Session EG: Biofluids IV: Cellular I

Complex motions of vesicles and capsules in flow

Membrane-bound particles exhibit rich dynamics when placed in flow. For example, in simple shear flow, vesicles made of lipid bilayers tank-tread or tumble. Capsules and red blood cells also show oscillations in the tank-treading inclination angle, called swinging. This motion originates from membrane shear--elasticity and non--spherical unstressed shape. We develop an analytical theory that quantitatively describes the swinging dynamics. Our analysis takes into account that the membrane is deformable, incompressible, and resists bending and shearing. Analytical results for the shape evolution are derived by considering a nearly-spherical particle shape. The phase diagram is constructed and compared to previous models which assume fixed ellipsoidal shape. Dynamics in quadratic and time-dependent flows is also discussed. Floquet analysis is conducted to investigate the vesicle dynamics and conditions for chaotic shape and flow dynamics are established.   

Why do red blood cells have asymmetric shapes even in a symmetric flow?

Understanding why red blood cells (RBCs) move with an asymmetric shape (slipper-like shape) in small blood vessels is a longstanding puzzle of the blood circulatory research. We discover, by considering a phospholipid bilayer model (a biomimetic system of RBCs), that slipper results from the loss of stability of the symmetric shape. It is shown that the birth of slipper results in a significant decline of velocity difference between the cell and the imposed flow, providing thus higher flow efficiency for RBCs. An increase of membrane rigidity is found to lead to a dramatic change of the slipper morphology, offering thus a potential diagnostic for cell pathologies.   

Tank-treading, swinging, and tumbling of elastic capsules

It is well known that deformable capsules, vesicles, and red blood cells undergo tank-treading or tumbling motion when freely suspended in shear flows. Recent experiments have shown the existence of a trembling or vacillating-breathing mode as well. Here we present three-dimensional simulations on the dynamics of elastic capsules in shear flow. Our objective is to investigate these different regimes of capsule dynamics, and the coupling between the shape deformation and orientation dynamics. By progressively increasing the viscosity ratio of the internal-to-external fluids at low shear rates, we predict the three distinct modes of motion: a swinging or oscillatory (OS) mode, a vacillating-breathing (VB) mode, and a pure tumbling mode (TU). We show how the coupling between the shape deformation and orientation dynamics influences the transition from the OS to VB to TU modes. At higher shear rates, we predict three new classes of transient motions during which the capsule switches from one mode to the other over time as (i) VB to OS, (ii) TU to VB to OS, and (iii) TU to VB. Phase diagrams showing various regimes are presented.   

Simulations of the tumbling and tank treading motions of cells immersed in fluid flow

We describe the development of computational techniques to study the deformation of cells modeled as liquid capsules enclosed by thin shells suspended in fluid flow. Computations are performed for cells with spherical, ellipsoidal and biconcave unstressed shapes over a wide range of the dimensionless shear rate and for a broad range of the ratio of the internal to surrounding fluid viscosities. Results for small deformations of initially spherical capsules are in quantitative agreement with analytic predictions. Under large deformations, the results show that spherical capsules deform to stationary configurations and the membranes undergo steady tank-treading motion. For capsules of ellipsoidal and biconcave unstressed shapes, the capsules exhibit either tumbling, tank-treading of the membrane about the viscous interior with periodic oscillations of the orientation angle, or intermittent behaviour in which the two modes occur alternately depending on the viscosity, membrane elasticity and shear rate. Our method provides an efficient way to study the tank-treading-to-tumbling transition of red blood cells in shear flows as the shear rate decreases. Observations of such motions may provide a sensitive mean of assessing cell membrane properties. Finally, we also describe simulations of the long-time behavior of a dense suspension of red-blood cells in a micro-channel to illustrate the efficiency of the method.   

Dynamics of suspensions of elastic capsules flowing in confined geometries

Modeling the behavior of fluid-filled capsules (a simple representation of red blood cells and vesicles), is not only important to understand biological processes, such as blood flow in the microcirculation, but also to help design and improve microfluidic devices for characterizing or separating such particles. The present work describes simulations of large numbers of deformable capsules with various properties in confined geometries. Our algorithm incorporates a General-Geometry-Ewald-Like method (GGEM) for efficiently calculating hydrodynamic interactions (O(N)) in an immersed-boundary method. With our algorithm, we have addressed several issues. The ability to quickly simulate large number of particles enables examinations of not only of the competition between shear-induced diffusion and wall-induced hydrodynamic migration of single particles, but also exploration of concentration effects and segregation by size, shape and/or deformability. Combined with the simulation of grooved channels, we propose a methodology to separate these cells depending on their deformability and size. Finally, the effect of addition of long-chained polymer molecules in blood flow, known to lower blood pressure, is investigated.   

Numerical simulation of platelet margination in microcirculation

The adhesion of platelets to vascular walls is the first step in clotting. This process critically depends on the preferential concentration of platelets near walls. The presence of red blood cells, which are the predominant blood constituents, is known to affect the steady state platelet concentration and the dynamic platelet margination, but the underlying mechanism is not well understood to-day. We use a direct numerical simulation to study the platelet margination process, with particular emphasis on the Stokesian hydrodynamic interactions among red cells, platelets, and vessel walls. Well-known mechanical models are used for the shearing and bending stiffness of red cell membranes, and the stiffer platelets are modeled as rigid discoids. A boundary integral formulation is used to solve the flow field, where the numerical solution procedure is accelerated by a parallel $O(N \log N)$ smooth particle-mesh Ewald method. The effects of red cell hematocrit and deformability will be discussed.   

The motion of a single red blood cell in a capillary

The collective vaso-occlusive event in sickle cell disease induced by multiple red blood cells (RBC's) has recently been evoked and controlled in vitro using a microfluidic platform [1]. The increase in the cells' stiffness in this disease is believed to be a predominant factor at the onset of the occlusion. We report here the motion of a single swollen RBC in a capillary. We use a tapered glass capillary with inner diameter as low as 3 microns, and track the squeezed cell driven by a controlled pressure drop. This allows us to simultaneously measure the variations of the RBC velocity as a function of the pressure gradient and of the local capillary diameter in a single experiment. We show that under certain regimes of confinement, the velocity increases with the pressure head with a characteristic power-law. We analyze our findings in terms of a elasto-hydrodynamical model for soft lubrication.\\[4pt] [1] Higgins et al., Proc. Natl. Acad. Sci. U.S.A. {\bf104}: 20496 (2007).   

Simulation of red blood cells flowing over wall-bound cells

Inter-cellular dynamics play a critical role in the phenomenology of the microcirculation. We present a quantitative investigation of the forces exerted by red cells on protrusions on a microvessel of diameter around 12 $\mu$m, which is $1.5$ times the longest dimension of a red cell at rest. This configuration serves as a model for white blood cells (leukocytes), which can bind nearly statically to the endothelial cells as part of the inflammation response. The simulation tools are based on an $O(N \log N)$ boundary integral formulation. It permits the cells to both be realistically flexible and to approach to very close separation distances. The red blood cells are modeled as finite-deformation elastic membranes with strong resistance to surface dilatation and relatively small but finite resistance to bending. The no-slip condition is applied on the protrusion as well as the vessel walls. Simulation results show that these forces are significantly augmented by the particulate character of blood. For a tube hematocrit of $30\%$ and a hemispherical protrusion with a height to tube diameter ratio of $0.4$, the average forces are increased by about $50\%$ and the local forces by more than two folds relative to forces from an effective viscosity homogenized blood. Different flow configurations are considered and analyzed.   

A computational study of male pronuclear migration in the C. elegans embryo

After fertilization the one-celled C. elegans embryo undergoes a series of complex but stereotyped dynamics that lead to proper progression of early development. This system offers a great opportunity to combine modeling and experimental approaches to learn about the biophysical properties underlying fundamental developmental events. In particular, we study the mechanisms underlying male pronuclear migration using a detailed computational model that captures important features of the system. We model the cytoplasmic flow as a Stokes fluid, accounting for the enclosing cell geometry. The fluid is two-way coupled to a rigid pronucleus that is subject to forces computed based on the dynamic instability model of microtubule dynamics. We use the computational model to study force models for microtubule based motility as well as the effects of the fluid drag and geometric confinement on the pronucleus and microtubules.