Theoretical model and experimental study of red blood cell (RBC) deformation in microchannels

The motion and deformation of red blood cells (RBCs) flowing in a microchannel were studied using a theoretical model and a novel automated rheoscope. The theoretical model was developed to predict the cells deformation under shear as a function of the cells geometry and mechanical properties. Fluid dynamics and membrane mechanics are incorporated, calculating the traction and deformation in an iterative manner. The model was utilized to evaluate the effect of different biophysical parameters, such as: inner cell viscosity, membrane shear modulus and surface to volume ratio on deformation measurements. The experimental system enables the measurement of individual RBCs velocity and their deformation at defined planes within the microchannel. Good agreement was observed between the simulation results, the rheoscope measurements and published ektacytometry results. The theoretical model results imply that such deformability measuring techniques are weakly influenced by changes in the inner viscosity of the cell or the ambient fluid viscosity. However, these measurements are highly sensitive to RBC shear modulus. The shear modulus, estimated by the model and the rheoscope measurements, falls between the values obtained by micropipette aspiration and laser trapping. The study demonstrates the integration of a theoretical model with a microfabricated device in order to achieve a better understanding of RBC mechanics and their measurement using microfluidic shear assays. The system and the model have the potential of serving as quantitative clinical tools for diagnosing deformability disorders in RBCs.     

Validation and application of an automated rheoscope for measuring red blood cell deformability distributions in different species

BACKGROUND: The deformability of red blood cells (RBCs) is of great importance for the conservation of oxygen delivery in the microcirculation. Even a small fraction of rigid cells is considered to harm the exchange of respiratory gases. Techniques that measure RBC deformability often provide an indication of the mean deformability. It may not be possible, however, to assess whether this mean value is reduced by the presence of a small rigid cell fraction or by a slight overall reduction in RBC deformability. A technique that provides a deformability distribution would be of great value to study diseases that are marked by subpopulations with a reduced deformability. METHODS: This paper describes a rheoscope system that uses advanced image analysis techniques to quickly quantify the deformability of many individual cells in shear flow, in order to find the RBC-deformability distribution. Since variations in the shear stress are responsible for variations in cell elongation, and hence introduce an additional spread in the cell deformability distribution, we first determined the spread caused by instrumental error. We then utilized the technique to investigate the relation between cell deformability and cell size of single blood samples of different species (human, pig, rat and rabbit). RESULTS: The spread caused by instrumental error was small compared to the actual RBC-deformability spread in blood samples. The deformability distribution of human and pig cells are alike although their cell sizes are different. Rat and rabbit cells show comparable deformability and size distributions. With this technique no correlation was found between cell deformability and cell size in animal RBCs. In the human sample a minor correlation was found between cell deformability and cell size. CONCLUSIONS: The automated rheoscope enables us to study the mechanical properties of RBCs more thoroughly by their deformability distribution. These deformability distributions are hardly influenced by the technique or by cell size.     

Measurement of the distribution of red blood cell deformability using an automated rheoscope

BACKGROUND: Red blood cells (RBCs) have to deform markedly to pass through the smallest capillaries of the microcirculation. Techniques for measuring RBC deformability often result in an indication of the mean value. A deformability distribution would be more useful for studying diseases that are marked by subpopulations of less deformable cells because even small fractions of rigid cells can cause circulatory problems. METHODS: We present an automated rheoscope that uses advanced image analysis techniques to determine a RBC deformability distribution (RBC-DD) by analyzing a large number of individual cells in shear flow. The sensitivity was measured from density-separated fractions of one blood sample and from cells rendered less deformable by heat treatment. A preliminary experiment included the RBC-DDs of a patient with sickle cell anemia, one on dialysis and being treated with erythropoietin, and one with elliptocytosis. RESULTS: Measurement of the RBC-DD was highly reproducible. The sensitivity test showed markedly different deformability distributions of density-separated cells and yielded distinct RBC-DDs after each additional minute of heat treatment. CONCLUSION: The automated rheoscope enabled the determination of RBC-DDs from which less deformable subpopulations can be established. The shape of an RBC-DD may be valuable in assessing cell fractions with normal and anomalous deformability within pathologic blood samples.     

Shear‐induced diffusion of red blood cells measured with dynamic light scattering‐optical coherence tomography

Quantitative measurements of intravascular microscopic dynamics, such as absolute blood flow velocity, shear stress and the diffusion coefficient of red blood cells (RBCs), are fundamental in understanding the blood flow behavior within the microcirculation, and for understanding why diffuse correlation spectroscopy (DCS) measurements of blood flow are dominantly sensitive to the diffusive motion of RBCs. Dynamic light scattering‐optical coherence tomography (DLS‐OCT) takes the advantages of using DLS to measure particle flow and diffusion within an OCT resolution‐constrained three‐dimensional volume, enabling the simultaneous measurements of absolute RBC velocity and diffusion coefficient with high spatial resolution. In this work, we applied DLS‐OCT to measure both RBC velocity and the shear‐induced diffusion coefficient within penetrating venules of the somatosensory cortex of anesthetized mice. Blood flow laminar profile measurements indicate a blunted laminar flow profile and the degree of blunting decreases with increasing vessel diameter. The measured shear‐induced diffusion coefficient was proportional to the flow shear rate with a magnitude of ~0.1 to 0.5 × 10^?6 mm². These results provide important experimental support for the recent theoretical explanation for why DCS is dominantly sensitive to RBC diffusive motion.      

In vitro confocal micro-PIV measurements of blood flow in a square microchannel: the effect of the haematocrit on instantaneous velocity profiles

A confocal microparticle image velocimetry (micro-PIV) system was used to obtain detailed information on the velocity profiles for the flow of pure water (PW) and in vitro blood (haematocrit up to 17%) in a 100-microm-square microchannel. All the measurements were made in the middle plane of the microchannel at a constant flow rate and low Reynolds number (Re=0.025). The averaged ensemble velocity profiles were found to be markedly parabolic for all the working fluids studied. When comparing the instantaneous velocity profiles of the three fluids, our results indicated that the profile shape depended on the haematocrit. Our confocal micro-PIV measurements demonstrate that the root mean square (RMS) values increase with the haematocrit implying that it is important to consider the information provided by the instantaneous velocity fields, even at low Re. The present study also examines the potential effect of the RBCs on the accuracy of the instantaneous velocity measurements.     

大分子吸附对低粘切变流场中红细胞取向的影响

采用一种在低粘切变流场中,将红细胞变形指数ＤＩ,分解为转向指数与小变形指数的新型激光衍射法,比较了有不同分子量右旋糖酐或ＰＶＰ处理的红细胞与正常对照组红细胞的（ＤＩ）ｏｒ－γ曲线,发现上述两类曲线间存在明显差异,这一事实表明,这种新型激光衍射法有助于分子水平的微观流变学的研究。     

Red blood cell motions in high-hematocrit blood flowing through a stenosed microchannel

We investigated the behavior of red blood cells (RBCs) in a microchannel with stenosis using a confocal micro-PTV system. Individual trajectories of RBCs in a concentrated suspension of up to 20% hematocrit (Hct) were measured successfully. Results indicated that the trajectories of healthy RBCs became asymmetric before and after the stenosis, while the trajectories of tracer particles in pure water were almost symmetric. The asymmetry was greater in 10% Hct than in 20% Hct. We also investigated the effect of deformability of RBCs on the cell-free layer thickness by hardening RBCs using a glutaraldehyde treatment. The results indicated that deformability is the key factor in the asymmetry of cell-free layer thickness. Therefore, the motions of RBCs are influenced strongly by the Hct, the deformability, and the channel geometry. These results give fundamental knowledge for a better understanding of blood flow in microcirculation and biomedical microdevices.     

Aggregation of human red blood cells after moderate heat treatment

The aggregation behaviour of normal and heat treated (48.4 degrees C, 48.8 degrees C, 49.5 degrees C) red blood cells (RBCs) suspended in dextran-saline solutions (Dx 70, Dx 173) was investigated by a laser light reflectometric method over a wide range of bridging energies. The characteristic times of rouleau formation were found to be increased after RBC heat treatment. The disaggregation shear stress is not significantly different between normal RBCs and heat treated RBCs. The loss of cell deformability is nevertheless shown to improve slightly the dissociation efficiency of the flowing liquid in a shear flow resulting in a small reduction of the disaggregation shear rate after heat treatment. Heat treatment is also shown to alter the structure of RBC network at equilibrium. These results indicate that heat induced alterations of erythrocytes only affects the mechanical properties of the cell membrane without significant changes in the macromolecular bridging energy.     

Visualization study of motion and deformation of red blood cells in a microchannel with straight,divergent and convergent sections

The size of red blood cells (RBC) is on the same order as the diameter of microvascular vessels. Therefore, blood should be regarded as a two-phase flow system of RBCs suspended in plasma rather than a continuous medium of microcirculation. It is of great physiological and pathological significance to investigate the effects of deformation and aggregation of RBCs on microcirculation. In this study, a visualization experiment was conducted to study the microcirculatory behavior of RBCs in suspension. Motion and deformation of RBCs in a microfluidic chip with straight, divergent, and convergent microchannel sections have been captured by microscope and high-speed camera. Meanwhile, deformation and movement of RBCs were investigated under different viscosity, hematocrit, and flow rate in this system. For low velocity and viscosity, RBCs behaved in their normal biconcave disc shape and their motion was found as a flipping motion: they not only deformed their shapes along the flow direction, but also rolled and rotated themselves. RBCs were also found to aggregate, forming rouleaux at very low flow rate and viscosity. However, for high velocity and viscosity, RBCs deformed obviously under the shear stress. They elongated along the flow direction and performed a tank-treading motion.     

Conductometric study of shear-dependent processes in red cell suspensions. II. Transient cross-stream hematocrit distribution

A novel experimental approach based on electrical properties of red blood cell (RBC) suspensions was applied to study the effects of the size and morphology of RBC aggregates on the transient cross-stream hematocrit distribution in suspensions flowing through a square cross-section flow channel. The information about the effective size of RBC aggregates and their morphology is extracted from the capacitance (C) and conductance (G) recorded during RBC aggregation, whereas a slower process of particle migration is manifested by delayed long-term changes in the conductance. Migration-induced changes in the conductance measured at low shear rates (< or =3.1 s(-1)) for suspensions of RBCs in a strongly aggregating medium reveal an increase to a maximum followed by a decrease to the stationary level. The ascending branch of G(t) curves reflects the aggregate migration in the direction of decreasing shear rate. A further RBC aggregation in the region of lower shear stresses leads to the formation of RBC networks and results in the transformation of the rheological behavior of suspensions from the thinning to the thickening. It is suggested that the descending branches of the G(t) curves recorded at low shear rates reflect an adjustment of the Hct distribution to a new state caused by a partial dispersion of RBC networks. For suspensions of non-aggregating RBCs it is found that depending on whether the shear rate is higher or lower compared with the prior value, individual RBCs migrate either toward the centerline of the flow or in the opposite direction.     

Sublethal Supraphysiological Shear Stress Alters Erythrocyte Dynamics in Subsequent Low-Shear Flows

Blood is a non-Newtonian, shear-thinning fluid owing to the physical properties and behaviors of red blood cells (RBCs). Under increased shear flow, pre-existing clusters of cells disaggregate, orientate with flow, and deform. These essential processes enhance fluidity of blood, although accumulating evidence suggests that sublethal blood trauma—induced by supraphysiological shear exposure—paradoxically increases the deformability of RBCs when examined under low-shear conditions, despite obvious decrement of cellular deformation at moderate-to-higher shear stresses. Some propose that rather than actual enhancement of cell mechanics, these observations are “pseudoimprovements” and possibly reflect altered flow and/or cell orientation, leading to methodological artifacts, although direct evidence is lacking. This study thus sought to explore RBC mechanical responses in shear flow using purpose-built laser diffractometry in tandem with direct optical visualization to address this problem. Freshly collected RBCs were exposed to a mechanical stimulus known to drastically alter cell deformability (i.e., prior shear exposure (PSE) to 100 Pa × 300 s). Samples were subsequently transferred to a custom-built slit-flow chamber that combined laser diffractometry with direct cell visualization. Cell suspensions were sheared in a stepwise manner (between 0.3 and 5.0 Pa), with each step being maintained for 15 s. Deformability and cell orientation indices were recorded for small-scatter Fraunhofer diffraction patterns and also visualized RBCs. PSE RBCs had significantly decreased visualized and laser-derived deformability at any given shear stress ≥1 Pa. Novel, to our knowledge, observations demonstrated that PSE RBCs had increased heterogeneity of direct visualized orientation with flow vector at any shear, which may be due to greater vorticity and thus instability in 5-Pa flow compared with unsheared control. These findings indicate that shear exposure and stress-strain history can alter subsequent RBC behavior in physiologically relevant low-shear flows. These findings may yield insight into microvascular disorders in recipients of mechanical circulatory support and individuals with hematological diseases that alter physical properties of blood.     

Computational modeling of biomechanics and biorheology of heated red blood cells

Because of their compromised deformability, heat denatured erythrocytes have been used as labeled probes to visualize spleen tissue or to assess the ability of the spleen to retain stiff red blood cells (RBCs) for over three decades, e.g., see Looareesuwan et al. N. Engl. J. Med. (1987). Despite their good accessibility, it is still an open question how heated RBCs compare to certain diseased RBCs in terms of their biomechanical and biorheological responses, which may undermine their effective usage and even lead to misleading experimental observations. To help answering this question, we perform a systematic computational study of the hemorheological properties of heated RBCs with several physiologically relevant static and hemodynamic settings, including optical-tweezers test, relaxation of prestretched RBCs, RBC traversal through a capillary-like channel and a spleen-like slit, and a viscometric rheology test. We show that our in silico RBC models agree well with existing experiments. Moreover, under static tests, heated RBCs exhibit deformability deterioration comparable to certain disease-impaired RBCs such as those in malaria. For RBC traversal under confinement (through microchannel or slit), heated RBCs show prolonged transit time or retention depending on the level of confinement and heating procedure, suggesting that carefully heat-treated RBCs may be useful for studying splenic- or vaso-occlusion in vascular pathologies. For the rheology test, we expand the existing bulk viscosity data of heated RBCs to a wider range of shear rates (1–1000 s⁻¹) to represent most pathophysiological conditions in macro- or microcirculation. Although heated RBC suspension shows elevated viscosity comparable to certain diseased RBC suspensions under relatively high shear rates (100–1000 s⁻¹), they underestimate the elevated viscosity (e.g., in sickle cell anemia) at low shear rates (<10 s⁻¹). Our work provides mechanistic rationale for selective usage of heated RBC as a potentially useful model for studying the abnormal traversal dynamics and hemorheology in certain blood disorders.     

Impedance spectroscopy flow cytometry: on-chip label-free cell differentiation.

BACKGROUND: The microfabricated impedance spectroscopy flow cytometer used in this study permits rapid dielectric characterization of a cell population with a simple microfluidic channel. Impedance measurements over a wide frequency range provide information on cell size, membrane capacitance, and cytoplasm conductivity as a function of frequency. The amplitude, opacity, and phase information can be used for discrimination between different cell populations without the use of cell markers. METHODS: Polystyrene beads, red blood cells (RBCs), ghosts, and RBCs fixed in glutaraldehyde were passed through a microfabricated flow cytometer and measured individually by using two simultaneously applied discrete frequencies. The cells were characterized at 1,000 per minute in the frequency range of 350 kHz to 20 MHz. RESULTS: Cell size was easily measured with submicron accuracy. Polystyrene beads and RBCs were differentiated using opacity. RBCs and ghosts were differentiated using phase information, whereas RBCs and fixed RBCs were differentiated using opacity. RBCs fixed using increasing concentrations of glutaraldehyde showed increasing opacity. This increased opacity was linked to decreased cytoplasm conductivity and decreased membrane capacitance, both resulting from protein cross-linking. CONCLUSIONS: This work presents label-free differentiation of cells in an on-chip flow cytometer based on impedance spectroscopy, which will be a powerful tool for cell characterization.     

Low viscosity Ektacytometry and its validation tested by flow chamber.

The flow chamber was used to observe the orientation and small deformation of red blood cells (RBCs) in a shear flow of low viscosity. With the aid of computer software, the percentage of RBCs oriented to the C=0 orbit (OI)(F) and the degree of deformation (DI)(F) of such RBCs were calculated by processing the photographs. It was found that these parameters were highly correlated, respectively, to the orientation index (OI)(E) and the small deformation index (DI)(E) obtained by our low viscosity Ektacytometry (LVE). Thus, our flow chamber research has provided direct evidence to validate the use of this low viscosity Ektacytometry. Although there are relative merits for the flow chamber method using low viscosity medium, the LVE is more likely to be applied in clinic for its simplicity and convenience.     

Reduced erythrocyte deformability alters pulmonary hemodynamics

Isolated rat lungs were perfused with suspensions containing normal and stiffened erythrocytes (RBCs) to assess the effect of altered RBC deformability on pulmonary hemodynamics. RBC suspensions were prepared using cells previously incubated in isosmolar phosphate-buffered saline with or without 0.0125 or 0.01875% glutaraldehyde. Washed RBCs were resuspended in isosmolar 4% albumin saline solution. Isolated rat lungs were perfused with control and stiffened cells by the use of a perfusion system that allowed rapid switching between suspensions. Pressure-flow (P/Q) curves were constructed by measuring pulmonary arterial pressure (Ppa) over a range of flow rates. In a second set of experiments, P/Q curves were generated for perfusion with control and stiffened cells (0.0125% glutaraldehyde) before and after vasoconstriction with a synthetic prostaglandin analogue (U 46619). RBC deformability was quantified in all experiments by determination of filtration time of a dilute cell suspension through a 4.7 microns Nuclepore filter. Incubation with 0.0125 or 0.01875% glutaraldehyde produced a 6 or 21% decrease in RBC deformability, respectively. These decreases in deformability were associated with significant increases in Ppa at each flow rate. The increases in Ppa correlated significantly with the degree of RBC stiffening. With 0.0125% glutaraldehyde, the P/Q curve was shifted upward without a change in slope, whereas incubation with 0.01875% glutaraldehyde resulted in a significant increase in slope. Vasoconstriction and perfusion with stiffened RBCs had additive effects on Ppa. These findings suggest that decreases in RBC deformability cause physiologically significant elevations in hemodynamic resistance in the pulmonary circuit independent of vasoactivity.     

Flow-pressure drop measurement and calculation in a tapered femoral artery of a dog

This study describes the in vivo measurement of pressure drop and flow during the cardiac cycle in the femoral artery of a dog, and the computer simulation of the experiment based on the use of the measured flow, vessel dimensions and blood viscosity. In view of the experimental uncertainty in obtaining the accurate velocity profile at the wall region, the velocity pulse at the center was measured and numerical calculations were performed for the center Une instantaneous velocity and within the two limits of spatial distribution of inlet flow conditions: uniform and parabolic. Temporal and spatial variations of flow parameters, i.e., velocity profile, shear rate, non-Newtonian viscosity, wall shear stress, and pressure drop were calculated. There existed both positive and negative shear rates during a pulse cycle, i.e., the arterial wall experiences zero shear three times during a cardiac cycle. For the parabolic inlet condition, the taper of the artery not only increased the magnitude of the positive and negative shear rates, but caused a steep gradient in shear rate, a phenomenon which in turn affects wall shear stress and pressure. In contrast, for the uniform inlet condition, the flow through the tapered artery was predominantly the developing type, which resulted in reduction in magnitude of wall shear rate along the axial direction.     

Three-dimensional focusing of red blood cells in microchannel flows for bio-sensing applications

Three-dimensional (3D) focusing of particles in microchannels has been a long-standing issue in the design of biochemical/biomedical microdevices. Current microdevices for 3D cell or bioparticle focusing involve complex channel geometries in view of their fabrication because they require multiple layers and/or sheath flows. This paper proposes a simple method for 3D focusing of red blood cells (RBCs) in a single circular microcapillary, without any sheath flows, which is inspired from the fluid dynamics phenomenon in that a spherical particle lagging behind a Poiseuille flow migrates toward and along the channel axis. More explicitly, electrophoresis of RBCs superimposed on the pressure-driven flow is utilized to generate an RBC migration mode analogous to this phenomenon. A particle-tracking scheme with a sub-pixel resolution is implemented to spatially position red blood cells flowing through the channel, so that a probability density function (PDF) is constructed to evaluate the tightness of the cell focusing. Above a specific strength of the electric field, approximately 90% of the sheep RBCs laden in the flow are tightly focused within a beam diameter that is three times the cell dimension. Particle shape effect on the focusing is discussed by making comparisons between the RBCs and the spherical particles. The lateral migration velocity, predicted by an existing theoretical model, is in good agreement with the present experimental data. It is noteworthy that 3D focusing of non-spherical particles, such as RBCs, has been achieved in a circular microchannel, which is a significant improvement over previous focusing methodologies.     

Stiffened erythrocytes augment the pulmonary hemodynamic response to hypoxia

Isolated rat lungs were perfused with suspensions containing normal and stiffened erythrocytes (RBCs) during normoxic and hypoxic ventilation to assess the effect of reduced RBC deformability on the hypoxic pressor response. RBC suspensions were prepared with cells previously incubated in isotonic phosphate-buffered saline with or without 0.0125% glutaraldehyde. The washed RBCs were resuspended in isotonic bicarbonate-buffered saline (with 4% albumin) to hematocrits of approximately 35%. The lungs were perfused with control and experimental cell suspensions in succession while pulmonary arterial pressure was measured during normoxic (21% O2) and hypoxic (3% O2) ventilation. On the attainment of a peak hypoxic pressor response, flow rate was changed so that pressure-flow curves could be constructed for each suspension. RBC deformability was quantified by a filtration technique using 4.7-microns-pore filters. Glutaraldehyde treatment produced a 10% decrease in RBC deformability (P less than 0.05). Over the range of flow rates, Ppa was increased by 15-17% (P less than 0.05) and 26-31% (P less than 0.05) during normoxic and hypoxic ventilation, respectively, when stiffened cells were suspended in the perfusate. The magnitude of the hypoxic pressor response was 50-54% greater with stiffened cells over the three flow rates. In a separate set of experiments, normoxic and hypoxic arterial blood samples from conscious unrestrained rats were used to investigate the effects of acute hypoxia on RBC deformability. Deformability was measured with the same filtration technique. There was no difference in the deformability of hypoxic compared with normoxic RBCs. We conclude that the presence of stiffened RBCs enhances the hemodynamic response to hypoxia but acute hypoxia does not affect RBC deformability.     

Radial displacement of red blood cells during hemodilution and the effect on arteriolar oxygen profile

In this study, we assessed the magnitude of the erratic deviations in the radial position of red blood cells (RBCs) in the laminar flow regime of arterioles in a hamster window preparation and the intraluminal Po(2) profile to determine whether this variability affects the intraluminal distribution of oxygen in conditions of normal hematocrit and hemodilution. A gated image intensifier was used to visualize fluorescently labeled RBCs in tracer quantities and obtain multiple measurements of RBC radial and longitudinal positions at time intervals on the order of 5 ms within single arterioles (diameter range 40-95 microm). RBCs in the velocity range of 0.3-14 mm/s exhibit a mean coefficient of variation of velocity of 16.9 +/- 10.5% and a SD of the radial position of 1.98 +/- 0.98 microm. Both quantities were inversely related to hematocrit, and the former was significantly lowered by hemodilution. Our experimental results presented very similar values and shape compared with the intraluminal oxygen profile derived theoretically for normal hematocrit, suggesting that shear-augmented diffusion due to the measured radial displacement of RBCs did not significantly affect oxygen diffusion from blood into the arteriolar vessel wall. Po(2) profiles in the arterioles assumed an increasingly parabolic configuration with increasing levels of hemodilution.     

Effect of pH on the velocity of erythrocyte aggregation

The effect of pH on the velocity of aggregation of human erythrocytes was quantitatively examined with a rheoscope combined with a video-camera, an image analyzer and a computer, in relation to the morphological changes of erythrocytes and their aggregates. (i) With increasing pH of the medium, the velocity of erythrocyte aggregation increased. (ii) The rouleaux formed at high pH were longer in shape and more stable against the increase of shear rate than those formed at low pH. (iii) With increasing pH, the diameter of erythrocyte increased, the (maximum) thickness decreased, and the cell volume decreased. The pH dependency of erythrocyte aggregation may be mainly due to the morphological change of erythrocytes, and partly due to the changes of erythrocyte deformability and of interaction with macromolecules.