Forced motion of a cylinder within a liquid-filled elastic tube with application to minimally invasive medical procedures

We analyze the forced motion of an internal concentric rigid cylinder within an elastic liquid-filled tube. This configuration is relevant to various minimally invasive medical procedures in which solid devices are inserted into fluid-filled biological vessels (such as percutaneous revascularization, interventional radiology, endoscopies and catheterization). Insertion of the cylinder at a constant force is shown to involve three distinct regimes and time-scales: (i) initial shear dominant regime, (ii) increased fluidic pressure and a propagating peeling front regime, (iii) quasi-steady flow regime. A uniform solution for all regimes is presented. In the opposite case of extraction of the cylinder from the tube, the negative gauge pressure reduces the gap between the cylinder and the tube till a radial contact of the two solids. Asymptotic and numeric solutions are presented for the dynamics of the near-contact and full contact limits. We find that the cylinder exits the tube in a finite time for sufficiently small or large forces, while for an intermediate range of forces the radial contact creates a locking of the cylinder inside the tube.