REMODELING OF THE RETINAL ARTERIOLES IN DESCENDING OPTIC ATROPHY FOLLOWS THE PRINCIPLE OF MINIMUM WORK

Mathematical modelling indicates that the minimum energy cost for bloo d flow is achieved when the arteries are arranged in a branching hiera rchy 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 a pply over several magnitudes of vessel calibres, and in many different organs, including the brain, in humans and in animals. This paper add resses the issue of remodelling of one and the same arterial network t o long-term changes in blood flow. This has not been studied previousl y in humans. We measured the radius of parent (r(0)) and branch segmen ts (r(1) and r(2)) of the retinal arteriolar network in fundus photogr aphs of six patients with blinding, non-vascular retrobulbar optic ner ve lesions, mostly traumatic in origin, before and after the developme nt of descending optic atrophy. Attenuation of retinal arterioles is a well-known phenomenon in descending optic atrophy, and is attributabl e to decreased metabolic demand secondary to loss of the retinal gangl ion 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 (r(1)(2) + r(2)(2))r(0)(-2), was 1.23 +/- 0.2 before, and 1.18 +/- 0.2 after optic atrophy (n = 36); t he 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 r(0)(3) = r(1)(3) + r(2)(3). Bifurcation exponents corrected for the Fahraeus-Lindquist effect wer e approximate to 3 before optic atrophy and remained unchanged after r emodelling of the arterioles. It is concluded that the branching of th e retinal arterioles and their adaptation to longterm changes in blood flow in descending optic atrophy obey the principle of minimum work.