Codice  QDD 191 
Titolo  On a semilinear elliptic boundary value problem arising in cardiac electrophysiology 
Data  20150113 
Autore/i  Beretta, E.; Cerutti, M.C.; Manzoni, A.; Pierotti, D. 
Link  Download full text 
Abstract  In this paper we provide a representation formula for boundary voltage perturbations caused
by internal conductivity inhomogeneities of low volume fraction in a simplied monodomain model
describing the electric activity of the heart. We derive such a result in the case of a nonlinear
problem. Our longterm goal is the solution of the inverse problem related to the detection of regions
aected by heart ischemic disease, whose position and size are unknown. We model the presence
of ischemic regions in the form of small inhomogeneities. This leads to the study of a boundary
value problem for a semilinear elliptic equation. We rst analyze the wellposedness of the problem
establishing some key energy estimates. These allow us to derive rigorously an asymptotic formula
of the boundary potential perturbation due to the presence of the inhomogeneities, following an
approach similar to the one introduced by Capdeboscq and Vogelius in [7] in the case of the linear
conductivity equation. Finally, we propose some ideas of the reconstruction procedure that might
be used to detect the inhomogeneities. 
