Vol. 33

Latest Volume
All Volumes
All Issues
2011-07-25

Nonlinear Interaction of Electromagnetic Radiation at the Cell Membrane Level: Response to Stochastic Fields

By Assunta De Vita, Rocco Paolo Croce, Innocenzo Pinto, and Bisceglia Bruno
Progress In Electromagnetics Research B, Vol. 33, 45-67, 2011
doi:10.2528/PIERB11053005

Abstract

A general rigorous analytic framework for computing the transmembrane potential shift resulting from the nonlinear voltage-current membrane relationship in response to wideband stochastic electromagnetic radiation is outlined, based on Volterra functional series. The special case of an insulated cylindrical cell with Hodgkin-Huxley membrane in an infinite homogeneous medium is worked out in detail, for the simplest case where the applied electric is normal to the cell axis, and independent from the axial coordinate. Representative computational results for a zero-average stationary band-limited white Gaussian incident field are illustrated and briefly discussed.

Citation


Assunta De Vita, Rocco Paolo Croce, Innocenzo Pinto, and Bisceglia Bruno, "Nonlinear Interaction of Electromagnetic Radiation at the Cell Membrane Level: Response to Stochastic Fields," Progress In Electromagnetics Research B, Vol. 33, 45-67, 2011.
doi:10.2528/PIERB11053005
http://test.jpier.org/PIERB/pier.php?paper=11053005

References


    1. Schwan, H. P., "Dielectric polarization mechanisms: Potential importance for resonant interactions on biological systems," Resonance and Other Interaction Mechanisms of Electromagnetic Fields with Living Systems, B. Norden and C. Ramel (eds.), Oxford University Press, London, 1992.

    2. Foster, K. R. and H. P. Schwan, "Dielectric properties of tissues: A review," Handbook of Biological E®ects of Electromagnetic Radiation, C. Polk and E. Postow (eds.), CRC Press, Boca Raton (FL), 1995.

    3. Barnes, F. S. and C. L. Hu, "Model of some non-thermal effects of radio and microwave fields in biological membranes," IEEE Trans. Microw. Theory Tech., Vol. 25, No. 9, 742-746, 1977.
    doi:10.1109/TMTT.1977.1129205

    4. Berkovitz, G. C. and F. S. Barnes, "The effects of nonlinear membrane capacity on the interaction of microwave and radio frequency fields with biological materials," IEEE Trans. Microw. Theory Tech., Vol. 27, No. 2, 204-207, 1979.
    doi:10.1109/TMTT.1979.1129587

    5. Chang, S. K. W., "Electric-field-induced volume and membrane ionic permeability changes of red blood cells," EEE Trans. Biomed. Eng., Vol. 40, No. 10, 1054-1059, 1993.
    doi:10.1109/10.247804

    6. Wachtel, H., "Firing-pattern changes and trans-membrane currents produced by ELF fields in pacemaker neuron," 18th Annual Meeting, Hanford Life Sciences Symposium, WA (USA), Richland, Oct. 16-18, 1978.

    7. Postow, E. and M. L. Swicord, "Modulated fields and window effects," Handbook of Biological Effects of Electromagnetic Fields, C. Polk and E. Postow (eds.), CRC Press, Boca Raton, FL, 1995.

    8. Franceschetti, G. and I. M. Pinto, "Cell membrane nonlinear response to an applied electromagnetic field," IEEE Trans. Microw. Theory Tech., Vol. 32, No. 7, 653-658, 1984.
    doi:10.1109/TMTT.1984.1132749

    9. Franceschetti, G. and I. M. Pinto, "Who is who in nonlinear electromagnetics," Electromagnetics, Vol. 11, 281-305, 1991.
    doi:10.1080/02726349108908282

    10. Casaleggio, A., L. Marconi, G. Morgavi, S. Ridella, and C. Rolando, "Current flow in a cell with a non-linear membrane stimulated by an electric field," Bioelectrochemistry and Bioenergetics, Vol. 14, No. 1-3, 13-21, 1985.
    doi:10.1016/0302-4598(85)85002-9

    11. Marconi, L., G. Morgavi, S. Ridella, and C. Rolando, "Non-linear ionic fluxes in an electrically exposed cell," Bioelectrochemistry and Bioenergetics, Vol. 16, No. 1, 89-98, 1986.
    doi:10.1016/0302-4598(86)80048-4

    12. Bisceglia, B., G. Franceschetti, I. M. Pinto, and M. R. Scarfi, "Volterra series solution of Hodgkin-Huxley equation," Atti V RiNEM, 1-5, Saint Vincent (IT), 1984.

    13. Kistler, W., W. Gerstner, and J. L. Van Hemmen, "Reduction of the Hodgkin Huxley equation to a single-variable threshold model," Neural Comput., Vol. 9, No. 5, 1015-1045, 1997.
    doi:10.1162/neco.1997.9.5.1015

    14. Hodgkin, A. L. and A. F. Huxley, "A quantitative description of membrane current and its application to conduction and excitation in nerves," J. Physiol., Vol. 117, No. 4, 500-544, 1952.

    15. De Vita, A., B. Bisceglia, R. P. Croce, and I. M. Pinto, "An analytic model for the response of an excitable cell with a nonlinear Hodgkin-Huxley membrane radiated by a stochastic electromagnetic field ," Proc. 2008 URSI General Assembly, paper K01p5, 2008.

    16. Middleton, D., "Statistical physical models of urban radio noise environments --- Part I: Foundations," IEEE Transactions on Electromagn. Compatib., Vol. 14, 38-56, 1972.
    doi:10.1109/TEMC.1972.303188

    17. Middleton, D., "Man-made noise in urban environments and transportation systems: Models and measurements," IEEE Transactions on Electromagn. Compatib., Vol. 21, 1232-1241, 1973.

    18. Middleton, D., "Statistical-physical models of electromagnetic interference ," IEEE Transactions on Electromagn. Compatib., Vol. 19, 106-127, 1977.
    doi:10.1109/TEMC.1977.303527

    19. De Felice, L. J., Introduction to Membrane Noise, Plenum Press, New York, 1981.

    20. Guttman, R., L. Feldman, and H. Lecar, "Squid axon membrane response to white noise stimulation," Biophys. J., Vol. 14, No. 12, 941-955, 1974.
    doi:10.1016/S0006-3495(74)85961-8

    21. Horikawa, Y., "Noise effects on spike propagation in the stochastic Hodgkin-Huxley models," J. Biological Cybernetics, Vol. 66, No. 1, 190-196, 1991.

    22. Tanaka, H. and K. Aihara, "Analysis of the Hodgkin-Huxley equations with noise: The effects of noise on chaotic neurodynamics ," Artificial Life and Robotics, Vol. 8, No. 2, 190-196, 2004.
    doi:10.1007/s10015-004-0311-y

    23. Luchian, T., B. Bancia, C. Pavel, and G. Popa, "Biomembrane excitability studied within a wideband frequency of an interacting exogenous electric field ," Electromagnetic Biology and Medicine, Vol. 21, 287-291, 2002.
    doi:10.1081/JBC-120016003

    24. McDonnell, M. D. and D. Abbott, "What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology," PLoS Comput. Biol., Vol. 5, No. 5, e1000348, 2009.

    25. Collins, J., C. C. Chow, A. C. Capela, and T. T. Imhoff, "Aperiodic stochastic resonance," Physical Review E, Vol. 54, 5575-5584, 1996.
    doi:10.1103/PhysRevE.54.5575

    26. Paffi, A., M. Liberti, F. Apollonio, M. Gianni, and G. D'Inzeo, "Modeling electromagnetic fields detectability in a HH-like neuronal system: Stochastic resonance and window behavior," Biol. Cybernetics, Vol. 94, 118-127, 2006.

    27. Paffi, A., M. Liberti, F. Apollonio, M. Gianni, and G. D'Inzeo, "Effects of exogenous noise in a silent neuron model: Firing induction and EM signal detection," Proc. 28th IEEE-EMBS Ann. Intl. Conf., Vol. 1, 4183-4186, 2006.

    28. Volterra, V., Theory of Functionals and of Integral and Integro-Differential Equations, , Dover, New York, 1959.

    29. Schetzen, M., The Volterra and Wiener Theories of Nonlinear Systems, Wiley and Sons, New York, 1980.

    30. Aidley, D. J., The Physiology of Excitable Cells, Cambridge University Press, UK, 2000.

    31. FitzHugh, R., "Impulses and physiological states in theoretical models of nerve membrane ," Biophys. J., Vol. 1, No. 6, 445-466, 1961.
    doi:10.1016/S0006-3495(61)86902-6

    32. Izhikevich, E. M., "Simple model of spiking neurons," IEEE Trans. Neural Netw., Vol. 14, No. 6, 1569-1572, 2003.
    doi:10.1109/TNN.2003.820440

    33. Phillipson, P. E. and P. Schuster, "A Comparative study of the HH and Fitzhugh Nagumo models of neuron pulse propagation," Int. J. Bifurc. and Chaos, Vol. 15, 3851-3866, 2005.
    doi:10.1142/S0218127405014349

    34. Cain, C. A., "A theoretical basis for microwave and RF field effects on excitable cellular membranes ," IEEE Trans. Microw. Theory .

    35. See, C. H., R. A. Abd-Alhameed, and P. S. Excell, "Computation of electromagnetic field in assemblages of biological cells using a modi¯ed ¯nite di®erence time domain scheme," IEEE Trans. Microw. Theory Tech., Vol. 55, No. 9, 1986-1994, 2007.
    doi:10.1109/TMTT.2007.904064

    36. Fitzhugh, R. and J. Gen. Physiol., "Theoretical effects of temperature on threshold ," Theoretical effects of temperature on threshold in the Hodgkin-Huxley nerve model, Vol. 49, No. 5, 989-1005, 1966.

    37. Bedrosian, E. and S. O. Rice, "The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and gaussian inputs," Proc. IEEE, Vol. 59, 1688-1707, 1971.
    doi:10.1109/PROC.1971.8525

    38. Isserlis, L., "On a formula for the product-moment coefficient of any order of a normal frequency distribution in any number of variables," Biometrika, Vol. 12, 134-139, 1918.

    39. Stogryn, A., "Equations for calculating the dielectric constant of saline water," IEEE Trans. Microw. Theory Tech., Vol. 19, No. 8, 733-736, 1971.
    doi:10.1109/TMTT.1971.1127617

    40. Klein, L. A. and C. T. Swift, "An improved model for the dielectric constant of sea water at microwave frequencies," IEEE Trans. Antennas Propagat., Vol. 25, No. 1, 104-111, 1977.
    doi:10.1109/TAP.1977.1141539

    41. Cowalkzuk, C. C., G. Yarwood, R. Blackwell, M. Priestner, Z. Sienkiewicz, S. Bou²er, I. Ahmed, R. Abd-Alhameed, P. Excell, V. Hodzic, C. Davis, R. Gammon, and Q. Balzano, "Absence of nonlinear responses in cells and tissues exposed to RF energy at mobile phone frequencies using a doubly resonant cavity," Bioelectromagnetics, Vol. 31, 556-565, 2010.
    doi:10.1002/bem.20597

    42. Davis, C. C. and Q. Balzano, "The brain is not a radio receiver for wireless phone signals: Human tissue does not demodulate a modulated radiofrequency carrier," Comp. Rend. Physique, Vol. 11, 585-591, 2011.
    doi:10.1016/j.crhy.2010.09.002

    43. Nawarathna, D., J. R. Claycomb, G. Cardenas, J. Gardner, D. Warmflash, J. H. Miller, and W. R. Widger, "Harmonic generation by yeast cells in response to low-frequency electric fields," Physical Review E, Vol. 73, 0519141-0519146, 2006.

    44. Lev, D., A. Puzenko, A. Manevitch, Z. Manevitch, L. Livshits, Y. Feldman, and A. Lewis, "D-glucose-induced second harmonic generation response in human erythrocytes," J. Phys. Chem., Vol. B113, 2513-2518, 2009.

    45. Fishman, H. M. and H. R. Leuchtag, "Electrical noise in physics and biology," Curr. Topics Membr. Transp., Vol. 37, S. I. Helman and W. Van Driessche, Eds., Academic Press, 1990.

    46. Weaver, J. C. and R. D. Astumian, "The response of cells to very weak electric fields. The thermal noise limit," Science, Vol. 247, No. 4941, 459-462, 1990.
    doi:10.1126/science.2300806

    47. Weaver, J. C. and R. D. Astumian, "Estimates for ELF effects: Noise-based thresholds and the number of experimental conditions required for empirical searches," Bioelectromagnetics Suppl., Vol. 1, 119-138, 1992.
    doi:10.1002/bem.2250130712

    48. Derksen, H. E. and A. A. Verveen, "Fluctuation of resting neural membrane potential," Science, Vol. 151, No. 3716, 1388-1389, 1966.
    doi:10.1126/science.151.3716.1388

    49. Bevan, S., R. Kullberg, and J. Rice, "An analysis of cell membrane noise," Ann. Statist., Vol. 7, No. 2, 237-257, 1979.
    doi:10.1214/aos/1176344609

    50. Eisenberg, R. S., M. Frank, and C. F. Stevens, "Membranes, Channels and Noise," Plenum Press, New York, 1984.

    51. Bier, M., "How to evaluate the electric noise in a cell membrane," Acta Physica Polonica, Vol. 37, No. 5, 1409-1424, 2006.

    52. Bukhari, M. S. H., J. H. Miller, and Z. H. Shah, "Intrinsic electromagnetic noise in living cells in vitro and its spectroscopy," J. Basic Appl. Sci., Vol. 5, 65-71, 2009.

    53. Bukhari, M. S. H., J. H. Miller, and Z. H. Shah, "Intrinsic membrane noise in living cells and its coupling to external fields," Proc. 2nd International Conference on Computer Research and Development (ICCRD 2010), 540-544, IEEE Computer Society Press, 2010.