CN113143247A - Method for constructing brain function hyper-network - Google Patents

Abstract

The invention discloses a method for constructing a brain function hyper-network, which comprises the following steps: performing format conversion and pretreatment on brain function magnetic resonance imaging; dividing a brain into a plurality of brain areas, and extracting a time sequence of each brain area; extracting a derivative function time sequence of each brain region; extracting a super edge generated by a sparse linear regression model of each brain region derivative function time sequence, and constructing a super edge set; constructing an initial hyper-network, and setting a threshold value according to the relationship between GE and PSW; solving a causal relationship coefficient between each brain area in each super edge as a result brain area and the rest brain areas by constructing a complete quadratic autoregressive model and a multivariate vector regression model; screening the brain areas contained by each super edge according to the causal relationship coefficient and the threshold value of the causal brain areas; and finally, obtaining an optimized super-edge set and constructing a brain function super-network. The method has important application value for cognitive dysfunction of the brain and information interaction in multiple brain areas.

Description

Method for constructing brain function hyper-network

Technical Field

The invention belongs to the technical field of biomedical information, and relates to a processing method of brain function magnetic resonance imaging, in particular to a method for constructing a brain function hyper-network.

Background

The human brain is a very complex system existing in nature, and various neuronal cells are connected together through synapses to form a very complex brain structure network which is the structural basis of the brain for performing various physiological and cognitive activities. During the process of active or passive activity caused by external stimulation, each neuron or nerve dynamic process extends into a complex brain function network, which is a visual description of brain nerve activity change. It can be seen that functional connections in brain networks are closely related to structural connections, which are limited by structural connections, but functional connections of the network can also be predicted by structural connections.

Resting state functional magnetic resonance imaging detects spontaneous low frequency neural activity of the brain, revealing a network of related neural activity. Based on brain data obtained by functional magnetic resonance imaging, a considerable number of brain functional connectivity modeling methods have been proposed, including correlation-based methods, partial correlation-based methods, and graphical modeling methods. However, the correlation-based method can capture only paired information, and thus cannot comprehensively reflect interactions between a plurality of brain regions. Furthermore, there are many false connections due to arbitrarily chosen thresholds based on the relevant network. Partial correlation estimation is typically achieved by Maximum Likelihood Estimation (MLE) using an inverse covariance matrix, and reliable estimation requires a data sample size much larger than the number of brain regions modeled. Graphical models are used to study the lack of prior knowledge of brain connections. Higher order information may be important for disease diagnosis because recent neuroscience research identifies important higher order interactions in neuronal isotopic tracing, local field potentials, and cortical activity. In order to apply high-order information to brain function network research, a hyper-network construction method is provided.

A hyper-network represents a network, each edge of which represents interactions between multiple brain regions. In the existing literature, brain function hyper-networks are constructed using sparse linear regression methods; wherein, the method of LASSO (last Absolute Shrinkage and Selection operator) is adopted for solving the sparse linear regression. Even though the LASSO method has been successfully applied to many studies, it has limitations: in the process of constructing the hyperedge, after one brain area is selected, if strong correlation exists between other brain areas, only one of a group of brain areas with group effect is selected randomly when the brain area related to the selection is selected, and possibly some related brain areas cannot be selected, so that the capability of explaining the grouping effect information is lacked.

The Granger cause and effect (GC) has originated in the field of economics, and was proposed and given a definite calculation formula in 1969 by the knobel prize holder winner in economics, forming a Granger cause and effect Analysis (GCA) method. Granger defines the Granger cause and effect as: for two stationary time series X and Y, Y is considered to be the cause of the granger of X if predicting the X current value by the values of X and Y past times is more effective than predicting the X current value by only the X past values. Subsequently, glange causal analysis is widely used in the fields of economics, engineering, signal processing, etc. since it does not require any prior knowledge and is effective in measuring causal relationships between time series. In 1984, J.Geweke proposes a conditional gram cause and effect, populates the traditional two-variable gram cause and effect to a multivariable gram cause and provides a calculation model.

Disclosure of Invention

Aiming at the defects existing in the prior art and the requirement of practical application, the invention provides a method for constructing a brain function hyper-network, and aims to solve the problems that:

the method for constructing the brain function super network based on the multivariate granger causal analysis is provided, the brain function super network is constructed by utilizing a sparse linear regression model and the multivariate granger causal analysis, and the classification method has important application value for brain cognitive function research.

In order to achieve the purpose, the invention adopts the following technical scheme:

a method for constructing a brain function hyper-network is characterized by comprising the following steps:

1) reading and format conversion are carried out on the acquired brain function magnetic resonance imaging, and then preprocessing is carried out;

2) selecting a standardized brain area template to divide the brain function magnetic resonance imaging into a plurality of brain areas, wherein each brain area is abstracted into a node in a brain function network;

3) extracting the average time sequence of all voxels in each brain region, and setting the ith brain region time sequence as X_i＝<x_i1,x_i2,...,x_in>The set of segmentation points is X_i'＝<x_i1',x_i2',...,x_im'>；X_iThe piecewise linearity of (d) is expressed as:

X_Li＝(f₁(x_i1′,x_i2′),f₂(x_i2′,x_i3′),...,f_m-1(x_i(m-1)′,x_im′)) (1)

in the formula: f. of_m-1(x_i(m-1)',x_im') is represented by [ x ]_i(m-1)',x_im']A linear fit function within;

4) to X_LiThe linear fitting function of each interval in the process is subjected to derivation to obtain corresponding interval derivative functions, all the interval derivative functions are combined together, and X_LiThe combined interval derivative function of (a) is expressed as:

X_Li′＝(f₁′(x_i1′,x_i2′),f₂′(x_i2′,x_i3′),...,f_m-1′(x_i(m-1)′,x_im′)) (2)

5) mixing X_iInterval of (1) [ x ]_i1,x_in]Taking a plurality of time points at equal intervals according to X_LiCalculating the derivative value corresponding to each time point to obtain the derivative time sequence X of the ith brain region time sequence_s＝<x_s1,x_s2,...,x_sq>(ii) a Extracting a derivative function time sequence of each brain region time sequence;

6) let X be ═ X_s1,...,X_si,...,X_sM]^T∈R^M×dRepresenting a data matrix, M being the number of brain regions, X_siA derivative time series representing the ith brain region, d being the length of the derivative time series; x_siViewed as a response vector, which can utilize the derivative time series of other M-1 brain regionsLinear combination estimation:

X_si＝A_iα_i+τ_i (3)

in the formula: a. the_i＝[X_s1,...,X_s(i-1),0,X_s(i+1),...,X_sM]^TA data matrix representing a time series of derivative functions including brain regions other than the ith brain region; alpha is alpha_iRepresenting a weight vector, measuring the influence degree of other brain areas on the ith brain area, and representing the interaction between the corresponding brain area and the ith brain area by using non-zero elements; tau is_iRepresenting a noise term;

7) to X_siThe linear combination of (a) and (b) constructs a sparse linear regression model, the optimization objective function of which is:

min||X_si-A_iα_i||₂+λ||α_i||₁ (4)

in the formula: λ is a regularization parameter that controls model sparsity;

8) generating a set of super-edges by varying the lambda value within a specified range, the super-edges including the ith brain region and others at alpha_iThe non-zero elements in the weight vector correspond to brain regions, and the change of the lambda value is from lambda_minTo lambda_maxThe increment is delta lambda; extracting a super edge generated by a sparse linear regression model of each brain region derivative function time sequence, and constructing a super edge set Q;

9) building an initial super network H_first(V, Q), V denotes a set of nodes; setting a threshold value p, determined by formula (8);

in the formula: GE is Global Efficiency (GE) of the initial super network; PSW is the Strong connection Proportion of the initial hyper-network (PSW);

10) constructing a multivariate granger causal analysis model for each super edge in Q; screening the brain areas contained by each super edge in the Q according to the causal relationship coefficient of the result brain area and the causal brain area and the size relationship of a threshold value p, and finally obtaining an optimized super edge set;

11) and (V, E) constructing a brain function super network H, wherein V represents a node set, E represents an optimized super edge set, and a correlation matrix with the dimension of | V | × | E | is used for representing H:

in the formula: v is a node as V; e is a super edge of H.

Further, the pretreatment in the step 1) comprises: removing the influence of the initial time point, the interlayer time correction, the cranial movement correction, the standardization, the smoothing processing, the linear drift removal, the filtering and the cranial movement parameter, the white matter signal and the cerebrospinal fluid signal covariate.

Further, the step 10) specifically includes the following steps:

10.1) selecting N brain areas contained in the jth super edge, constructing a multiple regression-based Glan's causal analysis model, sequentially selecting each brain area as a result brain area A, using the rest brain areas as cause brain areas B, and respectively extracting a derivative function time sequence X of the result brain area A_AAnd the derivative function time series X of the causal brain region B_b1,...,X_b(N-1)Constructing a matrix X of time series of B derivatives of the causal brain region_B＝[X_b1,X_b2,...,X_b(N-1)]^T∈R^(N-1)×dEstablishing a complete quadratic autoregressive model of the result brain area A:

in the formula: p₁Order of the autoregressive model, beta_iAnd beta_jkIs the coefficient of the autoregressive model, ε_tIs a residual error;

establishing a multivariate vector regression model of the result brain region A:

in the formula: p₂Is the order, omega, of a multivariate vector regression model_iIs the ith row vector of the first coefficient matrix of the vector regression model_iIs the ith row vector of the second coefficient matrix of the vector regression model, F_iIs X_BThe ith column vector of (a) is,

is the kronecker product of two vectors, epsilon_t' is the residual error;

10.2) respectively carrying out iterative solution on an autoregressive model and a vector regression model of the result brain area A through regression analysis to finally obtain a residual error epsilon_tAnd ε_t'; the causal relationship coefficients between causal brain area B and causal brain area a were obtained from Granger Causality Analysis (GCA):

in the formula: r₁Is a residual epsilon_tCovariance of (var (epsilon)_t)，R₂Is a residual epsilon_t' covariance var (ε)_t')；

10.3) regarding N brain areas in the jth super-edge, sequentially taking one of the brain areas as a result brain area A, and taking the rest brain areas as a reason brain area B; if the causal relation coefficient corresponding to the causal brain area B and the effect brain area A is more than or equal to p, the effect brain area A is reserved in the jth super edge; otherwise, the result brain area A is removed from the jth super edge.

The invention has the beneficial effects that: the invention provides a method for constructing a brain function hyper-network, which can effectively extract multi-brain-area interaction information of the brain function network and has a certain reference value for researching cognitive dysfunction of the brain.

Drawings

Fig. 1 is a flow chart of a method of constructing a brain function hyper-network.

FIG. 2 is an exemplary diagram of a local super network comprising 8 nodes, 6 super edges.

FIG. 3 is a correlation matrix for a local super-network comprising 8 nodes, 6 super-edges.

Detailed Description

For the purpose of enhancing the understanding of the present invention, the present invention will be described in further detail with reference to the accompanying drawings and examples, which are provided for the purpose of illustration only and are not intended to limit the scope of the present invention.

As shown in fig. 1 to 3, a method for constructing a brain function super network based on multivariate glange causal analysis includes the following steps:

1) the brain resting state functional magnetic resonance image of each tested brain is collected firstly, reading and format conversion are carried out, the physical state of a volunteer needs to be known before testing, the tested person is reminded of keeping a clear state, and no conscious thinking activity is needed. Acquiring brain fMRI data by using a PHILIPS 3.0-Tesla scanner, converting the read fMRI data into an NIFTI format by utilizing a DICOM format, and then removing the influence of a starting time point, interlayer time correction, cephalodynamic correction, standardization, smoothing processing, linear drift removal, filtering, cephalodynamic parameters, white matter signals and cerebrospinal fluid signal covariates, and reducing low-frequency drift and high-frequency biological noise. In this example, 30 normal volunteers (20 men and 10 women) and 30 early mild cognitive impairment (15 men and women) were selected, and the low-frequency signal filtering range was 0.01Hz to 0.08 Hz.

2) A standardized brain partition template (such as an AAL partition template, a Brodmann partition template, a CH2 partition template and the like) is selected to divide the brain function magnetic resonance image into a plurality of brain areas, and each brain area corresponds to a node in the brain function network. In this embodiment, an AAL partition template is selected to divide the brain area, and the human brain is divided into 90 brain areas (45 brain areas for each of the left and right brains), where the 90 brain areas correspond to 90 nodes in the brain function network.

3) Extracting the average time sequence of all voxels in each brain region, and setting the ith brain region time sequence as X_i＝<x_i1,x_i2,...,x_in>The set of segmentation points is X_i'＝<x_i1',x_i2',...,x_im'>；X_iThe piecewise linearity of (d) is expressed as:

X_Li＝(f₁(x_i1′,x_i2′),f₂(x_i2′,x_i3′),...,f_m-1(x_i(m-1)′,x_im′)) (1)

in the formula: f. of_m-1(x_i(m-1)',x_im') is represented by [ x ]_i(m-1)',x_im']A linear fit function within;

4) to X_LiThe linear fitting function of each interval in the process is subjected to derivation to obtain corresponding interval derivative functions, all the interval derivative functions are combined together, and X_LiThe combined interval derivative function of (a) is expressed as:

X_Li′＝(f₁′(x_i1′,x_i2′),f₂′(x_i2′,x_i3′),...,f_m-1′(x_i(m-1)′,x_im′)) (2)

5) mixing X_iInterval of (1) [ x ]_i1,x_in]Taking a plurality of time points at equal intervals according to X_LiCalculating the derivative value corresponding to each time point to obtain the derivative time sequence X of the ith brain region time sequence_s＝<x_s1,x_s2,...,x_sq>(ii) a Extracting a derivative function time sequence of each brain region time sequence;

6) let X be ═ X_s1,...,X_si,...,X_sM]^T∈R^M×dRepresenting a data matrix, M being the number of brain regions, X_siA derivative time series representing the ith brain region, d being the length of the derivative time series; x_siViewed as a response vector, can be estimated using linear combinations of time series of derivative functions of other M-1 brain regions:

X_si＝A_iα_i+τ_i (3)

in the formula: a. the_i＝[X_s1,...,X_s(i-1),0,X_s(i+1),...,X_sM]^TThe representation contains other than the ith brain regionA data matrix of a time series of derivative functions of the brain region; alpha is alpha_iRepresenting a weight vector, measuring the influence degree of other brain areas on the ith brain area, and representing the interaction between the corresponding brain area and the ith brain area by using non-zero elements; tau is_iRepresenting a noise term;

7) to X_siThe linear combination of (a) and (b) constructs a sparse linear regression model, the optimization objective function of which is:

min||X_si-A_iα_i||₂+λ||α_i||₁ (4)

in the formula: λ is a regularization parameter that controls model sparsity;

8) generating a set of super-edges by varying the lambda value within a specified range, the super-edges including the ith brain region and others at alpha_iThe non-zero elements in the weight vector correspond to brain regions, and the change of the lambda value is from lambda_minTo lambda_maxThe increment is delta lambda; extracting a super edge generated by a sparse linear regression model of each brain region derivative function time sequence, and constructing a super edge set Q;

9) building an initial super network H_first(V, Q), V denotes a set of nodes; setting a threshold value p, determined by formula (8);

in the formula: GE is Global Efficiency (GE) of the initial super network; PSW is the Strong connection Proportion of the initial hyper-network (PSW);

10) constructing a multivariate granger causal analysis model for each super edge in Q; screening the brain areas contained by each super edge in the Q according to the causal relationship coefficient of the result brain area and the causal brain area and the size relationship of a threshold value p, and finally obtaining an optimized super edge set;

11) and (V, E) constructing a brain function super network H, wherein V represents a node set, E represents an optimized super edge set, and a correlation matrix with the dimension of | V | × | E | is used for representing H:

in the formula: v is a node as V; e belongs to a super edge of H; in this embodiment, a local super network including 8 nodes and 6 super edges is shown in fig. 2, and an association matrix thereof is shown in fig. 3.

Wherein, the step 10) specifically comprises the following steps:

10.1) selecting N brain areas contained in the jth super edge, constructing a multiple regression-based Glan's causal analysis model, sequentially selecting each brain area as a result brain area A, using the rest brain areas as cause brain areas B, and respectively extracting a derivative function time sequence X of the result brain area A_AAnd the derivative function time series X of the causal brain region B_b1,...,X_b(N-1)Constructing a matrix X of time series of B derivatives of the causal brain region_B＝[X_b1,X_b2,...,X_b(N-1)]^T∈R^(N-1)×dEstablishing a complete quadratic autoregressive model of the result brain area A:

in the formula: p₁Order of the autoregressive model, beta_iAnd beta_jkIs the coefficient of the autoregressive model, ε_tIs a residual error;

establishing a multivariate vector regression model of the result brain region A:

in the formula: p₂Is the order, omega, of a multivariate vector regression model_iIs the ith row vector of the first coefficient matrix of the vector regression model_iIs the ith row vector of the second coefficient matrix of the vector regression model, F_iIs X_BThe ith column vector of (a) is,

is twoKronecker product of vectors, epsilon_t' is the residual error;

10.2) respectively and iteratively solving an autoregressive model and a vector regression model of the result brain area A by using a Bayesian method and a maximum Expectation-Maximization algorithm (EM), and finally obtaining a residual error epsilon_tAnd ε_t'; the causal relationship coefficients between causal brain area B and causal brain area a were obtained from Granger Causality Analysis (GCA):

in the formula: r₁Is a residual epsilon_tCovariance of (var (epsilon)_t)，R₂Is a residual epsilon_t' covariance var (ε)_t')；

10.3) regarding N brain areas in the jth super-edge, sequentially taking one of the brain areas as a result brain area A, and taking the rest brain areas as a reason brain area B; if the causal relation coefficient corresponding to the causal brain area B and the effect brain area A is more than or equal to p, the effect brain area A is reserved in the jth super edge; otherwise, the result brain area A is removed from the jth super edge.

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 merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the 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 (3)

1. A method for constructing a brain function hyper-network is characterized by comprising the following steps:

1) reading and format conversion are carried out on the acquired brain function magnetic resonance imaging, and then preprocessing is carried out;

2) selecting a standardized brain area template to divide the brain function magnetic resonance imaging into a plurality of brain areas, wherein each brain area is abstracted into a node in a brain function network;

3) extracting the average time sequence of all voxels in each brain region, and setting the ith brain region time sequence as X_i＝<x_i1,x_i2,...,x_in>The set of segmentation points is X_i'＝<x_i1',x_i2',...,x_im'>；X_iThe piecewise linearity of (d) is expressed as:

X_Li＝(f₁(x_i1′,x_i2′),f₂(x_i2′,x_i3′),...,f_m-1(x_i(m-1)′,x_im′)) (1)

in the formula: f. of_m-1(x_i(m-1)',x_im') is represented by [ x ]_i(m-1)',x_im']A linear fit function within;

4) to X_LiThe linear fitting function of each interval in the process is subjected to derivation to obtain corresponding interval derivative functions, all the interval derivative functions are combined together, and X_LiThe combined interval derivative function of (a) is expressed as:

X_Li′＝(f₁′(x_i1′,x_i2′),f₂′(x_i2′,x_i3′),...,f_m-1′(x_i(m-1)′,x_im′)) (2)

5) mixing X_iInterval of (1) [ x ]_i1,x_in]Taking a plurality of time points at equal intervals according to X_LiCalculating the derivative value corresponding to each time point to obtain the derivative time sequence X of the ith brain region time sequence_s＝<x_s1,x_s2,...,x_sq>(ii) a Extracting a derivative function time sequence of each brain region time sequence;

6) let X be ═ X_s1,...,X_si,...,X_sM]^T∈R^M×dRepresenting a data matrix, M being the number of brain regions, X_siA derivative time series representing the ith brain region, d being the length of the derivative time series; x_siTreated as a response vector, using the functions of the other M-1 brain regionsLinear combination estimation of time series of numbers:

X_si＝A_iα_i+τ_i (3)

in the formula: a. the_i＝[X_s1,...,X_s(i-1),0,X_s(i+1),...,X_sM]^TA data matrix representing a time series of derivative functions including brain regions other than the ith brain region; alpha is alpha_iRepresenting a weight vector, measuring the influence degree of other brain areas on the ith brain area, and representing the interaction between the corresponding brain area and the ith brain area by using non-zero elements; tau is_iRepresenting a noise term;

7) to X_siThe linear combination of (a) and (b) constructs a sparse linear regression model, the optimization objective function of which is:

min||X_si-A_iα_i||₂+λ||α_i||₁ (4)

in the formula: λ is a regularization parameter that controls model sparsity;

8) generating a set of super-edges by varying the lambda value within a specified range, the super-edges including the ith brain region and others at alpha_iThe non-zero elements in the weight vector correspond to brain regions, and the change of the lambda value is from lambda_minTo lambda_maxThe increment is delta lambda; extracting a super edge generated by a sparse linear regression model of each brain region derivative function time sequence, and constructing a super edge set Q;

9) building an initial super network H_first(V, Q), V denotes a set of nodes; setting a threshold value p, determined by formula (8);

in the formula: GE is the global cost efficiency of the initial hyper-network; PSW is the strong connection proportion of the initial hyper-network;

10) constructing a multivariate granger causal analysis model for each super edge in the super edge set Q; screening the brain areas contained by each super edge in the Q according to the causal relationship coefficient of the result brain area and the causal brain area and the size relationship of a threshold value p to obtain an optimized super edge set;

11) and (V, E) constructing a brain function super network H, wherein V represents a node set, E represents an optimized super edge set, and a correlation matrix with the dimension of | V | × | E | is used for representing H:

in the formula: v is a node as V; e is a super edge of H.

2. The pretreatment in the step 1) comprises the following steps: removing the influence of the initial time point, the interlayer time correction, the cranial movement correction, the standardization, the smoothing processing, the linear drift removal, the filtering and the cranial movement parameter, the white matter signal and the cerebrospinal fluid signal covariate.

3. The step 10) specifically comprises the following steps:

10.1) selecting N brain areas contained in the jth super edge, constructing a multiple regression-based Glan's causal analysis model, sequentially selecting each brain area as a result brain area A, using the rest brain areas as cause brain areas B, and respectively extracting a derivative function time sequence X of the result brain area A_AAnd the derivative function time series X of the causal brain region B_b1,...,X_b(N-1)Constructing a matrix X of time series of B derivatives of the causal brain region_B＝[X_b1,X_b2,...,X_b(N-1)]^T∈R^(N-1)×dEstablishing a complete quadratic autoregressive model of the result brain area A:

in the formula: p₁Order of the autoregressive model, beta_iAnd beta_jkIs the coefficient of the autoregressive model, ε_tIs a residual error;

establishing a multivariate vector regression model of the result brain region A:

in the formula: p₂Is the order, omega, of a multivariate vector regression model_iIs the ith row vector of the first coefficient matrix of the vector regression model_iIs the ith row vector of the second coefficient matrix of the vector regression model, F_iIs X_BThe ith column vector of (a) is,

is a kronecker product of two vectors, epsilon'_tIs a residual error;

10.2) respectively carrying out iterative solution on an autoregressive model and a vector regression model of the result brain area A through regression analysis to finally obtain a residual error epsilon_tAnd epsilon'_t(ii) a The causal relationship coefficients between causal brain area B and causal brain area a were obtained from Granger Causality Analysis (GCA):

in the formula: r₁Is a residual epsilon_tCovariance of (var (epsilon)_t)，R₂Is residual epsilon'_tOf covariance var (ε'_t)；

10.3) regarding N brain areas in the jth super-edge, sequentially taking one of the brain areas as a result brain area A, and taking the rest brain areas as a reason brain area B; if the causal relation coefficient corresponding to the causal brain area B and the effect brain area A is more than or equal to p, the effect brain area A is reserved in the jth super edge; otherwise, the result brain area A is removed from the jth super edge.

Images