Conforming discretizations of boundary element solutions to the electroencephalography forward problem

We report on the fact that several standardly used discretizations of these formulations are consistent only with an L 2 -framework, requiring the expansion term to be a square integrable function (i.e., in a Petrov–Galerkin scheme with expansion and testing functions). Instead, those techniques are not consistent when a more appropriate mapping in terms of fractional-order Sobolev spaces is considered. Such a mapping allows the expansion function term to be a less regular function, thus sensibly reducing the need for mesh refinements and low-precisions handling strategies that are currently required. These more favorable mappings, however, require a different and conforming discretization, which must be suitably adapted to them. In order to appropriately fulfill this requirement, we adopt a mixed discretization based on dual boundary elements residing on a suitably defined dual mesh. We devote also a particular attention to implementation-oriented details of our new technique that will allow the rapid incorporation of our finding in one's own EEG forward solution technology. We conclude by showing how the resulting forward EEG problems show favorable properties with respect to previously proposed schemes, and we show their applicability to real-case modeling scenarios obtained from Magnetic Resonance Imaging (MRI) data.

Source: Comptes Rendus Physique - April 14, 2018 Category: Physics Source Type: research