A simple model to understand the effect of membrane shear elasticity and stress-free shape on the motion of red blood cells in shear flow

The effect of rigid cells on blood viscosity: linking rheology and sickle cell anemia

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.

Heterogeneity of Red Blood Cells: Causes and Consequences

Mean values of hematological parameters are currently used in the clinical laboratory settings to characterize red blood cell properties. Those include red blood cell indices, osmotic fragility test, eosin 5-maleimide (EMA) test, and deformability assessment using ektacytometry to name a few. Diagnosis of hereditary red blood cell disorders is complemented by identification of mutations in distinct genes that are recognized "molecular causes of disease." The power of these measurements is clinically well-established. However, the evidence is growing that the available information is not enough to understand the determinants of severity of diseases and heterogeneity in manifestation of pathologies such as hereditary hemolytic anemias. This review focuses on an alternative approach to assess red blood cell properties based on heterogeneity of red blood cells and characterization of fractions of cells with similar properties such as density, hydration, membrane loss, redox state, Ca2+ levels, and morphology. Methodological approaches to detect variance of red blood cell properties will be presented. Causes of red blood cell heterogeneity include cell age, environmental stress as well as shear and metabolic stress, and multiple other factors. Heterogeneity of red blood cell properties is also promoted by pathological conditions that are not limited to the red blood cells disorders, but inflammatory state, metabolic diseases and cancer. Therapeutic interventions such as splenectomy and transfusion as well as drug administration also impact the variance in red blood cell properties. Based on the overview of the studies in this area, the possible applications of heterogeneity in red blood cell properties as prognostic and diagnostic marker commenting on the power and selectivity of such markers are discussed.

Optical Tweezers in Studies of Red Blood Cells

Optical tweezers (OTs) are innovative instruments utilized for the manipulation of microscopic biological objects of interest. Rapid improvements in precision and degree of freedom of multichannel and multifunctional OTs have ushered in a new era of studies in basic physical and chemical properties of living tissues and unknown biomechanics in biological processes. Nowadays, OTs are used extensively for studying living cells and have initiated far-reaching influence in various fundamental studies in life sciences. There is also a high potential for using OTs in haemorheology, investigations of blood microcirculation and the mutual interplay of blood cells. In fact, in spite of their great promise in the application of OTs-based approaches for the study of blood, cell formation and maturation in erythropoiesis have not been fully explored. In this review, the background of OTs, their state-of-the-art applications in exploring single-cell level characteristics and bio-rheological properties of mature red blood cells (RBCs) as well as the OTs-assisted studies on erythropoiesis are summarized and presented. The advance developments and future perspectives of the OTs' application in haemorheology both for fundamental and practical in-depth studies of RBCs formation, functional diagnostics and therapeutic needs are highlighted.

Self-organization of red blood cell suspensions under confined 2D flows

Dynamic self-organized structures with long-range order have been observed in emulsions and suspensions of particles under confined flows. Here, experiments on red blood cell suspensions under quasi-2D confined flows and numerical simulations were combined to explore long-distance self-organization as a function of the channel width, red blood cell concentration and flow rate. They reveal and quantitatively describe the existence of red blood cell long-range alignments and heterogeneous cross-stream concentration profiles characterized by red blood cell-enriched bands parallel to the flow. Numerical simulations show that, in addition to the degree of lateral confinement, the key factor for the structural self-organization of a suspension of particles under a confined flow is the deformability of the constituent particles.

Self-assembly of phospholipid molecules in solutions under shear flows: Microstructures and phase diagrams

Shear-induced microstructures and their phase diagrams were investigated for phospholipid molecules in aqueous solution by dissipative particle dynamic simulation. Self-assembled microstructures, including spherical and cylindrical micelles, spherical vesicles, lamellae, undulated lamellae, perforated lamellae, and continuous networks, were observed under various shear flows and phospholipid concentrations, where the spatial inhomogeneity and symmetry were analysed. A series of phase diagrams were constructed based on the chain lengths under various phospholipid concentrations. The phase distributions showed that the structures with spherical symmetry could be shear-induced to structures with cylindrical symmetry in the dilute solutions. In the semi-concentrated solutions, the lamellae were located in most spaces under zero shear flows, which could be shear-induced into undulated lamellae and then into cylindrical micelles. For the concentrated solutions, the strong shear flows oriented the directions of multilayer lamellae and phase transitions appeared between several cylindrical network structures. These observations on shear-induced microstructures and their distributions revealed a promising approach that could be used to design bio-microstructures based on phospholipid molecules under shear flows.

Flow-Induced Transitions of Red Blood Cell Shapes under Shear

A recent study of red blood cells (RBCs) in shear flow [Lanotte et al., Proc. Natl. Acad. Sci. U.S.A. 113, 13289 (2016)PNASA60027-842410.1073/pnas.1608074113] has demonstrated that RBCs first tumble, then roll, transit to a rolling and tumbling stomatocyte, and finally attain polylobed shapes with increasing shear rate, when the viscosity contrast between cytosol and blood plasma is large enough. Using two different simulation techniques, we construct a state diagram of RBC shapes and dynamics in shear flow as a function of shear rate and viscosity contrast, which is also supported by microfluidic experiments. Furthermore, we illustrate the importance of RBC shear elasticity for its dynamics in flow and show that two different kinds of membrane buckling trigger the transition between subsequent RBC states.

The dynamics of a healthy and infected red blood cell in flow through constricted channels: A DPD simulation

Understanding the dynamics of red blood cell (RBC) motion under in silico conditions is central to the development of cost-effective diagnostic tools. Specifically, unraveling the relationship between the rheological properties and the nature of shape change in the RBC (healthy or infected) can be extremely useful. In case of malarial infection, RBC progressively loses its deformability and tends to occlude the microvessel. In the present study, detailed mesoscopic simulations are performed to investigate the deformation dynamics of an RBC in flow through a constricted channel. Specifically, the manifestation of viscous forces (through flow rates) on the passage and blockage characteristics of a healthy red blood cell (hRBC) vis-á-vis an infected red blood cell (iRBC) are investigated. A finite-sized dissipative particle dynamics framework is used to model plasma in conjunction with a discrete model for the RBC. Instantaneous wall boundary method was used to model no-slip wall boundary conditions with a good control on the near-wall density fluctuations and compressibility effects. To investigate the microvascular occlusion, the RBC motion through 2 types of constricted channels, viz, (1) a tapered microchannel and (2) a stenosed-type microchannel, were simulated. It was observed that the deformation of an infected cell was much less compared with a healthy cell, with an attendant increase in the passage time. Apart from the qualitative features, deformation indices were obtained. The deformation of hRBC was sudden, while the iRBC deformed slowly as it traversed through the constriction. For higher flow rates, both hRBC and iRBC were found to undergo severe deformation. Even under low flow rates, hRBC could easily traverse past the constricted channel. However, for sufficiently slow flow rates (eg, capillary flows), the microchannel was found to be completely blocked by the iRBC.

Red cells' dynamic morphologies govern blood shear thinning under microcirculatory flow conditions

Blood viscosity decreases with shear stress, a property essential for an efficient perfusion of the vascular tree. Shear thinning is intimately related to the dynamics and mutual interactions of RBCs, the major component of blood. Because of the lack of knowledge about the behavior of RBCs under physiological conditions, the link between RBC dynamics and blood rheology remains unsettled. We performed experiments and simulations in microcirculatory flow conditions of viscosity, shear rates, and volume fractions, and our study reveals rich RBC dynamics that govern shear thinning. In contrast to the current paradigm, which assumes that RBCs align steadily around the flow direction while their membranes and cytoplasm circulate, we show that RBCs successively tumble, roll, deform into rolling stomatocytes, and, finally, adopt highly deformed polylobed shapes for increasing shear stresses, even for semidilute volume fractions of the microcirculation. Our results suggest that any pathological change in plasma composition, RBC cytosol viscosity, or membrane mechanical properties will affect the onset of these morphological transitions and should play a central role in pathological blood rheology and flow behavior.