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Modelling the cell cycle

Chaffey, Gary S. (2015) Modelling the cell cycle Doctoral thesis, University of Surrey.

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This thesis may be divided into two related parts. The �rst 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 e�ectively, 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 e�ect treatment e�cacy and planning. In this thesis mathematical models are used to explore the factors that e�ect the phase distributions of the population. In this thesis it is shown that two di�erent transition rates at the G1-S checkpoint provide a good �t to a growth curve obtained experimentally. However, the di�erent transition functions predict a di�erent phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is e�ected by the phase distribution of the population this di�erence 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, di�erent transition functions are obtained. A suitable �nite di�erence scheme for the numerical simulation of the model is derived and shown to be stable. The model is then �tted using the di�erent probability transition functions to experimental data and the e�ects of the di�erent probability transition functions on the model's results are discussed. i In contrast to the population balance approach a more simplistic compartmental model is also considered. This model results in a system of linear ordinary di�erential equations which, under speci�c circumstances may be solved analytically. It is shown that whilst not as accurate as the population balance model this model provides an adequate �t 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 di�erent 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 e�ects 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 di�erential equations. Additionally, the interaction of a simple (PKPD) drug model with these populations of cells may be considered. Keywords and AMS Classi�cation Codes: Cell Cycle, phase distribution, age structured mathematical model, mathematical modelling, 35Q92, 92C37 ii

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors :
Chaffey, Gary
Date : 27 February 2015
Contributors :
ContributionNameEmailORCID, Anne, David, Norman
Depositing User : Gary Chaffey
Date Deposited : 09 Mar 2015 12:12
Last Modified : 09 Nov 2018 16:40

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