A novel tube law analysis under anisotropic external load

In this work we provide a new empirical constitutive law for compliant tubes relating the tube cross-section and the transmural pressure. The novelty is in considering a radial anisotropic external load acting on the tube, in other words we consider the external load acting anisotropically in the plane of the tube cross-section. We formulate 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 human vessels. Besides the analytical formulation of a new law, we performed laboratory experiments of flows in a compliant tube anisotropically loaded. The flow dynamics are also numerically simulated and the proposed pressure-area relationship is tested against the experimental data. Indeed, the current work encompasses three ingredients which complement and strengthen each other: a conceptual and analytical model, laboratory experiments and numerical simulations.