Microscopic photometric quantification of stiffness and relaxation time of red blood cells in a flow chamber

The Microscopic Photometric Monolayer Technique provides a tool to measure red blood cell (RBC) stiffness (resistance to elongation) and relaxation time. It combines many of the advantages of flow channel studies of point-attached RBCs with the simplicity, sensitivity and accuracy of photometric light transmission measurement This technique allows the study of the effects of physicochemical factors on the elongation and relaxation time of the same cells within an average of four to five thousand cells adhered as a monolayer to glass. Further, the time course of physicochemical effects on cell membrane and wash-in/wash-out kinetics of interactions can be followed. An automated version of this technique was developed. A dense monolayer of point-attached RBCs was prepared at the bottom of a flow-chamber. A steady-state flow, with stepwise increases of flow rate, induced the RBC elongation. The light transmission perpendicular through the monolayer plane was measured photometrically. Photomicrographs compared with photometric results showed that the flow-induced bending and curvature change of RBC membrane was associated with the increase of light transmission. There was a linear correlation between the photometric index of elongation and the elongation taken from photomicrographs for shear stresses up to 0.75 Pa. A stiffness parameter, S (in Pa), was defined as the ratio of shear stress and elongation at a shear stress of 0.25 Pa. Following a sudden flow stoppage, the RBCs returned to their resting shape and the RBC relaxation time was measured. The stiffness-relaxation time product, V (in mPas), was calculated to provide an estimate of viscosity. Diamide treatment, known to stiffen RBCs, did result in dose-dependent decreases of elongation and relaxation time. With increasing temperature, the relaxation time decreased at a rate of −2.96 ms/K; the stiffness increased significantly at a rate of 0.0038 Pa/K, and the stiffness-relaxation time product decreased with −2.95 mPas/K, reflecting an inverse relationship between RBC viscosity and temperature. Using the automated version of this technique (Elias-c-) to test RBCs of 36 healthy subjects, we found the inter-individual coefficients of variation to be 8.6% for stiffness, 7.9% for relaxation time and 12.4% for stiffness-relaxation time product.     

Oral shear stress predicts flavour perception in viscous solutions

The perception of sweetness and flavour were studied in viscous solutions containing 50 g/l sucrose, 100 p.p.m. iso-amyl acetate and varying concentrations of three hydrocolloid thickeners (guar gum, lambda-carrageenan and hydroxypropylmethyl cellulose). Zero-shear viscosity of the samples ranged from 1 to 5000 mPas. Perception of both sweetness and aroma was suppressed at thickener concentrations above c* (coil overlap concentration, the point at which there is an abrupt increase in solution viscosity as thickener concentration is increased). Sensory data for the three hydrocolloids was only loosely correlated with their concentration relative to c* (c/c* ratio), particularly above c*. However, when perceptual data were plotted against the Kokini oral shear stress (tau), calculated from rheological measurements, data for the three hydrocolloids aligned to form a master-curve, enabling the prediction of flavour intensity in such systems. The fact that oral shear stress can be used to model sweetness and aroma perception supports the hypothesis that somatosensory tactile stimuli can interact with taste and aroma signals to modulate their perception.     

Hydrodynamic shear breakage of DNA

The rate of breakage of duplex DNA molecules by laminar flow through a capillary has been studied. For λb2b5c DNA (molecular wt., M = 25 × 10⁶) the point at which breakage occurs is normally distributed around the center of the molecule with a standard deviation of 12.5% of the molecular length. At constant shear stress or shear rate, the breakage rate is independent of ionic strength. Thus, shear induced local denaturation is not a rate limiting, preliminary step in breakage. In experiments at constant temperature with varying solvent viscosity (controlled by added sucrose) the breakage rate is a function of shear rate, not of shear stress. The rate of opening of hydrogenbonded circles into linear molecules by hydrodynamic shear is also shown to be a function of shear rate and not of shear stress. The breakage rate at constant shear rate is not greatly dependent on temperature. The shear rate required to achieve breakage is inversely proportional to M^1,2. The breakage rate constant, k varies as a very high power of the shear rate; at 25°C, d In k/d In Gm ～ 15; at 10°C, d In k/d In Gm ～ 26, where Gm is the maximum shear rate at the capillary wall. The unexpected result that breakage rate is mainly dependent on shear rate, not shear stress, supports a model in which the DNA molecule is distorted with a driving force which depends on the hydrodynamic shear stress, ηG, but the rate limiting step is segment diffusion into a highly extended configuration. The characteristic time to achieve this configuration is proportional to solvent viscosity, η, hence the breakage rate is dependent on ηG/η or G, the shear rate.     

Dynamic deformation and recovery response of red blood cells to a cyclically reversing shear flow: Effects of frequency of cyclically reversing shear flow and shear stress level

Dynamic deformation and recovery responses of red blood cells (RBCs) to a cyclically reversing shear flow generated in a 30-microm clearance, with the peak shear stress of 53, 108, 161, and 274 Pa at the frequency of 1, 2, 3, and 5 Hz, respectively, were studied. The RBCs' time-varying velocity varied after the glass plate velocity without any time lag, whereas the L/W change, where L and W were the major and minor axes of RBCs' ellipsoidal shape, exhibited a rapid increase and gradual decay during the deformation and recovery phase. The time of minimum L/W occurrence lagged behind the zero-velocity time of the glass plate (zero stress), and the delay time normalized to the one-cycle duration remained constant at 8.0%. The elongation of RBCs at zero stress time became larger with the reversing frequency. A simple mechanical model consisting of an elastic linear element during a rapid elongation period and a parallel combination of elements such as a spring and dashpot during the nonlinear recovery phase was suggested. The dynamic response behavior of RBCs under a cyclically reversing shear flow was different from the conventional shape change where a steplike force was applied to and completely released from the RBCs.     

Red blood cell orientation in orbit C = 0.

Two modes of behavior of single human red cells in a shear field have been described. It is known that in low viscosity media and at shear rates less than 20 s-1, the cells rotate with a periodically varying angular velocity, in accord with the theory of Jeffery (1922) for oblate spheroids. In media of viscosity greater than approximately 5 mPa s and sufficiently high shear rates, the cells align themselves at a constant angle to the direction of flow with the membrane undergoing tank-tread motion. Also, in low viscosity media, as the shear rate is increased, more and more cells lie in the plane of shear, undergoing spin with their axes of symmetry aligned with the vorticity axis of the shear field in an orbit "C = 0" (Goldsmith and Marlow, 1972). We have explored this latter phenomenon using two experimental methods. First, the erythrocytes were observed in the rheoscope and their diameters measured. Forward light scattering patterns were correlated with the red cell orientation mode. Light flux variations after flow onset or stop were measured, and the characteristic times of erythrocyte orientation and disorientation were assessed. The characteristic time of erythrocyte orientation in Orbit C = 0 is proportional to the inverse of the shear rate. The corresponding coefficient of proportionality depends on the suspending medium viscosity eta o. The disorientation time tau D, after flow has been stopped, is such that the ratio tau D/eta o is independent of the initial applied shear stress. However, tau D is much shorter than one would expect if pure Brownian motion were involved. The proportion of erythrocytes in orbit C = 0 was also measured. It was found that this proportion is a function of both the shear rate and eta o. At low values of eta o, the proportion increases with increasing shear rate and then reaches a plateau. For higher values of eta o (5 to 10 mPa s), the proportion of RBC in orbit C = 0 is a decreasing function of the shear stress. A critical transition between orbit C = 0 and parallel alignment was observed at high values of eta o, when the shear stress is on the order of 1 N/m2. Finally, the effect of altering membrane viscoelastic properties (by heat or diamide treatment) was tested. The proportion of oriented cells is a steep decreasing function of red cell rigidity.     

Tube flow of human blood at near zero shear

Pressure-velocity relations were obtained in vertical and horizontal glass tubes (I.D. 26 to 83 micron) perfused with normal human blood at feed hematocrits between 0.25 and 0.65. Perfusion pressures used corresponded to wall shear stresses up to 0.27 dyn cm-2. Red cell velocity measurements were made both immediately following implementation of perfusion pressure (with red cells still disaggregated) and in a steady state situation (with red cells aggregated). Analysis of the slopes of the linear relations between perfusion pressure and velocity showed apparent viscosity to decrease with the manifestation of red cell aggregation. In horizontal tubes, sedimentation and aggregation occurred simultaneously, and apparent viscosity increased due to axial asymmetry of cell concentration. Evidence for a yield shear stress (flow stagnation at positive driving pressure) was not observed.     

Effects of biaxial oscillatory shear stress on endothelial cell proliferation and morphology

Wall shear stress (WSS) on anchored cells affects their responses, including cell proliferation and morphology. In this study, the effects of the directionality of pulsatile WSS on endothelial cell proliferation and morphology were investigated for cells grown in a Petri dish orbiting on a shaker platform. Time and location dependent WSS was determined by computational fluid dynamics (CFD). At low orbital speed (50 rpm), WSS was shown to be uniform (0-1 dyne/cm(2)) across the bottom of the dish, while at higher orbital speed (100 and 150 rpm), WSS remained fairly uniform near the center and fluctuated significantly (0-9 dyne/cm(2)) near the side walls of the dish. Since WSS on the bottom of the dish is two-dimensional, a new directional oscillatory shear index (DOSI) was developed to quantify the directionality of oscillating shear. DOSI approached zero for biaxial oscillatory shear of equal magnitudes near the center and approached one for uniaxial pulsatile shear near the wall, where large tangential WSS dominated a much smaller radial component. Near the center (low DOSI), more, smaller and less elongated cells grew, whereas larger cells with greater elongation were observed in the more uniaxial oscillatory shear (high DOSI) near the periphery of the dish. Further, cells aligned with the direction of the largest component of shear but were randomly oriented in low magnitude biaxial shear. Statistical analyses of the individual and interacting effects of multiple factors (DOSI, shear magnitudes and orbital speeds) showed that DOSI significantly affected all the responses, indicating that directionality is an important determinant of cellular responses.     

Tank treading of optically trapped red blood cells in shear flow

Tank-treading (TT) motion is established in optically trapped, live red blood cells (RBCs) held in shear flow and is systematically investigated under varying shear rates, temperature (affecting membrane viscosity), osmolarity (resulting in changes in RBC shape and cytoplasmic viscosity), and viscosity of the suspending medium. TT frequency is measured as a function of membrane and cytoplasmic viscosity, the former being four times more effective in altering TT frequency. TT frequency increases as membrane viscosity decreases, by as much as 10% over temperature changes of only 4°C at a shear rate of ∼43 s⁻¹. A threshold shear rate (1.5 ± 0.3 s⁻¹) is observed below which the TT frequency drops to zero. TT motion is also observed in shape-engineered (spherical) RBCs and those with cholesterol-depleted membranes. The TT threshold is less evident in both cases but the TT frequency increases in the latter cells. Our findings indicate that TT motion is pervasive even in folded and deformed erythrocytes, conditions that occur when such erythrocytes flow through narrow capillaries.     

A reevaluation and discussion on the threshold limit for hemolysis in a turbulent shear flow

One major factor of red blood cell damage induced by artificial heart valves is the magnitude of turbulent shear stresses in the flow field. An often-cited threshold for hemolysis is 400 N/m(2) (Sallam and Hwang, Biorheology 21 (1984) 783). This value, however, was measured with a one-component laser Doppler anemometer and was not calculated from the major principal Reynolds shear stress, therefore underestimating the threshold. This study performed flow field measurements under similar conditions, using a two-component laser Doppler anemometer and determining major principal Reynolds shear stress, to reevaluate the hemolytic threshold as 800 N/m(2) with an exposure time of 1 ms. The Kolmogorov length scales, approximately 9 microm, are capable of inflicting direct damage to the red blood cells. These results will serve as a more accurate reference in future heart valve design and testing.     

The superposition of steady on oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid

To understand the pulsatility of human blood flow in vivo, it is necessary to separately investigate (1) steady shear and oscillatory flow, and (2) the superposition of steady shear flow on oscillatory flow performed under in vitro conditions. In this study a variable steady shear rate was superimposed in parallel on oscillatory shear at a constant frequency (0.5 Hz) for human blood (45% hematocrit), and an aqueous polyacrylamide polymer solution (AP 30E, concentration 300 ppm). The effect of superposition of the above two shear flows on the viscoelasticity of blood was more pronounced for the elastic (η′') than for the viscous (η′) component of viscoelasticity. With increasing superimposed shear rate, both η′ and η′' decreased, especially at the low shear region. This behavior can be explained by the viscoelastic properties of blood and the phenomena of blood aggregation and disaggregation. Quantitatively, the dependence of the viscous component of complex viscosity on superimposed shear for both blood and polymer solution is described by a modified Carreau equation. The elastic component of complex viscosity decreased exponentially with increasing superimposed shear, and it is described by an exponential model. © 1997 Elsevier Science Ltd     

The elongation and orientation of cultured endothelial cells in response to shear stress

Vascular endothelial cells appear to be aligned with the flow in the immediate vicinity of the arterial wall and have a shape which is more ellipsoidal in regions of high shear and more polygonal in regions of low shear stress. In order to study quantitatively the nature of this response, bovine aortic endothelial cells grown on Thermanox plastic coverslips were exposed to shear stress levels of 10, 30, and 85 dynes/cm2 for periods up to 24 hr using a parallel plate flow chamber. A computer-based analysis system was used to quantify the degree of cell elongation with respect to the change in cell angle of orientation and with time. The results show that (i) endothelial cells orient with the flow direction under the influence of shear stress, (ii) the time required for cell alignment with flow direction is somewhat longer than that required for cell elongation, (iii) there is a strong correlation between the degree of alignment and endothelial cell shape, and (iv) endothelial cells become more elongated when exposed to higher shear stresses.     

Role of p38 MAP kinase in endothelial cell alignment induced by fluid shear stress

The p38/mitogen-activated protein (MAP) kinase-activated protein kinase 2 (MAPKAP kinase 2)/heat shock protein (HSP)25/27 pathway is thought to play a critical role in actin dynamics. In the present study, we examined whether p38 was involved in the morphological changes seen in endothelial cells (EC) exposed to shear stress. Cultured bovine aortic EC were subjected to 14 dyn/cm(2) laminar steady shear stress. Peak activation of p38, MAPKAP kinase 2, and HSP25 were sixfold at 5 min, sixfold at 5 min, and threefold at 30 min compared with static control, respectively. SB-203580 (1 microM), a specific inhibitor of p38, abolished the activation of MAPKAP kinase 2 and HSP25 as well as EC elongation and alignment in the direction of flow elicited by shear stress. The mean orientation angle of cells subjected to shear without SB-203580, with SB-203580, or static control were 17, 50, and 43 degrees, respectively (P < 0. 05). EC transfected with the dominant negative mutant of p38-alpha aligned randomly with no stress fiber formation despite exposure to shear stress. These data suggests that the pathway of p38/MAPKAP kinase 2/HSP25/27 is activated in response to shear stress, and this pathway plays an important role in morphological changes induced by shear stress.     

Quantitative morphodynamics of endothelial cells within confluent cultures in response to fluid shear stress

To evaluate shear stress-induced effects on cultured cells we have extended the mechanical setup of a multichannel in vitro rheological system and developed software allowing entire processing control and image data analysis. The values of cell motility, degree of orientation (alignment), and cell elongation were correlated as a function of time (morphodynamics). Collective and individual endothelial cells within confluent cultures displayed a shear stress-dependent characteristic phase behavior of the following time course: resting conditions (phase I), change of motility (phase II), onset of alignment (phase III), and finally cell elongation (phase IV). Especially cell motility was characterized by a randomized zigzag movement around mean trajectories (fluctuations) together with mean cell locomotion. Onset of shear stress caused a down-regulation of fluctuations of 30% within <10 min and simultaneously increased locomotion velocities preferring the flow direction (phase II). After a lag period of 10 to 20 min cells orientated in the direction of flow (phase III) without significant cell elongation, which finally occurs within hours (phase IV). These data provide first evidence that cells within confluent endothelial monolayers respond to shear stress with a characteristic phase behavior.     

Predicted wall shear rate gradients in T-type arteriolar bifurcations

The purpose of this study was to examine the theoretical impact of the local bifurcation geometry on the shear rate gradient in a divergent arteriolar-type bifurcation. Newtonian flow through an arteriolar bifurcation was modeled using 3-dimensional computational fluid dynamics (CFD). Branching angles of 30 degrees, 50 degrees, 70 degrees, 90 degrees, 110 degrees, 130 degrees, and 150 degrees were studied at a Reynolds number (Re) of 0.01 in seven separate models. Both the flow split (30%) and the branch to main vessel diameter ratio (4/5) were held constant. Velocity profiles were predicted to deviate significantly from a parabolic form, both immediately before and after the branch. This deviation was shown to be a function of the local bifurcation geometry of each model, which consisted of a branching angle and associated feed-branch intersection shape. Immediately before and after the branch, the shear rate along the lateral branching wall was predicted to exceed (5-fold) that calculated for fully developed flow in the feed. In vivo data were from the anesthetized (pentobarbital, 70 mg/kg) hamster cremaster muscle preparation. Red blood cells were used as flow markers in arteriolar branch points (n = 74) show that a significant gradient in shear rate occurs at the locations and branch shapes predicted by the computational model. Thus, for low Re divergent flow, the gradient in shear rate measured for non-Newtonian conditions, is approximated by a finite element fluid dynamics model of Newtonian flow.     

Shape and compliance of endothelial cells after shear stress in vitro or from different aortic regions: scanning ion conductance microscopy study

Objective

To measure the elongation and compliance of endothelial cells subjected to different patterns of shear stress in vitro, and to compare these parameters with the elongation and compliance of endothelial cells from different regions of the intact aorta.

Materials and Methods

Porcine aortic endothelial cells were cultured for 6 days under static conditions or on an orbital shaker. The shaker generated a wave of medium, inducing pulsatile shear stress with a preferred orientation at the edge of the well or steadier shear stress with changing orientation at its centre. The topography and compliance of these cells and cells from the inner and outer curvature of ex vivo porcine aortic arches were measured by scanning ion conductance microscopy (SICM).

Results

Cells cultured under oriented shear stress were more elongated and less compliant than cells grown under static conditions or under shear stress with no preferred orientation. Cells from the outer curvature of the aorta were more elongated and less compliant than cells from the inner curvature.

Conclusion

The elongation and compliance of cultured endothelial cells vary according to the pattern of applied shear stress, and are inversely correlated. A similar inverse correlation occurs in the aortic arch, with variation between regions thought to experience different haemodynamic stresses.     

Magnetic resonance microscopy determined velocity and hematocrit distributions in a Couette viscometer

Magnetic resonance microscopy is used to non-invasively measure the radial velocity distribution in Couette flow of erythrocyte suspensions of varying aggregation behavior at a nominal shear rate of 2.20 s(-1) in a 1 mm gap. Suspensions of red blood cells in albumin-saline, plasma and 1.48% Dextran added plasma at average hematocrits near 0.40 are studied, providing a range of aggregation ability. The spatial distribution of the red blood cell volume fraction, hematocrit, is calculated from the velocity distribution. The hematocrit profiles provide direct measure of the thickness of the aggregation and shear rate dependent red blood cell depletion at the Couette surfaces. At the nominal shear rate studied hematocrit distributions for the red blood cells in plasma show a depletion zone near the inner Couette wall but not the outer wall. The red blood cells in plasma with Dextran show cell depletion regions of approximately 100 mum at both the inner and outer Couette surfaces, with greater depletion at the inner wall, but approach the normal blood hematocrit distribution with a doubling of shear rate due to decreased aggregation. The material response of the blood is spatially dependent with the shear rate and the hematocrit distribution non-uniform across the gap.     

Red blood cell deformation in shear flow. Effects of internal and external phase viscosity and of in vivo aging.

Shear deformation of young and old human red blood cells was examined over a range of shear stresses and suspending phase viscosities (eta o) using a cone-plate Rheoscope. The internal viscosities (eta i) of these cell types differ, and further changes in internal viscosity were induced by alteration of suspension osmolality and hence cell volume. For low suspending viscosities (0.0555 or 0.111 P) old cells tended to tumble in shear flow, whereas young cells achieved stable orientation and deformed. Changes in osmolality, at these external viscosities, altered the percentage of cells deforming, and for each cell type threshold osmolalities (Osm-50) were determined where 50% of cells deformed. The threshold osmolalities were higher for younger cells than for older cells, but the internal viscosities of the two cell types were similar at their respective Osm-50. Threshold osmolalities were also higher for the higher external viscosity, but the ratio of internal to external viscosities (i.e., eta i/eta o) was nearly constant for both external viscosities. Deformation of stably oriented cells increased with increasing shear stress and approached a value limited by cell surface area and volume. For isotonic media, over a wide range of external viscosities and shear stresses, deformation was greater for younger cells than for older cells. However, deformation vs. shear stress data for the two cell types became nearly coincident if young cells were osmotically shrunk to have their internal viscosity close to that for old cells. Increases in external viscosity, at constant shear stress, caused greater deformation for all cells. This effect of external viscosity was not equal for young and old cells; the ratio of old/young cell deformation increased with increasing eta o. However, if deformation was plotted as a function of the ratio lambda = eta i/eta o, at constant shear stress, young and old cell data followed similar paths. Thus the ratio lambda is a major determinant of cell deformation as well as a critical factor affecting stable orientation in shear flow.     

Intraerythrocytic parasites and red cell deformability: Plasmodium berghei and Babesia microti

In the studies reported here, we examined the effects of two intraerythrocytic parasites (Plasmodium berghei and Babesia microti) on the deformability of their host red cells. Red cell deformability was assessed by three criteria: 1) the prevalence of tank-treading (the tank-tread-like movement of the red cell membrane around its cytoplasmic contents), 2) elongation under fluid shear stress (the steady-state length: width ratio), and 3) the time required for the red cell to reduce its steady-state elongation by 63.2% after the abrupt release of the shear stress (the characteristic shape-recovery time). Trophozoite-stage parasites of both species reduced the prevalence of tank-treading. Ring- and trophozoite-stage parasites of both species reduced steady-state elongation, and ring-stage P. berghei prolonged the shape-recovery time. These results suggest that altered red cell deformability is a common feature of infection with intraerythrocytic parasites.     

Rapid cell-deformability sensing system based on slit-flow laser diffractometry with decreasing pressure differential

A slit-flow apparatus with a laser-diffraction method has been developed with significant advances in ektacytometry design, operation and data analysis. In the slit-flow ektacytometry, the deformation of red blood cells subjected to continuously decreasing shear stress in slit-flow can be quickly measured with adopting a laser-diffraction technique. Both the laser-diffraction image and pressure were measured with respect to time, which enable to determine the elongation index (EI) and the shear stress. The range of shear stress is 0-35 Pa and the measuring time is < 2 min. The EI is determined from an isointensity curve in the diffraction pattern using an ellipse-fitting program. The present study proposed the deformability index (DI) as a new measure of the RBC deformability, which is defined as an integral area under the EI curve between 0 and tau10 (tau(w) = 0-10). The key advantage of this design is the incorporation of a disposable element that holds the blood sample, which enables the present system to be easily used in a clinical setting.     

Nitric oxide production by bone cells is fluid shear stress rate dependent

Shear stress due to mechanical loading-induced flow of interstitial fluid through the lacuno-canalicular network is a likely signal for bone cell adaptive responses. Moreover, the rate (determined by frequency and magnitude) of mechanical loading determines the amount of bone formation. Whether the bone cells' response to fluid shear stress is rate dependent is unknown. Here we investigated whether bone cell activation by fluid shear stress is rate dependent. MC3T3-E1 osteoblastic cells were subjected for 15 min to fluid shear stress of varying frequencies and amplitudes, resulting in peak fluid shear stress rates ranging from 0 to 39.6 Pa-Hz. Nitric oxide production, a parameter for bone cell activation, was found to be linearly dependent on the fluid shear stress rate; the slope was steepest at 5 min (0.11 Pa-Hz(-1)) and decreased to 0.03 Pa-Hz(-1) at 15 min. We conclude that the fluid shear stress rate is an important parameter for bone cell activation.