An automated cell analysis sensing system based on a microfabricated rheoscope for the study of red blood cells physiology

An automated rheoscope has been developed, utilizing a microfabricated glass flow cell, high speed camera and advanced image-processing software. RBCs suspended in a high viscosity medium were filmed flowing through a microchannel. Under these conditions, RBCs exhibit different orientations and deformations according to their location in the velocity profile. The rheoscope system produces valuable data such as velocity profile of RBCs, spatial distribution within a microchannel and deformation index (DI) curves. The variation of DI across the channel height, due to change in shear stress, was measured carrying implications for diffractometry methods. These curves of DI were taken at a constant flow rate and cover most of the relevant shear stress spectrum. This is an improvement of the existing techniques for deformability measurements and may serve as a diagnostic tool for certain blood disorders. The DI curves were compared to measurements of the flowing RBCs velocity profile. In addition, we found that RBCs flowing in a microchannel are mostly gathered in the center of the flow and maintain a characteristic spatial distribution. The spatial distribution in this region changes slightly with increasing flow rate. Hence, the system described, provides means for examining the behavior of individual RBCs, and may serve as a microfabricated diagnostic device for deformability measurement.     

Computational Analysis of Dynamic Interaction of Two Red Blood Cells in a Capillary

The dynamic interaction of two red blood cells (RBCs) in a capillary is investigated computationally by the two-fluid model, including their deformable motion and interaction. For characterization of the deformation, the RBC membrane is treated as a curved two-dimensional shell with finite thickness by the shell model, and allowed to undergo the stretching strain and bending deformation. Moreover, a Morse potential is adopted to model the intercellular interaction for the aggregation behavior, which is characterized as the weak attraction at far distance and strong repulsion at near distance. For validation of the present technique, the dynamic interaction of two RBCs in static blood plasma is simulated firstly, where the RBCs aggregate slowly until a balanced configuration is achieved between the deformation and aggregation forces. The balanced configuration is in good agreement with the results reported previously. Three important effects on the dynamic behavior of RBCs are then analyzed, and they are the initial RBC shape, RBC deformability, and the intercellular interaction strength. It is found that the RBC is less deformed into a well-known parachute shape when the initial RBC shape is larger. Similarly, if the elastic shear modulus and bending stiffness of RBC membrane increase, the RBC resistance to deformation becomes higher, such that the RBC is less deformed. The simulation results also demonstrate that the RBC deformability strongly depends on the intercellular interaction strength. The RBCs deform more easily as the intercellular interaction strength increases.     

Effect of N‐ethylmaleimide,chymotrypsin, and H2O2 on the viscoelasticity of human erythrocytes: Experimental measurement and theoretical analysis

The physiological functions of erythrocytes depend critically on their morphology, deformability, and aggregation capability in response to external physical and chemical stimuli. The dynamic deformability can be described in terms of their viscoelasticity. We applied jumping optical tweezers to trap and stretch individual red blood cells (RBCs) to characterize its viscoelasticity in terms of the Young's modulus and viscosity by analyzing the experimental data of dynamic deformation using a 2‐parameter Kelvin solid model. The effects of three chemical agents (N ‐ethylmaleimide, Chymotrypsin, and Hydrogen peroxide) on RBC's mechanical properties were studied by comparing the Young's modulus and viscosity of RBCs with and without these chemical treatments. Although the effects of each of these chemicals on the molecular structures of RBC may not be exclusive, based on the dominant effect of each chemical, we attempted to dissect the main contributions of different constituents of the RBC membrane to its viscosity and elasticity. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Effect of lanthanum on red blood cell deformability

Prior reports describing the effects of lanthanum (La(3+)) on red blood cells (RBC) have focused on the effects of this lanthanide on cell fusion or on membrane characteristics (e.g., ion movement across membrane, membrane protein aggregation); the present study explores its rheological and biophysical effects. Normal human RBC were exposed to La(3+) levels up to 200 microM then tested for: (1) cellular deformability using a laser-based ektacytometer and an optical-based rheoscope; (2) membrane viscoelastic behavior via micropipettes; (3) surface charge via micro electrophoresis. La(3+) concentrations of 12.5 to 200 microM caused dose-dependent decreases of deformability that were greatest at low stresses: these rheological changes were completely reversible upon removing La(3+) from the media either by washing with La(3+)-free buffer or by suspending La(3+)-exposed cells in La(3+)-free media (i.e., viscous dextran solution). Both membrane shear elastic modulus and membrane surface viscosity were increased by 25-30% at 100 or 200 microM. As expected, La(3+) decreased RBC electrophoretic mobility (EPM), with EPM inversely but not linearly associated with deformability; changes of EPM were also completely reversible. These results thus indicate novel aspects of RBC cellular and membrane rheological behavior yet raise questions regarding specific mechanisms responsible for La(3+)-induced alterations.     

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.     

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.     

Alteration of red cell membrane viscoelasticity by heat treatment: effect on cell deformability and suspension viscosity

The membrane shear elastic modulus (mu) and the time constant for extensional shape recovery (tc) were measured for normal, control human red blood cells (RBC) and for RBC heat treated (HT) at 48 degrees C. Three separate methods for the measurement of mu were compared (two used a micropipette and one employed a flow channel), and the membrane viscosity (n) was calculated from the relation n = mu. tc. The deformability of HT and control cells was evaluated using micropipette techniques, and the bulk viscosity of RBC suspensions at 40% hematocrit was measured. The shear elastic modulus, or "membrane rigidity", was more than doubled by heat treatment, although both the absolute value for mu and the estimate of the increase induced by heat treatment varied depending on the method of measurement. Heat treatment caused smaller increases in membrane viscosity and in membrane bending resistance, and only minimal changes in cell geometry. The deformability of HT cells was reduced: 1) the pressure required for cell entry (Pe) into 3 micrometers pipettes was increased, on average, by 170%; 2) at an aspiration pressure (Pa) exceeding Pe, longer times were required for cell entry into the same pipettes. However, when Pa was scaled relative to the mean entry pressure for a given sample (i.e, Pa/Pe), entry times were similar for control and HT cells. Bulk viscosity of HT RBC suspensions was elevated by approximately 12% on average (shear rates 75 to 1500 inverse seconds). These findings suggest that alteration of RBC membrane mechanical properties, similar to those induced by heat treatment, would most affect the in vivo circulation in regions where vessel dimensions are smaller than cellular diameters.     

How malaria parasites reduce the deformability of infected red blood cells

The pathogenesis of malaria is largely due to stiffening of the infected red blood cells (RBCs). Contemporary understanding ascribes the loss of RBC deformability to a 10-fold increase in membrane stiffness caused by extra cross-linking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of ～3-fold in the shear modulus. We believe the discrepancy stems from the rigid parasite particles inside infected cells, and have carried out numerical simulations to demonstrate this mechanism. The cell membrane is represented by a set of discrete particles connected by linearly elastic springs. The cytosol is modeled as a homogeneous Newtonian fluid, and discretized by particles as in standard smoothed particle hydrodynamics. The malaria parasite is modeled as an aggregate of particles constrained to rigid-body motion. We simulate RBC stretching tests by optical tweezers in three dimensions. The results demonstrate that the presence of a sizeable parasite greatly reduces the ability of RBCs to deform under stretching. With the solid inclusion, the observed loss of deformability can be predicted quantitatively using the local membrane elasticity measured by micropipettes.     

结合AFM探测副伤寒沙门氏茵B感染红细胞膜的生物力学特性

采用原子力显微镜和衍射显微术,在纳米精确尺度探测副伤寒沙门氏菌B（Sp B）感染宿主红细胞（RBC）膜微观结构和力学特性,涉及细胞的形变、膜面内剪切模量和弯曲模量。结合这两种单分子测量技术,利用相关的数学模型表述RBC膜对菌体印B的入侵非常敏感。实验结果显示,不同感染期间的SpB寄生菌体,能够引起宿主RBC膜结构改变,形变能力降低,膜剪切模量和弯曲模量显著增加。这些力学特性的变化影响RBC的输氧和循环功能。实验结果表明,印B具有独特的鞭毛调控系统,入侵的毒性菌体寄生蛋白与血影蛋白网络中的运输蛋白有特异结合位点,导致RBC膜骨架网络、波动力学和细胞内、外基质都产生应激反应,这有可能为理解勋曰感染RBC的发病机理和寄生途径提供一些新的实验思路和分析依据。     

Tank-treading dynamics of red blood cells in shear flow: On the membrane viscosity rheology

In this article, extensive three-dimensional simulations are conducted for tank-treading (TT) red blood cells (RBCs) in shear flow with different cell viscous properties and flow conditions. Apart from recent numerical studies on TT RBCs, this research considers the uncertainty in cytoplasm viscosity, covers a more complete range of shear flow situations of available experiments, and examines the TT behaviors in more details. Key TT characteristics, including the rotation frequency, deformation index, and inclination angle, are compared with available experimental results of similar shear flow conditions. Fairly good simulation-experiment agreements for these parameters can be obtained by adjusting the membrane viscosity values; however, different rheological relationships between the membrane viscosity and the flow shear rate are noted for these comparisons: shear thinning from the TT frequency, Newtonian from the inclination angle, and shear thickening from the cell deformation. Previous studies claimed a shear-thinning membrane viscosity model based on the TT frequency results; however, such a conclusion seems premature from our results and more carefully designed and better controlled investigations are required for the RBC membrane rheology. In addition, our simulation results reveal complicate RBC TT features and such information could be helpful for a better understanding of in vivo and in vitro RBC dynamics.     

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.     

Mixed Exciton-Charge-Transfer States in Photosystem II: Stark Spectroscopy on Site-Directed Mutants

Sickle erythrocytes exhibit abnormal morphology and membrane mechanics under deoxygenated conditions due to the polymerization of hemoglobin S. We employed dissipative particle dynamics to extend a validated multiscale model of red blood cells (RBCs) to represent different sickle cell morphologies based on a simulated annealing procedure and experimental observations. We quantified cell distortion using asphericity and elliptical shape factors, and the results were consistent with a medical image analysis. We then studied the rheology and dynamics of sickle RBC suspensions under constant shear and in a tube. In shear flow, the transition from shear-thinning to shear-independent flow revealed a profound effect of cell membrane stiffening during deoxygenation, with granular RBC shapes leading to the greatest viscosity. In tube flow, the increase of flow resistance by granular RBCs was also greater than the resistance of blood flow with sickle-shape RBCs. However, no occlusion was observed in a straight tube under any conditions unless an adhesive dynamics model was explicitly incorporated into simulations that partially trapped sickle RBCs, which led to full occlusion in some cases.     

Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering

Red blood cells (RBCs) present unique reversible shape deformability, essential for both function and survival, resulting notably in cell membrane fluctuations (CMF). These CMF have been subject of many studies in order to obtain a better understanding of these remarkable biomechanical membrane properties altered in some pathological states including blood diseases. In particular the discussion over the thermal or metabolic origin of the CMF has led in the past to a large number of investigations and modeling. However, the origin of the CMF is still debated. In this article, we present an analysis of the CMF of RBCs by combining digital holographic microscopy (DHM) with an orthogonal subspace decomposition of the imaging data. These subspace components can be reliably identified and quantified as the eigenmode basis of CMF that minimizes the deformation energy of the RBC structure. By fitting the observed fluctuation modes with a theoretical dynamic model, we find that the CMF are mainly governed by the bending elasticity of the membrane and that shear and tension elasticities have only a marginal influence on the membrane fluctations of the discocyte RBC. Further, our experiments show that the role of ATP as a driving force of CMF is questionable. ATP, however, seems to be required to maintain the unique biomechanical properties of the RBC membrane that lead to thermally excited CMF.     

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.     

A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics

Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and by the external/internal fluid and membrane viscosities. We present a multiscale RBC model that is able to predict RBC mechanics, rheology, and dynamics in agreement with experiments. Based on an analytic theory, the modeled membrane properties can be uniquely related to the experimentally established RBC macroscopic properties without any adjustment of parameters. The RBC linear and nonlinear elastic deformations match those obtained in optical-tweezers experiments. The rheological properties of the membrane are compared with those obtained in optical magnetic twisting cytometry, membrane thermal fluctuations, and creep followed by cell recovery. The dynamics of RBCs in shear and Poiseuille flows is tested against experiments and theoretical predictions, and the applicability of the latter is discussed. Our findings clearly indicate that a purely elastic model for the membrane cannot accurately represent the RBC's rheological properties and its dynamics, and therefore accurate modeling of a viscoelastic membrane is necessary.     

Multiscale modeling of red blood cell mechanics and blood flow in malaria

Red blood cells (RBCs) infected by a Plasmodium parasite in malaria may lose their membrane deformability with a relative membrane stiffening more than ten-fold in comparison with healthy RBCs leading to potential capillary occlusions. Moreover, infected RBCs are able to adhere to other healthy and parasitized cells and to the vascular endothelium resulting in a substantial disruption of normal blood circulation. In the present work, we simulate infected RBCs in malaria using a multiscale RBC model based on the dissipative particle dynamics method, coupling scales at the sub-cellular level with scales at the vessel size. Our objective is to conduct a full validation of the RBC model with a diverse set of experimental data, including temperature dependence, and to identify the limitations of this purely mechanistic model. The simulated elastic deformations of parasitized RBCs match those obtained in optical-tweezers experiments for different stages of intra-erythrocytic parasite development. The rheological properties of RBCs in malaria are compared with those obtained by optical magnetic twisting cytometry and by monitoring membrane fluctuations at room, physiological, and febrile temperatures. We also study the dynamics of infected RBCs in Poiseuille flow in comparison with healthy cells and present validated bulk viscosity predictions of malaria-infected blood for a wide range of parasitemia levels (percentage of infected RBCs with respect to the total number of cells in a unit volume).     

Wall shear stress-based model for adhesive dynamics of red blood cells in malaria

Red blood cells (RBCs) infected by the Plasmodium falciparum (Pf-RBCs) parasite lose their membrane deformability and they also exhibit enhanced cytoadherence to vascular endothelium and other healthy and infected RBCs. The combined effect may lead to severe disruptions of normal blood circulation due to capillary occlusions. Here we extend the adhesion model to investigate the adhesive dynamics of Pf-RBCs as a function of wall shear stress (WSS) and other parameters using a three-dimensional, multiscale RBC model. Several types of adhesive behavior are identified, including firm adhesion, flipping dynamics, and slow slipping along the wall. In particular, the flipping dynamics of Pf-RBCs observed in experiments appears to be due to the increased stiffness of infected cells and the presence of the solid parasite inside the RBC, which may cause an irregular adhesion behavior. Specifically, a transition from crawling dynamics to flipping behavior occurs at a Young's modulus approximately three times larger than that of healthy RBCs. The simulated dynamics of Pf-RBCs is in excellent quantitative agreement with available microfluidic experiments if the force exerted on the receptors and ligands by an existing bond is modeled as a nonlinear function of WSS.     

Red Blood Cell Shape and Fluctuations: Cytoskeleton Confinement and ATP Activity

We review recent theoretical work that analyzes experimental measurements of the shape and fluctuations of red blood cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the situation of elastic cells with that of fluid-filled vesicles. In red blood cells (RBCs), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wave vector and frequency dependence of the fluctuation spectrum of RBCs indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect the transient defects induced in the cytoskeleton network by ATP.     

Effects of inner solution viscosity and membrane stiffness on erythrocyte deformability on passing through a microchannel: prediction by two-dimensional simulation

We studied erythrocyte deformability in an effort to develop diagnostic methods based on its measurement and thus aid in the development of therapies for circulatory diseases. In the reported work, we performed two-dimensional numerical simulations of blood flow through a microchannel (MC) to evaluate erythrocyte deformability, applying the immersed boundary method to simulate erythrocyte movement and deformation. To evaluate deformability, MC transit capacity and shape recoverability were considered, defined as the time required to pass through the MC and the time constant during the shape-recovery process after exiting the MC, respectively. The simulation results showed that the erythrocyte MC transit time increased when the viscosity of the inner solution or the stiffness of the membrane increased. The time constant for erythrocyte shape recovery increased as the inner solution viscosity increased. In contrast, the time constant decreased as the erythrocyte membrane stiffness increased. These time-constant trends were in agreement with a theoretical equation derived using the Kelvin model and with previous experimental results. This diagnostic method of measuring erythrocyte shape recoverability and MC transit capacity is anticipated to have clinical application.