In this paper, we explore the multiple source localisation problem in the cerebral cortex using magnetoencephalography (MEG) data. We model neural currents as point-wise dipolar sources which dynamically evolve over time, then model dipole dynamics using a probabilistic state space model in which dipole locations are strictly constrained to lie within the cortex. Based on the proposed models, we develop a Bayesian particle filtering algorithm for localisation of both known and unknown numbers of dipoles. The algorithm consists of a region of interest (ROI) estimation step for initial dipole number estimation, a Gibbs multiple particle filter (GMPF) step for individual dipole state estimation, and a selection criterion step for selecting the final estimates. The estimated results from the ROI estimation are used to adaptively adjust particle filter's sample size to reduce the overall computational cost. The proposed models and the algorithm are tested in numerical experiments. Results are compared with existing particle filtering methods. The numerical results show that the proposed methods can achieve improved performance metrics in terms of dipole number estimation and dipole localisation.
There are two main types of methods: distributed source approaches, and point-wise dipole approaches @cite_17 . Distributed source methods identify the potential active brain sources that are distributed on a dense grid of fixed locations throughout the whole cerebral cortex (or the whole brain volume if under a looser constraint). Since the number of unknown sources is larger than the number of the M EEG sensors, mathematical assumptions or constraints are required for an unique solution. Some existing methods include the least squares minimum norm estimation (MNE) @cite_17 , dynamic statistical parametric mapping (dSPM) @cite_29 , standardized low-resolution electromagnetic tomography (sLORETA) @cite_13 , and Kalman filter related approaches @cite_10 @cite_4 .
@cite_13 @cite_4 @cite_29 @cite_10 @cite_17
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Scalp electric potentials (electroencephalograms) and extracranial magnetic fields (magnetoencephalograms, are due to the primary (impressed) current density distribution that arises from neuronal postsynaptic processes. A solution to the inverse problem-the computation of images of electric neuronal activity based on extracranial measurements-would provide important information on the time-course and localization of brain function. In general, there is no unique solution to this problem. In particular, an instantaneous, distributed, discrete, linear solution capable of exact localization of point sources is of great interest, since the principles of linearity and superposition would guarantee its trustworthiness as a functional imaging method, given that brain activity occurs in the form of a finite number of distributed hot spots. Despite all previous efforts, linear solutions, at best, produced images with systematic nonzero localization errors. A solution reported here yields images of standardized current density with zero local-ization error. The purpose of this paper is to present the technical details of the method, allowing researchers to test, check, reproduce and yalidate the new method. Abstract Functional magnetic resonance imaging (fMRI) can provide maps of brain activation with millimeter spatial resolution but is limited in its temporal resolution to the order of seconds. Here, we describe a technique that combines structural and functional MRI with magnetoencephalography (MEG) to obtain spatiotemporal maps of human brain activity with millisecond temporal resolution. This new technique was used to obtain dynamic statistical parametric maps of cortical activity during semantic processing of visually presented words. An initial wave of activity was found to spread rapidly from occipital visual cortex to temporal, pariet al, and frontal areas within 185 ms, with a high degree of temporal overlap between different areas. Repetition effects were observed in many of the same areas following this initial wave of activation, providing evidence for the involvement of feedback mechanisms in repetition priming. We present a new approach for estimating solutions of the dynamical inverse problem of EEG generation. In contrast to previous approaches, we reinterpret this problem as a filtering problem in a state space framework; for the purpose of its solution, we propose a new extension of Kalman filtering to the case of spatiotemporal dynamics. The temporal evolution of the distributed generators of the EEG can be reconstructed at each voxel of a discretisation of the gray matter of brain. By fitting linear autoregressive models with neighbourhood interactions to EEG time series, new classes of inverse solutions with improved resolution and localisation ability can be explored. For the purposes of model comparison and parameter estimation from given data, we employ a likelihood maximisation approach. Both for instantaneous and dynamical inverse solutions, we derive estimators of the time-dependent estimation error at each voxel. The performance of the algorithm is demonstrated by application to simulated and clinical EEG recordings. It is shown that by choosing appropriate dynamical models, it becomes possible to obtain inverse solutions of considerably improved quality, as compared to the usual instantaneous inverse solutions. Magnetoencephalography (MEG) is a noninvasive technique for investigating neuronal activity in the living human brain. The time resolution of the method is better than 1 ms and the spatial discrimination is, under favorable circumstances, 2--3 mm for sources in the cerebral cortex. In MEG studies, the weak 10 fT--1 pT magnetic fields produced by electric currents flowing in neurons are measured with multichannel SQUID (superconducting quantum interference device) gradiometers. The sites in the cerebral cortex that are activated by a stimulus can be found from the detected magnetic-field distribution, provided that appropriate assumptions about the source render the solution of the inverse problem unique. Many interesting properties of the working human brain can be studied, including spontaneous activity and signal processing following external stimuli. For clinical purposes, determination of the locations of epileptic foci is of interest. The authors begin with a general introduction and a short discussion of the neural basis of MEG. The mathematical theory of the method is then explained in detail, followed by a thorough description of MEG instrumentation, data analysis, and practical construction of multi-SQUID devices. Finally, several MEG experiments performed in the authors' laboratory are described, covering studies of evoked responses and of spontaneousmore » activity in both healthy and diseased brains. Many MEG studies by other groups are discussed briefly as well.« less