A Hybrid Discrete-Continuum Mathematical Model of Pattern Prediction in the Developing Retinal Vasculature

Dr. Michael Watson (Heriot-Watt University)

Thursday 19th May, 2016 14:00-15:00 Maths 204


Pathological angiogenesis has been extensively explored by the mathematical modelling community over recent decades, specifically in the contexts of wound healing and tumour-induced vascularisation. However, there have been relatively few attempts to model angiogenesis associated with normal development, despite the availability of animal models with experimentally accessible and highly ordered vascular topologies. One such model is the developing superficial retinal vascular plexus (RVP) in neonatal wild-type mice, the manner of which poses an interesting challenge for a mathematical modelling study.

The spatio-temporal formation of the superficial RVP in wild-type mice occurs in a well-defined sequence. Prior to birth, astrocyte sprouting and proliferation begin around the edge of the optic nerve chiasm and subsequent astrocyte migration in response to a chemotactic gradient of PDGF-A results in the formation of a dense scaffold on the surface of the inner retina. Hypoxic astrocytes express a variety of chemotactic and haptotactic proteins, which subsequently induce endothelial cell sprouting and modulate growth of the RVP.

In this talk we present an experimentally informed, two-dimensional hybrid discrete-continuum mathematical model that tracks the migration of individual astrocytes and endothelial tip cells towards the outer retinal boundary in response to the appropriate biochemical cues. The vascular architectures generated by the model are not, however, inert structures; blood perfusion is included throughout development of the plexus and the evolving retinal trees are allowed to adapt and remodel by means of several biological stimuli. The resulting wild-type in silico RVP structures are compared with corresponding experimental whole-mounts taken at various stages of development and agreement between the respective vascular morphologies is found to be excellent.

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