Dissipative Particle Dynamics (DPD) is a mesoscopic simulation method, potentially very effective in simulating mesoscale hydrodynamics and soft matter. This thesis addresses open theoretical and algorithmic questions of DPD and demonstrates the new developments with applications to blood flow in health as well as in sickle cell anemia. The first part investigates the intrinsic relation of DPD to the microscopic Molecular Dynamics (MD) method through the Mori-Zwanzig theory. We provide a physical explanation for the dissipative and random forces by constructing a mesoscopic system directly from a microscopic one. The relationship between DPD and MD is quantified and the many-body effect on the hydrodynamics of the coarse grained system is discussed. We then address algorithmic issues and develop a simple approach for imposing proper no-slip boundary conditions for wall-bounded fluid systems and outflow boundary conditions for open fluid systems. The second part deals with blood flow applications. First, we use DPD and multi-scale red blood cell models to investigate the transition of blood flow from Newtonian to non-Newtonian behavior as the arteriole size decreases. Then, we develop a multi-scale model for the sickle red blood cells (RBCs), accounting for diversity in shapes and polymerization of hemoglobin. Subsequently, we use this model to investigate abnormal rheology and hemo-dynamics of the sickle blood flow under different physiological conditions. Despite the increased flow resistance, no occlusion was observed in a straight tube under any conditions unless an adhesive dynamics model was explicitly incorporated into our simulations. This new adhesion model includes both sickle RBCs as well as leukocytes. The former interact with the vascular endothelium, with the deformable sickle cells (SS2) exhibiting larger adhesion. The adherent SS2 cells further trap rigid irreversible sickle cells (SS4) resulting in vaso-occlusion in vessels less than 15 micrometers. Under inflammation, adherent leukocytes may also trap SS4 cells resulting in vaso-occlusion in even larger vessels.
"Dissipative Particle Dynamics: Theory, algorithms and application to sickle cell anemia"
Applied Mathematics Theses and Dissertations.
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