Mathematical Modelling of the Role of Haptotaxis in Tumour Growth and Invasion
Mallet, Daniel Gordon (2004) Mathematical Modelling of the Role of Haptotaxis in Tumour Growth and Invasion. PhD thesis, Queensland University of Technology.
In this thesis, a number of mathematical models of haptotactic cell migration are developed. The modelling of haptotaxis is presented in two distinct parts - the ﬁrst comprises an investigation of haptotaxis in pre-necrotic avascular tumours, while the second consists of the modelling of adhesion-mediated haptotactic cell migration within tissue, with particular attention paid to the biological appropriateness of the description of cell-extracellular matrix adhesion.
A model is developed that describes the eﬀects of passive and haptotactic migration on the cellular dynamics and growth of pre-necrotic avascular tumours. The model includes a description of the extracellular matrix and its eﬀect on cell migration. Questions are posed as to which cell types act as a source of the extracellular matrix, and the model is used to simulate the possible eﬀects of diﬀerent matrix sources. Simulations in one-dimensional and spherically symmetric geometry are presented, displaying familiar results such as three-phase tumour growth and tumours comprising a rim of proliferating cells surrounding a non-proliferating region. Novel eﬀects are also described such as cell population splitting and tumour shrinkage due to haptotaxis and appropriate extracellular matrix construction. The avascular tumour model is then extended to describe the internalisation of labelled cells and inert microspheres within multicell tumour spheroids.
A novel model of adhesion-receptor mediated haptotactic cell migration is presented and speciﬁc applications of the model to tumour invasion processes are discussed. This model includes a more biologically realistic description of cell adhesion than has been considered in previous models of cell population haptotaxis. Through assumptions of fast kinetics, the model is simpliﬁed with the identiﬁcation of relationships between the simpliﬁed model and previous models of haptotaxis.
Further simpli.cations to the model are made and travelling wave solutions of the original model are then investigated. It is noted that the generic numerical solution routine NAG D03PCF is not always appropriate for the solution of the model, and can produce oscillatory and inaccurate solutions. For this reason, a control volume numerical solver with .ux limiting is developed to provide a better method of solving the cell migration models.
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|Item Type:||QUT Thesis (PhD)|
|Supervisor:||Pettet, Graeme, McElwain, Donald, & Turner, Ian|
|Keywords:||Adhesion Receptors, Anoikis, Cancer, Cell Migration, Chemotaxis, Control Volume Method, Extracellular Matrix, ﬂux Limiting, Haptotactic Boundary Layer, Haptotaxis, Integrin Blocking, Integrins, Internalisation, Invasion, Lamellipod, Landau Transformation, Ligand, Metastasis, Multicell Spheroid, Newtons Method, Phase Plane, Protease, Taxis, Travelling Wave, Tumor, Tumour, Wall Of Singularities|
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
Past > Schools > Mathematical Sciences
|Department:||Faculty of Science|
|Institution:||Queensland University of Technology|
|Copyright Owner:||Copyright Daniel Gordon Mallet|
|Deposited On:||03 Dec 2008 13:53|
|Last Modified:||22 Feb 2013 12:18|
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