Dispersive Biological Tissue FDTD Analysis using a Single Pole Z-Transform Conductivity Model

C. Rappaport, E. Bishop, and P. Kosmas (USA)


Modeling, FDTD, Dispersion, Wave propagation.


Frequency dependent biological tissue is effectively modeled over a wide microwave bandwidth with FDTD, using a supplemental equation to account for dispersion. The varying wave velocity and atten uation is accurately accounted for with a simple single pole rational conductivity function of the Z-transform variable (Z = ejt), along with constant real dielectric constant. Tt is possible to generate a supplemental dis cretized time domain equation which closely matches measured values across more than a decade of fre quency. The agreement between measured and mod eled propagation constant and decay rate for more than 30 tissue types are often to within 5%. This formu lation avoids memory-intensive convolution operations and is at least as accurate as Debye models. Special sta bility conditions are derived using von Neumann anal ysis. The resulting requirement that all zeros of the stability equation be within the unit circle sets a min imum grid spacing interval. A tabulation of 2 ps time step models for 33 measured tissues is provided A three dimensional breast cancer simulation which makes use of four types of dispersive tissue is studied as an exam ple of the effectiveness of this model.

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