Development of a variational scheme for model inversion of multi-area model of brain. Part II: VBEM method

In Part I and Part II of these two companion papers (henceforth called Part I and Part II), we develop and evaluate a variational Bayesian expectation maximization (VBEM) method for model inversion of our multi-area extended neural mass model (MEN). In this paper, we develop the VBEM method to estimate posterior distributions of parameters of MEN. We choose suitable prior distributions for the model parameters in order to use properties of a conjugate-exponential model in implementing VBEM. Consequently, VBEM leads to analytically tractable forms. The proposed VBEM algorithm starts with initialization and consists of repeated iterations of a variational Bayesian expectation step (VB E-step) and a variational Bayesian maximization step (VB M-step). Posterior distributions of the model parameters are updated in the VB M-step. Distribution of the hidden state is updated in the VB E-step. We develop a variational extended Kalman smoother (VEKS) to infer the distribution of the hidden state in the VB E-step and derive the forward and backward passes of VEKS, analogous to the Kalman smoother. In Part I, we evaluate and validate the VBEM method using simulation studies.     

Modelling and detecting deep brain activity with MEG and EEG

We introduce an anatomical and electrophysiological model of deep brain structures dedicated to magnetoencephalography (MEG) and electroencephalography (EEG) source imaging. So far, most imaging inverse models considered that MEG/EEG surface signals were predominantly produced by cortical, hence superficial, neural currents. Here we question whether crucial deep brain structures such as the basal ganglia and the hippocampus may also contribute to distant, scalp MEG and EEG measurements. We first design a realistic anatomical and electrophysiological model of these structures and subsequently run Monte-Carlo experiments to evaluate the respective sensitivity of the MEG and EEG to signals from deeper origins. Results indicate that MEG/EEG may indeed localize these deeper generators, which is confirmed here from experimental MEG data reporting on the modulation of alpha (10–12 Hz) brain waves.     

A review of EEG and MEG for brainnetome research

The majority of brain activities are performed by functionally integrating separate regions of the brain. Therefore, the synchronous operation of the brain’s multiple regions or neuronal assemblies can be represented as a network with nodes that are interconnected by links. Because of the complexity of brain interactions and their varying effects at different levels of complexity, one of the corresponding authors of this paper recently proposed the brainnetome as a new –ome to explore and integrate the brain network at different scales. Because electroencephalography (EEG) and magnetoencephalography (MEG) are noninvasive and have outstanding temporal resolution and because they are the primary clinical techniques used to capture the dynamics of neuronal connections, they lend themselves to the analysis of the neural networks comprising the brainnetome. Because of EEG/MEG’s applicability to brainnetome analyses, the aim of this review is to identify the procedures that can be used to form a network using EEG/MEG data in sensor or source space and to promote EEG/MEG network analysis for either neuroscience or clinical applications. To accomplish this aim, we show the relationship of the brainnetome to brain networks at the macroscale and provide a systematic review of network construction using EEG and MEG. Some potential applications of the EEG/MEG brainnetome are to use newly developed methods to associate the properties of a brainnetome with indices of cognition or disease conditions. Associations based on EEG/MEG brainnetome analysis may improve the comprehension of the functioning of the brain in neuroscience research or the recognition of abnormal patterns in neurological disease.     

Electro/magnetoencephalography beamforming with spatial restrictions based on sparsity

We present a source localization method for electroencephalographic (EEG) and magnetoencephalographic (MEG) data which is based on an estimate of the sparsity obtained through the eigencanceler (EIG), which is a spatial filter whose weights are constrained to lie in the noise subspace. The EIG provides rejection of directional interferences while minimizing noise contributions and maintaining specified beam pattern constraints. In our case, the EIG is used to estimate the sparsity of the signal as a function of the position, then we use this information to spatially restrict the neural sources to locations out of the sparsity maxima. As proof of the concept, we incorporate this restriction in the “classical” linearly constrained minimum variance (LCMV) source localization approach in order to enhance its performance. We present numerical examples to evaluate the proposed method using realistically simulated EEG/MEG data for different signal-to-noise (SNR) conditions and various levels of correlation between sources, as well as real EEG/MEG measurements of median nerve stimulation. Our results show that the proposed method has the potential of reducing the bias on the search of neural sources in the classical approach, as well as making it more effective in localizing correlated sources.     

Classification methods for ongoing EEG and MEG signals

Classification algorithms help predict the qualitative properties of a subject's mental state by extracting useful information from the highly multivariate non-invasive recordings of his brain activity. In particular, applying them to Magneto-encephalography (MEG) and electro-encephalography (EEG) is a challenging and promising task with prominent practical applications to e.g. Brain Computer Interface (BCI). In this paper, we first review the principles of the major classification techniques and discuss their application to MEG and EEG data classification. Next, we investigate the behavior of classification methods using real data recorded during a MEG visuomotor experiment. In particular, we study the influence of the classification algorithm, of the quantitative functional variables used in this classifier, and of the validation method. In addition, our findings suggest that by investigating the distribution of classifier coefficients, it is possible to infer knowledge and construct functional interpretations of the underlying neural mechanisms of the performed tasks. Finally, the promising results reported here (up to 97% classification accuracy on 1-second time windows) reflect the considerable potential of MEG for the continuous classification of mental states.     

脑磁源的定位研究

在脑电脑磁研究中,常将大脑视为一电磁系统,利用准静态近似下的麦克斯韦方程,可以发现代表脑神经元活动的原在电流密度与脑外磁场之间呈线性关系。在高斯哭喊杨存在的情况下,采用极大似然估计理论,讨论了一种基于脑磁场时域－罕注解磁源定位问题的一般方法。球对称导体模型下的模拟计算表明,这一方法是有效的。对于考虑真实头模型下的磁源定位问题求解磁源定位,提出了一种联合使用脑磁脑电数据的近似方法。     

Revealing Time-Unlocked Brain Activity from MEG Measurements by Common Waveform Estimation

Brain activities related to cognitive functions, such as attention, occur with unknown and variable delays after stimulus onsets. Recently, we proposed a method (Common Waveform Estimation, CWE) that could extract such brain activities from magnetoencephalography (MEG) or electroencephalography (EEG) measurements. CWE estimates spatiotemporal MEG/EEG patterns occurring with unknown and variable delays, referred to here as unlocked waveforms, without hypotheses about their shapes. The purpose of this study is to demonstrate the usefulness of CWE for cognitive neuroscience. For this purpose, we show procedures to estimate unlocked waveforms using CWE and to examine their role. We applied CWE to the MEG epochs during Go trials of a visual Go/NoGo task. This revealed unlocked waveforms with interesting properties, specifically large alpha oscillations around the temporal areas. To examine the role of the unlocked waveform, we attempted to estimate the strength of the brain activity of the unlocked waveform in various conditions. We made a spatial filter to extract the component reflecting the brain activity of the unlocked waveform, applied this spatial filter to MEG data under different conditions (a passive viewing, a simple reaction time, and Go/NoGo tasks), and calculated the powers of the extracted components. Comparing the powers across these conditions suggests that the unlocked waveforms may reflect the inhibition of the task-irrelevant activities in the temporal regions while the subject attends to the visual stimulus. Our results demonstrate that CWE is a potential tool for revealing new findings of cognitive brain functions without any hypothesis in advance.     

A neural mass model based on single cell dynamics to model pathophysiology

Neural mass models are successful in modeling brain rhythms as observed in macroscopic measurements such as the electroencephalogram (EEG). While the synaptic current is explicitly modeled in current models, the single cell electrophysiology is not taken into account. To allow for investigations of the effects of channel pathologies, channel blockers and ion concentrations on macroscopic activity, we formulate neural mass equations explicitly incorporating the single cell dynamics by using a bottom-up approach. The mean and variance of the firing rate and synaptic input distributions are modeled. The firing rate curve (F(I)-curve) is used as link between the single cell and macroscopic dynamics. We show that this model accurately reproduces the behavior of two populations of synaptically connected Hodgkin-Huxley neurons, also in non-steady state.     

A model of neurovascular coupling and the BOLD response PART II

A mathematical model is developed which describes a signalling mechanism of neurovascular coupling with a model of a pyramidal neuron and its corresponding fMRI BOLD response. In the first part of two papers (Part I) we described the integration of the neurovascular coupling unit extended to include a complex neuron model, which includes the important Na/K ATPase pump, with a model that provides a BOLD signal taking its input from the cerebral blood flow and the metabolic rate of oxygen consumption. We showed that this produced a viable signal in terms of initial dip, positive and negative BOLD signals. In this paper (PART II) our model predicts the variations of the BOLD response due to variations in neuronal activity and indicates that the BOLD signal could be used as an initial biomarker for neuronal dysfunction or variations in the perfusion of blood to the cerebral tissue. We have compared the simulated hypoxic BOLD response to experimental BOLD signals observed in the hippocampus during hypoxia showing good agreement. This approach of combined quantitative modelling of neurovascular coupling response and its BOLD response will enable more specific assessment of a brain region.     

Constrained brain volume in an efficient coding model explains the fraction of excitatory and inhibitory neurons in sensory cortices

The number of neurons in mammalian cortex varies by multiple orders of magnitude across different species. In contrast, the ratio of excitatory to inhibitory neurons (E:I ratio) varies in a much smaller range, from 3:1 to 9:1 and remains roughly constant for different sensory areas within a species. Despite this structure being important for understanding the function of neural circuits, the reason for this consistency is not yet understood. While recent models of vision based on the efficient coding hypothesis show that increasing the number of both excitatory and inhibitory cells improves stimulus representation, the two cannot increase simultaneously due to constraints on brain volume. In this work, we implement an efficient coding model of vision under a constraint on the volume (using number of neurons as a surrogate) while varying the E:I ratio. We show that the performance of the model is optimal at biologically observed E:I ratios under several metrics. We argue that this happens due to trade-offs between the computational accuracy and the representation capacity for natural stimuli. Further, we make experimentally testable predictions that 1) the optimal E:I ratio should be higher for species with a higher sparsity in the neural activity and 2) the character of inhibitory synaptic distributions and firing rates should change depending on E:I ratio. Our findings, which are supported by our new preliminary analyses of publicly available data, provide the first quantitative and testable hypothesis based on optimal coding models for the distribution of excitatory and inhibitory neural types in the mammalian sensory cortices.     

Brain rhythms reveal a hierarchical network organization

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or "virtual brains", whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.     

Complex networks and deep learning for EEG signal analysis

Electroencephalogram (EEG) signals acquired from brain can provide an effective representation of the human’s physiological and pathological states. Up to now, much work has been conducted to study and analyze the EEG signals, aiming at spying the current states or the evolution characteristics of the complex brain system. Considering the complex interactions between different structural and functional brain regions, brain network has received a lot of attention and has made great progress in brain mechanism research. In addition, characterized by autonomous, multi-layer and diversified feature extraction, deep learning has provided an effective and feasible solution for solving complex classification problems in many fields, including brain state research. Both of them show strong ability in EEG signal analysis, but the combination of these two theories to solve the difficult classification problems based on EEG signals is still in its infancy. We here review the application of these two theories in EEG signal research, mainly involving brain–computer interface, neurological disorders and cognitive analysis. Furthermore, we also develop a framework combining recurrence plots and convolutional neural network to achieve fatigue driving recognition. The results demonstrate that complex networks and deep learning can effectively implement functional complementarity for better feature extraction and classification, especially in EEG signal analysis.     

Hierarchical models in the brain

This paper describes a general model that subsumes many parametric models for continuous data. The model comprises hidden layers of state-space or dynamic causal models, arranged so that the output of one provides input to another. The ensuing hierarchy furnishes a model for many types of data, of arbitrary complexity. Special cases range from the general linear model for static data to generalised convolution models, with system noise, for nonlinear time-series analysis. Crucially, all of these models can be inverted using exactly the same scheme, namely, dynamic expectation maximization. This means that a single model and optimisation scheme can be used to invert a wide range of models. We present the model and a brief review of its inversion to disclose the relationships among, apparently, diverse generative models of empirical data. We then show that this inversion can be formulated as a simple neural network and may provide a useful metaphor for inference and learning in the brain.     

Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media

The resistive or non-resistive nature of the extracellular space in the brain is still debated, and is an important issue for correctly modeling extracellular potentials. Here, we first show theoretically that if the medium is resistive, the frequency scaling should be the same for electroencephalogram (EEG) and magnetoencephalogram (MEG) signals at low frequencies (<10 Hz). To test this prediction, we analyzed the spectrum of simultaneous EEG and MEG measurements in four human subjects. The frequency scaling of EEG displays coherent variations across the brain, in general between 1/f and 1/f ², and tends to be smaller in parietal/temporal regions. In a given region, although the variability of the frequency scaling exponent was higher for MEG compared to EEG, both signals consistently scale with a different exponent. In some cases, the scaling was similar, but only when the signal-to-noise ratio of the MEG was low. Several methods of noise correction for environmental and instrumental noise were tested, and they all increased the difference between EEG and MEG scaling. In conclusion, there is a significant difference in frequency scaling between EEG and MEG, which can be explained if the extracellular medium (including other layers such as dura matter and skull) is globally non-resistive.     

Towards a large-scale model of patient-specific epileptic spike-wave discharges

Clinical electroencephalographic (EEG) recordings of the transition into generalised epileptic seizures show a sudden onset of spike-wave dynamics from a low-amplitude irregular background. In addition, non-trivial and variable spatio-temporal dynamics are widely reported in combined EEG/fMRI studies on the scale of the whole cortex. It is unknown whether these characteristics can be accounted for in a large-scale mathematical model with fixed heterogeneous long-range connectivities. Here, we develop a modelling framework with which to investigate such EEG features. We show that a neural field model composed of a few coupled compartments can serve as a low-dimensional prototype for the transition between irregular background dynamics and spike-wave activity. This prototype then serves as a node in a large-scale network with long-range connectivities derived from human diffusion-tensor imaging data. We examine multivariate properties in 42 clinical EEG seizure recordings from 10 patients diagnosed with typical absence epilepsy and 50 simulated seizures from the large-scale model using 10 DTI connectivity sets from humans. The model can reproduce the clinical feature of stereotypy where seizures are more similar within a patient than between patients, essentially creating a patient-specific fingerprint. We propose the approach as a feasible technique for the investigation of patient-specific large-scale epileptic features in space and time.     

Two Distinct Dynamic Modes Subtend the Detection of Unexpected Sounds

The brain response to auditory novelty comprises two main EEG components: an early mismatch negativity and a late P300. Whereas the former has been proposed to reflect a prediction error, the latter is often associated with working memory updating. Interestingly, these two proposals predict fundamentally different dynamics: prediction errors are thought to propagate serially through several distinct brain areas, while working memory supposes that activity is sustained over time within a stable set of brain areas. Here we test this temporal dissociation by showing how the generalization of brain activity patterns across time can characterize the dynamics of the underlying neural processes. This method is applied to magnetoencephalography (MEG) recordings acquired from healthy participants who were presented with two types of auditory novelty. Following our predictions, the results show that the mismatch evoked by a local novelty leads to the sequential recruitment of distinct and short-lived patterns of brain activity. In sharp contrast, the global novelty evoked by an unexpected sequence of five sounds elicits a sustained state of brain activity that lasts for several hundreds of milliseconds. The present results highlight how MEG combined with multivariate pattern analyses can characterize the dynamics of human cortical processes.     

Dynamics on Networks: The Role of Local Dynamics and Global Networks on the Emergence of Hypersynchronous Neural Activity

Graph theory has evolved into a useful tool for studying complex brain networks inferred from a variety of measures of neural activity, including fMRI, DTI, MEG and EEG. In the study of neurological disorders, recent work has discovered differences in the structure of graphs inferred from patient and control cohorts. However, most of these studies pursue a purely observational approach; identifying correlations between properties of graphs and the cohort which they describe, without consideration of the underlying mechanisms. To move beyond this necessitates the development of computational modeling approaches to appropriately interpret network interactions and the alterations in brain dynamics they permit, which in the field of complexity sciences is known as dynamics on networks. In this study we describe the development and application of this framework using modular networks of Kuramoto oscillators. We use this framework to understand functional networks inferred from resting state EEG recordings of a cohort of 35 adults with heterogeneous idiopathic generalized epilepsies and 40 healthy adult controls. Taking emergent synchrony across the global network as a proxy for seizures, our study finds that the critical strength of coupling required to synchronize the global network is significantly decreased for the epilepsy cohort for functional networks inferred from both theta (3–6 Hz) and low-alpha (6–9 Hz) bands. We further identify left frontal regions as a potential driver of seizure activity within these networks. We also explore the ability of our method to identify individuals with epilepsy, observing up to 80 predictive power through use of receiver operating characteristic analysis. Collectively these findings demonstrate that a computer model based analysis of routine clinical EEG provides significant additional information beyond standard clinical interpretation, which should ultimately enable a more appropriate mechanistic stratification of people with epilepsy leading to improved diagnostics and therapeutics.     

Source localization of induced cortical oscillations during tactile finger stimulation.

We investigated the EEG beta event-related synchronization (ERS) after tactile finger stimulation in three subjects. Prior studies from our group using electrical stimulation and self-paced movement showed a beta rebound within one second after stimulation respectively movement offset. As the tactile-stimulation-data showed a similar ERS behaviour, we extracted the cortical sources for this beta rebound by the linear estimation method in order to see whether the representation areas of different fingers were distinguishable (as is possible with MEG data). Although realistic head models of two subjects were used for the calculations the fingers could not be spatially distinguished. However, regarding the whole spatio-temporal pattern of the ERS for different fingers clear differences can be observed.     

Non-zero mean alpha oscillations revealed with computational model and empirical data

Ongoing oscillations and evoked responses are two main types of neuronal activity obtained with diverse electrophysiological recordings (EEG/MEG/iEEG/LFP). Although typically studied separately, they might in fact be closely related. One possibility to unite them is to demonstrate that neuronal oscillations have non-zero mean which predicts that stimulus- or task-triggered amplitude modulation of oscillations can contribute to the generation of evoked responses. We validated this mechanism using computational modelling and analysis of a large EEG data set. With a biophysical model, we indeed demonstrated that intracellular currents in the neuron are asymmetric and, consequently, the mean of alpha oscillations is non-zero. To understand the effect that neuronal currents exert on oscillatory mean, we varied several biophysical and morphological properties of neurons in the network, such as voltage-gated channel densities, length of dendrites, and intensity of incoming stimuli. For a very large range of model parameters, we observed evidence for non-zero mean of oscillations. Complimentary, we analysed empirical rest EEG recordings of 90 participants (50 young, 40 elderly) and, with spatio-spectral decomposition, detected at least one spatially-filtred oscillatory component of non-zero mean alpha oscillations in 93% of participants. In order to explain a complex relationship between the dynamics of amplitude-envelope and corresponding baseline shifts, we performed additional simulations with simple oscillators coupled with different time delays. We demonstrated that the extent of spatial synchronisation may obscure macroscopic estimation of alpha rhythm modulation while leaving baseline shifts unchanged. Overall, our results predict that amplitude modulation of neural oscillations should at least partially explain the generation of evoked responses. Therefore, inference about changes in evoked responses with respect to cognitive conditions, age or neuropathologies should be constructed while taking into account oscillatory neuronal dynamics.