing novel therapeutic strategies. The emergence of spatial transcriptomics technology enables researchers to measure gene expression levels while preserving information about the spatial location of cells, opening new opportunities for biological research. However, the processing and analysis of spatial transcriptomics data currently face numerous challenges, which limit its in-depth application in biomedical research.

[0003] Spatial transcriptome data are usually obtained in the form of two-dimensional slices, which cannot intuitively present the three-dimensional structure of tissues and the spatial relationship between cells. Inferring three-dimensional structure from two-dimensional slice data has always been a research difficulty in this field. Traditional reconstruction methods are mainly based on manual features and machine learning algorithms. For example, reconstruction methods based on morphological features require manual definition and extraction of complex features. This is not only labor-intensive and inefficient, but also has poor adaptability to different types of tissues. Although machine learning-based methods have improved the degree of automation of reconstruction to a certain extent, due to the inability to fully explore the complex spatial information and gene expression associations in the data, the reconstruction accuracy is difficult to meet actual research needs.

[0004] Spatial transcriptome data suffer from noise interference and data sparsity problems. Technical errors in the experimental process, differences in sample processing, and other factors can introduce noise, affecting the accuracy of gene expression signals. At the same time, due to sequencing depth limitations and the cell-specificity of gene expression, data sparsity is prevalent, which makes it difficult to accurately capture gene expression patterns and cell-to-cell interactions. Existing noise filtering and data filling methods are unable to effectively deal with these problems, resulting in reduced reliability of subsequent analysis results. For example, some noise filtering methods based on statistical models are prone to losing some real biological signals while removing noise; simple data filling strategies may introduce erroneous information and fail to accurately reflect the true situation of gene expression.

[0005] Existing technologies lack the ability to deeply explore the relationship between gene expression data and three-dimensional structure. Gene expression patterns are closely related to the spatial position of cells. However, most studies only analyze gene expression data and the three-dimensional structure of tissues separately, failing to fully integrate the information of the two. This makes it difficult for researchers to understand the intrinsic connection between cell function and tissue spatial structure at the molecular level, limiting in-depth exploration of the mechanisms of disease occurrence and development. For example, in tumor research, it is impossible to accurately determine the relationship between changes in the expression of specific genes in tumor cells and the three-dimensional morphological evolution of tumor tissue, which affects the understanding of the mechanisms of tumor growth and metastasis.

[0006] As biomedical research evolves toward precision and personalization, higher demands are placed on 3D reconstruction techniques for spatial transcriptome data. Developing an efficient and accurate 3D reconstruction algorithm for spatial transcriptome data can overcome the shortcomings of existing technologies, integrate multimodal information, and achieve high-precision 3D reconstruction, which is of great practical significance for advancing biomedical research. Summary of the Invention

[0007] The purpose of the present invention is to provide a neural network algorithm for three-dimensional reconstruction of spatial transcriptome data to solve the problems raised in the above background technology.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a neural network algorithm for three-dimensional reconstruction of spatial transcriptome data, the method comprising:

[0009] Step T1: Perform multimodal fusion preprocessing on the original spatial transcriptome data, including spatial coordinate alignment of the gene expression matrix, noise filtering and sparsity correction, to generate standardized spatial gene expression data;

[0010] Step T2: constructing a deep neural network model based on graph convolution and 3D voxel encoding, wherein the model includes a spatial graph embedding module, a multi-scale 3D convolution module, and a dynamic attention fusion module;

[0011] Step T3: Optimizing the deep neural network model based on the adversarial training strategy, generating a three-dimensional probability distribution feature of the spatial transcriptome through adversarial learning between the generator and the discriminator;

[0012] Step T4: using a differentiable three-dimensional mesh deformation algorithm to convert the three-dimensional probability distribution features into a continuous three-dimensional geometric structure, and correcting geometric anomalies through topological constraints;

[0013] Step T5: Iteratively update the 3D geometric structure and neural network parameters, fuse local geometric details with global spatial consistency through the implicit field optimization algorithm, and output high-resolution 3D reconstruction results.

[0014] Preferably, in step T1, the multimodal fusion preprocessing includes the following operations:

[0015] Cross-slice coordinate alignment is achieved through rigid registration between spatial transcriptome slices and non-rigid deformation field calculation;

[0016] A noise filtering method based on low-rank matrix decomposition is used to separate technical noise and biological variation in gene expression signals;

[0017] Exploiting graph structure priors of gene co-expression networks to perform graph Laplacian regularization filling on sparse gene expression data.

[0018] Preferably, in step T2, the spatial graph embedding module aggregates neighborhood gene expression features through a graph attention mechanism; the multi-scale three-dimensional convolution module adopts a structure combining dilated convolution and residual connection to extract cross-scale three-dimensional spatial features; the dynamic attention fusion module dynamically integrates graph embedding features and three-dimensional voxel features through learnable weights.

[0019] Preferably, in step T3, the generator takes spatial gene expression data as input and outputs three-dimensional probability distribution features; the discriminator adopts a multi-branch structure to evaluate the authenticity, topological rationality and gene expression consistency of the three-dimensional distribution respectively; and a gradient penalty term is introduced in adversarial training to stabilize the training process.

[0020] Preferably, in step T4, the differentiable three-dimensional mesh deformation algorithm includes the following steps:

[0021] Initialize an isosurface grid based on a three-dimensional probability distribution;

[0022] Optimize the spatial positions of mesh vertices by using differentiable moving least squares method;

[0023] Smooth mesh surfaces using a curvature flow algorithm and detect and repair holes and non-manifold structures using topological constraints.

[0024] Preferably, in step T5, the implicit field optimization algorithm represents the three-dimensional geometry through a signed distance function, jointly optimizes the signed distance value of the implicit field and the neural network feature map, and the constraints include local curvature continuity, global volume conservation and spatial alignment of gene expression gradients.

[0025] Preferably, the deep neural network model adopts a hybrid loss function in the training phase, including:

[0026] Adversarial loss, which measures the difference between the generated distribution and the true distribution;

[0027] Geometric reconstruction loss, which calculates the Chamfer distance between the predicted 3D structure and the reference structure;

[0028] Biological consistency loss,reconstructs spatial gene expression patterns based on gene co-expression network constraints.

[0029] Preferably, the graph attention mechanism adopts a multi-head attention structure, in which the attention weight is calculated by a joint function of gene expression similarity and spatial distance.

[0030] Preferably, the topological constraint condition quantifies the topological characteristics of the three-dimensional grid through the persistent homology theory, and constructs a topological loss function to drive the topology preservation during the grid deformation process.

[0031] Preferably, an adaptive sampling strategy is introduced into the implicit field optimization algorithm to dynamically adjust the sampling density according to the probability distribution characteristics, and give priority to optimizing the three-dimensional geometric details of the high uncertainty area.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] During the data processing phase, multimodal fusion preprocessing effectively addresses key issues with raw data. Cross-slice coordinate alignment is achieved through rigid registration of spatial transcriptome slices and calculation of non-rigid deformation fields, enabling precise integration of data from different slices into a common coordinate system. This enables subsequent analysis based on accurate spatial location information, significantly improving data usability. For example, when studying spatial transcriptome data from brain tissue, accurate coordinate alignment helps researchers clearly visualize gene expression changes across different brain regions and differences in cell distribution across these regions. A noise filtering method based on low-rank matrix factorization effectively separates technical noise from biological variation in gene expression signals, improving data quality. The processed data provides clearer gene expression signals, reducing noise interference in subsequent analysis and providing a reliable data foundation for accurate analysis of gene expression patterns. Graph Laplacian regularization, leveraging the graph structure prior of the gene co-expression network, mitigates data sparsity. This method leverages the co-expression relationships between genes to appropriately fill in missing gene expression data, resulting in a more complete gene expression profile and facilitating the discovery of potential gene regulatory networks.

[0034] The design of the deep neural network model is innovative and highly efficient. The spatial graph embedding module uses a graph attention mechanism to aggregate neighborhood gene expression features. Through its multi-head attention architecture, it can learn feature information about neighboring genes from multiple perspectives, comprehensively capturing interactions between genes. This is crucial for understanding the coordinated changes in gene expression and the influence of the cellular microenvironment on gene expression. The multi-scale 3D convolution module combines dilated convolution with residual connections to effectively extract cross-scale 3D spatial features. Dilated convolution expands the receptive field of the convolution kernel, enabling the model to extract features at different scales, capturing rich spatial information from the microscopic cellular level to the macroscopic tissue level. Residual connections address the vanishing gradient problem during deep neural network training, ensuring model training stability and accuracy. The dynamic attention fusion module dynamically integrates graph embedding features and 3D voxel features using learnable weights. This adaptively adjusts the fusion ratio of different features based on data characteristics, improving feature fusion and providing more representative feature data for subsequent 3D reconstruction.

[0035] Based on an adversarial training strategy, the deep neural network model is optimized. Through adversarial learning between the generator and the discriminator, the generated three-dimensional probability distribution features of the spatial transcriptome are more accurate. The discriminator adopts a multi-branch structure to evaluate the authenticity, topological rationality, and gene expression consistency of the three-dimensional distribution. This multi-dimensional evaluation method makes the generated results more reliable in terms of biological significance and spatial structure. For example, when reconstructing the three-dimensional structure of tumor tissue, it can accurately reflect the distribution of tumor cells, the tumor boundary, and the heterogeneity within the tumor. The introduction of a gradient penalty term in adversarial training stabilizes the training process, avoids the problem of gradient vanishing or gradient exploding during the model training process, and ensures the convergence and stability of the model.

[0036] The differentiable 3D mesh deformation algorithm transforms 3D probability distribution features into a continuous 3D geometric structure and corrects geometric anomalies through topological constraints. Initializing the isosurface mesh based on the 3D probability distribution provides a reasonable starting point for subsequent mesh optimization. The differentiable moving least squares method optimizes the spatial position of the mesh vertices so that the mesh can better fit the data features. The curvature flow algorithm is used to smooth the mesh surface, improving the quality and visualization of the mesh. Topological constraints are used to detect and repair holes and non-manifold structures, ensuring the topological rationality of the reconstructed 3D geometric structure. This is of great significance for accurately understanding the spatial structure and function of tissues. For example, when reconstructing vascular networks, it can accurately reflect the connectivity and branching structure of blood vessels.

[0037] The implicit field optimization algorithm achieves the fusion of local geometric details and global spatial consistency by jointly optimizing the signed distance value of the implicit field and the neural network feature map, combined with constraints such as local curvature continuity, global volume conservation, and spatial alignment of gene expression gradients. This allows the final output of high-resolution three-dimensional reconstruction results to not only accurately reflect the morphology and distribution of cells in microscopic details, but also maintain the overall structure and spatial layout of the tissue at a macroscopic level. For example, when reconstructing liver tissue, the arrangement of liver cells and the overall structure of the liver lobules can be clearly displayed. The introduced adaptive sampling strategy dynamically adjusts the sampling density according to the probability distribution characteristics, prioritizes the optimization of three-dimensional geometric details in high-uncertainty areas, improves the resolution and accuracy of the reconstruction results, and also improves computational efficiency and reduces unnecessary waste of computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a working principle diagram of the neural network algorithm for three-dimensional reconstruction of spatial transcriptome data according to the present invention;

[0039] Figure 2 This is the flow chart of the differentiable 3D mesh deformation algorithm;

[0040] Figure 3Flowchart for calculating and optimizing training loss for deep neural network models;

[0041] Figure 4 Flowchart for the attention mechanism weight calculation. DETAILED DESCRIPTION

[0042] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0043] See also Figure 1-4 The present invention provides a neural network algorithm for three-dimensional reconstruction of spatial transcriptome data, and its overall implementation scheme is as follows:

[0044] Step T1: Multimodal Fusion Preprocessing: The raw spatial transcriptome data are processed to generate standardized spatial gene expression data. Specific operations include spatial coordinate alignment, noise filtering, and sparsity correction. Rigid registration and non-rigid deformation field calculation between spatial transcriptome slices achieve cross-slice coordinate alignment, ensuring accurate spatial alignment between slices. A noise filtering method based on low-rank matrix decomposition is used to separate technical noise from biological variation in gene expression signals to improve data quality. Graph structure priors of gene co-expression networks are used to perform graph Laplacian regularization on the sparse gene expression data to optimize data sparsity.

[0045] Step T2: Constructing a deep neural network model: The constructed model includes a spatial graph embedding module, a multi-scale 3D convolution module, and a dynamic attention fusion module. The spatial graph embedding module aggregates neighborhood gene expression features through a graph attention mechanism; the multi-scale 3D convolution module uses a structure combining dilated convolution and residual connections to extract cross-scale 3D spatial features; and the dynamic attention fusion module dynamically integrates graph embedding features and 3D voxel features using learnable weights.

[0046] Step T3: Model Optimization Based on Adversarial Training: The deep neural network model is optimized using an adversarial training strategy. The generator takes spatial gene expression data as input and outputs a three-dimensional probability distribution. The discriminator employs a multi-branch structure to evaluate the authenticity, topological plausibility, and gene expression consistency of the three-dimensional distribution. A gradient penalty term is introduced during adversarial training to stabilize the training process.

[0047] Step T4: Convert to 3D Geometric Structure and Correct Anomalies: A differentiable 3D mesh deformation algorithm is used to convert the 3D probability distribution features into a continuous 3D geometric structure, and geometric anomalies are corrected using topological constraints. This algorithm involves initializing an isosurface mesh based on the 3D probability distribution; optimizing the spatial positions of the mesh vertices using a differentiable moving least squares method; smoothing the mesh surface using a curvature flow algorithm; and detecting and repairing holes and non-manifold structures using topological constraints.

[0048] Step T5: Iterative Update and Output: The 3D geometry and neural network parameters are iteratively updated, integrating local geometric details with global spatial consistency through an implicit field optimization algorithm. The implicit field optimization algorithm represents the 3D geometry using a signed distance function and jointly optimizes the signed distance values ​​of the implicit field and the neural network feature map, subject to constraints such as local curvature continuity, global volume conservation, and spatial alignment of gene expression gradients. The final output is a high-resolution 3D reconstruction.

[0049] The technical solution of the present invention is further described in detail below through specific embodiments:

[0050] Example 1: In this example, the multimodal fusion preprocessing operation in step T1 is described in detail. The spatial transcriptome data comes from multiple slices, and there are position deviations between different slices. Through rigid registration, the slice coordinates are preliminarily aligned using the rotation matrix R and the translation vector t. The transformation formula is X aligned =R×X original +t, where X original is the original coordinate, X aligned The aligned coordinates are then calculated using a non-rigid deformation field. Using the thin plate spline interpolation algorithm, the deformation field is constructed based on the displacement information of the control points, allowing for more precise alignment of the coordinates.

[0051] In terms of noise filtering, based on low-rank matrix decomposition, the gene expression matrix G is decomposed into a low-rank matrix L and a sparse matrix S, that is, G = L + S. Among them, L represents biological signals and S represents technical noise. By solving the optimization problem Determine the values ​​of L and S to achieve noise separation. Here, ‖·‖ F is the Frobenius norm, ‖·‖ * is the nuclear norm, ‖·‖1 is the L1 norm, and λ1 and λ2 are balance parameters.

[0052] For sparsity correction, the graph structure prior of the gene co-expression network is used. A gene co-expression graph G = (V, E) is constructed, where the nodes V represent genes and the edges E represent the co-expression relationships between genes. The sparse gene expression data x is filled by graph Laplace regularization, and the optimization objective is in, is the original sparse data, L is the graph Laplacian matrix, α is the regularization parameter, and tr(·) represents the trace of the matrix.

[0053] Example 2:

[0054] The spatial graph embedding module in step T2 uses a graph attention mechanism to aggregate neighborhood gene expression features, and the graph attention mechanism adopts a multi-head attention structure. For each gene node i, its feature is represented as h i The formula for calculating attention weight is:

[0055]

[0056] Where k represents the index of the attention head, W k is the projection matrix, a k is the attention vector, is the set of neighboring nodes of node i, [h i ‖h j ] represents feature concatenation, and LeakyReLU is the activation function.

[0057] The multi-head attention mechanism calculates multiple attention heads in parallel and then concatenates the results. The formula is:

[0058]

[0059] Where N is the total number of nodes, K is the number of attention heads, and W O is the output projection matrix. In this way, we can capture the neighborhood gene expression characteristics from different angles and enhance the model's understanding of spatial relationships.

[0060] Example 3:

[0061] This embodiment details the multi-scale 3D convolution module in step T2. This module uses a structure that combines dilated convolution with residual connections. Dilated convolution introduces a dilated rate d based on ordinary convolution. The convolution kernel skips some pixels during sampling to expand the receptive field. For the input feature map F and the convolution kernel K, the calculation formula for dilated convolution is:

[0062]

[0063] Among them, y[i,j] is the value of the output feature map at position (i,j), and (m,n) is the index of the convolution kernel.

[0064] The residual connection adds the input directly to the output of the convolutional layer. The formula is:

[0065] F out =F in +H(F in )

[0066] Among them, F in is the input feature map, F out is the output feature map, H(F in ) is the output of the convolutional layer. Through dilated convolution and residual connections, the model can extract cross-scale three-dimensional spatial features while avoiding the gradient vanishing problem and improving model training results.

[0067] Example 4: Elucidating the dynamic attention fusion module in step T2. This module dynamically integrates the graph embedding feature h through learnable weights graph With the 3D voxel feature h voxel The formula for calculating the fusion weight is:

[0068] β=σ(W1[h graph ‖h voxel ]+b1)

[0069] Among them, σ is the Sigmoid function, W1 is the weight matrix, b1 is the bias vector, [h graph ‖h voxel ] indicates feature splicing.

[0070] The fused feature h fusion for:

[0071] h fusion =βh graph +(1-β)h voxel

[0072] By dynamically adjusting the fusion weights, the model can adaptively integrate graph embedding features and 3D voxel features according to different input features, thereby improving the accuracy of feature representation.

[0073] Example 5:

[0074] This example is used to explain the adversarial training process in step T3. The generator takes spatial gene expression data x as input and outputs a three-dimensional probability distribution feature y gen The discriminator adopts a multi-branch structure to evaluate the authenticity of the three-dimensional distribution, topological rationality and gene expression consistency respectively.

[0075] The loss function (adversarial loss) used by the discriminator to evaluate authenticity is:

[0076]

[0077] Among them, p data is the true data distribution, p z is the noise distribution of the generator input, G is the generator, and D real is the branch for discriminating real data, D genIt is the branch for discriminating generated data.

[0078] In order to stabilize the training process, the gradient penalty term L is introduced gp , the formula is:

[0079]

[0080] Among them, λ is the penalty coefficient, is an interpolated distribution between the real data and the generated data, is the discriminator pair Through adversarial training, the generator and the discriminator compete with each other and continuously optimize, making the generated three-dimensional probability distribution characteristics closer to the real distribution.

[0081] Example 6:

[0082] This embodiment specifically describes the differentiable three-dimensional mesh deformation algorithm in step T4. First, an isosurface mesh based on a three-dimensional probability distribution is initialized. Assuming the three-dimensional probability distribution function is P(x, y, z), the initial isosurface mesh is generated using the Marching Cubes algorithm.

[0083] Then the spatial position of the mesh vertices is optimized by differentiable moving least squares method. i , its optimized position The calculation formula is:

[0084]

[0085] Among them, N i is the vertex v i The neighborhood vertex set of x j is the position of the neighborhood vertex, w ij (x) is the weight function, usually calculated based on the distance between vertices.

[0086] The mesh surface is smoothed based on the curvature flow algorithm. The formula of the curvature flow algorithm is:

[0087]

[0088] Where v is the vertex position, t is time, κ is the curvature, and n is the normal vector. Through continuous iteration, the mesh surface is smoothed, while topological constraints are used to detect and repair holes and non-manifold structures to ensure the topological correctness of the mesh.

[0089] Example 7:

[0090] The implicit field optimization algorithm in step T5 represents the three-dimensional geometry through the signed distance function SDF(x), and jointly optimizes the signed distance value of the implicit field and the neural network feature map.

[0091] The local curvature continuity constraint is implemented by calculating the second-order derivative of the signed distance function, as follows:

[0092]

[0093] Where Ω is the three-dimensional space region, is the Laplace operator.

[0094] The global volume conservation constraint calculates the volume by integration, using the formula:

[0095]

[0096] Where n is the surface normal vector. During the optimization process, the volume is maintained constant to ensure the rationality of the reconstruction results. Furthermore, spatial alignment of gene expression gradients is used to better align the reconstructed 3D structure with the gene expression data. An adaptive sampling strategy is introduced to dynamically adjust the sampling density based on the probability distribution characteristics, prioritizing optimization of 3D geometric details in areas of high uncertainty, thereby improving the resolution and accuracy of the reconstruction results.

[0097] It should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "includes," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that includes a list of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus.

[0098] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A neural network algorithm for three-dimensional reconstruction of spatial transcriptome data, characterized in that: The following steps are involved: Step T1: Perform multimodal fusion preprocessing on the original spatial transcriptome data, including spatial coordinate alignment of the gene expression matrix, noise filtering and sparsity correction, to generate standardized spatial gene expression data; Step T2: constructing a deep neural network model based on graph convolution and 3D voxel encoding, wherein the model includes a spatial graph embedding module, a multi-scale 3D convolution module, and a dynamic attention fusion module; Step T3: Optimizing the deep neural network model based on the adversarial training strategy, generating a three-dimensional probability distribution feature of the spatial transcriptome through adversarial learning between the generator and the discriminator; Step T4: using a differentiable three-dimensional mesh deformation algorithm to convert the three-dimensional probability distribution features into a continuous three-dimensional geometric structure, and correcting geometric anomalies through topological constraints; Step T5: Iteratively update the 3D geometric structure and neural network parameters, fuse local geometric details with global spatial consistency through the implicit field optimization algorithm, and output high-resolution 3D reconstruction results.

2. The algorithm according to claim 1, characterized in that: In step T1, the multimodal fusion preprocessing includes the following operations: Cross-slice coordinate alignment is achieved through rigid registration between spatial transcriptome slices and non-rigid deformation field calculation; A noise filtering method based on low-rank matrix decomposition is used to separate technical noise and biological variation in gene expression signals; Exploiting graph structure priors of gene co-expression networks to perform graph Laplacian regularization filling on sparse gene expression data.

3. The algorithm according to claim 1, characterized in that: In step T2, the spatial graph embedding module aggregates neighborhood gene expression features through a graph attention mechanism; the multi-scale three-dimensional convolution module uses a structure combining dilated convolution and residual connection to extract cross-scale three-dimensional spatial features; The dynamic attention fusion module dynamically integrates graph embedding features and 3D voxel features through learnable weights.

4. The algorithm according to claim 1, wherein: In step T3, the generator takes spatial gene expression data as input and outputs three-dimensional probability distribution features; The discriminator adopts a multi-branch structure to evaluate the authenticity, topological rationality and gene expression consistency of the three-dimensional distribution respectively; a gradient penalty term is introduced in the adversarial training to stabilize the training process.

5. The algorithm according to claim 1, characterized in that: In step T4, the differentiable three-dimensional mesh deformation algorithm includes the following steps: Initialize an isosurface grid based on a three-dimensional probability distribution; Optimize the spatial positions of mesh vertices by using differentiable moving least squares method; Smooth mesh surfaces using a curvature flow algorithm and detect and repair holes and non-manifold structures using topological constraints.

6. The algorithm according to claim 1, characterized in that: In step T5, the implicit field optimization algorithm represents the three-dimensional geometry through a signed distance function, and jointly optimizes the signed distance value of the implicit field and the neural network feature map. The constraints include local curvature continuity, global volume conservation, and spatial alignment of gene expression gradients.

7. The algorithm according to claim 1, characterized in that: The deep neural network model adopts a hybrid loss function during the training phase, including: Adversarial loss, which measures the difference between the generated distribution and the true distribution; Geometric reconstruction loss, which calculates the Chamfer distance between the predicted 3D structure and the reference structure; Biological consistency loss,reconstructs spatial gene expression patterns based on gene co-expression network constraints.

8. The algorithm according to claim 3, characterized in that: The graph attention mechanism adopts a multi-head attention structure, where the attention weight is calculated by a joint function of gene expression similarity and spatial distance.

9. The algorithm according to claim 5, characterized in that: The topological constraint condition quantifies the topological characteristics of the three-dimensional mesh through the persistent homology theory, and constructs a topological loss function to drive the topology preservation during the mesh deformation process.

10. The algorithm according to claim 6, characterized in that: An adaptive sampling strategy is introduced into the implicit field optimization algorithm to dynamically adjust the sampling density according to the probability distribution characteristics, and prioritize the optimization of three-dimensional geometric details in high uncertainty areas.

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