ORCID Profile
0000-0001-5727-2160
Current Organisation
University of St Andrews
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Publisher: The Royal Society
Date: 21-03-2012
Abstract: The manner in which the superficial retinal vascular plexus (RVP) develops in neonatal wild-type mice is relatively well documented and poses an interesting challenge to the mathematical modelling community. Prior to birth, astrocyte sprouting and proliferation begin around the edge of the optic nerve head, and subsequent astrocyte migration in response to a chemotactic gradient of platelet-derived growth factor (PDGF)-A results in the formation of a dense scaffold on the surface of the inner retina. Astrocytes express a variety of chemotactic and haptotactic proteins that subsequently induce endothelial cell sprouting and modulate growth of the RVP. An experimentally informed, two-dimensional hybrid partial differential equation-discrete model is derived to track the outward migration of in idual astrocyte and endothelial tip cells in response to the appropriate biochemical cues. Blood perfusion is included throughout the 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. Subsequent numerical predictions help elucidate some of the key biological processes underlying retinal development and demonstrate the potential of the virtual retina for the investigation of various vascular-related diseases of the eye.
Publisher: Elsevier BV
Date: 11-2001
Publisher: Springer Science and Business Media LLC
Date: 25-07-2012
DOI: 10.1007/S11538-012-9754-9
Abstract: 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 ex le, 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 in idual astrocytes and endothelial tip cells towards the outer retinal boundary. Blood perfusion is included throughout plexus development and the emergent retinal architectures adapt and remodel in response to various biological factors. The resulting in silico RVP structures are compared with whole-mounted retinal vasculatures at various stages of development, and the agreement is found to be excellent. Having successfully benchmarked the model against wild-type data, the effect of transgenic over-expression of various genes is predicted, based on the ocular-specific expression of VEGF-A during murine development. These results can be used to help inform future experimental investigations of signalling pathways in ocular conditions characterised by aberrant angiogenesis.
Publisher: Springer Science and Business Media LLC
Date: 02-2011
DOI: 10.1007/S11538-011-9631-Y
Abstract: Angiogenesis, the process of new vessel growth from pre-existing vasculature, is crucial in many biological situations such as wound healing and embryogenesis. Angiogenesis is also a key regulator of pathogenesis in many clinically important disease processes, for instance, solid tumour progression and ocular diseases. Over the past 10-20 years, tumour-induced angiogenesis has received a lot of attention in the mathematical modelling community and there have also been some attempts to model angiogenesis during wound healing. However, there has been little modelling work of vascular growth during normal development. In this paper, we describe an in silico representation of the developing retinal vasculature in the mouse, using continuum mathematical models consisting of systems of partial differential equations. The equations describe the migratory response of cells to growth factor gradients, the evolution of the capillary blood vessel density, and of the growth factor concentration. Our approach is closely coupled to an associated experimental programme to parameterise our model effectively and the simulations provide an excellent correlation with in vivo experimental data. Future work and development of this model will enable us to elucidate the impact of molecular cues upon vasculature development and the implications for eye diseases such as diabetic retinopathy and neonatal retinopathy of prematurity.
Publisher: World Scientific Pub Co Pte Lt
Date: 03-2002
DOI: 10.1142/S0218339002000251
Abstract: A minimal model of nematode migration through soil in response to a chemical gradient is presented. We consider Fickian, fractal and porous-media type diffusion of the nematodes, for which the steady-state nematode distributions are found to compare favourably with experimental observations. Analytical results for Fickian nematode diffusion are presented, which are appropriate for the small- and large-time evolution of a nematode distribution. Numerical integrations allow us to compare the three types of nematode diffusion, to provide numerical validation of our analytical results, and to investigate the dependence of the results of our model upon certain key parameters. We conclude with a summary of results and a call for further experimental work.
Publisher: Wiley
Date: 24-03-2011
DOI: 10.1111/J.1549-8719.2010.00076.X
Abstract: The most critical determinant of restoration of tissue structure during wound healing is the re-establishment of a functional vasculature, which largely occurs via angiogenesis, specifically endothelial sprouting from the pre-existing vasculature. We used confocal microscopy to capture sequential images of perfused vascular segments within the injured panniculus carnosus muscle in the mouse dorsal skin-fold window chamber to quantify a range of microcirculatory parameters during the first nine days of healing. This data was used to inform a mathematical model of sequential growth of the vascular plexus. The modeling framework mirrored the experimental circular wound domain and incorporated capillary sprouting and endothelial cell (EC) sensing of vascular endothelial growth factor gradients. Wound areas, vessel densities and vessel junction densities obtained from the corresponding virtual wound were in excellent agreement both temporally and spatially with data measured during the in vivo healing process. Moreover, by perturbing the proliferative ability of ECs in the mathematical model, this leads to a severe reduction in vascular growth and poor healing. Quantitative measures from this second set of simulations were found to correlate extremely well with experimental data obtained from animals treated with an agent that targets endothelial proliferation (TNP-470). Our direct combination and comparison of in vivo longitudinal analysis (over time in the same animal) and mathematical modeling employed in this study establishes a useful new paradigm. The virtual wound created in this study can be used to investigate a wide range of experimental hypotheses associated with wound healing, including disorders characterized by aberrant angiogenesis (e.g., diabetic models) and the effects of vascular enhancing/disrupting agents or therapeutic interventions such as hyperbaric oxygen.
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
No related grants have been discovered for Mark Chaplain.