Experimental and theoretical investigations of the dynamics of collective phenomena in blood II: Towards a physically more realistic model

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The aim of the present project is to study via experiments and computer simulations suspensions of red blood cells (RBCs) under externally imposed shear flow with a focus on collective dynamics and non-linear response at high concentrations. This project builds upon the part I of the same initiative entitled “Experimental and theoretical investigations of the dynamics of collective phenomena in blood I: Idealized vesicle/fluid droplet models”. Thanks to the achievements of the previous project (cf. progress report below), we are now able to investigate a physically more realistic –as compared to droplets– model of RBCs in the parameter range of interest in terms of shear rate, cell deformability and volume fraction/ hematocrit (the portion of the channel volume occupied by the cells). Results obtained with the newly developed model are very promising and deserve more elaborate investigations. In particular, the following open issues shall be addressed both experimentally and via computer simulations. • Shear-induced diffusivity: Even at a rather low volume fraction of ≈6%, our simulations show that (flow-mediated) collisions between red blood cells significantly alter their individual dynamics. In addition to the flow, RBCs seem to exhibit a diffusive motion at sufficiently large times with, approximately, a Gaussian distribution of particle displacements. This is best visible when monitoring displacements perpendicular to the flow direction. An interesting question here is how this shear-induced diffusion varies with imposed shear rate and how does this compare to the shear rate dependence of the effective viscosity. Furthermore, at a sufficiently high hematocrit, the suspension starts to develop a solid-like character and issues such as dynamic yielding and shear driven melting become relevant. In this case, we expect strong deviations from Gaussian behavior to develop at some typical time and length scales. It would then be very interesting to study how these length and time scales depend on shear rate and hematocrit. • Cooperative motion: An issue, closely related to the above aspect, concerns the possibility of dynamic correlations. Indeed, a non-Gaussian distribution of particle displacements provides a hint on the presence of correlations in the dynamics of particles (here red blood cells). It is interesting to investigate whether and under which conditions dynamically correlated clusters of RBCs exist. We expect the life time of these clusters to decrease with the imposed shear rate and to increase at higher concentration/hematocrit. Similar to the above raised question on the relation between shear-induced diffusion and viscosity, it is very interesting to study whether physical laws governing the life time of dynamically correlated clusters compare to those describing diffusion and viscosity. Answer to this question is far from being trivial and will certainly require a thorough study of the length scale of these clusters as a function of shear rate and hematocrit: Diffusion over a distance of a particle size may be sufficient to destroy small clusters. However, particle motion on a lager scale may be necessary for a decay of dynamic correlations within a cluster which contains a large number of particles. • Yield stress: As already mentioned, at high concentrations, suspensions of red blood cellsmay develop a solid-like character. In addition to the above discussed dynamic issues, thismay also manifest itself in the emergence of a yield stress (defined here as the minimumstress needed to maintain the flow). The presence of a finite yield stress may have severebiological consequences, since it may lead to a flow blockage if the viscous stress in theblood vessel falls below the yield stress. As can be shown by a simple argument, this may indeed occur in narrow vessels, if the vessel radius is below a certainvalue. Therefore, it is important to study the issue of yield stress and its dependence onhematocrit and other system parameters.• The effect of RBC-deformability: The above issues do in general depend on the deformability of red blood cells. For instance, the effect of cell-cell collision and the resulting effective diffusion is expected to be felt at a lower volume fraction if the deformability of red blood cells is reduced. Similarly, with increasing cell-stiffness (caused e.g. via sickle cell anemia or other widespread diseases such as diabetes mellitus or malaria) one expects that yield stress may grow faster with hematocrit and thus lead to a higher probability of flow blockage. A question of interest here is whether both shear rate and deformability/cell-stiffness play qualitatively independent roles, or a single dimensionless parameter such as the ratio of shear energy to the elastic deformation energy is sufficient to describe the system behavior in a certain parameter-range.