A novel tube law analysis under anisotropic external load

Mathematical and physical modeling of flows in collapsible pipes often relates the flow area to the difference between the internal and the external pressures (i.e. the transmural pressure). The relation is used to model the conduits of the human body transporting biological fluids, is called tube law and usually considers the transmural pressure resulting from isotropic external pressure only. We provide a new empirical tube law considering anisotropic conditions of the external load; our formulation is based on the hypothesis, supported by clinical and experimental findings, that in physiological conditions both isotropic and anisotropic stresses are combined in the external load acting on vessels. The proposed mathematical model was validated through laboratory experiments reproducing the flow through a collapsible tube representing the physiological conditions of male urethra during micturition. The proposed tube law better agrees with the experimental observations, in comparison to classic formulations available in literature, thus showing that the proposed model better describes the physiological condition of flow in collapsible tubes subjected to anisotropic external load. The application of our model can be readily extended to several types of vessels.