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

Pathological angiogenesis has been extensively explored by the mathematical modelling community over the past few decades, specifically in the contexts of tumour-induced vascularisation and wound healing. However, there have been relatively few attempts to model angiogenesis associated with normal d...

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Bibliographic Details
Published in:Bulletin of mathematical biology 2012-10, Vol.74 (10), p.2272-2314
Main Authors: McDougall, S. R., Watson, M. G., Devlin, A. H., Mitchell, C. A., Chaplain, M. A. J.
Format: Article
Language:English
Subjects:
Animals
Animals, Newborn
Cell Biology
Chemotaxis - physiology
Computer Simulation
Endothelium, Vascular - cytology
Endothelium, Vascular - metabolism
Endothelium, Vascular - physiology
Life Sciences
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Mice
Mice, Inbred C57BL
Models, Biological
Original Article
Retina - cytology
Retina - metabolism
Retina - physiology
Retinal Vessels - cytology
Retinal Vessels - metabolism
Retinal Vessels - physiology
Vascular Endothelial Growth Factor A - metabolism
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Summary:Pathological angiogenesis has been extensively explored by the mathematical modelling community over the past few decades, specifically in the contexts of tumour-induced vascularisation and wound healing. 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: for example, growth and development of the vascular plexus layers in the murine retina. The current study aims to address this issue through the development of a hybrid discrete-continuum mathematical model of the developing retinal vasculature in neonatal mice that is closely coupled with an ongoing experimental programme. The model of the functional vasculature is informed by a range of morphological and molecular data obtained over a period of several days, from 6 days prior to birth to approximately 8 days after birth. The spatio-temporal formation of the superficial retinal vascular plexus (RVP) in wild-type mice occurs in a well-defined sequence. Prior to birth, astrocytes migrate from the optic nerve over the surface of the inner retina in response to a chemotactic gradient of PDGF-A, formed at an earlier stage by migrating retinal ganglion cells (RGCs). Astrocytes express a variety of chemotactic and haptotactic proteins, including VEGF and fibronectin (respectively), which subsequently induce endothelial cell sprouting and modulate growth of the RVP. The developing RVP is not an inert structure; however, the vascular bed adapts and remodels in response to a wide variety of metabolic and biomolecular stimuli. The main focus of this investigation is to understand how these interacting cellular, molecular, and metabolic cues regulate RVP growth and formation. In an earlier one-dimensional continuum model of astrocyte and endothelial migration, we showed that the measured frontal velocities of the two cell types could be accurately reproduced by means of a system of five coupled partial differential equations (Aubert et al. in Bull. Math. Biol. 73:2430–2451, 2011 ). However, this approach was unable to generate spatial information and structural detail for the entire retinal surface. Building upon this earlier work, a more realistic two-dimensional hybrid PDE-discrete model is derived here that tracks the migration of individual astrocytes and endothelial tip cells towards the outer retinal boundary. Blood perfusion is included throug
ISSN:0092-8240
1522-9602
DOI:10.1007/s11538-012-9754-9