Analysis of spontaneous collapse in elastic tubes

Interaction of fluid with elastic tube is complicated issue studied by many scientific departments around the world. Object of this thesis is to analyze simplified one-dimensional model. At the beginning, used balance equations and basics of hyper-elasticity are presented. Then we review three most common materials used for the description of blood vessels and other soft tissues. For these materials we introduce a method which we use to derive a relation between tube deformation and transmural pressure (i.e. difference between inner and outer pressure). In mathematical section we give brief review of theory of nonlinear hyperbolic equations and some relatively new results in the field of existence and uniqueness of a solution of one-dimensional hyperbolic system. The "building stone" of these results is a solution of the so-called Riemann problem. We use a method for finding exact solutions to the Riemann problem to analyze studied model of fluid-tube interaction and study dependence of the qualitative behavior of the solution on the material properties of the tube wall