阅读说明：本技术 基于R-vine Copula的皮层肌肉功能网络构建方法 (Cortical muscle function network construction method based on R-vine Copula ) 是由 汪婷 席旭刚 樊竹尧 文燕 赵云波 于 2021-06-25 设计创作，主要内容包括：本发明公开了一种基于R-vine Copula的皮层肌肉功能网络构建方法。本发明首先,同步记录来自多名受试者的脑电信号和表面肌电信号,要求根据节拍器指令执行特定的任务。对采集的脑肌电数据采用独立分量分析分离其它伪迹和小波阈值去噪。其次,构建一种新的皮层肌肉功能方法用来定量分析皮层肌肉信号间的复杂因果关系。利用R-vine Copula进行脑肌电非线性耦合分析和脑肌功能网络建模,通过大量实验,验证了本发明可以有效地描述特定步行状态下的皮层肌肉连接性,以及构建的皮层肌肉功能网络是有意义的。(The invention discloses a cortical muscle function network construction method based on R-vine Copula. Firstly, electroencephalogram signals and surface electromyogram signals from a plurality of subjects are synchronously recorded, and a specific task is required to be executed according to a metronome instruction. And (3) carrying out independent component analysis on the acquired brain and muscle electrical data to separate other artifacts and carrying out wavelet threshold denoising. Secondly, a new cortical muscle function method was constructed to quantitatively analyze the complex causal relationship between cortical muscle signals. The R-vine Copula is utilized to carry out the brain-muscle and muscle electrical nonlinear coupling analysis and the brain-muscle function network modeling, and a large number of experiments prove that the cortical muscle connectivity under the specific walking state can be effectively described, and the constructed cortical muscle function network is significant.)

1. A cortical muscle function network construction method based on R-vine Copula is characterized by comprising the following steps:

step 1: synchronously recording electroencephalogram signals and surface electromyogram signals of different human body actions from a plurality of testees; denoising acquired electroencephalogram signals and surface electromyogram signal data by adopting a wavelet threshold value and removing artifacts by adopting independent component analysis;

step 2: analyzing the connectivity of electroencephalogram signals and surface electromyogram signals of different human body actions by using an R-Vine Copula model, and constructing a cortical muscle function network based on Vine Vine structure correlation coefficients;

and step 3: and (3) discarding the weighted edge smaller than the threshold value in the cortical muscle function network by using a threshold value method to obtain the difference of the network model expressing the corresponding networks of different actions.

2. The method for constructing the cortical muscle function network based on the R-vine Copula according to claim 1, wherein the R-vine Copula model in the step 2 is specifically designed as follows:

firstly, randomly combining random variables formed by two random electroencephalogram signal and surface electromyogram signal channels to calculate a Kendall-tau rank correlation coefficient;

generating a first Tree Tree1 of the R-vine structure by a maximum spanning Tree algorithm, namely maximizing the sum of absolute values of all Kendall-tau correlation coefficients in the Tree;

selecting an optimal binary Copula function for each edge of the tree according to the Chichi information standard and the Bayesian information standard, and calculating a corresponding conditional distribution function;

finding out all condition-related random variable combinations of each layer, and calculating corresponding Kendall-tau rank correlation coefficients by combining the condition distribution function obtained by calculation in the step (c);

fifthly, repeating the steps from (a) to (b) according to the Kendall-tau rank correlation coefficient obtained in the step (b) until the last tree with the R-vine structure is obtained.

3. The method for constructing the cortical muscle function network based on the R-Vine Copula of claim 1, wherein prior to the specific design of the R-Vine Copula model, the preferential selection of the Vine tree structure, the selection of the Copula function and the parameter estimation of the Copula function need to be performed.

4. The method for constructing the cortical muscle function network based on the R-Vine Copula according to claim 3, wherein the preferential selection of the Vine tree structure is specifically as follows:

selecting R-Vine as the structure of the Vine Copula function;

determining an edge distribution of each EEG and sEMG signal;

selecting a proper Copula function, and deducing joint probability distribution between any two signals;

for the problem of connectivity between the electroencephalogram signal and the surface electromyogram signal, analysis was performed using R-vine.

5. The method for constructing the R-vine Copula-based cortical muscle function network according to claim 3, wherein the Copula function is selected specifically as follows:

selecting the minimum value of the Chichi information standard and the Bayesian information standard to determine a Copula function between variables; the best Pair-Copula function was selected from Gauss Copula, Student-t Copula, Clayton Copula, Gumbel Copula, Frank Copula.

6. The method for constructing a cortical muscle function network based on R-vine Copula as claimed in claim 5, wherein when the two criteria select different Copula functions, the final decision weight is mainly made by the akachi pool information criteria.

7. The method for constructing the R-vine Copula-based cortical muscle function network according to claim 3, wherein the parameter estimation of the Copula function is specifically as follows: and simultaneously estimating parameters in the edge distribution and the Copula function by an accurate maximum likelihood estimation method.

Technical Field

The invention belongs to the field of signal processing, and relates to a cortical muscle function network construction method based on R-vine Copula.

Background

The rehabilitation therapy for the lower limbs after the cerebral apoplexy is affected is extremely important for recovering the walking function. Walking is a complex task requiring coordinated and flexible activity of several muscles, depending on complex controls on the central nervous system to cope with changing environmental challenges. The complex control between cerebral cortex and muscle is mainly embodied by the degree of connection between EEG signals EEG, surface electromyography signals sEMG and EEG-sEMG signals. The coupling of the features of the EEG-sEMG signal and the EEG-sEMG signal may reflect the brain function control and the functional connection principle with the muscles. Research results obtained at present show that walking training can adjust the functional state of the brain and the excitation degree of the spinal cord of the lower limbs when the lower limbs move after stroke. In the implementation process of clinical exercise rehabilitation therapy at home and abroad, walking training is gradually researched and applied widely in promoting the recovery of lower limb exercise functions.

In the process of motion control, the condition that the cerebral cortex transmits control instructions to the muscles and the muscles feed back to the cerebral cortex is mainly reflected by the coupling strength of the brain-muscle-electric function, namely the functional connection between the brain and the muscle tissue can be analyzed by utilizing the connectivity between EEG and sEMG signals. The methods mainly applied by researchers are based on coherent analysis and analyze EEG and sEMG signals from time, frequency, time-frequency and causal relations. Common linear and nonlinear analysis methods include coherent analysis, granger causal analysis, mutual information and entropy transfer, etc. The brain muscle coupling analysis method has made great progress, and most studies on the connectivity of the EEG-sEMG are based on a linear algorithm at present. With the continuous improvement of nonlinear analysis methods, their application in brain-muscle connectivity is gradually receiving attention. However, the interaction between neural activity-producing signals is highly non-linear and non-stationary. Most of the analysis methods can only describe the linear relation of the connectivity between signals, and the complex causal relations such as nonlinearity, high order and the like are difficult to quantitatively analyze.

In view of the above problems, Copula theory, which is slowly developed from the fields of mathematics and statistics, has great advantages in solving the structure of correlation dependence among a plurality of variables, it helps to solve the correlation problem and can be applied to correlation analysis of a plurality of time series in neuroscience. Dauwels et al use Copula to model gaussian maps and use multichannel EEG signals to infer interactions between different brain regions. Hu et al studied the correlation between data composed of a sequence of discrete nerve spikes and a sequence of continuous local field potentials using the Copula method and revealed complex coupling relationships between the sequences. Although the Copula-based framework has universality, as the problems of development and research of Copula theory become more complicated, constructing high-dimensional Copula becomes a difficult problem; the Vine Copula proposed by Bedford can be used to construct more flexible and diverse multivariate distributions, separating unit variables from multivariate distributions in the dependency structure, and better solving the problem of "dimension cursing" of parameter estimation in the case of multivariate.

Compared with the traditional Copula, the Vine Copula enables a high-dimensional multivariate problem to be more intuitive, the existing research focuses on the condition that variables such as selection of a binary function family and parameter estimation thereof are few, but the problem of the brain-muscle electrical connectivity is the related structural problem among multiple cortices and muscles. Vine Copula is used for brain myoelectricity nonlinear coupling analysis and brain function network modeling, and means that a Copula function can be directly used for connecting multivariate distribution and one-dimensional marginal substitution thereof to define multivariate inter-multivariate combined distribution. The Vine graphic tool introduced by the invention can reconsider the dependence problem of related structures under multivariate variables, so that the described result is consistent with the actual situation as much as possible. From the analysis, the Vine Copula method is firm in theoretical foundation and infinite in potential, and can develop a new idea for correlation analysis among physiological signal variables.

Disclosure of Invention

Aiming at the defects of the prior art, the invention provides a cortical muscle function network construction method based on R-vine Copula.

The invention first of all, simultaneously recording EEG signals and sEMG signals from a plurality of subjects, requiring specific tasks to be performed according to metronome instructions. And (3) carrying out independent component analysis on the acquired electroencephalogram and electromyogram data to separate other artifacts and carrying out wavelet threshold denoising. Secondly, a new cortical muscle function method was constructed to quantitatively analyze the complex causal relationship between cortical muscle signals. The R-vine Copula is utilized to carry out electroencephalogram and electromyogram nonlinear coupling analysis and cortical muscle function network construction, and a large number of experiments prove that the cortical muscle connectivity under a specific walking state can be effectively described, and the constructed cortical muscle function network is meaningful.

In order to achieve the above object, the method of the present invention mainly comprises the following steps:

synchronously recording EEG signals and surface electromyogram signals sEMG from a plurality of subjects. And denoising the collected EEG and sEMG data by adopting a wavelet threshold value and removing artifacts by adopting independent component analysis.

And (2) analyzing the connectivity of EEG and sEMG of different human body actions by using an R-vine Copula model, and verifying that the connectivity of EEG signals of cerebral cortex and sEMG signals of different muscles under different actions has obvious difference. In view of the fact that information interaction exists between cerebral cortex and muscles in the execution process of lower limb movement, a method for constructing a cortical muscle function network based on Vine rattan structure correlation coefficients is provided. And (4) discarding the weaker weighted edge by using a threshold value method to obtain the difference of the network model expressing the corresponding networks of different actions.

The R-vine Copula model is specifically designed as follows:

(1) and (4) selecting a Vine tree structure preferentially. The R-Vine becomes the structure selection range of the Vine Copula function due to the flexibility of the structure.

Any n-dimensional joint distribution function can be decomposed into n marginal distribution functions and a Copula function. If F is an n-dimensional random variable { x₁,x₂,…,x_nAnd with a marginal distribution function F_i(x_i) (i ═ 1,2, …, n) of the joint distribution function, then Copula function C:

F(x₁,x₂,…,x_n)＝C(F₁(x₁),F₂(x₂),…,F_n(x_n)) (1)

when F of the n-dimensional joint distribution function F_i(x_i) When (i ═ 1,2, …, n) are consecutive, then the n-dimensional Copula function C exists and is unique. If F_i(i-1, 2, …, n) has an inverse function of F_i ^-1(i-1, 2, …, n) and u_i＝F_i(i ═ 1,2, …, n), obey [0.1]Even distribution, its Copula function can be calculated as:

equations (1) and (2) are reciprocal, and by deriving equation (1), the joint probability density function of F can be obtained:

wherein the content of the first and second substances,it is an n-dimensional Copula density function, f_i(x_i) Is a marginal density function.

As can be seen from the above principle, the edge distribution of each EEG and sEMG signal is determined according to the actual situation, and then the joint probability distribution between any two signals can be derived by selecting an appropriate Copula function. For the connectivity problem between EEG and sEMG, analysis was performed using R-vine. Again, for R-vine, strictly defined:

if T ═ T₁,T₂,…,T_n-1}，T₁Is that the node is N₁1, …, n, edge E₁The tree of (2).

2, …, n-1, T_iIs satisfying N_i＝E_i-1。

C 2, …, n-1, { a, b }. epsilon.e_iWherein a ═ a₁,a₂}，b＝{b₁,b₂And }, # (a, b) ═ 1, # denotes the base of the set.

Thus one isThe n-dimensional R-vine structure can be represented by n-1 trees (T)_jThere are n +1-j nodes and n-j edges, which means that there are n-j Copula density functions. Tree T_jThe edges sharing a node will become nodes and will be represented by the tree T_j+1The other edges in (1) are connected. The R-vine density function is given in formula (4):

wherein x is (x)₁,…,x_n) And e ═ { a, b } is the edge between node a and node b in the Vine Copula tree structure, D_eRefers to a set of variables, C, contained in the edge_e,a,C_e,a|D_eRepresenting a binary Copula function characterizing the edge.

(2) And (4) selecting a Copula function. And selecting the minimum value of two model selection criteria-Chichi information criterion (AIC) and Bayesian Information Criterion (BIC) to determine a Copula function between variables. When the two criteria choose different Copula functions, the final decision weight is mainly made by AIC. The optimal Pair-Copula function is selected from basic binary functions such as Gauss Copula, Student-t Copula, Clayton Copula, Gumbel Copula, Frank Copula and the like.

WhereinIs the estimated probability, m is the number of tunable parameters in the Copula function, and n is the number of data points.

(3) Parameter estimation of Copula function.

Simultaneously estimating parameters in the edge distribution and the Copula function by an EML method, wherein the obtained maximum likelihood estimation hasAsymptotic normality. Random variable u of any two channels₁,u₂Can be represented by the respective edge distributions and Copula function C representing the correlation between the two, the density function of the joint distribution function is:

h(u₁,u₂,θ)＝c(F₁(u₁,α₁),F₂(u₂,α₂),δ)f₁(u₁,α₁)f₂(u₂,α₂). (7)

the log-maximum likelihood function for an observation sample is:

maximum likelihood estimationIt is a differential equationThe solution of (1).

And (3) researching the functional coupling relation of the cortical muscles of different actions by constructing an R-vine Copula model. The method comprises the following steps of participating in model construction by adopting a Maximum Spanning Tree (MST) algorithm:

firstly, in a processed sample data set, random variable combinations formed by random pairs of EEG and sEMG channels are randomly combined to calculate Kendall-tau rank correlation coefficients.

Secondly, generating a first Tree Tree1 of the R-vine structure by using the MST algorithm, namely maximizing the sum of absolute values of all Kendall-tau correlation coefficients in the Tree.

And thirdly, selecting an optimal binary Copula function for each edge of the tree by a binary Copula function selection method (AIC and BIC), and calculating a corresponding conditional distribution function.

Finding out random variable combinations related to all conditions of each layer under the condition of meeting the definition, and calculating corresponding Kendall-tau rank correlation coefficients by combining the condition distribution functions obtained by calculation in the step (c).

Fifthly, repeating the steps from (a) to (b) according to the Kendall-tau rank correlation coefficient obtained in the step (b) until the last tree with the R-vine structure is obtained.

The invention has the beneficial effects that: because a general Copula function can only represent the correlation between two variables, the traditional Copula function is difficult to solve when the problem of complex correlation existing between a plurality of random variables is researched. The Vine Copula appeared and developed based on the traditional Copula function. The method not only retains the advantages of the traditional Copula function on the description of the correlation, but also introduces a Vine tool to solve the high-dimensional problem and strengthen the flexible and diversified description of the correlation problem under the multivariate condition. The Vine Copula model has various forms, and the main researches at present comprise three types, namely Canonical Vine, Drawable Vine and Regular Vine (R-Vine). The Vine Copula model with different forms and structures provides different ideas for researching various data. There is no specific rule for the dependent structure of each layer of R-vine. A specific problem-specific analysis is therefore required when selecting the appropriate Vine structure. The R-vine structure can describe the dependency relationship between variables more flexibly due to the unique structure flexibility advantage, so that the correlation result is closer and closer to reality. Meanwhile, the binary Copula can be expanded into a Copula model with any dimension by the R-vine, so that the processing capacity of high-dimensional data is improved, and the method is attracted by attention. In R-vine Copula, the Copula function between the channels in the first level tree structure describes the unconditional correlation between the channels. In addition to the first level tree structure, the remaining Copula functions in the second to fourteenth level trees also describe conditional correlations, the correlation coefficient indicating the degree of correlation between different channels.

The method effectively considers the influence of other variables on the correlation of the researched variables, and improves the accuracy of estimating the real connectivity. The functional coupling analysis method adopted by the invention is helpful to strengthen the understanding of the intrinsic rehabilitation mechanism of nerves, further explore the motor control mechanism of brain and muscle, and provide the neurophysiological evidence for the wide use of rehabilitation technology such as walking training.

Drawings

FIG. 1 is a flow chart of an embodiment of the present invention;

fig. 2 is an experimental diagram of synchronous acquisition of EEG signals and sEMG signals;

FIG. 3 is a schematic illustration of muscle selection;

FIG. 4 is a diagram of brain electrode distribution;

fig. 5 is a graph of partial results after pretreatment of EEG signals and sEMG signals;

FIG. 6 is a first level tree structure (a) of R-vine forward walk (60bmp) for different actions; (b) positive walk (120 bmp); (c) back-off (60 bmp); (d) backward walking (120 bmp); (e) go upstairs (8 steps); (f) go down stairs (8 steps).

Detailed Description

The embodiment is implemented on the premise of the technical scheme of the invention, and a detailed implementation mode and a specific operation process are given. The embodiments of the present invention will be described in detail below with reference to the accompanying drawings:

as shown in fig. 1, the present embodiment includes the following steps:

step one, in the whole experiment data acquisition process, a total of 12 healthy subjects (6 male and female respectively; age: 21-26 years; height: 164-. Recording EEG signals and sEMG signals from multiple subjects simultaneously as in fig. 2 requires a straight forward and backward walk on a level ground to be accomplished at metronome commanded speeds (60bmp and 120bmp) and two 8-step stair walk up and down tasks of 2 minutes duration. Two sets of instruments, Wireless EEG amplifier neusen. w64, neuron Inc, China and trigno tm Wireless EMG System, Delsys Inc, nature, MA, were used herein to simultaneously record EEG signals and sEMG signals during the course of the subject experiment. All data recordings were time synchronized by the tag and all experiments were video recordings. According to the acquisition instrument it is shown that the sampling rate of the EEG signal is 256Hz and the sampling frequency of the sEMG is 1000 Hz. Human lower limb movement requires lower limb muscle group synergy, and the double leg lower limb muscles of fig. 3 are selected, including: tibialis Anterior (TA), Semitendinosus (SEM), Vastus Medialis (VM). The lower limb muscles thus selected include the left (left) leg muscles abbreviated TAL, SEML, VML and the right (right) leg muscles abbreviated TAR, SEMR, VMR. The electroencephalograph is used for selecting a standard electrode (the double ear mastoid) as a reference potential, and selecting the position of an electroencephalogram signal acquisition electrode shown in figure 4 to acquire 64 paths of electroencephalogram signals. This experiment focused on EEG signals for nine channels F3, Fz, F4, C3, Cz, C4, P3, POz, P4. To facilitate the dependency structure analysis, the following convention is applied for each channel and related implementation, with 15 signal channels numbered as shown in table 1. And (3) carrying out independent component analysis on the acquired brain and muscle electrical data to separate other artifacts and carrying out wavelet threshold denoising, wherein a result graph after partial preprocessing is shown in figure 5.

TABLE 1 channel numbering

And step two, constructing a novel cortical muscle function method for quantitatively analyzing complex causal relationship among cortical muscle signals. The Vine Copula is used for carrying out brain and muscle electricity nonlinear coupling analysis and brain and muscle function network modeling, and has the great advantage that related dependent structures can be constructed under different actions to describe the connectivity between cortical muscles. The construction mode of the Vine Copula coupling analysis method can be divided into three parts:

(1) and (4) selecting a Vine tree structure preferentially. It is a matter of great concern as to which vine structure is used for a set of multivariate data sets, and different vine structures can dissect the same set of data from different perspectives. Compared with C-Vine and D-Vine structures, R-Vine becomes the structure selection range of the Vine Copula function in the text due to the flexibility of the structure.

(2) And (4) selecting a Copula function. And selecting a proper Vine structure, thereby determining the connection mode among the variables. Selecting the best binary Copula function family to use to connect the variables requires stacking the tree structures of the layers. The methods used to select the appropriate Copula family of functions are broadly divided into two categories: the image tool includes, for example, an isocratic map, a λ function map, and various technical criteria. The method adopts criterion judgment, and two model selection criteria, namely an Akaichi Information Criterion (AIC) and a Bayesian Information Criterion (BIC), are selected for judgment.

(3) Parameter estimation of Copula function.

As a basic work, the parameters of a binary Copula function need to be estimated here using (EML) before selecting a suitable Copula function to describe the correlation between EEG and sEMG signals. When the most important practical problem is researched, the mean value transformation of sample data is often needed to obtain a random variable set approximately obeying U [0,1], which is called Copula data and is also source data for establishing a Vine Copula model. And (3) researching the functional coupling relation of the cortical muscles of different actions by constructing an R-vine Copula model.

The model construction is participated in by using a Maximum Spanning Tree (MST) algorithm. The first level tree structure for different activities of R-vine is shown in fig. 6. Wherein the channel numbers are shown in table 1. The determination of the tree structure allows a good direct and indirect observation of the dependencies of each channel.

And step three, providing a construction method for constructing a cortical muscle function network based on Vine Vine structure correlation coefficients. And taking the Kendall-tau rank correlation coefficient value of the first tree as the embodiment of the cortical muscle function coupling relation, and respectively calculating the Kendall-tau rank correlation coefficient values between every two of EEG and sEMG signals of each channel to form a weighted adjacency matrix so as to construct a cortical muscle function network. Extracting basic network characteristics describing the relationship between the network nodes, and carrying out physiological significance analysis and experiments on the characteristic parameters.

The present invention seeks to understand the correlation between cortical and muscle signals, initially studied using R-vine Copula for the connectivity problem between EEG and sEMG, and analyzed the relevant data for functional network construction. The method used in the present invention can well describe the effective connectivity between EEG-EEG, sEMG-sEMG and EEG-sEMG. Successful construction of the network indicates that there is indeed information transfer between different partitions of the cortex, between muscles and between cortex and muscle when the body performs lower limb movements. It also shows that the Vine Copula approach is feasible, i.e. significant changes in the underlying cortical muscle network of lower limb movements can be quantified by effective connectivity. The study of bioelectric signal connectivity will be more intensive and mature, which will help to understand the principle of cortical muscle control in human gait movements and its application in the field of rehabilitation therapy and assessment.