Advanced Search
Article Contents
Article Contents

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

Abstract Related Papers Cited by
  • 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.
    Mathematics Subject Classification: Primary: 65M32, 65N21, 92C55; Secondary: 65Z05, 65M60.


    \begin{equation} \\ \end{equation}
  • [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.


    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.


    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.


    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.


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


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


    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.


    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.


    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.


    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.


    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.


    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.


    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.


    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.


    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.


    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.


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


    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.


    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.


    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.


    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.


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


    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.


    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.


    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.


    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.


    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.


    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.


    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.


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


    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.


    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.


    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.


    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.


    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.


    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.


    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.


    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.


    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.


    C. Lieberman, K. Willcox and O. Ghattas, Parameter and state model reduction for large-scale statistical inverse problems, SIAM Journal on Scientific Computing, 32 (2010), 2523-2542.doi: 10.1137/090775622.


    S. Lindgren, H. Odenstedt, C. Olegård, S. Söndergaard, S. Lundin and O. Stenqvist, Regional lung derecruitment after endotracheal suction during volume-or pressure-controlled ventilation: A study using electric impedance tomography, Intensive care medicine, 33 (2007), 172-180.doi: 10.1007/s00134-006-0425-x.


    D. Liu, A. Seppänen, A. Nissinen, V. Kolehmainen, S. Siltanen and A. M. Laukkanen, Preliminary results on 3D electrical impedance tomography imaging of vocal folds, in 8th International Conference on Voice Physiology and Biomechanics, Erlangen, Germany, 2012.


    J. Mueller and S. Siltanen, Linear and Nonlinear Inverse Problems with Practical Applications, SIAM, Philadelphia, PA, 2012.doi: 10.1137/1.9781611972344.


    A. Nissinen, L. Heikkinen, V. Kolehmainen and J. Kaipio, Compensation of errors due to discretization, domain truncation and unknown contact impedances in electrical impedance tomography, Meas. Sci. Technol., 20 (2009), 105504 (13pp).doi: 10.1088/0957-0233/20/10/105504.


    A. Nissinen, V. Kolehmainen and J. P. Kaipio, Reconstruction of domain boundary and conductivity in electrical impedance tomography using the approximation error approach, International Journal for Uncertainty Quantification, 1 (2011), 203-222.doi: 10.1615/Int.J.UncertaintyQuantification.v1.i3.20.


    A. Nissinen, V. P. Kolehmainen and J. P. Kaipio, Compensation of modelling errors due to unknown domain boundary in electrical impedance tomography, Medical Imaging, IEEE Transactions on, 30 (2011), 231-242.doi: 10.1109/TMI.2010.2073716.


    J. Nocedal and S. J. Wright, Numerical Optimization, vol. 2, Springer New York, 1999.doi: 10.1007/b98874.


    D. L. Phillips, A technique for the numerical solution of certain integral equations of the first kind, J Assoc Comput Mach, 9 (1962), 84-97.doi: 10.1145/321105.321114.


    S. Pulletz, A. Adler, M. Kott, G. Elke, B. Gawelczyk, D. Schädler, G. Zick, N. Weiler and I. Frerichs, Regional lung opening and closing pressures in patients with acute lung injury, Journal of Critical Care, 27 (2012), p323e11-P323e18.doi: 10.1016/j.jcrc.2011.09.002.


    M. Rothenberg, A multichannel electroglottograph, Journal of Voice, 6 (1992), 36-43.doi: 10.1016/S0892-1997(05)80007-4.


    L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, 60 (1992), 259-268.doi: 10.1016/0167-2789(92)90242-F.


    D. Scott and H. McCann (eds.), Handbook of Process Imaging for Automatic Control, CRC Press, 2005.


    A. Seppänen, A. Nissinen, V. Kolehmainen, S. Siltanen and A. M. Laukkanen, Electrical impedance tomography imaging of larynx, in Models and analysis of vocal emissions for biomedical applications, 7th International Workshop, Firenze, Italy, (2011), 27-29.


    A. Seppänen, M. Vauhkonen, P. Vauhkonen, E. Somersalo and J. Kaipio, State estimation with fluid dynamical evolution models in process tomography - an application to impedance tomography, Inverse Problems, 17 (2001), 467-483.doi: 10.1088/0266-5611/17/3/307.


    S. Siltanen, J. Mueller and D. Isaacson, An implementation of the reconstruction algorithm of A. Nachman for the 2-D inverse conductivity problem, Inverse Problems, 16 (2000), 681-699.doi: 10.1088/0266-5611/16/3/310.


    E. Somersalo, M. Cheney and D. Isaacson, Existence and uniqueness for electrode models for electric current computed tomography, SIAM Journal on Applied Mathematics, 52 (1992), 1023-1040.doi: 10.1137/0152060.


    T. Tidswell, A. Gibson, R. H. Bayford and D. S. Holder, Three-dimensional electrical impedance tomography of human brain activity, NeuroImage, 13 (2001), 283-294.doi: 10.1006/nimg.2000.0698.


    M. Vauhkonen, D. Vadasz, J. Kaipio, E. Somersalo and P. Karjalainen, Tikhonov regularization and prior information in electrical impedance tomography, IEEE Trans Med Imaging, 17 (1998), 285-293.doi: 10.1109/42.700740.


    P. Vauhkonen, Image Reconstruction in Three-Dimensional Electrical Impedance Tomography, PhD thesis, University of Kuopio, Kuopio, Finland, 2004.


    P. Vauhkonen, M. Vauhkonen, T. Savolainen and J. Kaipio, Three-dimensional electrical impedance tomography based on the complete electrode model, IEEE Trans. Biomed. Eng, 46 (1999), 1150-1160.doi: 10.1109/10.784147.


    J. A. Victorino, J. B. Borges, V. N. Okamoto, G. F. Matos, M. R. Tucci, M. P. Caramez, H. Tanaka, F. S. Sipmann, D. C. Santos and C. S. Barbas et al., Imbalances in regional lung ventilation a validation study on electrical impedance tomography, American Journal of Respiratory and Critical Care Medicine, 169 (2004), 791-800.doi: 10.1164/rccm.200301-133OC.


    T. Vilhunen, J. Kaipio, P. Vauhkonen, T. Savolainen and M. Vauhkonen, Simultaneous reconstruction of electrode contact impedances and internal electrical properties. Part I: Theory, Meas. Sci. Technol., 13 (2002), 1848-1854.


    S. Wanjun, Y. Fusheng, Z. Wei, Z. Hongyi, F. Feng, S. Xuetao, L. Ruigang, X. Canhua, D. Xiuzhen and B. Tingyi, Image monitoring for an intraperitoneal bleeding model of pigs using electrical impedance tomography, Physiological Measurement, 29 (2008), p217.doi: 10.1088/0967-3334/29/2/005.


    Y. Zou and Z. Guo, A review of electrical impedance techniques for breast cancer detection, Medical engineering & physics, 25 (2003), 79-90.doi: 10.1016/S1350-4533(02)00194-7.

  • 加载中

Article Metrics

HTML views() PDF downloads(117) Cited by(0)

Access History



    DownLoad:  Full-Size Img  PowerPoint