Characterizing Variability of Modular Brain Connectivity with Constrained Principal Component Analysis

Characterizing the variability of resting-state functional brain connectivity across subjects and/or over time has recently attracted much attention. Principal component analysis (PCA) serves as a fundamental statistical technique for such analyses. However, performing PCA on high-dimensional connectivity matrices yields complicated "eigenconnectivity" patterns, for which systematic interpretation is a challenging issue. Here, we overcome this issue with a novel constrained PCA method for connectivity matrices by extending the idea of the previously proposed orthogonal connectivity factorization method. Our new method, modular connectivity factorization (MCF), explicitly introduces the modularity of brain networks as a parametric constraint on eigenconnectivity matrices. In particular, MCF analyzes the variability in both intra-and inter-module connectivities, simultaneously finding network modules in a principled, data-driven manner. The parametric constraint provides a compact module based visualization scheme with which the result can be intuitively interpreted. We develop an optimization algorithm to solve the constrained PCA problem and validate our method in simulation studies and with a resting-state functional connectivity MRI dataset of 986 subjects. The results show that the proposed MCF method successfully reveals the underlying modular eigenconnectivity patterns in more general situations and is a promising alternative to existing methods.Peer reviewe

MEG Source Imaging and Group Analysis Using VBMEG

Variational Bayesian Multimodal EncephaloGraphy (VBMEG) is a MATLAB toolbox that estimates distributed source currents from magnetoencephalography (MEG)/electroencephalography (EEG) data by integrating functional MRI (fMRI) (https://vbmeg.atr.jp/). VBMEG also estimates whole-brain connectome dynamics using anatomical connectivity derived from a diffusion MRI (dMRI). In this paper, we introduce the VBMEG toolbox and demonstrate its usefulness. By collaborating with VBMEG's tutorial page (https://vbmeg.atr.jp/docs/v2/static/vbmeg2_tutorial_neuromag.html), we show its full pipeline using an open dataset recorded by Wakeman and Henson (2015). We import the MEG data and preprocess them to estimate the source currents. From the estimated source currents, we perform a group analysis and examine the differences of current amplitudes between conditions by controlling the false discovery rate (FDR), which yields results consistent with previous studies. We highlight VBMEG's characteristics by comparing these results with those obtained by other source imaging methods: weighted minimum norm estimate (wMNE), dynamic statistical parametric mapping (dSPM), and linearly constrained minimum variance (LCMV) beamformer. We also estimate source currents from the EEG data and the whole-brain connectome dynamics from the MEG data and dMRI. The observed results indicate the reliability, characteristics, and usefulness of VBMEG

BCI training to move a virtual hand reduces phantom limb pain: A randomized crossover trial

Objective: To determine whether training with a brain–computer interface (BCI) to control an image of a phantom hand, which moves based on cortical currents estimated from magnetoencephalographic signals, reduces phantom limb pain. Methods: Twelve patients with chronic phantom limb pain of the upper limb due to amputation or brachial plexus root avulsion participated in a randomized single-blinded crossover trial. Patients were trained to move the virtual hand image controlled by the BCI with a real decoder, which was constructed to classify intact hand movements from motor cortical currents, by moving their phantom hands for 3 days (“real training”). Pain was evaluated using a visual analogue scale (VAS) before and after training, and at follow-up for an additional 16 days. As a control, patients engaged in the training with the same hand image controlled by randomly changing values (“random training”). The 2 trainings were randomly assigned to the patients. This trial is registered at UMIN-CTR (UMIN000013608). Results: VAS at day 4 was significantly reduced from the baseline after real training (mean [SD], 45.3 [24.2]–30.9 [20.6], 1/100 mm; p = 0.009 0.025). Compared to VAS at day 1, VAS at days 4 and 8 was significantly reduced by 32% and 36%, respectively, after real training and was significantly lower than VAS after random training (p < 0.01). Conclusion: Three-day training to move the hand images controlled by BCI significantly reduced pain for 1 week. Classification of evidence: This study provides Class III evidence that BCI reduces phantom limb pain

Dynamic Information Flow Based on EEG and Diffusion MRI in Stroke: A Proof-of-Principle Study

In hemiparetic stroke, functional recovery of paretic limb may occur with the reorganization of neural networks in the brain. Neuroimaging techniques, such as magnetic resonance imaging (MRI), have a high spatial resolution which can be used to reveal anatomical changes in the brain following a stroke. However, low temporal resolution of MRI provides less insight of dynamic changes of brain activity. In contrast, electro-neurophysiological techniques, such as electroencephalography (EEG), have an excellent temporal resolution to measure such transient events, however are hindered by its low spatial resolution. This proof-of-principle study assessed a novel multimodal brain imaging technique namely Variational Bayesian Multimodal Encephalography (VBMEG), which aims to improve the spatial resolution of EEG for tracking the information flow inside the brain and its changes following a stroke. The limitations of EEG are complemented by constraints derived from anatomical MRI and diffusion weighted imaging (DWI). EEG data were acquired from individuals suffering from a stroke as well as able-bodied participants while electrical stimuli were delivered sequentially at their index finger in the left and right hand, respectively. The locations of active sources related to this stimulus were precisely identified, resulting in high Variance Accounted For (VAF above 80%). An accurate estimation of dynamic information flow between sources was achieved in this study, showing a high VAF (above 90%) in the cross-validation test. The estimated dynamic information flow was compared between chronic hemiparetic stroke and able-bodied individuals. The results demonstrate the feasibility of VBMEG method in revealing the changes of information flow in the brain after stroke. This study verified the VBMEG method as an advanced computational approach to track the dynamic information flow in the brain following a stroke. This may lead to the development of a quantitative tool for monitoring functional changes of the cortical neural networks after a unilateral brain injury and therefore facilitate the research into, and the practice of stroke rehabilitation

MEG current source reconstruction using a meta-analysis fMRI prior

Magnetoencephalography (MEG) offers a unique way to noninvasively investigate millisecond-order cortical activities by mapping sensor signals (magnetic fields outside the head) to cortical current sources using current source reconstruction methods. Current source reconstruction is defined as an ill-posed inverse problem, since the number of sensors is less than the number of current sources. One powerful approach to solving this problem is to use functional MRI (fMRI) data as a spatial constraint, although it boosts the cost of measurement and the burden on subjects. Here, we show how to use the meta-analysis fMRI data synthesized from thousands of papers instead of the individually recorded fMRI data. To mitigate the differences between the meta-analysis and individual data, the former are imported as prior information of the hierarchical Bayesian estimation. Using realistic simulations, we found out the performance of current source reconstruction using meta-analysis fMRI data to be better than that using low-quality individual fMRI data and conventional methods. By applying experimental data of a face recognition task, we qualitatively confirmed that group analysis results using the meta-analysis fMRI data showed a tendency similar to the results using the individual fMRI data. Our results indicate that the use of meta-analysis fMRI data improves current source reconstruction without additional measurement costs. We assume the proposed method would have greater effect for modalities with lower measurement costs, such as optically pumped magnetometers

Dynamical EEG Inverse Problem and Causality Analysis of fMRI Data

　Human being has long been challenging to understand functions and organizations of the brain. With striking developments of various measurement apparatus and methodology after twentieth century, we have accumulated not only the knowledge about the mechanism of our brain but also measurements of brain activities from various aspects. In order to make the best use of these data combined with a priori knowledge, the development of statistical methods is indispensable. Nowadays the functional Magnetic Resonance Imaging (fMRI)technique and the electroencephalography (EEG) are two common tools for the understanding of human cognition as well as for the clinical diagnosis. By the fMRI technique, the change of regional cerebral blood flow, which is supposed to result from electrical neuronal activities on the corresponding local region, is measured as temporally successive images covering the whole brain volume with high spatial resolution but low temporal resolution. By the EEG, evoke potentials can be measured in several tens positions on the scalp surface with high temporal resolution as a consequence of the transmission of electric currents (a collection of electrical neuronal activities) inside the brain.　In this thesis, for the purpose of analyzing these two kind of the data sets, the methodology in the field of time series analysis will be applied and developed. Since these two data sets have distinct properties, the purpose and the tool for analysis are also distinct. Therefore this thesis consists of two parts, the inverse problem of the EEG and the causal analysis for the fMRI data.　In the first part of this thesis, the dynamical inverse problem of the EEG generation will be discussed. Since the EEG recording is an indirect observation of electrical sources inside the brain, the inference to localize the sources, called the \u27inverse problem\u27 are necessary. In general, in order to solve the inverse problem we have to combine additional information to the observation because it is impossible to uniquely determine the solution from the observation itself. In this thesis, we will consider the dynamical inverse problem so that general spatio-temporal constraints can be incorporated. This aspect has been neglected in many previous studies of the inverse problem of the EEG generation in spite of its importance. 　Mathematically the dynamical inverse problem will be formulated as the state estimation problem. The system equation in the state space representation describes general spatio-temporal constraints. By assuming a parametric model for the dynamics, we can choose in a sense the \u27best fitting\u27 constraints onto the solution. In principle both the parameter estimation and the state estimation (the solution) can be done by means of the celebrated Kalman filtering algorithm. 　However due to high dimensionality of the state in the EEG application, the difficulty occurs in the computational aspect. As alternatives of ordinary Kalman filtering, the author will propose three approximate filtering algorithms; the recursive penalized least squares (RPLS) method, observable projection Kalman filtering and partitioned (spatio-temporal) Kalman filtering. The different ways of approximation of covariance matrices of the filtered and predicion states are employed in these algorithms. The simulation study will demonstrate similarity of the solutions via three methods in the case of simple dynamics. However the difference of three solutions could become larger when the dynamics becomes complex. It would be necessary to examine the situation of problems and validity of the assumption. 　The data analysis of real α wave will show two sources located in the occipital region of both the left and right hemisphere, which has been reported in the previous studies. In addition, the estimated dynamics inside and outside the occipital region is observed to differ in periodicity using a regional AR model as the dynamics. 　In the latter part of this thesis, the methodology to evaluate the effective connectivity of the fMRI data will be investigated. In the fMRl studies, recently, more attention has been paid to the analysis of the effective connectivity defined as "the influence that one neural system exerts over another" (Friston 1995). In order to accomplish this purpose, the method developed in the multivariate time series analysis will be applied. It is a crucial advantage of this approach that no assumption about the direction of connectivity is required, whereas the structural equation model, the most common approach to evaluate the effective connectivity so far, requires to determine and to restrict the direction of connectivity apriori. 　For this purpose, the author proposes to apply the Akaike\u27s noise contribution ratio (ANCR), which quantifies the influence on one time series from another time series. Using the data from the random dot experiment, the change of the connectivity between two conditions will be evaluated by the ANCR as a measure. As a result, the increase of the connectivity on the task condition is observed compared with the connectivity on the control condition