Computational haemodynamics of small vessels using the Moving Particle Semi-implicit (MPS) method

The simulation of whole blood stands as a complex multi-body problem. The Moving Particle Semi-implicit method, a Lagrangian particle method to solve the incompressible Navier–Stokes (NS) equations, is developed to perform simulations in complex periodic domains. Red blood cells are modelled using the spring network approach, that act as body force terms in the NS equations. Detailed presentation and derivation of both the MPS method and different spring network models is given. An adaptive time step and an implicit scheme are adopted, improving the stability and overall computational efficiency.The findings from the simulations show evidence that in proximity to the vessel wall, the red blood cells expose a larger surface area by orientation and deformation, due to the presence of a high velocity gradient. The greatest membrane internal stresses occur in the core region of the flow. The intra-cell interaction is driven by a complex flow field that can be visualised in a Lagrangian framework, and highlights vortex structures in the wakes and in between the cells. The stresses the blood exerts on the vessel wall are influenced by this complex flow field and by the presence of red blood cells.