Increasing Accuracy Of Electrophysiological Brain Connectivity Estimation By Structured Sparsity

Estimating brain connectivity with electrophysiological data is an important approach to study the dynamic of the brain.The electromagnetic signals from the sophisticated nervous system provide a way to study its biophysical processes.EEG(Electroencephalography)and MEG(Magnetoencephalography)can non-invasively record high-time resolution electrophysiological data.With the inverse method of EEG/MEG,people can reconstruct the electrophysiological signal in the intracranial source space,moreover,the source connectivity can also be estimated.However,source space connectivity estimation with EEG/MEG has the challenge of source leakage which causes false connectivity.Therefore,this thesis discussed connectivity reconstruction schemes from the perspective of the leakage with the linear source model,and put forward a verification experiment to evaluate the leakage elimination performance of connectivity estimation methods,and proved that the method of structured sparsity can be more accurate estimates brain electrophysiological connectivity:First,the theoretical framework of the state space and graphical model established by the EEG biophysical process was introduced.With this theory,the source signal reconstruction and source connectivity reconstruction methods were reviewed.This thesis pointed out the drawback of four key steps in the current two-step connectivity estimation practice using leakage correction,especially proved the source space leakage should be non-zero phase effect.This thesis gave solutions: compared with the time-domain band-limited signal,it was more accurate to use the band-limited Hilbert envelope to estimate the inverse problem in the frequency domain;in order to preserve the phase information,it should be the source space complex Hilbert envelope to calculate the covariance;since the source leakage does not only affect the zero-phase correlation,based on the Graphical Ridge estimation of partial coherence,this thesis eliminated the non-zero phase connectivity distortion caused by instantaneous leakage by solving the algebraic Riccati equation of the true cross spectrum;according to the structured sparsity of the connectivity,the unbiased Hermitian Graphical LASSO(hgLASSO)was used to estimate the inverse covariance matrix to obtain partial coherence.According to the structured sparsity assumption,to reduce the dimension of connectivity estimation,this thesis re-examined the inverse problem in the Bayesian framework,led to the source spatial signal reconstruction method-the Spectral structured sparse Bayesian learning(sSSBL)proposed by Paz-Linares et al.Since the one-step estimation method for directly estimating model parameters using observation data—Hidden Gaussian Graphical Source-model(HIGGS)requires sSSBL to screen the vertices and set initial values to ensure convergence.After introducing the precise source localization performance of sSSBL,this thesis used canonical correlation analysis to calculate the frequency coupling between the reconstructed source electrophysiological signal and hemodynamic signal.According to the results,it was found that the spectral coupling relationship between the two was consistent with the relationship between the local field potential(LFP)and blood oxygen level dependent(BOLD)signal previously reported in the literature,which proved that the reconstructed source signal also has good frequency characteristics,and further verifies that it can accurately estimate the source space signal.On the other hand,the Bayesian framework also revealed the problem of fixing source covariance as the prior in the two-step estimation,and then this thesis introduced the three-layer Bayesian model HIGGS and the unbiased hgLASSO for partial coherent estimation designed by Paz-Linares et al.Finally,in order to compare various source connectivity reconstruction schemes,this thesis used the vector autoregressive model based on the xi-alpha model and the Hermitian Gaussian Graphical Model(hGGM)model to establish a time-domain simulation that was more in line with the spatiotemporal characteristics of real brain electrophysiology.By comparing the performance of each method in the simulation,it was proved that this thesis was effective to improve the two-step method with AREC method and other strategies above.The HIGGS accurately reconstructed the connectivity in the simulation of this thesis,which provided a reliable means for EEG and MEG to estimate the connectivity of the brain.In summary,this thesis provided theoretical and methodological support for the study of high-dimensional neurodynamics using brain electrophysiological data.The results of simulation and real data verified the reliability of the connectivity estimation methods and promoted the development of the application of EEG and MEG connectivity estimation in brain cognitive and medical health.