Computational Analysis of Oxygen Transport in the Retinal Arterial Network

Liu, D.; Wood, Nigel B.; Witt, Nicholas; Hughes, Alun D.; Thom, Simon; Xu, X. Yun

doi:10.3109/02713680903230079

Cited by 47 publications

(41 citation statements)

References 44 publications

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“…However, there have been few attempts at modelling this fascinating developmental process. Maggelakis & Savakis [32,33] have employed a continuum PDE approach to investigate the interplay between VEGF, oxygen and capillary density in pathological retinal angiogenesis, whereas Liu et al [34] have used a small digitized network taken from the human retina to predict distributions of flow and oxygen partial pressure. A numerical haemodynamic analysis has recently been reported by Ganesan et al [35], predicting haematocrit and shear stress distributions in a fully developed adult murine retinal network.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of angiogenesis during murine retinal development: a coupledin vivoandin silicostudy

Watson

McDougall

Chaplain

et al. 2012

J. R. Soc. Interface.

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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 individual 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.

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Section: Introductionmentioning

confidence: 99%

Dynamics of angiogenesis during murine retinal development: a coupledin vivoandin silicostudy

Watson

McDougall

Chaplain

et al. 2012

J. R. Soc. Interface.

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“…13.3. To generate the vascular bed, the branches of a fractal tree terminate, when the daughter vessel reaches a diameter below 30 m and has an equal relative pressure P end of 0 mmHg [14]. The outflow boundary condition at each outlet is given by the pressure drop…”

Section: Methodsmentioning

confidence: 99%

“…The vessel walls were assumed to be rigid [14] and the density of the blood was set to 1055 kg/m 3 [20]. Because the diameters of the visible arteries are in the range of 15-120 m and the complex characteristic of blood, a non-Newtonian fluid model has to be considered.…”

Section: Methodsmentioning

confidence: 99%

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Fundus Image Based Blood Flow Simulation of the Retinal Arteries

Kristen

Kelsey

Wintermantel³

et al. 2016

Computational Biomechanics for Medicine

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“…Interestingly, various modeling approaches have been proposed to model retinal blood flow [2,23,39,44], and leverage information from fundus images to improve physically based models [19,20,33].…”

Section: Introductionmentioning

confidence: 99%

Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

Dziubek

Guidoboni

Harris

et al. 2015

Biomech Model Mechanobiol

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Thistleton, W. (2016Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational modelReceived: date / Accepted: date Abstract A computational model for retinal hemodynamics accounting for ocular curvature is presented. The model combines: (i) a hierarchical Darcy model for the flow through small arterioles, capillaries and small venules in the retinal tissue, where blood vessels of different size are comprised in different hierarchical levels of a porous medium; and (ii) a one-dimensional network model for the blood flow through retinal arterioles and venules of larger size. The non-planar ocular shape is included by: (i) defining the hierarchical Darcy flow model on a two-dimensional curved surface embedded in the three-dimensional space; and (ii) mapping the simplified one-dimensional network model onto the curved surface. The model is solved numerically using a finite element method in which spatial domain and hierarchical levels are discretized separately. For the finite element method we use an exterior calculus based implementation which permits an easier treatment of non-planar domains. Numerical solutions are verified against suitably constructed analytical solutions. Numerical experiments are performed to investigate how

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Computational Analysis of Oxygen Transport in the Retinal Arterial Network

Cited by 47 publications

References 44 publications

Dynamics of angiogenesis during murine retinal development: a coupledin vivoandin silicostudy

Dynamics of angiogenesis during murine retinal development: a coupledin vivoandin silicostudy

Fundus Image Based Blood Flow Simulation of the Retinal Arteries

Effect of ocular shape and vascular geometry on retinal hemodynamics: a computational model

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