Modeling of the Deformation of Flexible Tubes Using a Single Law: Application to Veins of the Lower Limb in Man

Abstract

The topic of this study mainly concerns a representative model of the behavior of flexible ducts such as elastic tubes or veins. This model is based on a phenomenological approach of the inflation and collapse of the tube. It leads to a single “universal” analytical expression of the tube law, valid for a wide range of positive and negative transmural pressures, which presents a significant improvement compared to previous theoretical studies defined with different expressions on restricted ranges of pressure. Moreover, the theoretical approaches most often require simplifying hypotheses—no longitudinal tension, no surrounding tissues—which are quite unrealistic both in the physiological case and in the experimental setup. These theoretical models can therefore be expected only roughly to describe the actual behavior of such vessels. The representative model, on the contrary, allows one to account for the deformation—inflating as well as collapse—of elastic tubes or veins with better accuracy. The tube law is a function of six parameters chosen in order to fit the experimental data. A comparison between results obtained in our laboratory using silicone tubes and representative models is presented. The model is then applied to physiological data obtained in vivo on human leg veins.