Shapes and Dynamics of Blood Cells in Poiseuille and Shear Flows

The dynamics, shape, deformation, and orientation of red blood cells in microcirculation affect the rheology, flow resistance and transport properties of whole blood. This leads to important correlations of cellular and continuum scales. Furthermore, the dynamics of RBCs subject to different flow conditions and vessel geometries is relevant for both fundamental research and biomedical applications (e.g drug delivery). In this thesis, the behaviour of RBCs is investigated for different flow conditions via computer simulations. We use a combination of two mesoscopic particle-based simulation techniques, dissipative particle dynamics and smoothed dissipative particle dynamics. We focus on the microcapillary scale of several μm. At this scale, blood cannot be considered at the continuum but has to be studied at the cellular level. The connection between cellular motion and overall blood rheology will be investigated. Red blood cells are modelled as viscoelastic objects interacting hydrodynamically with a viscous fluid environment. The properties of the membrane, such as resistance against bending or shearing, are set to correspond to experimental values. Furthermore, thermal fluctuations are considered via random forces. Analyses corresponding to light scattering measurements are performed in order to compare to experiments and suggest for which situations this method is suitable. Static light scattering by red blood cells characterises their shape and allows comparison to objects such as spheres or cylinders, whose scattering signals have analytical solutions, in contrast to those of red blood cells. Dynamic light scattering by red blood cells is studied concerning its suitability to detect and analyse motion, deformation and membrane fluctuations. Dynamic light scattering analysis is performed for both diffusing and flowing cells. We find that scattering signals depend on various cell properties, thus allowing to distinguish different cells. The scattering of diffusing cells allows to draw conclusions on their bending rigidity via the effective diffusion coefficient. The scattering of flowing cells allows to draw conclusions on the shear rate via the scattering amplitude correlation. In flow, a RBC shows different shapes and dynamic states, depending on conditions such as confinement, physiological/pathological state and cell age. Here, two essential flow conditions are studied: simple shear flow and tube flow. Simple shear flow as a basic flow condition is part of any more complex flow. The velocity profile is linear and shear stress is homogeneous. In simple shear flow, we find a sequence of different cell shapes by increasing the shear rate. With increasing shear rate, we find rolling cells with cup shapes, trilobe shapes and quadrulobe shapes. This agrees with recent experiments. Furthermore, the impact of the initial orientation on the dynamics is studied. To study crowding and collective effects, systems with higher haematocrit are set up. Tube flow is an idealised model for the flow through cylindric microvessels. Without cell, a parabolic flow profile prevails. A single red blood cell is placed into the tube and subject to a Poiseuille profile. In tube flow, we find different cell shapes and dynamics depending on confinement, shear rate and cell properties. For strong confinements and high shear rates, we find parachute-like shapes. Although not perfectly symmetric, they are adjusted to the flow profile and maintain a stationary shape and orientation. For weak confinements and low shear rates, we find tumbling slippers that rotate and moderately change their shape. For weak confinements and high shear rates, we find tank-treading slippers that oscillate in a limited range of inclination angles and strongly change their shape. For the lowest shear rates, we find cells performing a snaking motion. Due to cell properties and resultant deformations, all shapes differ from hitherto descriptions, such as steady tank-treading or symmetric parachutes. We introduce phase diagrams to identify flow regimes for the different shapes and dynamics. Changing cell properties, the regime borders in the phase diagrams change. In both flow types, both the viscosity contrast and the choice of stress-free shape are important. For in vitro experiments, the solvent viscosity has often been higher than the cytosol viscosity, leading to a different pattern of dynamics, such as steady tank-treading. The stress-free state of a RBC, which is the state at zero shear stress, is still controversial, and computer simulations enable direct comparisons of possible candidates in equivalent flow conditions.

Computer simulations of soft particles in flow

Understanding the dynamics of blood cells is a crucial element to discover biological mechanisms, to develop new efficient drugs, design sophisticated microfluidic devices, for diagnostics. In this work, we focus on the dynamics of red blood cells in microvascular flow. Microvascular blood flow resistance has a strong impact on cardiovascular function and tissue perfusion. The flow resistance in microcirculation is governed by flow behavior of blood through a complex network of vessels, where the distribution of red blood cells across vessel cross-sections may be significantly distorted at vessel bifurcations and junctions. We investigate the development of blood flow and its resistance starting from a dispersed configuration of red blood cells in simulations for different hematocrits, flow rates, vessel diameters, and aggregation interactions between red blood cells. Initially dispersed red blood cells migrate toward the vessel center leading to the formation of a cell-free layer near the wall and to a decrease of the flow resistance. The development of cell-free layer appears to be nearly universal when scaled with a characteristic shear rate of the flow, which allows an estimation of the length of a vessel required for full flow development, $l_c \approx 25D$, with vessel diameter $D$. Thus, the potential effect of red blood cell dispersion at vessel bifurcations and junctions on the flow resistance may be significant in vessels which are shorter or comparable to the length $l_c$. The presence of aggregation interactions between red blood cells lead in general to a reduction of blood flow resistance. The development of the cell-free layer thickness looks similar for both cases with and without aggregation interactions. Although, attractive interactions result in a larger cell-free layer plateau values. However, because the aggregation forces are short-ranged at high enough shear rates ($\bar{\dot{\gamma}} \gtrsim 50~\text{s}^{-1}$) aggregation of red blood cells does not bring a significant change to the blood flow properties. Also, we develop a simple theoretical model which is able to describe the converged cell-free-layer thickness with respect to flow rate assuming steady-state flow. The model is based on the balance between a lift force on red blood cells due to cell-wall hydrodynamic interactions and shear-induced effective pressure due to cell-cell interactions in flow. We expect that these results can also be used to better understand the flow behavior of other suspensions of deformable particles such as vesicles, capsules, and cells. Finally, we investigate segregation phenomena in blood as a two-component suspension under Poiseuille flow, consisting of red blood cells and target cells. The spatial distribution of particles in blood flow is very important. For example, in case of nanoparticle drug delivery, the particles need to come closer to microvessel walls, in order to adhere and bring the drug to a target position within the microvasculature. Here we consider that segregation can be described as a competition between shear-induced diffusion and the lift force that pushes every soft particle in a flow away from the wall. In order to investigate the segregation, on one hand, we have 2D DPD simulations of red blood cells and target cell of different sizes, on the other hand the Fokker-Planck equation for steady state. For the equation we measure force profile, particle distribution and diffusion constant across the channel. We compare simulation results with those from the Fokker-Planck equation and find a very good correspondence between the two approaches. Moreover, we investigate the diffusion behavior of target particles for different hematocrit values and shear rates. Our simulation results indicate that diffusion constant increases with increasing hematocrit and depends linearly on shear rate. The third part of the study describes development of a simulation model of complex vascular geometries. The development of the model is important to reproduce vascular systems of small pieces of tissues which might be gotten from MRI or microscope images. The simulation model of the complex vascular systems might be divided into three parts: modeling the geometry, developing in- and outflow boundary conditions, and simulation domain decomposition for an efficient computation. We have found that for the in- and outflow boundary conditions it is better to use the SDPD fluid than DPD one because of the density fluctuations along the channel of the latter. During the flow in a straight channel, it is difficult to control the density of the DPD fluid. However, the SDPD fluid has not that shortcoming even in more complex channels with many branches and in- and outflows because the force acting on particles is calculated also depending on the local density of the fluid.