State-space modeling of MEG time series

Abstract

Magnetoencephalography (MEG) non-invasively offers information about neural activity in the brain by measuring its magnetic field. Estimating the cerebral sources of neural activity from MEG is an ill-posed inverse problem that presents several challenges. First, this inverse problem is high-dimensional, as the number of possible sources exceeds the number of MEG recording sensors by at least an order of magnitude. Second, even though the neural activity has a strong temporal dynamic and the MEG recordings are made at high-temporal resolution, the temporal dynamic is usually not exploited to enhance the spatial accuracy of the source localization. Third, whereas a dynamic form of the MEG source localization problem can be easily formulated as a state-space model (SSM) problem, the high dimension of the resulting state-space makes this approach computationally impractical. In this thesis we use a SSM to characterize from MEG recordings the spatiotemporal dynamics of underlying neural activity. We use the Kalman fixed-interval smoother (KS) to obtain maximum a posteriori (MAP) estimates of the hidden states, the expectation-maximization (EM) algorithm to obtain maximum-likelihood (ML) estimates of the parameters defining the SSM, and standard model-selection criteria to choose among competing SSMs. Because of the high dimensionality of the SSM, the computational requirements of these algorithms are high, and preclude the use of current frameworks for MEG analysis. We address these computational problems by developing an accelerated, distributed-memory version of the KS+EM algorithm appropriate for the analysis of high-dimensional data sets. Using the accelerated KS+EM algorithm, we introduce two SSM-based algorithms for MEG data analysis: KronEM (Kronecker Product modeling using KS+EM) and StimEM (Stimulus effect estimation using KS+EM). KronEM characterizes the spatiotemporal covariance of MEG recordings using an parameterization that efficiently describes the rhythmicity present in resting state neural activity. KronEM describes the data as a sum of components composed of a time-invariant spatial signature and a temporal second-order autorregresive process. In comparison with previous attempts at modeling resting-state activity, the KronEM algorithm estimates the number of such components using the data, and is able to identify an arbitrary number of them. We illustrate these properties on a simulation study, and then analyze MEG recordings collected from a human subject in resting state. The KronEM algorithm recovered components consistent with well-known physiological rhythmic activity. We then compare the resulting topographic maps of frequency with multi-taper based ones, and show that KronEM-based maps better localize naturally occurring rhythms. These results make the KronEM algorithm a useful single-trial frequency analysis technique. StimEM estimates neural activity using MEG recordings made in evoked-potential studies, in which the subject is repeatedly presented with a stimulus and only the stimulus effect is of interest. In contrast with other dynamic source-localization techniques, StimEM accepts arbitrary description of neural dynamics, parameterized as a weighted sum of user-defined candidates, and finds the MAP estimate of the weights. Using the estimated dynamics, StimEM generates a time-resolved ML estimate of the evoked-potential activity in the cortex. We illustrate the ability of StimEM to identify dynamics in a simulated data set of realistic dimensions, and show that the estimates improve substantially when dynamics are taken into account. We next analyze experimental MEG data from an auditory evoked-potential study and show that StimEM identifies dynamics consistent with neurophysiology and neuroanatomy and improves the localization of the evoked cortical response. In summary, we establish the feasibility of non-approximate SSM-based analysis of high-dimensional state-space models using a distributed-memory implementation of an accelerated KS+EM algorithm. We develop two novel algorithms to analyze MEG data in resting-state and evoked potential studies, and show that SSM analysis improves substantially on previous non-SSM based techniques.