title: Stability of a microvessel subject to structural adaptation of diameter and wall thickness.
abstract: 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.
authors.affiliation: Franklin W. Olin College of Engineering, Needham, MA 02492, USA.
authors.forename: Ilari
authors.initials: I
authors.lastname: Shafer
authors.forename: Rachel
authors.initials: R
authors.lastname: Nancollas
authors.forename: Morgan
authors.initials: M
authors.lastname: Boes
authors.forename: Alisha L
authors.initials: AL
authors.lastname: Sieminski
authors.forename: John B
authors.initials: JB
authors.lastname: Geddes
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology*; D006439:Hemodynamics / Q000502:physiology; D006801:Humans; D006973:Hypertension / Q000503:physiopathology; D055806:Microvessels / Q000033:anatomy & histology* / Q000502:physiology; D008955:Models, Cardiovascular; D009716:Numerical Analysis, Computer-Assisted