Brain function activity nonlinear modeling method and system and storage medium

Abstract

The invention provides a brain functional activity nonlinear modeling method and system and a storage medium, and relates to the technical field of functional magnetic resonance imaging data analysis, and the method comprises the steps: dividing a BOLD signal of a cerebral cortex in a task period into a plurality of task segments, and respectively mapping the BOLD signal to a group level unit spherical manifold and an individual level unit spherical manifold; obtaining a distance matrix between the BOLD signals according to the group horizontal unit spherical manifold; performing dimension reduction processing on the group horizontal unit spherical manifold according to the distance matrix, and distributing a functional neighborhood for each cerebral cortex vertex according to a low-dimensional embedded manifold obtained by the dimension reduction processing; and according to the average signal corresponding to the functional neighborhood, determining local synchronism measurement of the vertex of the cerebral cortex, and according to the local synchronism measurement, obtaining a related functional activation map of the cerebral cortex. According to the method, distance calculation and manifold learning are carried out on the group horizontal unit spherical manifold, so that the capacity of capturing nonlinear features of the brain function activity is enhanced, and the modeling precision of the brain function activity is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of functional magnetic resonance imaging data analysis, in particular to a brain function activity nonlinear modeling method, system and storage medium. BACKGROUND

[0002] As an important tool for studying brain function, functional magnetic resonance imaging technology needs to collect and continuously acquire blood oxygen level dependent signals (BOLD signals) at tens of thousands of brain region sites for hundreds of time points, indirectly reflect neuron activity by measuring blood oxygen level dependent signals, and on this basis, generally use a common linear model to simplify the relationship between task stimulation and blood oxygen level dependent signals as a linear convolution process to achieve linear modeling of brain function activity.

[0003] In related technologies, due to the existence of nonlinear response characteristics in brain neural activity, such as task dependence, context regulation and complex dynamic characteristics such as cross-brain region asynchronous cooperation, modeling based on linear modeling cannot effectively represent these nonlinear response characteristics. In addition, the blood oxygen level dependent signal has characteristics such as high dimension, high coupling and low signal-to-noise ratio, and the linear model is difficult to fully reveal the potential low-dimensional geometric structure, which comprehensively leads to the lack of the ability of the existing linear model to accurately model brain function activity. SUMMARY

[0004] The problem solved by the present application is how to improve the accuracy of modeling brain function activity.

[0005] To solve the above problems, the present application provides a brain function activity nonlinear modeling method, system and storage medium.

[0006] In a first aspect, a brain function activity nonlinear modeling method of the present application comprises: acquiring fMRI data of the brain cortex in a task cycle, the fMRI data comprising BOLD signals of each time frame in the task cycle for each brain cortex vertex in the brain cortex; dividing the BOLD signals into a plurality of task segments, and mapping the BOLD signals corresponding to each task segment into a group-level unit spherical manifold and an individual-level unit spherical manifold, respectively; performing distance calculation according to the group-level unit spherical manifold to obtain a distance matrix between each BOLD signal and other BOLD signals; performing manifold learning dimension reduction processing on the group-level unit spherical manifold according to the distance matrix to obtain a low-dimensional embedded manifold, and assigning a functional neighborhood to each brain cortex vertex according to the low-dimensional embedded manifold; determining, from the individual-level unit sphere manifold, average signals corresponding to the functional neighborhood of each of the brain cortical vertices; determining, from the average signals, local synchrony metrics of each of the brain cortical vertices; obtaining, from the local synchrony metrics of all the brain cortical vertices, a relevant functional activation map of the brain cortex during the task cycle.

[0007] Optionally, the dividing the BOLD signals into a plurality of task segments and mapping the BOLD signals corresponding to each of the task segments into a group-level unit sphere manifold and an individual-level unit sphere manifold respectively comprises: determining, according to a preset task design, all tasks included in the task cycle, each of the tasks corresponding to a task segment; preprocessing the BOLD signals to obtain group-level BOLD signals and individual-level BOLD signals; extracting time series of the BOLD signals of each of the brain cortical vertices in each of the task segments at the group level and the individual level respectively to obtain original vectors of each of the task segments at the group level and the individual level respectively; normalizing the original vectors corresponding to the group level and the individual level respectively to obtain unit sphere vectors corresponding to the group level and the individual level respectively, and obtaining the group-level unit sphere manifold and the individual-level unit sphere manifold according to the unit sphere vectors corresponding to the group level and the individual level respectively of all the task segments.

[0008] Optionally, the distance calculation according to the group-level unit sphere manifold to obtain a distance matrix between each of the BOLD signals and other BOLD signals comprises: obtaining a point set of the group-level unit sphere manifold according to the unit sphere vectors in the group-level unit sphere manifold, wherein each of the unit sphere vectors corresponds to a point of the point set; calculating, by means of geodesic distance measurement, the unit sphere vectors corresponding to any two points in the point set respectively to obtain a spherical distance between the two points; arranging the spherical distances between each point in the point set and other points to obtain the distance matrix.

[0009] Optionally, the manifold learning dimension reduction processing of the group-level unit sphere manifold according to the distance matrix to obtain a low-dimensional embedding manifold comprises: constructing an adjacency graph of the point set according to the distance matrix by means of a manifold learning algorithm; According to the adjacency graph, a fuzzy topological structure of the group-level unit sphere manifold is obtained; According to the fuzzy topological structure, low-dimensional coordinate optimization is performed to determine the Euclidean distance distribution of the point set in the target low-dimensional space; According to the Euclidean distance distribution, a low-dimensional embedded manifold with a dimension lower than the group-level unit sphere manifold is generated.

[0010] Optionally, the functional neighborhood of each brain cortex vertex is assigned according to the low-dimensional embedded manifold, comprising: According to the low-dimensional embedded manifold of the group level, the low-dimensional coordinates corresponding to each brain cortex vertex are determined; According to the low-dimensional coordinates corresponding to each brain cortex vertex, a plurality of other brain cortex vertices closest to the brain cortex vertex in the individual-level unit sphere manifold are determined by K-neighbor algorithm; According to a plurality of other brain cortex vertices, a vertex set of the functional neighborhood is obtained; The vertex set is mapped back to the individual-level unit sphere manifold to obtain the functional neighborhood of each brain cortex vertex.

[0011] Optionally, the average signal corresponding to the functional neighborhood is determined from the individual-level unit sphere manifold according to the functional neighborhood of each brain cortex vertex, comprising: The functional neighborhood of each brain cortex vertex is extracted to obtain a unit sphere vector set corresponding to the functional neighborhood; According to the Riemann center calculation rule, all unit sphere vectors in the unit sphere vector set are iteratively solved to obtain the Karcher average signal of the functional neighborhood; According to the Karcher average signal of the functional neighborhood, an iterative convergence is performed to obtain the average signal corresponding to the functional neighborhood.

[0012] Optionally, the local synchrony measure of each brain cortex vertex is determined according to the average signal, comprising: The geodesic line of each point in the individual-level unit sphere manifold is calculated to obtain the geodesic distance between the unit sphere vector corresponding to each point and the average signal corresponding to the unit sphere vector; According to the geodesic distance, a geodesic line distance synchrony index is constructed, wherein the geodesic line distance synchrony index includes the activation direction and local synchronization strength of the brain cortex vertex and other brain cortex vertices in the functional neighborhood corresponding to the brain cortex vertex in the time dimension; The geodesic line distance synchrony index is taken as the local synchrony measure of the brain cortex vertex.

[0013] Optionally, the obtaining the relevant functional activation atlas of the brain cortex during the task cycle according to the local synchronism measure of all the brain cortex vertices comprises: mapping the local synchronism measure of each brain cortex vertex to the brain cortex spatial coordinate corresponding to the brain cortex vertex; generating a vertex-level synchronism value field of the brain cortex according to the brain cortex spatial coordinates of all the brain cortex vertices; encoding the vertex-level synchronism value field to obtain a visualization layer of the brain cortex; superimposing the visualization layer to a preset standard brain cortex template to obtain the relevant functional activation atlas of the brain cortex during the task cycle.

[0014] In a second aspect, a brain function activity nonlinear modeling system is provided, comprising: a data acquisition module configured to acquire fMRI data of a brain cortex during a task cycle, wherein the fMRI data comprises BOLD signals of each brain cortex vertex in the brain cortex in each time frame during the task cycle; a task segmentation and mapping module configured to divide the BOLD signals into a plurality of task segments, and map the BOLD signals corresponding to each task segment into a group-level unit sphere manifold and an individual-level unit sphere manifold, respectively; a distance calculation module configured to perform distance calculation according to the group-level unit sphere manifold to obtain a distance matrix between each BOLD signal and other BOLD signals; a manifold dimension reduction and neighborhood assignment module configured to perform manifold learning dimension reduction processing on the group-level unit sphere manifold according to the distance matrix to obtain a low-dimensional embedded manifold, and assign a functional neighborhood to each brain cortex vertex according to the low-dimensional embedded manifold; an average signal calculation module configured to determine an average signal corresponding to the functional neighborhood from the individual-level unit sphere manifold according to the functional neighborhood of each brain cortex vertex; a local synchronism measure module configured to determine a local synchronism measure of each brain cortex vertex according to the average signal; an atlas generation module configured to obtain a relevant functional activation atlas of the brain cortex during the task cycle according to the local synchronism measure of all the brain cortex vertices.

[0015] In a third aspect, a computer readable storage medium having a computer program stored thereon is provided, wherein the computer program, when executed by a processor, implements the brain function activity nonlinear modeling method as described above.

[0016] The brain function activity nonlinear modeling method, system and storage medium of the application first acquire fMRI data of the brain cortex in a task cycle, which contains the BOLD signal of each time frame of each brain cortex vertex in the task cycle. By task segment division of the BOLD signal and mapping of the BOLD signal corresponding to each task segment to the group level unit spherical manifold and the individual level unit spherical manifold respectively, the time sequence characteristics of the BOLD signal are effectively utilized, the data integrity and accuracy are ensured, and the dynamic change of the brain function activity is facilitated to be captured. Distance calculation is performed in the group level unit spherical manifold to obtain a distance matrix between each BOLD signal and other BOLD signals, and the nonlinear relationship between brain regions is quantified from a geometric angle. The generation of the low-dimensional embedded manifold enables subsequent analysis to be performed in a lower-dimensional space, improves the calculation efficiency and reduces the influence of data noise. The average signal corresponding to the functional neighborhood of each brain cortex vertex is determined from the individual level unit spherical manifold according to the functional neighborhood of each brain cortex vertex, and the analysis of the brain function activity is further refined. In combination with the geodesic distance synchrony index, the local synchrony measure of each brain cortex vertex is determined according to the average signal, the task-induced activation region is identified, including the region showing an atypical activation mode, and the adaptability and explanatory power of the model under complex tasks and disease states are enhanced. Finally, the local synchrony measure of all brain cortex vertices is integrated to generate a related functional activation atlas of the brain cortex in the task cycle, so that the atlas not only contains the traditional activation region, but also can reveal the region with nonlinear and asymmetric response, and more comprehensively reflects the real functional response of the brain. It is ensured that each step from data preprocessing to functional activation atlas generation can effectively capture and reflect the complexity of brain function activity. In summary, the application significantly enhances the ability to capture the nonlinear characteristics of brain function activity by distance calculation and manifold learning on the group level unit spherical manifold. At the same time, through geometric perception dimension reduction and local characteristic analysis, a more comprehensive and detailed understanding of brain function activity is provided, so that the model can more accurately reveal the functional mechanism of the brain under different task states, and the modeling accuracy of brain function activity is improved. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 A flowchart of the brain function activity nonlinear modeling method of the embodiment of the application is shown in the figure. Figure 2 A flowchart of the brain function activity nonlinear modeling method of the embodiment of the application is shown in the figure. Figure 3 A structure diagram of the brain function activity nonlinear modeling system of the embodiment of the application is shown in the figure. DETAILED DESCRIPTION

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Although some embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the accompanying drawings and embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0019] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0020] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the following description. It should be noted that the concepts of "first," "second," etc., mentioned in this invention are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0021] It should be noted that the terms "a" and "a plurality of" used in this invention are illustrative rather than restrictive. Those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0022] To address the problems existing in the aforementioned related technologies, this embodiment provides an intelligent site selection system, method, and storage medium based on multi-source terrain fusion.

[0023] Combination Figure 1 As shown in the figure, an embodiment of the present invention provides a nonlinear modeling method for brain functional activity, comprising: Acquire fMRI data of the cerebral cortex during the task cycle, wherein the fMRI data includes the BOLD signal of each cortical vertex in the cerebral cortex at each time frame during the task cycle.

[0024] Specifically, the fMRI data includes time-series BOLD signals of each cortical vertex during the task cycle, serving as the basis for the modeling method. In embodiments of this invention, it is combined with... Figure 2As shown, firstly, fMRI data of multiple subjects for tasks of brain cortex, such as subject-1 and subject-2, and the like, are required, and the fMRI data is preprocessed, wherein the preprocessing includes spatial alignment, time denoising, signal standardization, and the like, of the original data, so as to ensure the consistency of the fMRI data of different subjects in space and time. The pre-acquired fMRI data can be stored in a database or a storage medium, and the fMRI data is directly acquired from the database or the storage medium for processing in the embodiment, that is, the embodiment mainly relates to the processing process of the fMRI data, and does not relate to the improvement of the acquisition of the fMRI data from the human body.

[0025] The BOLD signals are divided into multiple task segments, and the BOLD signals corresponding to each of the task segments are respectively mapped into group-level unit spherical manifolds and individual-level unit spherical manifolds.

[0026] Specifically, the BOLD signals are divided into multiple task segments and are respectively mapped into group-level unit spherical manifolds and individual-level unit spherical manifolds. Specifically, a task period is divided into multiple non-overlapping task segments, and each task segment corresponds to a specific experimental condition. For the BOLD signal of each brain cortex vertex in each task segment, a time sequence is extracted to obtain an original vector, and then the original vector is mapped onto a unit spherical manifold through a normalization operation. At the group level, the data of all subjects are integrated for unified processing; and at the individual level, the data of each subject is processed respectively. In the embodiment of the present application, the group-level unit spherical manifold is calculated by combining the data of all subjects, and the individual-level unit spherical manifold is calculated by combining the data of each subject. Figure 2 As shown, the division of the task segments is based on the task start time in the experimental design. After the time sequence of the BOLD signal of each brain cortex vertex in each task segment is extracted to obtain an original vector, the norm of the vector is calculated, and the original vector is divided by the norm to realize the normalization processing of the vector, so as to be mapped into a unit spherical manifold. In combination with the above-mentioned embodiment, the vector is mapped into a unit spherical manifold through the normalization processing. Figure 2 As shown, subject-1, subject-2, and subject-n jointly constitute a preset task design, and respectively correspond to a task segment, and the tasks are divided into task1 and task2 according to time periods, and the task period is divided into multiple continuous task segments, and each task segment corresponds to a specific task, and the blue and orange respectively represent task1 and task2, so as to reveal the spatial distribution and time dynamics of the brain function.

[0027] According to the group-level unit spherical manifold, distance calculation is performed to obtain a distance matrix between each of the BOLD signals and other BOLD signals.

[0028] Specifically, the normalized BOLD signals of all the brain cortex vertices in each task segment are regarded as a set of points on the group-level unit sphere manifold. For any two points in the set of points, the spherical distance between the two points is calculated by using the geodesic distance metric. In an embodiment of the present application, a distance matrix is generated by calculating the geodesic distance between each pair of points on the group-level unit sphere manifold and arranging the distance values in matrix form. Figure 2 The distance matrix comprehensively reflects the nonlinear relationship between the brain cortex vertices, providing a key quantitative basis for subsequent manifold learning dimension reduction.

[0029] According to the distance matrix, manifold learning dimension reduction processing is performed on the group-level unit sphere manifold to obtain a low-dimensional embedded manifold, and a functional neighborhood is assigned to each brain cortex vertex according to the low-dimensional embedded manifold.

[0030] Specifically, first, at the group level, a manifold learning algorithm is selected, the distance matrix is taken as input, an adjacency graph of the set of points is constructed, and a fuzzy topological structure of the group-level unit sphere manifold is further obtained. In an embodiment of the present application, the UMAP algorithm can be used for manifold learning dimension reduction processing. The UMAP algorithm constructs an adjacency graph between data points at the group level according to the spherical distance in the distance matrix, estimates the local topological structure, and optimizes the embedded coordinates in the low-dimensional space, so that the distance between points in the low-dimensional embedded manifold is consistent with the topological structure of the original manifold, thereby realizing dimension reduction. The low-dimensional embedded manifold after dimension reduction not only reduces the complexity of the data, but also retains the key structural information of the data, facilitating subsequent analysis and processing. Secondly, at the individual level, the functional neighborhood is assigned. In a preferred embodiment of the present application, the assignment operation is performed by the K-nearest neighbor algorithm.

[0031] According to the functional neighborhood of each brain cortex vertex, the average signal corresponding to the functional neighborhood is determined from the individual-level unit sphere manifold.

[0032] Specifically, at the individual level, after obtaining the functional neighborhood corresponding to each brain cortex vertex, a set of unit sphere vectors corresponding to the functional neighborhood is extracted from the individual-level unit sphere manifold. Karcher average signal calculation is performed on these unit sphere vectors to obtain the average signal of the functional neighborhood. In an embodiment of the present application, as shown in Figure 2 For the functional neighborhood of each brain cortex vertex, first, all the unit sphere vectors in the neighborhood are determined, and then the Karcher average signal algorithm in Riemannian geometry is used to iteratively solve the average value of the vectors, thereby obtaining the average signal of the functional neighborhood. The average signal can represent the signal characteristics in the functional neighborhood and provide a basis for subsequent synchrony analysis.

[0033] determine a local synchrony measure for each of the brain cortical vertices based on the average signals.

[0034] Specifically, a geodesic distance synchrony index between each brain cortical vertex and other vertices is calculated based on the average signals of the functional neighborhood of each brain cortical vertex. The geodesic distance synchrony index comprehensively considers the activation direction and local synchrony strength of the brain cortical vertex and other vertices in the functional neighborhood in the time dimension. In embodiments of the present application, the geodesic distance synchrony index is constructed by calculating the geodesic distance between the unit spherical vector of each brain cortical vertex and the Karcher mean signal of the functional neighborhood, and the index can quantify the synchrony between vertices. According to the index, a local synchrony measure for each brain cortical vertex is determined.

[0035] According to the local synchrony measures of all the brain cortical vertices, a task-related functional activation map of the brain cortex during the task cycle is obtained.

[0036] Specifically, the local synchrony measures of all the brain cortical vertices are integrated and mapped to the brain cortex surface to generate a task-related functional activation map. The map presents the functional activity pattern of the brain cortex during the task cycle in a visual manner. In embodiments of the present application, the local synchrony measure of each brain cortical vertex can be mapped to a standard brain template by a visualization tool to generate an intuitive color-coded or intensity-coded layer, and finally output the functional activation map of the brain cortex during the task cycle. This helps researchers to deeply understand the functional mechanism of the brain in different task states.

[0037] The brain function activity nonlinear modeling method, system and storage medium of the application first acquire fMRI data of the brain cortex in a task cycle, which contains the BOLD signal of each time frame of each brain cortex vertex in the task cycle. By dividing the BOLD signal into task segments and mapping the BOLD signal corresponding to each task segment to the group level unit spherical manifold and the individual level unit spherical manifold respectively, the time sequence characteristics of the BOLD signal are effectively utilized, the data integrity and accuracy are ensured, and the dynamic changes of brain function activity are easily captured. The distance calculation is performed in the group level unit spherical manifold to obtain the distance matrix between each BOLD signal and other BOLD signals, and the nonlinear relationship between brain regions is quantified from the geometric angle. The generation of the low-dimensional embedded manifold enables the subsequent analysis to be performed in a lower-dimensional space, improves the calculation efficiency, and reduces the influence of data noise. By determining the average signal corresponding to the functional neighborhood of the individual level unit spherical manifold according to the functional neighborhood of each brain cortex vertex, the analysis of brain function activity is further refined. Combined with the geodesic distance synchrony index, the local synchrony measure of each brain cortex vertex is determined according to the average signal, which can identify the activation regions induced by the task, including the regions showing atypical activation patterns, and enhances the adaptability and explanatory power of the model under complex tasks and disease states. Finally, the local synchrony measure of all brain cortex vertices is integrated to generate the related functional activation atlas of the brain cortex in the task cycle, so that the atlas not only contains the traditional activation regions, but also reveals the regions with nonlinear and asymmetric responses, and more comprehensively reflects the real functional response of the brain. It is ensured that each step from data preprocessing to functional activation atlas generation can effectively capture and reflect the complexity of brain function activity. In summary, the application significantly enhances the ability to capture the nonlinear characteristics of brain function activity by performing distance calculation and manifold learning on the group level unit spherical manifold. At the same time, through geometric perception dimension reduction and local property analysis, a more comprehensive and detailed understanding of brain function activity is provided, so that the model can more accurately reveal the functional mechanism of the brain under different task states, and the modeling accuracy of brain function activity is improved.

[0038] Optionally, the BOLD signal is divided into a plurality of task segments, and the BOLD signal corresponding to each task segment is mapped to a group level unit spherical manifold and an individual level unit spherical manifold, respectively, comprising: According to a preset task design, all tasks included in the task cycle are determined, and each task corresponds to a task segment; The BOLD signal is preprocessed to obtain a group level BOLD signal and an individual level BOLD signal; time series extraction is performed on the BOLD signal of each brain cortex vertex in each task segment at the group level and the individual level, to obtain original vectors of each task segment at the group level and the individual level; normalization processing is performed on the original vectors corresponding to the group level and the individual level respectively, to obtain unit spherical vectors corresponding to the group level and the individual level respectively, and the group level unit spherical manifold and the individual level unit spherical manifold are obtained according to the unit spherical vectors corresponding to all the task segments at the group level and the individual level.

[0039] Specifically, first, all tasks included in the task period are determined according to a preset task design, and each task corresponds to a task segment. Then, the BOLD signal is preprocessed to obtain the BOLD signal at the group level and the BOLD signal at the individual level. The preprocessing step ensures the consistency of the data in space and time, and lays the foundation for subsequent analysis. Next, time series extraction is performed on the BOLD signal of each brain cortex vertex in each task segment at the group level and the individual level, to obtain original vectors of each task segment at the group level and the individual level. Finally, normalization processing is performed on the original vectors corresponding to the group level and the individual level respectively, to obtain unit spherical vectors corresponding to the group level and the individual level respectively, and the group level unit spherical manifold and the individual level unit spherical manifold are obtained according to the unit spherical vectors corresponding to all the task segments at the group level and the individual level. Among them, in combination with Figure 2 It is shown that the BOLD signal at the group level is the average BOLD signal, so after normalization of the average BOLD signal at the group level, the obtained unit spherical vector is the average unit spherical vector, that is, Figure 2 , , and . The BOLD signal at the individual level is the BOLD signal at the individual level during the task, that is, Figure 2 q1, q2, q3,..., q v。

[0040] In the preferred embodiment of the present application, in combination with Figure 2 It is shown that according to the task information marked in the task graph of the preset task design at each time point, the entire fMRI scanning sequence can be divided into multiple segments corresponding to each task. In the task-state fMRI analysis, the fMRI segment corresponding to the jth task contains T j frames and V vertices. Let f i represent the real value vector of the BOLD time series of the i th vertex of the cerebral cortex during the j th task. If T j = n + 1, then the BOLD signal f​i Euclidean space of n dimensions. Since in practical applications, the number of frames in a single fMRI scan is usually in the hundreds to thousands, and the number of voxels V can reach the order of 104 to 105. Therefore, the brain function research based on fMRI faces the complexity challenge brought by the high dimensionality and high coupling of data. In task-induced fMRI research, the mainstream method (such as the general linear model) mainly focuses on the relationship between the change of BOLD signal in the time dimension and the task structure, rather than the absolute signal strength, because the latter is difficult to accurately define physiologically and has limited analytical significance.

[0041] Based on this assumption, in addition to spatial smoothing, the present application also performs normalization preprocessing on the input fMRI time series to eliminate features related to signal amplitude. The normalized BOLD signal is denoted as: ; where, denotes the vector 2 norm. This processing makes the norm of all equal to 1, meaning that is a point on the unit sphere in n-dimensional space. The unit n-dimensional sphere refers to the set of all points in Euclidean space with a distance of 1 from the origin. Thus, the set of normalized BOLD signals of all vertices of the cerebral cortex is a subset of the n-dimensional unit sphere Based on the geometric interpretation, it is possible to apply differential geometry tools in a non-Euclidean framework to analyze the statistical structure of the normalized BOLD signal time series. In addition, the unit sphere is a compact, smooth, and boundaryless Riemannian manifold equipped with a standard metric induced by its embedding in Euclidean space.

[0042] In an embodiment of the present application, by mapping the BOLD signal to the unit sphere manifold, the difference in signal strength is eliminated, allowing subsequent analysis to focus on the pattern and dynamic changes of the signal. The normalized unit sphere vector set constitutes the unit sphere manifold, providing a mathematical basis for subsequent distance calculation and manifold learning, improving the accuracy and reliability of modeling, and ensuring accurate capture and analysis of brain function activities.

[0043] Optionally, the distance calculation according to the group-level unit sphere manifold to obtain a distance matrix between each BOLD signal and other BOLD signals includes: According to the unit sphere vector in the group-level unit sphere manifold, a point set of the group-level unit sphere manifold is obtained, wherein each unit sphere vector corresponds to a point in the point set; The spherical distance between any two points in the point set is obtained by calculating the unit spherical vector corresponding to each of the two points respectively according to the geodesic distance measurement. The distance matrix is obtained by arranging the spherical distance between each point in the point set and other points.

[0044] Specifically, the fMRI data is composed of BOLD signals, which is time series data with high spatial and temporal resolution. This high resolution characteristic provides rich information and accurate analysis capability for brain function research, but also brings significant data high-dimensional challenge. In most natural task states, the physiological activity of the brain is excited by limited specific stimulus conditions, which means that complex brain function dynamics can be described by a set of low-dimensional latent variables. In order to better represent the cross-subject cortical function structure, first, according to the unit spherical vector in the group-level unit spherical manifold, the point set of the group-level unit spherical manifold is obtained, wherein each unit spherical vector corresponds to a point in the point set, which simplifies the complex high-dimensional data into a set of points, providing a basis for subsequent distance calculation. Next, the spherical distance between any two points in the point set is obtained by calculating the unit spherical vector corresponding to each of the two points respectively according to the geodesic distance measurement. Geodesic distance measurement is a geometric calculation method based on unit sphere, which can accurately reflect the actual distance of two points on the sphere. Finally, the distance matrix is obtained by arranging the spherical distance between each point in the point set and other points. The distance matrix comprehensively quantifies the nonlinear relationship between brain regions, providing a key quantitative basis for subsequent manifold learning dimension reduction and functional neighborhood assignment.

[0045] In the embodiment of the present application, the geodesic distance measurement accurately captures the nonlinear relationship between BOLD signals, ensuring the accuracy and reliability of the distance matrix, not only reflecting the similarity between the vertices of the brain cortex, but also providing a quantitative basis for subsequent functional neighborhood assignment and average signal calculation, thereby improving the accuracy and efficiency of the entire modeling method.

[0046] Optionally, the manifold learning dimension reduction processing of the group-level unit spherical manifold according to the distance matrix to obtain a low-dimensional embedded manifold comprises: An adjacency graph of the point set is constructed according to the distance matrix by a manifold learning algorithm; A fuzzy topological structure of the group-level unit spherical manifold is obtained according to the adjacency graph; Low-dimensional coordinate optimization is performed according to the fuzzy topological structure to determine the Euclidean distance distribution of the point set in the target low-dimensional space; The low-dimensional embedded manifold with a dimension lower than the group-level unit spherical manifold is generated according to the Euclidean distance distribution.

[0047] Specifically, first, an adjacency graph of the point set is constructed from the distance matrix by a manifold learning algorithm. The construction of the adjacency graph is based on the similarity between points in the point set, reflecting the local topological structure of the data. Next, a fuzzy topological structure of the group-level unit sphere manifold is obtained from the adjacency graph, which further characterizes the overall topological features of the data, providing a basis for low-dimensional embedding. Then, low-dimensional coordinate optimization is performed according to the fuzzy topological structure to determine the Euclidean distance distribution of the point set in the target low-dimensional space. The goal of low-dimensional coordinate optimization is to make the distance between points in the low-dimensional embedded manifold as close as possible to the topological structure in the original high-dimensional space. Finally, a low-dimensional embedded manifold with a dimension lower than the group-level unit sphere manifold is generated according to the Euclidean distance distribution. The low-dimensional embedded manifold not only reduces the dimension of the data, but also preserves the key structural information of the data, making subsequent analysis more efficient and accurate. This step is performed at the group level, meaning it is cross-individual, reflecting the integrated results of multiple subject data.

[0048] In a preferred embodiment of the present application, the present application averages and time-normalizes the task-evoked BOLD signals of multiple subjects at each cortical vertex, then applies a manifold learning method (Uniform Manifold Approximation and Projection-UMAP) to the set to discover the underlying low-dimensional structure in the normalized activation patterns. It should be noted that, due to Operations such as interpolation, averaging, and statistical modeling located in the curvature space must respect the properties of spherical geometry. If linear Euclidean operations are applied directly on the manifold, the results may deviate from the manifold and fail to accurately characterize the intrinsic structure of the normalized BOLD signal space. Therefore, UMAP uses the pair-wise distance matrix calculated from the geodesic distance on the group-level unit sphere manifold to perform dimensionality reduction analysis, thereby ensuring that the angular relationships between normalized BOLD signals are faithfully preserved. UMAP constructs an adjacency graph based on the number of nearest neighbors (hyperparameter n r The resulting embedded point set forms a point cloud structure in three-dimensional Euclidean space, reflecting the manifold structure of the whole brain cortical BOLD signals. The learned manifold not only preserves the structural adjacency between adjacent cortical vertices, but also reveals the functional proximity between distant brain regions, thereby jointly modeling the local and non-local functional relationships in a way that has geometric perception capabilities.

[0049] In the embodiments of the present application, by constructing the adjacency graph and the fuzzy topology structure, this step can accurately capture the local and global features of the data, providing a solid foundation for subsequent functional neighborhood allocation and average signal calculation. The generation of the low-dimensional embedding manifold not only improves the calculation efficiency, but also enhances the interpretability and robustness of the model, making the subsequent analysis more efficient and accurate.

[0050] Optionally, the functional neighborhood is allocated to each of the brain cortex vertices according to the low-dimensional embedding manifold, comprising: determining the low-dimensional coordinates corresponding to each of the brain cortex vertices according to the low-dimensional embedding manifold at the group level; determining a plurality of other brain cortex vertices closest to the brain cortex vertex in the individual level unit sphere manifold by K-Nearest Neighbor algorithm, taking the low-dimensional coordinates corresponding to each of the brain cortex vertices as the center; obtaining the vertex set of the functional neighborhood according to the plurality of other brain cortex vertices; mapping the vertex set back to the individual level unit sphere manifold to obtain the functional neighborhood of each of the brain cortex vertices.

[0051] Specifically, first, at the individual level, the low-dimensional coordinates corresponding to each of the brain cortex vertices are determined according to the low-dimensional embedding manifold. The low-dimensional embedding manifold is obtained by manifold learning dimension reduction processing, which retains the key structure and topological information of the data. Then, taking the low-dimensional coordinates corresponding to each of the brain cortex vertices as the center, a plurality of other brain cortex vertices closest to the brain cortex vertex are determined by K-Nearest Neighbor algorithm. K-Nearest Neighbor algorithm is a distance-based clustering method that can effectively identify local features in the data. Then, according to these nearest neighbor plurality of other brain cortex vertices, the vertex set of the functional neighborhood is formed. The vertex set represents the brain cortex vertices with similar features to the current vertex in the low-dimensional embedding manifold. Finally, the vertex set is mapped back to the individual level unit sphere manifold to obtain the functional neighborhood, which not only ensures that the determination of the functional neighborhood is based on the reduced data, but also reflects the geometric structure in the original data.

[0052] In the preferred embodiments of the present application, it is assumed that the coordinates of the currently processed brain cortex vertex A in the low-dimensional embedding manifold are and all other brain cortex vertices also have their own coordinates in this low-dimensional space. K-Nearest Neighbor algorithm calculates the Euclidean distance between vertex A and each other vertex, for example, the coordinates of vertex B are , then the distance between them is: ; The algorithm filters out the k vertices closest to vertex A according to these distance values, and the k vertices constitute the neighborhood set of the functional neighborhood of vertex A. For example, if k = 5 is selected, the 5 vertices closest to vertex A will be identified as the neighborhood vertices with strong functional association with A. In this way, the K-Nearest Neighbor algorithm accurately locates other vertices in the functional neighborhood of each brain cortex vertex, thereby supporting subsequent synchronization measurement analysis and ensuring that the analysis results accurately reflect the functional connection patterns between brain regions. In actual operation, the selection of k value needs to consider the local sensitivity and topological stability. For example, a small k value is beneficial to capture local features but may be affected by noise, and a large k value provides global stability but may blur local details.

[0053] In the embodiments of the present application, the plurality of other brain cortex vertices determined by the K-Nearest Neighbor algorithm can reflect the similarity and correlation between the brain cortex vertices. Mapping the vertex set back to the individual level unit spherical manifold further ensures that the determination of the functional neighborhood is consistent with the geometric structure of the original data.

[0054] Optionally, determining the average signal corresponding to the functional neighborhood from the individual level unit spherical manifold according to the functional neighborhood of each brain cortex vertex comprises: extracting the functional neighborhood of each brain cortex vertex to obtain a unit spherical vector set corresponding to the functional neighborhood; iteratively solving all unit spherical vectors in the unit spherical vector set by the Riemann center calculation rule to obtain the Karcher average signal of the functional neighborhood; iteratively converging according to the Karcher average signal of the functional neighborhood to obtain the average signal corresponding to the functional neighborhood.

[0055] Specifically, unlike the traditional general linear model that models the BOLD signal as the convolution of task events and a fixed HRF function, the present application characterizes functional synchrony through the consistency of BOLD signal trajectories within the neighborhood at the individual level. When a certain vertex is activated under task stimulation, its BOLD signal should exhibit higher synchrony with the signals of other vertices within its spatial neighborhood, while the non-activated regions lack such consistency. On the learned low-dimensional embedding manifold, the BOLD signal generally exhibits spatial clustering due to functional partitioning and structural connectivity constraints. To extract this local synchrony, first, the functional neighborhood of each of the brain cortex vertices is extracted to obtain a set of unit sphere vectors corresponding to the functional neighborhood, which ensures that subsequent calculations are based on the correct data set; next, all the unit sphere vectors in the set of unit sphere vectors are iteratively solved by the Riemann center of mass rule to obtain the Karcher mean signal of the functional neighborhood, which is a method for calculating the average value on the Riemann manifold and can effectively reflect the central tendency of the signals within the functional neighborhood; finally, the Karcher mean signal of the functional neighborhood is iteratively converged to obtain the average signal corresponding to the functional neighborhood, which represents the common activation pattern of the brain regions within the functional neighborhood and provides a basis for subsequent synchrony measurement.

[0056] In the embodiments of the present application, the average signal of the functional neighborhood is calculated to provide a key quantitative indicator for modeling brain functional activity. The introduction of the Karcher mean signal enables accurate calculation of the average signal in non-Euclidean space, which is more suitable for processing vector data on the sphere than the traditional Euclidean average. This step not only improves the accuracy of modeling, but also enhances the ability of the model to capture the complexity of brain functional activity. Through the iterative convergence process, the stability and reliability of the average signal are ensured, laying a solid foundation for subsequent synchrony measurement and generation of functional activation atlas.

[0057] Optionally, the determination of the local synchrony measure of each brain cortex vertex according to the average signal comprises: geodesic line calculation is performed on each point in the individual level unit sphere manifold to obtain the geodesic distance between the unit sphere vector corresponding to each point and the average signal corresponding to the unit sphere vector; a geodesic line distance synchrony index is constructed according to the geodesic distance, wherein the geodesic line distance synchrony index includes the activation direction and local synchrony strength of the brain cortex vertex and other brain cortex vertices within the functional neighborhood corresponding to the brain cortex vertex in the time dimension; the geodesic line distance synchrony index is taken as the local synchrony measure of the brain cortex vertex.

[0058] Specifically, by accurately calculating the geodesic distance between each unit spherical vector and the average signal, the degree of difference between them on the sphere can be quantified. Subsequently, based on the geodesic distance, a geodesic distance synchronization index is constructed, which integrates the activation direction and local synchronization intensity information of the cortical vertex and other vertices within its functional neighborhood in the time dimension. Finally, the constructed geodesic distance synchronization index is used as a measure of the local synchronization of cortical vertices, providing crucial data support for the subsequent generation of functional activation maps, enabling the model to accurately capture and reflect the detailed features of brain functional activity. In a preferred embodiment of the invention, firstly, the neighborhood signal set of each vertex... Calculate the Karcher average signal This serves as the representative trajectory for that neighborhood. Subsequently, a geodesic distance-based synchronization metric (GDSM) is constructed, as follows: ; in, Represents a vector consisting entirely of 1s. For Riemannian manifold The geodesic distance defined above, The total activation direction of this trajectory is given by the set of signals from each vertex i and its neighborhood. Its GDSM value is denoted as k is the neighborhood index. This is the Karcher average signal.

[0059] The above calculation formula is divided into two parts: The first part represents the local synchronicity strength, which is a reciprocal form of the average geodesic distance. It measures the "unity" among the neighborhood signals of vertex i. Neighborhood set : Represents the neighborhood set of vertex i (e.g., the 36 nearest vertices to it). This represents the normalized BOLD signal of vertex i. Represents the neighborhood set The Karcher average signal of all BOLD signals within a region can be understood as the "central trend" of the neighborhood signals. It is a unit sphere The geodesic distance is used to measure the similarity between signals. If neighboring signals are very similar, then the mean distance is close, the denominator is small, the GDSM is large, and thus the synchronization is strong.

[0060] The second part indicates the activation direction, which is the normalized BOLD signal for vertex i. To perform a summation at all points in time, using a sign function. The result is used to determine whether the sum is positive or negative. If the result is +1 (positive), it indicates that the average signal in this area is "activating"; if the result is -1 (negative), it indicates an "inhibitory" response, such as an overall decrease or trough in the signal. This item allows the synchronicity index to distinguish between "activating synchronicity" and "inhibitory synchronicity," providing neurological significance for subsequent interpretation.

[0061] In summary, in the preferred embodiment of the present invention, for the i-th vertex of the brain, and the aforementioned neighborhood set... ( shared within k (Number of neighboring vertices).

[0062] The first step is based on the unit sphere. The geometric properties were calculated Karcher average signal of the BOLD signal of the inner neighborhood vertex , as the representative trajectory of this neighborhood.

[0063] The second step is to select neighborhood sets one by one. The BOLD signal of vertex j within the range is represented as: ,calculate arrive distance Repeat the above steps and add the obtained distances together, that is: .

[0064] The third step is to multiply the sum of the distances by [a certain factor]. That is, to obtain the neighborhood set The average distance from all BOLD signals within the range to their Karcher average signal, then taking the reciprocal, is the result. .

[0065] The fourth step is to normalize the BOLD signal of vertex i. Left-multiplying the transpose of a vector of all 1s T The result will be a scalar value, and then the sign of this scalar value is taken, i.e. This term represents the activation or suppression discrimination sign of the signal, and is then multiplied by the result obtained in the third step, which is the final GDSM value of the i-th vertex.

[0066] In this embodiment of the invention, by quantifying the synchronicity between cortical vertices, not only is the understanding of brain functional activity mechanisms deepened, but a solid and reliable data foundation is also laid for the subsequent generation of functional activation maps, which helps to reveal the functional characteristics and activity patterns of the brain under different task states more deeply.

[0067] Optionally, the obtaining the relevant functional activation map of the cerebral cortex during the task cycle according to the local synchrony metric of all the cerebral cortex vertices comprises: mapping the local synchrony metric of each cerebral cortex vertex to the cerebral cortex spatial coordinate corresponding to the cerebral cortex vertex; generating a vertex-level synchrony value field of the cerebral cortex according to the cerebral cortex spatial coordinates of all the cerebral cortex vertices; performing encoding processing on the vertex-level synchrony value field to obtain a visualization layer of the cerebral cortex; superimposing the visualization layer to a preset standard cerebral cortex template to obtain the relevant functional activation map of the cerebral cortex during the task cycle.

[0068] Specifically, first, the local synchrony metric of each cerebral cortex vertex is mapped to the corresponding cerebral cortex spatial coordinate. This step ensures that the synchrony metric of each vertex is associated with its actual position on the cerebral cortex. Next, based on the spatial coordinates of all vertices and their corresponding synchrony metrics, a vertex-level synchrony value field is generated. The vertex-level synchrony value field is a data structure that records the synchrony metric value of each position on the cerebral cortex. Subsequently, the vertex-level synchrony value field is encoded to generate a visualization layer. The visualization layer visually displays the degree of synchrony in different regions of the cerebral cortex through color or intensity coding. Finally, the visualization layer is superimposed on the preset standard cerebral cortex template to generate the final functional activation map. This map presents the functional activity pattern of the cerebral cortex during the task cycle in an intuitive way. In the preferred embodiment of the present application, the synchrony metric can be calculated for all vertices in the whole brain, forming a task-related functional activation map on the cerebral cortex. This map not only contains traditional activation regions, but also reveals regions with nonlinear and asymmetric responses, such as signal delay, adaptive weakening, down-regulation, etc., providing a more comprehensive reflection of the real functional response of the brain.

[0069] In the embodiment of the present application, by mapping the local synchrony metric to the cerebral cortex spatial coordinate and generating a visualization layer, the intuitive display of brain functional activity is achieved. This method not only captures the synchrony differences between cerebral cortex vertices, but also enhances the readability of the map through color coding. Superimposing the visualization layer on the standard brain template makes it possible to compare results between different studies, and also facilitates the combination with existing neuroanatomical knowledge.

[0070] In summary, the present application combines Figure 2As shown in the group-level flow, the fMRI data of N subjects are preprocessed first to obtain the preprocessed BOLD signals. These data include the time series BOLD signals of each cortical vertex in the task period. Then, according to the task design, the task period is divided into multiple task segments, such as task1 and task2, and the BOLD signals corresponding to each task segment are mapped to the group-level unit sphere manifold. The signals of each subject are averaged to obtain the group-level averaged BOLD signals, and then normalized to obtain the unit sphere vector q i . Subsequently, using these unit sphere vectors, the geodesic distance between any two points in the point set of the group-level unit sphere manifold is calculated to construct a distance matrix. Through manifold learning dimension reduction by the UMAP algorithm, a low-dimensional embedding manifold I k (i) is obtained, which is represented in the low-dimensional space R³. Finally, the Karcher mean signal is calculated by searching for neighborhood points on the low-dimensional manifold embedding through the KNN algorithm, and the local synchrony measure GDSM of each cortical vertex is obtained. In the individual-level flow, the BOLD signals of each subject are preprocessed similarly, then divided into segments according to the task start and end time, and normalized. The individual-level BOLD signals are mapped to the individual-level unit sphere manifold to obtain the unit sphere vector q i . Unlike the group-level flow, the individual-level analysis focuses on the unique neural activity pattern of each subject. On the individual level, the individual-level functional neighborhood is determined by calculating the Karcher mean of the BOLD signals within the neighborhood of each vertex. Then, based on the geodesic distance, the local synchrony measure GDSM is calculated, which reflects the synchrony of the individual's neural activity in a specific task segment. Finally, the local synchrony measures of all subjects are integrated to generate the individual's functional activation map, revealing the spatial distribution of the individual's brain function activity in the task period. The parameters involved in this flow include the number of subjects N, the number of vertices V, the number of time frames T, the number of tasks J, and the normalized unit sphere vectors q i and q v , as well as the point coordinates z i (i) in the low-dimensional embedding manifold.

[0071] As shown in Figure 3 , a brain function activity nonlinear modeling system of the present application comprises: A data acquisition module is configured to acquire fMRI data of a brain cortex in a task period, wherein the fMRI data includes BOLD signals of each cortical vertex of the brain cortex in each time frame of the task period. a task segmentation and mapping module, configured to divide the BOLD signals into a plurality of task segments, and map the BOLD signals corresponding to each of the task segments into a group-level unit sphere manifold and an individual-level unit sphere manifold, respectively; a distance calculation module, configured to perform distance calculation according to the group-level unit sphere manifold, to obtain a distance matrix between each of the BOLD signals and other BOLD signals; a manifold dimension reduction and neighborhood assignment module, configured to perform manifold learning dimension reduction processing on the group-level unit sphere manifold according to the distance matrix, to obtain a low-dimensional embedded manifold, and assign a functional neighborhood to each of the brain cortex vertices according to the low-dimensional embedded manifold; an average signal calculation module, configured to determine an average signal corresponding to the functional neighborhood from the individual-level unit sphere manifold according to the functional neighborhood of each of the brain cortex vertices; a local synchrony measure module, configured to determine a local synchrony measure of each of the brain cortex vertices according to the average signal; a map generation module, configured to obtain a relevant functional activation map of the brain cortex during the task period according to the local synchrony measures of all the brain cortex vertices.

[0072] The brain function activity nonlinear modeling system of the present application has the same advantages as the brain function activity nonlinear modeling method of the present application, which will not be repeated here.

[0073] The present application also provides a computer readable storage medium, wherein the storage medium stores a computer program, and when the computer program is executed by a processor, the brain function activity nonlinear modeling method described above is realized.

[0074] The computer readable storage medium of the present application has the same advantages as the brain function activity nonlinear modeling method of the present application, which will not be repeated here.

[0075] Although the present application is disclosed as above, the protection scope of the present application is not limited to this. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present application, and these changes and modifications will fall within the protection scope of the present application.

Claims

1. A nonlinear modeling method for brain functional activity, characterized in that, include: Acquire fMRI data of the cerebral cortex during the task cycle, wherein the fMRI data includes the BOLD signal of each cortical vertex in the cerebral cortex at each time frame during the task cycle; The BOLD signal is divided into multiple task segments, and the BOLD signal corresponding to each task segment is mapped to a group of horizontal unit spherical manifolds and an individual horizontal unit spherical manifold, respectively. Distance calculations are performed based on the group of horizontal unit spherical manifolds to obtain the distance matrix between each BOLD signal and other BOLD signals; Based on the distance matrix, manifold learning and dimensionality reduction are performed on the group of horizontal unit spherical manifolds to obtain a low-dimensional embedded manifold, and a functional neighborhood is assigned to each of the cerebral cortex vertices based on the low-dimensional embedded manifold. Based on the functional neighborhood of each of the cerebral cortex vertices, the average signal corresponding to the functional neighborhood is determined from the individual horizontal unit spherical manifold; Based on the average signal, a measure of local synchronicity is determined for each of the cerebral cortex vertices; Based on the local synchronicity measure of all the vertices of the cerebral cortex, a relevant functional activation map of the cerebral cortex during the task cycle is obtained.

2. The nonlinear modeling method for brain functional activity according to claim 1, characterized in that, The step of dividing the BOLD signal into multiple task segments and mapping the BOLD signal corresponding to each task segment to a group of horizontal unit spherical manifolds and an individual horizontal unit spherical manifold, respectively, includes: Based on the preset task design, all tasks included in the task cycle are determined, and each task corresponds to a task segment; The BOLD signal is preprocessed to obtain group-level BOLD signal and individual-level BOLD signal; Time series extraction is performed on the BOLD signal of each cortical vertex in each task segment at both the group and individual levels to obtain the original vectors of each task segment at both the group and individual levels. The original vectors corresponding to the group level and individual level are normalized to obtain the unit spherical vectors corresponding to the group level and individual level, respectively. Based on the unit spherical vectors corresponding to all task segments at the group level and individual level, the unit spherical manifolds at the group level and the unit spherical manifolds at the individual level are obtained.

3. The nonlinear modeling method for brain functional activity according to claim 2, characterized in that, The step of calculating the distance based on the group of horizontal unit spherical manifolds to obtain the distance matrix between each BOLD signal and other BOLD signals includes: Based on the unit spherical vectors in the group of horizontal unit spherical manifolds, the set of points of the group of horizontal unit spherical manifolds is obtained, wherein each unit spherical vector corresponds to a point in the set of points; By using geodesic distance measurement, the spherical distance between any two points in the set of points is calculated by taking the unit spherical vectors corresponding to those points. The spherical distances between each point in the set of points and other points are arranged to obtain the distance matrix.

4. The nonlinear modeling method for brain functional activity according to claim 3, characterized in that, The step of performing manifold learning and dimensionality reduction processing on the group of horizontal unit spherical manifolds based on the distance matrix to obtain a low-dimensional embedded manifold includes: An adjacency graph of the point set is constructed based on the distance matrix using a manifold learning algorithm. Based on the adjacency graph, the fuzzy topological structure of the group of horizontal unit spherical manifolds is obtained; Based on the fuzzy topology, low-dimensional coordinate optimization is performed to determine the Euclidean distance distribution of the point set in the target low-dimensional space. Based on the Euclidean distance distribution, the low-dimensional embedded manifold with a dimension lower than that of the group of horizontal unit spherical manifolds is generated.

5. The nonlinear modeling method for brain functional activity according to claim 1, characterized in that, The assignment of functional neighborhoods to each of the cortical vertices based on the low-dimensional embedding manifold includes: Based on the low-dimensional embedding manifold at the group level, determine the low-dimensional coordinates corresponding to each of the cortical vertices; Using the low-dimensional coordinates corresponding to each of the cerebral cortex vertices as the center, the K-nearest neighbor algorithm is used to determine the multiple other cerebral cortex vertices in the individual horizontal unit spherical manifold that are closest to the cerebral cortex vertex. The set of vertices of the functional neighborhood is obtained based on multiple other vertices of the cerebral cortex; Mapping the set of vertices back to the individual horizontal unit spherical manifold yields the functional neighborhood of each of the cerebral cortex vertices.

6. The nonlinear modeling method for brain functional activity according to claim 5, characterized in that, The step of determining the average signal corresponding to the functional neighborhood from the individual-level unit spherical manifold based on the functional neighborhood of each of the cerebral cortex vertices includes: The functional neighborhood of each of the cerebral cortex vertices is extracted to obtain the set of unit spherical vectors corresponding to the functional neighborhood; By using the Riemann center calculation rule, all the unit spherical vectors in the set of unit spherical vectors are iteratively solved to obtain the Karcher average signal of the functional neighborhood; The average signal corresponding to the functional neighborhood is obtained by iterative convergence based on the Karcher average signal of the functional neighborhood.

7. The nonlinear modeling method for brain functional activity according to claim 3, characterized in that, The step of determining the local synchronicity measure of each of the cerebral cortex vertices based on the average signal includes: Geodesic calculations are performed on each point in the individual horizontal unit spherical manifold to obtain the geodesic distance between the unit spherical vector corresponding to each point and the average signal corresponding to the unit spherical vector; Based on the geodesic distance, a geodesic distance synchronization index is constructed, wherein the geodesic distance synchronization index includes the activation direction and local synchronization intensity of the cortical vertex and other cortical vertices in the functional neighborhood corresponding to the cortical vertex in the time dimension. The geodesic distance synchronization index is used as the measure of local synchronization at the vertices of the cerebral cortex.

8. The nonlinear modeling method for brain functional activity according to claim 7, characterized in that, The step of obtaining the relevant functional activation map of the cerebral cortex during the task cycle based on the local synchronicity measure of all the cerebral cortex vertices includes: Map the local synchronicity measure of each of the cerebral cortex vertices to the cerebral cortex spatial coordinates corresponding to the cerebral cortex vertices; Generate a vertex-level synchronization field of the cerebral cortex based on the spatial coordinates of all the vertices of the cerebral cortex; The vertex-level synchronization field is encoded to obtain a visualization layer of the cerebral cortex. The visualization layer is overlaid onto a preset standard cerebral cortex template to obtain the relevant functional activation map of the cerebral cortex during the task cycle.

9. A nonlinear modeling system for brain functional activity, characterized in that, include: The data acquisition module is used to acquire fMRI data of the cerebral cortex during the task cycle. The fMRI data includes the BOLD signal of each cortical vertex in the cerebral cortex for each time frame in the task cycle. The task segmentation and mapping module is used to divide the BOLD signal into multiple task segments and map the BOLD signal corresponding to each task segment into a group of horizontal unit spherical manifolds and an individual horizontal unit spherical manifold, respectively. The distance calculation module is used to perform distance calculation based on the group of horizontal unit spherical manifolds to obtain the distance matrix between each BOLD signal and other BOLD signals. The manifold dimensionality reduction and neighborhood assignment module is used to perform manifold learning dimensionality reduction processing on the group of horizontal unit spherical manifolds according to the distance matrix to obtain a low-dimensional embedded manifold, and to assign a functional neighborhood to each of the cerebral cortex vertices according to the low-dimensional embedded manifold. An average signal calculation module is used to determine the average signal corresponding to the functional neighborhood from the individual horizontal unit spherical manifold based on the functional neighborhood of each of the cerebral cortex vertices. A local synchronicity measurement module is used to determine the local synchronicity measurement of each of the cerebral cortex vertices based on the average signal. The atlas generation module is used to obtain the relevant functional activation atlas of the cerebral cortex during the task cycle based on the local synchronicity measure of all the cerebral cortex vertices.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the nonlinear modeling method for brain functional activity as described in any one of claims 1-8.

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