Planar elastica inside a curved tube with clearance

In this paper, we study the planar deformation of a thin elastic wire inside a tubular housing with clearance. The center line of the tube is assumed to be in the shape of a planar circular arc. The wire is under longitudinal compression at the ends. This mechanics problem can be found in the stent deployment procedure commonly adopted in treating patients with coronary artery diseases. The tube and the wire are meant to model the patient’s artery and the thin guidewire used in endovascular surgery, respectively. When the leading end of the guidewire encounters a blockage in the artery, the total length of the guidewire inside the artery varies as the wire undergoes bending deformation through the pushing at the other end. As a consequence, the leading end of the guidewire may not move forward the same distance that it is pushed in by the surgeon from the input end. It is also found that there exists a range of pushing force magnitude, in which one force magnitude may correspond to three different deformation patterns. Therefore, a deformation pattern jump may occur simply by adjusting the direction of the input force while holding the magnitude of the force constant. All these mechanics problems add more challenges to the surgeon’s delicate tasks in performing the surgery effectively.