A Semi-Analytical Study of Neuronal Signal Transmission Across Multi-Layered Head Models: Analysis and Computational Experiments

Electroencephalography from scalp potentials (EEG) is the recording of the electrical activity of the cerebral cortex detected by scalp electrodes as a function of time. While spontaneous fluctuations and event-related potentials of the EEG provide fundamental information for diagnosis of neurological diseases, this technique often fails to precisely localize the active areas of the brain due its low spatial resolution. Researchers has been attempting to localize EEG sources by combining knowledge from biology and physics in order to define mathematical models of the head tissues and the pyramidal neuron cells of the cerebral cortex, which are the generators of the extracellular potential responsible for the EEG. The computation of the parameters that produce the best fit between these mathematical models and detected scalp EEG should provide information about the position of the active brain areas. Multi-layer spherical models describe the main compartments of human head (brain, skull, scalp) as concentric spheres and the active pyramidal cells as current dipoles, thus resulting in semi-analytical solutions of the Poisson’s equation through a multipole expansion. Starting with the description of the underlying physiology and physics, this thesis first provides an overview of the available semi-analytical models of the human head and investigates the effects of modifications which allow to incorporate multiple source dipoles with arbitrary locations and evaluate the electric potential even inside the head compartments. Then, the semi-analytical solution for the full head volume is modified so that the equation can be easily adapted for an arbitrary number of tissue layers. Finally, the solutions of surface potential from the two methods are compared in order to evaluate the effect of the source dipole positioning and orientation and the effect of the thickness of the skull layer. The semi-analytical solutions of Poisson’s equation for the spherical models are implemented in MATLAB and the same models are numerically simulated using a finite element method (FEM) solver (COMSOL Multiphysics). The methods and the results in this thesis will be useful for the development of more complex semi-analytic solutions of the Poisson’s equation for the EEG source localization problem and the assessment of anatomically more realistic models of the human head through FEM technique.