Mathematical modelling of angiogenesis in wounds, tumours and retinae: The good, the bad and the beautiful.
Prof. Mark Chaplain (University of St Andrews)
Thursday 4th February, 2016 14:00-15:00 Maths 203
Angiogenesis is the growth of a new network of blood vessels from a pre-existing vasculature. As a process, angiogenesis is a well-orchestrated sequence of events involving endothelial cell migration and proliferation; degradation of tissue; new capillary vessel (sprout) formation; loop formation (anastomosis) and, crucially, blood flow through the network. Once there is blood flow associated with the nascent network, the subsequent growth of the network evolves both temporally and spatially in response to the combined effects of angiogenic factors, migratory cues via the extracellular matrix and perfusion-related haemodynamic forces in a manner that may be described as both adaptive and dynamic. Angiogenesis is a vital component of both normal and pathological processes such as wound healing, solid tumour growth and retinal development.
In this talk we will present a basic mathematical model for the development of a vascular network which simultaneously couples vessel growth with blood flow through the vessels – a dynamic adaptive vasculature model. We will then apply the model to three different biological scenarios: (i) tumour-induced angiogenesis; (ii) wound healing and (iii) the developing retina. The computational simulation results will be compared with experimental data and the predictions of the model discussed with regard to scheduling of the delivery of chemotherapy drugs to solid tumours.