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A stochastically perturbed avascular tumour growth model
Author
Tan, Liang Soon
Supervisor
Ang, Keng Cheng
Abstract
In this thesis, a mathematical model of avascular tumour growth with stochastic perturbation is developed. The modelling is presented in two distinct parts–the first comprises modelling avascular tumour growth with random variation, while the second consists of refining the modelling approach to develop a stochastically perturbed avascular tumour model.
The model includes a more biologically realistic description of avascular tumour growth by taking into account stochastic cellular and extracellular tumour growth processes. The random effects due to the disparate cell clones, cell stress and necrotic inhibiting factors are considered in the model. The model is initially formulated as a set of partial differential equations describing the spatio-temporal changes in cell concentrations based on reaction-diffusion dynamics and the law of mass conservation. Appropriate stochastic perturbation function are then proposed to model the interrelation of the random processes on distinct time scales.
A numerical solution method was developed to solve the model with stochastic perturbation, producing a reasonable set of solution results. The model results were calibrated and fitted against published experimental data. The model results has shown a reasonably good fit for the experimental data. Convergence analysis of the model solution was also investigated and weak convergence of the model solution is evident. In addition, simulation results are able to generate the familiar structure of a multicellular spheroid with proliferating rim, quiescent interior and a distinct necrotic core. The biological and clinical implications of these results are also discussed.
The model includes a more biologically realistic description of avascular tumour growth by taking into account stochastic cellular and extracellular tumour growth processes. The random effects due to the disparate cell clones, cell stress and necrotic inhibiting factors are considered in the model. The model is initially formulated as a set of partial differential equations describing the spatio-temporal changes in cell concentrations based on reaction-diffusion dynamics and the law of mass conservation. Appropriate stochastic perturbation function are then proposed to model the interrelation of the random processes on distinct time scales.
A numerical solution method was developed to solve the model with stochastic perturbation, producing a reasonable set of solution results. The model results were calibrated and fitted against published experimental data. The model results has shown a reasonably good fit for the experimental data. Convergence analysis of the model solution was also investigated and weak convergence of the model solution is evident. In addition, simulation results are able to generate the familiar structure of a multicellular spheroid with proliferating rim, quiescent interior and a distinct necrotic core. The biological and clinical implications of these results are also discussed.
Date Issued
2007
Call Number
RC254.5 Tan
Date Submitted
2007