A Multimodal Brain Network Fusion Method Based on Tensor Spectrum Clustering

Abstract

This invention relates to the field of brain network analysis technology, specifically to a multimodal brain network fusion method based on tensor spectral clustering. The method includes: acquiring multimodal brain network data, including structural magnetic resonance imaging (SMRI) data, functional magnetic resonance imaging (fMRI) data, and diffusion tensor imaging (DTI) data; preprocessing the multimodal brain network data; constructing individual morphological brain networks, functional brain networks, and structural brain networks based on the preprocessed multimodal brain network data, and performing normalization processing; fusing the normalized multimodal brain networks using a tensor spectral clustering algorithm to obtain a fused brain network; acquiring the subject's behavioral data, inputting the behavioral data into the fused brain network, and calculating the subject's behavioral prediction values. This invention not only advances research in neuroscience, cognitive science, and psychology but also provides strong support for related clinical applications and personalized medicine.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of brain network analysis, and particularly relates to a multi-modal brain network fusion method based on tensor spectral clustering. BACKGROUND

[0002] With the continuous development of imaging technology, neuroimaging has become an important basis for clinical diagnosis and is widely used in tumor screening, radiotherapy, surgical planning and pathological diagnosis. Researchers can use various imaging methods to collect different modalities of neuroimaging of the same subject, such as structural magnetic resonance imaging (sMRI), functional magnetic resonance imaging (fMRI) and diffusion tensor imaging (DTI), to provide information about brain anatomy and function from different angles.

[0003] However, in the prior art, the analysis of single modality data is difficult to verify the joint information between different modalities (such as the relationship between brain structure and function), and multi-modal neuroimaging fusion analysis can more comprehensively and deeply reveal the brain mechanism and its abnormalities in diseases. Multi-modal neuroimaging technology can provide rich brain disease diagnosis information for doctors and researchers, but the huge amount of data also brings challenges. Relying only on identifying a large number of original neuroimages to diagnose diseases requires rich clinical experience and takes a long time, greatly affecting the timeliness and effectiveness of diagnosis. Therefore, neuroimaging fusion technology has attracted widespread attention.

[0004] The present application adopts the tensor spectral clustering (TSC) method to fuse multi-modal brain networks. TSC is an extension of spectral clustering algorithm on high-order data, which can handle the complex multi-dimensional structure of multi-modal neuroimaging and reveal the potential patterns of brain functional networks. In the past decade, data-driven predictive modeling methods have been widely used to study the relationship between brain and behavior. These methods can generate individual-level clinical information predictions, including diagnosis, symptom characteristics and treatment response, and determine the underlying neurobiological mechanisms related to different behaviors. Based on these models, multi-modal fusion of brain network behavior data prediction becomes possible, providing new tools for predicting individual differences in cognition, personality, mental health, etc.

[0005] Current neuroimaging studies can be divided into two categories according to the structure of the data used: one focuses on obtaining time series of different neuroimaging modalities through signal processing techniques; the other focuses on using imaging features of voxels or regions of interest (ROI). However, more and more evidence shows that the brain is organized and functionalized based on the interaction between multiple brain regions, especially in explaining the clinical phenotypes related to the brain. Therefore, brain network analysis has gradually attracted attention, which can more comprehensively reveal the functional and structural connections between brain regions by regarding the brain as a network composed of nodes and edges, helping to deeply understand the complex operation mechanism of the brain. The fusion of brain networks can improve the sensitivity and specificity of data analysis, especially in distinguishing specific diseases or functional states (such as Alzheimer's disease and depression), and fusion analysis can provide better diagnostic and grouping basis. In addition, brain network fusion also has important applications in individual difference analysis, by evaluating the differences between individuals and groups, identifying the network characteristics of specific populations, and providing support for personalized medicine.

[0006] In the fusion process of multi-modal brain networks, traditional clustering algorithms (such as K-Means) can only handle two-dimensional data in matrix form, while tensor spectral clustering can directly handle multi-modal data and preserve the internal structure and correlation of the original data during clustering. Compared with traditional clustering algorithms, tensor spectral clustering has better robustness to noise in the dimension reduction process and can more effectively extract essential features from complex data. Since tensor spectral clustering can utilize the interrelationships between different dimensions of multi-modal data, its accuracy in clustering tasks is often higher than that of traditional clustering methods. Therefore, tensor spectral clustering algorithms have broad application potential in the field of brain network fusion.

[0007] The present application proposes a multi-modal brain network fusion method based on tensor spectral clustering (TSC) for autism spectrum disorder (ASD) to reveal the association between brain networks and behavioral data. The complex network connectivity of the human brain plays a key role in cognitive and behavioral support and changes during development, aging, and disease. Although existing neuroimaging techniques (such as sMRI, fMRI, and DTI) can provide information on brain structure and function, single-modal analysis cannot fully reveal the brain mechanisms. The present application fuses multi-modal data through TSC, constructs common and specific brain networks, and combines machine learning models to predict behavioral indicators, providing new perspectives and methods for neurobiological research and clinical diagnosis of ASD. SUMMARY

[0008] According to the technical problems proposed above, a multi-modal brain network fusion method based on tensor spectral clustering is provided.The present application mainly fuses sMRI, fMRI and DTI multi-modal brain networks by using tensor spectral clustering (TSC), and combines a regression model to predict behavioral characteristics, thereby overcoming the dimension limitation of traditional methods, enhancing the robustness of brain network fusion, improving the prediction accuracy of behavioral characteristics, and supporting precision medicine applications.

[0009] The technical means adopted by the present application are as follows:

[0010] A multi-modal brain network fusion method based on tensor spectral clustering comprises the following steps:

[0011] Collecting multi-modal brain network data, the multi-modal brain network data comprising structural magnetic resonance imaging data, functional magnetic resonance imaging data and diffusion tensor imaging data;

[0012] Pretreating the multi-modal brain network data;

[0013] Based on the pretreated multi-modal brain network data, constructing a morphological brain network matrix, a functional connection matrix and a structural connection matrix, respectively;

[0014] Normalizing the morphological brain network matrix, the functional connection matrix and the structural connection matrix;

[0015] Fusing the normalized morphological brain network matrix, the functional connection matrix and the structural connection matrix by using a tensor spectral clustering algorithm to obtain a fused brain network;

[0016] Obtaining behavioral data of a subject, inputting the behavioral data into the fused brain network, and calculating a behavioral prediction value of the subject.

[0017] Further, the specific steps of constructing the morphological brain network matrix comprise:

[0018] Firstly, according to the pretreated structural magnetic resonance imaging data, extracting and constructing an individual morphological brain network based on the gray matter image of the subject, wherein the nodes in the individual morphological brain network represent brain regions, and the edges represent the similarity of morphological measurement distribution between two regions;

[0019] Secondly, dividing the gray matter image into a plurality of regions of interest by using an automatic anatomical marker template;

[0020] Finally, the quantification of the network edge adopts a similarity based on the symmetric Kullback-Leibler divergence, and the morphological brain network matrix is constructed according to the divergence similarity, and the symmetric Kullback-Leibler divergence similarity calculation formula is:

[0021]

[0022] where KLS(p,q) is the divergence similarity, p and q represent the gray matter density probability distribution of two different brain regions, and n is the number of sampling points.

[0023] Further, the specific steps of constructing the functional connection matrix comprise:

[0024] Firstly, according to the pre-processed functional magnetic resonance imaging data, the brain regions are partitioned and labeled by using an automatic anatomical labeling template, and a plurality of regions of interest are obtained;

[0025] Secondly, the voxel time series of each region of interest is averaged to obtain a node signal time series;

[0026] Finally, based on the node signal time series, the functional connection strength between brain regions is calculated by using the Pearson correlation coefficient, and the functional connection matrix is constructed.

[0027] Further, the specific steps of constructing the structural brain network comprise:

[0028] Firstly, according to the pre-processed diffusion tensor imaging data, the connection between different regions is determined along the direction of the fiber bundle by using the diffusion tensor information according to the axonal fiber bundle between regions;

[0029] Finally, after determining the connectivity, different regions of the brain are regarded as nodes, and the structural brain network is constructed according to the strength of the connection.

[0030] Further, the specific steps of constructing the structural brain network further comprise:

[0031] Firstly, according to the pre-processed diffusion tensor imaging data, the strength of the connection is determined according to the spatial distance between regions and the similarity of the diffusion tensor;

[0032] Finally, after determining the connectivity, different regions of the brain are regarded as nodes, and the structural brain network is constructed according to the strength of the connection.

[0033] Further, the calculation formula for the normalization processing of the morphological brain network matrix, the functional connection matrix and the structural connection matrix is:

[0034]

[0035] where m = 1, 2, 3, is the corresponding connection value of region i and region j in the morphological brain network matrix, is the corresponding connection value of region i and region j in the functional connection matrix, is the corresponding connection value of region i and region j in the structural connection matrix, a morphological brain network connection matrix, a functional brain network connection matrix, a structural brain network connection matrix, an average value of the morphological brain network connection matrix, an average value of the functional brain network connection matrix, an average value of the structural brain network connection matrix, a standard deviation of the morphological brain network connection matrix, a standard deviation of the functional brain network connection matrix, a standard deviation of the structural brain network connection matrix, a normalized morphological brain network matrix, a normalized functional brain network matrix, a normalized structural brain network matrix.

[0036] Further, the normalized morphological brain network matrix, the functional connection matrix and the structural connection matrix are fused by using a tensor spectral clustering algorithm to obtain a fused brain network, and the method comprises the following steps:

[0037] The normalized morphological brain network matrix, the functional connection matrix and the structural connection matrix are respectively taken as undirected weighted graphs to generate a morphological weighted adjacency matrix, a functional weighted adjacency matrix and a structural weighted adjacency matrix;

[0038] A generalized degree matrix of a vertex is calculated according to the morphological weighted adjacency matrix, the functional weighted adjacency matrix and the structural weighted adjacency matrix:

[0039]

[0040] wherein m = 1, 2, 3, D (1) a morphological generalized degree matrix of the vertex, D (2) a functional generalized degree matrix of the vertex, D (3) a structural generalized degree matrix of the vertex, and e is a vector with all elements being 1, the morphological weighted adjacency matrix, the functional weighted adjacency matrix, the structural weighted adjacency matrix;

[0041] A Laplacian matrix is defined according to the generalized degree matrix of the vertex and the morphological weighted adjacency matrix, the functional weighted adjacency matrix and the structural weighted adjacency matrix:

[0042]

[0043] wherein m = 1, 2, 3, D (1) a morphological generalized degree matrix of the vertex, D (2)D is a functional generalized degree matrix of the vertex, (3) e is a structural generalized degree matrix of the vertex, is a morphological weighted adjacency matrix, is a functional weighted adjacency matrix, is a structural weighted adjacency matrix, (1) is a morphological Laplacian matrix, (2) is a functional Laplacian matrix, (3) is a structural Laplacian matrix,

[0044] According to the morphological weighted adjacency matrix, the functional weighted adjacency matrix, the structural weighted adjacency matrix and the generalized degree matrix of the vertex, a transition matrix is calculated:

[0045]

[0046] wherein m = 1, 2, 3, is a morphological weighted adjacency matrix, is a functional weighted adjacency matrix, is a structural weighted adjacency matrix, (1) is a morphological transition matrix, (2) is a functional transition matrix, (3) is a structural transition matrix, (1) is a morphological generalized degree matrix of the vertex, (2) is a functional generalized degree matrix of the vertex, (3) is a structural generalized degree matrix of the vertex,

[0047] According to the transition matrix, a generalized transition tensor is generated:

[0048] P I × P (1) × P (2) × P (3) ,

[0049] wherein, P is a generalized transition tensor, (1) is a morphological transition matrix, (2) is a functional transition matrix, (3) is a structural transition matrix, I is a four-dimensional unit tensor,

[0050] The generalized transition tensor is singular value decomposed to obtain a right singular matrix, and eigenvectors corresponding to the first R maximum values in the right singular matrix are selected, and a eigenvector matrix is constructed according to the eigenvectors.

[0051] The eigenvector matrix is subjected to an outer product operation to generate a fused brain network.

[0052] ​Further, the behavior data of the subject is acquired, the behavior data is input into the fused brain network, and a behavior prediction value of the subject is calculated, comprising:

[0053] Given n subjects and m edges, the Pearson correlation coefficient of each edge is calculated:

[0054] R i = r(A i ,b),

[0055] Wherein, R i is the Pearson correlation coefficient of the ith edge, A i is the connection strength of the subject on the ith edge, b is the behavior data, and r is the function of the Pearson correlation coefficient.

[0056] The connection strength of each subject is calculated, the connection strength of the subject is weighted, and the behavior prediction value of the subject is calculated according to the Pearson correlation coefficient of each edge:

[0057]

[0058] Wherein, S j is the behavior prediction value of the jth subject, A j,x is the connection strength of the jth subject on the xth edge, and R x is the Pearson correlation coefficient of the xth edge.

[0059] Compared with the prior art, the present application has the following advantages:

[0060] The method has remarkable beneficial effects. First, by the tensor spectral clustering method, brain imaging data of multiple modalities such as functional magnetic resonance imaging (fMRI), structural magnetic resonance imaging (sMRI) and diffusion tensor imaging (DTI) can be efficiently integrated, the complexity and inefficiency of multi-modal data fusion in the prior art are overcome, meanwhile, advanced preprocessing and standardization methods are adopted to ensure the consistency and reliability of different modal data, thus providing a solid foundation for subsequent analysis. Secondly, the present application can accurately identify common brain networks and specific brain networks, reveal the common functional patterns of the group and the differences between individuals, and thus deeply understand the complexity of brain function and structure, providing a new perspective for basic research in neuroscience. In addition, the prediction model established by machine learning technology can accurately capture the correlation between brain network features and behavior performance, effectively predict individual behavior performance, support personalized cognitive assessment, and help clinical diagnosis and personalized medicine. The optimized tensor spectral clustering algorithm still maintains high efficiency and accuracy in the environment with limited computing resources, has wide applicability, and can be popularized to other multi-modal data analysis fields. Overall, the present application not only promotes the research of neuroscience, cognitive science and psychology, but also provides strong support for related clinical applications and personalized medicine.

[0061] For the above reasons, the present application can be widely popularized in the field of brain network analysis. BRIEF DESCRIPTION OF DRAWINGS

[0062] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0063] Figure 1 The flowchart of the multi-modal brain network fusion method based on tensor spectral clustering of the present application. DETAILED DESCRIPTION

[0064] In order to enable the personnel in the technical field to better understand the present application scheme, the technical solutions in the embodiments of the present application will be described clearly and completely in the following by combining the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should belong to the scope of protection of the present application.

[0065] As shown in Figure 1 The present application provides a multi-modal brain network fusion method based on tensor spectral clustering, and the steps thereof include:

[0066] S1. Collecting multi-modal brain network data, the multi-modal brain network data comprising structural magnetic resonance imaging data, functional magnetic resonance imaging data and diffusion tensor imaging data.

[0067] S2. Preprocessing the multi-modal brain network data.

[0068] For the structural magnetic resonance imaging data, the preprocessing comprises head motion correction, head removal, spatial normalization, image segmentation and data smoothing.

[0069] For the functional magnetic resonance imaging data, the common steps of preprocessing include head motion correction, time slice correction, head motion related signal removal, spatial normalization and low frequency trend removal.

[0070] For the diffusion tensor imaging data, the preprocessing steps include head motion correction, magnetic field inhomogeneity removal, diffusion weighted image calibration, tensor fitting and spatial normalization.

[0071] S3. Constructing morphological brain network matrix, functional connectivity matrix and structural connectivity matrix respectively based on the preprocessed multi-modal brain network data.

[0072] The specific steps of constructing the morphological brain network matrix are as follows:

[0073] First, according to the preprocessed structural magnetic resonance imaging data, the gray matter (GM) image of the subject is extracted and based on which the individual morphological brain network (MBNs) is constructed, in which the nodes represent brain regions and the edges represent the similarity of morphological measurement distribution between two regions.

[0074] Secondly, the gray matter image is divided into 90 regions of interest (ROI) by using the automatic anatomical labeling (AAL) template.

[0075] Finally, the network edge is quantified by using the similarity of Kullback-Leibler divergence (KLS) based on symmetry, and the morphological brain network matrix is constructed according to the divergence similarity, and the formula for calculating the Kullback-Leibler divergence similarity is as follows:

[0076]

[0077] Wherein, KLS(p, q) is the divergence similarity, p and q represent the gray matter density probability distribution of two different brain regions respectively, and n is the number of sampling points. The value range of KLS is 0 to 1, wherein 1 indicates that p and q have the same distribution.

[0078] In the process of constructing brain networks, we apply an iterative algorithm to calculate individual-specific functional networks, thus more accurately revealing the association between brain activity and behavior. The specific steps of constructing the functional connection matrix include:

[0079] First, according to the pre-processed functional magnetic resonance imaging data, the brain regions are partitioned and labeled by the automatic anatomical labeling (AAL) template, obtaining 90 ROIs.

[0080] Second, in the subsequent experiment, the voxel time series of each ROI is averaged to obtain the node signal time series, in order to calculate the time course of individual subjects.

[0081] Finally, based on the node signal time series, the functional connection strength between brain regions is calculated using the Pearson correlation coefficient (r), and the functional connection matrix is constructed.

[0082] The specific steps of constructing structural brain networks include:

[0083] The process of constructing DTI brain networks includes two parts: determining connectivity and network construction. The process of determining connectivity includes using diffusion tensor information to calculate the connectivity between different regions. This can be achieved by two commonly used methods: one is to track the axon fiber bundle between regions, and use the diffusion tensor information to determine the connection between different regions along the direction of the fiber bundle; the other is spatial distance weighted connection, which determines the strength of the connection according to the spatial distance and the similarity of the diffusion tensor between regions.

[0084] Finally, after determining the connectivity, different regions of the brain are regarded as nodes, and the structural brain network is constructed according to the strength of the connection. The adjacency matrix is usually used to represent the brain network, where each element represents the connection strength between two nodes.

[0085] S4. Normalize the morphological brain network matrix, functional connection matrix and structural connection matrix.

[0086] The specific normalization formula is as follows:

[0087]

[0088] Where m = 1, 2, 3, is the corresponding connection value of region i and region j in the morphological brain network matrix, is the corresponding connection value of region i and region j in the functional connection matrix, is the corresponding connection value of region i and region j in the structural connection matrix, is the morphological brain network connection matrix, is the functional brain network connection matrix, is the structural brain network connection matrix, is the average value of the morphological brain network connection matrix, is the average value of the functional brain network connection matrix, is the average value of the structural brain network connection matrix, is the standard deviation of the morphological brain network connection matrix, is the standard deviation of the functional brain network connection matrix, is the standard deviation of the structural brain network connection matrix, is the normalized morphological brain network matrix, is the normalized functional brain network matrix, is the normalized structural brain network matrix. is the normalized morphological brain network matrix, is the normalized morphological brain network matrix,

[0089] S5. The normalized morphological brain network matrix, functional connection matrix and structural connection matrix are fused by using tensor spectral clustering algorithm to obtain the fused brain network.

[0090] The normalized morphological brain network matrix, functional connection matrix and structural connection matrix are respectively taken as an undirected weighted graph, G=(V, E). V is a set of nodes, representing the regions of interest. E is a set of edges between nodes. The weighted adjacency matrix of G is represented as a symmetric matrix W (m) . According to the three modal brain networks, the weighted adjacency matrix of each dimension is constructed The morphological weighted adjacency matrix, functional weighted adjacency matrix and structural weighted adjacency matrix are generated.

[0091] According to the morphological weighted adjacency matrix, functional weighted adjacency matrix and structural weighted adjacency matrix, the generalized degree matrix of the vertex is calculated:

[0092]

[0093] wherein, m=1, 2, 3, D (1) is the morphological generalized degree matrix of the vertex, D (2) is the functional generalized degree matrix of the vertex, D (3) is the structural generalized degree matrix of the vertex, e is an element vector with all elements being 1, is the morphological weighted adjacency matrix, is the functional weighted adjacency matrix, is the structural weighted adjacency matrix.

[0094] According to the generalized degree matrix of the vertex and the morphological weighted adjacency matrix, functional weighted adjacency matrix and structural weighted adjacency matrix, the Laplacian matrix is defined:

[0095]

[0096] where m = 1, 2, 3, D (1) is the morphological degree matrix of vertices, D (2) is the functional degree matrix of vertices, D (3) is the structural degree matrix of vertices, e is a vector with all elements being 1, is the morphological weighted adjacency matrix, is the functional weighted adjacency matrix, is the structural weighted adjacency matrix, K (1) is the morphological Laplacian matrix, K (2) is the functional Laplacian matrix, K (3) is the structural Laplacian matrix.

[0097] According to the morphological weighted adjacency matrix, the functional weighted adjacency matrix, the structural weighted adjacency matrix and the degree matrix of vertices, a transition matrix is calculated:

[0098]

[0099] where m = 1, 2, 3, is the morphological weighted adjacency matrix, is the functional weighted adjacency matrix, is the structural weighted adjacency matrix, P (1) is the morphological transition matrix, P (2) is the functional transition matrix, P (3) is the structural transition matrix, D (1) is the morphological degree matrix of vertices, D (2) is the functional degree matrix of vertices, D (3) is the structural degree matrix of vertices.

[0100] According to the transition matrix, a generalized transition tensor is generated:

[0101] P = I × P (1) × P (2) × P (3) ,

[0102] where, P is the generalized transition tensor, P (1) is the morphological transition matrix, P (2) is the functional transition matrix, P (3) is the structural transition matrix, I is a four-dimensional unit tensor.

[0103] The singular value decomposition is performed on the generalized transition tensor to obtain a right singular matrix, and R eigenvectors v1, v2, …, vR corresponding to the first R maximum values in the right singular matrix are selected R, and the feature vectors are merged to form a feature vector matrix V = [v1, v2, …, vn] R ].

[0104] The feature vector matrix is subjected to an outer product operation to generate a fused brain network. Specifically, a fused brain network matrix N = V x V is constructed from the matrix V ′ , where

[0105] S6. Obtain the behavioral data of the subject, and input the behavioral data into the fused brain network to calculate the behavioral prediction value of the subject.

[0106] In order to predict the characteristics according to the fused brain network matrix, a regression algorithm is used, and the specific steps are as follows:

[0107] Given n subjects and m edges (depending on the brain partition), first obtain the Pearson correlation coefficient R of each edge with a size of m from the correlation between the non-standardized connection strength matrix A (containing the vectorized connection matrix of each subject as a row) with a size of n x m and the attribute of interest. i The calculation formula of the Pearson correlation coefficient of each edge is:

[0108] R i = r(A i , b),

[0109] where R i is the Pearson correlation coefficient of the i-th edge, A i is the connection strength of the subject on the i-th edge, b is the behavioral data, and r is the function of the Pearson correlation coefficient. The correlation vector R i contains the Pearson correlation coefficient r between A i (A i is the i-th column of matrix A) and b, and b is a vector of length n containing the value of the behavioral data (such as age) of each subject.

[0110] The connection strength of each subject is calculated, and the connection strength of the subject is weighted, and the behavioral prediction value of the subject is calculated according to the Pearson correlation coefficient of each edge:

[0111]

[0112] where S j is the behavioral prediction value of the j-th subject, A j,x is the connection strength of the j-th subject on the x-th edge, and R x is the Pearson correlation coefficient of the x-th edge.

[0113] According to the predicted values, we fitted a linear least squares regression model and then used it to predict the feature values of interest. To evaluate and compare the prediction quality, 10-fold cross-validation was performed for each dataset. The mean absolute error (MAE) and the range-normalized absolute error (NMAE) between the predicted and actual values were calculated for each subject only from the training data, and the MAE was calculated from the ten iterations of cross-validation. The formula for calculating the MAE is:

[0114]

[0115] where MAE is the mean absolute error, S i is the predicted value, b i is the true value, and n is the total number of samples.

[0116] The mean absolute error (MAE) is the norm of the difference between the predicted and actual values. The range-normalized mean absolute error (NMAE) can be obtained by dividing the MAE by the difference between the maximum and minimum values of the data, so it can better compare different datasets.

[0117] The above S1-S6 are sequentially executed.

[0118] By analyzing the common brain network and the specific brain network, the present application can explore the brain functional connection patterns that are common among different ASD patients. These patterns may be closely related to the defects in basic social skills such as social perception, social cognition, social communication, social motivation, and autistic behavior. Applying the prediction model to find the correlation between these brain networks and the corresponding behavioral data can provide a new perspective for understanding the neurobiological basis of ASD, and may provide important evidence for individualized diagnosis and intervention.

[0119] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for part or all of the technical features; and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A multi-modal brain network fusion method based on tensor spectral clustering, characterized in that, The method comprises the following steps: Collecting multi-modal brain network data, wherein the multi-modal brain network data comprises structural magnetic resonance imaging data, functional magnetic resonance imaging data and diffusion tensor imaging data; Preprocessing the multi-modal brain network data; Based on the preprocessed multi-modal brain network data, a morphological brain network matrix, a functional connection matrix and a structural connection matrix are constructed respectively, and the specific steps of constructing the morphological brain network matrix comprise: Firstly, according to the preprocessed structural magnetic resonance imaging data, an individual morphological brain network is constructed based on the gray matter image of the subject, wherein the nodes in the individual morphological brain network represent brain regions, and the edges represent the similarity of morphological measurement distribution between two regions; Secondly, the gray matter image is divided into a plurality of regions of interest by using an automatic anatomical marker template; Finally, the similarity based on the symmetric Kullback-Leibler divergence is used for quantifying the edges of the network, and the morphological brain network matrix is constructed according to the divergence similarity, and the formula for calculating the symmetric Kullback-Leibler divergence similarity is as follows: ， wherein, divergence similarity, and respectively denote the gray matter density probability distribution of two different brain regions, and n is the number of sampling points. The morphological brain network matrix, the functional connection matrix and the structural connection matrix are normalized; The normalized morphological brain network matrix, the functional connection matrix and the structural connection matrix are fused by using a tensor spectral clustering algorithm to obtain a fused brain network; Behavioral data of the subject are obtained, and the behavioral data are input into the fused brain network to calculate the behavioral prediction value of the subject.

2. The multi-modal brain network fusion method based on tensor spectral clustering according to claim 1, characterized in that, The specific steps of constructing the functional connection matrix comprise: Firstly, according to the preprocessed functional magnetic resonance imaging data, the brain regions are partitioned and labeled by using an automatic anatomical marker template to obtain a plurality of regions of interest; Secondly, the voxel time series of each region of interest are averaged to obtain a node signal time series; Finally, the functional connection strength between brain regions is calculated based on the node signal time series by using a Pearson correlation coefficient to construct a functional connection matrix.

3. The multi-modal brain network fusion method based on tensor spectral clustering according to claim 1, characterized in that, The specific steps of constructing the structural connection matrix comprise: Firstly, according to the preprocessed diffusion tensor imaging data, the connection between different regions is determined along the direction of the fiber bundle by using the diffusion tensor information according to the axon fiber bundle between the regions; Finally, after determining the connectivity, different regions of the brain are regarded as nodes, and a structural connection matrix is constructed according to the connection strength.

4. The multi-modal brain network fusion method based on tensor spectral clustering according to claim 1, characterized in that, The specific steps of constructing the structural connection matrix further comprise: Firstly, according to the preprocessed diffusion tensor imaging data, the connection strength is determined according to the spatial distance between regions and the similarity of diffusion tensors; Finally, after determining the connectivity, different regions of the brain are regarded as nodes, and a structural connection matrix is constructed according to the connection strength.

5. The multi-modal brain network fusion method based on tensor spectral clustering according to claim 1, characterized in that, The formula for normalizing the morphological brain network matrix, the functional connection matrix and the structural connection matrix is as follows: ， ， wherein m = 1, 2, 3, is the corresponding connection value of the region and the region in the morphological brain network matrix, is the corresponding connection value of the region and the region in the functional connection matrix, is the corresponding connection value of the region and the region in the structural connection matrix, is the morphological brain network connection matrix, is the functional brain network connection matrix, is the structural brain network connection matrix, is the average value of the morphological brain network connection matrix, is the average value of the functional brain network connection matrix, is the average value of the structural brain network connection matrix, is the standard deviation of the morphological brain network connection matrix, is the standard deviation of the functional brain network connection matrix, is the standard deviation of the structural brain network connection matrix, is the normalized morphological brain network matrix, is the normalized functional brain network matrix, is the normalized structural brain network matrix.

6. The multi-modal brain network fusion method based on tensor spectral clustering according to claim 1, characterized in that, The fusion of the normalized morphological brain network matrix, the functional connection matrix and the structural connection matrix by using the tensor spectral clustering algorithm to obtain the fused brain network comprises: The normalized morphological brain network matrix, the functional connection matrix and the structural connection matrix are respectively regarded as undirected weighted graphs to generate a morphological weighted adjacency matrix, a functional weighted adjacency matrix and a structural weighted adjacency matrix; According to the morphological weighted adjacency matrix, the functional weighted adjacency matrix and the structural weighted adjacency matrix, a generalized degree matrix of the vertex is calculated: ， wherein m = 1, 2, 3, is the modality generalization degree matrix of the vertex, is the function generalization degree matrix of the vertex, is the structure generalization degree matrix of the vertex, is a vector with all elements being 1, is the modality weighted adjacency matrix, is the function weighted adjacency matrix, is the structure weighted adjacency matrix; According to the generalized degree matrix of the vertex and the morphological weighted adjacency matrix, the functional weighted adjacency matrix and the structural weighted adjacency matrix, a Laplacian matrix is defined: ， where m = 1, 2, 3, is the morphological degree of generalization matrix of vertex, is the functional degree of generalization matrix of vertex, is the structural degree of generalization matrix of vertex, is the vector with all elements being 1, is the morphological weighted adjacency matrix, is the functional weighted adjacency matrix, is the structural weighted adjacency matrix, is the morphological Laplacian matrix, is the functional Laplacian matrix, is the structural Laplacian matrix. According to the morphological weighted adjacency matrix, the functional weighted adjacency matrix and the structural weighted adjacency matrix and the generalized degree matrix of the vertex, a transition matrix is calculated: ， wherein m = 1, 2, 3, is a morphological weighted adjacency matrix, is a functional weighted adjacency matrix, is a structural weighted adjacency matrix, is a morphological transition matrix, is a functional transition matrix, is a structural transition matrix, is a morphological generalized degree matrix of vertices, is a functional generalized degree matrix of vertices, is a structural generalized degree matrix of vertices. According to the transition matrix, a generalized transition tensor is generated: ， wherein, is the generalized transport tensor, is the morphic transport matrix, is the functional transport matrix, is the structural transport matrix, is the four-dimensional unit tensor; The generalized transition tensor is singular value decomposed to obtain a right singular matrix, and eigenvectors corresponding to the first R maximum values in the right singular matrix are selected, and a eigenvector matrix is constructed according to the eigenvectors; The eigenvector matrix is subjected to an outer product operation to generate a fused brain network.

7. The multi-modal brain network fusion method based on tensor spectral clustering according to claim 1, characterized in that, The behavior data of the subject is acquired, the behavior data is input into the fused brain network, and a behavior prediction value of the subject is calculated, including: Given n subjects and m edges, the Pearson correlation coefficient of each edge is calculated: wherein, is the Pearson correlation coefficient for the ith edge, is the connection strength of the subject on the ith edge, is the behavioral data, is a function of the Pearson correlation coefficient; The connection strength of each subject is calculated, the connection strength of the subject is weighted, and the behavior prediction value of the subject is calculated according to the Pearson correlation coefficient of each edge: wherein, is the behavioral prediction value for the jth subject, is the connection strength of the xth edge for the jth subject, is the Pearson correlation coefficient for the xth edge.

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