Abstract
A crucial aspect in clinical practice is the knowledge of whether Electroencephalographic (EEG) measurements can be assigned to the functioning of the brain or to geometrical deviations of the human cranium. The present work is focused on continuing to advance understanding on how sensitive the solution of the forward EEG problem is in regard to the geometry of the head. This has been achieved by developing a novel analytic algorithm by performing a perturbation analysis in the linear regime using a homogenous spherical model. Notably, the suggested procedure provides a criterion which recognizes whether surface deformations will have an impact on EEG recordings. The presented deformations represent two major cases: (1) acquired alterations of the surface inflicted by external forces and (2) deformations of the upper part of the human head where EEG signals are recorded. Our results illustrate that neglecting geometric variations present on the heads surface leads to errors in the recorded EEG measurements less than 2%. However, for severe instances of deformations combined with cortical brain activity in the vicinity of the distortion site, the errors rise to almost 25%. Therefore, the accurate description of the head shape plays an important role in understanding the forward EEG problem only in these cases.
Highlights
Reconstruction of cerebral activity via Electroencephalographic (EEG) recordings is an established tool and is of great medical significance
The geometry of the brain-head model holds a decisive role allowing the installation of analytic algorithms in a very limited number of cases [1,2,3,4] where else for realistic models computer simulations have to be introduced
An important question arises: how strong does the presence of cranial deformations influence the forward problem and the accurate reconstruction of the source? A precise answer is of significant importance in clinical applications where, as an example, the precise mapping of neuronal activity is a prerequisite for neurosurgical preoperative planning [5, 6]
Summary
Reconstruction of cerebral activity via Electroencephalographic (EEG) recordings is an established tool and is of great medical significance. The aforementioned authors, by realizing a perturbation technique different than the one displayed in the sequel, exploit the fact that if the shape of the head slightly varies from the sphere, one can accurately express the surface potential as a linear combination of spherical harmonics using only a small number of coefficients Their analytical solution, derived utilizing Geselowitz’s integral formula [18], does not involve a perturbation parameter in the usual sense. The general problem can be solved by considering a monopole source while the corresponding solution for a dipole source is evaluated by acting with the directional derivative correlated to the pair {r0, Q}. For this purpose we introduce the potential υ associated with a unit monopole source located at r0 as u (r, r0). The corresponding surface values are evaluated to be u (âr, r0)
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