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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

A survey on integral equations for bioelectric modeling

Une revue des équations intégrales pour la modélisation bioélectrique

Résumé

Many problems in bioelectric modeling can be approached through the formulation, and numerical resolution, of integral equations of the boundary element method. There has been a resurgence of interest in these surface integral methods due to the introduction of fast algorithms such as fast multipole methods (FMMs) in the context of bioelectricity problems. This survey aims to give a self-contained, detailed and rigorous account of several of the existing equations in the literature. With a particular focus on integral equations given in terms of the surface charge density between interfaces of different conductivity. These integral equations have received less attention in the literature, but recently it was shown that they are more suitable to the application of FMM acceleration. This has led in turn to impressive improvements in the quality of simulations of M/EEG and brain stimulation. We survey the major integral equations currently used, and showcase that the chargebased formulations are dual to the surface potential formulations, which have been so far more common in applications to bioelectricity. Some application examples are discussed, and we provide a summary of available software for electromagnetic modeling of the brain.
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Dates et versions

hal-04343472 , version 1 (13-12-2023)

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  • HAL Id : hal-04343472 , version 1

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Guillermo Nuñez Ponasso. A survey on integral equations for bioelectric modeling. 2023. ⟨hal-04343472⟩

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