Analytical solution to the three-dimensional electrical forward problem for a circular cylinder

This paper shows that the full analytical solution for the forward problem derived by the mode matching technique for a finite right circular cylinder using Laplace's equation with inhomogeneous boundary conditions reduces to the full analytical solution derived by the Green function technique for Poisson's equation using homogeneous boundary conditions when two identical rectangular electrodes are arbitrarily placed on the curved surface of the cylinder. Numerical comparisons between the full solution to Laplace's equation and a reduced form in terms of computed potentials on some points and reconstruction of equipotentials for an asymmetric configuration are also presented in this paper.

[1]  R J Lytle,et al.  Alternative methods for determining the electrical conductivity of core samples. , 1979, The Review of scientific instruments.

[2]  D. Isaacson.  Distinguishability of Conductivities by Electric Current Computed Tomography , 1986, IEEE Transactions on Medical Imaging.

[3]  David Isaacson,et al.  NOSER: An algorithm for solving the inverse conductivity problem , 1990, Int. J. Imaging Syst. Technol..

[4]  E Atalar,et al.  Electrical impedance tomography of translationally uniform cylindrical objects with general cross-sectional boundaries. , 1990, IEEE transactions on medical imaging.

[5]  William Robert Breckon.  Image reconstruction in electrical impedance tomography , 1990 .

[6]  S. R. Judah,et al.  Reduced form of the Green's functions for disks and annular rings , 1991 .

[7]  David Barber,et al.  Image reconstruction in electrical impedance tomography , 1992, Optics & Photonics.

[8]  F. J. Dickin,et al.  Determination of composition and motion of multicomponent mixtures in process vessels using electrical impedance tomography-I. Principles and process engineering applications , 1993 .

[9]  Maurice Beck,et al.  Experimental evaluation of capacitance tomographic flow imaging systems using physical models , 1994 .

[10]  Wuqiang Yang,et al.  High frequency and high resolution capacitance measuring circuit for process tomography , 1994 .

[11]  J P Morucci,et al.  3D reconstruction in electrical impedance imaging using a direct sensitivity matrix approach. , 1995, Physiological measurement.

[12]  B H Brown,et al.  Measured and expected Cole parameters from electrical impedance tomographic spectroscopy images of the human thorax. , 1995, Physiological measurement.

[13]  D. C. Barber,et al.  Three-dimensional electrical impedance tomography , 1996, Nature.

[14]  N. J. Avis,et al.  A comparison of voltage and sensitivity profiles from two forward problem solvers for three dimensional electrical impedance tomography , 1996, Proceedings of 18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[15]  D C Barber,et al.  Three-dimensional image reconstruction for electrical impedance tomography. , 1996, Physiological measurement.

[16]  William R B Lionheart,et al.  Conformal uniqueness results in anisotropic electrical impedance imaging , 1997 .

[17]  K. Boone,et al.  Imaging with electricity: report of the European Concerted Action on Impedance Tomography. , 1997, Journal of medical engineering & technology.

[18]  William R B Lionheart.  Boundary shape and electrical impedance tomography , 1998 .