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Ting Luo, Thomas Gast, Tyler Vermeer, Stephen A Burns; Murray’s law and vascular branching in normal and diabetic subjects. Invest. Ophthalmol. Vis. Sci. 2015;56(7 ):5301.
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To examine the branching pattern of the retinal vasculature using high resolution imaging with regard to vessel diameters and angle. The branching of the retinal vasculature is constrained by physical principles, which are expressed in Murray’s law, which states that the cube of a parent vessel's diameter is equal to the sum of the cubes of the branches. Studies have suggested that this is followed relatively well in normal for the large vessels of the eye and deviates for smaller vessels.
We used an adaptive optics scanning laser ophthalmoscope to measure the outer diameters for retinal vessels. We tested 10 normal and 11 diabetic subjects. Following imaging the resulting videos were averaged. Photoshop was used to measure the diameters of both parent and daughter branches of the images. For each vessel location, measurements were repeated five times and averaged. Averaged data were fit to a Murray’s law type power law, but determining the best fit exponent.
Vessels could be reliably measured for sizes from 10 to over 100 microns. While Murray’s law predicts a cubic relation between the parent vessel radius and the sum of the cubed daughter vessels we found that the best fit exponent was not 3. For both the arterioles and venules of normals, the best fit exponet for vessels greater than 10 microns was 2.4 (95% CI 2.3-2.5). For the diabetics we found a value of 2.5 (95% CI 2.3-2.8), also a deviation from the expected value of 3 . Angles for capillaries could be measured in the normals, and they had a high exponent of 3.4 (95% CI 3.0-3.8). In the diabetics, due to the variability in caillary diameter observed, we were unable to make a comparison to.<br />
While diabetes changes capillary diameters, it does not seem to be changing the bifurcation relations of vessels slightly larger than capillaries. In our analysis we measured sizes very close to the vessel bifurcation and it could be that the size relations vary more at larger distances from the bifurcation.
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