UBC Theses and Dissertations
Mathematical modelling of partially absorbing boundaries in biological systems Iyaniwura, Sarafa Adewale
This project presents a mathematical framework for identifying partially permeable biological boundaries, and estimating the rate of absorption of diffusing objects at such a boundary based on limited experimental data. We used partial differential equations (PDEs) to derive probability distribution functions for finding a particle performing Brownian motion in a region. These distribution functions can be fit to data to infer the existence of a boundary. We also used the probability distribution functions together with maximum likelihood estimation to estimate the rate of absorption of objects at the boundaries, based on simulated data. Furthermore, we consider a switching boundary and provide a technique for approximating the boundary with a partially permeable boundary.
Item Citations and Data
Attribution-NonCommercial-NoDerivatives 4.0 International