ON A NONLINEAR PARTIAL DIFFERENTIAL EQUATION ARISING IN MAGNETIC RESONANCE ELECTRICAL IMPEDANCE TOMOGRAPHY

This paper considers the fundamental questions, such as existence and uniqueness, of a mathematical model arising in the MREIT system, which is an electrical impedance tomography technique integrated with magnetic resonance imaging. The mathematical model for MREIT is the Neumann problem of a nonlinear elliptic partial differential equation del . (a(x)/vertical bar del u(x)vertical bar del u(x)) = 0. We show that this Neumann problem belongs to one of two cases: either infinitely many solutions exist or no solution exists. This explains rigorously the reason why we have used the modified model in [O. Kwon, E. J. Woo, J. R. Yoon, and J. K. Seo, IEEE Trans. Biomed. Engrg., 49 ( 2002), pp. 160-167], which is a system of the Neumann problem associated with two different Neumann data. For this modified system, we prove a uniqueness result on the edge detection of a piecewise continuous conductivity distribution.