Cancer therapy : origin and application

• Main Author: Roberts, Fiona L.
• Published: University of Strathclyde 2012
• Subjects: 616.99406
• Online Access: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.570596

In this thesis we use mathematical techniques to model two biological systems. First, we examine the growth dynamics of the antibiotic producing bacteria Streptomyces coelicolor and present a system of PDEs. We study the system both numerically and analytically. Due to oscillations in the numerical solution when solved using NAG, which uses a finite difference discretization, we change to a finite element discretization which corrects the oscillations. S. coelicolor also produces anticancer drugs, these can be encapsulated during the self-assembly of nanometre-sized vesicles, BPVs (biomimetic polymer vesicles) which are used as a novel targeted cancer therapy. We present a system of ODEs that focuses on the binding kinetics between cell-surface receptors and targeting molecules (ligands) on the BPV. We solve the system numerically, showing there is an optimal number of ligands per BPV for optimal uptake by tumour cells. We extend the model to allow for the infiltration of BPVs into tumour spheroids. Numerical solutions show that the growth of the spheroid is linear if the therapeutic BPVs are absent, and slows in the other case (for some parameter values). Using large time asymptotics we explore regions of parameter space where either steady states or travelling waves will occur.