TY - JOUR
T1 - On a nonlinear partial differential equation arising in magnetic resonance electrical impedance tomography
AU - Kim, Sungwhan
AU - Kwon, Ohin
AU - Seo, Jin Keun
AU - Yoon, Jeong Rock
PY - 2003
Y1 - 2003
N2 - 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 ∇ · (a(x)/|∇u(x)| ∇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.
AB - 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 ∇ · (a(x)/|∇u(x)| ∇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.
KW - Conductivity reconstruction
KW - Current density imaging
KW - Electrical impedance tomography
KW - Interior measurement
KW - Magnetic resonance imaging
KW - Uniqueness
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U2 - 10.1137/S0036141001391354
DO - 10.1137/S0036141001391354
M3 - Article
AN - SCOPUS:0037512368
SN - 0036-1410
VL - 34
SP - 511
EP - 526
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 3
ER -