Mathematical modelling of partially absorbing boundaries in biological systems
| Autor: | Iyaniwura, Sarafa Adewale |
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| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Druh dokumentu: | Text |
| Popis: | 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. Science, Faculty of Graduate |
| Databáze: | Networked Digital Library of Theses & Dissertations |
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