Comparison of erythrocyte dynamics in shear flow under different stress-free configurations

Abstract

An open question that has persisted for decades is whether the cytoskeleton of a red blood cell is stress-free or under a stress. This question is important in the context of theoretical modeling of cellular motion under a flowing condition where it is necessary to make an assumption about the stress-free state. Here, we present a 3D numerical study to compare the cell dynamics in a simple shear flow under two different stress-free states, a biconcave discocyte representing the resting shape of the cell, and a nearly spherical oblate shape. We find that whether the stress-free states make a significant difference or not depends on the viscosity of the suspending medium. If the viscosity is close to that of blood plasma, the two stress-free states do not show any significant difference in cell dynamics. However, when the suspending medium viscosity is well above that of the physiological range, as in many in vitro studies, the shear rate separating the tank-treading and tumbling dynamics is observed to be higher for the biconcave stress-free state than the spheroidal state. The former shows a strong shape oscillation with repeated departures from the biconcave shape, while the latter shows a nearly stable biconcave shape. It is found that the cell membrane in the biconcave stress-free state is under a compressive stress and a weaker bending force density, leading to a periodic compression of the cell. The shape oscillation then leads to a higher energy barrier against membrane tank-tread leading to an early transition to tumbling. However, if the cells are released with a large off-shear plane angle, the oscillations can be suppressed due to an azimuthal motion of the membrane along the vorticity direction leading to a redistribution of the membrane points and lowering of the energy barrier, which again results in a nearly similar behavior of the cells under the two different stress-free states. A variety of off-shear plane dynamics is observed, namely, rolling, kayaking, precession, and a new dynamics termed “hovering.” For the physiological viscosity range, the shear-plane tumbling appears to be relatively less common, while the rolling is observed to be more stable.

Mechanical response of red blood cells entering a constriction

“…In the absence of any induced torque, i.e., for a freely suspended particle with T * 0 o ¼ 0, then the particle angular velocity is simply one half of the local flow vorticity. 46 Note, however, that Eq. (1) is only valid for spheres, and a more complicated torque balance applies to other shapes.…”

“…A key consistency check is to determine whether the motions are qualitatively consistent with the applied shear stresses. Although the motion of RBCs has been the subject of extensive simulation and computational efforts, [42][43][44][45][46] little work has examined the motion of RBCs entering a constriction as tested here. In the absence of detailed predictions, we instead examine the limiting case of perfectly rigid ellipsoids.…”

Inertial migrations of cylindrical particles in rectangular microchannels: Variations of equilibrium positions and equivalent diameters

“…Available experimental evidence later reveals that the RBC under rolling motion has a stabilized cell membrane and can maintain its biconcave disk-like shape. [58][59][60] Under physiological conditions, a mature RBC is about 6-8 µm in diameter and 2 µm in thickness. A smooth-edged disk-like particle with L/D = 4:15 is used to model the RBC with 7.5 µm in diameter and 2 µm in thickness.…”

Motion of an elastic capsule in a constricted microchannel

“…Their deformations are measured as the displacements from a reference shape that is assumed to be spherical with radius a c (note that the debate is open on the possibility that a stress-free spherical shape is a correct descriptions for red blood cells [26,27]). We have chosen to describe the capsule through a neo-Hookean constitutive law according to which the local strain energy function is…”