Multipole approach to the inverse problem in electrocardiology: Convergence of the multipole equivalent generator on the inhomogeneous body conductor

The multipole approach to the inverse electrocardiological problem consists of estimating the multipole components of the cardiac electric generator, starting from the measured body surface potential. This paper presents a cr itical investigation of the basic premise for the applicability of the mult ipole approach, namely the convergence of the multipole equivalent generato r for the heart on the surface of an inhomogeneous body conductor. As an ex tension to multipole theory, a criterion for the convergence is derived. Ba sed on realistic models for the body conductor and the cardiac electric gen erator, we observe that the criterion is not strictly satisfied in realisti c conditions. Numerical simulations with the same models point out that the multipole equivalent generator is indeed not convergent in the strict math ematical sense. On the other hand, we show that the multipole equivalent ge nerator yields a rather close approximation of the electrocardiological pot ential for intermediate values of the order of the multipole generator. A d iscussion is given on how to explain the apparently ambiguous results for t he estimation of cardiac multipole components. (C) 2000 Society for Mathema tical Biology.