Mathematical modelling of partially absorbing boundaries in biological systems
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...
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| Language: | English |
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University of British Columbia
2016
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| Online Access: | http://hdl.handle.net/2429/58907 |
| Summary: | 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 |
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