Shape Of Red Blood Cells Research Articles

Elastic force of red blood cell membrane during tank-treading motion: Consideration of the membrane's natural state

The elastic force of a red blood cell (RBC) membrane during its tank-treading motion was estimated using a three-dimensional spring network model. An RBC membrane was modelled by an assembly of triangular elements in which stretch/compression and bending springs were placed to express planar shear and out-of-plane bending deformations, respectively. An areal incompressibility of the membrane and a volumetric constraint on the entire RBC were taken into account. Different natural states of an RBC membrane were considered by adjusting reference lengths and angles of the stretch/compression and bending springs, respectively. An elastic motion simulation was conducted using the spring network model to reproduce a tank-treading motion of the membrane for a constant biconcave discoid RBC under a fluid shear force. Given the simulated tank-treading motion, an additional membrane elastic force due to the motion was determined from the elastic energy changes during the motion. It was confirmed that the natural state of the RBC membrane should be nonuniform to generate the additional elastic force. Greater spring constants and greater natural state nonuniformity induced a greater additional elastic force, and the elastic force was regarded as a resistance against the tank-treading motion. Additional elastic forces due to the membrane tank-treading motion for different sets of spring constants and natural state nonuniformity values were determined, and they were compared with fluid shear forces at shear rates within the range of which a transition between tank-treading and tumbling motions of an RBC occurs in experiments. The results suggested that for the experimentally measured elastic moduli, natural state nonuniformity in a physiological state is moderate between that for a spherical or flat shape and that for the biconcave shape. Moderate nonuniformity was also confirmed by a simulated RBC shape in a minimum state of elastic energy.

Slipping through blood flow

Simulations provide insight into how viscous flow transforms the shapes of red blood cells, which may influence their physiological properties.

A curve flow evolved by a fourth order parabolic equation

We study a fourth order curve flow, which is the gradient flow of a functional describing the shapes of human red blood cells. We prove that for any smooth closed initial curve in ℝ2, the flow has a smooth solution for all time and the solution subconverges to a critical point of the functional.

Flickering Analysis of Erythrocyte Mechanical Properties: Dependence on Oxygenation Level, Cell Shape, and Hydration Level

Erythrocytes (red blood cells) play an essential role in the respiratory functions of vertebrates, carrying oxygen from lungs to tissues and CO 2 from tissues to lungs. They are mechanically very soft, enabling circulation through small capillaries. The small thermally induced displacements of the membrane provide an important tool in the investigation of the mechanics of the cell membrane. However, despite numerous studies, uncertainties in the interpretation of the data, and in the values derived for the main parameters of cell mechanics, have rendered past conclusions from the fluctuation approach somewhat controversial. Here we revisit the experimental method and theoretical analysis of fluctuations, to adapt them to the case of cell contour fluctuations, which are readily observable experimentally. This enables direct measurements of membrane tension, of bending modulus, and of the viscosity of the cell cytoplasm. Of the various factors that influence the mechanical properties of the cell, we focus here on: 1), the level of oxygenation, as monitored by Raman spectrometry; 2), cell shape; and 3), the concentration of hemoglobin. The results show that, contrary to previous reports, there is no significant difference in cell tension and bending modulus between oxygenated and deoxygenated states, in line with the softness requirement for optimal circulatory flow in both states. On the other hand, tension and bending moduli of discocyte- and spherocyte-shaped cells differ markedly, in both the oxygenated and deoxygenated states. The tension in spherocytes is much higher, consistent with recent theoretical models that describe the transitions between red blood cell shapes as a function of membrane tension. Cell cytoplasmic viscosity is strongly influenced by the hydration state. The implications of these results to circulatory flow dynamics in physiological and pathological conditions are discussed.

Swinging and synchronized rotations of red blood cells in simple shear flow

The dynamics of red blood cells (RBCs) in simple shear flow was studied using a theoretical approach based on three variables: a shape parameter, the inclination angle theta, and phase angle phi of the membrane rotation. At high shear rate and low viscosity contrast of internal fluid, RBCs exhibit tank-treading motion, where phi rotates with swinging oscillation of shape and theta . At low shear rate, tumbling motion occurs and theta rotates. In the middle region between these two phases, it is found that synchronized rotation of phi and theta with integer ratios of the frequencies occurs in addition to intermittent rotation. These dynamics are robust to the modification of the potential of the RBC shape and membrane rotation. Our results agree well with recent experiments.

Peculiar flow patterns of RBCs suspended in viscous fluids and perfused through a narrow tube (25 μm)

Red blood cells (RBCs) generally deform to adopt a parachute-like, torpedo-like, or other configuration to align and flow through a capillary that is narrower than their major axis. As described herein, even in a narrow tube (25 microm) with diameter much larger than that of a capillary, flowing RBCs at 1 mm/s align axially and deform to a paraboloid shape in a viscous Newtonian fluid (505 kDa dextran medium) with viscosity of 23.4-57.1 mPa.s. A high-speed digital camera image showed that the silhouette of the tip of RBCs fits a parabola, unlike the shape of RBCs in capillaries, because of the longer distance of the RBC-free layer between the tube wall and the RBC surface ( approximately 8.8 microm). However, when RBCs are suspended in a "non-Newtonian" viscous fluid (liposome-40 kDa dextran medium) with a shear-thinning profile, they migrate toward the tube wall to avoid the axial lining, as "near-wall-excess," which is usually observed for platelets. This migration results from the presence of flocculated liposomes at the tube center. In contrast, such near-wall excess was not observed when RBCs were suspended in a nearly Newtonian liposome-albumin medium. Such unusual flow patterns of RBCs would be explainable by the principle; a larger particle tends to flow near the centerline, and a small one tends to go to the wall to flow with least resistance. However, we visualized for the first time the complete axial aligning and near-wall excess of RBCs in the noncapillary size tube in some extreme conditions.

Numerical simulation of rheology of red blood cell rouleaux in microchannels

An elastic spring model is applied to simulate the skeletal structure of the red blood cell (RBC) membrane and to study the dynamical behaviors of the red blood cell rouleaux (aggregates) in microchannels. The biconcave shape of RBCs in static plasma and the tank-treading phenomenon of single RBCs in simple shear flows have been successfully captured using this model. The aggregation and dissociation of RBCs with different deformability have been investigated in both shear and Poiseuille flows by taking into consideration the rheology of the cells and the intercellular interaction kinetics. It is found that the equilibrium configuration of the rouleaux formed under no-flow condition, the motion of the rouleaux in the flows, and the rheological behavior of individual cells in the rouleaux is closely related to the intercellular interaction strength, hydrodynamic viscous forces, and the deformability of the cell membrane.

Blood cell transport and aggregation using discrete ellipsoidal particles

A computational model is presented for efficient mesoscale simulation of the transport, collision and aggregation of blood cells, which can be applied to examine red blood cells (RBCs), leukocytes, or platelets in various types of blood flows in which the fluid length scale is substantially larger than the particle length scale. This method is intended to be intermediate between microscale models, which examine deformation and flow around a small number of individual blood cells, and more phenomenological continuum models. The computational model utilizes a particle approximation for the blood cells and introduces other physically-justifiable approximations in order to accommodate computations with large numbers of cells. For instance, the non-spherical RBC and platelet shape is incorporated into the model by use of ellipsoidal particles. A novel method based on particle level-surfaces is presented for rapid identification of particle collision. It is shown that receptor–ligand binding between the cells can be modeled under certain conditions using a formulation that is mathematically similar to van der Waals adhesion of particles, but in which the surface energy density is variable in time. The method is demonstrated to provide computations of the interaction and adhesion of over 13,000 red-blood-cell particles on an ordinary workstation. These computations exhibit formation of chain-like rouleaux aggregates, modification of rouleaux structure due to shear flow, and capture and/or breakup of colliding rouleaux. The model predictions are examined for rouleaux size distribution in channel flow in comparison to experimental data, as well as for the effect of RBC aggregation on margination of white blood cells and platelets in channel flows.

Neuraminidase alters red blood cells in sepsis

To investigate the influence of neuraminidase, an enzyme that cleaves sialic acid from the red blood cell (RBC) membrane, on RBC shape and biochemistry in critically ill patients. Prospective, observational study and in vitro laboratory study. A 31-bed medico-surgical department of intensive care and a university-affiliated cell biology laboratory. Acutely ill patients with and without sepsis and healthy volunteers. Blood sampling in volunteers. Neuraminidase activity was measured using a fluorescent assay. RBC shape was assessed by the second coefficient of dissymmetry of Pearson using a flow cytometry technique at 25 degrees C. Intraerythrocytic 2,3-diphosphoglycerate and lactate contents were also measured. Neuraminidase activity was significantly higher in septic patients compared with nonseptic patients and healthy volunteers (5.42 [4.85-6.00] vs. 4.53 [4.23-5.23] and 1.26 [0.83-1.83] mU/mL; all p < 0.05). Neuraminidase treatment modified the RBC shape in vitro in a dose-response fashion, and most of these alterations were present after 10 hours of incubation. Incubation of RBCs with phosphatidylinositol phospholipase C modified RBC shape and increased sialic acid concentrations in the supernatant, suggesting a leakage of neuraminidase from the RBC membrane. Alterations in shape were associated with increased 2,3-diphosphoglycerate (0.46 +/- 0.25 vs. 0.19 +/- 0.05 mumol/mL; p = 0.006) and lactate content (0.81 +/- 0.07 vs. 0.66 +/- 0.05 mmoL/L; p = 0.002). In sepsis, desialylation under the influence of increased neuraminidase activity may contribute to the alterations in RBC rheology. Inhibition of neuraminidase may represent a new therapeutic option to ameliorate RBC rheology and perhaps oxygen delivery to the cells.

Low concentration of extracellular hemoglobin affects shape of RBC in low ion strength sucrose solution

When red blood cells (RBCs) are placed in isotonic sucrose solution with low chloride content dynamic shape response is observed. Generally, it consists of three phases: i) fast spherulation (phase 1), ii) restoration of shape close to discoid one (phase 2), followed by a second slower spherulation in stomatocyte direction (phase 3). This morphological transformation (morphological response (MR)) is rather a fast process, usually comprises 1–2 min interval with disc retransformation time within 20–30 s. We have found that low concentration of extracellular hemoglobin (Hb) in the range 14–44 nM derived from cell lysate significantly accelerated MR at any stage of process. Increasing NaCl concentration up to 10 mM completely eliminated any influence of Hb. Other inhibitors EDTA and chlorpromazine while retarding some phases of MR did not prevent its activation by Hb. It was established that at conditions of low ionic strength Hb strongly binds to native RBC membrane. The number of binding sites was found to be 1–1.6 × 10 6 molecules per cell and the equilibrium dissociation constant was less than 2 × 10 − 8 M. After heat denaturation of Hb at 70–72 °C an ability of Hb to affect MR was lost. Our data provide evidence that extracellular Hb could be involved in shape regulation of red blood cells at least in low ionic strength solutions.

Simultaneous monitoring of electrical conductance and light transmittance during red blood cell aggregation

The electrical properties of red blood cell (RBC) suspensions are influenced by flow conditions, and prior studies indicate that electrical properties may reflect the kinetics of RBC aggregation. Changes of conductance and capacitance were monitored and had a time course resembling a "syllectogram" (i.e., temporal change of light reflectance from an RBC suspension after sudden cessation of flow). In the present study, both AC electrical conductance (EC) across and light transmission (LT) through a 1 mm ID glass tube were recorded simultaneously after a sudden stoppage of flow for RBC at various hematocrits in plasma or in isotonic saline (PBS). Preliminary results indicate that EC and LT signals for RBC in plasma have similar time courses, both increasing after an initial decrement of a few seconds duration. Aggregation indexes and aggregation half times calculated using LT and EC showed a similar dependence on hematocrits between 30-50%. Interestingly, RBC in PBS also exhibited a syllectogram time course for conductance, whereas LT continued to decrease after an initial decline reflecting RBC shape recovery. These results suggest that electrical conductance in aggregating and non-aggregating suspensions may be sensitive to phenomena other than RBC aggregation.

Shape and size of red blood cells from the Pygoscelid penguins of Antarctica using atomic force microscopy

Antarctic biodiversity is evolutionarily com- plex, reXecting the extreme ambient conditions. Therefore, Antarctic organisms exhibit sophisticated adaptations in all organization levels, including organs, tissues, and cells. Since red blood cells (RBCs) travel through the vertebrates blood delivering O2 to all tissues and organs and purging the unwanted CO 2 , they represent an interesting model to investigate biological adaptations. We have used atomic force microscopy (AFM) to compare the shape and size of RBCs of the Pygoscelid penguins. A total of 18 landmarks were measured in AFM images. When analyzed individu- ally, the parameters were not capable of discriminating the RBCs of each species. However, the simultaneous use of multiple parameters discriminated (74%) among the RBCs. In addition, the use of RBC measurements was suYcient to hierarchically cluster the species in accordance to other common and reliable phylogenetic strategies. In light of these results, the use of RBC characters could eVectively beneWt taxonomic inferences.

Assessment of Effects of a Cordia salicifolia Extract on the Radiolabeling of Blood Constituents and on the Morphology of Red Blood Cells

Effects of a Cordia salicifolia (porangaba) extract on the labeling of blood cells (BCs) with technetium-99m ((99m)Tc) and on the morphology of red BCs were evaluated. Labeling of cellular and molecular structures with (99m)Tc depends on a reducing agent. Some physical characteristics, as visible absorbance spectrum, electric conductivity, and refractive index of this porangaba extract, were also determined. Blood samples from Wistar rats were incubated with porangaba extract or with 0.9% NaCl (control). Labeling of blood constituents with (99m)Tc was performed. Plasma (P) and BCs, both soluble (SF-P and SF-BC) and insoluble (IF-P and IF-BC) fractions, were separated. The radioactivity in each fraction was counted, and the percentage of radioactivity incorporated (%ATI) was calculated. Blood smears were prepared, fixed, and stained, and the morphology of the red BCs was evaluated. Data showed an absorbance peak at 480 nm and electric conductibility and refractive index concentration-dependent. Porangaba extract decreased significantly (P < .05) the BC, IF-P, and IF-BC %ATI, and no modifications were verified on the shape of red BCs. Analysis of the results reveals that some physical parameters could be useful to aid in characterizing the extract studied. Moreover, it is possible that chemical compounds of this extract could have chelating/redox actions or be capable of binding to plasma and/or cellular proteins.

Erythrocyte‐shape evolution recorded with fast‐measurement NMR diffusion–diffraction

To monitor red blood cell (RBC) shape evolution by (1)H(2)O diffusion-diffraction NMR in time steps comparable to those required for the acquisition of a (31)P NMR spectrum; thus, to correlate RBC mean diameter with ATP concentration after poisoning with NaF. Pulsed-field gradient-stimulated echo (PFGSTE) diffusion experiments were recorded on (1)H(2)O in RBC suspensions. Under conditions of restricted diffusion, q-space experiments report on mean RBC diameter. To decrease experiment time, the phase cycling of radiofrequency (RF) pulses was cut to two transients by using unbalanced pairs of gradient pulses. Data processing used a recent digital filter. Differential interference contrast (DIC) light microscopy also recorded shape changes. (31)P NMR spectroscopy gave estimates of mean ATP concentration. NaF caused RBC-shape evolution from discocytes, through various forms of echinocytes, to spherocytes, over approximately 6 h and approximately 10 h at 37 degrees C and 25 degrees C, respectively. ATP declined to approximately 0.5 its normal concentration before the first stage of discocyte transformation; the concentration was 0.0 after approximately 1.5 h and 3.0 h, respectively, at the two temperatures. RBC shape was readily monitored by NMR with a temporal resolution that was useful for correlations with both DIC microscopy and (31)P NMR spectra.

The Role of Red Blood Cells in Microvascular Blood Flow Alterations Caused by Gut Ischemia-Reperfusion Injury

Gut ischemia-reperfusion injury caused by various critical conditions (e.g. traumahemorrhagic shock, burn or sepsis) leads to the development of early multiple organ dysfunction syndrome (MODS). Microvascular blood flow alterations play an important role in initiation and manifestation of MODS. There are limited data showing that splanchnic hypoperfusion is associated with red blood cell (RBC) dysfunction. The role of RBCs in microvascular blood flow disorders caused by this acute state remains unknown. We tested the hypothesis that there is an interconnection between RBC deformability and shape abnormalities resulted from gut ischemia-reperfusion injury and alterations in microvascular blood flow and oxygen delivery in distant organs and tissues. Rat model of superior mesenteric artery occlusion (SMAO) lasting for 45 minutes, and followed by 3 hours of reperfusion was used to re-create gut ischemia-reperfusion injury. Rats subjected to sham SMAO were anesthetized, had a laparotomy, and had their superior mesenteric artery looped with a suture, but the vessel was not occluded. End-point parameters were determined at the end of a reperfusion period. Microvascular blood flow in the liver and femoral muscle, as well as muscle pO2 were measured by Oxyflow and Oxylite monitors. RBC shape and deformability were determined by scanning electron microscopy and laser ectacytometry, correspondingly. Bessis' classification was used to evaluate RBC shape changes. Elongation index (EI) served as a measure of RBC deformability. SMAO followed by 3 hour reperfusion period resulted in significantly decreased microvascular blood flow in the liver and femoral muscle, compared to sham SMAO (see Table). Muscle PO2 was also significantly decreased. SMAO-induced microvascular blood flow and oxygen delivery disorders were associated with RBC deformability and shape alterations. RBC Elongation Index was significantly decreased 3 hours after SMAO. The percentage of abnormal RBCs was significantly increased in SMAO animals, whereas the percentage of normal discocytes was decreased. Abnormal RBCs were mainly presented by echinocytes and spheroechinocytes. Linear regression showed a tight inverse correlation between the percentage of abnormal RBCs and the levels of hepatic and muscular microvascular blood flow (r = −0.82 and −0.84, correspondingly, p<0.01). There was also a correlation between RBC Elongation Index and microvascular blood flows in the liver and muscle (r = 0.76 and 0.78, correspondingly, p<0.01). These data indicate that microvascular disorders in the liver and femoral muscle resulted from gut ischemia-reperfusion injury are caused at least in part by RBC deformability and shape alterations.ParametersGroups of AnimalsSMAO (n=8)Sham SMAO (n=8)Liver Blood Flow (units)509.6±138.8*1211.7±272.4Muscle Blood Flow (units)163.5±82.1*483.9±238.7Muscle PO2 (mm Hg)32.0±7.2*66.2±7.3Percentage of Normal Discocytes (%)88.65±3.42*94.07±1.93Percentage of Abnormal Shaped RBC (%)11.35±3.57*5.93±2.08RBC Elongation Index0.051±0.009*0.064±0.005* p<0.05 vs. Sham SMAO

Zinc-oxide-eugenol alters labeling of blood constituents with technetium-99m and shape of red blood cells

Samples of blood incubated with OZE, stannous chloride, and 99 mTc were isolated and fractions were separated. Radioactivity of the blood constituents decreased significantly (p < 0.05) due to the OZE. Morphological alterations were also found. Although rats were utilized in these experiments, precaution is recommended in the interpretation of nuclear-medicine examinations in patients that have been treated with OZE in dentistry procedures.

Shapes of Red Blood Cells: Comparison of 3D Confocal Images with the Bilayer-Couple Model

Cells and organelles are shaped by the chemical and physical forces that bend cell membranes. The human red blood cell (RBC) is a model system for studying how such forces determine cell morphology. It is thought that RBCs, which are typically biconcave discoids, take the shape that minimizes their membrane-bending energies, subject to the constraints of fixed area and volume. However, recently it has been hypothesized that shear elasticity arising from the membrane-associated cytoskeleton (MS) is necessary to account for shapes of real RBCs, especially ones with highly curved features such as echinocytes. In this work we tested this hypothesis by following RBC shape changes using spherical harmonic series expansions of theoretical cell surfaces and those estimated from 3D confocal microscopy images of live cells. We found (i) quantitative agreement between shapes obtained from the theoretical model including the MS and real cells, (ii) that weakening the MS, by using urea (which denatures spectrin), leads to the theoretically predicted gradual decrease in spicule number of echinocytes, (iii) that the theory predicts that the MS is essential for stabilizing the discocyte morphology against changes in lipid composition, and that without it, the shape would default to the elliptocyte (a biconcave ellipsoid), (iv) that we were able to induce RBCs to adopt the predicted elliptocyte morphology by treating healthy discocytes with urea. The latter observation is consistent with the known connection between the blood disease hereditary elliptocytosis and spectrin mutations that weaken the cell cortex. We conclude that while the discocyte, in absence of shear, is indeed a minimum energy shape, its stabilization in healthy RBCs requires the MS, and that elliptocytosis can be explained based on purely mechanical considerations.

Micro-Macro Link in Rheology of Erythrocyte and Vesicle Suspensions

We report on the rheology of dilute suspensions of red blood cells (RBC) and vesicles. The viscosity of RBC suspensions reveals a previously unknown signature: it exhibits a pronounced minimum when the viscosity of the ambient medium is close to the value at which the transition from tank-treading to tumbling occurs. This bifurcation is triggered by varying the viscosity of the ambient fluid. It is found that the intrinsic viscosity of the suspension varies by about a factor of 4 in the explored parameter range. Surprisingly, this significant change of the intrinsic viscosity is revealed even at low hematocrit (5%). We suggest that this finding may be used to detect blood flow disorders linked to pathologies that affect RBC shape and mechanical properties. This opens future perspectives on setting up new diagnostic tools, with great efficiency even at very low hematocrit. Investigations are also performed on giant vesicle suspensions, and compared to RBCs.

Plasma microcirculation in alveolar capillaries: Effect of parachute-shaped red cells on gas exchange

The effects of plasma microcirculation speed and red blood cell (RBC) shape on CO exchange in alveolar capillaries is numerically investigated. In this study, blood is modeled as an inhomogeneous, two-constituent substance, with one of the constituents being the blood plasma, treated as a homogeneous Newtonian fluid, and the other being the RBCs, treated as discrete, suspended particles (i.e., solid bodies) flowing with the plasma. The RBC shape and blood speed effects on the alveolar diffusion process is observed not only by the variations in the iso-lines along the alveolar capillary but also by changes in the lung diffusing capacity. The simulations include varying the capillary blood speed from 1.0 to 10 mm/s and the capillary hematocrit from 3% to 55%. The RBC shape effect is established by comparing results obtained for circular RBCs to results for which the RBCs have a more realistic, parachute shape when flowing with the plasma. Results reveal the parachute-shaped RBCs yield higher lung diffusing capacity compared to the circular ones. Moreover, blood flow can increase the lung diffusing capacity by almost 50% in certain cases, with the effect being more predominant at high blood speed and low hematocrit. Finally, the effect of blood speed for parachute-shaped RBCs is quantified in terms of percentage-increase lung diffusing capacity and presented in a simple predictive equation.

Effects of Passiflora edulis flavicarpa on the radiolabeling of blood constituents, morphology of red blood cells and on the biodistribution of sodium pertechnetate in rats

The aim of this study was to evaluate possible effects of Passiflora edulis flavicarpa ( P. flavicarpa) extract on the labeling of blood constituents with 99mTc, on the morphology of red blood cells, and on the biodistribution of sodium pertechnetate (sodium 99mTc). Male Wistar rats were treated with either P. flavicarpa extract or 0.9% NaCl. After that, radiolabeling of blood constituents, morphological analysis of red blood cells and biodistribution of sodium 99mTc was evaluated. Radiolabeling of blood constituents and shape of red blood cells were not modified, but a significant ( p<0.05) alteration of the biodistribution of sodium 99mTc was observed after treatment with P. flavicarpa extract. Although our results were obtained with animals, they could contribute to reduce the risk of misdiagnosis and/or repetition of the examinations in nuclear medicine.