Numerical Simulation of Nanopulse Penetration of Biological Matter Using the z-Transform

  • S. Su
  • W. Dai
  • D. T. Haynie
  • R. Nassar
  • N. Simicevic
Article
Received:
Revised:

Abstract

Short duration, fast rise time ultra-wideband (UWB) electromagnetic pulses (“nanopulses”) are generated by numerous electronic devices in use today. Moreover, many new technologies involving nanopulses are under development and expected to become widely available soon. Study of nanopulse bioeffects is needed to probe their useful range in possible biomedical and biotechnological applications, and to ensure human safety. In this work we develop a computational approach to investigate electromagnetic fields in biological cells exposed to nanopulses. The simulation is based on a z-transformation of the electric displacement and a second-order Taylor approximation of a Cole–Cole expression for the frequency dependence of the dielectric properties of tissues, useful for converting from the frequency domain to the time domain. Maxwell’s equations are then calculated using the finite difference time domain method (FDTD), coupled with a perfectly matched layer to eliminate reflections from the boundary. Numerical results for a biological cell model are presented and discussed.

Keywords

Maxwell’s equations ultrashort electrical pulse FDTD z-transform biological cell 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Albanese, R., Blaschak, J., Medina, R. and Penn, J.: Ultrashort electromagnetic signals: Biophysical questions, safety issues, and medical opportunities, Aviat. Space Environ. Med. 65 (1994), A116–120. PubMedGoogle Scholar
  2. 2.
    Berenger, J. P.: A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 114 (1994), 185–200. CrossRefGoogle Scholar
  3. 3.
    Berenger, J. P.: Three-dimensional perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 127 (1996), 363–379. Google Scholar
  4. 4.
    Foster, K. R.: Thermal and nonthermal mechanisms of interaction of raio-frequency energy with biological systems, IEEE Trans. Plasma Sci. 28 (2000), 15–23. Google Scholar
  5. 5.
    Gabriel, C. and Gabriel, S.: Compilation of the dielectric properties of body tissues at RF and microwave frequencies, Preprint AL/OE-TR-1996-0037, Armstrong Laboratory Brooks AFB, San Antonio, Texas, 1996. Google Scholar
  6. 6.
    Gabriel, S., Lau, R. W. and Gabriel, C.: The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz, Phys. Med. Biol. 41 (1996), 2251–2269. PubMedGoogle Scholar
  7. 7.
    Joshi, R. P. and Schoenbach, K. H.: Electroporation dynamics in biological cells subjected to ultrafast electrical pulses: A numerical simulation study, Phys. Rev. E 62B (2000), 1025–1033. Google Scholar
  8. 8.
    Joshi, R. P., Hu, Q., Aly, R., Schoenbach, K. H. and Hjalmarson, H. P.: Self-consistent simulations of electroporation dynamics in biological cells subjected to ultrashort electrical pulses, Phys. Rev. E 64 (2001), 011913. Google Scholar
  9. 9.
    Joshi, R. P. and Schoenbach, K. H.: Mechanism for membrane electroporation irreversibility under high-intensity, ultrashort electrical pulse conditions, Phys. Rev. E 66 (2002), 052901. Google Scholar
  10. 10.
    Kunz, K. S. and Luebbers, R. J.: The Finite Difference Time Domain Method for Electromagnetics, CRC Press, Boca Raton, FL, 1993. Google Scholar
  11. 11.
    Luebbers, R. J., Kunz, K. S. and Chamberlin, K. A.: An interactive demonstration of electromagnetic wave propagation using time-domain finite differences, IEEE Transactions on Education 33 (1990), 60–68. Google Scholar
  12. 12.
    Polk, C. and Postow, E.: CRC Handbook of Biological Effects of Electromagnetic Fields, 2nd edn, CRC Press, Boca Raton, FL, 1995. Google Scholar
  13. 13.
    Sadiku, M. N. O.: Numerical Techniques in Electromagnetics, CRC Press, Boca Raton, FL, 1992. Google Scholar
  14. 14.
    Samn, S. and Mathur, S. P.: A mathematical model of a gigahertz transverse electromagnetic cell, I, AFRL-HE-TR-1999-0219, 1999, pp. 1–18. Google Scholar
  15. 15.
    Schoenbach, K. H., Beebe, S. J. and Buescher, E. S.: Intracellular effect of ultrashort electrical pulses, Bioelectromagnetics 22 (2001), 440–448. PubMedGoogle Scholar
  16. 16.
    Seaman, R. L., Belt, M. L., Doyle, J. M. and Mathur, S. P.: Ultra-wideband electromagnetic pulses and morphine-induced changes in nociception and activity in mice, Physiol. Behav. 65 (1998), 263–270. PubMedGoogle Scholar
  17. 17.
    Sullivan, D. M.: Electromagnetic Simulation Using the FDTD Method, IEEE, New York, 1999. Google Scholar
  18. 18.
    Yee, K. S.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Trans. Antennas and Propagation 14 (1966), 302–307. Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • S. Su
    • 1
  • W. Dai
    • 2
  • D. T. Haynie
    • 3
    • 4
    • 5
  • R. Nassar
    • 2
    • 5
  • N. Simicevic
    • 4
  1. 1.Ph.D. Program in Computational Analysis and Modeling, College of Engineering & ScienceLouisiana Tech UniversityRustonUSA
  2. 2.Mathematics & Statistics, College of Engineering & ScienceLouisiana Tech UniversityRustonUSA
  3. 3.Biomedical Engineering, College of Engineering & ScienceLouisiana Tech UniversityRustonUSA
  4. 4.Physics, College of Engineering & ScienceLouisiana Tech UniversityRustonUSA
  5. 5.Institute for Micromanufacturing, College of Engineering & ScienceLouisiana Tech UniversityRustonUSA

Personalised recommendations