Abstract
In this paper we consider the monodomain model of cardiac electrophysiology. After an analysis of the well-posedness of the model we determine an asymptotic expansion of the perturbed potential due to the presence of small conductivity inhomogeneities (modelling small ischemic regions in the cardiac tissue) and use it to detect the anomalies from partial boundary measurements. This is done by determining the topological gradient of a suitable boundary misfit functional. The robustness of the algorithm is confirmed by several numerical experiments.
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Recommended by Dr A L Mazzucato
Footnotes
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In loving memory of Maria Assunta Pozio.
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It follows by an application of the Lagrange's mean value theorem on the real-valued function h(τ) = ∫Ω(1 − χɛ)(f(u + τ(uɛ − u), w + τ(wɛ − w)) − f(u, w))Uɛ on the interval [0, 1]; the same holds for g.