3-D electrical impedance tomography for piecewise constant domains with known internal boundaries

IEEE Transactions on Biomedical Engineering

Volumn 54, Issue 1, 2007, Pages 2-10

  Babaeizadeh, Saeed ^a   Brooks, Dana H ^b   Isaacson, David ^c  

^a Advanced Algorithm Research Center (AARC)   (United States)

^b Northeastern University   (United States)

^c Research Rensselaer Polytechnic Institute   (United States)

Author keywords

Boundary element methods; Electrical impedance tomography; Finite element methods; Forward model; Inverse problem

Indexed keywords

BOUNDARY ELEMENT METHOD; ELECTRIC IMPEDANCE; FINITE ELEMENT METHOD; INVERSE PROBLEMS; MATHEMATICAL MODELS; THREE DIMENSIONAL;

COMPUTATIONAL EFFICIENCY; ELECTRICAL IMPEDANCE TOMOGRAPHY (EIT); MODEL CONDUCTIVITY ANISOTROPIES;

TOMOGRAPHY;

ARTICLE; COMPUTER ASSISTED IMPEDANCE TOMOGRAPHY; ELECTRIC CONDUCTIVITY; ELECTRIC POTENTIAL; FINITE ELEMENT ANALYSIS; GEOMETRY;

ALGORITHMS; COMPUTER SIMULATION; DIAGNOSIS, COMPUTER-ASSISTED; ELECTRIC IMPEDANCE; HEART; HUMANS; IMAGING, THREE-DIMENSIONAL; LUNG; MODELS, BIOLOGICAL; PLETHYSMOGRAPHY, IMPEDANCE; TOMOGRAPHY;

EID: 33846352801     PISSN: 00189294     EISSN: None     Source Type: Journal    
DOI: 10.1109/TBME.2006.886839     Document Type: Article

References (40)

1. G. J. Saulnier, R. S. Blue, J. C. Newell, D. Isaacson, and P. M. Edic, "Electrical impedance tomography," IEEE Signal Process. Magazine, vol. 18, no. 6, pp. 31-43, Nov. 2001.
2. B. H. Brown, "Electrical impedance tomography (EIT): A review," J. Med. Eng. Technol., vol. 3, no. 27, pp. 97-108, 2003.
3. W. R. Lionheart, "EIT reconstruction algorithms: Pitfalls, challenges and recent developments," Physiological Meas., vol. 1, no. 25, pp. 125-142, Feb. 2004.
4. D. S. Holder, Ed., Electrical Impedance Tomography: Methods, History and Applications, ser. Medical Physics and Biomedical Engineering. New York: Taylor & Francis, 2004.
5. R. Kohn and M. Vogelius, "Determining conductivity by boundary measurements II," Pure Appl. Math., vol. 38, pp. 643-667, 1985.
6. T. J. C. Faes, H. A. van der Meij, J. C. de Munck, and R. M. Heethaar, "The electric resistivity of human tissues (100 Hz-10 MHz): A meta-analysis of review studies," Physiological Meas., vol. 20, no. 4, pp. R1-R10, 1999.
7. S. Gonçalves, J. C. de Munck, J. P. A. Verbunt, F. Bijma, R. M. Heethaar, and F. L. Da Silva, "In vivo measurement of the brain and skull resistivities using an EIT-based method and realistic models for the head," IEEE Trans. Biomed. Eng., vol. 50, no. 6, pp. 754-767, Jun. 2003.
8. D. G. Gisser, D. Isaacson, and J. C. Newell, "Theory and performance of an adaptive current tomography system," Clin. Phys. Physiological Meas., vol. 9, pp. 35-41, 1988.
9. R. Duraiswami, G. L. Chahine, and K. Sarkar, "Boundary element techniques for efficient 2-D and 3-D electrical impedance tomography," Chem. Eng. Sci., vol. 52, no. 13, Jul. 1997.
10. J. C. De Munck, T. J. C. Faes, and R. M. Heethaar, "The boundary element method in the forward and inverse problem of electrical impedance tomography," IEEE Trans. Biomed. Eng., vol. 47, no. 6, pp. 792-800, Jun. 2000.
11. M. Hanke and M. Bruhl, "Recent progress in electrical impedance tomography," Inverse Prolems, vol. 19, pp. S65-S90, 2003.
12. J. J. M. Cuppen and A. van Oosterom, "Model studies with the inversely calculated isochrones of ventricular depolarization," IEEE Trans. Biomed. Eng., vol. BME-31, pp. 652-659, 1984.
13. A. J. Pullan, L. K. Cheng, M. P. Nash, C. P. Bradley, and D. J. Paterson, "Noninvasive electrical imaging of the heart: Theory and model development," Ann. Biomed. Eng., vol. 29, pp. 817-836, 2001.
14. R. C. Barr, M. Ramsey, and M. S. Spach, "Relating epicardial to body surface potential distribution by means of transfer coefficients based on geometry measurement," IEEE Trans. Biomed. Eng., vol. 24, no. 1, pp. 1-11, Jan. 1977.
15. P. C. Stanley, T. C. Pilkington, and M. N. Morrow, "The effects of thoracic inhomogeneities on the relationship between epicardial and torso potentials," IEEE Trans. Biomed. Eng., vol. BME-33, pp. 273-284, 1986.
16. J. C. De Munck, "Linear discretization of the volume conductor boundary integral equation using analytically integrated elements," IEEE Trans. Biomed. Eng., vol. 39, no. 9, pp. 986-990, Sep. 1992.
17. B. M. Eyuboglu, T. C. Pilkington, and P. D. Wolf, "Estimation of tissue resistivities from multiple electrode impedance measurements," Phys. Med. Biol., vol. 39, pp. 1-7, 1994.
18. R. Duraiswami, K. Sarkar, and G. L. Chahine, "Efficient 2D and 3D electrical impedance tomography using dual reciprocity boundary element techniques," Eng. Anal. with Boundary Elements, vol. 22, no. 1, pp. 13-31, 1998.
19. H. Jain, D. Isaacson, P. M. Edic, and J. C. Newell, "Electrical impedance tomography of complex conductivity distributions with noncircular boundary," IEEE Trans. Biomed. Eng., vol. 44, no. 11, pp. 1051-1060, Nov. 1997.
20. M. Vauhkonen, W. R. B. Lionheart, L. M. Heikkinen, P. J. Vauhkonen, and J. P. Kaipio, "A MATLAB package for the EIDORS project to reconstruct two-dimensional EIT images," Physiological Meas., vol. 22, no. 1, pp. 107-112, 2001.
21. N. Polydorides and W. R. B. Lionheart, "A MATLAB toolkit for three-dimensional electrical impedance tomography: A contribution to the electrical impedance and diffuse optical reconstruction software project," Meas. Sci. Technol., vol. 13, no. 1, pp. 1871-1883, 2002.
22. M. Glidwell and T. Ng, "Anatomically constrained electrical impedance tomography for anisotropic bodies via a two-step approach," IEEE Trans. Med. Imag., vol. 14, no. 3, pp. 498-503, Sep. 1995.
23. V. Kolehmainen, A. Voutilainen, and J. P. Kaipio, "Estimation of nonstationary region boundaries in EIT-state estimation approach," Inverse Problems, vol. 17, pp. 1937-1956, 2001.
24. K.-S. Cheng, D. Isaacson, J. C. Newell, and D. G. Gisser, "Electrode models for electric current computed tomography," IEEE Trans. Biomed. Eng., vol. 36, no. 9, pp. 918-924, Sep. 1989.
25. T. F. Coleman and Y. Li, "An interior, trust region approach for nonlinear minimization subject to bounds," SIAM J. Optimization, vol. 6, pp. 418-445, 1996.
26. A. L. Piccolomini and F. Zama, "The conjugate gradient regularization method in computed tomography problems," Appl. Math. Comp., vol. 102, pp. 87-99, 1999.
27. J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J., vol. 7, pp. 308-313, 1965.
28. S. Boyd, C. Crusius, and A. Hansson, "Control applications of nonlinear convex programming," J. Process Control, vol. 8, pp. 313-324, 1998.
29. M. Vauhkonen, Electrical impedance tomography and prior information Kuopio Univ., Dept. Appl. Phys., 1997, Ph.D..
30. S. Vavasis, "Stable finite elements for problems with wild coefficients," SIAM J. Numer. Anal., vol. 33, 1996.
31. M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, "Efficient nonlinear 3D electrical impedance tomography reconstruction," presented at the 2nd World Congr. Industrial Process Tomography, Hannover, Germany, Aug. 2001.
32. R. S. MacLeod, D. M. Weinstein, J. D. de St. Germain, D. H. Brooks, C. R. Johnson, and S. G. Parker, "SCIRun/BioPSE: Integrated problem solving environment," presented at the IEEE Int. Symp. Biomedical Imaging, Arlington, VA, 2004.
33. Scientific Computing and Imaging Institute (SCI), "BioPSE Datasets," Problem Solving Environment for modeling, simulation, image processing, and visualization for biomedical computing applications, 2002. [Online]. Available: http://software.sci.utah.edu/biopse.html
34. R. N. Klepfer, C. R. Johnson, and R. S. Macleod, "The effects of inhomogeneities and anisotropies on electrocardiographic fields: A three-dimensional finite element study," IEEE Trans. Biomed. Eng., vol. 44, no. 8, pp. 706-719, Aug. 1997.
35. D. G. Gisser, D. Isaacson, and J. C. Newell, "Electric current computed tomography and eigenvalues," SIAM J. Appl. Math., vol. 50, no. 6, pp. 1623-1634, Dec. 1990.
36. A. Wirgin, "The inverse crime," ArXiv Mathematical Physics e-prints, Jan. 2004.
37. J. P. Kaipio and E. Somersalo, "Statistical inverse problems: Discretization, model reduction and inverse crimes," J. Comput. Appl. Math., 2006, to be published.
38. E. Somersalo, M. Cheney, and D. Isaacson, "Existence and uniqueness for electrode models for electric current computed tomography," Inverse Problems, vol. 52, no. 4, 1992.
39. S. Babaeizadeh, D. H. Brooks, and D. Isaacson, "A deformable-radius B-spline method for shape-based inverse problems, as applied to electrical impedance tomography," in Proc. IEEE ICASSP, Philadelphia, PA, Mar. 2005, pp. 485-488.
40. S. Babaeizadeh and D. H. Brooks, "Spherical harmonics for shape-based inverse problems, as applied to electrical impedance tomography," in Electronic Imaging. San Jose, CA: IS&T and SPIE, 2006.