Abstract
In this Thesis, reactive multiparticle collision dynamics (RMPC) is used to simulate red blood cell cluster concentration profiles in the presence of aggregation, as well as when aggregation and break-up are present together. RMPC dynamics involves local collisions, reactions and free-streaming of particles. Reactive mechanisms are used to model the aggregation and break-up of particles. This analogy is motivated by a system of ODES called the Smoluchowski differential equations that have been used to model aggregating systems in the well-mixed case. Exact solutions for the (infinite) systems of ODEs for the Smoluchowski equation are compared to a numerical ODE system solution where the maximum cluster size is N (finite) rather than infinite as assumed in the Smoluchowski equation. The numerical ODE solution is compared to the exact solution in the infinite system when the maximum cluster size is 20 or less. Stochastic RMPC simulations are performed when the maximum cluster size N = 3, and the simulation domain is a cubic volume subject to periodic boundary conditions. Constant and equal aggregation and break-up rates are considered, as well as much smaller aggregation rates compared to break-up rates and vice-versa. Two different initial conditions are considered: monomer-only, as well as non-zero initial concentrations for clusters of all sizes. The simulation for the RMPC (finite), numerical ODE (finite) and exact (infinite) can be shown to have good agreement in the equilibrium concentrations of the chemical species in the system in some cases, although agreement is poor in other cases. This work is an important stepping stone that can be expanded to incorporate flow conditions into the particle dynamics in future work, so as to more accurately investigate pathological conditions including atherosclerotic plaque formation.
Highlights
To describe red blood cell (RBC) coagulation, or aggregation of red blood cells (RBCs), the collision theory of chemical reactions can be used as an analogy [23]
This is because the RBC interaction involves aggregation, which leads to larger three-dimensional clusters, which affect the overall viscosity of the flowing blood in the smaller vessels contained in the microcirculation
For reactive multiparticle collision dynamics (RMPC) results, N = 3 was considered, and applied to two different initial conditions for the following three cases: equal aggregation and breakup rates, aggregation rates that are much smaller than breakup rates, and breakup rates that are much smaller than aggregation rates
Summary
The blood circulation in the human body is a delicate system in which the essential functions of delivering oxygen and nutrients to the tissues and cells, and taking away metabolic waste products, is carried out by the heart, the blood and blood vessels. Significant efforts have been made to obtain correct models for blood flow so as to investigate mechanical and bio-chemical properties, as well as coagulation of blood in healthy and diseased conditions. The flow of blood is affected by three key parts: blood vessels, periodic pumping of the heart, and cellular constituents of blood itself. Blood vessels have varying diameters and elastic properties that influence blood flow and are categorized as arteries, veins and capillaries. The properties of blood depend on the extent of aggregation of suspended erythrocytes in plasma that grow in size as they aggregate [15], the total number of RBC aggregates in an elementary volume, and on the kinetic changes of the size distributions [22]. In 1 mm volume of blood, millions of red blood cells (RBCs) interact with each other and stick together
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