Haptotaxis in Tumour Growth and Invasion: A Mathematical Modelling Approach

In this work, a number of mathematical models ofhaptotactic cell migration are developed. Thesemodels of haptotaxis are presented in two distinctparts - the first comprises an investigation ofhaptotaxis in pre-necrotic avascular tumours, while the second consists of the modelling ofadhesion-mediated haptotactic cell migration withintissue, with particular attention paid to thebiological appropriateness of the description ofcell-extracellular matrix adhesion. A model isdeveloped that describes the effects of passive andactive haptotactic migration on the cellular dynamicsand growth of pre-necrotic avascular tumours. Thismodel is also extended to describe theinternalisation of labelled cells and inertmicrospheres within multicell tumour spheroids. Alsopresented is a novel model of adhesion-receptormediated haptotactic cell migration. Specificapplications of the model to tumour invasionprocesses are then discussed. This model includes amore biologically realistic description of celladhesion than has been considered in previous modelsof cell population haptotaxis.