- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Computational and Mathematical Methods in Medicine
Volume 2013 (2013), Article ID 353849, 10 pages
Effective Admittivity of Biological Tissues as a Coefficient of Elliptic PDE
1Department of Computational Science and Engineering, Advanced Science and Technology Center (ASTC), Yonsei University, 50 Yonsei-Ro, 134 Sinchon-dong, Seodaemun-gu, Seoul 120 749, Republic of Korea
2J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Biomedical Sciences Building JG-5, P.O. Box 116131, Gainesville, FL 32611, USA
Received 26 October 2012; Accepted 15 January 2013
Academic Editor: Eung Je Woo
Copyright © 2013 Jin Keun Seo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- L. A. Geddes and L. E. Baker, “The specific resistance of biological material-a compendium of data for the biomedical engineer and physiologist,” Medical and Biological Engineering, vol. 5, no. 3, pp. 271–293, 1967.
- S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz,” Physics in Medicine and Biology, vol. 41, no. 11, pp. 2251–2269, 1996.
- C. Gabriel, S. Gabriel, and E. Corthout, “The dielectric properties of biological tissues: I. Literature survey,” Physics in Medicine and Biology, vol. 41, no. 11, pp. 2231–2249, 1996.
- S. Gabriel, R. W. Lau, and C. Gabriel, “The dielectric properties of biological tissues: III. Parametric models for the dielectric spectrum of tissues,” Physics in Medicine and Biology, vol. 41, no. 11, pp. 2271–2293, 1996.
- S. Grimnes and G. Martinsen, Bioimpedance and Bioelectricity Basics, Academic Press, San Diego, Calif, USA, 2008.
- A. Bensoussan, J. L. Lions, and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, Elsevier, 1978.
- H. Fricke, “A mathematical treatment of the electrical conductivity of colloids and cell suspensions,” Journal of General Physiology, vol. 4, pp. 375–383, 1924.
- O. G. Martinsen, S. Grimnes, and H. P. Schwan, “Interface phenomena and dielectric properties of biological tissue,” Encyclopedia of Surface and Colloid Science, vol. 20, pp. 2643–2653, 2002.
- J. C. Maxwell, Electricity and Magnetism, 1st edition, 1873.
- S. D. Poisson, Mémoires De L'Académie RoyaLe Des Sciences De L'Institut De France, vol. 5, p. 488, 1826.
- S. S. Dukhin, “Dielectric properties of disperse systems,” in Surface and Colloid Science, E. Matijevic, Ed., vol. 3, pp. 83–165, Wiley-Interscience, New York, NY, USA, 1971.
- M. Pavlin, T. Slivnik, and D. Miklavčič, “Effective conductivity of cell suspensions,” IEEE Transactions on Biomedical Engineering, vol. 49, no. 1, pp. 77–80, 2002.
- M. Pavlin, N. Pavšelj, and D. Miklavčič, “Dependence of induced transmembrane potential on cell density, arrangement, and cell position inside a cell system,” IEEE Transactions on Biomedical Engineering, vol. 49, no. 6, pp. 605–612, 2002.
- H. Pauly and H. P. Schwan, “Über die impedanz einer suspension von kugelformigen teilchen mit einer schale,” Zeitschrift für Naturforschung B, vol. 14, pp. 125–131, 1959.
- H. Ammari, H. Kang, and K. Touibi, “Boundary layer techniques for deriving the effective properties of composite materials,” Asymptotic Analysis, vol. 41, no. 2, pp. 119–140, 2005.
- H. Ammari and H. Kang, Polarization and Moment Tensors: With Applications to Inverse Problems and Effective Medium Theory, vol. 162, Springer, 2007.
- H. Ammari, P. Garapon, H. Kang, and H. Lee, “Effective viscosity properties of dilute suspensions of arbitrarily shaped particles,” The Journal of Physical Chemistry, vol. 80, pp. 189–211, 2012.
- W. Graeme, Milton the Theory of Composites, Cambridge University Press.
- M. Pavlin and D. Miklavčič, “Effective conductivity of a suspension of permeabilized cells: A theoretical analysis,” Biophysical Journal, vol. 85, no. 2, pp. 719–729, 2003.
- J. K. Seo and E. J. Woo, Nonlinear Inverse Problems in Imaging, John Wiley & Sons, 2012.
- W. Kuang and S. O. Nelson, “Low-frequency dielectric properties of biological tissues: a review with some new insights,” Transactions of the American Society of Agricultural Engineers, vol. 41, no. 1, pp. 173–184, 1998.
- W. E. Vaughan, “Dielectric relaxation,” Annual Review of Physical Chemistry, vol. 30, pp. 103–124, 1979.
- H. P. Schwan, “Electrical properties of tissue and cell suspensions,” in Advances in Biological and Medical Physics, J. H. Lawrence and C. A. Tobias, Eds., vol. V, pp. 147–209, Academic Press, New York, NY, USA, 1957.
- H. P. Schwan, “Electrical properties of tissues and cell suspensions: mechanisms and models,” in Proceedings of the 16th Annual International Conference of the IEEE, vol. 1, pp. A70–A71, 1994.
- K. R. Foster and H. P. Schwan, “Dielectric properties of tissues and biological materials: a critical review.,” Critical Reviews in Biomedical Engineering, vol. 17, no. 1, pp. 25–104, 1989.
- T. Hao, Electrorheological Fluids: The Non-Aqueous Suspensions, Elsevier, 2005.
- K. S. Cole, Membranes, Ions and Impulses, University of California Press, Berkeley, Calif, USA.
- H. P. Schwan, “Electrical properties of muscle tissue at low frequencies,” Zeitschrift für Naturforschung B, vol. 9, p. 245, 1954.
- G. Falkand and P. Fatt, “Linear electrical properties of striated muscle fibers observed with intracellular electrodes,” Proceedings of the Royal Society of London B, vol. 160, pp. 69–123, 1964.
- G. Schwarz, “A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solution,” Journal of Physical Chemistry, vol. 66, no. 12, pp. 2636–2642, 1962.
- J. Thuery, Microwaves: Industrial, Scientific and Medical Applications, Artech House, Boston, Mass, USA, 1991.
- S. O. Nelson, “Dielectric properties of agricultural products measurements and applications,” IEEE Transactions on Electrical Insulation, vol. 26, no. 5, pp. 845–869, 1991.
- A. C. Metaxas and R. J. Meredith, Industrial Microwave Heating, Peter Peregrinus, London, UK, 1983.
- B. Rajewsky and H. P. Schwan, “The dielectric constant and conductivity of blood at ultrahigh frequencies,” Naturwissenschaften, vol. 35, p. 315, 1948.
- H. P. Schwan, “Mechanisms responsible for electrical properties of tissues and cell suspensions,” Medical Progress through Technology, vol. 19, no. 4, pp. 163–165, 1993.
- H. M. Fishman, D. J. M. Poussart, L. E. Moore, and E. Siebenga, “K+ conduction description from the low frequency impedance and admittance of squid axon,” Journal of Membrane Biology, vol. 32, no. 3-4, pp. 255–290, 1977.
- R. D. Stoy, K. R. Foster, and H. P. Schwan, “Dielectric properties of mammalian tissues from 0.1 to 100 MHz; a summary of recent data,” Physics in Medicine and Biology, vol. 27, no. 4, pp. 501–513, 1982.
- K. W. Wagner, “Erklarung der dielectrischen nachwirkungsworgange auf grund maxwellscher vorstellungen,” Archiv für Elektrotechnik, vol. 2, pp. 371–387, 1914.
- H. Fricke, “The complex conductivity of a suspension of stratified particles of spherical or cylindrical form,” Journal of Physical Chemistry, vol. 59, no. 2, pp. 168–170, 1955.
- D. Gakkai, “Japan society for medical electronics and biological engineering,” in Proceedings of 5th International Conference on Electrical Bio-Impedance, p. 261, Business Center for Academic Societies Japan, 1888.