Effects of a Reduction in the Bifurcation Exponent from 3.00 to 2.85 on Microcirculation

Abstract

Microcirculation in the human retina has been examined by two hemodynamic simulations under two mathematical models of the microcirculatory network to determine the physiological significance of a reduction in the bifurcation exponent from 3.00 to 2.85. Takahashi’s symmetrical branching network model consists of the bifurcation exponent 2.85 and the branch length–radius relation l = 7.4r ^1.15. Murray’s symmetrical branching network model consists of the bifurcation exponent 3.00 and the branch length–radius relation l = 9.084r ^1.00. With regard to the network topological properties, there are no differences in the number of individual vessels classified according to branching generations or the total volume of blood within all the vessels between the two networks.

The arteriovenous distributions of blood flow velocity, vascular resistance to flow, wall shear rate and stress, and the total mechanical energy cost for blood flow within the retinal microcirculatory network with a bifurcation exponent of 2.85 are higher than those with a bifurcation exponent of 3.00. In contrast, the arteriovenous distributions of intravascular pressure and circumferential wall stress within the network with the exponent 2.85 are lower than those with the exponent 3.00. The network of the exponent 2.85 requires 24.3 % more energy for perfusing blood throughout the network compared to that of the exponent 3.00. However, the arteriovenous distribution of blood pressure with the bifurcation exponent 2.85 is in good agreement with the results of in vivo measurements in the literature. These results suggest that a bifurcation exponent of 2.85, which defines the branching geometry of the network, can play an important role in reducing blood pressure in the microcirculation to appropriate levels. The bifurcation exponent, which includes information about the fractal dimension and the branch length exponent, should provide insights into pathological changes in individual microvessels and the microvasculature as well as the density and complexity of a normal network.