Bileaflet mechanical heart valves (BMHVs) are among the most popular prostheses to replace defective native valves. However, complex flow phenomena caused by the prosthesis are thought to induce serious thromboembolic complications. This study aims at employing a novel multiscale numerical method that models realistic sized suspended platelets for assessing blood damage potential in flow through BMHVs. A previously validated lattice-Boltzmann method (LBM) is used to simulate pulsatile flow through a 23 mm St. Jude Medical (SJM) Regent™ valve in the aortic position at very high spatiotemporal resolution with the presence of thousands of suspended platelets. Platelet damage is modeled for both the systolic and diastolic phases of the cardiac cycle. No platelets exceed activation thresholds for any of the simulations. Platelet damage is determined to be particularly high for suspended elements trapped in recirculation zones, which suggests a shift of focus in blood damage studies away from instantaneous flow fields and toward high flow mixing regions. In the diastolic phase, leakage flow through the b-datum gap is shown to cause highest damage to platelets. This multiscale numerical method may be used as a generic solver for evaluating blood damage in other cardiovascular flows and devices.