Dynamics of red blood cells in oscillating shear flow

Abstract

We present a three-dimensional computational study of fully deformable red blood cells of the biconcave resting shape subject to sinusoidally oscillating shear flow. A comprehensive analysis of the cell dynamics and deformation response is considered over a wide range of flow frequency, shear rate amplitude and viscosity ratio. We observe that the cell exhibits either a periodic motion or a chaotic motion. In the periodic motion, the cell reverses its orientation either by passing through the flow direction (horizontal axis) or by passing through the flow gradient (vertical axis). The chaotic dynamics is characterized by a non-periodic sequence of horizontal and vertical reversals. The study provides the first conclusive evidence of the chaotic dynamics of fully deformable cells in oscillating flow using a deterministic numerical model without the introduction of any stochastic noise. In certain regimes of the periodic motion, the initial conditions are completely forgotten and the cells become entrained in the same sequence of horizontal reversals. We show that chaos is only possible in certain frequency bands when the cell membrane can rotate by a certain amount, allowing the cells to swing near the maximum shear rate. As such, the bifurcation between the horizontal and vertical attractors in phase space always occurs via a swinging inflection. While the reversal sequence evolves in an unpredictable way in the chaotic regime, we find a novel result that there exists a critical inclination angle at the instant of flow reversal which determines whether a vertical or horizontal reversal takes place, and is independent of the flow frequency. The chaotic dynamics, however, occurs at a viscosity ratio less than the physiological values. We further show that the cell shape in oscillatory shear at large amplitude exhibits a remarkable departure from the biconcave shape, and that the deformation is significantly greater than that in steady shear flow. A large compression of the cells occurs during the reversals which leads to over/undershoots in the deformation parameter. We show that due to the large deformation experienced by the cells, the regions of chaos in parameter space diminish and eventually disappear at high shear rate, in contradiction to the prediction of reduced-order models. While the findings bolster support for reduced-order models at low shear rate, they also underscore the important role that the cell deformation plays in large-amplitude oscillatory flows.

Modeling of biomechanics and biorheology of red blood cells in type-2 diabetes mellitus

“…Decreased cell deformability and increased cell volume in T2DM have shown significant implications for microcirculatory alterations. Computational modeling and simulations help in predicting how RBCs behave in shear flow and providing insights into how viscous flow transforms RBC shapes, and vice versa, how deformed RBCs distort the surrounding flow (24,42,43,(78)(79)(80)(81)(82). Here, in order to address the effects of cell elasticity and shape on the biorheological behavior of individual T2DM RBCs, we investigate the dynamic behavior of T2DM RBCs in a microfluidic channel with constriction.…”

Complex viscosity of dilute capsule suspensions: a numerical study

“…These previous studies can be categorized into the research field of biorheology because blood contains many red blood cells, which can be modelled as the capsules. In recent years, several researchers started to investigate the dynamics of capsules in unsteady flow (Zhao and Bagchi 2011;Matsunaga et al 2015;Zhu et al 2015;Cordasco and Bagchi 2016). In our previous study (Matsunaga et al 2015), we reported the capsule deformation under oscillating shear flow.…”

Possible Error in Reflection Pulse Oximeter Readings as a Result of Applied Pressure

“…However, in capillary and arterioles, it is reasonable to assume that the development of the branched structures is limited, and linear aggregates prevail. The average length of the RBC aggregates is dependent on shear forces and thus, varies periodically with changes in the blood flow [9, 10]. According to this relationship, the frequency of disassembling and reassembling the aggregates is controlled by the heartbeat, which evokes shear force modulation [11].…”

“…The aggregation and disaggregation of RBCs are dynamic processes. This shear-dependent variation is the primary cause of the non-Newtonian behavior of blood in human blood vessels [10]. As blood pressure increases to its peak, the flow velocity and shear rate gradually increase, and as the pressure decreases, the velocity and shear rate decrease.…”