A mathematical model for the distribution of hemodynamic parameters in the human retinal microvascular network

To quantitatively assess the arteriovenous distribution of hemodynamic parameters throughout the microvascular network of the human retina, we constructed a retinal microcirculatory model consisting of a dichotomous symmetric branching system. This system is characterized by a diameter exponent of 2.85, instead of 3 as dictated by Murray’s law, except for the capillary networks. The value of 2.85 was the sum of a fractal dimension (1.70) and a branch exponent (1.15) of the retinal vasculature. Following the feeding artery (central retinal artery), each bifurcation was recursively developed at a distance of an individual branch length L(r) = 7.4r ^1.15] by a centrifugal scheme. The venular tree was formed in the same way. Using this model, we evaluated hemodynamic parameters, including blood pressure, blood flow, blood velocity, shear rate, and shear stress, within the retinal microcirculatory network as a function of vessel diameter. The arteriovenous distributions of blood pressure and velocity in the simulation were consistent with in vivo measurements in the human retina and other vascular beds of small animals. We therefore conclude that the current theoretical model was useful for quantifying hemodynamics as a function of vessel diameter within the retinal microvascular network.