A novel measure to characterise optimality of diameter relationships at retinal vascular bifurcations

Conventionally, the relationship between parent and daughter vessels at vascular bifurcations has been expressed by the junction exponent (x), and deviations of this parameter from the optimal conditions predicted by Murray's law (x = 3) have been shown to be associated with vascular disease. However, the junction exponent is normally calculated iteratively from diameter measurements, and Monte-Carlo simulation studies show the junction exponent to be biased in the presence of measurement noise.We present an alternative parameter, referred to as optimality ratio, that is simpler to compute and also more robust in the presence of noise.To demonstrate the sensitivity of the optimality ratio to alterations in topography of the retinal vascular network, we analysed the effect of inducing endothelial dysfunction by infusion of NG-monomethyl-l-arginine (l-NMMA), a nitric oxide synthase inhibitor, compared to placebo in a double-blind crossover study. The optimality ratio showed a significant increase (p = 0.03) during infusion of l-NMMA compared to placebo.We propose that a measure of the extent of departure of optimality ratio from its optimal value of 2−1/3 may be a useful indicator of microvascular endothelial dysfunction in vivo.