Numerical Investigation of Biotransport in a Tumor with Uncertain Material Properties

Abstract

In biomedical engineering, it is a challenge to deliver therapeutic agents to the entire tumor region effectively due to its material heterogeneity. Therefore, one basic issue that needs to be resolved is whether there is an efficient way to quantify the effects of structural irregularities on drug delivery in tumors. In this work, different from previous studies, which treat the material property of tumors as a uniform one or a heterogeneous one but with deterministic values, we approximate tumor material properties as random fields, and develop stochastic models to analyze the resultant heterogeneous biotransport. Specifically, the uncertain permeability is modeled as a log-normal random field, and represented by a truncated Karhunen-Loeve (KL) expansion. The uncertain porosity is modeled as a log-normal random variable. On propagating the randomness in the inputs (i.e., permeability and porosity) into the governing partial differential equations, as a result, uncertain flow features such as pressure, velocity and concentration fields can be quantified mathematically. We demonstrate that our stochastic model is an effective representation of the uncertain heterogeneous structure in tumors, and can be used to efficiently quantify the impact of material heterogeneities on drug delivery process in porous media.