Stability of a microvessel subject to structural adaptation of diameter and wall thickness

Vascular adaptation—or structural changes of microvessels in response to physical and metabolic stresses—can influence physiological processes like angiogenesis and hypertension. To better understand the influence of these stresses on adaptation, Pries et al. (1998, 2001a,b, 2005) have developed a computational model for microvascular adaptation. Here, we reformulate this model in a way that is conducive to a dynamical systems analysis. Using th ese analytic methods, we determine the equilibrium geometries of a single vessel under different conditions and classify its type of stability. We demonstrate that our closed-form solution for vessel geometry exhibits the same regions of stability as the numerical predictions of Pries et al. (2005, Remodeling of blood vessels: responses of diameter and wall thickness to hemodynamic and metabolic stimuli. Hypertension, 46, 725–731). Our analytic approach allows us to predict the existence of limit-cycle oscillations and to extend the model to consider a fixed pressure across the vessel in addition to a fixed flow. Under these fixed pressure conditions, we show that the vessel stability is affected and that the multiple equilibria can exist.