Use of the z‐transform to investigate nanopulse penetration of biological matter

Abstract

Short duration, fast rise time electromagnetic ultra-wideband (UWB) pulses ("nanopulses") are generated by numerous electronic devices. Many new technologies involving nanopulses are under development and expected to become widely available soon. Study of nanopulse bioeffects therefore is needed to ensure human safety and to probe the useful range of nanopulses in possible biomedical and biotechnological applications. In this article, we present a new approximation of the Cole-Cole expression for the frequency dependence of the dielectric properties of tissues. The approximation is based on a z-transformation of the electric displacement and a second-order Taylor approximation of the Cole-Cole expression. The approach has been applied to investigating the penetration of nanopulses into biological matter as a function of the dielectric properties of tissue and pulse width. Solutions to Maxwell's equations are calculated using the finite difference time domain method (FDTD).

Effect of electromagnetic nanopulses onC. elegans fertility

“…In this context we have also investigated nanopulse production [Sunkam et al, 2005] and computational approaches to characterizing nanopulse propagation in biological matter Su et al, 2005]. Three broad classes of model have been selected for experimental study: macromolecules (manuscript in preparation), proliferative cells [Dorsey et al, 2005;Sylvester et al, 2005] and non-proliferative cells (manuscript in preparation), and whole organisms (the present report).…”

“…The precise magnitude of the field inside the worms during exposure was not determined experimentally: the length of an animal at adulthood is but 1 mm, the width about 0.1 mm. In separate work [namely Simicevic and Haynie, 2005;Su et al, 2005], we have reported results of computer simulations of nanopulse propagation in biological matter. There is no known inconsistency between the results of the C. elegans experiments reported here and our simulations.…”

A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model

“…By substituting the bilinear transform where and are one of the , , or components of and at time step , respectively. The key issue is how to obtain a recursive formula to discretize the fractional-order differentiator in (9). We rewrite (9) (13) and then use a th-order polynomial to approximate the fractional-order differentiator as (14) where and 0 1 are the coefficients of the polynomials corresponding to 1 and 1 , respectively.…”

“…The key issue is how to obtain a recursive formula to discretize the fractional-order differentiator in (9). We rewrite (9) (13) and then use a th-order polynomial to approximate the fractional-order differentiator as (14) where and 0 1 are the coefficients of the polynomials corresponding to 1 and 1 , respectively. Because the time stable condition of the FDTD approach guarantees that the time growth factor satisfies (15) the region of is 1,1 .…”

“…It can be seen that the result presented here matches the exact solution very well. As a comparison, a fifth-order Taylor series [9] is also used to approximate the fractional-order differentiator in (14). The Taylor result is much poorer because of its low convergence speed.…”