Cooperative and competitive functional brain network construction method based on Isin model

Abstract

The invention discloses a collaborative and competitive function brain network construction method based on an Isin model, and the method comprises the steps: extracting a BOLD signal of each brain region in brain image data, and carrying out the first-order difference and binarization processing, and obtaining the binary time sequence state data of each brain region; calculating the probability of same-direction and reverse-direction state changes between every two brain intervals at all time points, and establishing a likelihood function of the probability of interaction between the brain intervals based on an Isin model; solving the likelihood function to obtain a probability matrix of interaction between brain intervals; and converting the probability matrix into a brain region connection relationship in the brain network through a Bayesian multiplication formula. A BOLD signal is processed into a state time sequence, fluctuation information is reserved while data are simplified, it is ensured that real data information is effectively utilized, two opposite action relations are represented by means of different state change conditions of paired brain intervals, the interaction relation of the brain intervals is represented from the two aspects of cooperation and competition, and the accuracy of the brain interaction is improved. And the constructed brain network is more comprehensive in representation of brain physiological dynamics.

Description

Technical Field

[0001] The present invention relates to brain network construction, and in particular to a method for constructing a brain network with cooperative and competitive functions based on an Ising model. Background Art

[0002] The human brain is one of the most complex systems known in nature. Various brain regions are interconnected by fiber bundles to form a complex structural network, and various daily functions are completed through interactions between brain regions. The current mainstream brain networks can be roughly divided into two categories: structural connection networks and functional connection networks. Among them, the structural connection network reflects the similarity of structural morphology in the cerebral cortex, but it is limited to only one brain T1 image for each subject, so the network is mostly constructed in a group manner. Functional magnetic resonance imaging (fMRI) is a non-invasive imaging technology that indirectly measures brain functional activity based on the blood oxygen level-dependent (BOLD) signal generated by neural activity. The construction of functional brain networks is usually based on fMRI technology and is achieved by calculating functional connectivity, which describes the statistical correlation between brain regions in a specific time period. More and more studies have shown that the clinical symptoms of many mental illnesses are related to brain networks connecting different regions. For example, the existing technology has found that the default network of patients with depression has reduced connectivity with the central executive network. When studying schizophrenia, it was found that patients had significant abnormalities in the thalamus-cortex connection circuit. At present, complex network theory of brain networks has been widely used in the research of cognitive neuroscience and clinical medicine. This is mainly because it has the potential to quantitatively elucidate the functional patterns of networks and disease-related brain changes, providing a new perspective for studying how the brain works and understanding the pathological mechanisms of neuropsychiatric diseases.

[0003] Many methods for constructing functional brain networks have been developed so far. Commonly used methods include two categories: hypothesis-driven methods and data-driven methods. The hypothesis-driven method assumes that the interaction between two signals is linear and can directly calculate the connection strength. For example, the brain functional network between two brain regions was constructed through Pearson correlation, and it was confirmed that it has small-world properties. Another example is the Spearman rank correlation, which studies the differences in brain functional networks of patients with cognitive impairment in different age domains and genders, and identifies subnetworks related to the severity of patients' symptoms. The data-driven method relies on a specific data-driven model to solve directional information, thereby constructing a directed network to evaluate the causal relationship between neurons. This method can reflect the abnormality of brain circuit activity and help understand the underlying mechanism of neuronal dynamics. For example, a dynamic causal modeling (DCM) is used to construct a directed brain network. This model is based on the Bayesian inference model and jointly considers information such as neural activity, neurovascular coupling, and hemodynamic state to describe the causal relationship between node pairs, reflecting the abnormality of brain circuit activity. In addition to the commonly used Bayesian inference model, information connectivity (IC) does not directly use the signal correlation between brain regions, but considers the possible connection between brain regions with similar responses to the same stimulation pattern. However, when constructing a brain network with the above methods, only one interaction relationship can exist between different brain regions, that is, the network edge weights are either positive or negative. During analysis, one relationship is often obscured, and the synergistic competitive relationship between brain regions cannot be fully described, resulting in the inaccurate construction of the brain network. Summary of the invention

[0004] Purpose of the invention: In view of the above shortcomings, the present invention provides a method for constructing a collaborative and competitive functional brain network based on the Ising model to improve the accuracy of brain network representation.

[0005] Technical solution: To solve the above problems, the present invention adopts a method for constructing a collaborative and competitive functional brain network based on the Ising model, comprising the following steps:

[0006] (1) Obtain historical brain imaging data and extract BOLD signals from each brain region;

[0007] (2) Performing first-order difference processing on the BOLD signals of each brain region, and binarizing the signals after first-order difference processing to obtain binary time series state data of each brain region;

[0008] (3) Based on the binary time series state data of each brain region, the probability of the same-direction state change and the probability of the opposite-direction state change between any two brain regions at all time points are calculated. Based on the calculated probabilities and the Ising model, a likelihood function of the probability of interaction between brain regions is established;

[0009] (4) By iteratively maximizing the established likelihood function, the probability matrix of interactions between brain regions is solved;

[0010] (5) The probability matrix is ​​converted into the brain region connection relationship in the collaborative and competitive functional brain network through the Bayesian multiplication formula.

[0011] Furthermore, the first-order difference processing of the BOLD signal of each brain region in step (2) is as follows: subtracting the value of the BOLD signal at the previous time point from the value at the next time point;

[0012] In the step (2), the signal after the first-order difference processing is binarized as follows: a signal greater than 0 in the signal after the first-order difference processing is assigned a value of 1, and a signal less than or equal to 0 is assigned a value of 0.

[0013] Furthermore, the calculation of the probability of the same-direction state change and the probability of the opposite-direction state change between two brain regions at all time points in step (3) includes:

[0014] The probability of the same-direction state change between every two brain regions is calculated using the following formula:

[0015]

[0016] The probability of reverse state change between every two brain regions is calculated using the following formula:

[0017]

[0018] in, is the probability that the i-th brain region and the j-th brain region undergo the same-direction state change; is the probability of reverse state change between the i-th brain region and the j-th brain region; is the state of the ith brain region at time t, is the state of the i-th brain region at time t+1; is the state of the jth brain region at time t, is the state of the jth brain region at time t+1.

[0019] Furthermore, in step (3), the expectation of the relationship between cooperation and competition between two brain regions is calculated based on the Ising model according to the calculated probability, and the calculation formula is:

[0020]

[0021] in, is the expectation of the state change of the i-th brain region from time t to time t+1; is the probability that the jth brain region has a direct impact on the ith brain region when the ith brain region and the jth brain region undergo state changes in the same direction, is the probability that the kth brain region has a direct impact on the ith brain region when the ith brain region and the kth brain region undergo reverse state changes; is the conditional variable for whether the jth brain region and the ith brain region undergo the same state change from time t to time t+1, is the conditional variable for whether the kth brain region and the ith brain region undergo a reverse state change from time t to time t+1; is a confounding variable that has a random effect on the i-th brain region at time t.

[0022] Furthermore, the likelihood function of the probability of interaction between brain regions is:

[0023]

[0024] in, is the conditional variable for whether the i-th brain region has a state change event from time t to time t+1; Θ is and T is the total number of time points for BOLD signal sampling; N is the total number of brain regions.

[0025] Furthermore, the step (5) converts the probability matrix into the brain region connection relationship in the collaborative and competitive functional brain network through the Bayesian multiplication formula, specifically:

[0026]

[0027]

[0028] in, is the synergistic connection between the i-th brain region and the j-th brain region, is the competitive connection between the ith brain region and the kth brain region, P(j→i) is the probability that the ith brain region is directly affected by the jth brain region, and P(k→i) is the probability that the ith brain region is directly affected by the kth brain region.

[0029] Furthermore, the brain imaging data includes resting-state functional magnetic resonance imaging data and task-state functional magnetic resonance brain imaging data.

[0030] Furthermore, the preprocessed brain image data is divided into brain regions according to a brain atlas, and the brain atlas includes an AAL atlas.

[0031] The present invention also adopts a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the above method when executing the computer program.

[0032] The present invention also adopts a computer-readable storage medium on which a computer program is stored, characterized in that the computer program implements the steps of the above method when executed by a processor.

[0033] Beneficial effects: Compared with the prior art, the significant advantage of the present invention is that the BOLD signal is processed into a state time series through first-order difference and binarization operations, and the fluctuation information of the BOLD signal is retained while simplifying the data. It is used as observation data to participate in the maximum likelihood estimation, ensuring that the constructed brain network can effectively utilize the information of the real data, and making the network connection approximately obey the normal distribution, which is helpful for statistical inference. Different from the traditional functional connection method, the different state changes between paired brain regions are used to characterize two opposite interaction relationships, and the synergistic and competitive effects of a certain brain region on other brain regions are distinguished, rather than being either positive or negative, that is, only describing one action relationship. It can dig out the interaction characteristics between brain regions from the perspectives of synergy and competition, so that the constructed brain network can more comprehensively characterize the physiological dynamics of the brain. The two types of connections are obtained simultaneously in the paired brain regions, which effectively avoids the disadvantage of the two types of connections interfering with each other in the traditional network construction, so that the relationship between brain regions can be described reliably and comprehensively, providing a more comprehensive perspective for discovering abnormal network connections related to brain diseases. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 Schematic diagram of the process of constructing a midbrain network according to the present invention.

[0035] Figure 2 Schematic diagram of the distribution of network connection features obtained by the midbrain network construction method of the present invention, considering the schizophrenia (SZ) group and the healthy control (HC) group on the HCP dataset and the BSNIP dataset separately, and merging the two groups.

[0036] Figure 3 The similarities of the collaborative and competitive network connection features obtained by the midbrain network construction method of the present invention on the HCP dataset between multiple scans of the same subject and between different subjects.

[0037] Figure 4 This is a schematic diagram of the inter-group comparison of brain area connections after the collaborative and competitive brain networks are constructed on the BSNIP dataset by the midbrain network construction method of the present invention.

[0038] Figure 5 Schematic diagram of the brain network patterns of schizophrenia (SZ) and healthy controls (HC) after the collaborative competitive hybrid network is constructed on the BSNIP dataset by the midbrain network construction method of the present invention. DETAILED DESCRIPTION

[0039] like Figure 1 As shown, a method for constructing a collaborative and competitive functional brain network based on the Ising model in this embodiment includes the following steps:

[0040] Step S1: extracting BOLD signals of each brain region from functional magnetic resonance imaging data based on brain atlas.

[0041] In this step, the preprocessing steps for the original functional magnetic resonance brain image data include: first, head motion correction; second, inter-layer time correction; then, the image is normalized to the Montreal Neurological Institute (MNI) template and the voxel size is resampled to 3mm×3mm×3mm; then, the covariate is removed, and the 6 head motion parameters and white matter (WM), gray matter (GM), cerebrospinal fluid (CSF) are regressed out; finally, the 8mm half-full width maximum Gaussian filter kernel is used for spatial smoothing. In terms of brain map selection, the Automated Anatomical Labeling (AAL) brain map can be selected for partitioning, and other structural or functional brain maps of different sizes can also be selected according to actual conditions.

[0042] Step S2: Perform first-order difference and binarization processing on all BOLD signals to obtain the binary time series state of each brain region.

[0043] The first-order difference and binarization steps are as follows: First, subtract the value of the previous time point from the value of the next time point in the extracted BOLD signal, that is, S′ t =S t+1 -S t (t=1,2,…,T-1), where T represents the total number of time points; then, the part of the signal after differential processing that is greater than 0 is assigned to 1, and the part that is less than or equal to 0 is assigned to 0.

[0044] The above processing is performed on the BOLD signal of each brain region, and the binary time series state of all brain regions is obtained.

[0045] Step S3: Based on the binary state data obtained in step S2, the probability of the same or opposite state changes between two brain regions at all time points is calculated as the observed variable, and the likelihood function is established according to the Ising model and the interaction relationship between brain regions.

[0046] Specifically, the state change probability is calculated for the observed binary time series state based on the following formula as the observed variable:

[0047] Calculate the conditional probability of the same-direction state change occurring between every two brain regions:

[0048]

[0049] Calculate the conditional probability of reverse state changes between every two brain regions:

[0050]

[0051] in, and They refer to the conditional probability of the i-th brain region and the j-th brain region undergoing the same / opposite state change calculated from the observed data; and They refer to the states of the ith brain region and the jth brain region at time t, respectively, and take values ​​of 0 or 1, indicating the falling state or rising state of the BOLD signal, respectively.

[0052] According to the Ising model, the expectation of the relationship between cooperation and competition between two brain regions is calculated:

[0053]

[0054] in, It refers to the expectation of the state change of the i-th brain region from time t to t+1; and They refer to the probability that brain region j / k has a direct impact on brain region i when the i-th brain region and the j / k-th brain region undergo state changes in the same direction / opposite direction, respectively, and are latent variables to be solved; and refers to the conditional variable of whether the j / k-th brain area and the i-th brain area have the same / opposite state change event from time t to t+1, and the value is 0 or 1, indicating the non-occurrence or occurrence of the event, respectively; Refers to the confounding variable that has a random effect on the i-th brain region at time t.

[0055] Poisson distribution is used to characterize the randomness of the number of brain region mutations within a period of time. Given the brain region mutation events at all times, a likelihood function for the hidden variables to be solved is established:

[0056]

[0057] in, It refers to the conditional variable of whether the state change event occurs in the i-th brain area from time t to t+1, and its value is 0 or 1, indicating the non-occurrence or occurrence of the event respectively; T refers to the total number of time points of BOLD signal sampling; Θ refers to the latent variable to be solved and A collection of brain regions; N refers to the total number of brain regions processed by the brain atlas.

[0058] Step S4: By iteratively maximizing the likelihood function established in step S3, the probability matrix of interaction between brain regions under the two state changes is solved respectively.

[0059] The formula after converting the likelihood function established in step S3 into logarithmic form is as follows:

[0060]

[0061] The desired expectation Substituting into the above formula and applying Jensen's inequality to The likelihood function to be maximized can be converted into the following equivalent formula:

[0062]

[0063] The above transformation is valid if and only if the following equation is satisfied:

[0064]

[0065]

[0066]

[0067] The steps to solve the maximization problem of the target likelihood function include: and Initialized to 1, by respectively finding right and The partial derivative of and setting it equal to 0 can be solved and The above steps are repeated for each brain region to obtain the probability matrix of the interaction between brain regions under the two state changes.

[0068] Step S5: The probability matrix is ​​converted into the brain region connection relationship in the collaborative and competitive functional brain network through the Bayesian multiplication formula.

[0069] The elements of the two probability matrices are converted to brain area connections in the cooperative and competitive functional brain networks based on the following Bayesian multiplication formula:

[0070]

[0071]

[0072] in, and refers to the synergistic / competitive connection between the ith brain region and the j / kth brain region, respectively. P(j→i) and P(k→i) refer to the probability that the ith brain region is directly affected by the j / kth brain region, respectively. The partial correlation between the BOLD signals of the ith brain region and the j / kth brain region is used for approximate calculation.

[0073] This example uses the Bipolar and Schizophrenia Network of Intermediate Phenotypes (BSNIP) dataset (containing fMRI data of 178 schizophrenia patients and 219 healthy subjects) and the Human Connectome Project (HCP) dataset (containing fMRI data of 980 healthy subjects who have undergone 4 scans) for testing.

[0074] like Figure 2 As shown, the distribution of collaborative and competitive network connection features obtained by the construction method of this embodiment through cross-dataset and cross-group calculations is compared, and the distribution properties of the features extracted by this method across HCP and BSNIP datasets and across schizophrenia and healthy controls are exemplarily shown, proving that the results of the method proposed in this embodiment on different datasets approximately follow the normal distribution, which is helpful for subsequent statistical analysis of the features. Figure 3 As shown, the similarities of the collaborative and competitive network connection features obtained by the method between multiple scans of the same subject and between different subjects are compared, and the similarity of the features constructed by the method on the HCP dataset between multiple scans of the same subject is significantly higher than the similarity between different subjects, which proves the reliability of the method proposed in the embodiment of the present invention; Figure 2 and Figure 3 The results jointly prove the effectiveness of the collaborative and competitive network connection features calculated by the method proposed in the embodiment; Figure 4 The network connection strengths of schizophrenia patients and healthy controls on the cooperative and competitive networks were compared, specifically showing that brain diseases lead to changes in brain connections on the cooperative and competitive networks; Figure 5 Schematic diagram comparing the brain functional network patterns of schizophrenia and healthy controls on the mixed co-competitive network, specifically showing the differences in connection patterns between schizophrenia and healthy controls on the fusion network.

[0075] In summary, the effectiveness of the brain network features constructed by the brain network construction method of this embodiment is verified. First, the normal properties of the features extracted from healthy subjects in the HCP dataset and schizophrenia patients and healthy subjects in the BSNIP dataset prove that the proposed method can effectively perform subsequent statistical analysis; secondly, the results of the similarity test for the same subject under multiple scanning sessions further illustrate the reliability of the results of the proposed method. On this basis, this method uses the mined robust features of the brain network to perform inter-group comparisons to explore the changes in brain network functional patterns caused by brain diseases.

Claims

1. A method for constructing a collaborative and competitive functional brain network based on the Ising model, characterized in that: The following steps are involved: (1) Obtain historical brain imaging data and extract BOLD signals from each brain region; (2) Performing first-order difference processing on the BOLD signals of each brain region, and binarizing the signals after first-order difference processing to obtain binary time series state data of each brain region; (3) Based on the binary time series state data of each brain region, the probability of the same-direction state change and the probability of the opposite-direction state change between any two brain regions at all time points are calculated. Based on the calculated probabilities and the Ising model, a likelihood function of the probability of interaction between brain regions is established; (4) By iteratively maximizing the established likelihood function, the probability matrix of interactions between brain regions is solved; (5) The probability matrix is ​​converted into the brain region connection relationship in the collaborative and competitive functional brain network through the Bayesian multiplication formula.

2. The method for constructing a collaborative and competitive functional brain network based on the Ising model according to claim 1, characterized in that: The first-order difference processing of the BOLD signal of each brain region in step (2) is as follows: subtracting the value of the BOLD signal at the previous time point from the value at the next time point; In the step (2), the signal after the first-order difference processing is binarized as follows: a signal greater than 0 in the signal after the first-order difference processing is assigned a value of 1, and a signal less than or equal to 0 is assigned a value of 0.

3. The method for constructing a collaborative and competitive functional brain network based on the Ising model according to claim 2, characterized in that: The calculation of the probability of the same-direction state change and the probability of the opposite-direction state change between two brain regions at all time points in step (3) includes: The probability of the same-direction state change between every two brain regions is calculated using the following formula: The probability of reverse state change between every two brain regions is calculated using the following formula: in, is the probability that the i-th brain region and the j-th brain region undergo the same-direction state change; is the probability of reverse state change between the i-th brain region and the j-th brain region; is the state of the ith brain region at time t, is the state of the i-th brain region at time t+1; is the state of the jth brain region at time t, is the state of the jth brain region at time t+1.

4. The method for constructing a collaborative and competitive functional brain network based on the Ising model according to claim 3, characterized in that: In step (3), the expectation of the relationship between cooperation and competition between two brain regions is calculated based on the Ising model according to the calculated probability, and the calculation formula is: in, is the expectation of the state change of the i-th brain region from time t to time t+1; is the probability that the jth brain region has a direct impact on the ith brain region when the ith brain region and the jth brain region undergo state changes in the same direction, is the probability that the kth brain region has a direct impact on the ith brain region when the ith brain region and the kth brain region undergo reverse state changes; is the conditional variable for whether the jth brain region and the ith brain region undergo the same state change from time t to time t+1, is the conditional variable for whether the kth brain region and the ith brain region undergo a reverse state change from time t to time t+1; is a confounding variable that has a random effect on the i-th brain region at time t.

5. The method for constructing a collaborative and competitive functional brain network based on the Ising model according to claim 4, characterized in that: The likelihood function of the probability of interaction between the brain regions is: in, is the conditional variable for whether the i-th brain region has a state change event from time t to time t+1; Θ is and T is the total number of time points for BOLD signal sampling; N is the total number of brain regions.

6. The method for constructing a collaborative and competitive functional brain network based on the Ising model according to claim 5, characterized in that: The step (5) converts the probability matrix into the brain area connection relationship in the collaborative and competitive functional brain network through the Bayesian multiplication formula, specifically: in, is the synergistic connection between the i-th brain region and the j-th brain region, is the competitive connection between the ith brain region and the kth brain region, P(j→i) is the probability that the ith brain region is directly affected by the jth brain region, and P(k→i) is the probability that the ith brain region is directly affected by the kth brain region.

7. The method for constructing a collaborative and competitive functional brain network based on the Ising model according to claim 1, characterized in that: The brain image data includes resting state functional magnetic resonance imaging data and task state functional magnetic resonance brain image data.

8. The method for constructing a collaborative and competitive functional brain network based on the Ising model according to claim 1, characterized in that: The preprocessed brain image data is divided into brain regions according to a brain atlas, which includes an AAL atlas.

9. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

Images