A Stochastic FCC-FDTD Method for Uncertainty Quantification of Electromagnetic Field in Biological Tissues

Abstract

A stochastic face-centered cubic finite-difference time-domain (S-FCC-FDTD) method is proposed to calculate the mean and standard deviation of the electromagnetic fields in biological tissues, which takes into account the uncertainty and variability of the electrical properties of the media. To improve accuracy, the updating formulas for the mean and standard deviation fields are derived from the deterministic FCC-FDTD method by using the delta method. Due to the frequency-dependent properties of biological tissues, the dispersive S-FCC-FDTD method for the Debye model is also developed to solve problems involving dispersive media. To truncate the computational domain constructed by the S-FCC-FDTD method, the complex-frequency-shifted perfectly matched layer (CFS-PML) is designed for absorbing the standard deviation waves, which is derived from the existing CFS-PML for mean electromagnetic waves, and exhibits excellent absorption performance. Then, the stability of the S-FCC-FDTD method is analytically and numerically analyzed in detail. Three numerical examples, the pulse propagation in a fat medium and a multilayer human tissue, specific absorption rate (SAR) of an extremely complex head model are carried out to validate its performance. The numerical results demonstrate that the S-FCC-FDTD method has good accuracy and stability in the analysis of statistical variation, with broad applications in bioelectromagnetic effects.