State space methods for MEG source reconstruction

Abstract

Introduction and problem formulation Elucidating how the human brain is structured and how it functions is a fundamental aim of human neuroscience. To achieve such an aim, the activity of the human brain has been measured using noninvasive neuroimaging techniques, the most popular of which is functional magnetic resonance imaging (fMRI) (Ogawa et al . 1990). The fMRI signals are obtained at a spatial resolution of typically 3mm and measure changes of blood flow and blood oxygen consumption whose temporal dynamics are slower than that of neuronal electrical activities, resulting in a poor temporal resolution of the order of seconds. In contrast, magnetoencephalography (MEG) and electroencephalography (EEG) can detect changes of neuronal activities by the millisecond measurement of magnetic and electric fields, respectively, outside the skull (Hamalainen et al . 1993; Nunez & Srinivasan 2006). The high temporal resolution of MEG (and EEG) is useful, especially for studying the dynamic integration of functionally specialized brain regions, which is a subject of growing interest in human neuroscience (de Pasquale et al . 2012). The major problem of MEG is that spatial brain activity patterns are not easily understandable from sensor measurements. This is because the magnetic fields produced by neuronal current sources are superimposed to form rather uninterpretable spatial patterns of signals on sensors. Estimating the position and intensity of these current sources from the sensor measurements is called source reconstruction, or source localization. Solving the source reconstruction problem allows the mapping of temporally dynamic electrical activities in the human brain (Baillet et al . 2001). Since how brain regions are dynamically integrated to produce a variety of functions is of great interest in human neuroscience research, the mission of MEG source reconstruction is not only to localize position of the current sources, but also to identify directed interactions between these sources. A possible approach to this involves constructing a dynamic model of brain electrical activities, as well as developing an estimation algorithm for the source positions and interactions that are parametrized in this model.