| Poster PS03A | |
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| Marine Aubert |
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| University of Dundee |
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| Title | A hybrid continuum-discrete mathematical model of the developing retinal vasculature: A combined experimental and theoretical study |
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| Abstract | Angiogenesis is the process of blood vessel growth and is crucial in many biological situations such as wound healing and embryogenesis. Angiogenesis (neovascularization) also plays a crucial role in pathological situations such as the growth and development of solid tumours and in the developing retina where it impacts on diseases such as retinopathy. Although tumour-induced angiogenesis has been well-studied experimentally and has received a lot of attention in the mathematical modelling community there has been less modelling work in the other areas. Our current work is to create mathematical models of the developing retinal vasculature. The first step was to establish a continuum model consisting of a system of partial differential equations. These equations describe the migratory response of astrocytes and endothelial cells to molecular cues and haptotaxis. We then discretized the partial differential equations to develop a hybrid continuum-discrete modelfor cell migration. This model enables us to track individual cells (astrocytes and endothelial cells) and to incorporate the dynamic remodelling effects of blood perfusion on the architecture of the developing vascular plexus. Our approach is closely coupled to an associated experimental programme to parametrise our model effectively. The simulations of the discrete model are compared with the astrocyte and the vascular networks observed in in vivo experiments. Our aim is to use this model to elucidate the impact of molecular cues upon vasculature development and the implications for various eye diseases such as retinopathy. |
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| Location | Woodward Lobby (Monday-Tuesday) |
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