Introduction and motivation According to the literature, the annual deaths caused by cardiovascular diseases are dramatically increasing.^1,2 Atherosclerosis is a cardiovascular disease characterised by increasing arterial inflammation, which causes the blockage of the arterial lumen and the reduction of blood supply to important parts of the human body. This process is driven by fluid-mechanical forces.³ Therefore, understanding variations in blood flow characteristics driven by the erythrocytes might result in new insights on atheroma development. Hence, in this work, we present an in-deep study of haemorheological blood flow, under disease condition. Formerly, we presented a model of blood-erythrocytes in large arteries,³ comprising an established multiphase technique.^4,5 This was coupled with a new fluid-structure interaction (FSI) methodology,^3,6,7 which is based on immersed boundary techniques.⁸ Prior research reported on changes in flow due to plasma-erythrocytes interactions.⁹ This leads to non-Newtonian effects that are here addressed considering the effects of growing haematocrit.^3,10,11 Methodology: The interaction between blood and the artery is simulated using an immersed boundary-based technique.^3,7 The plasma is modelled as a Newtonian incompressible fluid using the Navier-Stokes equations.^3,7 The erythrocytes are modelled as spherical particles.³ Moreover, forces resulting from the plasma-erythrocytes interactions are considered to be elastic and based on Hooke’s law (DEM model of collisions), which is attained by using a multiphase flow methodology.⁴

Results Simulations of a single-phase fluid-structure interaction (FSI) model that mimic the coupling blood-artery have yielded results comparable with the literature.^3,6,10,11 This was important to assess both the integrity and the capability of the methodology. To analyse how the erythrocytes modulate flow, we have considered a series of volume fractions (0.00, 0.15, 0.30, and 0.45) -- hematocrit. We observed that, while differences in the distribution of velocities increase with increasing hematocrit, flow recirculation decreases proportionally. This indicates that the inclusion of erythrocytes might result in flow laminarization. The variations in the flow characteristics are more prominent at predilection sites for plaque deposition. We infer this might result from a natural enhancement of flow features, due to the arterial geometry at those locations.

References

1. S. Mendis et al. WHO 2011

2. BHF CPANCDP Annual Statistics. 2014

3. G. Pereira. Imperial College London, Thesis submitted 2015

4. C. Crowe et al. CRC Press 1998

5. Y. Tsuji et al. Powder Tech. 1992

6. G. Pereira. Biophy J. 2013

7. G. Pereira et al. SIAM MMS under review 2015

8. C.S. Peskin. J. Comput. Phys. 1972

9. J. Jung et al. J. Biomech. 2006

10. G. Pereira et al. BAS. 2014

11. G. Pereira et al. BAS/BSCR 2015

12. Zhao et al. J. Comput. Phy. 2011