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Title: Modelling the cell cycle
Author: Chaffey, Gary S.
ISNI:       0000 0004 5349 098X
Awarding Body: University of Surrey
Current Institution: University of Surrey
Date of Award: 2015
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This thesis may be divided into two related parts. The first of which considers a population balance approach to modelling a population of cells, with particular emphasis on how the cells pass between the G1 and S phases of the cell cycle. In the second part of the thesis a model is described which combines a cell cycle model with a simple Pharmacokinetic/Pharmacodynamic (PKPD) drug model. This model is then discussed in detail. Knowledge of how a population of cancerous cells progress through the cell cycle is vital if the population is to be treated effectively, as treatment outcome is dependent on the phase distributions of the population. Estimates on the phase distribution may be obtained experimentally however the errors present in these estimates may effect treatment efficacy and planning. In this thesis mathematical models are used to explore the factors that effect the phase distributions of the population. In this thesis it is shown that two different transition rates at the G1-S checkpoint provide a good fit to a growth curve obtained experimentally. However, the different transition functions predict a different phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is effected by the phase distribution of the population this difference may be critical in treatment planning. Using an age-structured population balance approach the cell cycle is modelled with particular emphasis on the G1-S checkpoint. By considering the probability of cells transitioning at the G1-S checkpoint, different transition functions are obtained. A suitable finite difference scheme for the numerical simulation of the model is derived and shown to be stable. The model is then fitted using the different probability transition functions to experimental data and the effects of the different probability transition functions on the model's results are discussed. In contrast to the population balance approach a more simplistic compartmental model is also considered. This model results in a system of linear ordinary differential equations which, under specific circumstances may be solved analytically. It is shown that whilst not as accurate as the population balance model this model provides an adequate fit to experimental data with the results for the total cell population lying within the bounds of experimental error. The ODE compartment model is combined with a simple PKPD model to allow a detailed analysis of the equations for this combined model to be undertaken for different drug-cell interactions. These results are then discussed. As a tumour grows many of the cells receive oxygen and nutrients from blood vessels formed within the tumour, these provide a less than ideal supply, resulting in areas that are well perfused, hypoxic and necrotic. In hypoxic regions the lack of oxygen and nutrients limit the cells' growth by increasing their cycle time and also reducing the effects of radiation and chemotherapy. In the conclusion of this thesis the idea of separating a tumour into three regions, normoxic, hypoxic and necrotic is discussed. Each of these regions may then be modelled using three coupled compartments, each of which contain a cell cycle model, modelled using a set of ordinary differential equations. Additionally, the interaction of a simple (PKPD) drug model with these populations of cells may be considered.
Supervisor: Skeldon, Anne; Lloyd, David; Kirkby, Norman Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available