CN111710415A - Whole brain oriented network analysis method based on Granger neuropathy - Google Patents

Whole brain oriented network analysis method based on Granger neuropathy Download PDF

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CN111710415A
CN111710415A CN202010561100.7A CN202010561100A CN111710415A CN 111710415 A CN111710415 A CN 111710415A CN 202010561100 A CN202010561100 A CN 202010561100A CN 111710415 A CN111710415 A CN 111710415A
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唐艳
孙蔓
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Abstract

The invention discloses a nerve disease whole brain directed network analysis method based on Granger, which consists of fMRI data, an lsGC method and graph theory analysis, wherein the fMRI data are preprocessed, a human brain is divided into a plurality of interested areas through a brain map, and a time sequence is extracted; the lsGC method establishes a causal relationship among time sequences, constructs a whole brain directed weight network, selects a proper threshold value, converts a full connection network into a sparse network, and performs global and local analysis on the network. The invention is helpful for researching the flowing situation of human whole brain network information and the overall and local topological structure of the brain network. If the object is a patient with neuropsychiatric diseases, the brain area affected by the diseases can be favorably positioned, a potential pathogenic mechanism can be found, and medical diagnosis can be assisted.

Description

Whole brain oriented network analysis method based on Granger neuropathy
Technical Field
The invention belongs to the technical field of network analysis, and particularly relates to a Granger-based neural disease whole brain directed network analysis method.
Background
In recent years, the prevalence rate of neuropsychiatric diseases such as alzheimer's disease and parkinson's disease has gradually increased worldwide, which has a serious impact on both individuals and families of patients. However, the pathogenic mechanism of the diseases is not clear, and no medical treatment measures for curing the diseases are available. In view of the central role of the human brain in human perception and behavior, it is of vital importance to study the human brain.
The human brain is a huge physical tissue formed by connecting brain regions with different functions and is responsible for multiple high-level functions such as language, hearing, cognition and the like, and meanwhile, respective functional connection systems exist among partial brain regions. The higher functions of the brain cannot be understood simply as a synthesis of local activation, and also need to combine separate and integrated functions in the network. Early neuroscience studies were primarily concerned with brain regions by functional connectivity, but few have studied the direction of information transfer within brain networks. Therefore, exploring the directionality of functional interactions between brain regions helps in the study of the nervous system.
In the field of neuroscience, the most common method for achieving directional connections between brain regions is Granger causal analysis. However, the conventional GC method is suitable for the case that the number of time series is small and the length of the time series is large. With the increase of time series in a system, the complexity of a model is increased, the problem is particularly prominent when multivariate analysis is performed on fMRI data, in order to avoid the problem, some researches select partial brain regions related to corresponding functions or adopt a template with a small number of brain regions when the brain regions are divided, but a local network or the brain regions are constructed with a small functional division, and the analysis of the whole brain is lacked.
The directed network framework is formed on the basis of the whole brain by utilizing the lsGC algorithm, and the local and global topological structures of the brain network are analyzed on the basis, so that the special information of the directed network is found, and the discovery of the prior researchers in the field of neuroscience is enriched.
Most of existing human brain network analysis is based on a functional network and lacks directional information of network connection, however, research on the directed brain network is based on a local brain network and lacks refinement and integrity analysis of the whole brain. In conclusion, I design a whole brain directed network analysis method for neurological diseases based on Granger.
Disclosure of Invention
In order to solve the existing problems, the invention provides a Granger-based neural disease whole brain directed network analysis method.
The invention is realized by the following technical scheme:
a nerve disease whole brain directed network analysis method based on Granger comprises fMRI data and an lsGC method, wherein the fMRI data are preprocessed, a brain map divides a human brain into a plurality of interested areas, and a time sequence is extracted; the lsGC method establishes a causal relationship among time sequences, constructs a whole brain directed weight network, selects a proper threshold value, converts a full connection network into a sparse network, and performs global and local analysis on the network.
As a further optimization scheme of the invention, the lsGC method and the graph theory analysis method are responsible for exploring the causal relationship among time sequences after fMRI data preprocessing and constructing a human directed weight brain network; the latter is responsible for analyzing the topology of the directed network.
Compared with the prior art, the invention has the beneficial effects that: the invention is helpful for researching the flowing situation of human whole brain network information and the overall and local topological structure of the brain network. If the object is a patient with neuropsychiatric diseases, the brain area affected by the diseases can be favorably positioned, a potential pathogenic mechanism can be found, and medical diagnosis can be assisted.
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FIG. 1 is a flow chart of the present invention.
In the figure: 1. fMRI data; 2. lsGC method.
Detailed Description
The invention is described in further detail below with reference to the following detailed description and accompanying drawings:
as shown in fig. 1, a Granger-based neural disease whole brain oriented network analysis method is composed of fMRI data (1) and an lsGC method (2), wherein the fMRI data (1) is preprocessed, collected images are subjected to time correction, head movement correction, space coordinate standardization, smoothing processing, linear trend removing, filtering and covariate regression analysis, a brain is divided into a plurality of regions of interest (ROIs) through a brain region map, and a time sequence of each brain region is extracted; the lsGC method (2) establishes a causal relationship among time sequences, establishes a whole brain directed weight network, selects a proper threshold value, converts a fully connected network into a sparse network, and performs global and local analysis on the network; establishing a causal relationship between time sequences by using an lsGC (gas chromatography) method, and establishing a whole brain directed weight network;
X＝(x1，x2，…，xN) For a matrix containing N ROI time-sequences, principal component analysis was performed on all time-sequences, preserving the top m components with the largest variance, and projecting all time-sequences to the low-dimensional feature space.
Z＝WX
Where the matrix W is an mxn transform matrix and Z is a set of the first m high-power components of X.
The multivariate vector autoregressive (mvar (q)) model with time lag order q is estimated using signals from an m-dimensional feature space as follows:
Figure BDA0002546093180000041
Figure BDA0002546093180000042
where z (t) is the (m × 1) vector from the reduced-dimension feature space, AjIs the estimated (m × m) autoregressive coefficient for the jth lag, e (t) is an unobservable zero-mean white noise (m × 1);
Figure BDA0002546093180000043
corresponding to the estimated time series.
The r-th time series is removed from X and the MVAR model is re-estimated to obtain the effect of this ROI on all other ROI time series.
The errors of the original model and the simplified model are compared, and after projection back to the high-dimensional signal space, the Granger causal relationship is calculated using the following equation:
Figure BDA0002546093180000044
wherein the content of the first and second substances,
Figure BDA0002546093180000045
refers to the error variance associated with the s-th ROI without the r-th ROI information,
Figure BDA0002546093180000046
representing some ROI error variance using the full MVAR model. If the error variance of merging information from the r ROIs into the entire model is small, XrGranger leads to Xs。
And selecting an optimal threshold value, and converting the dense network into a sparse network. Computing global cost efficiency GCE ═ E for directed networksglobal-Threshold, wherein
Figure BDA0002546093180000047
EiIs the local efficiency of node i. When the global cost efficiency is the greatest, Threshold is the optimal Threshold with which to convert a fully connected network to a sparse network.
And extracting network characteristic attributes in the brain network, wherein the network characteristic attributes comprise global attributes such as clustering coefficients, characteristic paths, small world characteristics and homozygosity, and local characteristics such as node degree, strength and local efficiency.
The clustering coefficient is the average strength of the triangles around the node and describes the degree of aggregation between nodes in the network.
Figure BDA0002546093180000051
Wherein eiIs the number of edges, k, connected by node iiIs the order of node i.
The characteristic path length refers to the average shortest path between all pairs of nodes in the network. A short characteristic path length represents the potential for achieving a high degree of integration throughout the network.
Figure BDA0002546093180000052
Wherein L isiIs the average shortest path of all connections of node i, dijIs the shortest path length between nodes i and j in the network.
The small world characteristic is that 1000 random networks are generated firstly, and the same number of nodes, the distribution of out-degree and in-degree as the real network are reserved. The clustering coefficients and the characteristic path lengths of the random networks are obtained by averaging 1000 corresponding random networks. Final calculation
Figure BDA0002546093180000053
Figure BDA0002546093180000054
If the result is greater than 1, the network may be determined to be a small-world network.
The homozygosity is used for detecting whether nodes with similar values in a network have a mutual connection trend, and can be quantified by calculating a Pearson correlation coefficient of degrees between connected vertex pairs:
Figure BDA0002546093180000055
where M is the total number of connections in the network, jiAnd kiThe homography in the directed weighting network is roughly divided into three conditions, namely ① in-strength which measures the connection trend of nodes with similar input strength, ② out-strength which measures the connection trend of nodes with similar output strength, ③ homography in different directions, which comprises in-strength/out-strength coefficients and out-strength/in-strength coefficients.
The degree of a node is the number of edges connected to the node, d (i) ═ ∑j≠i∈Geij. The out-degree and in-degree can be obtained in the same way. On the basis of the above, P (k) ═ NkN is the degree distribution of the network, where NkThe node with the degree of k is NkSimilarly, the out-degree distribution and the in-degree distribution can be obtained.
For a weighted network, the node strength is the sum of the weights connected to the node, and the strength of a node in a directed network is the sum of the outgoing strength and the incoming strength of the node.
Local efficiency measures the ability of a node in the network to transmit information,
Figure BDA0002546093180000061
Figure BDA0002546093180000062
wherein L isijIs the shortest path length between node i and node j.
And finding out the difference of the network structure between the patient and the normal person according to nonparametric inspection.
The lsGC method (2) and the graph theory analysis method are used for exploring the causal relationship among time sequences after fMRI data (1) are preprocessed and constructing a human directed weight brain network; the latter is responsible for analyzing the topology of the directed network.
Said invention device in this embodiment, the invention is useful for studying the flow of human whole brain network information, and the topology of the brain network in whole and in part. If the object is a patient with neuropsychiatric diseases, the brain area affected by the diseases can be favorably positioned, a potential pathogenic mechanism can be found, and medical diagnosis can be assisted.
The foregoing illustrates and describes the principles, general features, and advantages of the present invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (2)

1. A nerve disease whole brain directed network analysis method based on Granger is composed of fMRI data, an lsGC method and graph theory analysis, and is characterized in that: preprocessing the fMRI data, dividing the human brain into a plurality of interested regions through a brain map, and extracting a time sequence; the lsGC method establishes a causal relationship among time sequences, constructs a whole brain directed weight network, selects a proper threshold value, converts a full connection network into a sparse network, and performs global and local analysis on the network.
2. The Granger-based neural disease whole brain directed network analysis method as claimed in claim 1, wherein: the lsGC method and the graph theory analysis method are used for exploring the causal relationship among time sequences after fMRI data preprocessing and constructing a human directed weight brain network; the latter is responsible for analyzing the topology of the directed network.
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CN116009517A (en) * 2023-01-18 2023-04-25 北京控制工程研究所 Method and device for constructing performance-fault relation map of spacecraft control system
CN116009517B (en) * 2023-01-18 2023-08-29 北京控制工程研究所 Method and device for constructing performance-fault relation map of spacecraft control system

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