A brain network analysis method based on hypergraph and gravity model

Abstract

The application discloses a brain network analysis method based on a hypergraph and a gravity model, relates to the technical field of electroencephalogram signal analysis and complex network science, and comprises the following steps: S1, acquiring multi-channel stereoelectroencephalogram signals, and calculating the phase locking values between each pair of channels; and S2, based on the phase locking values, taking the stereoelectroencephalogram channels as nodes, and constructing a 3-consistent weighted hypergraph, wherein each hyperedge in the 3-consistent weighted hypergraph comprises three nodes, and the nodes in the 3-consistent weighted hypergraph are divided into multiple groups; the driving force between groups is obtained through layer-by-layer deduction, the high-order correlation characteristics between brain groups can be reflected in multiple dimensions, the interaction of different brain groups can be quantified from the aspect of the driving direction, the multiple quantitative indexes derived can enrich the analysis dimension of the driving relationship between brain groups, and the method is suitable for various brain signal research scenes, so as to meet the actual research and use requirements of the fine analysis of brain interaction mechanisms.

Description

Technical Field

[0001] This invention relates to the fields of electroencephalogram (EEG) signal analysis and complex network science and technology, and in particular to a brain network analysis method based on hypergraphs and gravity models. Background Technology

[0002] Epilepsy EEG network analysis technology is a quantitative method that reveals the information transmission patterns between different brain regions by constructing a functional connectivity model of multi-channel intracranial EEG signals.

[0003] Currently, when conducting quantitative analysis of epileptic EEG networks, the main approach is to introduce hypergraphs as a high-order interaction modeling tool, allowing a single hyperedge to connect multiple nodes simultaneously, thereby characterizing group-level interactions and overcoming the limitations of traditional graph theory frameworks in complex dynamic processes involving the collaborative participation of multiple brain groups. In addition, traditional causal analysis methods are used to provide directional information between time series for pairwise causal correlation calculations to capture the unidirectional information transmission characteristics between two brain groups.

[0004] However, existing hypergraph-based epilepsy research focuses primarily on the identification of static higher-order structures or node centrality ranking, such as detecting the importance of brain groups or computational nodes that constitute higher-order coupled communities. However, it cannot analyze the driving and response roles of different brain group groups in different seizure stages of epilepsy, and it is difficult to characterize the dynamic transmission path of discharge signals across brain group groups. Traditional causal analysis methods are limited to pairwise analysis between two channels, making it difficult to effectively capture the collaborative driving patterns between three or more brain group groups. Therefore, existing technologies cannot quantify the directed driving relationships between different brain group groups from the perspective of intergroup driving forces, resulting in a failure to meet the actual research needs of functional grouping in epileptic brain networks. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a brain network analysis method based on hypergraphs and gravity models, which solves the technical problem that existing technologies are unable to quantify the directed driving relationships between different brain groups from the perspective of inter-group driving forces and cannot meet the needs of practical research.

[0006] The technical means employed in this invention are as follows: In a first aspect, the present invention provides a brain network analysis method based on a hypergraph and gravity model, comprising: S1. Acquire multi-channel stereo EEG signals and calculate the phase lock value between each pair of channels; S2. Based on the phase-locked value, a 3-consistent weighted hypergraph is constructed using the stereo EEG channel as nodes. Each hyperedge in the 3-consistent weighted hypergraph includes three nodes, and the nodes in the 3-consistent weighted hypergraph are divided into multiple groups. S3. Based on the cyclic mean of the instantaneous phase of each node in the 3-consistent weighted hypergraph, calculate the cyclic correlation coefficient between each pair of nodes in each hyperedge; S4. Construct a cyclic correlation coefficient matrix based on the cyclic correlation coefficient, and calculate the probability of the eigenvalues ​​in the cyclic correlation coefficient matrix; S5. Based on the probability of the feature value, calculate the cycle-related complexity of each of the hyperedges; S6. Based on the aforementioned cyclic complexity, calculate the bisection-induced hyperedge degree; S7. Calculate the bisection induction index based on the bisection induction hyperedge degree; S8. Calculate the intergroup driving index based on the dichotomy induction index; S9. Calculate the higher-order distance between groups; S10. Construct a gravity model based on the inter-group driving index and the inter-group higher-order distance, and calculate the inter-group driving force between the two groups based on the gravity model; S11. Repeat steps S2-S10 to obtain the inter-group driving forces among multiple groups, and perform brain network analysis based on the inter-group driving forces among multiple groups.

[0007] Furthermore, the formula for calculating the phase-locked value is as follows: , Wherein, PLV is the phase-locked value. and Signal sequences from two stereo EEG channels and The instantaneous phase at time t, where T is the total length of time. The imaginary unit, This is the modulo operator for complex numbers.

[0008] Furthermore, the expression for the hyperedge in the 3-consistent weighted hypergraph is: , in, For the time series of the i-th channel, For the remaining channels except for the i-th channel -1 channel time series, Let be the influence coefficient of the i-th channel on the remaining n-1 channels. Let be the phase-locking value between the i-th channel and the remaining n-1 channels. This is the regularization parameter.

[0009] Furthermore, the formula for calculating the cyclic correlation coefficient is as follows: , in, Let be the cyclic correlation coefficient between node i and node j, t be the discrete time step index, and T be the total sample length of the phase sequence. Let be the instantaneous phase of node i at time t. Let be the cyclic mean of the instantaneous phase of node i. Let be the instantaneous phase of node j at time t. Let be the cyclic mean of the instantaneous phase of node j.

[0010] Furthermore, the formula for calculating the cyclic complexity is as follows: , in, For loop-related complexity, The entropy of the eigenvalue distribution. The maximum possible entropy of the three-channel system. The probability of being the k-th eigenvalue.

[0011] Furthermore, the formula for calculating the bisection-induced hypermargin is: , in, Let i be the bisection-induced hyperedge degree of node i in group A with respect to group B. Let k be the superedge. Let W be the weight of the k-th superedge, and W be the set of weights. This indicates that the superedge e includes at least one node from group A. This indicates that the superedge e includes at least one node from group B.

[0012] Furthermore, the formula for calculating the inter-group driving index is as follows: , in, This represents the inter-group driving index between group A and group B, where A is the source group and B is the target group. Let V be the bisection induction index of node i in group A with respect to group B. A Let A be the set of nodes in source group A; The formula for calculating the dichotomous induction index is as follows:

[0013] in, Let i be the bisection-induced hyperedge degree of node i in group A with respect to group B. Let be the total weighted hyperedge degree of node i within the 3-uniform hypergraph.

[0014] Furthermore, the formula for calculating the inter-group driving force is as follows: , in, This is the inter-group driving force between group A and group B. This represents the inter-group driving index between group A and group B. For the total degree of group A, For the total degree of group B, This represents the higher-order inter-group distance from group A to group B.

[0015] Furthermore, after step S11, the following steps are also included: S12. Draw the box plot and mean plot of the inter-group driving force distribution; S13. Calculate the relative driving force based on the inter-group driving force between the two groups; S14. Calculate the average relative driving force based on the relative driving force; S15. Draw a graph of the relative driving force mean; S16. Based on the inter-group driving force between the two groups, calculate the net driving force of each group; S17. Based on the net driving force, calculate the average net driving force for each group; S18. Draw a diagram of the net driving force mean.

[0016] Furthermore, the formula for calculating the net driving force is: , in, For group A, Let A be the sum of the driving forces of group A on all groups B and C. This is the sum of the driving forces of group B and group C on group A.

[0017] Compared with the prior art, the present invention has the following advantages: This invention constructs a 3-consistent weighted hypergraph using three-dimensional EEG signals. Based on the cyclic correlation coefficient, cyclic correlation complexity, dichotomous induced correlation index, and higher-order distance between groups, it deduces the inter-group driving force layer by layer. This can reflect the higher-order association characteristics between brain groups in multiple dimensions and quantify the interaction between different brain groups from the perspective of directed driving. The derived quantitative indicators, such as relative driving force, average relative driving force, and net driving force, can enrich the analytical dimensions of driving relationships between brain groups and adapt to various brain signal research scenarios to meet the practical research needs of refined analysis of brain interaction mechanisms.

[0018] Based on the above reasons, this invention can be widely applied in fields such as electroencephalogram (EEG) signal analysis and complex network science. Attached Figure Description

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

[0020] Figure 1 This is a flowchart illustrating a brain network analysis method based on a hypergraph and gravity model in an embodiment of the present invention. Figure 2 This is a schematic diagram of the topology of the 3-consistent weighted hypergraph in an embodiment of the present invention; Figure 3 This is a schematic diagram of the process for calculating the Intergroup Driving Index (IGDI) in an embodiment of the present invention; Figure 4 This is a schematic diagram of the process for calculating higher-order distances between groups in an embodiment of the present invention; Figure 5 This is a box plot showing the distribution of the six directed intergroup driving forces (IGDF) in each attack stage in an embodiment of the present invention. Figure 6 This is a heatmap of the average intergroup driving force (gIGDF) of the six directed connections in each attack phase in an embodiment of the present invention. Figure 7 This is a line graph showing the change of the average relative driving force (RDF) of the three regions in this embodiment of the invention with the attack stage; Figure 8 This is a bar chart showing the average net driving force (NDF) of the three regions in each attack stage in an embodiment of the present invention. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0022] It should be noted that the terms "comprising" and "having" and any variations thereof in this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0023] The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0024] Please see Figure 1 , Figure 1 This is a flowchart illustrating a brain network analysis method based on a hypergraph and gravity model, as described in an embodiment of the present invention.

[0025] This invention provides a brain network analysis method based on a hypergraph and gravity model, comprising: S1. Acquire multi-channel stereoscopic EEG signals and calculate the phase lock value between each pair of channels. By acquiring multi-channel stereoscopic EEG signals and solving for the phase lock value between channels, the degree of phase synchronization between the intracranial EEG acquisition channels is quantitatively characterized.

[0026] Multi-channel stereoscopic EEG signals are acquired by collecting intracranial electroencephalogram (EEG) signals. Based on the seizure onset and termination times marked by clinicians, the multi-channel EEG signals are temporally segmented along the time axis, dividing the EEG signal corresponding to a single seizure into five temporal sub-signals: pre-seizure, early-seizure, mid-seizure, late-seizure, and post-seizure. A sliding time window is defined for each seizure stage, and gamma-band (30–80 Hz) bandpass filtering is applied to all channels within the sliding time window. Instantaneous phase sequences are extracted from the filtered EEG signals, and the phase locking value (PLV) between each pair of paired channels is calculated based on these instantaneous phase sequences to quantify the phase synchronization between multiple channels. By solving for the phase locking value of each paired channel in stages and within sliding time windows, the strength of phase synchronization between different intracranial EEG acquisition channels at different seizure stages can be accurately quantified.

[0027] In some embodiments, the phase-locked value is calculated using the following formula: , Wherein, PLV is the phase-locked value. and Signal sequences from two stereo EEG channels and The instantaneous phase at time t, where T is the total length of time. The imaginary unit, This is the complex number modular arithmetic operator. The phase lock value ranges from 0 to 1. A value of 0 indicates that there is no synchronicity between the two brain channels, meaning that the phase difference between them at different times has no obvious bias or regularity. A value of 1 indicates that the two brain channels are completely phase locked, meaning that the phase difference between them remains constant at all times, indicating that the two brain channels are highly synchronized.

[0028] S2. Based on phase-locked values, a 3-consistent weighted hypergraph is constructed using stereo EEG channels as nodes. Each hyperedge in the 3-consistent weighted hypergraph includes three nodes, and the nodes in the 3-consistent weighted hypergraph are divided into multiple groups. By constructing a 3-consistent weighted hypergraph with stereo EEG channels as nodes using phase-locked values ​​and grouping the nodes, the ternary synergistic association and grouping distribution characteristics between EEG channels can be presented.

[0029] Using stereo EEG channels as hypergraph nodes, a 3-consistent weighted hypergraph is constructed for each sliding time window using the PLASO (Phase-weighted Least Absolute Shrinkage and Selection Operator) method. The PLASO method sets the phase lock value as an adaptive weight and incorporates it into the penalty term corresponding to the Least Absolute Shrinkage and Selection Operator (LASSO) regression to screen stereo EEG channel triples with nonlinear high-order interaction associations. The screened channel triples are used as hyperedges to construct a 3-consistent weighted hypergraph under a single sliding time window.

[0030] By incorporating phase-locked values ​​as adaptive weights into the minimum absolute contraction and selection operator regression penalty term and screening high-order interaction channel triplets to construct a hypergraph, we can accurately extract ternary high-order synergistic correlation features between intracranial multi-channel EEG signals. These ternary high-order synergistic correlation features overcome the limitations of traditional dual-channel binary phase synchronization analysis, which can only capture second-order coupling relationships. They reconstruct the physiological mechanism of synchronous and coordinated firing of neuronal clusters across multiple brain groups during epileptic seizures, avoiding the loss of information on the collective coordinated pathogenesis patterns of multiple brain groups.

[0031] Please see Figure 2 , Figure 2This is a schematic diagram of the topological structure of a 3-consistent weighted hypergraph in an embodiment of the present invention. The dashed triangles on the left side of the figure illustrate the composition rules of a single hyperedge. The set of nodes {A,B,C} together form a hyperedge, satisfying the setting that a single hyperedge of a 3-consistent hypergraph contains three nodes. The right side of the figure shows the complete 3-consistent weighted hypergraph. v1, v2, v3, and v4 are the nodes corresponding to the stereo EEG channels. The solid triangles containing e1-e7 are the hyperedges in the hypergraph, and each hyperedge connects three nodes. The nodes are grouped using differentiated features, and each hyperedge uses the phase-locked value as an adaptive weight, intuitively reflecting the high-order interaction relationship between multiple intracranial EEG channels.

[0032] In some embodiments, the expression for a hyperedge in a 3-consistently weighted hypergraph is: , in, For the time series of the i-th channel, For the remaining channels except for the i-th channel -1 channel time series, Let be the influence coefficient of the i-th channel on the remaining n-1 channels. Let be the phase-locking value between the i-th channel and the remaining n-1 channels. This is the regularization parameter. and The value can be 0.5, used to control the sparsity of the solutions. Additionally, setting... =0.2, for The correlation coefficients are used to filter out unimportant interactions and reduce redundant connections.

[0033] S3. Based on the cyclic mean of the instantaneous phase of each node in the 3-consistent weighted hypergraph, calculate the cyclic correlation coefficient between each pair of nodes in each hyperedge. For the three stereo EEG channel nodes in a single hyperedge, calculate the cyclic correlation coefficient between the stereo EEG channels within the hyperedge using the cyclic mean of the instantaneous phase. This coefficient reflects the degree of linear correlation between the two phase sequences on the circumference.

[0034] In some embodiments, the formula for calculating the cyclic correlation coefficient is: , in, Let be the cyclic correlation coefficient between node i and node j, t be the discrete time step index, and T be the total sample length of the phase sequence. Let be the instantaneous phase of node i at time t. Let be the cyclic mean (circular average) of the instantaneous phase of node i. Let be the instantaneous phase of node j at time t. Let be the cyclic mean (circular average) of the instantaneous phase of node j.

[0035] S4. Construct a cyclic correlation coefficient matrix based on the cyclic correlation coefficient, and calculate the probability of the eigenvalues ​​in the cyclic correlation coefficient matrix.

[0036] Constructing a cycle correlation coefficient matrix based on the cycle correlation coefficient Calculate the probability distribution of eigenvalues ​​in the cyclic correlation coefficient matrix to calculate the cyclic correlation complexity.

[0037] The formula for calculating the eigenvalue probabilities in the cyclic correlation coefficient matrix is: , in, This represents the probability distribution of the k-th eigenvalue. Let represent the k-th eigenvalue of the cyclic correlation coefficient matrix R, where k=1, 2, 3 correspond to the three nodes inside the hyperedge.

[0038] S5. Calculate the cyclic dependency complexity of each hyperedge based on the probabilities corresponding to the eigenvalues. By calculating the cyclic dependency complexity of the hyperedge based on the probabilities corresponding to the eigenvalues, the degree of phase coupling between the three nodes within the hyperedge is quantitatively characterized. The higher the cyclic dependency complexity, the stronger the phase coupling between the three nodes within the hyperedge.

[0039] In some embodiments, the formula for calculating the complexity of loop-related problems is: , in, For loop-related complexity, The entropy of the eigenvalue distribution. The maximum possible entropy of the three-channel system. The probability is the k-th eigenvalue. COC is used to represent the weight of the hyperedge, with a value range of [0,1]. The closer it is to 1, the stronger the phase coupling between the three channels.

[0040] S6. Calculate the bisection-induced hyperboundary based on cyclic correlation complexity. Solve the bisection-induced hyperboundary using a weighted calculation method. This bisection-induced hyperboundary can characterize the intensity differences in higher-order interactions between different stereo EEG channel groups.

[0041] In some embodiments, the formula for calculating the bisection-induced hypermargin is: , in, Let i be the bisection-induced hyperedge degree of node i in group A with respect to group B. Let be the hyperedge involving node i and group B. Let W be the weight of the k-th superedge, where the loop-related complexity COC can be used as the weight, and W is the set of weights. This indicates that the superedge e includes at least one node from group A. This indicates that the superedge e includes at least one node from group B.

[0042] S7. Calculate the bisection induced hyperedge degree based on the bisection induced hyperedge degree. The bisection induced index is calculated by taking the ratio of the bisection induced hyperedge degree of a node to the total hyperedge degree of the node. This index reflects the degree of participation of a node in the group in cross-group interactions.

[0043] The formula for calculating the dichotomous induction index is: , in, Let be the bisection induction index of node i in group A with respect to group B. Let i be the bisection-induced hyperedge degree of node i in group A with respect to group B. Let be the total weighted hyperedge degree of node i within the 3-uniform hypergraph.

[0044] S8. Calculate the intergroup driving index based on the dichotomous induction index. The intergroup driving index can quantitatively characterize the overall driving potential of stereo EEG channel group A for stereo EEG channel group B.

[0045] In some embodiments, the formula for calculating the inter-group driving index is: , in, This represents the inter-group driving index between group A and group B, where A is the source group and B is the target group. Let V be the bisection induction index of node i in group A with respect to group B. A Let A be the set of nodes of source group A.

[0046] Please see Figure 3 , Figure 3 This is a flowchart illustrating the calculation of the Inter-Group Driving Index (IGDI) in an embodiment of the present invention. The calculation process is as follows: First, the bisection induction index of each node within a group relative to the target group is calculated. Taking nodes v2, v3, and v4 in the attached figure as examples, the bisection induction index corresponding to each node is defined as the ratio of the higher-order bisection distance from the node to the target group to the total weighted degree of the node. Then, the inter-group driving index is solved. The inter-group driving index is defined as the sum of the bisection induction indices of all nodes in the source group A corresponding to the target group B.

[0047] S9. Calculate the higher-order distance between groups. By calculating the higher-order distance between groups, the overall degree of difference between the two groups of data can be intuitively reflected.

[0048] The formula for calculating the higher-order distance between groups is: , in, The higher-order distance between groups A and B is defined as the mean of the higher-order distances between all node pairs between the two groups. Let be the higher-order distance between node u in group A and node v in group B, set as the minimum sum of the inverses of the weights of the hyperedges in the path plus one. If there is no path between the two nodes, then... Let it be the sum of the reciprocals of the weights of all hyperedges in the hypergraph; and These represent the number of nodes in group A and group B, respectively.

[0049] Please see Figure 4 , Figure 4 This is a flowchart illustrating the calculation of higher-order distances between groups in an embodiment of the present invention. The complete definition of the higher-order distance between two groups of nodes is as follows: For any two nodes, the higher-order distance between them is the result of adding the minimum value of the inverse sum of the weights of all hyperedges corresponding to all connected paths between them to a constant; if there is no connected path between two nodes, the higher-order distance between them is assigned the inverse sum of the weights of all hyperedges within the current hypergraph. For node v within group A... i With group B internal node v j The steps for calculating higher-order distances are: Solve for the path set P ij This set is collected from node v i Proceed to node v j All superedges traversed during the process; based on the path set P ij For each connected path within the group, calculate the inverse sum of the weights of the hyperedges corresponding to each path, and then extract the minimum value among all the sums. Add the minimum value to a constant, and the result is the value of node v in group A. i With group B node v j The higher-order distance between groups.

[0050] S10. Construct a gravitational model based on the inter-group driving index and the higher-order inter-group distance, and calculate the inter-group driving force between two groups based on the gravitational model. The inter-group driving index characterizes the nodal gravitational mass in the gravitational model, and the higher-order inter-group distance characterizes the spatial distance between groups in the gravitational model. The inter-group driving force is defined as the structural influence between two independent groups in the hypergraph, in order to distinguish the strength of the interaction between different groups and reflect the degree of correlation between the inter-group structures.

[0051] In some embodiments, the formula for calculating the inter-group driving force is: , in, The inter-group driving force from group A to group B, This represents the inter-group driving index between group A and group B. For the total degree of group A, For the total degree of group B, This represents the higher-order inter-group distance from group A to group B. The larger the value, the stronger the structural driving effect of group A on group B.

[0052] S11. Repeat steps S2-S10 to obtain the inter-group driving forces among multiple groups, and perform brain network analysis based on the inter-group driving forces among multiple groups.

[0053] Repeat steps S2 to S10 to obtain the intergroup driving forces between all groups; the multiple groups can be epileptogenic zone group, propagation zone group and irrelevant zone group, and the intergroup driving forces between the three groups in six conduction directions, namely: epileptogenic zone group to propagation zone group, propagation zone group to epileptogenic zone group, epileptogenic zone group to irrelevant zone group, irrelevant zone group to epileptogenic zone group, propagation zone group to irrelevant zone group, and irrelevant zone group to propagation zone group.

[0054] It is worth noting that the gravity model refers to the interaction force between two groups of objects, used to quantify the unidirectional structural influence between the two groups. This invention uses the dichotomous induction index to characterize the driving volume between different brain region groups as the mass parameter in the gravity model, and the high-order topological distance between hypergraph groups as the distance parameter in the gravity model. Based on the quantification of these two parameters, the unidirectional inter-group driving force is obtained. Directed gravity calculation is achieved through a 3-consistent weighted hypergraph, which can distinguish the asymmetric relationship between driving and driven between different brain region groups. With the help of a sliding time window, the strength of gravity and role evolution of high-order information interaction between brain regions in the epileptogenic region group, the propagation region group, and the irrelevant region group can be dynamically tracked throughout the entire epileptic seizure process, quantitatively reflecting the information driving effect brought about by the high-order phase coupling between brain regions.

[0055] In some embodiments, after step S11, the method further includes: S12, plotting box plots and mean plots of the inter-group driving forces; this step is used to present the statistical distribution and central tendency of the driving force indicators among all groups, and simultaneously executes a three-stage multiple comparison correction process, which sequentially includes the following three test methods: 1. Friedman test; 2. Wilcoxon signed-rank test; 3. Wilcoxon signed-rank test with exploratory directional comparison function. Visualizing the overall statistical characteristics of inter-group driving forces and performing three-stage multiple comparison correction tests in a hierarchical manner accurately identifies statistical differences in driving force values ​​between different groups, improving the reliability of the inter-group difference determination results.

[0056] Please see Figure 5 , Figure 5This is a box plot showing the distribution of the six directed intergroup driving forces (IGDF) at each seizure stage in an embodiment of the present invention. The boxes represent interquartile ranges, the inner horizontal lines represent the median, and the superimposed scatter plots show the data distribution for each seizure. A three-stage multiple comparison correction strategy was employed: the first stage performed Friedman's test (Bonferroni correction) on each direction. =0.05 / 6≈0.0083), the results showed significant overall stage differences in all six directions; the second stage performed a Wilcoxon signed-rank test (Bonferroni corrected) on adjacent stages. =0.05 / 24≈0.00208); the third phase involved three exploratory directional comparisons (Bonferroni correction, =0.05 / 3≈0.0167), the results showed that the driving force from the transmission zone to the epileptogenic zone significantly increased from the early to late stage (W=26, p=0.015), the parentheses ( The test statistic is the W value (or W value).

[0057] Please see Figure 6 , Figure 6 This is a heatmap of the average intergroup driving force (gIGDF) of the six directed connections in each seizure phase in an embodiment of the present invention. The color intensity corresponds to the strength of the driving force, from light (low) to dark (high). The results show that there is a systematic redistribution pattern of driving forces in different directions during seizure phases, rather than a simple monotonic change.

[0058] S13. Calculate the relative driving force based on the intergroup driving force between the two groups. The relative driving force is used to characterize the directional advantage of the driving force between the two groups. By performing a difference operation on the bidirectional intergroup driving force to solve for the relative driving force, the difference in the directional strength of the driving force between the two groups can be intuitively quantified.

[0059] The formula for calculating the intergroup driving force is: , in, The relative driving force of group A on group B, The inter-group driving force from group A to group B, This represents the inter-group driving force from group B to group A.

[0060] S14. Calculate the average relative driving force based on the relative driving force; calculate the average relative driving force for each of the three groups (epileptic zone group, propagation zone group, and irrelevant zone group) to assess the directional driving advantage among the groups.

[0061] S15. Draw a relative driving force mean map; the relative driving force mean map can be used to compare the differences in driving directionality between different regions.

[0062] Please see Figure 7 , Figure 7 This is a line graph showing the change in the average relative driving force (RDF) of the three regional pairs as a function of seizure stage in this embodiment of the invention. The solid lines connect the mean RDF values ​​at each stage, and the shaded bands represent the standard error of the mean. The zero baseline is marked by a dashed line, indicating that the RDF of the epileptogenic zone to the propagation zone pair is negative in all stages (-0.089 to -0.021), indicating that the propagation zone always maintains a driving advantage over the epileptogenic zone, and this advantage is further deepened in the middle and late stages of the seizure; the absolute value of the RDF of the epileptogenic zone-irrelevant zone pair is relatively small (-0.035 to -0.008), approaching equilibrium in the middle of the seizure, and showing differentiation in the late stage; the RDF of the propagation zone-irrelevant zone pair reaches its peak in the early stage of the seizure and then gradually decays, indicating that the driving advantage of the propagation zone over the irrelevant zone gradually weakens as the seizure progresses.

[0063] S16. Based on the inter-group driving force between two groups, calculate the net driving force of each group; the sum of the inter-group driving forces generated by target group A on all other groups, minus the sum of the inter-group driving forces generated by all other groups on target group A, is used to determine whether group A is a net driver or a net receiver. This can distinguish the primary and secondary attributes of the overall output and reception driving effects of each group, and intuitively determine the dominant role of the overall signal transmission of the group.

[0064] In some embodiments, the formula for calculating net driving force is: , in, For group A, Let A be the sum of the driving forces of group A on all groups B and C. This is the sum of the driving forces of group B and group C on group A. When When >0, group A is the net driving force. When <0, group A is the net receiver.

[0065] S17. Based on net driving force, calculate the average net driving force of each group. By calculating the average net driving force of each group (epilepsogenic zone group, propagation zone group, and irrelevant zone group), it can be determined whether each group is a net driver or a net receiver in the global interaction.

[0066] S18. Draw a mean net driving force plot. The mean net driving force plot can be used to analyze the changing trends of net driving force in each group.

[0067] Please see Figure 8 , Figure 8This is a bar chart showing the mean net driving force (NDF) of the three regions in this embodiment of the invention at each seizure stage. Positive values ​​represent net driving forces, and negative values ​​represent net receiving forces. The mean net driving force of the epileptogenic region remains negative throughout the seizure cycle, maintaining its role as a net receiving force; the mean net driving force of the propagation region remains positive, maintaining its role as a net driving force; the mean net driving force of the irrelevant region is negative (net receiving force) in the early stage of the seizure and turns positive (net driving force) in the late stage, showing a descriptive role switching trend.

[0068] This invention integrates a gravity model into a hypergraph analysis framework to quantify the directional driving force between brain region groups. The inter-group driving force index combines the inter-group driving index and the inter-group higher-order distance. The inter-group driving index represents the equivalent quality, and the inter-group higher-order distance represents the topological spacing. Within a unified analysis framework, it represents the directional interaction between different brain region groups.

[0069] The bipartite induced hyperedge degree index and bipartite induced index constructed in this invention utilize the basic structural unit composed of a single node in a 3-consistent weighted hypergraph paired with two nodes of the same group to quantify the mediating role of nodes in cross-group high-order interactions. Compared with conventional node centrality indices, these two indices can intuitively reflect the attribute information corresponding to the group to which a node belongs.

[0070] The relative driving force index and net driving force index proposed in this invention map the complex interaction relationships between multiple groups to two independent quantitative dimensions, which correspond to the degree of asymmetry in the directionality of the interaction and the role of the node in the global hypergraph network, respectively. This dimensionality reduction strategy enables complex multi-group directed interaction networks to be described and compared with simple quantitative indicators, which facilitates visualization and statistical analysis in clinical applications.

[0071] This invention achieves dynamic tracking of driving force indicators based on a sliding time window strategy, which can reveal the complete evolution trajectory of the driving-receiving relationship between brain regions from the beginning to the end of the seizure process, providing a time-resolved quantitative analysis method for analyzing the seizure network mechanism of brain diseases such as epilepsy.

[0072] This invention constructs a 3-consistent weighted hypergraph using three-dimensional EEG signals. Based on the cyclic correlation coefficient, cyclic correlation complexity, dichotomous induced correlation index, and higher-order distance between groups, it deduces the inter-group driving force layer by layer. This can reflect the higher-order association characteristics between brain groups in multiple dimensions and quantify the interaction between different brain groups from the perspective of directed driving. The derived quantitative indicators, such as relative driving force, average relative driving force, and net driving force, can enrich the analytical dimensions of driving relationships between brain groups and adapt to various brain signal research scenarios to meet the practical research needs of refined analysis of brain interaction mechanisms.

[0073] In summary, this invention constructs a 3-consistent weighted hypergraph by acquiring multi-channel stereo EEG signals, and fully reconstructs the high-order correlation structure of brain channels using three-node hyperedges. It obtains the inter-group driving index by solving layer by layer using the cyclic correlation coefficient, cyclic correlation complexity, bipartite induced hyperedge degree, and bipartite induced index, and calculates the inter-group driving force by normalizing the high-order distance between groups, thus quantifying the bidirectional structural influence of each group. Furthermore, it derives and solves for relative driving force, average relative driving force, net driving force, and average net driving force, hierarchically characterizing the directional driving advantage and overall transmission attributes of groups, comprehensively depicting the directional driving correlation between brain groups from multiple dimensions, and adapting to the actual research needs of brain analysis.

[0074] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A brain network analysis method based on hypergraphs and gravity models, characterized in that, include: S1. Acquire multi-channel stereo EEG signals and calculate the phase lock value between each pair of channels; S2. Based on the phase-locked value, a 3-consistent weighted hypergraph is constructed using the stereo EEG channel as nodes. Each hyperedge in the 3-consistent weighted hypergraph includes three nodes, and the nodes in the 3-consistent weighted hypergraph are divided into multiple groups. S3. Based on the cyclic mean of the instantaneous phase of each node in the 3-consistent weighted hypergraph, calculate the cyclic correlation coefficient between each pair of nodes in each hyperedge; S4. Construct a cyclic correlation coefficient matrix based on the cyclic correlation coefficient, and calculate the probability of the eigenvalues ​​in the cyclic correlation coefficient matrix; S5. Based on the probability of the feature value, calculate the cycle-related complexity of each of the hyperedges; S6. Based on the aforementioned cyclic complexity, calculate the bisection-induced hyperedge degree; S7. Calculate the bisection induction index based on the bisection induction hyperedge degree; S8. Calculate the intergroup driving index based on the dichotomy induction index; S9. Calculate the higher-order distance between groups; S10. Construct a gravity model based on the inter-group driving index and the inter-group higher-order distance, and calculate the inter-group driving force between the two groups based on the gravity model; S11. Repeat steps S2-S10 to obtain the inter-group driving forces among multiple groups, and perform brain network analysis based on the inter-group driving forces among multiple groups. The formula for calculating the bisection-induced hypermargin is: ， in, Let i be the bisection-induced hyperedge degree of node i in group A with respect to group B. Let k be the superedge. Let W be the weight of the k-th superedge, and W be the set of weights. This indicates that the superedge e includes at least one node from group A. This indicates that the superedge e includes at least one node from group B; The formula for calculating the inter-group driving index is as follows: ， in, This represents the inter-group driving index between group A and group B, where A is the source group and B is the target group. Let V be the bisection induction index of node i in group A with respect to group B. A Let A be the set of nodes in source group A; The formula for calculating the dichotomous induction index is as follows: in, Let i be the bisection-induced hyperedge degree of node i in group A with respect to group B. Let i be the total weighted hyperedge degree of node i within the 3-consistent weighted hypergraph; The formula for calculating the inter-group driving force is: ， in, This is the inter-group driving force between group A and group B. This represents the inter-group driving index between group A and group B. For the total degree of group A, For the total degree of group B, This represents the higher-order inter-group distance from group A to group B. The formula for calculating the higher-order distance between groups is: ， in, This represents the higher-order inter-group distance between group A and group B. Let u be the higher-order distance between node u in group A and node v in group B. and These represent the number of nodes in group A and group B, respectively.

2. The brain network analysis method based on hypergraphs and gravity models according to claim 1, characterized in that, The formula for calculating the phase lock value is as follows: ， Wherein, PLV is the phase-locked value. and Signal sequences from two stereo EEG channels and The instantaneous phase at time t, where T is the total length of time. The imaginary unit, This is the modulo operator for complex numbers.

3. The brain network analysis method based on a hypergraph and gravity model according to claim 1, characterized in that, The expression for the hyperedge in the 3-consistent weighted hypergraph is: ， in, For the time series of the i-th channel, For the remaining channels except for the i-th channel -1 channel time series, Let be the influence coefficient of the i-th channel on the remaining n-1 channels. Let be the phase-locking value between the i-th channel and the remaining n-1 channels. This is the regularization parameter.

4. The brain network analysis method based on a hypergraph and gravity model according to claim 1, characterized in that, The formula for calculating the cyclic correlation coefficient is as follows: ， in, Let be the cyclic correlation coefficient between node i and node j, t be the discrete time step index, and T be the total sample length of the phase sequence. Let be the instantaneous phase of node i at time t. Let be the cyclic mean of the instantaneous phase of node i. Let be the instantaneous phase of node j at time t. Let be the cyclic mean of the instantaneous phase of node j.

5. The brain network analysis method based on a hypergraph and gravity model according to claim 1, characterized in that, The formula for calculating the complexity of the loop is: ， in, For loop-related complexity, The entropy of the eigenvalue distribution. The maximum possible entropy of the three-channel system. The probability of being the k-th eigenvalue.

6. The brain network analysis method based on a hypergraph and gravity model according to claim 1, characterized in that, Following step S11, the following is also included: S12. Draw the box plot and mean plot of the inter-group driving force distribution; S13. Calculate the relative driving force based on the inter-group driving force between the two groups; S14. Calculate the average relative driving force based on the relative driving force; S15. Draw a graph of the relative driving force mean; S16. Based on the inter-group driving force between the two groups, calculate the net driving force of each group; S17. Based on the net driving force, calculate the average net driving force for each group; S18. Draw a diagram of the net driving force mean.

7. The brain network analysis method based on a hypergraph and gravity model according to claim 6, characterized in that, The formula for calculating the net driving force is: ， in, For group A, Let A be the sum of the driving forces of group A on all groups B and C. This is the sum of the driving forces of group B and group C on group A.

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