A mathematical model to predict the in vivo pulsatile drag forces acting on bifurcated stent grafts used in endovascular treatment of abdominal aortic aneurysms (AAA)

Endovascular treatment of abdominal aortic aneurysms (AAA) is a promising new alternative to the traditional surgical repair. However, the endovascular approach suffers problems such as stent graft migration, endoleaks and stent mechanism breakage. Fatigue failure is believed to be the major cause of stent graft migration and device breakage. Knowledge of the in vivo forces acting on such devices is a basic requirement for the design of a successful endovascular device. Using a Fourier series trigonometric fit of a typical pressure and flow relationship, a mathematical model, using the control volume method, was developed to predict the pulsatile drag forces acting on various bifurcated stent graft geometries. It was found that for an iliac angle of 30°, a proximal diameter of 24 mm and an iliac diameter of 12 mm, the drag force varied, over the cardiac cycle, between 3.9 and 5.5 N in the axial direction. It was noted that for a specific iliac angle the drag force variation with proximal diameter approximates a quadratic fit, with an increase in proximal diameter producing an increase in drag force. The more compliant the aorta the higher the drag force. Previously published results demonstrated the axial loads (axial drag forces) required for stent graft migration for certain stents types are lower than the drag forces calculated in this study. It is believed that the results of this study can provide guidelines for the quantitative analyses of the in vivo drag forces experienced by stent grafts and could therefore be used as design criteria for such devices.