Modeling FDTD wave propagation in dispersive biological tissue using a single pole Z-transform function

To analyze lossy, frequency dependent biological tissue over a wide RF bandwidth with FDTD, it Is important to capture the wave velocity and attenuation with a simple, e±cient model. Using a single pole rational function of the Z-transform variable (Z = e^{j ! ⊄ t}) to model tissue conductivity along with constant real dielectric constant, it is possible to generate a supplemental discretized time domain equation which closely matches measured values across more than a decade of frequency. The agreement between measured and modeled propagation constant and decay rate for more than 30 tissue types are often to within 5%. This formulation avoids memory-intensive convolution operations and is at least as accurate as Debye models. Special stability conditions are derived using von Neumann analysis. The resulting requirement that all zeros of the stability equation be within the unit circle sets a minimum grid spacing interval. A tabulation of 2 ps time step models for 34 measured tissues is provided.