Dynamics of red blood cells in oscillating shear flow

2016 ◽  
Vol 800 ◽  
pp. 484-516 ◽  
Author(s):  
Daniel Cordasco ◽  
Prosenjit Bagchi
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Red Blood Cells ◽  
Periodic Motion ◽  
Blood Cells ◽  
Large Amplitude ◽  
Chaotic Dynamics ◽  
Viscosity Ratio ◽  
Reduced Order Models ◽  
Reduced Order

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.

State diagram for wall adhesion of red blood cells in shear flow: from crawling to flipping

Soft Matter ◽  
2019 ◽  
Vol 15 (27) ◽  
pp. 5511-5520 ◽  
Author(s):  
Anil K. Dasanna ◽  
Dmitry A. Fedosov ◽  
Gerhard Gompper ◽  
Ulrich S. Schwarz
Keyword(s):  
Angular Momentum ◽  
Shear Rate ◽  
Shear Flow ◽  
Red Blood Cells ◽  
Blood Cells ◽  
State Diagram ◽  
Momentum Conservation ◽  
Collision Dynamics ◽  
Multiparticle Collision Dynamics

Using multiparticle collision dynamics with angular momentum conservation, we investigated the role of shear rate, stiffness and viscosity contrast for the adhesion of biconcave deformable cells or capsules in shear flow.

The Effect of Red Blood Cells on the ADP-induced Aggregation of Human Platelets in Flow Through Tubes

1990 ◽  
Vol 63 (01) ◽  
pp. 112-121 ◽  
Author(s):  
David N Bell ◽  
Samira Spain ◽  
Harry L Goldsmith
Keyword(s):  
Platelet Aggregation ◽  
Shear Rate ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Platelet Rich Plasma ◽  
Mean Transit Time ◽  
White Blood Cells ◽  
Aggregate Size ◽  
Human Platelets ◽  
Induced Aggregation

SummaryThe effect of red blood cells, rbc, and shear rate on the ADPinduced aggregation of platelets in whole blood, WB, flowing through polyethylene tubing was studied using a previously described technique (1). Effluent WB was collected into 0.5% glutaraldehyde and the red blood cells removed by centrifugation through Percoll. At 23°C the rate of single platelet aggregtion was upt to 9× greater in WB than previously found in platelet-rich plasma (2) at mean tube shear rates Ḡ = 41.9,335, and 1,920 s−1, and at both 0.2 and 1.0 µM ADP. At 0.2 pM ADP, the rate of aggregation was greatest at Ḡ = 41.9 s−1 over the first 1.7 s mean transit time through the flow tube, t, but decreased steadily with time. At Ḡ ≥335 s−1 the rate of aggregation increased between t = 1.7 and 8.6 s; however, aggregate size decreased with increasing shear rate. At 1.0 µM ADP, the initial rate of single platelet aggregation was still highest at Ḡ = 41.9 s1 where large aggregates up to several millimeters in diameter containing rbc formed by t = 43 s. At this ADP concentration, aggregate size was still limited at Ḡ ≥335 s−1 but the rate of single platelet aggregation was markedly greater than at 0.2 pM ADP. By t = 43 s, no single platelets remained and rbc were not incorporated into aggregates. Although aggregate size increased slowly, large aggregates eventually formed. White blood cells were not significantly incorporated into aggregates at any shear rate or ADP concentration. Since the present technique did not induce platelet thromboxane A2 formation or cause cell lysis, these experiments provide evidence for a purely mechanical effect of rbc in augmenting platelet aggregation in WB.

Dynamics of a non-spherical microcapsule with incompressible interface in shear flow

2011 ◽  
Vol 678 ◽  
pp. 221-247 ◽  
Author(s):  
P. M. VLAHOVSKA ◽  
Y.-N. YOUNG ◽  
G. DANKER ◽  
C. MISBAH
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Viscosity Ratio ◽  
Perturbation Expansion ◽  
Shear Plane ◽  
Creeping Flow ◽  
Regular Perturbation ◽  
Cell Dynamics ◽  
Initial Shape ◽  
Flow Equations

We study the motion and deformation of a liquid capsule enclosed by a surface-incompressible membrane as a model of red blood cell dynamics in shear flow. Considering a slightly ellipsoidal initial shape, an analytical solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, area-incompressibility and resistance to bending. The theory captures the observed transition from tumbling to swinging as the shear rate increases and clarifies the effect of capsule deformability. Near the transition, intermittent behaviour (swinging periodically interrupted by a tumble) is found only if the capsule deforms in the shear plane and does not undergo stretching or compression along the vorticity direction; the intermittency disappears if deformation along the vorticity direction occurs, i.e. if the capsule ‘breathes’. We report the phase diagram of capsule motions as a function of viscosity ratio, non-sphericity and dimensionless shear rate.

scholarly journals Patient-Specific Adhesion of Sickle Red Blood Cells in Shear-Gradient Microscale Flow

Blood ◽  
2017 ◽  
Vol 130 (Suppl_1) ◽  
pp. 964-964
Author(s):  
Erdem Kucukal ◽  
Jane A. Little ◽  
Umut A. Gurkan
Keyword(s):  
Shear Rate ◽  
Blood Cell ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Flow Direction ◽  
Patient Specific ◽  
Shear Rates ◽  
Microscale Flow ◽  
Shear Gradient ◽  
Equity Ownership

Abstract The pathophysiology of sickle cell disease (SCD) involves altered biophysical properties of red blood cells (RBCs) and increased cellular adhesion, which can synergistically trigger recurrent and painful vaso-occlusive events in the microcirculatory network. RBC adhesion to the endothelial wall is heterogeneous and may initiate such occlusions by disrupting the local flow thus activating platelets and promoting subsequent cell-cell interactions. Moreover, these episodic events take place within a wide range of dynamically changing shear rates at the microscale. In order to better understand the role of shear rate on this process, we quantified shear-dependent RBC adhesion to endothelial proteins fibronectin (FN) and laminin (LN) utilizing a microfluidic system that can simulate physiologically relevant shear gradients of microcirculatory blood flow at a single flow rate. Whole blood samples were collected from 20 patients (10 males and 10 females) with homozygous SCD (HbSS). Samples were perfused through FN and LN immobilized shear-gradient microchannels (Fig. 1A) in which the shear rate continuously changes along flow direction. Computational simulations characterized the flow dynamics near the adherent RBCs (Fig. 1B). Based on the numerical results, a rectangular "field of interest (FOI)", along which the shear rate dropped approximately three-fold, was chosen for quantification of shear-dependent RBC adhesion. We observed changes in RBC adhesion to LN and FN in the shear gradient flow. Figure 1C and 1D show typical adhesion curves of surface adherent RBCs for an individual SCD sample within the FOI. To assess patient specific shear-dependent adhesion, we defined a parameter, "shear dependent adhesion rate (SDAR)", which is the slope of the adhesion curves based on normalized RBC adhesion numbers. A higher SDAR value was indicative of marked numbers of adherent RBCs that detach at higher shear rates whereas the effect of shear rate on RBC detachment was less for a lower SDAR. We observed an inverse relationship between SDAR and number of persistently adherent RBCs at high shear rates. Shear-dependent RBC adhesion to LN was heterogeneous among SCD patients. Patients with higher WBC counts constituted the low SDAR population with a threshold SDAR value of 60 (Fig. 1E, p=0.005, ANOVA). WBCs from patients with higher SDARs (and fewer persistently adhered cells) were all within the normal range. Patients in the low SDAR group also had significantly elevated absolute neutrophil counts (Fig. 1F, p=0.006, ANOVA), and ferritin levels (Fig. 1G, p=0.007, ANOVA). The mean ferritin level of those with low SDAR was nearly ten times greater than normal (mean= [3272.3 ± 791.9] μg/L vs. [784.5±219.6] μg/L). No white blood cell (WBC) adhesion was observed in the experiments. Here, we report a novel shear dependent adhesion ratio of sickle RBCs utilizing LN and FN functionalized microchannels. The approach presented here enabled us to create a shear gradient throughout the channel which may simulate the physiological flow conditions in the post-capillary venules. We further analyzed shear-dependent RBC adhesion in a patient specific manner and identified patient groups with low and high SDAR. The findings also suggested a link between lower shear dependent sickle RBC adhesion to LN and patient clinical phenotypes including inflammation and iron overload. Acknowledgments: This work was supported by grant #2013126 from the Doris Duke Charitable Foundation, National Heart Lung and Blood Institute R01HL133574, and National Science Foundation CAREER Award 1552782. Figure 1: Shear-dependent sickle RBC adhesion in microscale flow. (A) Macroscopic image of the shear-gradient microchannel with the arrow indicating flow direction. (B) Velocity and shear rate contours on a 2D plane above the bottom surface. The dashed rectangular area indicates the field of interest (FOI) where the experimental data were obtained. (C, D) Typical distribution of adherent deformable and non-deformable RBCs in LN and FN functionalized microchannels with the shear gradient. Dashed lines represent the adhesion curves and the corresponding equations were used to quantify shear dependent adhesion data. Shear-dependent RBC adhesion was lower (nSDAR<60) in patients with elevated white blood cell counts (E), absolute neutrophil counts (F), and serum ferritin levels (G). The dashed rectangles indicate the normal clinical values. Figure 1 Figure 1. Disclosures Little: Hemex Health: Equity Ownership. Gurkan: Hemex Health: Employment, Equity Ownership.

scholarly journals Spherization of red blood cells and platelets margination in COPD patients

2020 ◽  
Author(s):  
Karim Zouaoui Boudjeltia ◽  
Christos Kotsalos ◽  
Daniel Ribeiro ◽  
Alexandre Rousseau ◽  
Christophe Lelubre ◽  
...  
Keyword(s):  
Shear Rate ◽  
Numerical Simulations ◽  
Red Blood Cells ◽  
Conformational Changes ◽  
Blood Cells ◽  
Mean Square Displacement ◽  
Neuraminidase Treatment ◽  
Copd Patients ◽  
Platelet Aggregates

AbstractRationaleThere are important interactions between Red Blood Cells (RBCs) and platelets in the bloodstream. These interactions lead to a phenomenon called margination. RBCs in pathological situations undergo biochemical and conformational changes leading to alterations in blood rheology.AimRBCs shape in volunteers (21), stable (42) and exacerbated (31) COPD patients was analyzed. We studied the effect of the RBCs spherization on the platelets transport experimentally, in vitro, and by using numerical simulations.MethodsRBC shape was estimated by the second moment of Pearson obtained through flow cytometry on fsc histogram. In vitro experiments were performed to analyze the effect of RBC shape on platelets adhesion/aggregation in dynamic conditions. Neuraminidase treatment was used to induce RBCs spherization. Numerical simulation were performed to determine the effect of RBCs spherization on platelets mean square displacement (MSD) to provide a physical explanation.ResultsSignificant increase of RBC sphericity was observed in COPD patients compared to volunteers (Kruskal-Wallis: p<0.0001). In vitro experiments, at shear rate of 100 s-1, we observed that RBCs treated with neuraminidase mainly affect the number of platelet aggregates (p = 0.004). There was no change in the aggregates size. At a shear rate of 400 sec-1 neuraminidase treatment changes both the size of the aggregates (p = 0.009) and the number of platelet aggregates (p = 0.008).Numerical simulations indicated that RBCs spherization induces an increase of MSD and the effect was more pronounced when the shear rate increased.ConclusionOur results show that the RBCs of COPD patients are more spherical than those of healthy volunteers. Experimentally we observe that the RBCs spherization induces an increase platelet transport to the wall. Additional studies are needed to better understand the possible association between the RBCs effect on the platelets transport and the increased cardiovascular events observed in COPD patients.

scholarly journals Blood Crystal: Emergent Order of Red Blood Cells Under Wall-Confined Shear Flow

2018 ◽  
Vol 120 (26) ◽  
Author(s):  
Zaiyi Shen ◽  
Thomas M. Fischer ◽  
Alexander Farutin ◽  
Petia M. Vlahovska ◽  
Jens Harting ◽  
...  
Keyword(s):  
Shear Flow ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Emergent Order

Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities

1998 ◽  
Vol 361 ◽  
pp. 117-143 ◽  
Author(s):  
S. RAMANUJAN ◽  
C. POZRIKIDIS
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Simple Shear ◽  
Large Deformations ◽  
Viscosity Ratio ◽  
Curvilinear Coordinates ◽  
Triangular Element ◽  
Elastic Membrane ◽  
Simple Shear Flow ◽  
Liquid Drops

The deformation of a liquid capsule enclosed by an elastic membrane in an infinite simple shear flow is studied numerically at vanishing Reynolds numbers using a boundary-element method. The surface of the capsule is discretized into quadratic triangular elements that form an evolving unstructured grid. The elastic membrane tensions are expressed in terms of the surface deformation gradient, which is evaluated from the position of the grid points. Compared to an earlier formulation that uses global curvilinear coordinates, the triangular-element formulation suppresses numerical instabilities due to uneven discretization and thus enables the study of large deformations and the investigation of the effect of fluid viscosities. Computations are performed for capsules with spherical, spheroidal, and discoidal unstressed shapes over an extended 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 spherical capsules are in quantitative agreement with the predictions of perturbation theories. Results for large deformations of spherical capsules and deformations of non-spherical capsules are in qualitative agreement with experimental observations of synthetic capsules and red blood cells. We find that initially spherical capsules deform into steady elongated shapes whose aspect ratios increase with the magnitude of the shear rate. A critical shear rate above which capsules exhibit continuous elongation is not observed for any value of the viscosity ratio. This behaviour contrasts with that of liquid drops with uniform surface tension and with that of axisymmetric capsules subject to a stagnation-point flow. When the shear rate is sufficiently high and the viscosity ratio is sufficiently low, liquid drops exhibit continuous elongation leading to breakup. Axisymmetric capsules deform into thinning needles at sufficiently high rates of elongation, independent of the fluid viscosities. In the case of capsules in shear flow, large elastic tensions develop at large deformations and prevent continued elongation, stressing the importance of the vorticity of the incident flow. The long-time behaviour of deformed capsules depends strongly on the unstressed shape. Oblate capsules exhibit unsteady motions including oscillation about a mean configuration at low viscosity ratios and continuous rotation accompanied by periodic deformation at high viscosity ratios. The viscosity ratio at which the transition from oscillations to tumbling occurs decreases with the sphericity of the unstressed shape. Results on the effective rheological properties of dilute suspensions confirm a non-Newtonian shear-thinning behaviour.

Threshold shear stress for the transition between tumbling and tank-treading of red blood cells in shear flow: dependence on the viscosity of the suspending medium

2013 ◽  
Vol 736 ◽  
pp. 351-365 ◽  
Author(s):  
Thomas M. Fischer ◽  
Rafal Korzeniewski
Keyword(s):  
Shear Flow ◽  
Red Blood Cells ◽  
Blood Cells ◽  
Theoretical Models ◽  
Red Cells ◽  
Theoretical Modelling ◽  
Glass Capillary ◽  
Basic Model ◽  
A Value ◽  
The Subject

AbstractRed blood cells are the subject of diverse studies. One branch is the observation and theoretical modelling of their behaviour in a shear flow. This work deals with the flow of single red cells suspended in solutions much more viscous than blood plasma. Below a critical shear rate (${\dot {\gamma } }_{t} $) the red cells rotate with little change of their resting shape. Above that value they become elongated and aligned in the shear field. We measured${\dot {\gamma } }_{t} $at viscosities (${\eta }_{0} $) ranging from 10.7 to 104 mPa s via observation along the vorticity of a Poiseuille flow in a glass capillary;${\eta }_{0} {\dot {\gamma } }_{t} $decreased steeply with increasing${\eta }_{0} $up to a value of 25 mPa s and remained constant for higher values. Present theoretical models are not in keeping with the measured data. Modifications of basic model assumptions are suggested.

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