Abstract
The paper presents heuristics to reduce several difficulties related to the determination of the transmembrane voltage potential (TMP) on cells with arbitrary smooth shape. We show how the thin weakly conducting membrane can be replaced by asymptotically equivalent transmission conditions at the interface between the cell interior (the cytoplasm) and the extracellular medium. We describe our formal asymptotic method for constructing precise models of cells. This method is based on an appropriate change of variables in the thin membrane. Our frequency dependent models is helpfull to determine the TMP on cells on which experiment measurements are prohibited. We end the paper by presenting briefly the sketch of the proofs of the asymptotics and the a priori error estimates.
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