Numerical Study of Shear-Induced Thrombus Formation Over Aterial Stent Struts

Abstract

Thrombosis remains an important problem in both bare-metal and drug eluting stents. Platelet accumulation appears to be highly shear dependent in uniform parallel plate and stenosis models. This study was performed to evaluate thrombus formation location and size with respect to time for a stent. A three-dimensional laminar flow field was modeled via computational fluid dynamics through a stent-containing coronary sized vessel. Platelet deposition and accumulation was then simulated using a shear dependent accumulation function. The platelet deposition rate is given by the function: 3.2γ̇+67 platelets/mm2 /s, where γ̇ is the shear rate, which comes from a linear regression to data presented in Ku and Flannery 2007. A three-dimensional stent with a helical strut matrix design and a pitch of 21 mm was designed around a 3 mm diameter vessel. Square strut designs of 0.15mm×0.15mm and 0.30mm×0.30mm were considered, with each strut embedded halfway into the vessel. A 30° section of the stent was modeled because of stent symmetry. The inlet was set at a mean Reynolds number of 200 by specifying a pressure differential across the length of the vessel. Thrombus growth based on shear rate was set through the equation: dΦ/dt=(3.2γ̇+67)(Vplatelet/V)∑n=0MAn. V is volume, Φ is the volume fraction of thrombus, M is the number of surrounding faces that are either a wall face or are neighboring a computational cell denoted as occluded by thrombus, associated with area, A. Each term without a subscript pertains to the local computational cell prescribed as undergoing thrombus growth. Thrombus cell occlusion was assumed to occur when thrombus filled 80% of the cell's volume. Maximum shear rates occur near the edges along the inner blood surface side of the stent struts. Thrombus growth increases more in the axial direction of the stent relative to the radial direction for the larger strut size. Conversely, the thrombus growth is more uniform in all directions along the smaller struts. The difference emanates from the two distinctly localized high shear contours near the edges of the larger stent struts, while the high shear regions were less distinct for the smaller strut size. Quadrupling the cross sectional area of a strut increases the initial maximum shear rate along the strut by 50%, in addition to doubling the available surface area for platelet deposition. Therefore, increasing strut size has a threefold effect on platelet deposition rate, leading to faster vessel occlusion. This computational technique may be extended to approximate where thrombus may grow to completely occlude a blood vessel and the length of time occlusion would take. The CFD modeling technique may also be used to evaluate thrombus deposition on medical devices such as heart valves and ventricular assist devices.