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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The brain network is usually constructed by estimating the connectivity matrix and thresholding it at an arbitrary level. The problem with this standard method is that we do not have any generally accepted criteria for determining a proper threshold. Thus, we propose a novel multiscale framework that models all brain networks generated over every possible threshold. Our approach is based on persistent homology and its various representations such as the Rips filtration, barcodes, and dendrograms. This new persistent homological framework enables us to quantify various persistent topological features at different scales in a coherent manner. The barcode is used to quantify and visualize the evolutionary changes of topological features such as the Betti numbers over different scales. By incorporating additional geometric information to the barcode, we obtain a single linkage dendrogram that shows the overall evolution of the network. The difference between the two networks is then measured by the Gromov-Hausdorff distance over the dendrograms. As an illustration, we modeled and differentiated the FDG-PET based functional brain networks of 24 attention-deficit hyperactivity disorder children, 26 autism spectrum disorder children, and 11 pediatric control subjects. Electroencephalography (EEG) and magnetoencephalography (MEG) provide insight into neuronal processes in the brain in a real-time scale. Brain activity can be modeled in terms of a source distribution found by solving the bioelectromagnetic inverse problem, e.g. using linear source reconstruction methods. Such methods are particularly suitable to be used on modern highly parallel processing systems, such as widely available graphic processing units (GPUs). The utilization of these capabilities paves the way for online neuroelectromagnetic source imaging. We present a system that, according to its modular scheme, can be configured in a very flexible way using graphical building blocks. It allows to use different preprocessing algorithms together with a linear source reconstruction method. The algorithms use both CPU and GPU resources. 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. This chapter discusses the principles of classical architectonic mapping in the context of recent imaging techniques. It presents an observer-independent approach for a quantitative analysis of cortical areas and their borders, which is based on a multivariate statistical analysis of the cytoarchitecture and illustrates the application of this approach for the cytoarchitectonic mapping of the human visual cortex. Important criteria for cytoarchitectonic mapping are the absolute thickness of cortical layers, the proportionate thickness of a layer relative to the other cortical layers and to the total cortical depth, the presence of clearly recognizable laminar borders and vertical columns, the packing density and size of neuronal cell bodies, the homogeneous or clustered distribution of cell bodies throughout the layers, and the presence of special cell types such as Betz cells. Understanding the regional distributions of neurotransmitter receptors is likely to provide a crucial intermediary level of description between function and structure, since different cytoarchitectonic and functional areas have different mean receptor densities as well as distinct laminar distribution patterns. Another way for a better understanding of brain function and the underlying anatomy is to compare architectonic maps obtained in postmortem brains with activation maps obtained in functional imaging studies in a common spatial reference system. Since these two kinds of maps stem from different subsets of brains, such a comparison must be performed on a probabilistic basis.