Estimation of dynamic neural activity using a Kalman filter approach based on physiological models

Bridging M/EEG Source Imaging and Independent Component Analysis Frameworks Using Biologically Inspired Sparsity Priors

Electromagnetic source imaging (ESI) and independent component analysis (ICA) are two popular and apparently dissimilar frameworks for M/EEG analysis. This letter shows that the two frameworks can be linked by choosing biologically inspired source sparsity priors. We demonstrate that ESI carried out by the sparse Bayesian learning (SBL) algorithm yields source configurations composed of a few active regions that are also maximally independent from one another. In addition, we extend the standard SBL approach to source imaging in two important directions. First, we augment the generative model of M/EEG to include artifactual sources. Second, we modify SBL to allow for efficient model inversion with sequential data. We refer to this new algorithm as recursive SBL (RSBL), a source estimation filter with potential for online and offline imaging applications. We use simulated data to verify that RSBL can accurately estimate and demix cortical and artifactual sources under different noise conditions. Finally, we show that on real error-related EEG data, RSBL can yield single-trial source estimates in agreement with the experimental literature. Overall, by demonstrating that ESI can produce maximally independent sources while simultaneously localizing them in cortical space, we bridge the gap between the ESI and ICA frameworks for M/EEG analysis.

Structural connectivity to reconstruct brain activation and effective connectivity between brain regions

OBJECTIVE

Understanding how brain regions interact to perform a specific task is very challenging. EEG and MEG are two non-invasive imaging modalities that allow the measurement of brain activation with high temporal resolution. Several works in EEG/MEG source reconstruction show that estimating brain activation can be improved by considering spatio-temporal constraints but only few of them use structural information to do so.

APPROACH

In this work, we present a source reconstruction algorithm that uses brain structural connectivity, estimated from diffusion MRI (dMRI), to constrain the EEG/MEG source reconstruction. Contrarily to most source reconstruction methods which reconstruct activation for each time instant, the proposed method estimates an initial reconstruction for the first time instants and a multivariate autoregressive model that explains the data in further time instants. This autoregressive model can be thought as an estimation of the effective connectivity between brain regions. We called this algorithm iterative Source and Dynamics reconstruction (iSDR).

MAIN RESULTS

This paper presents the overall iSDR approach and how the proposed model is optimized to obtain both brain activation and brain region interactions. The accuracy of our method is demonstrated using synthetic data in which it shows a good capability to reconstruct both activation and connectivity. iSDR is also tested with real data obtained from (Wakeman D and Henson R 2015 A multi-subject, multi-modal human neuroimaging dataset Scientific Data 2 15001) (face recognition task). The results are in phase with other works published with the same data and others that used different imaging modalities with the same task showing that the choice of using an autoregressive model gives relevant results.

SIGNIFICANCE

This work shows that complex EEG/MEG datasets can be explained by an initial state and a MAR model for effective connectivity. This is a compact way to describe brain dynamics and offers a direct access to effective connectivity.

SEREEGA: Simulating event-related EEG activity

BACKGROUND

Electroencephalography (EEG) is a popular method to monitor brain activity, but it is difficult to evaluate EEG-based analysis methods because no ground-truth brain activity is available for comparison. Therefore, in order to test and evaluate such methods, researchers often use simulated EEG data instead of actual EEG recordings. Simulated data can be used, among other things, to assess or compare signal processing and machine learning algorithms, to model EEG variabilities, and to design source reconstruction methods.

NEW METHOD

We present SEREEGA, Simulating Event-Related EEG Activity. SEREEGA is a free and open-source MATLAB-based toolbox dedicated to the generation of simulated epochs of EEG data. It is modular and extensible, at initial release supporting five different publicly available head models and capable of simulating multiple different types of signals mimicking brain activity. This paper presents the architecture and general workflow of this toolbox, as well as a simulated data set demonstrating some of its functions. The toolbox is available at https://github.com/lrkrol/SEREEGA.

RESULTS

The simulated data allows established analysis pipelines and classification methods to be applied and is capable of producing realistic results.

COMPARISON WITH EXISTING METHODS

Most simulated EEG is coded from scratch. The few open-source methods in existence focus on specific applications or signal types, such as connectivity. SEREEGA unifies the majority of past simulation methods reported in the literature into one toolbox.

CONCLUSION

SEREEGA is a general-purpose toolbox to simulate ground-truth EEG data.

Exploiting neurovascular coupling: a Bayesian sequential Monte Carlo approach applied to simulated EEG fNIRS data

OBJECTIVE

Electrical and hemodynamic brain activity are linked through the neurovascular coupling process and they can be simultaneously measured through integration of electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS). Thanks to the lack of electro-optical interference, the two procedures can be easily combined and, whereas EEG provides electrophysiological information, fNIRS can provide measurements of two hemodynamic variables, such as oxygenated and deoxygenated hemoglobin. A Bayesian sequential Monte Carlo approach (particle filter, PF) was applied to simulated recordings of electrical and neurovascular mediated hemodynamic activity, and the advantages of a unified framework were shown.

APPROACH

Multiple neural activities and hemodynamic responses were simulated in the primary motor cortex of a subject brain. EEG and fNIRS recordings were obtained by means of forward models of volume conduction and light propagation through the head. A state space model of combined EEG and fNIRS data was built and its dynamic evolution was estimated through a Bayesian sequential Monte Carlo approach (PF).

MAIN RESULTS

We showed the feasibility of the procedure and the improvements in both electrical and hemodynamic brain activity reconstruction when using the PF on combined EEG and fNIRS measurements.

SIGNIFICANCE

The investigated procedure allows one to combine the information provided by the two methodologies, and, by taking advantage of a physical model of the coupling between electrical and hemodynamic response, to obtain a better estimate of brain activity evolution. Despite the high computational demand, application of such an approach to in vivo recordings could fully exploit the advantages of this combined brain imaging technology.

Hybrid Cubature Kalman filtering for identifying nonlinear models from sampled recording: Estimation of neuronal dynamics

Kalman filtering methods have long been regarded as efficient adaptive Bayesian techniques for estimating hidden states in models of linear dynamical systems under Gaussian uncertainty. Recent advents of the Cubature Kalman filter (CKF) have extended this efficient estimation property to nonlinear systems, and also to hybrid nonlinear problems where by the processes are continuous and the observations are discrete (continuous-discrete CD-CKF). Employing CKF techniques, therefore, carries high promise for modeling many biological phenomena where the underlying processes exhibit inherently nonlinear, continuous, and noisy dynamics and the associated measurements are uncertain and time-sampled. This paper investigates the performance of cubature filtering (CKF and CD-CKF) in two flagship problems arising in the field of neuroscience upon relating brain functionality to aggregate neurophysiological recordings: (i) estimation of the firing dynamics and the neural circuit model parameters from electric potentials (EP) observations, and (ii) estimation of the hemodynamic model parameters and the underlying neural drive from BOLD (fMRI) signals. First, in simulated neural circuit models, estimation accuracy was investigated under varying levels of observation noise (SNR), process noise structures, and observation sampling intervals (dt). When compared to the CKF, the CD-CKF consistently exhibited better accuracy for a given SNR, sharp accuracy increase with higher SNR, and persistent error reduction with smaller dt. Remarkably, CD-CKF accuracy shows only a mild deterioration for non-Gaussian process noise, specifically with Poisson noise, a commonly assumed form of background fluctuations in neuronal systems. Second, in simulated hemodynamic models, parametric estimates were consistently improved under CD-CKF. Critically, time-localization of the underlying neural drive, a determinant factor in fMRI-based functional connectivity studies, was significantly more accurate under CD-CKF. In conclusion, and with the CKF recently benchmarked against other advanced Bayesian techniques, the CD-CKF framework could provide significant gains in robustness and accuracy when estimating a variety of biological phenomena models where the underlying process dynamics unfold at time scales faster than those seen in collected measurements.

EEG-fMRI Bayesian framework for neural activity estimation: a simulation study

OBJECTIVE

Due to the complementary nature of electroencephalography (EEG) and functional magnetic resonance imaging (fMRI), and given the possibility of simultaneous acquisition, the joint data analysis can afford a better understanding of the underlying neural activity estimation. In this simulation study we want to show the benefit of the joint EEG-fMRI neural activity estimation in a Bayesian framework.

APPROACH

We built a dynamic Bayesian framework in order to perform joint EEG-fMRI neural activity time course estimation. The neural activity is originated by a given brain area and detected by means of both measurement techniques. We have chosen a resting state neural activity situation to address the worst case in terms of the signal-to-noise ratio. To infer information by EEG and fMRI concurrently we used a tool belonging to the sequential Monte Carlo (SMC) methods: the particle filter (PF).

MAIN RESULTS

First, despite a high computational cost, we showed the feasibility of such an approach. Second, we obtained an improvement in neural activity reconstruction when using both EEG and fMRI measurements.

SIGNIFICANCE

The proposed simulation shows the improvements in neural activity reconstruction with EEG-fMRI simultaneous data. The application of such an approach to real data allows a better comprehension of the neural dynamics.

Multivariate autoregressive model constrained by anatomical connectivity to reconstruct focal sources

In this paper, we present a framework to reconstruct spatially localized sources from Magnetoencephalography (MEG)/Electroencephalography (EEG) using spatiotemporal constraint. The source dynamics are represented by a Multivariate Autoregressive (MAR) model whose matrix elements are constrained by the anatomical connectivity obtained from diffusion Magnetic Resonance Imaging (dMRI). The framework assumes that the whole brain dynamic follows a constant MAR model in a time window of interest. The source activations and the MAR model parameters are estimated iteratively. We could confirm the accuracy of the framework using simulation experiments in both high and low noise levels. The proposed framework outperforms the two-stage approach.

EEG source localization based on multivariate autoregressive models using Kalman filtering

The estimation of current distributions from electroencephalographic recordings poses an inverse problem, which can approximately be solved by including dynamical models as spatio-temporal constraints onto the solution. In this paper, we consider the electrocardiography source localization task, where a specific structure for the dynamical model of current distribution is directly obtained from the data by fitting multivariate autoregressive models to electroencephalographic time series. Whereas previous approaches consider an approximation of the internal connectivity of the sources, the proposed methodology takes into account a realistic structure of the model estimated from the data, such that it becomes possible to obtain improved inverse solutions. The performance of the new method is demonstrated by application to simulated electroencephalographic data over several signal to noise ratios, where the source localization task is evaluated by using the localization error and the data fit error. Finally, it is shown that estimating MVAR models makes possible to obtain inverse solutions of considerably improved quality, as compared to the usual instantaneous inverse solutions, even if the regularized inverse of Tikhonov is used.