ADE-TLM Algorithm for Modeling Wave Propagation in Biological Tissues with Debye Dispersion

Abstract

In this paper we present a Transmission Line Matrix (TLM) algorithm for the simulation of electromagnetic wave interaction with a Debye dispersive medium. This new formulation is based on the use of the polarization currents in the medium. The auxiliary differential equation (ADE) method is considered to deal with dispersion after the classical discretization. The accuracy and efficiency of this approach were tested on 1D Debye medium by calculating the reflection coefficient on an air-dielectric interface. The potential of the developed algorithm to model the existence of tumors in a human breast is also demonstrated. The obtained results compared with the analytic model show a good agreement. The number of operations needed for each iteration has been reduced, hence the computational time in comparison with time convolution techniques, while maintaining a comparable numerical accuracy.

The New ADE-TLM Algorithm for Modeling Debye Medium

“…The results obtained using our new ADE-TLM approach are in excellent agreement with both the analytical values of the reflection coefficient and the ADE-TLM method described in [23], demonstrating the efficiency and validity of the suggested method. Future work will integrate the new ADE-TLM algorithm into Kerr and Raman nonlinear dispersive media.…”

“…An efficient agreement was noted between the simulation results obtained employing the new ADE-TLM method, the ADE-TLM method described in [23] and the analytical results for the reflection coefficient at different frequencies as defined by Eq. ( 22).…”

“…In contrast, the derivation of our new ADE-TLM algorithm, which utilizes the centered derivative approximation, is simpler in comparison to the derivation of the ADE-TLM algorithm discussed in [23].…”

“…7. Comparison of the new ADE-TLM calculatedwith the analytical solution (eq.22) for the magnitude of the reflection and the ADE-TLM method described in[23]…”