Abstract
BackgroundThe aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest. It consists of solving forward and inverse problems. The forward problem is solved by starting from a given electrical source and calculating the potentials at the electrodes. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes.MethodsWhile other reviews give an extensive summary of the both forward and inverse problem, this review article focuses on different aspects of solving the forward problem and it is intended for newcomers in this research field.ResultsIt starts with focusing on the generators of the EEG: the post-synaptic potentials in the apical dendrites of pyramidal neurons. These cells generate an extracellular current which can be modeled by Poisson's differential equation, and Neumann and Dirichlet boundary conditions. The compartments in which these currents flow can be anisotropic (e.g. skull and white matter). In a three-shell spherical head model an analytical expression exists to solve the forward problem. During the last two decades researchers have tried to solve Poisson's equation in a realistically shaped head model obtained from 3D medical images, which requires numerical methods. The following methods are compared with each other: the boundary element method (BEM), the finite element method (FEM) and the finite difference method (FDM). In the last two methods anisotropic conducting compartments can conveniently be introduced. Then the focus will be set on the use of reciprocity in EEG source localization. It is introduced to speed up the forward calculations which are here performed for each electrode position rather than for each dipole position. Solving Poisson's equation utilizing FEM and FDM corresponds to solving a large sparse linear system. Iterative methods are required to solve these sparse linear systems. The following iterative methods are discussed: successive over-relaxation, conjugate gradients method and algebraic multigrid method.ConclusionSolving the forward problem has been well documented in the past decades. In the past simplified spherical head models are used, whereas nowadays a combination of imaging modalities are used to accurately describe the geometry of the head model. Efforts have been done on realistically describing the shape of the head model, as well as the heterogenity of the tissue types and realistically determining the conductivity. However, the determination and validation of the in vivo conductivity values is still an important topic in this field. In addition, more studies have to be done on the influence of all the parameters of the head model and of the numerical techniques on the solution of the forward problem.
Highlights
Since the 1930s electrical activity of the brain has been measured by surface electrodes connected to the scalp [1]
The information extracted from these brain waves was, and still is instrumental in the diagnoses of neurological diseases [2], mainly epilepsy
Researchers nowadays are still searching for new event-related potentials (ERPs) protocols which may be able to distinguish between ERPs of patients with a certain condition and ERPs of normal subjects
Summary
Since the 1930s electrical activity of the brain has been measured by surface electrodes connected to the scalp [1] Potential differences between these electrodes were plotted as a function of time in a so-called electroencephalogram (EEG). Researchers nowadays are still searching for new ERP protocols which may be able to distinguish between ERPs of patients with a certain condition and ERPs of normal subjects This could be instrumental in disorders, such as psychiatric and developmental disorders, where there is often a lack of biological objective measures. The aim of electroencephalogram (EEG) source localization is to find the brain areas responsible for EEG waves of interest It consists of solving forward and inverse problems. These evaluations are necessary to solve the inverse problem which is defined as finding brain sources which are responsible for the measured potentials at the EEG electrodes
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