CN116564484A - Brain function network construction method based on network sparsity threshold selection - Google Patents

Brain function network construction method based on network sparsity threshold selection Download PDF

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CN116564484A
CN116564484A CN202310546130.4A CN202310546130A CN116564484A CN 116564484 A CN116564484 A CN 116564484A CN 202310546130 A CN202310546130 A CN 202310546130A CN 116564484 A CN116564484 A CN 116564484A
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刘爽
张波
明东
刘潇雅
何雨晨
柯余峰
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Abstract

The invention discloses a brain function network construction method based on network sparseness threshold selection, which comprises the following steps: performing sparsification treatment on a matrix of an initial brain function network, defining sparsity S of the matrix as the ratio of the edge with the value of 0 to all edge numbers in the matrix, and if the sparsity of the network is 0.01, reserving the edge with the connection weight of the first 99%; performing first-level sparseness threshold range definition on the functional network based on small world attributes, wherein sparseness is 0.01Performing small world attribute analysis on the functional network in the range of 0.99; performing second-level sparseness threshold range definition on the functional network based on module stability; the final sparsity threshold range S is obtained through the limitation of two-stage sparsity threshold values 3 ,S 4 ]And (5) completing the construction of the brain function network. The invention constructs the brain function network with high accuracy and robustness.

Description

Brain function network construction method based on network sparsity threshold selection
Technical Field
The invention relates to the technical field of brain function network construction, in particular to a brain function network construction method based on network sparseness threshold selection.
Background
Functional magnetic resonance imaging (functional magnetic resonance imaging, fMRI) allows for non-invasive imaging of functional activity within the brain by detecting changes in brain blood oxygen level signals. Numerous fMRI-based studies have found that the brain is not stationary in rest but is in constant neural activity and that there is synchronicity of low frequency oscillations between different regions of the brain as found in fMRI signals. Therefore, the brain network with the multi-region cooperative working mode in the brain gradually becomes an important technical means for exploring brain working mechanisms such as vision, hearing, movement, language, emotion, cognition and the like by human beings, and has important value for exploring pathophysiological mechanisms of mental diseases.
The construction of a brain function network mainly involves two elements, namely the nodes of the network and the edges of the network. Nodes are typically defined by brain patterns that differentiate brain based on brain structure or function (e.g., AAL brain patterns, harvard-Oxford brain patterns, dosenbach brain patterns); edges are typically represented by correlations (e.g., pearson correlation coefficient, partial correlation coefficient) of fMRI time series between brain regions. However, the weight values of the edges of the brain network, which are measured by the correlation coefficients, are typically continuous values of-1 to 1, which contain a large number of pseudo-connections, affecting the accuracy of the functional network construction. Therefore, thresholding of the original functional network is required to remove the pseudo-connection to ensure accuracy and robustness of the functional network.
Currently, there is no unified method for how to choose the network threshold. In recent years, researchers have proposed thresholding of functional networks based on subjective definition, degree distribution and other methods, but have the disadvantages of strong subjectivity, insufficient theoretical basis, low accuracy and the like.
Disclosure of Invention
The invention provides a brain function network construction method based on network sparseness threshold selection, which is based on the consideration that the human brain has an efficient information processing mode, utilizes the topological characteristics of brain function network small world attributes [1] and modularized [2] attributes to remove pseudo connection in a function network, and constructs a brain function network with high accuracy and robustness, and is described in detail below:
a brain function network construction method based on network sparseness threshold selection, the method comprising:
performing sparsification treatment on a matrix of an initial brain function network, defining sparsity S of the matrix as the ratio of the edge with the value of 0 to all edge numbers in the matrix, and if the sparsity of the network is 0.01, reserving the edge with the connection weight of the first 99%;
performing first-level sparsity threshold range definition on the functional network based on the small world attributes, and performing small world attribute analysis on the functional network with sparsity in the range of 0.01 to 0.99;
performing second-level sparseness threshold range definition on the functional network based on module stability;
the final sparsity threshold range S is obtained through the limitation of two-stage sparsity threshold values 3 ,S 4 ]And (5) completing the construction of the brain function network.
Wherein, the small world attribute analysis is:
wherein gamma is a normalized cluster coefficient, lambda is a normalized characteristic path length, C random Clustering coefficients representing random networks, C real Clustering coefficients representing real networks, characteristic path lengths representing random networks, L real Representing the characteristic path length of a real network, N represents all node sets in the network, N represents the number of nodes, and k represents the number of nodes i Node degree, t, representing node i i Represents the number of triangle connections around node i, d ij Representing the length of the characteristic path between node i and node j, and C representing the clustering coefficient of the network for calculating C random And C real ，C i The cluster coefficient representing the node i, L represents the characteristic path length of the network and is used for calculating L random And L real ，L i Representing the characteristic path length of node i, screening the meeting condition sigma>1.1 sparseness value corresponding to brain function network, the sparseness range meeting the criterion is defined as S E S 1 ,S 2 ]。
The second-stage sparseness threshold range limitation of the functional network based on the module stability is specifically defined as follows:
constructing a module connection matrix according to the module index, wherein the connection weight between nodes of the same module is 1 (MCM) s (i,j)＝1，M s (i)＝M s (j) The connection weight between the nodes of the different modules is 0 (MCM) s (i,j)＝0，M s (i)≠M s (j))；
Defining distance parameters D between MCM matrixes under different sparsity x and y x,y As a module stability index:
wherein the MCM x (i, j) is the module connection matrix at sparsity x, MCM y (i, j) is a module connection matrix under the sparsity y, n is the number of nodes, i and j represent the nodes, x and y are sparsity, after obtaining the distance of MCM matrix under different sparsity, 0-1 normalization processing is carried out, and a limiting condition D is set x,y <0.3, the sparsity threshold range is further defined as S ε [ S ] 3 ,S 4 ]。
Further, the module index is:
for S E S 1 ,S 2 ]And (3) calculating the module index of each node based on graph theory by the functional network under each sparsity in the range, wherein the modularized index Q value is defined as follows:
wherein A is an adjacent matrix corresponding to the network, and when brain region i and brain region j are connected, A is ij =1; m is the number of all connections in the network; k (k) i And k j The degrees of brain region i and brain region j, respectively; s is S ir Is a matrix of n x r, where n is the number of nodes, r is the number of network modules, if node i belongs to module r, S ir =1; confirming a module index M according to the module division condition when the Q value is maximum s Represented by a vector of n 1.
The technical scheme provided by the invention has the beneficial effects that:
1. the invention provides a brain function network construction method based on network sparsity threshold selection based on the consideration that the human brain has an efficient information processing mode, and utilizes the topological characteristics of the brain function network small world attribute and the modularized organization structure to optimize the function network, so that the function network constructed by the method has a remarkable small world attribute and a stable module structure, and the rationality and the accuracy of the function network are improved;
2. the invention can reduce errors when constructing the brain function network by using the correlation analysis method through the determined threshold value, reasonably remove pseudo connection in the brain network, and improve the accuracy and the robustness of the brain function network construction.
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FIG. 1 is a schematic diagram of a method of constructing a brain function network based on network sparsity threshold selection;
FIG. 2 is a schematic illustration of second level sparseness threshold range definition for a functional network based on module stability.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in further detail below.
Example 1
A brain function network construction method based on network sparseness threshold selection, see fig. 1, the method comprising:
101: resting fMRI data acquisition and preprocessing operation;
the method comprises the following specific steps: the first 10 unstable time points, temporal layer correction, head motion correction, spatial normalization, filtering, smoothing, etc. are removed.
102: defining brain function network nodes;
based on the prior brain map, dividing the whole brain into n brain regions, namely nodes of a brain network, wherein the brain map can be selected from an AAL brain map, a Harvard-Oxford brain map and a Dosenbach brain map.
103: brain function network edge definition:
the average time series of each node is calculated first, and then the Pearson correlation coefficient or the partial correlation coefficient of the time series between every two nodes is calculated as the edge of the network. At this time, a matrix of n x n can be obtained, and the negative value in the matrix is taken as the absolute value, so as to obtain the initial brain function network.
104: and (5) performing sparsification processing on the matrix of the initial brain function network. Defining the sparsity S of the matrix as the ratio of the edges with the value of 0 to all the edge numbers in the matrix, and if the sparsity of the network is 0.01, reserving the edges with the connection weight of the first 99 percent;
the sparsity range is set to be 0.01-0.99, namely S epsilon [0.01,0.99], the step length is set to be 0.01, and the initial brain function network is divided into 99 networks according to different sparsities.
105: performing first-level sparsity threshold range definition on the functional network based on the small world attribute, performing small world attribute analysis on the functional network with sparsity within the range of 0.01 to 0.99, wherein a small world attribute sigma calculation formula is as follows:
wherein gamma is a normalized cluster coefficient, lambda is a normalized characteristic path length, C random Clustering coefficients representing random networks, C real Clustering coefficients representing real networks, characteristic path lengths representing random networks, L real Representing the characteristic path length of a real network, N represents all node sets in the network, N represents the number of nodes, and k represents the number of nodes i Node degree, t, representing node i i Represents the number of triangle connections around node i, d ij Representing the length of the characteristic path between node i and node j, and C representing the clustering coefficient of the network for calculating C random And C real ，C i Representation ofThe clustering coefficient of the node i, L represents the characteristic path length of the network and is used for calculating L random And L real ，L i Representing the characteristic path length of node i.
After calculating the small world attribute sigma of the brain function network under each sparsity, screening to meet the condition sigma>1.1, guaranteeing that the functional network within the range has obvious small world attribute. At this time, the sparsity range meeting the criterion is defined as S [ S ] 1 ,S 2 ]。
106: performing second-level sparseness threshold range definition on the functional network based on module stability;
referring to FIG. 2, first, for S ε [ S ] 1 ,S 2 ]The functional network under each sparseness in the range calculates the module index of each node based on graph theory method, the module index is the network module to which each node belongs, M in FIG. 2 x Module index, M, representing a functional network at sparsity x y A module index representing the functional network at sparsity y. Therefore, it is first necessary to confirm the number of network module divisions. All possible cases of network module division are traversed, and the division case meeting the maximization of the modularized index Q value is the optimal network module division result. The modularized index Q value is defined as follows:
wherein A is an adjacency matrix corresponding to the network, and when brain region i and brain region j are connected, A ij =1, otherwise 0; m is the number of all connections in the network; k (k) i And k j The degrees of brain region i and brain region j, respectively; s is S ir Is a matrix of n x r, where n is the number of nodes, r is the number of network modules, if node i belongs to module r, S ir =1, otherwise 0. Confirming a module index M according to the module division condition when the Q value is maximum s Represented by a vector of n 1. The calculation process is realized through GRETNA (http:// www.nitrc.org/projects/GRETNA) toolkit under MATLAB platform。
Then, a module connection matrix (MCM, modular connectivity matrix) is constructed according to the module index, and the connection weight between the nodes of the same module is 1 (MCM) s (i,j)＝1，M s (i)＝M s (j) The connection weight between the nodes of the different modules is 0 (MCM) s (i,j)＝0，M s (i)≠M s (j) Thus at each sparsity s an MCM can be obtained s A matrix.
Defining distance parameters D between MCM matrixes under different sparsity x and y x,y The specific calculation mode of the module stability index is shown in the formula (7).
Wherein the MCM x (i, j) is the module connection matrix at sparsity x, MCM y (i, j) is a module connection matrix under the sparsity y, n is the number of nodes, i and j represent nodes, and x and y are sparsity. And after obtaining the distance of the MCM matrix under different sparsity, carrying out 0-1 normalization processing. D (D) x,y The closer the value is to 0, the smaller the distance between the sparsity x and the module connection matrix under the sparsity y, that is, the higher the similarity, the more stable the module structure representing the functional network. Setting a limiting condition D x,y <0.3, the functional network satisfying the condition has a stable module structure, and the sparseness threshold range is further limited in S epsilon S 3 ,S 4 ]。
107: the final sparsity threshold range S is obtained through the limitation of the two sparsity thresholds 3 ,S 4 ]The functional network under the sparseness has the small world attribute and the module stability of the real brain network, and the construction of the brain functional network is completed.
Example 2
The scheme of example 1 is further described in conjunction with specific examples, as follows:
201: preprocessing the resting fMRI data using a Data Processing Assistant for Resting-State fMRI (DPARSF) kit under Matlab platform;
the method comprises the following specific steps of: remove the first 10 unstable time points, time layer correction, head movement correction, spatial normalization, filtering to 0.01 to 0.1Hz, 6mm*6mm*6mm Gaussian gauss smoothing.
202: constructing a brain function network;
based on the prior brain map, dividing the whole brain into n brain regions, namely nodes of a brain network, wherein the brain map can be selected from an AAL brain map, a Harvard-Oxford brain map and a Dosenbach brain map. Based on the preprocessed data, extraction of the average time series within each brain region is performed using DPARSF toolkit. And then calculating the Pearson correlation coefficient or the partial correlation coefficient of the time sequence between every two brain regions as the edge of the network to obtain a matrix of n, and taking the absolute value of the negative value in the matrix to obtain the initial brain function network.
203: performing sparsification treatment on the initial functional network matrix;
the sparsity of the matrix is defined as the ratio of the edges with the value of 0 to all the edges in the matrix. The sparsity range is set to be 0.01-0.99, the step length is set to be 0.01, and the initial brain function network is divided into 99 networks according to different sparsities.
204: performing a first level sparsity threshold range definition on the functional network based on the small world attributes, performing small world attribute analysis on the functional network with sparsity in the range of 0.01 to 0.99,
the small world attribute σ calculation formula is referred to step 105 in embodiment 1, and this will not be described in detail in the embodiment of the present invention. The brain function network has significant small world attributes, thus setting the first level sparseness threshold selection criteria to σ>1.1 to ensure that the functional network built has significant small world properties. At this time, the sparsity range meeting the criterion is defined as S [ S ] 1 ,S 2 ]。
205: and performing second-stage sparseness threshold range definition on the functional network based on the module stability.
First, for S ε [ S ] 1 ,S 2 ]Functional network under each sparseness in range, based on graph theory for eachCalculating a module to which a node brain area belongs to obtain a module index vector of n 1; then, a module connection matrix (MCM, modular connectivity matrix) is constructed, the connection weight among the nodes of the same module is 1, and the connection weight among the nodes of different modules is 0, so that an MCM matrix can be obtained under each sparseness. Defining distance parameters D between MCM matrixes under different sparsity x and y x,y As a module stability index, set D x,y <0.3, sparseness threshold range S ε [ S ] under this condition 3 ,S 4 ]The threshold range of the sparseness of the functional network is obtained.
Reference to the literature
[1]Bassett D S,Bullmore E T.Small-world brain networks[J].Neuroscientist,2006,12(6):512-23.
[2]Newman M E J.Modularity and community structure in networks[J].Proceedings of the National Academy of Sciences of the United States of America,2006,103(23):8577-82.
The embodiment of the invention does not limit the types of other devices except the types of the devices, so long as the devices can complete the functions.
Those skilled in the art will appreciate that the drawings are schematic representations of only one preferred embodiment, and that the above-described embodiment numbers are merely for illustration purposes and do not represent advantages or disadvantages of the embodiments.
The foregoing description of the preferred embodiments of the invention is not intended to limit the invention to the precise form disclosed, and any such modifications, equivalents, and alternatives falling within the spirit and scope of the invention are intended to be included within the scope of the invention.

Claims (4)

1. A brain function network construction method based on network sparseness threshold selection, the method comprising:
performing sparsification treatment on a matrix of an initial brain function network, defining sparsity S of the matrix as the ratio of the edge with the value of 0 to all edge numbers in the matrix, and if the sparsity of the network is 0.01, reserving the edge with the connection weight of the first 99%;
performing first-level sparsity threshold range definition on the functional network based on the small world attributes, and performing small world attribute analysis on the functional network with sparsity in the range of 0.01 to 0.99;
performing second-level sparseness threshold range definition on the functional network based on module stability;
the final sparsity threshold range S is obtained through the limitation of two-stage sparsity threshold values 3 ,S 4 ]And (5) completing the construction of the brain function network.
2. The method for constructing a brain function network based on network sparseness threshold selection according to claim 1, wherein the small world attribute analysis is:
wherein gamma is a normalized cluster coefficient, lambda is a normalized characteristic path length, C random Clustering coefficients representing random networks, C real Clustering coefficients representing real networks, characteristic path lengths representing random networks, L real Feature path representing a real networkLength, N, represents all node sets in the network, N represents the number of nodes, k i Node degree, t, representing node i i Represents the number of triangle connections around node i, d ij Representing the length of the characteristic path between node i and node j, and C representing the clustering coefficient of the network for calculating C random And C real ，C i The cluster coefficient representing the node i, L represents the characteristic path length of the network and is used for calculating L random And L real ，L i Representing the characteristic path length of node i, screening the meeting condition sigma>1.1 sparseness value corresponding to brain function network, the sparseness range meeting the criterion is defined as S E S 1 ,S 2 ]。
3. The method for constructing a brain function network based on network sparsity threshold selection according to claim 1, wherein the second-stage sparsity threshold range definition for the function network based on module stability is specifically:
constructing a module connection matrix according to the module index, wherein the connection weight between nodes of the same module is 1 (MCM) s (i,j)＝1，M s (i)＝M s (j) The connection weight between the nodes of the different modules is 0 (MCM) s (i,j)＝0，M s (i)≠M s (j))；
Defining distance parameters D between MCM matrixes under different sparsity x and y x,y As a module stability index:
wherein the MCM x (i, j) is the module connection matrix at sparsity x, MCM y (i, j) is a module connection matrix under the sparsity y, n is the number of nodes, i and j represent the nodes, x and y are sparsity, after obtaining the distance of MCM matrix under different sparsity, 0-1 normalization processing is carried out, and a limiting condition D is set x,y <0.3, the sparsity threshold range is further defined as S ε [ S ] 3 ,S 4 ]。
4. The method for constructing a brain function network based on network sparseness threshold selection according to claim 1, wherein the module index is:
for S E S 1 ,S 2 ]And (3) calculating the module index of each node based on graph theory by the functional network under each sparsity in the range, wherein the modularized index Q value is defined as follows:
wherein A is an adjacent matrix corresponding to the network, and when brain region i and brain region j are connected, A is ij =1; m is the number of all connections in the network; k (k) i And k j The degrees of brain region i and brain region j, respectively; s is S ir Is a matrix of n x r, where n is the number of nodes, r is the number of network modules, if node i belongs to module r, S ir =1; confirming a module index M according to the module division condition when the Q value is maximum s Represented by a vector of n 1.
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