Understanding the mechanisms of sickle cell disease by simulations with a discrete particle model

Abstract

Sickle cell disease (SCD) is an inherited blood disorder characterized by rigid, sickle-shaped red blood cells (RBCs). Because of their rigidity and shape, sickle cells can get stuck in smaller blood vessels, causing blockages and depriving oxygen to tissues. This study develops and applies mathematical models to better understand the mechanism of SCD. Two-dimensional models of RBCs and blood vessels have been constructed by representing them as discrete particles interacting with different forces. The nonlinear, elastic property of healthy RBCs could be adequately reproduced using a cosine angle bending force and a worm-like chain spring force. With the ability to deform, RBCs can squeeze through narrow blood vessels. In modeling sickle cells as rigid bodies and applying repelling and friction forces from the blood vessel, this study shows that geometrical factors (dimensions of the sickle cell and blood vessels) as well as rigidity and adhesiveness of the sickle cell all play an important role in determining how, and if, sickle cells become trapped within narrow blood capillaries. With lack of data to validate the model, this study primarily provides a sensitivity analysis of factors influencing sickle cell occlusion and identified critical data to support future modeling.