A tensor-based method for calculating node centrality in dynamic brain networks

Abstract

The present invention discloses a method for calculating the centrality of nodes in a dynamic brain network, comprising the following steps: preprocessing the collected resting-state functional magnetic resonance imaging and extracting a time series; using a sliding time window method to divide the time series into overlapping sub-segments of fixed length, calculating the correlation coefficient within each time sub-segment, and constructing a dynamic brain functional network that changes over time; representing the dynamic brain network as a fourth-order tensor; and using a power iteration method to calculate the centrality of each node in the dynamic brain network. This method takes into account both the number of neighbor nodes of the node in different layers and the centrality of each neighbor node when evaluating the centrality of a node. The present invention helps to accurately measure the centrality of nodes in a dynamic brain network, and has important application value in the field of brain function and structure research.

Description

Technical Field

[0001] The present invention belongs to the technical field of complex network analysis and relates to a tensor-based dynamic brain network node centrality calculation method. Background Art

[0002] Centrality is widely considered to be one of the key measures that provides insights into the structure and function of complex brain networks. However, so far, research on centrality methods has mainly focused on single-layer brain networks whose nodes are connected by a single interaction type. In fact, a large number of studies have found that the brain changes dynamically over time. Traditional static networks ignore the dynamic relationships between nodes over time, which may lead to incomplete capture of the details in the real system, which may lead to incorrect conclusions about topological and dynamical properties. Summary of the invention

[0003] In order to further extract information from the topological structure of multi-layer brain networks and fully consider the interactions within and between layers, the present invention provides a tensor-based method for calculating the node centrality of dynamic brain networks, introduces tensors to represent multi-layer brain networks, and proposes the use of power iteration method to evaluate the node centrality of dynamic brain networks.

[0004] The technical solution adopted by the present invention is a tensor-based dynamic brain network node centrality calculation method, comprising the following steps:

[0005] Step S1: preprocessing the brain functional magnetic resonance image of the subject to obtain a preprocessed brain functional magnetic resonance image;

[0006] Step S2: According to the selected standardized brain atlas, the preprocessed functional magnetic resonance imaging is segmented into 90 brain regions;

[0007] Step S3: extract the time series of each brain region, perform layered operations on the time series using the sliding time window technology, construct a multi-layer dynamic brain network, and represent the dynamic brain network based on tensors;

[0008] Step S4: using an iterative method to calculate the eigenvector centrality of nodes in the dynamic brain network;

[0009] Step S5: Compare the eigenvector centrality of the dynamic brain network nodes with the eigenvector centrality of the single-layer brain network nodes in terms of resolution entropy and global efficiency change ratio. Further, in step S1, the specific steps of preprocessing include: removing the first 10 time points, time point correction, head motion correction, spatial normalization, smoothing, removing linear drift and filtering.

[0010] Furthermore, in step S3,

[0011] The sliding time window technology is used to perform layered operations on time series. The specific steps include:

[0012] The number of sliding windows is calculated as follows:

[0013]

[0014] Where T is the length of the entire time series, W is the window size, and H is the moving step size; W = 1 / f min , where f min is the minimum frequency contained in the preprocessed data;

[0015] After data preprocessing, the minimum frequency of the data is 0.01 Hz, so the window size W is calculated to be 100 seconds, that is, 50 time points; at the same time, this experiment determines the window moving step H to be 2 seconds, that is, one time point, so 93 time windows are generated, and finally a 93-layer dynamic brain network is constructed, with 90 nodes in each layer of the network.

[0016] Furthermore, in step S3, the dynamic brain network is represented based on tensors, specifically including:

[0017] A dynamic network is represented as W = {Φ, C};

[0018] Where Φ={G α :α∈{1,2,…,L}}, represents the set of L-layer networks, G α =(V α ,E α ), represents the network of the αth layer; V α represents the nodes in the αth layer of the network, E α Represents the edges in the αth layer of the network;

[0019] in, E αβ Represents the edge between the two layers of network α and β, V1=V2=…=V L ={v1,v2,…,v N}, indicating that the nodes in each layer of the network are the same, with a total of N;

[0020] A dynamic brain network can be represented as a fourth-order tensor, M = (M iαjβ )∈R N×L×N×L is a fourth-order adjacency tensor of a dynamic brain network;

[0021] in,

[0022] 1≤α,β≤L,1≤i,j≤N, Represents the i-node of layer α.

[0023] Furthermore, in step S4, an iterative method is used to calculate the node v in the dynamic brain network. i The eigenvector centrality DFC_EV(v i ), including:

[0024] Assume that at the kth iteration, node v i The eigenvector centrality of is E (k) (i,α);

[0025] (1)

[0026] (2) During iteration, Each element in is normalized by L2 norm, and we get E (k+1) (i,α);

[0027]

[0028] Among them, 1≤α≤L, 1≤i≤N, is a second-order tensor;

[0029] (3) The above iterative process continues until E (k+1) The end is when the change in the sum of the absolute values ​​of all elements in (i, α) is less than 0.01;

[0030] (4) After the above iterative calculation, find a maximum λ * and the corresponding second-order tensor E * , node v i The eigenvector centrality of is:

[0031]

[0032] Furthermore, the step S5 specifically includes:

[0033] According to entropy theory, resolution entropy RE is defined as follows:

[0034]

[0035] Where S = {e1, e2, …, e 90} is a one-dimensional vector composed of the centrality values ​​of 90 nodes, n i The node centrality value is e i According to the representation of RE, it can be clearly seen that when the centrality values ​​of all nodes are the same, RE obtains the minimum value RE min =0, and when the centrality values ​​of all nodes are not equal, RE obtains the maximum value RE max =log(N).

[0036] Furthermore, the step S5 specifically includes:

[0037] Global efficiency E glob Expressed as:

[0038]

[0039] Among them, d ij It refers to the minimum number of edges to go through from one node to another;

[0040] Assumption E glob Denotes the global efficiency before the network attack, E′ glob represents the global efficiency of the brain network after removing a key node, then the change ratio E of the global efficiency of the network is expressed as:

[0041]

[0042] The value range of E is 0≤E≤1.

[0043] Beneficial effects of the present invention: The present invention provides a tensor-based method for calculating the centrality of nodes in a dynamic brain network, introduces tensors to represent multi-layer brain networks, and proposes to use a power iteration method to evaluate the centrality of nodes in a dynamic brain network. From the resolution entropy and global efficiency change ratio indicators, compared with the centrality method of a single-layer network, experimental results show that the method proposed by the present invention can more accurately measure the centrality of nodes. The present invention helps to accurately calculate the centrality of nodes, provides a good foundation for future research on dynamic brain networks, and provides a systematic method for describing how centrality propagates across different layers, which has important application value in the field of brain function and structure research. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of the method of the present invention.

[0045] Figure 2 It is a bar graph of the resolution entropy of the present invention.

[0046] Figure 3 This is a diagram showing the changes in E after deleting the top-ranked nodes in the present invention. DETAILED DESCRIPTION

[0047] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] Test example

[0049] The data used in this experiment was provided by the UCLA Neuropsychiatry Consortium. This data was obtained through a public database, Open fMRI (https: / / openfmri.org / dataset / ds000030 / ). The resting state functional magnetic resonance imaging data included 40 healthy subjects. The specific subject information is shown in Table 1.

[0050] Table 1 Basic information of subjects

[0051]

[0052] Neuroimaging data of NC subjects were obtained by functional MRI scanning on a 3T Siemens Trio scanner. During the acquisition process, soft foam and earplugs were used to fix the subject's head to reduce noise during the scan. fMRI data were collected using a T2-weighted echo-planar imaging (EPI) sequence with the following parameters: slice thickness of 4 mm, slice number of 34, echo time of 30 ms, flip angle of 90°, field of view (FOV) of 192 mm, repetition time of 2 s, and resolution of 64 × 64. The resting-state fMRI data scanning process lasted a total of 304 s, and a total of 152 time points were obtained.

[0053] like Figure 1 As shown, the present invention uses Dparsf software to preprocess the brain functional magnetic resonance images, and the preprocessing specifically includes: removing the first 10 time points, time point correction, head movement correction, spatial standardization, smoothing, removing linear drift and filtering; then using the automatic anatomical labeling template, the preprocessed brain functional magnetic resonance images are segmented to divide the brain into 90 brain regions;

[0054] The sliding time window technique is used to perform layered operations on the time series of fMRI signals. The number of sliding windows is calculated as follows:

[0055]

[0056] Among them, T is the length of the entire time series, W is the window size, and H is the moving step size. This experiment uses 1 / f min To determine the window length, where f min is the minimum frequency of the data. After preprocessing the data, the minimum frequency of the data is 0.01 Hz, so the window size (W) is set to 100 seconds, that is, 50 time points. At the same time, this experiment sets the moving step (H) of the window to 2 seconds, that is, 1 time point. Therefore, 93 time windows are generated, and finally a 93-layer (L) dynamic brain network is constructed, with 90 (N) nodes in each layer. A dynamic network is represented by W = {Φ, C}, where Φ = {Gα :α∈{1,2,…,L}}, represents the set of L-layer networks, G α =(V α ,E α ), represents the network of layer α, V α represents the nodes in the αth layer of the network, E α represents the edges in the αth layer of the network, Where E αβ Represents the edge between the two layers of network α and β, V1=V2=…=V L ={v1,v2,…,v N}, indicating that the nodes in each layer of the network are the same, with a total of N nodes.

[0057] A dynamic brain network can be represented as a fourth-order tensor, M = (M iαjβ )∈R N×L×N×L is a fourth-order adjacency tensor of a dynamic brain network.

[0058] in,

[0059] 1≤α,β≤L,1≤i,j≤N, Represents the i-node of layer α.

[0060] Using iterative methods to calculate node v in dynamic brain networks i The eigenvector centrality DFC_EV(v i ), the calculation process is as follows:

[0061] Assume that at the kth iteration, node v i The eigenvector centrality of is E (k) (i,α),

[0062] (1)

[0063] (2) During iteration, Each element in is normalized by L2 norm, and we get E (k+1) (i,α)

[0064]

[0065] Among them, 1≤α≤L, 1≤i≤N, is a second-rank tensor.

[0066] (3) The above iterative process continues until E (k+1) The process ends when the change in the sum of the absolute values ​​of all elements in (i,α) is less than 0.01.

[0067] (4) After the above iterative calculation, find a maximum λ* and the corresponding second-order tensor E * , node v i The eigenvector centrality of is:

[0068]

[0069] In order to verify the effectiveness of the present invention, a single-layer static network containing N=90 nodes and a multi-layer dynamic brain network containing N=90 nodes and L=93 layers were constructed for 40 healthy subjects obtained from a public database. The eigenvector centrality (EV_S and DFC_EV) of each node in the single-layer network and the multi-layer network were calculated, and comparisons were made from the two indicators of resolution entropy and global efficiency change ratio.

[0070] Resolution entropy (RE) is an indicator used to predict node centrality and has a high degree of recognition of sorting results. In order to reveal the resolution of the new centrality method, according to entropy theory, resolution entropy RE is defined as follows:

[0071]

[0072] Where S = {e1, e2, …, e 90} is a one-dimensional vector composed of the centrality values ​​of 90 nodes, n i The node centrality value is e i According to the representation of RE, it can be clearly seen that when the centrality values ​​of all nodes are the same, RE obtains the minimum value RE min =0, and when the centrality values ​​of all nodes are not equal, RE obtains the maximum value RE max =log(N). Therefore, the centrality calculation method with a larger RE value can achieve higher resolution.

[0073] like Figure 2 As shown, compared with EV_S, the RE value of the DFC_EV method is the highest, indicating that the DFC_EV method can accurately measure the centrality of the node.

[0074] In order to further verify the ability of the present invention to measure node centrality, a selective attack experiment was conducted on the brain functional network. Specifically, the centrality values ​​of the nodes were calculated for the single-layer network and the multi-layer network, and the nodes with the highest centrality values ​​and their edges were deleted. By comparing the changes in the global efficiency of the network before and after the node was deleted, the degree of influence of the node deletion on the network was explained, thereby reflecting the ability to measure the node centrality.

[0075] The global efficiency of the network E glob Expressed as:

[0076]

[0077] Among them, d ij It refers to the minimum number of edges required to go from one node to another.

[0078] Assumption E glob Denotes the global efficiency before the network attack, E′ glob represents the global efficiency of the brain network after removing a key node, then the change ratio E of the global efficiency of the network is expressed as:

[0079]

[0080] The value range of E is 0≤E≤1.

[0081] like Figure 3 As shown in the figure, deleting core nodes according to the DFC_EV centrality method leads to the largest change in the global efficiency of the network, that is, the core nodes obtained according to DFC_EV have a greater impact on the global efficiency of the network than the core nodes obtained in the single-layer network. In other words, compared with EV_S, DFC_EV can accurately measure the centrality of nodes.

[0082] This paper uses a fourth-order tensor to represent a multi-layer dynamic brain network, proposes a tensor-based method for measuring the centrality of a dynamic brain network node, and compares the centrality calculation methods under a single-layer network and a multi-layer brain network. The results show that the fourth-order tensor can better describe the multi-layer characteristics and time characteristics of the network, reflect the inter-layer interactions between different timestamps, and explicitly merge the time dependency and multiple relationships of the topological structure into one system. At the same time, the tensor-based method for measuring the centrality of a dynamic brain network node can accurately measure the centrality of a node.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A tensor-based method for calculating the centrality of nodes in a dynamic brain network, characterized in that: The following steps are involved: Step S1: preprocessing the brain functional magnetic resonance image of the subject to obtain a preprocessed brain functional magnetic resonance image; Step S2: According to the selected standardized brain atlas, the preprocessed functional magnetic resonance imaging is segmented into 90 brain regions; Step S3: extract the time series of each brain region, perform layered operations on the time series using the sliding time window technology, construct a multi-layer dynamic brain network, and represent the dynamic brain network based on tensors; Step S4: using an iterative method to calculate the eigenvector centrality of nodes in the dynamic brain network; Step S5: comparing the eigenvector centrality of the dynamic brain network nodes with the eigenvector centrality of the single-layer brain network nodes in terms of resolution entropy and global efficiency change ratio; In the step S3, the dynamic brain network is represented based on tensors, specifically including: A dynamic network is represented as W = {Φ, C}; Where Φ={G α :α∈{1,2,…,L}}, represents the set of L-layer networks, G α =(V α ,E α ), represents the network of the αth layer; V α represents the nodes in the αth layer of the network, E α Represents the edges in the αth layer of the network; in, E αβ Represents the edge between the two layers of network α and β, V1=V2=…=V L ={v1,v2,…,v N }, indicating that the nodes in each layer of the network are the same, with a total of N; A dynamic brain network can be represented as a fourth-order tensor, M = (M iαjβ )∈R N×L×N×L is a fourth-order adjacency tensor of a dynamic brain network; in, 1≤α,β≤L,1≤i,j≤N, Represents the i-node of layer α; In step S4, an iterative method is used to calculate the node v in the dynamic brain network. i The eigenvector centrality DFC_EV(v i ), including: Assume that at the kth iteration, node v i The eigenvector centrality of is E (k) (i,α); (1) (2) During iteration, Each element in is normalized by L2 norm, and we get E (k+1) (i,α); Among them, 1≤α≤L, 1≤o≤N, is a second-order tensor; (3) The above iterative process continues until E (k+1) The end is when the change in the sum of the absolute values ​​of all elements in (i, α) is less than 0.01; (4) After the above iterative calculation, find a maximum λ * and the corresponding second-order tensor E * , node v i The eigenvector centrality of is:

2. According to claim 1, a tensor-based dynamic brain network node centrality calculation method is characterized in that: In step S1, the specific steps of preprocessing include: removing the first 10 time points, time point correction, head motion correction, spatial normalization, smoothing, removing linear drift and filtering.

3. According to the tensor-based dynamic brain network node centrality calculation method of claim 1, it is characterized in that: In the step S3, The sliding time window technology is used to perform layered operations on time series. The specific steps include: The number of sliding windows is calculated as follows: Where T is the length of the entire time series, W is the window size, and H is the moving step size; W = 1 / f min , where f min is the minimum frequency of the data; After preprocessing the data, the minimum frequency of the data is 0.01 Hz, so the window size W is calculated to be 100 seconds, that is, 50 time points; at the same time, this experiment determines the window moving step H to be 2 seconds, that is, 1 time point, so 93 time windows are generated, and finally a 93-layer dynamic brain network is constructed, with 90 nodes in each layer of the network.

4. The tensor-based dynamic brain network node centrality calculation method according to claim 1 is characterized in that: The step S5 specifically includes: According to entropy theory, resolution entropy RE is defined as follows: Where S = {e1, e2, …, e 90 } is a one-dimensional vector composed of the centrality values ​​of 90 nodes, n i The node centrality value is e i The number of nodes; According to the representation of RE, it is obvious that when the centrality values ​​of all nodes are the same, RE obtains the minimum value RE min =0, and when the centrality values ​​of all nodes are not equal, RE obtains the maximum value RE max =log(N).

5. The tensor-based dynamic brain network node centrality calculation method according to claim 1 is characterized in that: The step S5 specifically includes: Global efficiency E glob Expressed as: Among them, d ij It refers to the minimum number of edges to go through from one node to another; Assumption E glob Denotes the global efficiency before the network attack, E′ glob represents the global efficiency of the brain network after removing a key node, then the change ratio E of the global efficiency of the network is expressed as: The value range of E is 0≤E≤1.

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