A dynamic brain function network learning method based on a graph learning optimization algorithm

Abstract

The application discloses a dynamic brain function network learning method based on a graph learning optimization algorithm. Firstly, a basic mathematical model of a brain network is determined, and then real neuroimage data is preprocessed; a target function for obtaining a dynamic brain function connection network is constructed; and finally, a solution method for obtaining the dynamic brain function connection network is determined. The method can directly obtain the dynamic function connection network of the brain from fMRI signals. The dynamic brain function connection network can more reasonably and accurately reflect the connection strength between brain regions and the topological structure of the brain network.

Description

Technical Field

[0001] This invention relates to the field of graph machine learning, and more specifically to a dynamic brain functional network learning method based on graph learning optimization algorithms. Background Technology

[0002] Dynamic brain network research is an important direction in neuroscience and cognitive science, focusing on the changes in neural networks in the human brain at different time points, under different cognitive tasks, or under different cognitive states. This research helps to better understand the functions of brain networks in cognition, learning, memory, and neurological diseases, and can provide key information for fields such as precision medicine, brain-computer interfaces, and cognitive enhancement.

[0003] Brain imaging techniques such as functional magnetic resonance imaging (fMRI) and electroencephalography (EEG) can record changes in brain activity, aiding in the study of dynamic brain networks. fMRI provides high spatial resolution information on brain region activity, while EEG provides high temporal resolution data on brain electrical activity. Analyzing EEG data using graph machine learning and network analysis methods can help study the topology and connectivity patterns of brain networks. These methods can reveal the interactions between neural networks at different time points or under different tasks, as well as the ways in which information is transmitted between brain nodes.

[0004] Constructing dynamic brain network connectivity is the foundation and first step in dynamic brain network analysis. Traditional methods for constructing dynamic brain network functional connectivity typically involve acquiring fMRI signal fragments using a sliding window and then calculating the Pearson coefficients of the fMRI signals for each brain region and node. This method is highly susceptible to noise and ignores the temporal consistency of dynamic changes in fMRI signals. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a dynamic brain function network learning method based on graph learning optimization algorithms.

[0006] The method of this invention can directly extract the dynamic functional connectivity network of the brain from fMRI signals. The dynamic brain functional connectivity network can more reasonably and accurately reflect the connection strength between brain regions and the topological structure of the brain network.

[0007] A dynamic brain functional network learning method based on graph learning optimization algorithm includes the following steps:

[0008] Step (1) Determine the basic mathematical model of the brain network;

[0009] Step (2) Preprocess real neuroimaging data;

[0010] Step (3) Construct the objective function for finding the dynamic brain functional connectivity network;

[0011] Step (4) Determine the solution method for obtaining the dynamic brain functional connectivity network.

[0012] The specific method for step (1) is as follows:

[0013] Representing brain networks using graph theory is a common approach in neuroscience, allowing neurons and their connections to be expressed in graphical form. Specifically:

[0014] Brain nodes represent neurons: In the diagram, each neuron or brain region is represented as a brain node (vertex). Each brain node represents a neuron or a group of neurons, depending on the scale being studied.

[0015] Edges represent connections: Connections between neurons can be represented by edges. If there is a synaptic or functional connection between two neurons or a group of neurons, an edge is drawn between the corresponding brain nodes. Edges can be directional to indicate the direction of connection transmission.

[0016] Weights represent connection strength: Weights are attached to edges to represent the strength or weight of the connection. In brain networks, connection strength is related to the efficiency of synaptic transmission or other physiological parameters.

[0017] Graph Types: Different types of graphs are used depending on the problem. Common graph types include directed graphs and undirected graphs. Directed graphs are suitable for describing unidirectional connections, while undirected graphs are used to represent bidirectional connections or connections without directionality.

[0018] The brain is divided into different brain regions, which are represented by brain nodes. The set of brain nodes is represented as: V = {v1, v2, v3, ..., v...} N}, using a weighted adjacency matrix The brain functional connectivity network is represented in the form of w ij Represents brain node v i and v j The functional connectivity weight value between brain regions represents the strength of the functional connectivity between brain regions.

[0019] The signal at each brain node in the brain network is: X∈R N×m =[x1,...,x N ] T , where each row of X is x i ∈R n Represents brain node v i The electroencephalogram (EEG) signal selected in this invention is the BOLD signal.

[0020] Step (2) is performed as follows:

[0021] fMRI is a non-invasive brain imaging technique that reflects brain activity by measuring changes in blood oxygen levels. The steps to convert fMRI signals into blood oxygenation signals are as follows: fMRI scans generate a series of three-dimensional voxels (volume pixels). The raw fMRI data requires several preprocessing steps, such as head motion correction, temporal alignment, and noise removal. These steps help improve signal quality and accuracy.

[0022] By calculating the signal intensity of each voxel in the preprocessed data, a voxel time series is obtained, where each time point corresponds to the state of a three-dimensional voxel. The estimated blood oxygen (BOLD) signal is corrected and standardized for comparison and analysis among different subjects. The corrected blood oxygen signal can be used for various data analyses, such as functional connectivity analysis and brain region activity comparison analysis, to gain a deeper understanding of brain function.

[0023] The processed blood oxygenation signal is divided into multiple equally sized signals using a sliding window method. Specifically, a sliding window of size M×T is set, where M is the number of brain regions of interest (ROIs) and T is the number of sampling points. The window sliding step size is set to D sampling time points. By segmenting the BOLD signal using the sliding window, an M×T×N three-dimensional matrix is ​​obtained. S t ∈R M×T .

[0024] Step (3) is performed as follows:

[0025] For brain node pairs with high functional connectivity (v i ,v j The BOLD signals on brain node pairs exhibit similar characteristics. Since the signals on brain node pairs can be considered as a pair of vectors, as shown in equation (1), the similarity of the BOLD signals on brain node pairs is measured by calculating the square of the Euclidean distance between the two vectors:

[0026]

[0027] Wherein d(v i ,v j ) represents the pairwise distance, x i and x j These represent brain nodes v. i and v j The BOLD signal on the brain node is calculated. The pairwise distance of all brain node pairs is calculated and multiplied by the functional connectivity weight of the brain node pairs, as shown in Equation (2):

[0028]

[0029] Where X is the BOLD signal selected by the sliding window.

[0030] Furthermore, solving for the Laplace matrix of the brain functional connectivity network is transformed into solving the following optimization problem, as shown in equation (3):

[0031]

[0032] Since the optimized result of equation (3) is a Laplace matrix, it is difficult to obtain the brain functional connectivity matrix from the Laplace matrix. Therefore, equation (3) is rewritten to establish the objective function for solving the brain functional connectivity matrix. The specific operation is as follows:

[0033] definition Equation (2) can be equivalent to equation (4):

[0034]

[0035] Furthermore, as shown in equation (5), solving for the brain functional connectivity network is transformed into solving the following optimization problem:

[0036]

[0037] To ensure that each brain node maintains a connection with at least one other brain node, and because brain networks have small-world properties, the solved brain functional connectivity network W should be sparse. Therefore, a constraint term is added to the objective function (5), which is expressed as equation (6):

[0038]

[0039] Where 1 represents a vector whose elements are all 1s, i.e., 1 = [1,...,1] T The logarithmic constraint log(W1) ensures that the degree of the brain nodes in W is positive, but does not make any element in W zero, thus preventing trivial solutions from appearing in W. Add the F-norm constraint. To control the sparsity of the graph, parameters α and β are constraint weight parameters. The function of parameter α is to keep the edges in W connected, and the function of parameter β is to control the sparsity of W. The larger the value of parameter β, the sparser the solved W will be.

[0040] Step (4) is performed as follows:

[0041] The specific steps for solving the objective function constructed by equation (6) are as follows:

[0042] For the BOLD signal of each window, the dynamic brain functional connectivity network can be obtained by solving the brain functional connectivity network W of each window using equation (6). Because of the solution It is in W mSpace, W m Space can be described as: When solving the optimization problem of equation (6) using a specific optimization algorithm, the bilinear mapping method is used to transform W m Space transformed into W v Space, W v Space can be described as: In W v Space optimization will be easier. For example: in W v In the space, it is not necessary to deal with the symmetry problem of the functional connectivity matrix W, thus reducing the optimization difficulty.

[0043] Therefore, by using spatial transformation, equation (6) can be rewritten as equation (7):

[0044]

[0045] Where K is a linear operator satisfying W1 = Kw. Further, we define:

[0046] f1(w) = I{w≥0} + 2w T z

[0047] f2(d)=-α1 T log(d)

[0048] f3(w)=β||w|| 2

[0049] Where I{} is an indicator function, its value is zero when the condition in parentheses is met, and infinity otherwise, where d=Kw∈R m Then, the primal dual algorithm is used to solve equation (7) to obtain...

[0050] The beneficial effects of this invention are as follows:

[0051] This invention first processes fMRI data to obtain BOLD signals and uses a sliding window to divide the BOLD signals into multiple time periods; then, it designs an optimization algorithm based on graph learning to optimize and obtain a dynamic brain functional connectivity matrix, i.e., dynamic graph learning.

[0052] Dynamic brain functional connectivity networks are a method for measuring coordination between different brain regions. They study the information transmission and interaction patterns between brain regions and can be applied to many fields of neuroscience. The significance of this research includes, but is not limited to, the following:

[0053] 1. Understanding how the brain works: Dynamic brain connectivity networks can help us gain a deeper understanding of how the brain works, including the interactions between different areas, information processing, and transmission.

[0054] 2. Exploring Neurological Diseases: Research has found that the pathogenesis of mental illnesses may involve changes in the functional connectivity matrix of brain networks. For example, patients with schizophrenia may have abnormal connections in the prefrontal-amygdala pathway, while patients with depression may have weakened connections in the cingulate-amygdala pathway. Therefore, the dynamic graph learning method proposed in this invention can timely and accurately represent the evolution of the brain's functional connectivity network and the Laplace matrix, which can represent the brain's topological structure, playing a crucial role in the pathogenesis, prevention, and treatment of many diseases.

[0055] In summary, research on dynamic brain functional connectivity networks is of great significance for understanding the complexity of the brain and the mechanisms and treatments of neurological diseases. Attached Figure Description

[0056] The accompanying drawings, which are included to provide a further understanding of this specification and form part of this specification, illustrate exemplary embodiments and are used to explain this specification, but do not constitute an undue limitation thereof. In the drawings:

[0057] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0058] Figure 2 This is a schematic diagram of the sliding window processing of the BOLD signal according to an embodiment of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this specification will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of them. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this specification.

[0060] The technical solutions provided in the various embodiments of this specification are described in detail below with reference to the accompanying drawings.

[0061] like Figure 1 As shown, a dynamic brain function network learning method based on graph learning optimization algorithm is as follows:

[0062] Step (1): Determine the basic mathematical model of the brain network.

[0063] The AAL (Automated Anatomical Labeling) template is commonly used to partition the brain. It divides the brain's structure into different regions and assigns an anatomical label to each region. This template is widely used in neuroscience research to locate brain activity, analyze brain imaging data, and explore the functions of different brain regions. These regions include, but are not limited to, the following functional areas: 1. Prefrontal cortex: including the inferior frontal gyrus and dorsolateral prefrontal gyrus, involved in decision-making, planning, and emotional control. 2. Parietal lobe: including the superior and inferior parietal lobes, involved in spatial cognition, perception, and working memory. 3. Central gyrus: involved in motor control and motor execution. 4. Parieto-occipital gyrus: involved in visual processing and spatial cognition. 5. Occipital lobe: including the inferior temporal-occipital gyrus, involved in auditory processing and language comprehension. 6. Limbic system: involved in multimodal perception and attention allocation. 7. Facial sensorimotor area: involved in facial movement and sensation. Using the AAL template, the brain can be divided into 90 brain nodes. Therefore, the brain functional network can be modeled as follows: the set of brain nodes is represented as V = {v1, v2, v3, ..., v...} 90}, using a weighted adjacency matrix The brain functional connectivity network is encoded in the form of w ij Represents brain node v i and v j The functional connection weight values ​​between them.

[0064] Step (2): Preprocess real neuroimaging data.

[0065] First, raw functional magnetic resonance imaging (fMRI) signals at the blood oxygen-dependent level are acquired. The raw signals are four-dimensional matrices, i.e., three-dimensional space × one-dimensional time. The raw signals are then converted into a two-dimensional matrix V×L, where V represents the number of voxels in the MRI image and L is the number of sampling time points. Based on the Region of Interest (ROI) template, the average BOLD-fMRI signal of all voxels within each ROI is calculated. This average value represents the BOLD-fMRI signal value of that ROI. The two-dimensional matrix can be converted into M×L, where M is the number of brain ROIs and L is the number of sampling time points.

[0066] In this invention, experimental data were collected using fMRI signals from different body parts during task states. These signals were combinations of 2back-body, 0back-face, 2back-tools, 0back-body, 0bcak-place, 2bcak-face, 0back-tools, and 2back-place. Figure 2As shown, using the sliding window concept, the sliding window is set to 35, and the sliding step size of the window is 20. The dynamic functional connectivity network can be obtained by calculating the dynamic brain functional connectivity network corresponding to each window through the graph learning algorithm.

[0067] Step (3): Construct the objective function for obtaining the dynamic brain functional connectivity network.

[0068] For brain node pairs with high functional connectivity (v i ,v j The BOLD signals on brain node pairs exhibit similar characteristics. Since the signals on brain node pairs can be considered as a pair of vectors, as shown in equation (1), the similarity of the BOLD signals on brain node pairs is measured by calculating the square of the Euclidean distance between the two vectors:

[0069]

[0070] d(v) i ,v j ) represents the pairwise distance, x i and x j These represent brain nodes v. i and v j The BOLD signal on the brain node is calculated. The pairwise distance of all brain node pairs is calculated and multiplied by the functional connectivity weight of the brain node pairs, as shown in Equation (2):

[0071]

[0072] Where X is the BOLD signal selected by the sliding window.

[0073] Furthermore, solving for the Laplace matrix of the brain functional connectivity network is transformed into solving the following optimization problem, as shown in equation (3):

[0074]

[0075] Since the optimized result of equation (3) is a Laplace matrix, it is difficult to obtain the brain functional connectivity matrix from the Laplace matrix. Therefore, equation (3) is rewritten to establish the objective function for solving the brain functional connectivity matrix. The specific operation is as follows:

[0076] definition Equation (2) can be equivalent to equation (4):

[0077]

[0078] Furthermore, as shown in equation (5), solving for the brain functional connectivity network is transformed into solving the following optimization problem:

[0079]

[0080] To ensure that each brain node maintains a connection with at least another brain node, and because brain networks have small-world properties, the solved brain functional connectivity network W should be sparse. Therefore, a constraint term can be added to the objective function (5) to express it as equation (6):

[0081]

[0082] Where 1 represents a vector whose elements are all 1s, i.e., 1 = [1,...,1] T The logarithmic constraint log(W1) ensures that the degree of the brain nodes in W is positive, but does not make any element in W zero, thus preventing trivial solutions from appearing in W. Add the F-norm constraint. To control the sparsity of the graph, parameters α and β are constraint weight parameters. Parameter α is used to ensure that the edges in W have more connections, while parameter β is used to control the sparsity of W. The larger the value of parameter β, the sparser the solved W. Step (4): Determine the solution method for obtaining the dynamic brain functional connectivity network.

[0083] The W obtained by equation (6) is in W m space, When using specific optimization techniques to solve the optimization problem of equation (17), in order to make the optimization easier, W can be transformed through bilinear mapping. m Space transformed into W v space, Therefore, the symmetry problem of W can be avoided, thus reducing the optimization difficulty. In W v In space, matrices W and Z are represented using vectors, specifically described as: w = vec(W t ),w∈R 4005 ×1 z = vec(Z) Ft +Z Xt ),z∈R 4005×1 Some in W v Space and W v The equivalent terms in the space are shown in the table below:

[0084]

[0085] Therefore, as shown in equation (7), equation (6) can be transformed into the sum of the following three functions so that it can be solved using the primal dual algorithm:

[0086]

[0087] Where K is a linear operator satisfying W1 = Kw. Further, we define:

[0088] f1(w) = I{w≥0} + 2wT z

[0089] f2(d)=-α1 T log(d)

[0090] f3(w)=β||w|| 2

[0091] Where I{} is an indicator function, its value is zero when the condition in parentheses is satisfied, and infinity otherwise. Where d=Kw∈R m Then, the objective function is solved using the primal-dual algorithm to obtain the dynamic functional connectivity network. Spectral clustering is then used to perform cluster analysis on the functional connectivity matrices corresponding to different windows, thereby determining the brain's state.

[0092] The above description, in conjunction with specific / preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. Those skilled in the art can make various substitutions or modifications to these described embodiments without departing from the inventive concept, and all such substitutions or modifications should be considered within the scope of protection of the present invention.

[0093] The parts of this invention not described in detail are well-known to those skilled in the art.

Claims

1. A dynamic brain functional network learning method based on graph learning optimization algorithm, characterized in that, The steps include the following: Step (1) Determine the basic mathematical model of the brain network; Step (2) Preprocess real neuroimaging data; Step (3) Construct the objective function for obtaining the dynamic brain functional connectivity network; Step (4) Determine the solution method for obtaining the dynamic brain functional connectivity network; The specific method for step (1) is as follows: The neurons and their connections are represented in the form of a graph; specifically: Brain nodes represent neurons: In the diagram, each neuron or brain region is represented as a brain node; Edges represent connections: Connections between neurons can be represented by edges; Weights represent connection strength: Weights are attached to edges to represent the strength or weight of the connection; in brain networks, the strength of a connection is related to the efficiency of synaptic transmission or other physiological parameters. Graph types: Different types of graphs are used depending on the problem. The brain is divided into different brain regions, and these regions are represented by brain nodes. The set of brain nodes is represented as follows: Using a weighted adjacency matrix The brain functional connectivity network is represented in the form of , in which Represents brain nodes and The functional connectivity weight value between brain regions represents the strength of functional connectivity between brain regions. The signals at each brain node in the brain network are: Each row of X Represents brain nodes Blood oxygenation signal; Step (2) is performed as follows: The fMRI signal was preprocessed to convert it into a blood oxygenation signal; a voxel time series was obtained by calculating the signal intensity of each voxel in the preprocessed data, where each time point corresponds to the state of a three-dimensional voxel; the estimated blood oxygenation signal was corrected and standardized. The processed blood oxygenation signal is divided into multiple signals of equal size using a sliding window method. Specifically, a sliding window of size M×T is set, where M is the number of brain regions of interest (ROIs) and T is the number of sampling points; the window sliding step size is set to D sampling time points; and the blood oxygenation signal is segmented using the sliding window to obtain a three-dimensional matrix of size M×T×N. ; Step (3) is performed as follows: For brain node pairs with high functional connectivity The blood oxygenation signals on brain nodes show similar characteristics; Since the signals on a pair of brain nodes can be regarded as a pair of vectors, as shown in Equation (1), the similarity of blood oxygenation signals on a pair of brain nodes is measured by calculating the square of the Euclidean distance between the two vectors: (1) in, For paired distances, and Representing brain nodes and The blood oxygenation signal on the brain; calculate the pairwise distance of all brain node pairs and multiply it by the functional connectivity weight of the brain node pairs, as shown in Equation (2): (2) Where X is the blood oxygen signal selected by the sliding window; Furthermore, solving for the Laplace matrix of the brain functional connectivity network is transformed into solving the following optimization problem, as shown in equation (3): (3) Rewrite equation (3) to establish the objective function for solving the brain functional connectivity matrix. The specific steps are as follows: definition Equation (2) can be equivalent to equation (4): (4) Furthermore, as shown in equation (5), solving for the brain functional connectivity network is transformed into solving the following optimization problem: (5) To ensure that each brain node maintains a connection with at least one other brain node, and because brain networks have small-world properties, the solved brain functional connectivity network W should be sparse. Therefore, a constraint term is added to the objective function (5), which is expressed as equation (6): (6) Where 1 represents a vector whose elements are all 1s, i.e. Logarithmic constraint term make The degree of a midbrain node is positive, but this does not make it... The elements in the array are changed to 0, thereby avoiding A trivial solution appears; add an F-norm constraint term. To control the sparsity of the graph, parameters and For the constrained weight parameters, the parameters Its function is to make The edges in the data maintain a relatively large number of connections, and the parameters... Its function is to control sparsity, parameters The larger the value, the better the solution. The sparser.

2. The dynamic brain function network learning method based on graph learning optimization algorithm according to claim 1, characterized in that, Step (4) is performed as follows: The specific steps for solving the objective function constructed by equation (6) are as follows: For the blood oxygenation signal of each window, the brain functional connectivity network of each window is solved using Equation (6). This allows us to obtain dynamic brain functional connectivity networks. ; due to the solution Is space, Space can be described as: When using a specific optimization algorithm to solve the optimization problem of equation (6), the bilinear mapping method is used to... Space transformed space, Space can be described as: ; Therefore, by using spatial transformation, equation (6) can be rewritten as equation (7): （7） in It is to satisfy Linear operators; further, define: in It is an indicator function; its value is zero when the condition in parentheses is met, and infinite otherwise. Then, the primal dual algorithm is used to solve equation (7) to obtain... .

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