A STUDY OF THE BIFURCATION BEHAVIOR OF A MODEL OF FLOW-THROUGH A COLLAPSIBLE-TUBE

Most of the elastic tubes found in the mammalian body will collapse fr om a distended circular cross section and when collapsed may undergo f low-induced oscillations. A mathematical model describing fluid flow i n a collapsible tube is analysed using the software package AUTO-86. A UTO-86 is used for continuation and bifurcation problems in systems of non-linear ordinary differential equations. The model is a third-orde r lumped-parameter type and is based on the classical ''Starling resis tor''; it describes the unsteady flow behaviour and, in particular, th e experimentally observed self-excited oscillations, in a way which is simple enough to give physical understanding, yet still firmly based on fluid mechanical principles. Some of the bifurcation types found in this model bear close resemblance to the types suggested by experimen tal observations of self-excited oscillations in collapsible tubes; th ey thus shed some light on the various topological changes which occur in practice, particularly in view of the fact that some of the points found numerically are difficult to achieve experimentally, while the existence of others can only be inferred indirectly and uncertainly fr om experiment.