Currently, there is no definite mathematical model to evaluate damage to blood cells, especially for cardiovascular devices with complex flow profiles due to turbulent flow and moving parts. This paper describes a finite volume technique that can more accurately predict damage of red blood cells and platelets by tracking their shear stress history and calculating their accumulated damage. Three standard power-law models for calculating the damage to the blood cells are compared to a novel modified model which takes into account a particle accumulated history and corrects for issues in previous models that miscount for decreasing shear stress. As an example, the damage to blood cells are determined for specific streamlines along a prosthetic polymer-based aortic valve, which is a cardiac device with low levels of damage, allowing for the sensitivity of these models to be tested. The results suggest that the new modified model provides the most accurate prediction of damage.