Rheological comparison of hemoglobin solutions and erythrocyte suspensions

Hemoglobin Binding to the Red Blood Cell (RBC) Membrane Is Associated with Decreased Cell Deformability

The deformability of red blood cells (RBCs), expressing their ability to change their shape as a function of flow-induced shear stress, allows them to optimize oxygen delivery to the tissues and minimize their resistance to flow, especially in microcirculation. During physiological aging and blood storage, or under external stimulations, RBCs undergo metabolic and structural alterations, one of which is hemoglobin (Hb) redistribution between the cytosol and the membrane. Consequently, part of the Hb may attach to the cell membrane, and although this process is reversible, the increase in membrane-bound Hb (MBHb) can affect the cell's mechanical properties and deformability in particular. In the present study, we examined the correlation between the MBHb levels, determined by mass spectroscopy, and the cell deformability, determined by image analysis. Six hemoglobin subunits were found attached to the RBC membranes. The cell deformability was negatively correlated with the level of four subunits, with a highly significant inter-correlation between them. These data suggest that the decrease in RBC deformability results from Hb redistribution between the cytosol and the cell membrane and the respective Hb interaction with the cell membrane.

Hemoglobin in large vessel occlusion: Look further than collaterals

BACKGROUND

Abnormal hemoglobin (Hb) levels lead to poorer outcomes in ischemic stroke, though the mechanisms remain elusive. We aimed to study the role of Hb on imaging and clinical outcomes, namely on collaterals as it is a known mediator of infarct growth.

METHODS

Retrospective cohort study of patients with large vessel occlusion ischemic stroke admitted to our center. Demographics, clinical and imaging variables were collected, particularly baseline hemoglobin, presence of anemia and collateral score. Collaterals were scored from 0 to 3 and defined as poor if 0-1. Multivariable analyses were performed for collateral score and clinical outcomes (3-month mortality and good prognosis).

RESULTS

We included 811 patients, 215 (26.5 %) with anemia. Patients with anemia were older, had more comorbidities and more severe strokes. Hemoglobin levels and anemia were not associated with collateral score (OR 0.97, 95 % CI 0.89-1.05, p = 0.414 and OR 0.89, 95 % CI 0.64-1.24, p = 0.487, respectively) nor with poor collaterals (OR 0.96, 95 % CI 0.88-1.05, p = 0.398 and OR 0.86, 95 % CI 0.60-1.23, p = 0.406, respectively). Hb levels were associated with 3-month mortality (OR 0.85, 95 % CI 0.76-0.96, p = 0.008).

CONCLUSION

Hemoglobin or anemia were not found to be associated with collateral status. Our results raise further questions regarding the pathophysiology of anemia and outcomes in ischemic stroke, highlighting the need for future research.

Influence of Na+ disorder on cytoplasmic conductivity and cellular electromagnetic (EM) energy absorption of human erythrocytes (PONE-D-21-36089)

Cytoplasmic conductivity of human erythrocytes may be significantly disturbed by the composition of the external suspending media. Effects of external NaCl on cytoplasmic conductivity of human erythrocyte (Human Red Blood Cells, HRBC) were investigated in a simple NaCl system. Using thermodynamic theory cytoplasmic conductivities could be calculated from internal [K+], [Na+], [Cl-] and [HCO3-]. Effect of cell volume and cell water changes were introduced and allowed for using the Debye-Hückel-Onsager relation and Walden's rule of viscosity. Cell volume and cell water change of HRBCs were measured in suspending isotonic solutions with conductivities from 0.50 S m-1 up to hypertonic solutions of conductivity of 2.02 S m-1 at selected temperatures of 25°C (standard benchmark temperature) and 37°C (physiological temperature). In isotonic solutions, cytoplasmic conductivity of human erythrocyte decreases with rise in the external media ionic concentration and vice versa for hypertonic solutions. The HRBC is capable of rapidly regulating its volume (and shape) over quite a wide range of osmolality. Specific Absorption Rate (SAR, 900 MHz) values (W kg-1) of electromagnetic radiation are below safe limits at non-physiological 25°C but above legal limits at 37°C [National Council on Radiation Protection and Measurements, NCRP]. However, at 37°C under both hypertonic [Na+] and isotonic but low [Na+], SAR increases further beyond legal limits.

Red blood cell shape transitions and dynamics in time-dependent capillary flows

The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, nonsymmetric slipper shape is significantly faster than the opposite shape transition, which exhibits pronounced cell rotations. Complementary simulations indicate that these dynamics depend on the orientation of the RBC membrane in the channel during the time-dependent flow. Moreover, we show how the tank-treading movement of slipper-shaped RBCs in combination with the narrow channel leads to oscillations of the cell's center of mass. The frequency of these oscillations depends on the cell velocity, the viscosity of the surrounding fluid, and the cytosol viscosity. These results provide a potential framework to identify and study pathological changes in RBC properties.

Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension

The inner viscosity of a biological red blood cell is about five times larger than the viscosity of the blood plasma. In this work, we use dissipative particles to enable the proper viscosity contrast in a mesh-based red blood cell model. Each soft particle represents a coarse-grained virtual cluster of hemoglobin proteins contained in the cytosol of the red blood cell. The particle interactions are governed by conservative and dissipative forces. The conservative forces have purely repulsive character, whereas the dissipative forces depend on the relative velocity between the particles. We design two computational experiments that mimic the classical viscometers. With these experiments we study the effects of particle suspension parameters on the inner cell viscosity and provide parameter sets that result in the correct viscosity contrast. The results are validated with both static and dynamic biological experiment, showing an improvement in the accuracy of the original model without major increase in computational complexity.

Elucidating the rheological implications of adding particles in blood

In the past few decades, nanotechnology has been employed to provide breakthroughs in the diagnosis and treatment of several diseases using drug-carrying particles (DCPs). In such an endeavor, the optimal design of DCPs is paramount, which necessitates the use of an accurate and trustworthy constitutive model in computational fluid dynamics (CFD) simulators. We herein introduce a continuum model for elaborating on the rheological implications of adding particles in blood. The model is developed using non-equilibrium thermodynamics to guarantee thermodynamic admissibility. Red blood cells are modeled as deformed droplets with a constant volume that are able to aggregate, whereas particles are considered rigid spheroids. The model predictions are compared favorably against rheological data for both spherical and non-spherical particles immersed in non-aggregating blood. It is expected that the use of this model will allow for the testing of DCPs in virtual patients and for their tailor-design in treating various diseases.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00397-021-01289-x.

Molecular rotors as intracellular probes of red blood cell stiffness

The deformability of red blood cells is an essential parameter that controls the rheology of blood as well as its circulation in the body. Characterizing the rigidity of the cells and their heterogeneity in a blood sample is thus a key point in the understanding of occlusive phenomena, particularly in the case of erythrocytic diseases in which healthy cells coexist with pathological cells. However, measuring intracellular rheology in small biological compartments requires the development of specific techniques. We propose a technique based on molecular rotors - viscosity-sensitive fluorescent probes - to evaluate the above key point. DASPI molecular rotor has been identified with spectral fluorescence properties decoupled from those of hemoglobin, the main component of the cytosol. After validation of the rotor as a viscosity probe in model fluids, we showed by confocal microscopy that, in addition to binding to the membrane, the rotor penetrates spontaneously and uniformly into red blood cells. Experiments on red blood cells whose rigidity is varied with temperature, show that molecular rotors can detect variations in their overall rigidity. A simple model allowed us to separate the contribution of the cytosol from that of the membrane, allowing a qualitative determination of the variation of cytosol viscosity with temperature, consistent with independent measurements of the viscosity of hemoglobin solutions. Our experiments show that the rotor can be used to study the intracellular rheology of red blood cells at the cellular level, as well as the heterogeneity of this stiffness in a blood sample. This opens up new possibilities for biomedical applications, diagnosis and disease monitoring.

Energy absorption of human red blood cells and conductivity of the cytoplasm influenced by temperature

The energy absorbed into tissues is known as the specific energy absorption (SAR) which is dependent on conductivity of the tissue. We calculated cytoplasmic conductivity of human red blood cell (HRBC) using the intracellular ionic concentrations and the Debye-Hückel-Onsager relation. The overall concentration is determined by cell volume and cell water content. The calculated HRBC conductivity at 25 ^o C was σ_c,₂₅ = 0.5566 ± 0.0146 S m^-1, ±SE). It is exponentially related to temperature: Q₁₀ ≈ 1.866. At 37 ^o C, the calculated SAR value is 1.6 W kg^-1 using a linear temperature compensation of conductivity. However, if using a biologically realistic non-linear temperature compensated conductivity, the SAR is ≈ 2.62 ± 0.05 W kg^-1. The relationship between SAR and temperature increase is not straightforward. Since there is a wide variance in cellular ionic and water perfusion rates more tissue-specific SAR limits which consider temperature-related factors would be valuable.

A constitutive hemorheological model addressing the deformability of red blood cells in Ringer solutions

Red blood cells (RBCs) can deform substantially, a feature that allows them to pass through capillaries that are narrower than the largest dimension of an undeformed RBC. Clearly, to understand how they transport through our microcirculation, we need a constitutive model able of accurately predicting the deformability of RBCs, which seems currently unavailable. To address this void, we herein propose a new model that accounts for the deformability of RBCs by modeling them as deformed droplets with a constant volume. To make sure the model is by construction thermodynamically admissible we employ non-equilibrium thermodynamics as our tool. Since RBCs are merely droplets with the inner fluid exhibiting a higher viscosity than that of the outer one, RBCs are described by a conformation tensor constrained to have a constant determinant (volume). The model predicts the second normal stress coefficient in steady-state simple shear flow to first shear thicken and then shear thin, which is an unexpected behavior; however, we cannot judge whether such a prediction is aphysical or not due to unavailable experimental rheological data in the literature. We show that the new model is capable of addressing the deformability of isolated (very low hematocrit) RBCs in simple shear and the shear viscosity of non-aggregating blood. As derived the model addresses only non-aggregating blood, but can very easily be generalized to account for aggregating blood.

Large-scale simulation of biomembranes incorporating realistic kinetics into coarse-grained models

Biomembranes are two-dimensional assemblies of phospholipids that are only a few nanometres thick, but form micrometre-sized structures vital to cellular function. Explicit molecular modelling of biologically relevant membrane systems is computationally expensive due to the large number of solvent particles and slow membrane kinetics. Coarse-grained solvent-free membrane models offer efficient sampling but sacrifice realistic kinetics, thereby limiting the ability to predict pathways and mechanisms of membrane processes. Here, we present a framework for integrating coarse-grained membrane models with continuum-based hydrodynamics. This framework facilitates efficient simulation of large biomembrane systems with large timesteps, while achieving realistic equilibrium and non-equilibrium kinetics. It helps to bridge between the nanometer/nanosecond spatiotemporal resolutions of coarse-grained models and biologically relevant time- and lengthscales. As a demonstration, we investigate fluctuations of red blood cells, with varying cytoplasmic viscosities, in 150-milliseconds-long trajectories, and compare kinetic properties against single-cell experimental observations.

The influence of red blood cell deformability on hematocrit profiles and platelet margination

The influence of red blood cell (RBC) deformability in whole blood on platelet margination is investigated using confocal microscopy measurements of flowing human blood and cell resolved blood flow simulations. Fluorescent platelet concentrations at the wall of a glass chamber are measured using confocal microscopy with flowing human blood containing varying healthy-to-stiff RBC fractions. A decrease is observed in the fluorescent platelet signal at the wall due to the increase of stiffened RBCs in flow, suggesting a decrease of platelet margination due to an increased fraction of stiffened RBCs present in the flow. In order to resolve the influence of stiffened RBCs on platelet concentration at the channel wall, cell-pair and bulk flow simulations are performed. For homogeneous collisions between RBC pairs, a decrease in final displacement after a collision with increasing membrane stiffness is observed. In heterogeneous collisions between healthy and stiff RBC pairs, it is found that the stiffened RBC is displaced most. The influence of RBC deformability on collisions between RBCs and platelets was found to be negligible due to their size and mass difference. For a straight vessel geometry with varying healthy-to-stiff RBC ratios, a decrease was observed in the red blood cell-free layer and platelet margination due to an increase in stiffened RBCs present in flow.

An experimental erythrocyte rigidity index (Ri) and its correlations with Transcranial Doppler velocities (TAMMV), Gosling Pulsatility Index PI, hematocrit, hemoglobin concentration and red cell distribution width (RDW)

Brain artery velocities (Time-Averaged Maximum Mean Velocity, TAMMV) by Transcranial Doppler (TCD), hematocrit, hemoglobin, Red blood cell (RBC) Distribution Width (RDW) and RBC rigidity index (Ri), when reported together with their correlations, provide a accurate and useful diagnostic picture than blood viscosity measurements alone. Additionally, our study included a sixth parameter provided by TCD, the Gosling Pulsatility Index PI, which is an indicator of CBF (Cerebral Blood Flow) resistance. All these parameters are routine in Hematology except for values of Ri. The rigidity (Ri) of the RBC is the main rheological characteristic of the blood of Sickle Cell Anemia (SCA) patients and several pathologies. However, its quantification depends on many commercial and experimental techniques, none disseminated and predominant around the World. The difference in absorbance values of the blood, during the process of sedimentation in a microwell of a Microplate Reader, is a straightforward way of semi-quantifying the RBC rigidity Ri, since the fraction of irreversibly sickled red blood cells does not form rouleaux. Erythrocyte Rigidity Index (Ri) was calculated using initial absorbance A_initial (6 s) and final A_final (540 s), Ri = 1 / (Ai-Af). The Ri of 119 patients (2–17 y / o, M & F) SCA, SCC (Sickle Cell/hemoglobin C), SCD (Sickle Cell/hemoglobin D), Sβ0thal (Sickle Cell/hemoglobin Beta Zero Thalassemia) and 71 blood donors (20–65 y / o, M & F) were measured in our laboratory while the five parameters (TAMMV and PI by TCD, Hct, Hb and RDW) were obtained from medical records. The in vitro addition of hydroxyurea (HU, 50mg /dl, n = 51 patients, and n = 8 healthy donors) in the samples decreased the rouleaux adhesion strength of both donor and patients’ blood samples, leading to extraordinarily high Ri values. The correlation between the studied parameters was especially significant for the direct relationships between Ri, TAMMV, and PI.

Intravital Vascular Phototheranostics and Real-Time Circulation Dynamics of Micro- and Nanosized Erythrocyte-Derived Carriers

Erythrocyte-based carriers can serve as theranostic platforms for delivery of imaging and therapeutic payloads. Engineering these carriers at micro- or nanoscales makes them potentially useful for broad clinical applications ranging from vascular diseases to tumor theranostics. Longevity of these carriers in circulation is important in delivering a sufficient amount of their payloads to the target. We have investigated the circulation dynamics of micro (∼4.95 μm diameter) and nano (∼91 nm diameter) erythrocyte-derived carriers in real time using near-infrared fluorescence imaging, and evaluated the effectiveness of such carrier systems in mediating photothermolysis of cutaneous vasculature in mice. Fluorescence emission half-lives of micro- and nanosized carriers in response to a single intravenous injection were ∼49 and ∼15 min, respectively. A single injection of microsized carriers resulted in a 3-fold increase in signal-to-noise ratio that remained nearly persistent over 1 h of imaging time. Our results also suggest that a second injection of the carriers 7 days later can induce a transient inflammatory response, as manifested by the apparent leakage of the carriers into the perivascular tissue. The administration of the carriers into the mice vasculature reduced the threshold laser fluence to induce photothermolysis of blood vessels from >65 to 20 J/cm². We discuss the importance of membrane physicochemical and mechanical characteristics in engineering erythrocyte-derived carriers and considerations for their clinical translation.

Hemoglobin S and C affect biomechanical membrane properties of P. falciparum-infected erythrocytes

During intraerythrocytic development, the human malaria parasite Plasmodium falciparum alters the mechanical deformability of its host cell. The underpinning biological processes involve gain in parasite mass, changes in the membrane protein compositions, reorganization of the cytoskeletons and its coupling to the plasma membrane, and formation of membrane protrusions, termed knobs. The hemoglobinopathies S and C are known to partially protect carriers from severe malaria, possibly through additional changes in the erythrocyte biomechanics, but a detailed quantification of cell mechanics is still missing. Here, we combined flicker spectroscopy and a mathematical model and demonstrated that knob formation strongly suppresses membrane fluctuations by increasing membrane-cytoskeleton coupling. We found that the confinement increased with hemoglobin S but decreases with hemoglobin C in spite of comparable knob densities and diameters. We further found that the membrane bending modulus strongly depends on the hemoglobinopathetic variant, suggesting increased amounts of irreversibly oxidized hemichromes bound to membranes.

Numerical Investigation of the Effects of Red Blood Cell Cytoplasmic Viscosity Contrasts on Single Cell and Bulk Transport Behaviour

In-silico cellular models of blood are invaluable to gain understanding about the many interesting properties that blood exhibits. However, numerical investigations that focus on the effects of cytoplasmic viscosity in these models are not very prevalent. We present a parallelised method to implement cytoplasmic viscosity for HemoCell, an open-source cellular model based on immersed boundary lattice Boltzmann methods, using an efficient ray-casting algorithm. The effects of the implementation are investigated with single-cell simulations focusing on the deformation in shear flow, the migration due to wall induced lift forces, the characteristic response time in periodic stretching and pair collisions between red blood cells and platelets. Collective transport phenomena are also investigated in many-cell simulations in a pressure driven channel flow. The simulations indicate that the addition of a viscosity contrast between internal and external fluids significantly affects the deformability of a red blood cell, which is most pronounced during very short time-scale events. Therefore, modelling the cytoplasmic viscosity contrast is important in scenarios with high velocity deformation, typically high shear rate flows.

Numerical-experimental observation of shape bistability of red blood cells flowing in a microchannel

Red blood cells flowing through capillaries assume a wide variety of different shapes owing to their high deformability. Predicting the realized shapes is a complex field as they are determined by the intricate interplay between the flow conditions and the membrane mechanics. In this work we construct the shape phase diagram of a single red blood cell with a physiological viscosity ratio flowing in a microchannel. We use both experimental in vitro measurements as well as 3D numerical simulations to complement the respective other one. Numerically, we have easy control over the initial starting configuration and natural access to the full 3D shape. With this information we obtain the phase diagram as a function of initial position, starting shape and cell velocity. Experimentally, we measure the occurrence frequency of the different shapes as a function of the cell velocity to construct the experimental diagram which is in good agreement with the numerical observations. Two different major shapes are found, namely croissants and slippers. Notably, both shapes show coexistence at low (<1 mm s^-1) and high velocities (>3 mm s^-1) while in-between only croissants are stable. This pronounced bistability indicates that RBC shapes are not only determined by system parameters such as flow velocity or channel size, but also strongly depend on the initial conditions.

Characterization of erythrocyte membrane tension for hemolysis prediction in complex flows

Hemolysis is a persistent issue with blood-contacting devices. Many experimental and theoretical contributions over the last few decades have increased insight into the mechanisms of hemolysis in both laminar and turbulent flows, with the ultimate goal of developing a comprehensive, mechanistic hemolysis model. Many models assume that hemolysis scales with a resultant, scalar stress representing all components of the fluid stress tensor. This study critically evaluates this scalar stress hypothesis by calculating the response of the red blood cell membrane to different types of fluid stress (laminar shear and extension, and three turbulent shear and extension cases), each with the same scalar stress. It was found that even though the scalar stress is the same for all cases, membrane tension varied by up to three orders of magnitude. In addition, extensional flow causes constant tension, while tank-treading in shear flow causes periodic tension, with tank-treading frequency varying by three orders of magnitude among the cases. For turbulent flow, tension also depends on eddy size. It is concluded, therefore, that scalar stress alone is inadequate for scaling hemolysis. Fundamental investigations are needed to establish a new index of the fluid stress tensor that provides reliable hemolysis prediction across the wide range of complex flows that occur in cardiovascular devices.

Direct Cytoskeleton Forces Cause Membrane Softening in Red Blood Cells

Erythrocytes are flexible cells specialized in the systemic transport of oxygen in vertebrates. This physiological function is connected to their outstanding ability to deform in passing through narrow capillaries. In recent years, there has been an influx of experimental evidence of enhanced cell-shape fluctuations related to metabolically driven activity of the erythroid membrane skeleton. However, no direct observation of the active cytoskeleton forces has yet been reported to our knowledge. Here, we show experimental evidence of the presence of temporally correlated forces superposed over the thermal fluctuations of the erythrocyte membrane. These forces are ATP-dependent and drive enhanced flickering motions in human erythrocytes. Theoretical analyses provide support for a direct force exerted on the membrane by the cytoskeleton nodes as pulses of well-defined average duration. In addition, such metabolically regulated active forces cause global membrane softening, a mechanical attribute related to the functional erythroid deformability.

Inversion of hematocrit partition at microfluidic bifurcations

Partitioning of red blood cells (RBCs) at the level of bifurcations in the microcirculatory system affects many physiological functions yet it remains poorly understood. We address this problem by using T-shaped microfluidic bifurcations as a model. Our computer simulations and in vitro experiments reveal that the hematocrit (ϕ0) partition depends strongly on RBC deformability, as long as ϕ0<20% (within the normal range in microcirculation), and can even lead to complete deprivation of RBCs in a child branch. Furthermore, we discover a deviation from the Zweifach-Fung effect which states that the child branch with lower flow rate recruits less RBCs than the higher flow rate child branch. At small enough ϕ0, we get the inverse scenario, and the hematocrit in the lower flow rate child branch is even higher than in the parent vessel. We explain this result by an intricate up-stream RBC organization and we highlight the extreme dependence of RBC transport on geometrical and cell mechanical properties. These parameters can lead to unexpected behaviors with consequences on the microcirculatory function and oxygen delivery in healthy and pathological conditions.

Dynamics of a single red blood cell in simple shear flow

This work describes simulations of a red blood cell (RBC) in simple shear flow, focusing on the dependence of the cell dynamics on the spontaneous curvature of the membrane. The results show that an oblate spheroidal spontaneous curvature maintains the dimple of the RBC during tank-treading dynamics as well as exhibits off-shear-plane tumbling consistent with the experimental observations of Dupire et al. [J. Dupire, M. Socol, and A. Viallat, Proc. Natl. Acad. Sci. USA 109, 20808 (2012)] and their hypothesis of an inhomogeneous spontaneous shape. As the flow strength (capillary number Ca) is increased at a particular viscosity ratio between inner and outer fluid, the dynamics undergo transitions in the following sequence: tumbling, kayaking or rolling, tilted tank-treading, oscillating-swinging, swinging, and tank-treading. The tilted tank-treading (or spinning frisbee) regime has been previously observed in experiments but not in simulations. Two distinct classes of regime are identified: a membrane reorientation regime, where the part of membrane that is at the dimple at rest moves to the rim and vice versa, is observed in motions at high Ca such as tilted tank-treading, oscillating-swinging, swinging, and tank-treading, and a nonreorientation regime, where the part of the membrane starting from the dimple stays at the dimple, is observed in motions at low Ca such as rolling, tumbling, kayaking, and flip-flopping.

The wall-stress footprint of blood cells flowing in microvessels

It is well known that mechanotransduction of hemodynamic forces mediates cellular processes, particularly those that lead to vascular development and maintenance. Both the strength and space-time character of these forces have been shown to affect remodeling and morphogenesis. However, the role of blood cells in the process remains unclear. We investigate the possibility that in the smallest vessels blood's cellular character of itself will lead to forces fundamentally different than the time-averaged forces usually considered, with fluctuations that may significantly exceed their mean values. This is quantitated through the use of a detailed simulation model of microvessel flow in two principal configurations: a diameter D=6.5 μm tube-a model for small capillaries through which red blood cells flow in single-file-and a D=12 μm tube-a model for a nascent vein or artery through which the cells flow in a confined yet chaotic fashion. Results in both cases show strong sensitivity to the mean flow speed U. Peak stresses exceed their means by greater than a factor of 10 when U/D≲10 s(-1), which corresponds to the inverse relaxation time of a healthy red blood cell. This effect is more significant for smaller D cases. At faster flow rates, including those more commonly observed under normal, nominally static physiological conditions, the peak fluctuations are more comparable with the mean shear stress. Implications for mechanotransduction of hemodynamic forces are discussed.

Vesicle dynamics in a confined Poiseuille flow: from steady state to chaos

Red blood cells (RBCs) are the major component of blood, and the flow of blood is dictated by that of RBCs. We employ vesicles, which consist of closed bilayer membranes enclosing a fluid, as a model system to study the behavior of RBCs under a confined Poiseuille flow. We extensively explore two main parameters: (i) the degree of confinement of vesicles within the channel and (ii) the flow strength. Rich and complex dynamics for vesicles are revealed, ranging from steady-state shapes (in the form of parachute and slipper shapes) to chaotic dynamics of shape. Chaos occurs through a cascade of multiple periodic oscillations of the vesicle shape. We summarize our results in a phase diagram in the parameter plane (degree of confinement and flow strength). This finding highlights the level of complexity of a flowing vesicle in the small Reynolds number where the flow is laminar in the absence of vesicles and can be rendered turbulent due to elasticity of vesicles.

Simulation of malaria-infected red blood cells in microfluidic channels: Passage and blockage

Malaria-infected red blood cells (iRBCs) become less deformable with the progression of infection and tend to occlude microcapillaries. This process has been investigated in vitro using microfluidic channels. The objective of this paper is to provide a quantitative basis for interpreting the experimental observations of iRBC occlusion of microfluidic channels. Using a particle-based model for the iRBC, we simulate the traverse of iRBCs through a converging microfluidic channel and explore the progressive loss of cell deformability due to three factors: the stiffening of the membrane, the reduction of the cell's surface-volume ratio, and the growing solid parasites inside the cell. When examined individually, each factor tends to hinder the passage of the iRBC and lengthen the transit time. Moreover, at sufficient magnitude, each may lead to obstruction of narrow microfluidic channels. We then integrate the three factors into a series of simulations that mimic the development of malaria infection through the ring, trophozoite, and schizont stages. These simulations successfully reproduce the experimental observation that with progression of infection, the iRBC transitions from passage to blockage in larger and larger channels. The numerical results suggest a scheme for quantifying iRBC rigidification through microfluidic measurements of the critical pressure required for passage.

On the problem of slipper shapes of red blood cells in the microvasculature

Red blood cells (RBC) are known to exhibit non symmetric (slipper) shapes in the microvasculature. Vesicles have been recently used as a model for RBC and numerical simulations proved the existence of slipper shapes under Poiseuille flow (both in unconfined and confined geometry). However, in our recent numerical simulations the transition from symmetric (parachute) shape to the slipper one was found to take place upon decreasing the flow strength, while experiments on RBCs showed the contrary. In this work we show that if the viscosity contrast (ratio between the internal over external fluid viscosities) is different from unity, as is the case with RBCs, the transition from parachute to slipper shape occurs upon increasing the flow strength, in agreement with experiments. We provide the phase diagram of shapes in the microcirculation. The slipper is found to have a higher speed than the parachute (for the same parameters), that we believe to be the basic reason for its prevailing in the microvasculature. We provide a simple geometrical picture that explains the slipper flow efficiency over the parachute one. Finally, we show that there exists in parameter space regions of co-existence of slipper/parachute shapes and suggest simple experimental protocols to test these findings. The coexistence of shapes seems to be supported by experiments, though a systematic experimental study is lacking. A potential application of this work is to guide designing flow-based experiments in order to link the shape of RBCs to pathologies affecting cell deformability, such as sickle cell diseases, malaria, and those affecting blood hematocrit, as in polycythemia vera disease.

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.

ATP-dependent mechanics of red blood cells

Red blood cells are amazingly deformable structures able to recover their initial shape even after large deformations as when passing through tight blood capillaries. The reason for this exceptional property is found in the composition of the membrane and the membrane-cytoskeleton interaction. We investigate the mechanics and the dynamics of RBCs by a unique noninvasive technique, using weak optical tweezers to measure membrane fluctuation amplitudes with mus temporal and sub nm spatial resolution. This enhanced edge detection method allows to span over >4 orders of magnitude in frequency. Hence, we can simultaneously measure red blood cell membrane mechanical properties such as bending modulus kappa = 2.8 +/- 0.3 x 10(-19)J = 67.6 +/- 7.2 k(B)T, tension sigma = 6.5 +/- 2.1 x 10(-7)N/m, and an effective viscosity eta(eff) = 81 +/- 3.7 x 10(-3) Pa s that suggests unknown dissipative processes. We furthermore show that cell mechanics highly depends on the membrane-spectrin interaction mediated by the phosphorylation of the interconnection protein 4.1R. Inhibition and activation of this phosphorylation significantly affects tension and effective viscosity. Our results show that on short time scales (slower than 100 ms) the membrane fluctuates as in thermodynamic equilibrium. At time scales longer than 100 ms, the equilibrium description breaks down and fluctuation amplitudes are higher by 40% than predicted by the membrane equilibrium theory. Possible explanations for this discrepancy are influences of the spectrin that is not included in the membrane theory or nonequilibrium fluctuations that can be accounted for by defining a nonthermal effective energy of up to E(eff) = 1.4 +/- 0.1 k(B)T, that corresponds to an actively increased effective temperature.

Red cell membrane: past, present, and future

As a result of natural selection driven by severe forms of malaria, 1 in 6 humans in the world, more than 1 billion people, are affected by red cell abnormalities, making them the most common of the inherited disorders. The non-nucleated red cell is unique among human cell type in that the plasma membrane, its only structural component, accounts for all of its diverse antigenic, transport, and mechanical characteristics. Our current concept of the red cell membrane envisions it as a composite structure in which a membrane envelope composed of cholesterol and phospholipids is secured to an elastic network of skeletal proteins via transmembrane proteins. Structural and functional characterization of the many constituents of the red cell membrane, in conjunction with biophysical and physiologic studies, has led to detailed description of the way in which the remarkable mechanical properties and other important characteristics of the red cells arise, and of the manner in which they fail in disease states. Current studies in this very active and exciting field are continuing to produce new and unexpected revelations on the function of the red cell membrane and thus of the cell in health and disease, and shed new light on membrane function in other diverse cell types.

Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of ATP dependence

We have analyzed the fluctuations of the red blood cell membrane in both the temporal ((omega(s(-1))) and spatial (q(m(-1))) frequency domains. The cells were examined over a range of osmolarities leading to cell volumes from 50% to 170% of that in the isotonic state. The fluctuations of the isotonic cell showed an approximately q(-3)-dependence, indicative of a motion dominated by bending, with an inferred bending modulus of approximately 9 x 10(-19) J. When the cells were osmotically swollen to just below the point of lysis (166% of physiological volume), a q(-1)-dependence of the fluctuations supervened, implying that the motion was now dominated by membrane tension; estimated as approximately 1.3 x 10(-4) nm(-1). When, on the other hand, the cells were osmotically dehydrated, the fluctuation amplitude progressively decreased. This was caused by a rise in internal viscosity, as shown by measurements on resealed ghosts containing a reduced hemoglobin concentration, which displayed no such effect. We examined, in addition, cells depleted of ATP, before the onset of echinocytosis, and could observe no change in fluctuation amplitude. We conclude that the membrane fluctuations of the red cell are governed by bending modulus, membrane tension, and cytosolic viscosity, with little or no dependence on the presence or absence of ATP.

Viscoelasticity of the human red blood cell

We report here the first measurements of the complex modulus of the isolated red blood cell (RBC). Because the RBC is often larger than capillary diameter, important determinants of microcirculatory function are RBC deformability and its changes with pathologies, such as sickle cell disease and malaria. A functionalized ferrimagnetic microbead was attached to the membrane of healthy RBC and then subjected to an oscillatory magnetic field. The resulting torque caused cell deformation. From the oscillatory forcing and resulting bead motions, which were tracked optically, we computed elastic and frictional moduli, g′ and g‴, respectively, from 0.1 to 100 Hz. The g′ was nearly frequency independent and dominated the response at all but the highest frequencies measured. Over three frequency decades, g‴ increased as a power law with an exponent of 0.64, a result not predicted by any simple model. These data suggest that RBC relaxation times that have been reported previously, and any models that rest upon them, are artifactual; the artifact, we suggest, arises from forcing to an exponential fit data of limited temporal duration. A linear range of response was observed, but, as forcing amplitude increased, nonlinearities became clearly apparent. A finite element model suggests that membrane bending was localized to the vicinity of the bead and dominated membrane shear. While the mechanisms accounting for these RBC dynamics remain unclear, methods described here establish new avenues for the exploration of connections among the mechanical, chemical, and biological characteristics of the RBC in health and disease.

Biomechanics and biophysics of cancer cells

The past decade has seen substantial growth in research into how changes in the biomechanical and biophysical properties of cells and subcellular structures influence, and are influenced by, the onset and progression of human diseases. This paper presents an overview of the rapidly expanding, nascent field of research that deals with the biomechanics and biophysics of cancer cells. The review begins with some key observations on the biology of cancer cells and on the role of actin microfilaments, intermediate filaments and microtubule biopolymer cytoskeletal components in influencing cell mechanics, locomotion, differentiation and neoplastic transformation. In order to set the scene for mechanistic discussions of the connections among alterations to subcellular structures, attendant changes in cell deformability, cytoadherence, migration, invasion and tumor metastasis, a survey is presented of the various quantitative mechanical and physical assays to extract the elastic and viscoelastic deformability of cancer cells. Results available in the literature on cell mechanics for different types of cancer are then reviewed. Representative case studies are presented next to illustrate how chemically induced cytoskeletal changes, biomechanical responses and signals from the intracellular regions act in concert with the chemomechanical environment of the extracellular matrix and the molecular tumorigenic signaling pathways to effect malignant transformations. Results are presented to illustrate how changes to cytoskeletal architecture induced by cancer drugs and chemotherapy regimens can significantly influence cell mechanics and disease state. It is reasoned through experimental evidence that greater understanding of the mechanics of cancer cell deformability and its interactions with the extracellular physical, chemical and biological environments offers enormous potential for significant new developments in disease diagnostics, prophylactics, therapeutics and drug efficacy assays.

In vitro effects of NSAIDS and paracetamol on oxidative stress-related parameters of human erythrocytes

In vitro effects of widely used nonsteroidal antiinflammatory drugs (NSAIDs) and paracetamol were studied on oxidative stress-related parameters of human red blood cells (RBC). Membrane lipid integrity, activity of erythrocyte antioxidant enzymes; i.e. glutathione S-transferase (GST), selenium dependent-glutathione peroxidase (Se-GPx), and catalase (CAT), and hemolytic/stabilizing action of the drugs on erythrocyte membrane were assessed. Diclofenac, indomethacin and paracetamol at the therapeutic and higher concentrations, and dipyrone at the high concentration exerted a statistically significant inhibition on H2O2 forced erythrocytic membrane lipid peroxidation (EMLP). Increased hemolysis was observed by Na-salicylate, naproxen and ketorolac at therapeutic and higher concentrations, and by diclofenac and tiaprofenic acid at high concentrations, while the others seemed to stabilize the membrane at the same conditions. Na-salicylate inhibited GST activity at the therapeutic dose, however activated the same enzyme at high concentrations. Naproxen, tiaprofenic acid and piroxicam caused a decrease in GST activity at therapeutic doses. Paracetamol caused an activation at a high dose. Tiaprofenic acid, ketorolac, naproxen and piroxicam caused a significant Se-GPx inhibition. Erythrocyte CAT activity was increased by Na-salicylate, acemetacin, and tenoxicam at the therapeutic, and by dipyrone at the high concentration. Our results suggest that NSAIDs and paracetamol may be involved in oxidative/antioxidative processes of human erythrocytes. Also, the in vitro EMLP method can be considered as a simple test for evaluating possible antioxidant potency of chemicals.

Acoustic measurement of compressibility and thermal expansion coefficient of erythrocytes

Mechanical properties of human erythrocytes, namely adiabatic compressibility and thermal expansion coefficient, have been determined using a classical ultrasound velocity and attenuation burst transmission technique. The theoretical model concerns the corpuscular part of the elastic wave propagating in a suspension of viscous particles of small size compared with the wavelength. The thermal wave contribution was taken into account. Normal and stiffened red blood cells were suspended in saline of different NaCl concentration.

The red cell storage lesion and its implication for transfusion

Storage of red blood cells in preservative medium is associated with metabolic, biochemical and molecular changes to erythrocytes collectively referred to as the "storage lesion." In addition to corpuscular injury, bioreactive substances including cytokines and lipids accumulate in the medium during storage. We review evidence for those storage related changes and potential clinical implications for red blood cell transfusion.

Flow behaviour of erythrocytes - I. Rotation and deformation in dilute suspensions

The behaviour of individual human red cells and rouleaux were studied under the micro­scope in suspensions of < 2% haematocrit: (i) in Poiseuille flow by tracking the particles in glass tubes, and (ii) in Couette flow by observing cells in the stationary layer between counter-rotating glass disks. At shear stresses ≪ 0.1 N m -2 , the rotations of red cells in plasma were in accord with theory applicable to rigid disks. At shear stresses > 0.1 N m -2 , especially in viscous isotonic Dextran solutions, the cells oriented themselves at a constant angle to the flow and their membrane appeared to rotate about the interior. Although this behaviour was analogous to that of liquid drops, the concavity was still present in the de­formed erythrocytes, whose mean major diameters in plasma increased by 1.05 µm as the shear stress increased from 0 to 0.4 N m -2 . Deformation, through bending, was also observed with linear rouleaux of > 6 cells, here, at even the lowest shear stresses. By contrast, glutaraldehyde hardened cells and rouleaux rotated, without deforming, as rigid disks and rods respectively.

Comparison between internal microviscosity of low-density erythrocytes and the microviscosity of hemoglobin solutions: an electron paramagnetic resonance study

The hypothesis that the internal viscosity of erythrocytes is governed by the intracellular hemoglobin (Hb) concentration is examined. Here viscosity is determined by labeling of the cytoplasmic reduced glutathione with the spin label maleimido-Tempo. Erythrocyte populations with different Hb concentrations in isosmotic conditions were obtained through incomplete lysis, followed by cell resealing, and discontinuous density gradient separation. This procedure maintains normal cell shape and volume. Microviscosity of membrane-free Hb solutions was measured by addition of spin labeled glutathione. It was found that microviscosity values are similar for the erythrocyte cytoplasm and for Hb solutions of equivalent concentrations, showing that the erythrocyte membrane does not have any influence on internal microviscosity. The dependence of the microviscosity on the concentration of Hb solutions was compared with results of macroscopic viscosity obtained by other authors. It is concluded that microviscosity is sensitive to individual properties of the Hb molecule (intrinsic viscosity), but that it is not sensitive to intermolecular interactions. As the microviscosity behavior as a function of Hb concentration is the same in Hb solutions as in the erythrocyte cytoplasm, the inferences regarding macroscopic viscosity in Hb solutions could be translated to the rheological properties of the erythrocyte cytoplasm. Thus, these properties could be predicted from the values of the mean corpuscular Hb concentration.

In vitro effect of dextran-benzene-tetra-carboxylate hemoglobin on human blood rheological properties

While conducting pharmacological investigations into oxygen carriers, it is important to study the in vitro and in vivo rheological behavior of blood cells in the presence of such preparations. With regard to the original nature of human hemoglobin bound to benzene tetracarboxylate substituted dextran (Dex-BTC-Hb), it seemed necessary to study its rheological effect in a simulated in vitro hemorrhagic shock compensated by a blood substitute. The viscosity of substitutes was determined as well as several rheological parameters after 0, 3 and 6 hours incubation periods of red blood cells with substitutes: viscosity of blood-substitute mixtures at different levels of plasma substitution erythrocyte aggregation of blood-substitute mixtures by determining the velocity of rouleau formation and the cohesion of rouleau network. This work yielded several observations: The viscosity of Dex-BTC-Hb was slightly higher than those of solutions of native Hb, Dex-BTC T10, Dextran 40 (Plasmacair, modified fluid gelatin (Plasmion and hydroxyethyl starch 200 (Elohes). The substitution of a blood volume with Dex-BTC-Hb, corresponding to a compensated 45% hemorrhagic shock, slightly increased the viscosity of hemodiluted blood as compared to other substitutes. In the presence of Dex-BTC-Hb, the aggregation of erythrocytes appears to be increased as compared to standard solutions. Yet, the effect was close to that of Plasmion or Elohes.

Light scattering by red blood cells in ektacytometry: Fraunhofer versus anomalous diffraction

In the present literature on ektacytometry, small angle light scattering by ellipsoidal red blood cells is commonly approximated by Fraunhofer diffraction. Calculations on a sphere with the size and relative refractive index of a red cell, however, show that Fraunhofer diffraction deviates significantly from exact Mie theory. Anomalous diffraction is found to be a much better approximation. The anomalous diffraction theory is used to calculate the intensity distribution of the light scattered by an ellipsoidally deformed red blood cell. The derived expression shows that the ellipticity of isointensity curves in forward scattered light are equal to the ellipticity of the red blood cell. The theoretical expression is fitted to the intensity patterns measured with an ektacytometer. For the small observation angles used in ektacytometry, the experimental results confirm the validity of the anomalous diffraction approach.

Microviscosity of human erythrocytes studied using hypophosphite two-spin order relaxation

A new 31P NMR method is used to probe the cytoplasmic viscosity of human erythrocytes. The method is based on observing two-spin order relaxation of the 31P atom of the hypophosphite ion. This method is superior to our previous method, using the longitudinal relaxation time of the ion, because random field effects such as intermolecular dipole-dipole relaxation can be separated from intramolecular relaxation. This allows a more accurate determination of the effective reorientational correlation time from the measured intramolecular relaxation because it is now unaffected by random field effects. The new method also provides a means by which to estimate the random field effects. Both two-spin order and proton-decoupled T1 measurements were conducted on hypophosphite in water solutions at various temperatures, glycerol solutions of various viscosities, and in erythrocyte samples of various cell volumes. The results show that the effective reorientational correlation time of the hypophosphite ion varies from 7.2 to 15.2 ps in the cytoplasm of cells ranging in volume from 102 to 56 fl cells.

Erythrocyte rheology

Two main subjects of erythrocyte rheology, deformation and aggregation, are discussed in detail, on the basis of biochemical structure. The close relationship between the life span (or cell aging) and the rheology of individual erythrocytes is also briefly described. A currently important problem is emphasized, that is, the molecular aspect of the dynamic cytoskeletal structure and the mechanism of its regulation. This concerns not only the rheological function and the survival of circulating erythrocytes, but also the pathophysiology of abnormal erythrocytes.

Rheology of leukocytes

The rheological properties of human leukocytes (WBCs) have been studied by micropipette aspiration and filtration tests. A small aspiration pressure applied via a micropipette (diameter approximately equal to 3 micron) causes the WBC to undergo a rapid elastic deformation followed by a slow creep. The data can be analyzed with a viscoelastic model: an elastic element K1 in parallel with a Maxwell element (elastic element K2 in series with viscous element mu). Neutrophils and B lymphocytes are similar in K1, K2, and mu, but these values are higher for T lymphocytes. Treatment of neutrophils with colchicine decreases K2 and mu without changing K1, whereas cytochalasin B decreases all three coefficients; these results indicate the importance of cytoskeletal microtubules and microfilaments in WBC rheology. In the presence of Ca2+, WBCs form protopods which have increased viscoelastic coefficients. Inhibition of protopod formation with pentoxifylline is associated with an increase in WBC deformability. The ruffled surface of the apparently round WBC provides an area about twice that needed to enclose a smooth sphere of the same volume; this geometric feature plays an important role in whole WBC deformability tested through 4-5 micron filter pores or micropipettes. Because of its larger volume and higher cellular viscosity, each WBC is equivalent to approximately 700 erythrocytes in its tendency to block 5-micron channels. The rheology of WBCs has significant implications in their functional behavior, including flow through the microcirculation and interaction with endothelial cells.

Viscoelasticity of packed erythrocyte suspensions subjected to low amplitude oscillatory deformation

Concentrated adult erythrocyte suspensions were subjected to low amplitude oscillatory shear in a Weissenberg rheogoniometer equipped with a cone-and-plate assembly. The dynamic viscoelastic properties of the suspension were measured over a broad range of frequency by a numerical solution that accounted for fluid inertia. Variation of shear amplitude and cell volume percent, and comparison of buffered saline, plasma, and dextran as suspending media showed that the cellular elements had undergone small bending and shearing deformations. Studies of normal adult erythrocytes, hypotonically swollen cells, temperature-altered cells, and erythrocyte ghosts suggested that the method was evaluating membrane material properties. The normal membrane was found to exhibit a shear rate dependent elastic modulus that increased by more than a factor of 20 over a frequency range from 0.0076 Hz to 60 Hz. The membrane viscosity showed a substantial drop with frequency indicative of a frequency thinning phenomenon. At high frequency of deformation the viscous response of normal erythrocytes was no longer indicative of a membrane property due to the dominant influence of the internal hemoglobin solution. The studies generally supported the ability of the method to quantify relative membrane material properties and detect changes in membrane structure.