Brain network quantitative analysis method based on near-infrared signal time sequence dynamic graph Fourier transform

Abstract

The invention discloses a brain network quantitative analysis method based on near-infrared signal time sequence dynamic graph Fourier transform, which comprises the following steps: constructing a brain network based on fNIRS signals, optimizing time sequence alignment by using a dynamic time warping algorithm, and dividing dynamic network time periods by combining adaptive K-Means clustering with an elbow rule; a neighbor topology overlapping coefficient and feature vector centrality analysis are introduced, and a time sequence dynamic graph is constructed to quantify the connection stability between node layers; a time sequence dynamic graph Fourier transform method is provided, brain function signals are mapped to a time-space-frequency three-dimensional joint domain through spectral decomposition of a time-varying graph Laplacian matrix, and a dynamic spectrogram is generated to analyze a multi-scale spatio-temporal evolution mode; a filter is designed to separate low-frequency (global coordination) and high-frequency (local mutation) components, and a function-structure dynamic constraint model is established. According to the method, an efficient and accurate quantification tool is provided for revealing a brain network dynamic recombination mechanism and neural adaptability changes.

Description

Technical Field

[0001] The present invention belongs to the technical field of neural signal processing and motion control analysis, and particularly relates to a method for quantitative analysis of brain networks based on Fourier transform of near-infrared signal time series dynamic graphs. Background Art

[0002] Functional Near-Infrared Spectroscopy (fNIRS) is a non-invasive brain function imaging technology based on the neurovascular coupling mechanism. It emits near-infrared light with a wavelength of 600-900 nm to penetrate the scalp tissue, and uses the difference in the light absorption characteristics of oxygenated hemoglobin (HbO) and deoxygenated hemoglobin (HbR) to monitor the hemodynamic response of the cerebral cortex in real time, thereby indirectly reflecting neuronal activity. This technology collects signals through a multi-channel near-infrared probe, and the light intensity attenuation data between the light source and the detector is solved as a time series curve of hemoglobin concentration by the Modified Beer-Lambert Law. Compared with functional magnetic resonance imaging (fMRI) and electroencephalogram (EEG), fNIRS has both high time resolution and spatial localization ability, and the device is portable and has strong anti-motion interference, and has been widely used in clinical brain function evaluation and motion control research.

[0003] Functional Connectivity (FC) characterizes the information interaction and cooperation mechanism between brain regions by quantifying the statistical correlation of time series in different brain regions. Although the traditional static functional connectivity analysis method is easy to operate, the static connectivity matrix based on the averaging hypothesis cannot analyze the time-varying characteristics of functional connectivity. Therefore, the Dynamic Functional Connectivity (DFC) analysis method emerged. Its core strategy is to generate a time-varying connectivity matrix sequence through a sliding time window to capture the dynamic reconstruction characteristics of the brain network. However, this method has inherent limitations: the selection of the window length needs to balance time resolution and statistical reliability, and it is not sensitive enough to sudden state transitions, which is likely to cause loss of dynamic information.

[0004] To break through the sliding window limitation, the DFC analysis method based on state clustering explores the network state transition characteristics related to diseases or aging by classifying time-varying connectivity matrices into a finite number of brain states. However, such methods have significant drawbacks: the global state templates they construct are difficult to accurately represent individual-specific dynamic patterns and ignore the regulatory role of state temporal evolution on cognitive functions. Further research has found that there is a strong coupling relationship between the spatio-temporal patterns of brain functional activities and their underlying structural networks. The functional network can be regarded as the macroscopic emergent state of the structural network, and graph signal processing technology provides a new paradigm for such structure-function correlation analysis. By abstracting brain regions as graph nodes and defining the white matter fiber bundle density as the edge weight, functional signals can be mapped to the time-varying attributes on the graph nodes. As a core tool, the Graph Fourier Transform (GFT) can decompose graph signals into low-frequency (global coordination) and high-frequency (local mutation) spectral components, and then analyze the frequency-domain characteristics of functional activities constrained by the structural network. However, the existing applications of GFT are mostly limited to static graph structure analysis and fail to effectively integrate the time dimension and dynamic graph topology evolution, resulting in insufficient analytical ability for the dynamic reconstruction mechanism of brain networks under time-varying tasks such as motor control. Summary of the Invention

[0005] To overcome the deficiencies of the prior art, the present invention provides a brain network quantitative analysis method based on near-infrared signal temporal dynamic graph Fourier transform. By integrating functional near-infrared spectroscopy (fNIRS) technology and temporal dynamic graph signal processing, this method solves the deficiencies of traditional static functional connectivity analysis and dynamic sliding window methods in spatio-temporal dynamic analysis ability, dynamic information capture, and structure-function coupling analysis. The specific technical solutions include: constructing a brain network based on fNIRS signals, optimizing time series alignment using the dynamic time warping algorithm, and dividing dynamic network time periods through adaptive K-Means clustering combined with the elbow method; introducing the neighbor topological overlap coefficient and eigenvector centrality analysis to construct a temporal dynamic graph to quantify the connection stability between node layers; proposing a temporal dynamic graph Fourier transform method, mapping brain functional signals to the three-dimensional joint domain of time-space-frequency through spectral decomposition of the time-varying graph Laplacian matrix, and generating a dynamic spectrogram to analyze multi-scale spatio-temporal evolution patterns; designing a graph filter to separate low-frequency (global coordination) and high-frequency (local mutation) components and establishing a functional-structure dynamic constraint model. The present invention breaks through the limitations of traditional static networks and single-time-scale analysis, significantly improving the physiological consistency of dynamic brain network division; realizing the dynamic quantitative coupling of brain region spectral energy and motor behavior parameters, and providing an efficient and accurate quantitative tool for revealing the dynamic reorganization mechanism of brain networks and neural adaptive changes.

[0006] The technical solutions adopted by the present invention to solve its technical problems are as follows:

[0007] Step 1: Construct a dynamic brain network based on fNIRS signals. By defining a brain activity signal matrix to represent the temporal activities of different brain regions, calculate the similarity of time series and construct a connection matrix. After window segmentation and connection threshold processing, generate an adjacency matrix A to form a graph structure describing brain region interactions;

[0008] Step 2: For the dynamic time-domain characteristics of brain region interactions, design an adaptive dynamic graph structure model. By real-time optimizing the underlying connection topology, capture the time-varying characteristics of the relationships between brain regions during the task process, and achieve the representation of dynamic network structures based on different task stages and subject states;

[0009] Step 3: After completing clustering and dynamic network partitioning, divide the dynamic evolution stage of the brain network through a sliding time window. Quantify the connection stability between node layers based on the neighbor topological overlap coefficient, and combine eigenvector centrality analysis, i.e., principal eigenvector decomposition, to construct a temporal dynamic graph;

[0010] Step 4: Adopt a spectral domain analysis method based on graph Fourier transform (GFT). By performing eigenvalue decomposition on the graph Laplacian matrix to construct graph Fourier bases, project brain function signals into the frequency domain space, and use eigenvalues to divide low-frequency, i.e., smooth correlations, and high-frequency, i.e., abrupt connection components, to achieve multi-scale spectral feature analysis of dynamic brain network signals;

[0011] Step 5: Adopt the temporal dynamic graph Fourier transform (TDGFT) method. By dynamically constructing the spectral decomposition basis functions of the time-varying graph Laplacian matrix, map brain function signals to the time-frequency joint domain to generate a dynamic spectrogram, and extract the main frequency energy features to reveal the spatio-temporal evolution patterns of key brain region activities;

[0012] Step 6: Perform multi-scale decomposition on brain function signals through graph filters. Use low-frequency components to represent global coordinated activities, high-frequency components to depict local dynamic changes, and combine brain network topological constraints to analyze the dynamic quantitative coupling between functional signals and structural connections.

[0013] Preferably, the specific content of Step 1 is as follows:

[0014] Step 1-1: Through data preprocessing, obtain the brain activity level values of each cortical region in different brain regions at each time point, and then define a brain activity signal matrix X ∈ R^(t×n), where the i-th row represents the brain activity at time point j; t represents the time period, and n represents the dimension of the sample, i.e., the number of features;

[0015] Step 1-2: Use the dynamic time warping (DTW) algorithm to optimize the time series through non-linear warping, and correct the non-stationary time lag caused by the dynamic switching of brain states; specify the use of a preset window for data segmentation, and calculate the corresponding DTW values to construct a connection matrix; perform thresholding on the calculated connection matrix to obtain an adjacency matrix.

[0016] Preferably, step 2 is specifically as follows:

[0017] Step 2-1: Optimize the K-Means clustering algorithm to segment the time series data;

[0018] Randomly select K initial center points, then assign each data point to the cluster center closest to it, and then calculate the new cluster center, that is, the mean value of all points within each cluster. Repeat this process until the cluster center no longer changes or reaches the preset number of iterations;

[0019] Use the square of the Euclidean distance to measure the distance:

[0020]

[0021] where x and y represent two different samples;

[0022] The K-Means algorithm is optimized to minimize the sum of squared errors within clusters SSE:

[0023]

[0024] where, μ (j) represents the center of cluster j; m represents the number of clusters; w (i,j) represents the binary indicator function, indicating whether the i-th sample point belongs to the j-th cluster; x (i) represents the i-th sample point; μ (j) represents the center of the j-th cluster;

[0025] Step 2-2: Use the cosine similarity as an index to measure the similarity of the connection strength of the connection matrix; the cosine similarity evaluates the similarity degree between two vectors by calculating the angle between them, and the value range is from -1 to 1. The closer to 1, the higher the similarity between the vectors;

[0026] Step 2-3: Calculate the similarity of the topological structure using the shortest path graph kernel;

[0027] For the isolated time points after clustering, that is, the points where neither the left nor the right neighboring points exist, re-cluster them into the category to which the adjacent time points belong to ensure the continuity and logic of the division;

[0028] Step 2-4: Use the elbow method to calculate the SSE under different K values, and finally obtain s uneven time periods with adaptive division.

[0029] Preferably, step 3 is specifically as follows:

[0030] Step 3-1: Use the neighbor topological overlap coefficient to quantify the interlayer connection relationship;

[0031] Neighbor topological overlap coefficient It is calculated by the following formula:

[0032]

[0033] where a ij (t), a ij (t + 1) are the elements in the adjacency matrices corresponding to the adjacent network layers G t and G t+1 respectively. If there is an edge between node i and node j in the network Gt, then a ij (t) = 1; otherwise a ij (t) = 0; and only when node j is both a neighbor node of node i in the network layer G t and a neighbor node in the network layer G t+1 at the same time, there is a ij (t)a ij (t + 1) = 1, and in other cases a ij (t)a ij (t + 1) = 0;

[0034] Step 3 - 2: Construct a matrix A from the connection relationships of the nodes within the time period t, and introduce the inter - layer connection relationship C; by using the eigenvalue decomposition method in linear algebra, calculate the principal eigenvector v of the matrix A; each element in the principal eigenvector v represents the centrality of the corresponding node in the network; finally, through the principal eigenvector v, obtain the eigenvector centrality c(i, t) of node i at the t - th time period.

[0035] Preferably, the specific content of step 4 is as follows:

[0036] The graph Laplacian matrix L is defined as:

[0037] L = D - A (4)

[0038] where D is the degree matrix, which is a diagonal matrix, and the diagonal elements are expressed as:

[0039] D i,j = ∑W i,j (5)

[0040] W i,j represents the weight of the edge connecting node i and j; A is the adjacency matrix, representing the connection relationship between nodes in the graph:

[0041] A i,j = W i,j (6) [[ID=,68]]

[0042] The graph Laplacian matrix L is a real - symmetric matrix, and all its eigenvalues are non - negative; perform eigenvalue decomposition on the graph Laplacian matrix L:

[0043] L = U ∧ U T (7)

[0044] where: U = [u0, u1, …, u N-1 is the eigenvector matrix, and u i is the i-th eigenvector; ∧ = diag(λ0, λ1, …, λ N-1 ) is the eigenvalue matrix, and λ i is the i-th eigenvalue, representing frequency. The eigenvector u i represents the eigenvector corresponding to λ i ;

[0045] For a graph signal f, its graph Fourier transform is defined as:

[0046]

[0047] where represents the change of the i-th component of the signal on the graph set; represents the conjugate complex number of the eigenvector u of the signal i at the i-th component; f(i) represents the value at the i-th node; N represents the number of nodes in the graph; the smallest eigenvalue λ0 is zero, representing the DC component of the signal. Therefore, the eigenvector u0 associated with the smallest eigenvalue is a constant and is equal to

[0048]

[0049]

[0050] Preferably, step 5 is specifically as follows:

[0051] Step 5-1: According to the dynamic underlying graph structure E(t) and the functional activity signal F(t) introducing temporal information, construct the temporal dynamic graph G(t); for each time period t, calculate the graph Laplacian matrix L(t), and perform eigenvalue decomposition to obtain its eigenvector matrix U(t) and eigenvalue matrix ∧(t);

[0052] Step 5-2: Perform graph Fourier transform on the temporal dynamic graph for each time period t to obtain the graph Fourier transform coefficients for each time period; use the divided time periods to combine the graph Fourier coefficients of all time periods to construct a dynamic frequency spectrum graph; extract the spectral component with the highest content from the dynamic frequency spectrum graph, and for each main spectral component, extract the corresponding brain region energy value after restoration.

[0053] Preferably, step 6 is specifically as follows:

[0054] ​Step 6-1: By selecting spectral components within a specific frequency range, the low-frequency and high-frequency parts of the signal are separated;

[0055] The low-frequency graph filter retains spectral components with eigenvalues less than the threshold λ < λ i and sets the remaining components to zero, which is defined as follows:

[0056]

[0057] where U base represents the graph Fourier transform basis matrix; H low represents the diagonal low-frequency filtering matrix; represents the conjugate transpose of U base which transforms the graph signal from the node domain to the frequency domain; f (t) represents the original graph signal at time t;

[0058] The high-frequency graph filter retains spectral components with eigenvalues greater than the threshold λ > λ h and sets the remaining components to zero, which is defined as follows:

[0059]

[0060] where H high represents the diagonal high-frequency filtering matrix, sets the diagonal elements corresponding to the desired frequency modes to 1, and the remaining modes to 0; and represent the low-frequency and high-frequency parts of the signal respectively;

[0061] Step 6-2: By calculating the energy value of the low-frequency signal, the constraint value of the structural network on the functional activity is obtained; The low-frequency energy value is calculated by the formula:

[0062]

[0063] where is the value of the low-frequency signal at node i.

[0064] The beneficial effects of the present invention are as follows:

[0065] Compared with the prior art, the present invention not only realizes the joint analysis of the spatio-temporal-frequency three-dimensional dynamic spectral features of brain functional signals through the time-sequence dynamic graph Fourier transform, breaking through the analysis limitations of traditional methods on static networks and single time scales, but also significantly improves the dynamic brain network partitioning through adaptive graph structure modeling and topological continuity optimization; At the same time, it innovatively establishes a dynamic quantitative coupling between brain region spectral energy and movement behavior parameters, and realizes the collaborative optimization of computational efficiency and noise suppression ability with the help of graph filters. Specifically:

[0066] 1. Through the Temporal Dynamic Graph Fourier Transform (TDGFT) method, for the first time, brain functional signals are mapped to the three-dimensional joint domain of time-space-frequency, breaking through the limitation of traditional graph signal processing that only focuses on static topology or a single time point. The dynamic spectrogram can simultaneously depict the local high-frequency mutations (such as task responses) and global low-frequency coordination (such as resting-state networks) of brain region activities, providing a multi-scale observation window for the dynamic reorganization mechanism of brain networks.

[0067] 2. An adaptive dynamic graph structure model is introduced, combined with K-Means clustering optimization and topological continuity constraints, effectively eliminating the interference of isolated time points on network partitioning. In addition, based on the quantification of inter-layer stability using the neighbor topological overlap coefficient, the robust identification of the functional hub properties of key brain regions is enhanced.

[0068] 3. By designing a structure-functional dynamic constraint model, for the first time, the quantitative correlation between the spatio-temporal spectral energy of the brain network and the force level during a movement task is realized. A graph filter is used to separate task-related frequency bands, reducing the computational complexity compared to traditional fixed-frequency band filtering methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is a flowchart of the method of the present invention;

[0070] Figure 2 is a schematic diagram of the fNIRS signal acquisition device and headcap configuration of the present invention, (a) experimental paradigm, (b) motion visual feedback interface;

[0071] Figure 3 is a spectrogram of the temporal dynamic graph Fourier transform of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0072] The present invention will be further described below in conjunction with the drawings and embodiments.

[0073] The present invention proposes a method for quantitative analysis of brain networks based on the Temporal Dynamic Graph Fourier Transform (TDGFT) of near-infrared signals. By fusing the time dimension and dynamic graph topology, the joint analysis of the spatio-temporal spectral characteristics of brain networks is realized. Compared with traditional GFT, the advantages of TDGFT are reflected in three aspects: First, a time-varying Laplacian matrix is introduced to construct dynamic graph basis functions, mapping brain region functional signals to the spatio-temporal joint frequency domain; Second, a graph filter is designed to separate task-related frequency bands; Third, a structure-functional dynamic constraint model is established. Through the TDGFT method, the present invention realizes the dynamic quantitative coupling of the spatio-temporal spectral energy of the brain network and the force level during a movement task for the first time, providing a new quantitative perspective for clarifying the neuroadaptive changes in the brain.

[0074] The technical solutions adopted by the present invention to solve its technical problems are as follows:

[0075] Step 1: Construct a dynamic brain network based on fNIRS signals. By defining a brain activity signal matrix to represent the temporal activities of different brain regions, calculate the similarity of time series and construct a connection matrix. After window segmentation and connection threshold processing, generate an adjacency matrix A to form a graph structure describing brain region interactions.

[0076] Step 1.1: Through data preprocessing, the brain activity level values of each cortical region in different brain regions at each time point are obtained. Then, a brain activity signal matrix X∈R^(t×n) is defined, where the i-th row represents the brain activity at time point j.

[0077] Step 1.2: The present invention uses the Dynamic Time Warping (DTW) algorithm to optimize time series through non-linear warping, correcting the non-stationary time lag caused by the dynamic switching of brain states. The present invention specifies the use of a specific window for data segmentation and calculates the corresponding DTW values to construct a connection matrix. Threshold processing is performed on the calculated connection matrix to obtain an adjacency matrix.

[0078] Step 2: The present invention designs an adaptive dynamic graph structure model for the dynamic time domain characteristics of brain region interactions. By real-time optimizing the underlying connection topology, capture the time-varying characteristics of the relationships between brain regions during the task process, and realize the dynamic network structure representation based on different task stages and subject states.

[0079] Step 2.1: To ensure the accuracy and stability of the clustering results, the present invention optimizes the K-Means clustering algorithm to segment time series data. Randomly select K initial center points, then assign each data point to the cluster center closest to it, and then calculate the new cluster center (i.e., the mean of all points within each cluster). Repeat this process until the cluster center no longer changes significantly or reaches the preset number of iterations.

[0080] The commonly used distance metric standard is the square of the Euclidean distance:

[0081]

[0082] where x and y represent two different samples, and n represents the dimension of the samples (the number of features).

[0083] The K-Means algorithm is optimized to minimize the within-cluster sum of squared errors (SSE).

[0084]

[0085] where, μ (j)Represents the center of cluster j.

[0086] Step 2.2: To ensure that the clustering results can reflect the actual connection strength between brain regions, the present invention uses cosine similarity as an index to measure the similarity of the connection strength of the connection matrix. Cosine similarity evaluates the similarity between two vectors by calculating the angle between them, and the value ranges from -1 to 1. A value close to 1 indicates a higher similarity between the vectors.

[0087] Step 2.3: To consider the graph topological characteristics of the brain network, the present invention adopts the Graph Kernel for Shortest Paths to calculate the similarity of the topological structure. For the isolated time points after clustering (i.e., the points where neither their left nor right neighboring points exist), the present invention re-clusters them into the categories to which the adjacent time points belong to ensure the continuity and logic of the division. Ensuring the continuity of the clustering results can more accurately reflect the dynamic change process of brain region activities and avoid analysis breaks caused by isolated points.

[0088] Step 2.4: To determine the optimal K value, the present invention adopts the Elbow Method and calculates the SSE under different K values. Through these constraints and processes, the optimized K-Means can effectively divide the dynamic process, and finally obtain s non-uniform time periods with adaptive division.

[0089] Step 3: After completing clustering and dynamic network division, the present invention divides the dynamic evolution stage of the brain network through a sliding time window, quantifies the connection stability between node layers based on the neighbor topological overlap coefficient, and constructs a temporal dynamic graph by combining eigenvector centrality analysis (principal eigenvector decomposition).

[0090] Step 3.1: The present invention uses the neighbor topological overlap coefficient to quantify the inter-layer connection relationship. The neighbor topological overlap coefficient can be calculated by the following formula:

[0091]

[0092] where a ij (t), a ij (t + 1) are the elements in the adjacency matrices corresponding to the adjacent network layers G t and G t+1 respectively. If there is an edge between node i and node j in the network Gt, then a ij (t) = 1; otherwise a ij (t) = 0; and only when node j is both a neighbor node of node i in the network layer G t and a neighbor node in the network layer G t+1 , there is a ij(t)a ij (t + 1) = 1, a in other cases ij (t)a ij (t + 1) = 0.

[0093] Step 3.2: Construct a matrix A from the connection relationships of the nodes within the network layer (t), and introduce the inter-layer connection relationship C. By using the eigenvalue decomposition method in linear algebra, calculate the principal eigenvector v of matrix A. Each element in this eigenvector represents the centrality of the corresponding node in the network. Finally, through the vector v, we can obtain the eigenvector centrality c(i, t) of node i at the t-th time period..

[0094] Step 4: The present invention proposes a spectral domain analysis method based on Graph Fourier Transform (GFT). By performing eigenvalue decomposition on the graph Laplacian matrix to construct the graph Fourier basis, project the brain functional signals into the frequency domain space, and use the eigenvalues to divide the low-frequency (smooth correlation) and high-frequency (abrupt connection) components to achieve multi-scale spectral feature analysis of dynamic brain network signals.

[0095] The graph Laplacian matrix L is the core tool for graph signal analysis and is defined as:

[0096] L = D - A (4)

[0097] where D is the degree matrix, which is a diagonal matrix, and the diagonal elements are expressed as:

[0098] D i,j = ∑W i,j (5)

[0099] A is the adjacency matrix, representing the connection relationships between the nodes in the graph:

[0100] A i,j = W i,j (6)

[0101] The graph Laplacian matrix L is a real symmetric matrix, and all its eigenvalues are non-negative. The graph Laplacian matrix L can be eigen-decomposed:

[0102] L = U∧U T (7)

[0103] where: U = [u0, u1,..., u N-1 is the eigenvector matrix, u i is the i-th eigenvector; ∧ = diag(λ0, λ1,..., λ N-1 ) is the eigenvalue matrix, λ i is the i-th eigenvalue, representing the frequency, and the eigenvector u i represents λ iThe corresponding eigenvector.

[0104] For a graph signal f, its graph Fourier transform is defined as:

[0105]

[0106] where represents the change of the i-th component of the signal on the graph set; represents the eigenvector u of the signal i the conjugate complex number of the i-th component; f(i) represents the value at the i-th node; N represents the number of nodes in the graph; the smallest eigenvalue λ0 is zero, representing the DC component of the signal. Therefore, the eigenvector u0 associated with the smallest eigenvalue is a constant and is equal to

[0107] Correspondingly, the inverse graph Fourier transform converts the frequency-domain signal back to the node domain and is defined as follows:

[0108]

[0109] Step 5: The present invention proposes a Temporal Dynamic Graph Fourier Transform (TDGFT) method. By dynamically constructing the spectral decomposition basis function of the time-varying graph Laplacian matrix, the brain functional signal is mapped to the time-frequency joint domain to generate a dynamic spectrogram, and the main frequency energy feature is extracted to reveal the spatio-temporal evolution pattern of the key brain region activities.

[0110] Step 5.1: According to the dynamic underlying graph structure E(t) and the functional activity signal F(t) introducing temporal information, construct the temporal dynamic graph G(t). For each time segment t, calculate the graph Laplacian matrix L(t), and perform eigen-decomposition to obtain its eigenvector matrix U(t) and eigenvalue matrix ∧(t).

[0111] Step 5.2: Perform the graph Fourier transform on the temporal dynamic graph of each time segment t to obtain the graph Fourier transform coefficients of each time segment. Using the divided time periods, combine the graph Fourier coefficients of all time segments to construct a dynamic spectrogram. Extract the spectral component with the highest content from the dynamic spectrogram. For each main spectral component, restore and extract the corresponding brain region energy value.

[0112] Step 6: The present invention performs multi-scale decomposition on the brain functional signal by designing a graph filter, uses the low-frequency component to characterize the global coordinated activity (low-threshold truncation of eigenvalues), the high-frequency component to depict the local dynamic changes, and combines the brain network topology constraints to analyze the dynamic quantitative coupling between the functional signal and the structural connection.

[0113] Step 6.1: By selecting the spectral components within a specific frequency range, the low-frequency and high-frequency parts of the signal are separated. The low-frequency graph filter retains the spectral components with eigenvalues less than the threshold λ < λ l , and sets the remaining components to zero. It is defined as follows:

[0114]

[0115] The high-frequency graph filter retains the spectral components with eigenvalues greater than the threshold λ > λ h , and sets the remaining components to zero. It is defined as follows:

[0116]

[0117] where, H high represents the diagonal high-frequency filtering matrix, sets the diagonal elements corresponding to the desired frequency pattern to 1, and the remaining patterns to 0; and represent the low-frequency and high-frequency parts of the signal respectively.

[0118] Step 6.2: By calculating the energy value of the low-frequency signal, the constraint value of the structural network on the functional activity can be obtained. The low-frequency energy value is calculated as follows:

[0119]

[0120] where, is the value of the low-frequency signal at node i.

[0121] Example:

[0122] The present invention provides a brain network quantization analysis method based on near-infrared signal temporal dynamic graph Fourier transform, which combines time information and dynamic underlying graph structure, captures the dynamic changes of graph signals in time and space, and evaluates the dynamic changes of brain region energy and the degree of constraint of the brain structure network on functional activities in different tasks, as Figure 1 shown.

[0123] To achieve the above object of the present invention, the following technical solutions are adopted:

[0124] Step 1: Based on the fNIRS signal, a dynamic brain network is constructed. By defining the brain activity signal matrix to represent the temporal activities of different brain regions, calculating the time series similarity and constructing the connection matrix, and through window segmentation and connection threshold processing, the adjacency matrix A is generated to form a graph structure describing the interaction of brain regions.

[0125] Step 1.1: Exemplarily, use a multi-channel functional near-infrared spectroscopy (fNIRS) system to collect fNIRS signals at wavelengths of 730 nm and 850 nm with a sampling rate of 11 Hz. Collect cerebral blood oxygen signals during the isometric contraction of the elbow joint of 32 subjects, using a total of 30 channels covering 6 brain regions. The collection process is as Figure 2 shown.

[0126] Step 1.2: Preprocess the fNIRS signals, and apply the modified Beer-Lambert law to convert the original fNIRS signals into hemodynamic signals. Each fNIRS channel generates oxygenated hemoglobin concentration signals and deoxygenated hemoglobin concentration signals.) Concentration signals. Since the HbO signal shows a better signal-to-noise ratio, the HbO signal is selected as the key marker for evaluating cortical activation, and the task-related HbO concentration is calculated.

[0127] Step 1.3: Apply band-pass filtering to the original fNIRS signals, with the frequency range set to 0.01 Hz to 0.2 Hz. Effectively remove high-frequency noise (such as heartbeat and breathing) and low-frequency drift (such as motion artifacts).

[0128] Step 1.4: Through data preprocessing, the brain activity level values of each cortical region in different brain regions at each time point are obtained, and then a brain activity signal matrix X∈R^(165×6) is defined.

[0129] Step 1.5: Use a window of size 5 for data segmentation and calculate the corresponding DTW values to construct a connection matrix.

[0130] Step 1.6: To simplify the graph structure, threshold the calculated connection matrix and only retain the strongest 30% of the connections to obtain an adjacency matrix.

[0131] Step 2: The present invention designs an adaptive dynamic graph structure model for the dynamic time-domain characteristics of brain region interactions, captures the time-varying characteristics of the relationships between brain regions during the task process by real-time optimizing the underlying connection topology, and realizes the dynamic network structure representation based on different task stages and subject states.

[0132] Step 2.1: Randomly select K initial center points, then assign each data point to the cluster center closest to it, and then calculate the new cluster center (i.e., the mean of all points within each cluster), and repeat this process until the cluster center no longer changes significantly or reaches the preset number of iterations.

[0133] The commonly used distance metric standard is the square of the Euclidean distance:

[0134]

[0135] Among them, x and y represent two different samples, and n represents the dimension of the samples (the number of features).

[0136] The K-Means algorithm optimizes to minimize the within-cluster sum of squared errors (SSE).

[0137]

[0138] Among them, μ (j) represents the center of cluster j; m represents the number of clusters; w (i,j) represents the binary indicator function, indicating whether the i-th sample point belongs to the j-th cluster; x (i) represents the i-th sample point; μ (j) represents the center of the j-th cluster.

[0139] Step 2.2: To ensure that the clustering results can reflect the actual connection strength between brain regions, the present invention uses the cosine similarity as an index to measure the similarity of the connection strength of the connection matrix.

[0140] Step 2.3: The Graph Kernel for Shortest Paths is used to calculate the similarity of the topological structure.

[0141] Step 2.4: Through these constraints and processes, the optimized K-Means can effectively divide the dynamic process, and finally obtain s uneven time periods with adaptive division.

[0142] In this embodiment, by applying the elbow method, the influence of different numbers of clusters (K) on the within-cluster variance SSE is studied. The results show that the optimal number of clusters is K = 2. When K = 2, the within-cluster variance decreases significantly, while when the value of K continues to increase, the decrease in the variance is significantly reduced.

[0143] Step 3: After completing clustering and dynamic network division, the dynamic evolution stage of the brain network is divided by a sliding time window, the connection stability between node layers is quantified based on the neighbor topological overlap coefficient, and a temporal dynamic graph is constructed by combining eigenvector centrality analysis (principal eigenvector decomposition).

[0144] Step 3.1: The neighbor topological overlap coefficient is used to quantify the inter-layer connection relationship. The neighbor topological overlap coefficient can be calculated by the following formula:

[0145]

[0146] Among them, a ij (t), a ij (t + 1) are the adjacent network layers Gt , G t+1 For the elements in the corresponding adjacency matrix, if there is an edge between node i and node j in network Gt, then a ij (t) = 1; otherwise a ij (t) = 0; and only when node j is both a neighbor node of node i in network layer G t and a neighbor node in network layer G t+1 , there is a ij (t)a ij (t + 1) = 1, and in other cases a ij (t)a ij (t + 1) = 0.

[0147] Step 3.2: Construct matrix A from the connection relationships of nodes within network layer (t), and introduce the inter-layer connection relationship C. By using the eigenvalue decomposition method in linear algebra, calculate the principal eigenvector v of matrix A. Each element in this eigenvector represents the centrality of the corresponding node in the network. Finally, through vector v, we can obtain the eigenvector centrality c(i, t) of node i at the t-th time period.

[0148] Step 4: Construct the graph Fourier basis by performing eigenvalue decomposition on the graph Laplacian matrix, project the brain functional signals into the frequency domain space, and use the eigenvalues to divide the low-frequency (smooth correlation) and high-frequency (abrupt connection) components to achieve multi-scale spectral feature analysis of dynamic brain network signals.

[0149] The graph Laplacian matrix L is the core tool for graph signal analysis and is defined as:

[0150] L = D - A (4)

[0151] where D is the degree matrix, which is a diagonal matrix, and the diagonal elements are expressed as:

[0152] D i,j = ∑W i,j (5)

[0153] W i,j represents the weight of the edge connecting nodes i and j; A is the adjacency matrix, representing the connection relationships between nodes in the graph:

[0154] A i,j = W i,j (6)

[0155] The graph Laplacian matrix L is a real symmetric matrix, and all its eigenvalues are non-negative. The graph Laplacian matrix L can be eigen-decomposed:

[0156] L = U∧U T (7)

[0157] where: U = [u0, u1, …, u N-1 is the eigenvector matrix, and u i is the i-th eigenvector; ∧ = diag(λ0, λ1, …, λ N-1 ) is the eigenvalue matrix, and λ i is the i-th eigenvalue, representing the frequency. The eigenvector u i represents the eigenvector corresponding to λ i .

[0158] For a graph signal f, its graph Fourier transform is defined as:

[0159]

[0160] where represents the change of the i-th component of the signal on the graph set; represents the conjugate complex number of the eigenvector u of the signal at the i-th component; f(i) represents the value at the i-th node; N represents the number of nodes in the graph; the smallest eigenvalue λ0 is zero, representing the DC component of the signal. Therefore, the eigenvector u0 associated with the smallest eigenvalue is a constant and is equal to i at each vertex.

[0161] Correspondingly, the inverse graph Fourier transform converts the frequency-domain signal back to the node domain and is defined as follows:

[0162]

[0163] Step 5: By dynamically constructing the spectral decomposition basis functions of the time-varying graph Laplacian matrix, map the brain functional signals to the time-frequency joint domain to generate a dynamic spectrogram, and extract the dominant frequency energy features to reveal the spatio-temporal evolution pattern of the key brain region activities.

[0164] Step 5.1: According to the dynamic underlying graph structure E(t) and the functional activity signal F(t) introducing temporal information, construct the temporal dynamic graph G(t). For each time segment t, calculate the graph Laplacian matrix L(t), and perform eigen-decomposition to obtain its eigenvector matrix U(t) and eigenvalue matrix ∧(t).

[0165] Step 5.2: Perform the graph Fourier transform on the temporal dynamic graph for each time segment t to obtain the graph Fourier transform coefficients of each time segment. Using the divided time periods, combine the graph Fourier coefficients of all time segments to construct a dynamic spectrogram. Extract the spectral component with the highest content from the dynamic spectrogram. For each main spectral component, extract the corresponding brain region energy value after restoration.

[0166] Step 6: Multiscale decomposition of the brain functional signals is performed by designing graph filters. The global coordination activities are characterized by the low-frequency components (low-threshold truncation of eigenvalues), and the local dynamic changes are depicted by the high-frequency components. The cross-frequency coupling mechanism between the functional signals and the structural connections is analyzed by combining the topological constraints of the brain network.

[0167] Step 6.1: By selecting the spectral components within a specific frequency range, the low-frequency and high-frequency parts of the signal are separated. The low-frequency graph filter retains the spectral components with eigenvalues less than the threshold λ < λ l , and sets the remaining components to zero. Its definition is as follows:

[0168]

[0169] where U base represents the graph Fourier transform basis matrix; H low represents the diagonal low-frequency filtering matrix; represents the conjugate transpose of U base , which transforms the graph signal from the node domain to the frequency domain; f (t) represents the original graph signal at time t.

[0170] The high-frequency graph filter retains the spectral components with eigenvalues greater than the threshold λ > λ h , and sets the remaining components to zero. Its definition is as follows:

[0171]

[0172] where H high represents the diagonal high-frequency filtering matrix, with the diagonal elements corresponding to the desired frequency modes set to 1 and the remaining modes set to 0; and represent the low-frequency and high-frequency parts of the signal, respectively.

[0173] Step 6.2: By calculating the energy value of the low-frequency signal, the constraint value of the structural network on the functional activity can be obtained. The formula for the low-frequency energy value is:

[0174]

[0175] where is the value of the low-frequency signal at node i.

[0176] In this embodiment, the diagonal elements corresponding to the desired frequency modes are set to 1, and the remaining modes are set to 0.

[0177] Compared with traditional fNIRS signal processing methods, in the present invention, through the time-sequence dynamic graph Fourier transform signal processing method, the signal activation results are divided from the traditional spectral results into six different frequency bands from low frequency to high frequency, so as to identify the dual information of time and frequency in the movement task, and can more finely capture the instantaneous change characteristics of brain regions during task execution, such as Figure 3 as shown

Claims

1. A brain network quantization analysis method based on Fourier transform of near-infrared signal temporal dynamic graph, characterized in that, It includes the following steps: Step 1: Construct a dynamic brain network based on fNIRS signals. By defining a brain activity signal matrix to represent the temporal activities of different brain regions, calculate the similarity of time series and construct a connection matrix. After window segmentation and connection threshold processing, generate an adjacency matrix A to form a graph structure describing brain region interactions. Step 2: For the dynamic time-domain characteristics of brain region interactions, design an adaptive dynamic graph structure model. By optimizing the underlying connection topology in real time, capture the time-varying characteristics of the relationships between brain regions during the task process, and realize the representation of dynamic network structures based on different task stages and subject states. Step 3: After completing clustering and dynamic network partitioning, divide the dynamic evolution stage of the brain network through a sliding time window. Quantify the connection stability between node layers based on the neighbor topological overlap coefficient, and combine eigenvector centrality analysis, i.e., principal eigenvector decomposition, to construct a temporal dynamic graph. Step 4: Adopt a spectral domain analysis method based on graph Fourier transform (GFT). By performing eigenvalue decomposition on the graph Laplacian matrix to construct graph Fourier bases, project brain function signals into the frequency domain space, and use eigenvalues to divide low-frequency, i.e., smooth correlations, and high-frequency, i.e., abrupt connection components, to achieve multi-scale spectral feature analysis of dynamic brain network signals. Step 5: Adopt the temporal dynamic graph Fourier transform (TDGFT) method. By dynamically constructing the spectral decomposition basis function of the time-varying graph Laplacian matrix, map brain function signals to the time-frequency joint domain to generate a dynamic spectrogram, and extract the main frequency energy features to reveal the spatio-temporal evolution pattern of key brain region activities. Step 6: Perform multi-scale decomposition on brain function signals through a graph filter. Use low-frequency components to represent global coordinated activities, high-frequency components to depict local dynamic changes, and combine brain network topological constraints to analyze the dynamic quantitative coupling between functional signals and structural connections.

2. According to the method for quantitative analysis of a brain network based on temporal dynamic graph Fourier transform of near-infrared signals as described in claim 1, the specific content of step 1 is as follows: Step 1-1: Through data preprocessing, obtain the brain activity level values of each cortical region in different brain regions at each time point, and then define a brain activity signal matrix \(X\in R^{t\times n}\), where the \(i\)-th row represents the brain activity at time point \(j\); \(t\) represents the time period, and \(n\) represents the dimension of the sample, i.e., the number of features. Step 1-2: Use the dynamic time warping (DTW) algorithm to optimize the time series through non-linear warping to correct the non-stationary time lag caused by the dynamic switching of brain states. Specify the use of a preset window for data segmentation, and calculate the corresponding DTW values to construct a connection matrix. Perform thresholding processing on the calculated connection matrix to obtain an adjacency matrix.

3. According to the method for quantitative analysis of a brain network based on temporal dynamic graph Fourier transform of near-infrared signals as described in claim 2, the specific content of step 2 is as follows: Step 2-1: Optimize the K-Means clustering algorithm to segment time series data. Randomly select \(K\) initial center points, then assign each data point to the cluster center closest to it, and then calculate the new cluster center, i.e., the mean of all points within each cluster. Repeat this process until the cluster center no longer changes or reaches the preset number of iterations. Use the square of the Euclidean distance to measure the distance: where x and y represent two different samples; The K-Means algorithm optimizes to minimize the sum of squared errors within clusters SSE: Among them, μ (j) represents the center of cluster j; m represents the number of clusters; w (i,j) represents a binary indicator function indicating whether the i-th sample point belongs to the j-th cluster; x (i) represents the i-th sample point; μ (i) represents the center of the j-th cluster; Step 2-2: Use cosine similarity as an index to measure the similarity of the connection strength of the connection matrix; Cosine similarity evaluates the similarity between two vectors by calculating the angle between them, and the value ranges from -1 to 1, and a value close to 1 indicates a higher similarity between the vectors; Step 2-3: Use the shortest path graph kernel to calculate the similarity of the topological structure; For the isolated time points after clustering, that is, the points where neither their left nor right neighboring points exist, re-cluster them into the categories to which the adjacent time points belong to ensure the continuity and logic of the division; Step 2-4: Use the elbow method to calculate the SSE under different K values, and finally obtain s uneven time periods with adaptive division.

4. A method for quantitative analysis of brain networks based on near-infrared signal time-series dynamic graph Fourier transform according to claim 3, wherein the specific steps of step 3 are as follows: Step 3-1: Use the neighbor topological overlap coefficient to quantify the inter-layer connection relationship; Neighbor topological overlap coefficient Calculated by the following formula: where a ij (t), a ij (t + 1) are the elements in the adjacency matrices corresponding to adjacent network layers G t and G t+1 respectively. If there is an edge between node i and node j in network Gt, then a ij (t) = 1; otherwise a ij (t) = 0; and only when node j is both a neighbor node of node i in network layer G t and a neighbor node in network layer G t+1 , then a ij (t)a ij (t + 1) = 1, and in other cases a ij (t)a ij (t + 1) = 0; Step 3-2: Construct a matrix A for the connection relationship of nodes within the time period t, and introduce the inter-layer connection relationship C; By using the eigenvalue decomposition method in linear algebra, calculate the principal eigenvector v of matrix A; Each element in the principal eigenvector v represents the centrality of the corresponding node in the network; Finally, through the principal eigenvector v, obtain the eigenvector centrality c(i,t) of node i at the t-th time period.

5. A method for quantitative analysis of brain networks based on near-infrared signal time-series dynamic graph Fourier transform according to claim 4, wherein the specific steps of step 4 are as follows: The graph Laplacian matrix L is defined as: L = D - A (4) where D is the degree matrix, which is a diagonal matrix, and the diagonal elements are expressed as: D i,j = ∑W i,j (5) W i,j represents the weight of the edge connecting nodes i and j; A is the adjacency matrix, representing the connection relationship between nodes in the graph: A i,j = W i,j (6) The graph Laplacian matrix L is a real symmetric matrix, and all its eigenvalues are non-negative; Perform eigenvalue decomposition on the graph Laplacian matrix L: L = U ∧ U T (7) Among them: U = [u0, u1, …, u N-1 is the eigenvector matrix, and u i is the i-th eigenvector; ∧ = diag(λ0, λ1, …, λ N-1 ) is the eigenvalue matrix, and λ i is the i-th eigenvalue, representing the frequency, and the eigenvector u i represents the eigenvector corresponding to λ i . For a graph signal f, its graph Fourier transform is defined as: Among them, represents the change of the i-th component of the signal on the atlas; represents the signal eigenvector u i in the conjugate complex number of the i-th component; f(i) represents the value at the i-th node; N represents the number of nodes in the graph; the smallest eigenvalue λ0 is zero, representing the DC component of the signal. Therefore, the eigenvector u0 associated with the smallest eigenvalue is a constant and is equal to Correspondingly, the inverse graph Fourier transform converts the frequency-domain signal back to the node domain and is defined as follows:

6. A method for quantitative analysis of brain networks based on near-infrared signal time-series dynamic graph Fourier transform according to claim 5, wherein the specific steps of step 5 are as follows: Step 5-1: Construct a temporal dynamic graph G(t) based on the dynamic underlying graph structure E(t) and the functional activity signal F(t) introducing temporal information; for each time period t, calculate the graph Laplacian matrix L(t) and perform eigen-decomposition to obtain its eigenvectors Matrix U(t) and eigenvalue matrix ∧(t); Step 5-2: Perform graph Fourier transform on the time-series dynamic graph of each time period t to obtain the graph Fourier transform coefficients of each time period; Use the divided time periods to combine the graph Fourier coefficients of all time periods to construct a dynamic spectrum graph; Extract the spectrum component with the highest content from the dynamic spectrum graph, and for each main spectrum component, extract the corresponding brain region energy value after reduction.

7. A method for quantitative analysis of brain networks based on near-infrared signal time-series dynamic graph Fourier transform according to claim 6, wherein the specific steps of step 6 are as follows: Step 6-1: Separate the low-frequency and high-frequency parts of the signal by selecting the spectrum components within a specific frequency range; The low-frequency graph filter retains the spectral components with eigenvalues less than the threshold λ < λ i and sets the remaining components to zero, which is defined as follows: Among them, U base represents the graph Fourier transform basis matrix; H low represents the diagonal low-frequency filtering matrix; represents the conjugate transpose of U base which transforms the graph signal from the node domain to the frequency domain; f (t) represents the original graph signal at time t; The high-frequency graph filter retains the spectral components whose eigenvalues are greater than the threshold value λ > λ h and sets the remaining components to zero, which is defined as follows: Among them, H high represents a diagonal high-frequency filtering matrix, where the diagonal elements corresponding to the required frequency pattern are set to 1 and the remaining patterns are set to 0; and respectively represent the low-frequency and high-frequency parts of the signal; Step 6-2: Obtain the constraint value of the structural network on functional activities by calculating the energy value of the low-frequency signal; low-frequency energy value The calculation formula is as follows: Among them, is the value of the low-frequency signal at node i.

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