Blood vessels are capable of structural adaptation in response to changes in physiological conditions including blood flow rates and oxygen levels. A theoretical model is developed to simulate the changes in diameter of two neighboring microvessels connected in parallel. The model is used to examine the conditions leading to stability of this configuration or to pruning of one of the vessels. When two adjacent vessels supply blood to the same region of tissue, structural adaptation is governed by two competing mechanisms: the elimination of a redundant vessel to minimize the energy cost of sustaining blood flow, and the stabilization of both vessels to distribute oxygen more broadly. Therefore, the behavior of the system depends on both the strength of the metabolic oxygen demand from the tissue and the distance between the vessels. In the simulation, the diameters of two vessels connected in parallel vary based on the mechanical shear and pressure forces acting on the endothelial wall, an oxygen-dependent metabolic stimulus, and a constant tendency for vessels to shrink. The distribution of oxygen throughout the tissue is calculated using a Green’s function method. An initial condition is assumed in which the vessels have near equal diameters. The strength of the metabolic response needed to stabilize both vessels with equal diameters is determined as a function of the distance between the vessels. In cases where equal diameters are unstable, the condition for pruning of one of the vessels, defined as a diameter below 3 μm, is found. For a given spacing between the vessels, two critical values are found for the strength of the metabolic signal. Above the higher critical value, the two vessels are stable with equal diameters. Between the critical values, the two vessels approach a state with unequal diameters. The ability of vessels to stabilize at unequal vessel diameters may contribute to the heterogeneity of physiological vasculatures. Below the lower critical value, one of the vessels is pruned. Under the assumed conditions, both critical values decrease with increasing spacing up to about 70 μm, and are independent of spacing for larger distances. For a given strength of the metabolic signal, smaller spacing favors pruning of one of the vessels because their proximity allows one vessel to meet the metabolic demand of the tissue. The pruning of closely spaced vessels may contribute to the control of capillary density in tissues such as skeletal muscle. Further work is needed to determine whether similar behavior occurs in arrays of multiple capillaries as in muscle vasculature.
