On a Fast Solution Strategy for a Surface-Wire Integral Formulation of the Anisotropic Forward Problem in Electroencephalography

TL;DR

This paper introduces a fast, nearly linear algorithm for solving the anisotropic EEG forward problem using a hybrid surface-wire integral approach, leveraging block diagonal dominance and adaptive methods.

Contribution

It presents a novel quasi-linear complexity solver for the anisotropic EEG forward problem based on a hybrid surface-wire integral formulation exploiting block diagonal structures.

Findings

Algorithm achieves near-linear complexity with logarithmic factors.

Numerical results demonstrate high performance in realistic biomedical scenarios.

Method effectively handles neuronal fiber interactions and interface potentials.

Abstract

This work focuses on a quasi-linear-in-complexity strategy for a hybrid surface-wire integral equation solver for the electroencephalography forward problem. The scheme exploits a block diagonally dominant structure of the wire self block -- that models the neuronal fibers self interactions -- and of the surface self block -- modeling interface potentials. This structure leads to two Neumann iteration schemes further accelerated with adaptive integral methods. The resulting algorithm is linear up to logarithmic factors. Numerical results confirm the performance of the method in biomedically relevant scenarios.