Mathematical Modelling of the Chemotherapeutic Drug Paclitaxel

Paclitaxel (taxol) is front line chemotherapeutic that inhibits cell proliferation by inhibiting mitosis. Despite intense efforts by the research community to identify chemically similar compounds with fewer harmful side effects, progress has thus far been limited.

Adrian Saurin's (co-supervisor, Ninewells) lab has performed series of experiments measuring the uptake and transport of the Paclitaxel (taxol) in a variety of different experimental situations (e.g. cell lines and tumour spheroids). Isaac's project is focussed on using the experimental data to develop and validate mathematical models of transport and uptake of Paclitaxel in different situations. The model will then be adapted so as to describe drug uptake in tumour spheroids and, ultimately, in in vivo contexts.

Ultimately, the aim of the project is to better understand the mechanisms of taxol transport and uptake and to use this information to develop novel strategies for improving taxol treatment protocols.


Objectives:
(1) Use mathematical model to better understand taxol uptake and transport.
(2) Use mathematical models to explain puzzling aspects of the experimental data in a single theoretical framework.
(3) Identify model parameters using bespoke optimisation algorithms.
(5) Use mathematical models to explore different modes of therapy delivery.

Methodology
(1) Derive a novel system of nonlinear ordinary differential equations that describe relevant biological processes.
(2) Derive a novel system of nonlinear reaction diffusion equations that describe spatial transport of taxol in different experimental contexts.
(3) Estimate model parameters using bespoke algorithms that minimising error between experimental data and model solutions.
(4) Use the fitted models to make testable experimental predictions that will lead to novel experiments and treatment strategies.