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Angela McAllister, Michael Abramoff, Xiayu Xu; Deviation from the Optimal Branching Relationship of Retinal Vessels in Diabetes Mellitus. Invest. Ophthalmol. Vis. Sci. 2013;54(15):2421.
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Deviations of the relationship between the aperture of the parent and the two daughter branches of a vessel bifurcation have been associated with vascular disease. The optimal relationship, known as Murray’s Law, states that optimally the cube of the radius of the parent vessel is equal to the sum of the cubes of the radii of the daughter blood vessels. We propose to study this association in people with diabetes with little or no clinical signs of diabetic retinopathy.
Retinal color images were obtained from 874 people with diabetes, in which the prevalence of retinopathy is 20% (Abramoff et al, JAMA ophthalmology 2013). A fully automated method was used to determine the widths of each branch at each crossing, using our previously validated algorithm. From the above population, a subset was randomly selected for branch point measurement. Linear regression was used to find the power that best described the relationship between the arterial and venous radii.
Arterial and venous branches were measured on photos from 28 subjects from the diabetes population and on 150 fundus images from a normal population. From the diabetic population, 137 arterial branches and 215 venous branches were measured. The best fit power relationship was 4.9 and 3.3 for arterial and venous bifurcations respectively. From the normal population, 331 arteriolar branches and 573 venous branches were measured. The parent branch-daughter branch artery relationship fit Murray’s Law well with a third power relationship while the relationship in venular branches demonstrated a best fit of 2.4.
The apertures of the branches of arterial and venous bifurcations in the diabetic population deviate from the normal subjects. The daughters are wider than predicted by Murray’s Law. Previously, increased arterial flow and vessel wall irregularities have been described in subjects with diabetes. Possibly vessel widening is related to increased flow rate to maintain resistance and increased diameter compensates for increased resistance per unit area of vessel wall. Our findings may have important implications for early detection of retinal disease from diabetes mellitus even before retinopathy is clinically evident.
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