Spatial single-cell nuclear transcriptome densification methods, systems, electronic devices, and media

Abstract

The application provides a spatial single cell nucleus transcriptome densification method, system, electronic equipment and medium, and belongs to the technical field of biological information and artificial intelligence. The method comprises the following steps: extracting morphological features of each histological nucleus in a histological nucleus set, and determining an initial matching relationship between the histological nucleus set and a sequenced nucleus set; taking the morphological features matched by each sequenced nucleus as training data, and taking real gene expression data as training labels to train a reconstruction model; inputting the morphological features into the reconstruction model to obtain predicted gene expression data; updating the initial matching relationship according to the difference between the predicted gene expression data and the real gene expression data, and the spatial structure information of the two nucleus sets; and inputting the morphological features into the final reconstruction model to obtain final predicted gene expression data. Through the joint optimization of alignment and expression reconstruction, the expression densification is realized without relying on external single cell references.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics and artificial intelligence, and in particular to a method, system, electronic device, and medium for spatial single-cell nuclear transcriptome densification. Background Technology

[0002] Spatial transcriptomics technology can measure gene expression while preserving the spatial location of tissues. Spatial single-nucleus transcriptomics, in particular, performs sequencing by adding spatial barcodes to cell nuclei. However, in actual sample processing, significant nucleus loss occurs during the dissection and extraction of cell nuclei from tissue sections. This results in extremely sparse spatial distribution of the final single-nucleus sequencing data, with a large number of nuclei visible in histological images lacking corresponding sequencing expression data. Furthermore, the sections used for single-nucleus sequencing and the histological sections used for morphological imaging are usually physically adjacent, but their coordinate systems differ and their nucleus sets do not completely overlap.

[0003] Current processing solutions for spatial transcriptome data are mostly designed based on raster-level data. Some existing solutions directly predict gene expression from histological images, learning only the mixed expression at larger raster locations without incorporating single-nucleus resolution sequencing data as corresponding constraints. Other solutions heavily rely on external high-quality single-cell reference datasets for raster expression decomposition, making them unsuitable when faced with clinical tissue samples lacking readily available reference data. There is an urgent need in this field for a method that can recover single-nucleus resolution whole transcriptome expression data for all cell nuclei in histological images, even in the absence of external reference data and paired ground truth values. Summary of the Invention

[0004] This invention provides a spatial single-nucleus transcriptome densification method, system, electronic device, and medium to address the shortcomings of existing spatial single-nucleus transcriptome densification methods in recovering single-nucleus resolution whole transcriptome expression data missing from the cell nucleus under conditions of lack of external reference data and no one-to-one pairing true values.

[0005] This invention provides a method for spatial single-cell nuclear transcriptome densification, comprising: Histological images are segmented to obtain a set of histological cell nuclei. The morphological features of each histological cell nucleus are extracted, and the initial matching relationship between the set of histological cell nuclei and the set of sequenced cell nuclei of spatial single-cell transcriptome is determined. The initial matching relationship is determined only based on the spatial structural information of the set of histological cell nuclei and the set of sequenced cell nuclei. Iteratively execute the following steps until the first convergence condition is met: The morphological features matched by each sequenced cell nucleus in the sequenced cell nucleus set are used as training data, and the real gene expression data of each sequenced cell nucleus are used as training labels to train the reconstruction model. The matched morphological features are determined based on the initial matching relationship. The morphological features of each histological cell nucleus are input into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model; The initial matching relationship is updated based on the difference between the predicted gene expression data and the actual gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set. After the first convergence condition is met, the morphological features of each histological cell nucleus are input into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model.

[0006] In some embodiments, updating the initial matching relationship includes: The structural cost term is weighted based on the first dynamic weight, and the expression cost term is weighted based on the second dynamic weight to construct an objective function. The structural cost term is determined based on the spatial structure information, and the expression cost term is determined based on the degree of difference. The first dynamic weight and the second dynamic weight change dynamically with the increase of the iteration rounds, and the first dynamic weight shows a decreasing trend while the second dynamic weight shows an increasing trend. Solving the objective function yields the optimal matching matrix that minimizes the objective function. The elements in the optimal matching matrix represent the matching probability or matching indication between the set of histological cell nuclei and the set of sequenced cell nuclei. The initial matching relationship is updated based on the optimal matching matrix.

[0007] In some embodiments, the structural cost term is determined based on a first distance matrix formed by the spatial distances between each pair of nuclei in the histological cell nucleus set and a second distance matrix formed by the spatial distances between each pair of nuclei in the sequenced cell nucleus set, and is used to measure the degree of inconsistency between the histological cell nucleus set and the sequenced cell nucleus set in terms of internal spatial distance structure. The expression cost term is determined based on the expression cost matrix of the histological cell nucleus set and the sequenced cell nucleus set, and is used to measure the degree of difference between the predicted gene expression data and the actual gene expression data; the expression cost matrix includes the degree of difference between the predicted gene expression data of each histological cell nucleus and the actual gene expression data of each sequenced cell nucleus.

[0008] In some embodiments, the objective function further includes: An unbalanced relaxation term is used to constrain and penalize the degree to which the marginal distribution of the optimal matching matrix deviates from a preset reference distribution, wherein the preset reference distribution includes a first reference distribution and a second reference distribution. The non-equilibrium relaxation term is obtained by summing a first penalty weighting term and a second penalty weighting term. The first penalty weighting term is the product of a first penalty coefficient and a first relative entropy, and the second penalty weighting term is the product of a second penalty coefficient and a second relative entropy. The first relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the sequenced cell nucleus set and the first reference distribution, and the second relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the histological cell nucleus set and the second reference distribution. Furthermore, the first penalty coefficient is greater than the second penalty coefficient.

[0009] In some embodiments, the objective function further includes: An entropy regularization term is used to constrain the relative entropy between the optimal matching matrix and a preset joint reference distribution to smooth the optimal matching matrix. The preset joint reference distribution is the outer product of the first reference distribution and the second reference distribution.

[0010] In some embodiments, the training and reconstruction model includes a first training phase, which includes iteratively performing the following steps until a second convergence condition is met: The matched morphological features are input into the initial morphological encoder to obtain the predicted morphological conditional embedding output by the initial morphological encoder. The real gene expression data is input into the initial expression encoder to obtain the predicted latent expression variables output by the initial expression encoder; The predicted expression latent variable and the predicted morphological conditional embedding are concatenated and then input into the initial negative binomial decoder to obtain the predicted relative expression rate output by the initial negative binomial decoder. The predicted gene expression data are determined based on the predicted relative expression rate. Based on the predicted gene expression data and the real gene expression data, the likelihood loss function value is calculated, and combined with the relative entropy regularization term used to constrain the predicted expression latent variables, the parameters of the initial morphological encoder, the initial expression encoder, and the initial negative binomial decoder are updated. After the first training phase, the morphological encoder, the representation encoder, and the negative binomial decoder are obtained.

[0011] In some embodiments, the training reconstruction model further includes a second training phase, the second training phase comprising: The matched morphological features are input into the morphological encoder to obtain morphological conditional embeddings, and the real gene expression data are input into the expression encoder to obtain latent expression variables. Iteratively execute the following steps until the third convergence condition is met: Initial noise is sampled from a standard normal distribution, and a random time step is obtained. Based on the initial noise, the latent expression variable, and the time step, an interpolation latent variable is constructed between the initial noise and the latent expression variable. The interpolation latent variable, the time step, and the morphological condition are embedded into the velocity field network to obtain the predicted velocity vector output by the velocity field network. The target velocity vector is determined based on the numerical difference between the initial noise and the expressed latent variables, and the parameters of the velocity field network are updated based on the error between the predicted velocity vector and the target velocity vector. After the second training phase, the final reconstruction model is obtained, which includes the morphological encoder, the trained velocity field network, and the negative binomial decoder.

[0012] In some embodiments, the step of inputting the morphological features of each histological cell nucleus into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model includes: The morphological features of each histological cell nucleus are input into the morphological encoder to obtain the target morphological conditional embedding; Initial inference noise is sampled from the standard normal distribution; Using the target morphology conditional embedding as a condition, the trained velocity field network is used to solve the ordinary differential equation, and the integral is performed from the initial time step to the end time step to generate the target expression latent variable for each histological cell nucleus. The target expression latent variable and the target morphological condition are embedded into the negative binomial decoder to obtain the relative expression rate output by the negative binomial decoder; The library size of each histological cell nucleus is obtained by randomly sampling from the library size distribution of the sequenced cell nuclei; based on the library size and the relative expression rate, the gene count in integer form is obtained by gamma-Poisson sampling, which is used as the final predicted gene expression data.

[0013] In some embodiments, the extraction of morphological features from each histological cell nucleus includes: Using the centroid of each histological cell nucleus as the center, crop according to the bounding box of the histological cell nucleus to obtain a local image patch; The local image patch is input into the first image base model to obtain the local morphological features output by the first image base model; Cropping is performed with the centroid as the center to obtain a global image block with a size larger than the local image block; The global image patch is input into the second image base model to obtain the global morphological features output by the second image base model; By fusing the local morphological features and the global morphological features, the morphological features of each histological cell nucleus are obtained.

[0014] In some embodiments, after obtaining the final predicted gene expression data output by the final reconstruction model, the method further includes: Identify cavity regions in the histological images; Virtual cell nucleus nodes are deployed within the cavity area; Identify the real histological cell nucleus that is spatially nearest to the virtual cell nucleus node; Obtain the final predicted gene expression data corresponding to the actual histological cell nuclei; Based on the final predicted gene expression data corresponding to the real histological cell nuclei, spatial interpolation calculations are performed to obtain the complete gene expression data of the virtual cell nucleus nodes.

[0015] The present invention also provides a spatial single-cell nuclear transcriptome densification system, comprising: An initialization module is used to segment a histological image to obtain a set of histological cell nuclei, extract the morphological features of each histological cell nucleus, and determine the initial matching relationship between the set of histological cell nuclei and the set of sequenced cell nuclei of the spatial single-cell transcriptome. The initial matching relationship is determined only based on the spatial structure information of the set of histological cell nuclei and the set of sequenced cell nuclei. The iterative alignment module is used to iteratively execute the following steps until the first convergence condition is met: The morphological features matched by each sequenced cell nucleus in the sequenced cell nucleus set are used as training data, and the real gene expression data of each sequenced cell nucleus are used as training labels to train the reconstruction model. The matched morphological features are determined based on the initial matching relationship. The morphological features of each histological cell nucleus are input into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model; The initial matching relationship is updated based on the difference between the predicted gene expression data and the actual gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set. The dense inference module is used to input the morphological features of each histological cell nucleus into the final reconstruction model after the first convergence condition is met, so as to obtain the final predicted gene expression data output by the final reconstruction model.

[0016] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the spatial single-cell transcriptome densification method as described above.

[0017] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the spatial single-cell transcriptome densification method as described above.

[0018] This invention provides a spatial single-cell nuclear transcriptome densification method, system, electronic device, and medium. It determines the initial matching relationship between the histological nuclear set and the sequenced nuclear set by extracting the morphological features of each histological nuclear nucleus from a histological nuclear set. The following steps are iteratively executed until a first convergence condition is met: using the morphological features matched to each sequenced nuclear nucleus as training data and real gene expression data as training labels, a reconstruction model is trained; the morphological features are input into the reconstruction model to obtain predicted gene expression data; based on the difference between the predicted gene expression data and the real gene expression data, and the spatial structural information of the two nuclear sets, the initial matching relationship is updated, achieving iterative joint optimization of alignment and reconstruction models; the morphological features are input into the final reconstruction model to obtain the final predicted gene expression data. This method achieves expression densification for nucleus loss without relying on external single-cell references, improving effective cell coverage. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0020] Figure 1 This is one of the flowcharts of the spatial single-cell nuclear transcriptome densification method provided by the present invention.

[0021] Figure 2 This is the second schematic diagram of the spatial single-cell nuclear transcriptome densification method provided by the present invention.

[0022] Figure 3 This is a flowchart illustrating the training and inference process of the reconstruction model provided by this invention.

[0023] Figure 4 This is a schematic diagram of the spatial single-cell nuclear transcriptome densification process provided by the present invention.

[0024] Figure 5 This is a schematic diagram of the spatial single-cell nuclear transcriptome densification system provided by the present invention.

[0025] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0027] Figure 1 This is one of the flowcharts of the spatial single-cell nuclear transcriptome densification method provided by the present invention, such as... Figure 1 As shown, the method includes the following steps: Step 110: Segment the histological image to obtain the histological cell nucleus set, extract the morphological features of each histological cell nucleus, and determine the initial matching relationship between the histological cell nucleus set and the sequenced cell nucleus set of the spatial single-cell transcriptome. The initial matching relationship is determined only based on the spatial structural information of the histological cell nucleus set and the sequenced cell nucleus set.

[0028] Histological images refer to full-section images of stained tissue sections acquired by digital pathology scanning equipment, with pixels characterizing the tissue's microscopic morphology. Histological images are obtained from a first section via digital pathology scanning, while spatial single-nucleus transcriptomes are obtained from a second section adjacent to the first section via Slide-tags sequencing. The histological nucleus set refers to the dense set of histological nuclei obtained after identifying and delineating the boundaries of the histological image.

[0029] Morphological features refer to feature vectors that characterize the physical properties of a single cell nucleus, such as size, texture, and staining intensity. Extraction can be achieved by encoding features in image patches representing the region containing the cell nucleus using image processing algorithms or visual network models. The sequenced cell nuclei are those spatially barcoded and sequenced individually; each sequenced cell nucleus carries spatial coordinates and a complete transcriptome gene count. The sequenced cell nucleus set refers to the sparse collection of cell nuclei whose gene expression profiles were successfully captured and measured during the actual sequencing process.

[0030] Iteratively execute the following steps until the first convergence condition is met: Step 120: Using the morphological features matched by each sequenced cell nucleus in the sequenced cell nucleus set as training data and the real gene expression data of each sequenced cell nucleus as training labels, train the reconstruction model. The matched morphological features are determined based on the initial matching relationship.

[0031] In this context, real gene expression data refers to the total transcriptome gene count or molecular measurement values ​​obtained by actual sequencing equipment from a single sequenced cell nucleus. A reconstruction model refers to a machine learning or generative network model capable of establishing a mapping relationship between visual morphological conditions and molecular expression distribution.

[0032] Specifically, since the sequenced cell nuclei and the histological cell nuclei come from adjacent slices and there is no natural one-to-one correspondence, the most corresponding morphological features on the histological image can be found for each sequenced cell nucleus as input conditions based on the probability or weight assignment in the initial matching relationship.

[0033] Optionally, the internal parameters of the reconstruction model can be adjusted by optimizing the algorithm so that the expression results generated by the reconstruction model based on morphological features are as close as possible to the real sequencing tags.

[0034] Step 130: Input the morphological features of each histological cell nucleus into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model.

[0035] In this step, the reconstructed model, updated with parameters from step 120, is used to perform forward inference calculations on each histological cell nucleus segmented from the histological image. Regardless of whether the histological cell nucleus was lost during physical section preparation, the reconstructed model can infer a corresponding molecular expression feature, i.e., predict gene expression data, based on its extracted morphological features.

[0036] Step 140: Update the initial matching relationship based on the difference between the predicted gene expression data and the actual gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set.

[0037] Optionally, the distance between the predicted gene expression data and the actual gene expression data can be calculated to obtain the degree of difference.

[0038] Spatial structure information refers to the relative physical distance structure between all pairs of nuclei within each of the two sets of nuclei.

[0039] Optionally, the matching weights between the two types of cell nuclei can be adjusted by fusing spatial structure information and dissimilarity, so that the matching results simultaneously satisfy spatial proximity and expression similarity. As iterations progress, expression dissimilarity can help correct geometric mismatches where the spatial locations are close but the actual cell types are different.

[0040] Step 150: After satisfying the first convergence condition, input the morphological features of each histological cell nucleus into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model.

[0041] The first convergence condition refers to the matching relationship no longer changing significantly or the iteration reaching the set upper limit of rounds. When the system converges, both the matching relationship and the model parameters reach a stable and self-consistent state, at which point the model parameters are locked to obtain the final reconstructed model. The final predicted gene expression data refers to the single-cell resolution whole transcriptome expression data generated by the final reconstructed model from all histological cell nuclei on the histological image.

[0042] In this embodiment of the invention, by extracting the initial matching relationship between the set of histological cell nuclei and the set of sequenced cell nuclei, and continuously feeding back and updating the matching relationship using the predicted expression data output by the reconstruction model in the iterative closed loop, the spatial alignment and expression reconstruction mutually correct each other and gradually converge, overcoming the problem of cross-slice probability soft matching caused by nucleus loss and coordinate system differences between adjacent physical slices. As a result, the final reconstruction model can infer molecular expression data for all cell nuclei in the image based on cell morphology features, and achieve the densification of missing single-nucleus resolution whole transcriptome expression data without relying on external reference datasets.

[0043] Figure 2 This is the second schematic diagram of the spatial single-cell transcriptome densification method provided by the present invention, as shown below. Figure 2 As shown, the method includes the following steps: In the preparation layer, hematoxylin and eosin stained histological images are acquired, and cell nucleus segmentation and morphological feature extraction steps are performed. Hematoxylin and eosin staining is abbreviated as H&E. This step outputs the coordinate parameters and morphological features of the histological cell nuclei.

[0044] In the core layer, alignment and iterative closed-loop generation are performed. The coordinate parameters of the aforementioned histological cell nuclei are received, and sequenced cell nucleus data from adjacent slices are acquired. This sequenced cell nucleus data exhibits sparsity and contains spatial coordinates and true whole transcriptome expression information. The sequenced cell nucleus data is obtained using sliding-tag spatial sequencing technology.

[0045] The alignment sub-step employs the Fused Unbalanced Gromov-Wasserstein (FUGW) algorithm to solve for the matching relationships. In the initial rounds, the space-to-representation tradeoff coefficient is set to 1, and the initial transmission plan is derived using only spatial structure information. The space-to-representation tradeoff coefficient is denoted by parameter α, the transmission plan (i.e., the optimal matching matrix) is denoted by parameter π, and the initial matching matrix is ​​denoted by parameter π0.

[0046] In the generation sub-step, the morphological features output from the preparation layer are received, and a morphological conditional generation model is trained based on the aforementioned transport plan. During the iterative phase, only a subset of genes is used for model training and inference, outputting predicted gene expression data for histological cell nuclei. The predicted gene expression data is represented by the parameter Ŷ_A.

[0047] The predicted gene expression data is then fed back into the alignment step as a feature cost, simultaneously decreasing the tradeoff coefficient and tightening the top-match number parameter to resolve the transport plan. The top-k parameter controls the degree of constraint during the transition from soft to hard matching.

[0048] Once the tradeoff coefficient drops to the lower limit and the transmission plan stabilizes, the system exits the iterative loop, freezes the current transmission plan, and enters the output layer.

[0049] In the output layer, a whole-genome gene-genome prediction head covering all measured genes is used. With the final locked model parameters, single-nucleus resolution whole transcriptome expression data is output for all histological cell nuclei, ultimately achieving full-slice densification of sparse sequencing data.

[0050] Optionally, in the alignment step of the core layer, the formula for the fusion unbalanced optimal transmission objective function used to solve the matching relationship is: ; in, and This represents two distinct sequenced cell nuclei within the set of sequenced cell nuclei. and This indicates two distinct histological cell nuclei within a set of histological cell nuclei; Indicates the sequenced cell nucleus To the histological cell nucleus Transmitted non-negative soft matching weights; Indicates the sequenced cell nucleus To the histological cell nucleus Transmitted non-negative soft matching weights; This represents a tradeoff coefficient, used to dynamically adjust the proportion of structural cost and expression cost in the overall optimization objective; Indicates the sequenced cell nucleus With the sequenced cell nucleus Spatial distance matrix between them; Represents the histological cell nucleus With histological cell nucleus Spatial distance matrix between them; The feature cost matrix represents the histological cell nucleus. Predicted gene expression data and sequenced cell nuclei The degree of difference between real gene expression data; , These are non-equilibrium relaxation coefficients with unequal values, corresponding to the penalty intensity on the nuclear side of the sequenced cells and the nuclear side of the histological cells, respectively; Represents relative entropy, used to measure the difference in divergence between two probability distributions; Represents the transmission plan matrix The transpose of the matrix; , It is a column vector of all ones, used to calculate the marginal distribution of the transfer matrix; , The reference edge distribution is preset, such as a uniform distribution; This is the entropy regularization coefficient, used to control the smoothness of the transmission plan; It is the outer product of the reference marginal distribution, which serves as the joint reference distribution.

[0051] Optionally, in the initial training phase of representation reconstruction, the loss function formula used to optimize the feature extraction and dimensionality reduction components is: ; in, This represents the overall training loss function value of the model; The negative log-likelihood loss represents the negative binomial distribution and is used to measure the goodness of fit between the predicted distribution and the true count distribution. This represents the actual gene count tag of a single nucleus whole transcriptome; The mean parameter of the negative binomial distribution is obtained by multiplying the cell library size by the relative expression rate; This is the dispersion parameter of the negative binomial distribution, used to characterize the overdispersion of gene counting; It is an adjustment coefficient used to balance the reconstruction likelihood loss and the relative entropy regularization term; The relative entropy regularization term with free bit lower bound can prevent latent variable training collapse; It is the posterior probability distribution of the latent variables extracted by the encoder; It follows a standard normal prior distribution.

[0052] Optionally, in the latent space flow matching generation stage, the velocity matching objective function used to guide the evolution of features over time is formulated as follows: ; ; in, This represents the mean square error loss value of the velocity field network; Represents the mathematical expectation operation; This represents the predicted velocity vector output by the velocity field network; These are interpolated latent variables constructed based on time steps; Indicates the time step value; This represents the morphological conditional embedding vector extracted from the cell nucleus morphology; The target representing the evolutionary endpoint is expressed as a latent variable; This represents the initial noise sampled from the base distribution, indicating the starting point of the evolution. It indicates a standard uniform distribution.

[0053] Optionally, in the reasoning stage where expression characteristics are inferred from cell nuclei in histological images, the ordinary differential equation formula for solving the data evolution trajectory is: ; in, This represents the numerical value of the differential rate of change of the latent variable with respect to the time step; This indicates the state of the hidden variables at the current integration time point; Indicates the time step value; This represents the target morphological conditional embedding vector obtained after inputting the morphological features of a specific histological cell nucleus.

[0054] In some embodiments, step 110 extracts the morphological features of each histological cell nucleus, including: Step 111: Using the centroid of each histological cell nucleus as the center, crop according to the bounding box of the histological cell nucleus to obtain a local image patch.

[0055] Here, the centroid refers to the geometric center coordinates of the outline of a single cell nucleus obtained through the segmentation algorithm. The bounding box refers to the smallest bounding rectangle that exactly encloses the cell nucleus. Optionally, an image region containing the main body of a single cell nucleus is extracted from the histological image to obtain a local image patch, which focuses on preserving the microscopic visual details of the target cell nucleus.

[0056] Step 112: Input the local image patch into the first image base model to obtain the local morphological features output by the first image base model.

[0057] The first image-based model refers to a deep visual network model specifically trained for pathological images. After inputting a local image patch, the model outputs corresponding spatial feature labels for each spatial location in the image. By performing mean aggregation calculations on those spatial feature labels falling within the cell nucleus bounding box, a high-dimensional feature vector can be extracted. This vector represents the local morphological features, primarily used to accurately characterize the cell nucleus's size, texture, and the intensity of hematoxylin staining, among other physical properties.

[0058] Step 113: Crop the image with the centroid as the center to obtain a global image block with a size larger than the local image block.

[0059] In this approach, the cropping field of view is expanded based on the centroid coordinates of the same cell nucleus, and appropriate scaling is applied to meet the network input size requirements. This large-field-of-view global image patch is no longer limited to a single cell nucleus, but encompasses the contextual environment, including the distribution of glands around the target cell nucleus, the interstitial structure, and the aggregation density of adjacent cells.

[0060] Step 114: Input the global image block into the second image base model to obtain the global morphological features output by the second image base model.

[0061] The second image base model refers to a self-supervised visual base model with generalized feature extraction capabilities. After feeding the global image patch into this model, the mean space aggregation operation is also performed on its output spatial label map to obtain a global morphological feature vector used to characterize the micro-environment state of macro-scale organization.

[0062] Step 115: Integrate local and global morphological features to obtain the morphological features of each histological cell nucleus.

[0063] Optionally, local morphological features are concatenated with global morphological features, and the concatenated high-dimensional vector is standardized or normalized according to the statistical mean and variance of the training set, ultimately forming a comprehensive feature vector that combines microscopic and macroscopic information, which serves as the sole morphological feature representing the cell nucleus of this histological cell.

[0064] In this embodiment of the invention, by cropping image blocks of different field-of-view sizes and independently extracting features using the corresponding image base model, and fusing local and global morphological features, the morphological features of each histological cell nucleus are obtained, which can comprehensively capture cross-scale histopathological context information.

[0065] Figure 3 This is a flowchart illustrating the training and inference process of the reconstruction model provided by this invention. For example... Figure 3As shown, in some embodiments, training the reconstruction model in step 120 includes a first training phase, which includes iteratively performing the following steps until a second convergence condition is met: Step 121: Input the matched morphological features into the initial morphological encoder to obtain the predicted morphological conditional embedding output by the initial morphological encoder.

[0066] The initial morphological encoder refers to a network module used to process cell nuclear visual features that has not yet undergone parameter optimization, such as a fully connected network component like a multilayer perceptron. Predictive morphological conditional embedding refers to reducing the dimensionality of the original high-dimensional cell nuclear morphological features to a low-dimensional condensed feature vector, which will be used to guide the subsequent generation of single-cell expression profiles.

[0067] Step 122: Input the real gene expression data into the initial expression encoder to obtain the predicted latent expression variables output by the initial expression encoder.

[0068] The initial expression encoder refers to a network module capable of dimensionality compression and probability distribution transformation of molecular sequencing count features. Predictive expression latent variables refer to continuous feature representations extracted from a low-dimensional latent space that contain condensed information from the entire cellular transcriptome; these typically follow a predefined prior probability distribution.

[0069] Step 123: After concatenating the predicted expression latent variables and the predicted morphological conditional embeddings, input them into the initial negative binary decoder to obtain the predicted relative expression rate output by the initial negative binary decoder. Based on the predicted relative expression rate, determine the predicted gene expression data.

[0070] The initial negative binomial decoder refers to the generative network that generates statistical distribution parameters for inversely reconstructing low-dimensional spliced ​​features and inferring gene counts. The predicted relative expression rate refers to the inferred relative abundance of expression levels across all measured genes in the cell nucleus. By combining this relative expression rate with the total gene count of the cell nucleus, predicted gene expression data following a negative binomial distribution can be calculated.

[0071] Step 124: Based on the predicted gene expression data and the real gene expression data, calculate the likelihood loss function value, and combine it with the relative entropy regularization term used to constrain the predicted expression latent variables to update the parameters of the initial morphological encoder, the initial expression encoder, and the initial negative binomial decoder.

[0072] The relative entropy regularization term is a probability divergence penalty constraint imposed during training to prevent the predicted latent variables from collapsing into meaningless noise and causing feature loss. Parameter update refers to using the aforementioned loss values ​​and regularization constraints to adjust the weight parameters within these three network modules in reverse using the gradient descent algorithm.

[0073] After the first training phase, the morphological encoder, the representation encoder, and the negative binomial decoder are obtained.

[0074] Specifically, when the likelihood loss function value no longer decreases significantly or the parameter update magnitude is less than the set threshold and thus meets the second convergence condition, it indicates that the feature extraction and distribution reconstruction capabilities of the latent space have reached a stable state. At this time, the trained network modules are solidified and saved as morphological encoder, expression encoder and negative binomial decoder, respectively.

[0075] In this embodiment of the invention, by using an initial expression encoder to map real expression data into latent variables and splicing predicted morphological conditional embeddings, and then using an initial negative binomial decoder to restore the expression rate for likelihood loss calculation and regularization constraint to update parameters, a low-dimensional latent space that is guided by cell nuclear morphology and can maintain the discrete characteristics of gene counting is constructed. This allows the network components obtained through this training phase to effectively compress high-dimensional whole transcriptome information, while accurately characterizing the inherent over-discrete and sparse distribution statistical characteristics of single-nucleus sequencing.

[0076] In some embodiments, training the reconstruction model in step 120 further includes a second training phase, which includes: Step 125: Input the matched morphological features into the morphological encoder to obtain the morphological conditional embedding, and input the real gene expression data into the expression encoder to obtain the expression latent variables.

[0077] After the pre-training phase, the internal network parameters of both the morphology encoder and the expression encoder are frozen and no longer updated. By inputting matching morphological features of the cell nucleus into the frozen morphology encoder, morphological conditional embeddings used to guide subsequent generation are extracted. Simultaneously, real gene expression data is input into the frozen expression encoder to extract expression latent variables located in a low-dimensional latent space that represent the actual molecular sequencing state. These expression latent variables will serve as the endpoint target data that the subsequent flow matching generation network will approximate.

[0078] Iteratively execute the following steps until the third convergence condition is met: Step 126: Sample initial noise from the standard normal distribution and obtain a random time step. Based on the initial noise, the latent variable, and the time step, construct the interpolation latent variable between the initial noise and the latent variable.

[0079] Here, initial noise refers to a numerical vector randomly drawn from the base distribution, representing the chaotic initial state of the generation process. A time step refers to a scalar value randomly selected within a time interval to represent a node in the data evolution process. Constructing interpolated latent variables involves linearly weighting and fusing the initial noise (representing the starting point) and the latent variables (representing the ending point) according to the linear interpolation path rules of the corrective flow algorithm, based on the size of the time step, to obtain an intermediate feature transition state between a random, disordered state and a state of true data regularity.

[0080] Step 127: Embed the interpolation latent variables, time steps, and morphological conditions into the velocity field network to obtain the predicted velocity vector output by the velocity field network.

[0081] The velocity field network refers to a deep neural network containing a residual block structure used to fit the ordinary differential equations of the data evolution trajectory. The interpolated latent variables generated above, along with the time step features representing progress and the morphological conditions representing visual guidance information, are embedded and input into the velocity field network. The network outputs a predicted velocity vector with the same dimension as the latent variables through internal forward computation. The predicted velocity vector represents the evolution direction and rate of change of the current transition state towards the target true state.

[0082] Step 128: Determine the target velocity vector based on the numerical difference between the initial noise and the expressed latent variables, and update the parameters of the velocity field network based on the error between the predicted velocity vector and the target velocity vector.

[0083] The target velocity vector is obtained by directly calculating the numerical difference between the latent variable representing the endpoint and the initial noise representing the starting point. This difference represents the true optimal movement speed under a linear evolution path. The error refers to the mean square error of the predicted velocity vector deviating from the target velocity vector. This error value is used to adjust the neuron weight parameters in the velocity field network using a gradient optimization algorithm, so that the network's predicted movement direction continuously approaches the true linear evolution direction.

[0084] After the second training phase, the final reconstruction model is obtained, which includes a morphological encoder, a trained velocity field network, and a negative binomial decoder.

[0085] Specifically, when the error value drops to a minimum threshold or reaches the set upper limit of iteration rounds, thus satisfying the third convergence condition, the model's learning of the evolution path reaches a stable state. At this point, the representation encoder, which is only used to extract real target labels during training, is removed, and the trained velocity field network, which has the ability to generate data from pure noise, is retained. This network is then assembled with the morphological encoder and the negative binomial decoder to form the final reconstruction model that can independently perform generation tasks based on image morphology.

[0086] In this embodiment of the invention, by introducing a velocity field network inside the established discrete latent space and optimizing the velocity error along the linear interpolation path from the initial noise to the target expressed latent variable, the trained velocity field network can learn the dynamic trajectory law of controlling meaningless noise to accurately evolve into the corresponding molecular latent variable based solely on the morphological features of the cell nucleus. This gives the reconstruction model the ability to generate cross-modal conditions based on pure image morphology.

[0087] like Figure 3 As shown, in some embodiments, step 130 inputs the morphological features of each histological cell nucleus into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model, including: Step 131: Input the morphological features of each histological cell nucleus into the morphological encoder to obtain the target morphological conditional embedding.

[0088] The objects to be processed are all cell nuclei segmented from histological images, including those nuclei that have no sequencing data due to nucleus loss. By inputting the visual morphological features of these cell nuclei into a morphological encoder that has completed parameter training and is in a frozen state, a forward feature dimension transformation is performed to extract a condensed conditional vector, i.e., the target morphological conditional embedding, used to guide the generation of specific molecular data.

[0089] Step 132: Sample initial inference noise from the standard normal distribution.

[0090] The initial inference noise refers to a meaningless numerical vector randomly drawn from the base distribution. This noise vector serves as the starting point for the generative model to perform cross-modal inference, providing the necessary random variable input for the generation process.

[0091] Step 133: Using the target morphological conditional embedding as a condition, solve the ordinary differential equation using the trained velocity field network, and integrate from the initial time step to the final time step to generate the target expression latent variable for each histological cell nucleus.

[0092] Ordinary differential equations are mathematical models used to describe the continuous trajectory of data states evolving from pure noise to real molecular latent variables.

[0093] Specifically, a numerical integration algorithm is used to drive the trained velocity field network to calculate the evolution direction of each step within the interval from the initial time step representing the start to the end time step representing the end, based on the visual guidance features provided by the target morphology condition embedding. This drives the initial inference noise to evolve gradually along the trajectory, ultimately obtaining the target expression latent variable representing the sequencing state of the target molecule.

[0094] Step 134: Embed the target expression latent variables and target morphological conditions into the input negative binomial decoder to obtain the relative expression rate output by the negative binomial decoder.

[0095] Specifically, the latent expression variables generated by integrating ordinary differential equations are combined with the previously extracted target morphological conditional embeddings and fed into a fixed negative binomial decoder for inverse mapping. The negative binomial decoder outputs the relative expression abundance ratio of the cell nucleus across all measured genes, i.e., the relative expression rate, through fully connected layers and normalization calculations.

[0096] Step 135: Randomly sample from the library size distribution of the sequenced cell nuclei to obtain the library size of each histological cell nucleus; based on the library size and relative expression rate, obtain the gene count in integer form according to gamma-Poisson sampling, which is used as the final predicted gene expression data.

[0097] Optionally, the library size distribution of the sequenced cell nuclei can be obtained.

[0098] The library size refers to the sum of gene expression counts within a single cell nucleus. For each histological cell nucleus, the library size is randomly sampled from the distribution of library sizes in the sequenced nuclei. Gamma-Poisson sampling is a statistical random sampling method, mathematically equivalent to negative binomial distribution sampling. By combining the overall library size with the relative expression rate of each gene, this sampling operation forces the output to be discrete non-negative integers. This gene count represents the single-nucleus resolution whole transcriptome expression data supplemented for the missing sequenced cell nuclei.

[0099] In this embodiment of the invention, by using ordinary differential equations to control the pure noise to evolve into latent expression variables under the guidance of image morphology conditions, and combining the negative binomial decoder and gamma-Poisson sampling mechanism to output integer counts, the dense expression data inferred from the whole tissue cell nucleus by the reconstructed model can restore the inherent discreteness and sparsity of real single-nucleus sequencing, thereby ensuring that the generated molecular expression data can be directly used as reliable input to support downstream cell typing and spatial clustering analysis.

[0100] In some embodiments, updating the initial matching relationship in step 140 includes: Step 141: Weight the structural cost term based on the first dynamic weight, and weight the expression cost term based on the second dynamic weight to construct the objective function. The structural cost term is determined based on spatial structural information, and the expression cost term is determined based on the degree of difference.

[0101] Among them, the first dynamic weight and the second dynamic weight change dynamically with the increase of the iteration rounds, and the first dynamic weight shows a decreasing trend while the second dynamic weight shows an increasing trend.

[0102] The structural cost term is a mathematical penalty term used to measure the degree of inconsistency in the spatial geometric arrangement of two sets of cell nuclei. The expression cost term is a mathematical penalty term used to measure the degree of dissimilarity in the molecular sequencing expression characteristics of two sets of cell nuclei. The first dynamic weight and the second dynamic weight are numerical adjustment coefficients used to balance the proportion of the above two cost terms in the overall optimization objective.

[0103] The objective function refers to the optimal solution equation that combines spatial structure mismatch penalty and expression feature mismatch penalty. As the number of iterations increases, the first dynamic weight gradually decreases while the second dynamic weight gradually increases. This means that in the early stages of iteration, the model mainly relies on physical spatial location for initial alignment. However, as the model gradually learns and outputs increasingly accurate predicted expression data, the basis for alignment is gradually and smoothly shifted from pure spatial geometry to molecular expression similarity in a controlled manner.

[0104] Step 142: Solve the objective function to obtain the optimal matching matrix that minimizes the objective function. The elements in the optimal matching matrix represent the matching probability or matching indicator between the set of histological cell nuclei and the set of sequenced cell nuclei. Update the initial matching relationships based on the optimal matching matrix.

[0105] Optionally, an optimization algorithm can be used to find the parameter allocation scheme that minimizes the total cost of the objective function. The optimal matching matrix is ​​a two-dimensional numerical matrix, where the rows and columns correspond to the sequenced cell nuclei and the histological cell nuclei, respectively. The value of each element in the matrix directly represents the probability that a sequenced cell nucleus corresponds to a histological cell nucleus or the strength of the soft-match connection. By replacing the corresponding state of the previous iteration with this optimal matching matrix, the initial matching relationship can be dynamically updated and gradually tightened.

[0106] In some embodiments, the structural cost term is determined based on a first distance matrix formed by the spatial distances between each pair of nuclei in the histological cell nucleus set and a second distance matrix formed by the spatial distances between each pair of nuclei in the sequenced cell nucleus set, and is used to measure the degree of inconsistency between the histological cell nucleus set and the sequenced cell nucleus set in terms of internal spatial distance structure. The expression cost term is determined based on the expression cost matrix of the histological cell nucleus set and the sequenced cell nucleus set, and is used to measure the degree of difference between the predicted gene expression data and the actual gene expression data; the expression cost matrix includes the degree of difference between the predicted gene expression data of each histological cell nucleus and the actual gene expression data of each sequenced cell nucleus.

[0107] The first distance matrix is ​​a square matrix constructed by calculating the pairwise physical distances between all solid cell nuclei on the histological section, while the second distance matrix is ​​an internal square matrix constructed by calculating the pairwise physical distances between cell nuclei with sequencing data. The structural cost term evaluates spatial arrangement similarity by comparing these two independently constructed internal distance structural matrices, thus eliminating the need to require the two sets to be in the same rigid absolute coordinate system. The expression cost matrix is ​​a cross-set distance matrix calculated in the feature dimension, recording the feature divergence between each model-predicted single-nucleus expression profile and each actually measured single-nucleus expression profile.

[0108] In this embodiment of the invention, by constructing a first distance matrix and a second distance matrix of internal spatial distance as structural cost terms, the problem of non-rigid deformation and misalignment between different coordinate systems between adjacent physical slices can be effectively addressed. Furthermore, by adjusting the objective function through the first dynamic weight and the second dynamic weight, which change inversely with each iteration, the soft matching process of the two cell nucleus sets can naturally transition from initial spatial location filtering to fine-grained molecular similarity verification using predicted expression features. This effectively corrects spatial mismatches that cannot be distinguished by spatial location alone, thereby improving cross-slice alignment consistency under the condition of no one-to-one pairing truth value.

[0109] In some embodiments, the objective function further includes: The unbalanced relaxation term is used to constrain and penalize the degree to which the marginal distribution of the optimal matching matrix deviates from a preset reference distribution, which includes a first reference distribution and a second reference distribution. The non-equilibrium relaxation term is obtained by summing the first penalty weighting term and the second penalty weighting term. The first penalty weighting term is the product of the first penalty coefficient and the first relative entropy, and the second penalty weighting term is the product of the second penalty coefficient and the second relative entropy. The first relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the set of sequenced cell nuclei and the first reference distribution, and the second relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the set of histological cell nuclei and the second reference distribution. The first penalty coefficient is greater than the second penalty coefficient.

[0110] In this context, the unbalanced relaxation term refers to a mathematical constraint that allows the total number of elements in the two sets to be different and allows some elements to not participate in the matching process. The marginal distribution refers to the sum of matching probabilities of the optimal matching matrix along the row dimension of the sequenced cell nuclei or the column dimension of the histological cell nuclei. The preset reference distribution refers to the baseline probability distribution state set for each of the two sets, such as a uniform distribution.

[0111] Relative entropy and divergence are metrics used to quantify the difference between the actual marginal distribution and the set baseline distribution of the optimal matching matrix. Setting the first penalty coefficient to be greater than the second penalty coefficient means a stronger penalty for deviations in the marginal distribution of the sequenced cell nuclei set, while a weaker penalty for deviations in the marginal distribution of the histological cell nuclei set. This is because there is significant nucleus loss in actual spatial single-nucleus transcriptome sequencing, resulting in a much larger number of histological cell nuclei obtained through microscopic imaging than the actual number of sequenced cell nuclei captured. This asymmetric penalty coefficient setting forces the smaller number of sequenced cell nuclei to participate in matching as much as possible, while allowing for a large number of unmatched gaps at the ends of the numerous histological cell nuclei.

[0112] In some embodiments, the objective function further includes: The entropy regularization term is used to constrain the relative entropy between the optimal matching matrix and the preset joint reference distribution in order to smooth the optimal matching matrix. The preset joint reference distribution is the outer product of the first reference distribution and the second reference distribution.

[0113] Among them, the entropy regularization term refers to the regularization penalty term that introduces a measure of the disorder of the probability distribution to prevent the matching results from being too concentrated and extreme.

[0114] Optionally, the outer product of the baseline reference distributions of the sequenced cell nuclei and the histological cell nuclei is calculated to obtain an independent joint probability matrix as a preset joint reference distribution. By constraining the relative entropy between the optimal matching matrix and this joint reference distribution, the smoothness of the numerical distribution of the matching matrix can be effectively improved, transforming hard matching into probabilistic soft matching with a certain degree of redundancy, thereby significantly improving the numerical computational stability of the objective function containing large-scale variables during iterative solution.

[0115] In some embodiments, after obtaining the final predicted gene expression data output by the final reconstruction model, the method further includes: Identify cavity regions in the histological images; Virtual cell nucleus nodes are deployed within the void area; Identify the real histological cell nucleus that is spatially nearest to the virtual cell nucleus node; Obtain the final predicted gene expression data corresponding to the actual histological cell nuclei; Based on the final predicted gene expression data corresponding to the real histological cell nuclei, spatial interpolation calculations are performed to obtain the complete gene expression data of the virtual cell nucleus nodes.

[0116] In this context, "empty regions" refer to blank areas in histological images where cell nucleus segmentation algorithms fail to identify actual cell nuclei due to tearing, obscuring by dirt, or scanning defects during physical slide preparation. "Virtual cell nucleus nodes" are placeholder coordinate points generated by algorithms in these blank regions to maintain tissue spatial continuity; they do not correspond to actual physical cell nuclei in the image.

[0117] Among them, the real histological cell nucleus refers to the cell nucleus that was successfully identified by the segmentation algorithm in the aforementioned steps and has a real physical existence in the image.

[0118] Alternatively, the nearest real histological cell nuclei to the virtual cell nucleus node's physical coordinates can be found by calculating the spatial Euclidean distance or by using a spatial nearest neighbor search algorithm.

[0119] Optionally, numerical calculation methods such as inverse distance weighting or spatial smoothing fitting can be used to weight and fuse the molecular expression levels of surrounding real histological cell nuclei according to their spatial distance. Complete gene expression data refers to the inferred molecular characteristics assigned to the virtual cell nucleus node after interpolation calculations, thus enabling the cavity location to also possess an equivalent single-cell resolution expression profile.

[0120] In this embodiment of the invention, by placing virtual cell nucleus nodes in the void areas caused by image defects and using the predicted expression data of the surrounding real histological cell nuclei for spatial interpolation calculation, the final output dense expression data fills the gaps caused by physical slicing defects in spatial distribution, effectively ensuring the spatial continuity and integrity of the overall spatial transcriptome data of the tissue slice.

[0121] Figure 4 This is a schematic diagram of the spatial single-cell nuclear transcriptome densification process provided by the present invention, as shown below. Figure 4 As shown, this process demonstrates the data evolution flow from input data to the final dense reconstruction result.

[0122] Input data includes spatial sequencing data of adjacent slices and histological images of this slice stained with hematoxylin and eosin. Figure 4 The left panel shows the sparsely sequenced cell nuclei actually measured from adjacent slices, represented by solid dots. Due to nucleus loss during the physical experiments, the cell nuclei in this set are sparsely distributed in space.

[0123] Figure 4 The middle panel displays the dense histological cell nuclei obtained from the segmentation of this histological image, represented by hollow dots. The spatial locations of these histological cell nuclei are known, but the vast majority lack corresponding gene sequencing expression data.

[0124] Figure 4The dashed line connecting the left and middle panels represents the soft transport plan for cross-slice alignment. This transport plan is obtained by a fusion-based unbalanced optimal transport algorithm and represents a one-to-many probabilistic matching relationship. The thickness of the dashed line in the figure is proportional to the magnitude of the matching probability weight, thus indicating that the nucleus sets on the two sets of physical slices have a probabilistic soft correspondence, rather than a pre-known, precise one-to-one correspondence.

[0125] Figure 4 The right panel displays the final dense reconstruction output of this invention. Based on the matching relationship established through the aforementioned iterations, this embodiment of the invention infers the expression generation of each nucleus individually, relying on the morphological conditions of each histological cell nucleus. This generation process is not based on simple spatial neighborhood interpolation. After model inference, all hollow cell nuclei in the middle panel that originally lacked sequencing data obtained whole transcriptome expression data at single-cell resolution, thus transforming into densely distributed solid dots in the right panel, ultimately achieving the whole-slice density of spatial transcriptome sequencing data.

[0126] In one comparative study, a method was employed to directly predict gene expression from histological images. Specifically, image segments were processed through an image feature network to predict expression. This method is designed for raster data and does not incorporate single-nucleus resolution sequencing alignment. Test results indicate that this method does not address the challenge of cross-slice correspondence between sequenced cell nuclei and histological cell nuclei, nor does it perform single-cell-level densification to address nucleus loss; it only covers a single step of learning expression from images.

[0127] In another comparative example, a lattice deconvolution and decomposition method based on external single-cell references was employed. Specifically, using external single-cell sequencing reference data, the mixed expression of the lattice was deconvolved and decomposed to the single-cell level. Test results show that this method heavily relies on external reference data, primarily targeting the decomposition of mixed lattice data. It does not address the problem of nucleus recovery due to nucleus loss in spatial single-nucleus transcriptome sequencing, nor does it establish an optimal cross-slice transport correspondence between sparsely sequenced cell nuclei and dense histological cell nuclei.

[0128] In one embodiment, a process for densification and distribution fidelity preservation of six human clinical lung tissue samples under adjacent slices and no paired ground truth conditions is demonstrated.

[0129] The specific implementation involves segmenting cell nuclei in pathological histological images and extracting morphological features from each nucleus. For example, 1536-dimensional features at a single scale are extracted and optionally stitched together with 1024-dimensional global features to obtain 2560-dimensional features. Subsequently, a complete iterative alignment is performed on adjacent slices without paired ground truth values. Specifically, in the initial zero round, a tradeoff coefficient of 1 is used to solve for the unbalanced optimal transfer using only spatial structure to obtain the initial matching matrix. In subsequent iterations, a morphological conditional generation model is trained on approximately 50 hypervariable genes or a subset of marker genes using the current matching matrix to predict expression data for all histological cell nuclei. The predicted expression data is used as a feature cost, and the matching matrix is ​​gradually tightened according to a tradeoff coefficient of 0.8, 0.6, 0.4, 0.2, and 0.1, retaining the first few matching targets, and the matching matrix is ​​resolved.

[0130] The entire iterative loop, starting from the initial round, consists of approximately 10 rounds. After the tradeoff coefficients decrease to the lower bound and the matching matrix stabilizes, a freeze process is implemented. Next, a negative binomial variational autoencoder with 32-dimensional latent variables and 256-dimensional morphological conditional embeddings is trained on the sequenced cell nucleus data. A warm-up setting of 60 iterations and 0.3 free bits is used, and training continues for approximately 300 to 500 iterations. Finally, a morphological conditional correction flow network with a velocity field hidden dimension of 768 and 6 residual blocks is trained for approximately 500 to 800 iterations. During inference, approximately 200 steps of ordinary differential equation integration are performed on each histological cell nucleus. The data is then decoded using negative binomial methods and output as integer counts based on gamma-Poisson sampling.

[0131] Test results for approximately 3039 genes from the same pipeline and gene set showed that each sample contained approximately 3350 to 13075 sequenced cell nuclei, while the histological cell nuclei obtained from image segmentation ranged from approximately 21,800 to 78,200, representing a densification factor of approximately 2.8 to 8.4. The generated results showed a single-nucleus zero-expression ratio of approximately 0.77 to 0.87, consistent with the high zero-expression sparsity characteristics of real single-nucleus sequencing data. The correlation coefficient with the actual sequenced cell nuclei was 0.978 to 0.999, the distribution difference statistic was 0.012 to 0.039, and the effective dimension was 6.6 to 11.2 without collapse. This indicates that this embodiment achieved densification recovery of nucleus loss without relying on external references, and the generated results are highly close to real single-nucleus sequencing data in terms of distributional statistics.

[0132] In one embodiment, a cross-species and cross-tissue densification and distribution fidelity processing process is demonstrated. Using the same system architecture as in the previous embodiments, complete iterative closed-loop processing was independently executed on three organ tissues in mice: the olfactory bulb, kidney, and brain. The histological cell nuclei obtained from image segmentation for these three organs were approximately 38,100, 73,600, and 70,100, respectively. The actual sequenced cell nuclei were approximately 12,423, 7,709, and 13,338, respectively. The sequenced cell nuclei accounted for approximately 10% to 30% of the histological cell nuclei, consistent with the objective law that sequencing technology results in approximately 75% nucleus loss during extraction.

[0133] The test results show that this embodiment successfully denser the sparse sequenced cell nuclei into single-nucleus resolution whole transcriptome expression data covering all histological cell nuclei, with density folds of approximately 3.1, 9.6, and 5.3 times, respectively. The correlation coefficient with the actual sequenced cell nuclei was approximately 0.993 to 0.998, the distributional variance statistic was approximately 0.020 to 0.037, and the effective dimension was approximately 8.3 to 11.4 without collapse. This indicates that this embodiment can stably complete the densitying of missing cell nuclei in different species and tissue types, and the reconstruction results are consistent with the actual single-nucleus sequencing data at the distribution level, proving that this method is not limited to specific tissues.

[0134] In one embodiment, a validation process for discrete count fidelity and global covariance structure preservation is demonstrated. A human glioma sample was processed using the same system architecture as in the previous embodiments. This sample yielded approximately 10,974 sequenced cell nuclei, which were then segmented from histological images to obtain approximately 184,000 histological cell nuclei, representing a densification factor of approximately 17-fold. Using the same batch of approximately 4,046 genes and the same normalization caliber, the density results generated in this embodiment were compared with the actual sequenced cell nuclei, comparing the proportion of single-nucleus zero expression and inter-gene correlations. Principal component analysis was performed to compare the shape and effective dimension of the principal component spectra. The sample also included actual sequenced cell nuclei for item-by-item comparison with the generated results.

[0135] The test results show that in terms of discrete counting fidelity, the actual single-nucleus zero expression ratio (approximately 0.807) is almost identical to the generated single-nucleus zero expression ratio (approximately 0.808), and the average correlation between actual genes (approximately 0.13) is almost identical to the average correlation between generated genes (approximately 0.11), indicating that the generated results did not introduce artificially high correlations. Regarding the preservation of the global covariance structure, the inflection points of the principal component spectra of both are consistent, flattening out at the 7th to 8th principal components and becoming essentially flat after the 15th principal component, with the curves almost overlapping. The effective dimension of the generated sample (approximately 8.1) under normalization is very close to the effective dimension of the actual sequenced cell nuclei (approximately 7.7). This indicates that, under this glioma sample configuration, the densification process in this embodiment, while restoring single-nucleus resolution, neither excessively compresses the data into a low-dimensional state nor introduces artificial structural errors, thus fully preserving the discrete characteristics of single-nucleus counting and the global molecular covariance structure.

[0136] The spatial single-nucleus transcriptome densification system provided by the present invention is described below. The spatial single-nucleus transcriptome densification system described below and the spatial single-nucleus transcriptome densification method described above can be referred to in correspondence.

[0137] Figure 5 This is a schematic diagram of the spatial single-cell transcriptome densification system provided by the present invention, as shown below. Figure 5 As shown, the spatial single-cell transcriptome densification system 500 includes: The initialization module 510 is used to segment the histological image to obtain a set of histological cell nuclei, extract the morphological features of each histological cell nucleus, and determine the initial matching relationship between the set of histological cell nuclei and the set of sequenced cell nuclei of the spatial single-cell transcriptome. The initial matching relationship is determined only based on the spatial structural information of the histological cell nuclei set and the set of sequenced cell nuclei. Iterative alignment module 520 is used to iteratively execute the following steps until the first convergence condition is met: The morphological features matched by each sequenced cell nucleus in the sequenced cell nucleus set are used as training data, and the real gene expression data of each sequenced cell nucleus are used as training labels to train the reconstruction model. The matched morphological features are determined based on the initial matching relationship. The morphological features of each histological cell nucleus are input into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model; The initial matching relationship is updated based on the difference between the predicted gene expression data and the actual gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set. The dense inference module 530 is used to input the morphological features of each histological cell nucleus into the final reconstruction model after the first convergence condition is met, so as to obtain the final predicted gene expression data output by the final reconstruction model.

[0138] Optionally, update the initial matching relationships, including: The structural cost term is weighted based on the first dynamic weight, and the expression cost term is weighted based on the second dynamic weight to construct the objective function. The structural cost term is determined based on spatial structural information, and the expression cost term is determined based on the degree of difference. Among them, the first dynamic weight and the second dynamic weight change dynamically with the increase of the iteration rounds, and the first dynamic weight shows a decreasing trend while the second dynamic weight shows an increasing trend. Solving the objective function yields the optimal matching matrix that minimizes the objective function. The elements in the optimal matching matrix represent the matching probability or matching indicator between the set of histological cell nuclei and the set of sequenced cell nuclei. Update the initial matching relationships based on the optimal matching matrix.

[0139] Optionally, the structural cost term is determined based on a first distance matrix formed by the spatial distances between all pairs of nuclei in the histological cell nucleus set and a second distance matrix formed by the spatial distances between all pairs of nuclei in the sequenced cell nucleus set, and is used to measure the degree of inconsistency in the internal spatial distance structure between the histological cell nucleus set and the sequenced cell nucleus set; the expression cost term is determined based on the expression cost matrix of the histological cell nucleus set and the sequenced cell nucleus set, and is used to measure the degree of difference between the predicted gene expression data and the actual gene expression data; the expression cost matrix includes the degree of difference between the predicted gene expression data of each histological cell nucleus and the actual gene expression data of each sequenced cell nucleus.

[0140] Optionally, the objective function may also include: The unbalanced relaxation term is used to constrain and penalize the degree to which the marginal distribution of the optimal matching matrix deviates from a preset reference distribution, which includes a first reference distribution and a second reference distribution. The non-equilibrium relaxation term is obtained by summing the first penalty weighting term and the second penalty weighting term. The first penalty weighting term is the product of the first penalty coefficient and the first relative entropy, and the second penalty weighting term is the product of the second penalty coefficient and the second relative entropy. The first relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the set of sequenced cell nuclei and the first reference distribution, and the second relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the set of histological cell nuclei and the second reference distribution. The first penalty coefficient is greater than the second penalty coefficient.

[0141] Optionally, the objective function may also include: The entropy regularization term is used to constrain the relative entropy between the optimal matching matrix and the preset joint reference distribution in order to smooth the optimal matching matrix. The preset joint reference distribution is the outer product of the first reference distribution and the second reference distribution.

[0142] Optionally, training the reconstruction model includes a first training phase, which iteratively executes the following steps until a second convergence condition is met: The matched morphological features are input into the initial morphological encoder to obtain the predicted morphological conditional embedding output by the initial morphological encoder. Real gene expression data are input into the initial expression encoder to obtain the predicted latent expression variables output by the initial expression encoder; The predicted expression latent variable and the predicted morphological conditional embedding are concatenated and then input into the initial negative binomial decoder to obtain the predicted relative expression rate output by the initial negative binomial decoder. The predicted gene expression data are determined based on the predicted relative expression rate. Based on predicted gene expression data and real gene expression data, the likelihood loss function value is calculated, and combined with the relative entropy regularization term used to constrain the predicted expression latent variables, the parameters of the initial morphological encoder, the initial expression encoder, and the initial negative binomial decoder are updated. After the first training phase, the morphological encoder, the representation encoder, and the negative binomial decoder are obtained.

[0143] Optionally, training the reconstruction model may also include a second training phase, which includes: The matched morphological features are input into the morphological encoder to obtain the morphological conditional embedding, and the real gene expression data are input into the expression encoder to obtain the expression latent variables. Iteratively execute the following steps until the third convergence condition is met: Initial noise is sampled from a standard normal distribution, and a random time step is obtained. Based on the initial noise, the latent variable of expression, and the time step, an interpolation latent variable between the initial noise and the latent variable of expression is constructed. The interpolation latent variables, time steps, and morphological conditions are embedded into the velocity field network to obtain the predicted velocity vector output by the velocity field network. The target velocity vector is determined based on the numerical difference between the initial noise and the expressed latent variables, and the parameters of the velocity field network are updated based on the error between the predicted velocity vector and the target velocity vector. After the second training phase, the final reconstruction model is obtained, which includes a morphological encoder, a trained velocity field network, and a negative binomial decoder.

[0144] Optionally, the morphological features of each histological cell nucleus are input into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model, including: The morphological features of each histological cell nucleus are input into the morphological encoder to obtain the target morphological conditional embedding. Sample initial inference noise from a standard normal distribution; Using the target morphological conditional embedding as a condition, the trained velocity field network is used to solve the ordinary differential equation. The integral is performed from the initial time step to the final time step to generate the target expression latent variable for each histological cell nucleus. The target expression latent variables and target morphological conditions are embedded into the input negative binomial decoder to obtain the relative expression rate of the output of the negative binomial decoder; The library size of each histological cell nucleus was obtained by randomly sampling from the library size distribution of the sequenced cell nuclei; based on the library size and relative expression rate, the gene count in integer form was obtained by gamma-Poisson sampling, which was used as the final predicted gene expression data.

[0145] Optionally, morphological features of each histological cell nucleus are extracted, including: Using the centroid of each histological cell nucleus as the center, crop according to the bounding box of the histological cell nucleus to obtain local image patches; The local image patch is input into the first image base model to obtain the local morphological features output by the first image base model; Cropping is performed with the centroid as the center to obtain a global image patch with a size larger than the local image patch; The global image patch is input into the second image base model to obtain the global morphological features output by the second image base model; By integrating local and global morphological features, the morphological characteristics of each histological cell nucleus are obtained.

[0146] Optionally, the Spatial Single-Cell Transcriptome Denseization System 500 also includes a completion module, which is used after obtaining the final predicted gene expression data from the final reconstructed model output: Identify cavity regions in the histological images; Virtual cell nucleus nodes are deployed within the void area; Identify the real histological cell nucleus that is spatially nearest to the virtual cell nucleus node; Obtain the final predicted gene expression data corresponding to the actual histological cell nuclei; Based on the final predicted gene expression data corresponding to the real histological cell nuclei, spatial interpolation calculations are performed to obtain the complete gene expression data of the virtual cell nucleus nodes.

[0147] Figure 6 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 6As shown, the electronic device may include: a processor 610, a communication interface 620, a memory 630, and a communication bus 640, wherein the processor 610, the communication interface 620, and the memory 630 communicate with each other through the communication bus 640. The processor 610 can call logical instructions in the memory 630 to execute a spatial single-nucleus transcriptome densification method. This method includes: segmenting a histological image to obtain a set of histological nuclei; extracting the morphological features of each histological nucleus; determining an initial matching relationship between the histological nuclei set and the sequenced nuclei set of the spatial single-nucleus transcriptome, the initial matching relationship being determined solely based on the spatial structural information of the histological nuclei set and the sequenced nuclei set; iteratively executing the following steps until a first convergence condition is met: using the morphological features matched by each sequenced nucleus in the sequenced nuclei set as training data, and... The real gene expression data of each sequenced cell nucleus serves as the training label to train the reconstruction model. The matching morphological features are determined based on the initial matching relationship. The morphological features of each histological cell nucleus are input into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model. The initial matching relationship is updated based on the difference between the predicted gene expression data and the real gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set. After satisfying the first convergence condition, the morphological features of each histological cell nucleus are input into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model.

[0148] Furthermore, the logical instructions in the aforementioned memory 630 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0149] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a spatial single-nucleus transcriptome densification method provided by the methods described above. This method includes: segmenting a histological image to obtain a set of histological nuclei; extracting morphological features of each histological nucleus; determining an initial matching relationship between the histological nuclei set and the sequenced nuclei set of the spatial single-nucleus transcriptome, the initial matching relationship being determined solely based on the spatial structural information of the histological nuclei set and the sequenced nuclei set; iteratively executing the following steps until a first convergence condition is met: using each sequenced nucleus set... The morphological features of sequenced cell nuclei are used as training data, and the actual gene expression data of each sequenced cell nucleus is used as the training label to train the reconstruction model. The matching morphological features are determined based on the initial matching relationship. The morphological features of each histological cell nucleus are input into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model. The initial matching relationship is updated according to the difference between the predicted gene expression data and the actual gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set. After the first convergence condition is met, the morphological features of each histological cell nucleus are input into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model.

[0150] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0151] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for spatial single-cell nuclear transcriptome densification, characterized in that, include: Histological images are segmented to obtain a set of histological cell nuclei. The morphological features of each histological cell nucleus are extracted, and the initial matching relationship between the set of histological cell nuclei and the set of sequenced cell nuclei of spatial single-cell transcriptome is determined. The initial matching relationship is determined only based on the spatial structural information of the set of histological cell nuclei and the set of sequenced cell nuclei. Iteratively execute the following steps until the first convergence condition is met: The morphological features matched by each sequenced cell nucleus in the sequenced cell nucleus set are used as training data, and the real gene expression data of each sequenced cell nucleus are used as training labels to train the reconstruction model. The matched morphological features are determined based on the initial matching relationship. The morphological features of each histological cell nucleus are input into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model; The initial matching relationship is updated based on the difference between the predicted gene expression data and the actual gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set. After the first convergence condition is met, the morphological features of each histological cell nucleus are input into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model.

2. The spatial single-cell nuclear transcriptome densification method according to claim 1, characterized in that, Updating the initial matching relationship includes: The structural cost term is weighted based on the first dynamic weight, and the expression cost term is weighted based on the second dynamic weight to construct an objective function. The structural cost term is determined based on the spatial structure information, and the expression cost term is determined based on the degree of difference. The first dynamic weight and the second dynamic weight change dynamically with the increase of the iteration rounds, and the first dynamic weight shows a decreasing trend while the second dynamic weight shows an increasing trend. Solving the objective function yields the optimal matching matrix that minimizes the objective function. The elements in the optimal matching matrix represent the matching probability or matching indication between the set of histological cell nuclei and the set of sequenced cell nuclei. The initial matching relationship is updated based on the optimal matching matrix.

3. The spatial single-cell nuclear transcriptome densification method according to claim 2, characterized in that: The structural cost term is determined based on a first distance matrix formed by the spatial distances between each pair of nuclei in the histological cell nucleus set and a second distance matrix formed by the spatial distances between each pair of nuclei in the sequenced cell nucleus set, and is used to measure the degree of inconsistency between the histological cell nucleus set and the sequenced cell nucleus set in terms of internal spatial distance structure. The expression cost term is determined based on the expression cost matrix of the histological cell nucleus set and the sequenced cell nucleus set, and is used to measure the degree of difference between the predicted gene expression data and the actual gene expression data; the expression cost matrix includes the degree of difference between the predicted gene expression data of each histological cell nucleus and the actual gene expression data of each sequenced cell nucleus.

4. The spatial single-cell nuclear transcriptome densification method according to claim 2, characterized in that, The objective function also includes: An unbalanced relaxation term is used to constrain and penalize the degree to which the marginal distribution of the optimal matching matrix deviates from a preset reference distribution, wherein the preset reference distribution includes a first reference distribution and a second reference distribution. The non-equilibrium relaxation term is obtained by summing a first penalty weighting term and a second penalty weighting term. The first penalty weighting term is the product of a first penalty coefficient and a first relative entropy, and the second penalty weighting term is the product of a second penalty coefficient and a second relative entropy. The first relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the sequenced cell nucleus set and the first reference distribution, and the second relative entropy is the divergence between the marginal distribution of the optimal matching matrix on the histological cell nucleus set and the second reference distribution. Furthermore, the first penalty coefficient is greater than the second penalty coefficient.

5. The spatial single-cell nuclear transcriptome densification method according to claim 4, characterized in that, The objective function also includes: An entropy regularization term is used to constrain the relative entropy between the optimal matching matrix and a preset joint reference distribution to smooth the optimal matching matrix. The preset joint reference distribution is the outer product of the first reference distribution and the second reference distribution.

6. The spatial single-cell nuclear transcriptome densification method according to claim 1, characterized in that, The training and reconstruction model includes a first training phase, which includes iteratively executing the following steps until a second convergence condition is met: The matched morphological features are input into the initial morphological encoder to obtain the predicted morphological conditional embedding output by the initial morphological encoder. The real gene expression data is input into the initial expression encoder to obtain the predicted latent expression variables output by the initial expression encoder; The predicted expression latent variable and the predicted morphological conditional embedding are concatenated and then input into the initial negative binomial decoder to obtain the predicted relative expression rate output by the initial negative binomial decoder. The predicted gene expression data are determined based on the predicted relative expression rate. Based on the predicted gene expression data and the real gene expression data, the likelihood loss function value is calculated, and combined with the relative entropy regularization term used to constrain the predicted expression latent variables, the parameters of the initial morphological encoder, the initial expression encoder, and the initial negative binomial decoder are updated. After the first training phase, the morphological encoder, the representation encoder, and the negative binomial decoder are obtained.

7. The spatial single-cell nuclear transcriptome densification method according to claim 6, characterized in that, The training and reconstruction model further includes a second training phase, which includes: The matched morphological features are input into the morphological encoder to obtain morphological conditional embeddings, and the real gene expression data are input into the expression encoder to obtain latent expression variables. Iteratively execute the following steps until the third convergence condition is met: Initial noise is sampled from a standard normal distribution, and a random time step is obtained. Based on the initial noise, the latent expression variable, and the time step, an interpolation latent variable is constructed between the initial noise and the latent expression variable. The interpolation latent variable, the time step, and the morphological condition are embedded into the velocity field network to obtain the predicted velocity vector output by the velocity field network. The target velocity vector is determined based on the numerical difference between the initial noise and the expressed latent variables, and the parameters of the velocity field network are updated based on the error between the predicted velocity vector and the target velocity vector. After the second training phase, the final reconstruction model is obtained, which includes the morphological encoder, the trained velocity field network, and the negative binomial decoder.

8. The spatial single-cell nuclear transcriptome densification method according to claim 7, characterized in that, The step of inputting the morphological features of each histological cell nucleus into the final reconstruction model to obtain the final predicted gene expression data output by the final reconstruction model includes: The morphological features of each histological cell nucleus are input into the morphological encoder to obtain the target morphological conditional embedding; Initial inference noise is sampled from the standard normal distribution; Using the target morphology conditional embedding as a condition, the trained velocity field network is used to solve the ordinary differential equation, and the integral is performed from the initial time step to the end time step to generate the target expression latent variable for each histological cell nucleus. The target expression latent variable and the target morphological condition are embedded into the negative binomial decoder to obtain the relative expression rate output by the negative binomial decoder; The library size of each histological cell nucleus is obtained by randomly sampling from the library size distribution of the sequenced cell nuclei; based on the library size and the relative expression rate, the gene count in integer form is obtained by gamma-Poisson sampling, which is used as the final predicted gene expression data.

9. The spatial single-cell nuclear transcriptome densification method according to claim 1, characterized in that, The extraction of morphological features from each histological cell nucleus includes: Using the centroid of each histological cell nucleus as the center, crop according to the bounding box of the histological cell nucleus to obtain a local image patch; The local image patch is input into the first image base model to obtain the local morphological features output by the first image base model; Cropping is performed with the centroid as the center to obtain a global image block with a size larger than the local image block; The global image patch is input into the second image base model to obtain the global morphological features output by the second image base model; By fusing the local morphological features and the global morphological features, the morphological features of each histological cell nucleus are obtained.

10. The spatial single-cell nuclear transcriptome densification method according to claim 1, characterized in that, After obtaining the final predicted gene expression data output by the final reconstruction model, the method further includes: Identify cavity regions in the histological images; Virtual cell nucleus nodes are deployed within the cavity area; Identify the real histological cell nucleus that is spatially nearest to the virtual cell nucleus node; Obtain the final predicted gene expression data corresponding to the actual histological cell nuclei; Based on the final predicted gene expression data corresponding to the real histological cell nuclei, spatial interpolation calculations are performed to obtain the complete gene expression data of the virtual cell nucleus nodes.

11. A spatial single-cell nuclear transcriptome densification system, characterized in that, include: An initialization module is used to segment a histological image to obtain a set of histological cell nuclei, extract the morphological features of each histological cell nucleus, and determine the initial matching relationship between the set of histological cell nuclei and the set of sequenced cell nuclei of the spatial single-cell transcriptome. The initial matching relationship is determined only based on the spatial structure information of the set of histological cell nuclei and the set of sequenced cell nuclei. The iterative alignment module is used to iteratively execute the following steps until the first convergence condition is met: The morphological features matched by each sequenced cell nucleus in the sequenced cell nucleus set are used as training data, and the real gene expression data of each sequenced cell nucleus are used as training labels to train the reconstruction model. The matched morphological features are determined based on the initial matching relationship. The morphological features of each histological cell nucleus are input into the reconstruction model to obtain the predicted gene expression data output by the reconstruction model; The initial matching relationship is updated based on the difference between the predicted gene expression data and the actual gene expression data, as well as the spatial structure information of the histological cell nucleus set and the sequenced cell nucleus set. The dense inference module is used to input the morphological features of each histological cell nucleus into the final reconstruction model after the first convergence condition is met, so as to obtain the final predicted gene expression data output by the final reconstruction model.

12. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the spatial single-cell nuclear transcriptome densification method as described in any one of claims 1 to 10.

13. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the spatial single-cell nuclear transcriptome densification method as described in any one of claims 1 to 10.

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