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Giovanna Guidoboni, Francesca Malgaroli, Paola Causin, Riccardo Sacco, Brent A Siesky, Alon Harris; Theoretical investigation of factors influencing oxygen levels in retinal vessels and tissue. Invest. Ophthalmol. Vis. Sci. 2014;55(13):4323.
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Several retinopathies have been associated with alterations in oxygen (O2) tension in the retinal ganglion cells (O2-RGC) and in the O2 tension difference across the walls of retinal arterioles (O2-wall). Many factors influence O2-RGC and O2-wall, including blood pressure (Pin) and O2 tension (cin) upstream of the arterioles, hematocrit (HD) and plasma viscosity (μp). Current imaging techniques lack the ability to measure O2-RGC and O2-wall in vivo in humans at multiple sites, simultaneously. Here, we use a mathematical model to estimate, quantify and compare the influence of changes in Pin, cin, HD and μp on the levels of O2-RGC and O2-wall.
The retinal vasculature is modeled as a three-layered structure: arterioles and venules (described as fractal trees) lie in the superficial layer proximal to the vitreous; capillaries lie in the intermediate and deep layers. The retinal tissue is modeled as an eight-layered structure, with different metabolic demands in each layer. Blood flow is approximated using a generalization of Poiseuille’s law in each vascular segment, where blood viscosity is assumed to change with HD and μp. O2 transport, diffusion and consumption, as well as the interaction between them, are modeled along the vasculature, across the arteriolar walls and through the retinal tissue layers.
Baseline values are Pin = 40mmHg, cin = 100mmHg, HD = 0.45 and μp = 1cP, which correspond to O2-RGC= 31.78mmHg and O2-wall=25.45mmHg (dashed lines in the Figures). O2-RGC and O2-wall are simulated and compared for Pin in the range [20,100]mmHg, cin = [80,220]mmHg, HD = [0.3,0.8]and μp = [0.6,3]cP. The model predicts that changes in Pin, HD and μp induce pronounced variations in O2-RGC (32%, 18% and 21%, respectively) and only minimal variations in O2-wall (less than 4%). The level of cin has a substantial influence on both O2-RGC and O2-wall (14% and 45%, respectively).
The model predicts that O2-RGC is very sensitive to the individual patient’s conditions. In particular, elevated HD and μp noticeably reduce O2-RGC, and this might help explaining why these conditions are considered risk factors for ocular diseases. The model also predicts that O2-wall is particularly sensitive to cin but not to the other parameters. It would be interesting to test this concept experimentally, since O2-wall has been suggested as an important factor in retinal blood flow autoregulation.
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