February  2015, 9(1): 211-229. doi: 10.3934/ipi.2015.9.211

Estimation of conductivity changes in a region of interest with electrical impedance tomography

1. 

Department of Applied Physics, University of Eastern Finland, FIN-70211 Kuopio, Finland

2. 

University of Eastern Finland, Department of Applied Physics, P.O.Box 1627, 70211 Kuopio

3. 

University of Helsinki, Department of Mathematics and Statistics, FI-00014 Helsinki

4. 

School of Education, University of Tampere, FIN-33014 Tampere, Finland

5. 

Department of Applied Physics, University of Eastern Finland, 70211 Kuopio

Received  March 2014 Revised  September 2014 Published  January 2015

This paper proposes a novel approach to reconstruct changes in a target conductivity from electrical impedance tomography measurements. As in the conventional difference imaging, the reconstruction of the conductivity change is based on electrical potential measurements from the exterior boundary of the target before and after the change. In this paper, however, images of the conductivity before and after the change are reconstructed simultaneously based on the two data sets. The key feature of the approach is that the conductivity after the change is parameterized as a linear combination of the initial state and the change. This allows for modeling independently the spatial characteristics of the background conductivity and the change of the conductivity - by separate regularization functionals. The approach also allows in a straightforward way the restriction of the conductivity change to a localized region of interest inside the domain. While conventional difference imaging reconstruction is based on a global linearization of the observation model, the proposed approach amounts to solving a non-linear inverse problem. The feasibility of the proposed reconstruction method is tested experimentally and with a simulation which demonstrates a potential new medical application of electrical impedance tomography: imaging of vocal folds in voice loading studies.
Citation: Dong liu, Ville Kolehmainen, Samuli Siltanen, Anne-maria Laukkanen, Aku Seppänen. Estimation of conductivity changes in a region of interest with electrical impedance tomography. Inverse Problems and Imaging, 2015, 9 (1) : 211-229. doi: 10.3934/ipi.2015.9.211
References:
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show all references

References:
[1]

A. P. Bagshaw, A. D. Liston, R. H. Bayford, A. Tizzard, A. P. Gibson, A. T. Tidswell, M. K. Sparkes, H. Dehghani, C. D. Binnie and D. S. Holder, Electrical impedance tomography of human brain function using reconstruction algorithms based on the finite element method, Neuroimage, 20 (2003), 752-764. doi: 10.1016/S1053-8119(03)00301-X.

[2]

J. Binette, M. Garon, P. Savard, M. McKee and M. Buschmann et al., Tetrapolar measurement of electrical conductivity and thickness of articular cartilage, Journal of biomechanical engineering, 126 (2004), 475-484. doi: 10.1115/1.1785805.

[3]

G. Boverman, T.-J. Kao, R. Kulkarni, B. S. Kim, D. Isaacson, G. J. Saulnier and J. C. Newell, Robust linearized image reconstruction for multifrequency EIT of the breast, Medical Imaging, IEEE Transactions on, 27 (2008), 1439-1448.

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A. Boyle, A. Adler and W. Lionheart, Shape deformation in two-dimensional electrical impedance tomography, Medical Imaging, IEEE Transactions on, 31 (2012), 2185-2193. doi: 10.1109/TMI.2012.2204438.

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B. Brown, Electrical impedance tomography (EIT): A review, Journal of Medical Engineering & Technology, 27 (2003), 97-108. doi: 10.1080/0309190021000059687.

[6]

M. Cheney, D. Isaacson and J. C. Newell, Electrical impedance tomography, SIAM Rev, 41 (1999), 85-101. doi: 10.1137/S0036144598333613.

[7]

K.-S. Cheng, D. Isaacson, J. Newell and D. G. Gisser, Electrode models for electric current computed tomography, Biomedical Engineering, IEEE Transactions on, 36 (1989), 918-924.

[8]

V. Cherepenin, A. Karpov, A. Korjenevsky, V. Kornienko, Y. Kultiasov, M. Ochapkin, O. V. Trochanova and J. D. Meister, Three-dimensional EIT imaging of breast tissues: System design and clinical testing, IEEE Trans. Med. Imag, 21 (2002), 662-667. doi: 10.1109/TMI.2002.800602.

[9]

E. L. Costa, C. N. Chaves, S. Gomes, M. A. Beraldo, M. S. Volpe, M. R. Tucci, I. A. Schettino, S. H. Bohm, C. R. Carvalho and H. Tanaka et al., Real-time detection of pneumothorax using electrical impedance tomography*, Critical care medicine, 36 (2008), 1230-1238. doi: 10.1097/CCM.0b013e31816a0380.

[10]

E. L. Costa, R. G. Lima and M. B. Amato, Electrical impedance tomography, in Intensive Care Medicine, Springer, 15 (2009), 18-24. doi: 10.1097/MCC.0b013e3283220e8c.

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W. Daily, A. Ramirez, D. LaBrecque and J. Nitano, Electrical resistivity tomography of vadose water movement, Water. Resour. Res., 28 (1992), 1429-1442. doi: 10.1029/91WR03087.

[12]

J. Dardé, H. Hakula, N. Hyvönen and S. Staboulis, Fine-tuning electrode information in electrical impedance tomography, Inverse Probl. Imaging, 6 (2012), 399-421. doi: 10.3934/ipi.2012.6.399.

[13]

J. Dardé, N. Hyvönen, A. Seppänen and S. Staboulis, Simultaneous reconstruction of outer boundary shape and admittivity distribution in electrical impedance tomography, SIAM Journal on Imaging Sciences, 6 (2013), 176-198. doi: 10.1137/120877301.

[14]

J. Dardé, N. Hyvönen, A. Seppänen and S. Staboulis, Simultaneous recovery of admittivity and body shape in electrical impedance tomography: An experimental evaluation, Inverse Problems, 29 (2013), 085004, 16pp. doi: 10.1088/0266-5611/29/8/085004.

[15]

D. C. Dobson and F. Santosa, An image-enhancement technique for electrical impedance tomography, Inverse problems, 10 (1994), 317-334. doi: 10.1088/0266-5611/10/2/008.

[16]

A. V. Fiacco and G. P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, Second edition. Classics in Applied Mathematics, 4. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990. doi: 10.1137/1.9781611971316.

[17]

A. Fourcin and E. Abberto, First application of a new laryngograph, Med Biol Illustr, 21 (1971), 172-182.

[18]

I. Frerichs, J. Hinz, P. Herrmann, G. Weisser, G. Hahn, T. Dudykevych, M. Quintel and G. Hellige, Detection of local lung air content by electrical impedance tomography compared with electron beam CT, Journal of applied physiology, 93 (2002), 660-666.

[19]

C. Gabriel, A. Peyman and E. Grant, Electrical conductivity of tissue at frequencies below 1 mhz, Physics in medicine and biology, 54 (2009), p4863. doi: 10.1088/0031-9155/54/16/002.

[20]

L. M. Heikkinen, T. Vilhunen, R. M. West and M. Vauhkonen, Simultaneous reconstruction of electrode contact impedances and internal electrical properties: Ii. laboratory experiments, Measurement Science and Technology, 13 (2002), p1855. doi: 10.1088/0957-0233/13/12/308.

[21]

T. Hézard, T. Hélie, B. Doval, N. Henrich and M. Kob, Non-invasive vocal-folds monitoring using electrical imaging methods, in 100 years of electrical imaging, Paris, 2012.

[22]

D. S. Holder, Electrical Impedance Tomography: Methods, History and Applications, Medical Physics, 2004. doi: 10.1201/9781420034462.

[23]

T. Hou, K. Loh and J. Lynch, Spatial conductivity mapping of carbon nanotube composite thin films by electrical impedance tomography for sensing applications, Nanotechnology, 18 (2007), 315501. doi: 10.1088/0957-4484/18/31/315501.

[24]

T. Hou and J. Lynch, Electrical impedance tomographic methods for sensing strain fields and crack damage in cementitious structures, J. Intel. Mat. Syst. Str., 20 (2009), 1363-1379. doi: 10.1177/1045389X08096052.

[25]

D. Isaacson, J. Mueller, J. Newell and S. Siltanen, Reconstructions of chest phantoms by the d-bar method for electrical impedance tomography, IEEE Trans Med Imaging, 23 (2004), 821-828. doi: 10.1109/TMI.2004.827482.

[26]

D. Isaacson, J. Mueller, J. Newell and S. Siltanen, Imaging cardiac activity by the d-bar method for electrical impedance tomography, Physiological Measurement, 27 (2006), S43-S50. doi: 10.1088/0967-3334/27/5/S04.

[27]

B. Jin and P. Maass, Sparsity regularization for parameter identification problems, Inverse Problems, 28 (2012), 123001, 70pp. doi: 10.1088/0266-5611/28/12/123001.

[28]

J. P. Kaipio, V. Kolehmainen, E. Somersalo and M. Vauhkonen, Statistical inversion and monte carlo sampling methods in electrical impedance tomography, Inverse problems, 16 (2000), 1487-1522. doi: 10.1088/0266-5611/16/5/321.

[29]

J. Kaipio, V. Kolehmainen, M. Vauhkonen and E. Somersalo, Inverse problems with structural prior information, Inverse problems, 15 (1999), 713-729. doi: 10.1088/0266-5611/15/3/306.

[30]

J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Springer New York, 2005.

[31]

K. Karhunen, A. Seppänen, A. Lehikoinen, J. Blunt, J. Kaipio and J. Monteiro, Electrical resistance tomography for assessment of cracks in concrete, ACI mater. J., 107 (2010), 523-531.

[32]

K. Karhunen, A. Seppänen, A. Lehikoinen, P. Monteiro and J. Kaipio, Electrical resistance tomography imaging of concrete, Cement Concrete Res., 40 (2010), 137-145. doi: 10.1016/j.cemconres.2009.08.023.

[33]

K. Knudsen, M. Lassas, J. Mueller and S. Siltanen, Regularized D-bar method for the inverse conductivity problem, Inverse Problems and Imaging, 3 (2009), 599-624. doi: 10.3934/ipi.2009.3.599.

[34]

M. Kob and T. Frauenrath, A system for parallel measurement of glottis opening and larynx position, Biomedical Signal Processing and Control, 4 (2009), 221-228. doi: 10.1016/j.bspc.2009.03.004.

[35]

V. Kolehmainen, M. Lassas and P. Ola, The inverse conductivity problem with an imperfectly known boundary, SIAM Journal on Applied Mathematics, 66 (2005), 365-383. doi: 10.1137/040612737.

[36]

V. Kolehmainen, M. Lassas and P. Ola, The inverse conductivity problem with an imperfectly known boundary in three dimensions, SIAM Journal on Applied Mathematics, 67 (2007), 1440-1452. doi: 10.1137/060666986.

[37]

V. Kolehmainen, M. Lassas and P. Ola, Electrical impedance tomography problem with inaccurately known boundary and contact impedances, Medical Imaging, IEEE Transactions on, (2006), 1124-1127. doi: 10.1109/ISBI.2006.1625120.

[38]

J. Kourunen, T. Savolainen, A. Lehikoinen, M. Vauhkonen and L. Heikkinen, Suitability of a pxi platform for an electrical impedance tomography system, Measurement Science and Technology, 20 (2009), 015503. doi: 10.1088/0957-0233/20/1/015503.

[39]

S. Leonhardt and B. Lachmann, Electrical impedance tomography: The holy grail of ventilation and perfusion monitoring?, Intensive care medicine, 38 (2012), 1917-1929. doi: 10.1007/s00134-012-2684-z.

[40]

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