To accomplish their physiological function, arteries have to remain patent under physiological loads, exhibit sufficient mechanical strength, and be capable of preserving their configuration with a sufficient reserve of safety. The latter requirement means that an artery has to be a mechanically stable structure. Among possible patterns of loss of stability is a global beam-like instability of arterial segments of sufficiently large length/diameter ratio. There are data from in vitro experiments that showed that a straight arterial segment can buckle under appropriate combinations of internal pressure and longitudinal stretch ratio and a few mathematical models were addresses to predict this phenomenon (cf. [1]). Conclusions from these studies were extended to explain the origin of arterial tortuosity observed in vivo that might be associated with serious arterial disorders such as atherosclerosis and hypertension. However, in the living organism arteries are subjected to periodic pressure, and therefore data from static experiments and conclusions from mathematical models using the static criterion for instability, namely the occurrence of bifurcation of equilibrium configuration termed as buckling, cannot be directly related to the response of arteries in vivo. A mathematical model for studying dynamic stability of arteries subjected to a longitudinal extension and a periodic pressure was proposed recently [2]. The dynamic criterion for instability was used, based on analyzing the small transverse vibrations of the vessel considered as a straight beam. Though generalization of the model to include the effect of perivascular tissue was discussed, no analysis had been performed in [2]. The objective of this study is to build a predictive model for examining mechanical stability of relatively long arterial segments subjected to a periodic pressure and longitudinal stretch with an account for the effects of perivascular tissue. The occurrence of instability is interpreted as a plausible cause of certain vascular disorders.

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