Remodelling of the retinal arterioles in descending optic atrophy follows the principle of minimum work

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Abstract
Mathematical modelling indicates that the minimum energy cost for blood flow is achieved when the arteries are arranged in a branching hierarchy such that the radii of the vessels are adjusted to the cube root of the volumetric flow (principle of minimum work). This is known to apply over several magnitudes of vessel calibres, and in many different organs, including the brain, in humans and in animals. This paper addresses the issue of remodelling of one and the same arterial network to long‐term changes in blood flow. This has not been studied previously in humans. We measured the radius of parent (r0) and branch segments (rl and r2) of the retinal arteriolar network in fundus photographs of six patients with blinding, non‐vascular retrobulbar optic nerve lesions, mostly traumatic in origin, before and after the development of descending optic atrophy. Attenuation of retinal arterioles is a well‐known phenomenon in descending optic atrophy, and is attributable to decreased metabolic demand secondary to loss of the retinal ganglion cells and their axons. On average, arteriolar diameters decreased by 15.2±17.7% (SD), with 95% confidence intervals of 18.7% and 11.7%; the radii decreased significantly (P= 0.0001) (n= 99). The area ratio of the bifurcations, defined as (r21+r22)r‐02, was 1.23±0.2 before, and 1.18±0.2 after optic atrophy (n= 36); the change of area ratio was not significant. The branching geometry of the retinal arteriolar network obeyed strictly the optimum branching rule of the principle of minimum work, or r30=r31+r32. Bifurcation exponents corrected for the Fåhræus‐Lindquist effect were ˜˜ 3 before optic atrophy and remained unchanged after remodelling of the arterioles. It is concluded that the branching of the retinal arterioles and their adaptation to long‐term changes in blood flow in descending optic atrophy obey the principle of minimum work.