On the hp-adaptive solution of complete electrode model forward problems of electrical impedance tomography

Electrical impedance tomography is a noninvasive imaging technique based on measurements of currents and voltages on the boundary of the object of interest. The most accurate forward model for impedance tomography is the complete electrode model that takes into account the electrode shapes and the contact impedances at the corresponding interfaces; many practical reconstruction algorithms of electrical impedance tomography require repetitive computation of accurate forward solutions for the complete model. In this work, we introduce an hp-adaptive finite element method for solving the complete electrode forward problem and demonstrate its functionality via two-dimensional numerical studies.

[1]  Gunther Uhlmann,et al.  Electrical impedance tomography and Calderón's problem , 2009 .

[2]  D. Braess.  Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics , 1995 .

[3]  J C Newell,et al.  Imaging cardiac activity by the D-bar method for electrical impedance tomography , 2006, Physiological measurement.

[4]  J. Kaipio,et al.  Electrical Resistance Tomography Imaging of Concrete , 2010 .

[5]  E. Süli,et al.  A note on the design of hp-adaptive finite element methods for elliptic partial differential equations , 2005 .

[6]  L. Demkowicz.  One and two dimensional elliptic and Maxwell problems , 2006 .

[7]  Harri Hakula,et al.  Fine-tuning electrode information in electrical impedance tomography , 2012 .

[8]  D. Isaacson,et al.  Electrode models for electric current computed tomography , 1989, IEEE Transactions on Biomedical Engineering.

[9]  William F. Mitchell,et al.  A Collection of 2D Elliptic Problems for Testing Adaptive Algorithms , 2010 .

[10]  Martin Hanke,et al.  Recent progress in electrical impedance tomography , 2003 .

[11]  E. Somersalo,et al.  Existence and uniqueness for electrode models for electric current computed tomography , 1992 .

[12]  Harri Hakula,et al.  The Factorization Method Applied to the Complete Electrode Model of Impedance Tomography , 2008, SIAM J. Appl. Math..

[13]  Harri Hakula,et al.  Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography , 2007 .

[14]  Marjorie A. McClain,et al.  A Comparison of hp-Adaptive Strategies for Elliptic Partial Differential Equations , 2014, ACM Trans. Math. Softw..

[15]  I. Babuska,et al.  Rairo Modélisation Mathématique Et Analyse Numérique the H-p Version of the Finite Element Method with Quasiuniform Meshes (*) , 2009 .

[16]  Armin Lechleiter,et al.  Newton regularizations for impedance tomography: a numerical study , 2006 .

[17]  Armin Lechleiter,et al.  Newton regularizations for impedance tomography: convergence by local injectivity , 2008 .

[18]  Jari P. Kaipio,et al.  Simultaneous reconstruction of electrode contact impedances and internal electrical properties: I. Theory , 2002 .

[19]  I. Doležel,et al.  Higher-Order Finite Element Methods , 2003 .

[20]  E. Somersalo,et al.  Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography , 2000 .

[21]  Endre Süli,et al.  Sobolev Regularity Estimation for hp-Adaptive Finite Element Methods , 2003 .

[22]  David Isaacson,et al.  Electrical Impedance Tomography , 2002, IEEE Trans. Medical Imaging.

[23]  B. Guo,et al.  The hp version of the finite element method Part 1 : The basic approximation results , 2022 .

[24]  Nuutti Hyvönen,et al.  Approximating idealized boundary data of electric impedance tomography by electrode measurements , 2009 .

[25]  H. Engl,et al.  Regularization of Inverse Problems , 1996 .

[26]  Liliana Borcea,et al.  Electrical impedance tomography , 2002 .

[27]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[28]  J. Melenk,et al.  An adaptive strategy for hp-FEM based on testing for analyticity , 2007 .

[29]  E. Somersalo,et al.  Statistical and computational inverse problems , 2004 .

[30]  D. Isaacson,et al.  An implementation of the reconstruction algorithm of A Nachman for the 2D inverse conductivity problem , 2000 .

[31]  Maciej Paszyński,et al.  Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications , 2007 .

[32]  M. Hanke,et al.  Numerical implementation of two noniterative methods for locating inclusions by impedance tomography , 2000 .

[33]  Marjorie A. McClain,et al.  A Comparison of hp-adaptive Strategies for Elliptic Partial Differential Equations (long version) , 2011 .

[34]  Marko Vauhkonen,et al.  Simultaneous reconstruction of electrode contact impedances and internal electrical properties: II. Laboratory experiments , 2002 .