Finite-element method in electrical impedance tomography

In electrical impedance tomography (EIT), current patterns are injected into a subject and boundary voltages are measured to reconstruct a cross-sectional image of resistivity distribution. Static EIT image reconstruction requires a computer model of a subject, an efficient data-collection method and robust and fast reconstruction algorithms. The finite-element method is used as the computer model. The paper describes the finite-element analysis software package developed, including an interactive graphical mesh generator and fast algorithms for solving linear systems of equations using sparse-matrix and vector techniques. Various models of irregularly shaped subjects are developed using mesh-design tools, including automatic mesh generation and optimisation using the Delaunay algorithm. Even though the software package is customised for use in electrical impedance tomography, it can be used for other biomedical research areas, such as impedance cardiography, cardiac defibrillation and impedance pneumography.

[1]  Pin Tong,et al.  Finite-Element Method: Basic Technique and Implementation , 1977 .

[2]  F. Schoen,et al.  Effects of cardiac configuration, paddle placement and paddle size on defibrillation current distribution: a finite-element model , 1989, Medical and Biological Engineering and Computing.

[3]  David S. Burnett,et al.  Finite Element Analysis: From Concepts to Applications , 1987 .

[4]  William F. Tinney,et al.  Techniques for Exploiting the Sparsity or the Network Admittance Matrix , 1963 .

[5]  J. W. Walker,et al.  Direct solutions of sparse network equations by optimally ordered triangular factorization , 1967 .

[6]  M. Cheney,et al.  Layer-stripping reconstruction algorithm for impedance imaging , 1992, 1992 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[7]  B. Bhattacharya,et al.  Potential distribution in the thorax in relation to electrical field plethysmography , 2006, Medical and Biological Engineering and Computing.

[8]  David Isaacson,et al.  A Layer-stripping Reconstruction Algorithm For Impedance Imaging , 1991, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society Volume 13: 1991.

[9]  B. Carter,et al.  Cross-sectional anatomy: Computed tomography and ultrasound correlation , 1977 .

[10]  W. J. Tompkins,et al.  Iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography. , 1991, IEEE transactions on medical imaging.

[11]  V. Seshadri,et al.  Electric-field distribution in the human body using finite-element method , 2006, Medical and biological engineering.

[12]  P. Hua,et al.  Finite element modeling of electrode-skin contact impedance in electrical impedance tomography , 1993, IEEE Transactions on Biomedical Engineering.

[13]  L. Baker,et al.  Origins of the impedance change in impedance cardiography by a three-dimensional finite element model , 1988, IEEE Transactions on Biomedical Engineering.

[14]  A Wexler.  Electrical impedance imaging in two and three dimensions. , 1988, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[15]  Z. J. Cendes,et al.  Magnetic field computation using Delaunay triangulation and complementary finite element methods , 1983 .

[16]  W. F. Tinney,et al.  Sparse Vector Methods , 1985, IEEE Transactions on Power Apparatus and Systems.

[17]  Jean-Louis Coulomb,et al.  Finite Element Methods in CAD , 1987 .

[18]  Nitish V. Thakor,et al.  Three-dimensional computer model of electric fields in internal defibrillation , 1988, Proc. IEEE.

[19]  J. Pasciak,et al.  Computer solution of large sparse positive definite systems , 1982 .

[20]  I. Duff,et al.  Direct Methods for Sparse Matrices , 1987 .

[21]  Eung Je Woo,et al.  A robust image reconstruction algorithm and its parallel implementation in electrical impedance tomography , 1993, IEEE Trans. Medical Imaging.

[22]  Tadakuni Murai,et al.  Electrical Impedance Computed Tomography Based on a Finite Element Model , 1985, IEEE Transactions on Biomedical Engineering.

[23]  J G Webster,et al.  Three-dimensional reconstruction in electrical impedance tomography. , 1988, Clinical physics and physiological measurement : an official journal of the Hospital Physicists' Association, Deutsche Gesellschaft fur Medizinische Physik and the European Federation of Organisations for Medical Physics.

[24]  Fernando L. Alvarado.  Computational complexity of operations involving perfect elimination sparse matrices , 1977 .

[25]  Willis J. Tompkins,et al.  Comparing Reconstruction Algorithms for Electrical Impedance Tomography , 1987, IEEE Transactions on Biomedical Engineering.

[26]  N. G. Sepulveda,et al.  Finite element analysis of cardiac defibrillation current distributions , 1990, IEEE Transactions on Biomedical Engineering.

[27]  B. Guan,et al.  Generation of an anatomically correct human thorax finite element model , 1992, 1992 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[28]  H. Saunders,et al.  Book Reviews : THE FINITE ELEMENT METHOD FOR ENGINEERS K. E. Huebner John Wiley & Sons - New York (1975) , 1977 .

[29]  D. Lindholm,et al.  Automatic triangular mesh generation on surfaces of polyhedra , 1983 .

[30]  William G. Poole,et al.  An algorithm for reducing the bandwidth and profile of a sparse matrix , 1976 .

[31]  E. Heighway,et al.  Two dimensional automatic triangular mesh generation for the finite element electromagnetics package PE2D , 1982 .

[32]  K. Huebner.  The finite element method for engineers , 1975 .

[33]  Samuel Sideman,et al.  Three-dimensional computer simulation of the cardiac system , 1988, Proc. IEEE.

[34]  Zhanqing Yu,et al.  A semi-analytical approach to the evaluation of threshold voltage in depletion MOS's with nonuniformly doped substrates , 1988 .