Estimation of boundary properties using stochastic differential equations

Abstract

Recently, Modeling and detection of different boundary properties are becoming and essential tools in many applications such as drug delivery and modeling of capillary walls. In this paper, we propose computationally efficient framework for estimating the boundary properties using stochastic differential equations. The main advantage of this technique lies in the fact that it accounts for random effects such as Brownian motion which are not accounted for in commonly used classical techniques based on Fick's law of diffusion. We model the dispersion of particles in the presence of absorbing/reflecting boundaries using Fokker-Planck equation. We then derive the inverse model for the estimation of the absorbing region. We demonstrate the applicability of our results using numerical examples.