The endovascular repair of a traumatic rupture of the thoracic aorta - that would otherwise lead to the death of the patient - is performed by delivering a stent-graft into the vessel at the rupture location. The age range of the affected patients is large and the stent-graft will stay in the body for the remaining life. The technique is relatively new, and no experience with regard to long-term effects, and durability exists. To predict long-term complications, such as ruptures or destructive interactions with surrounding tissue during the life of the patient, it is important to understand the - rather intense and constant - movement of the stentgraft during the cardiac cycle. A computed tomography with heart gating (gated CT) acquires sequences that show the region of the stent-graft at different time points. We analyze the motion of stent-grafts with a model based approach. Stent-grafts are represented as sparse sets of axis points extracted from the gated CT, and motion patterns a...