Mechanical Instabilities of Biological Tubes

We study theoretically the shapes of biological tubes affected by various pathologies. When epithelial cells grow at an uncontrolled rate, the negative tension produced by their division provokes a buckling instability. Several shapes are investigated : varicose, enlarged, sinusoidal or sausage-like, all of which are found in pathologies of tracheal, renal tubes or arteries. The final shape depends crucially on the mechanical parameters of the tissues : Young modulus, wall-to-lumen ratio, homeostatic pressure. We argue that since tissues must be in quasistatic mechanical equilibrium, abnormal shapes convey information as to what causes the pathology. We calculate a phase diagram of tubular instabilities which could be a helpful guide for investigating the underlying genetic regulation.