Red blood cell mechanics and capillary blood rheology

Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessel walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic “tank-treading” motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.     

Red blood cell mechanics and capillary blood rheology.

Blood contains a high vol fraction of erythrocytes (red blood cells), which strongly influence its flow properties. Much is known about the mechanical properties of red cells, providing a basis for understanding and predicting the rheological behavior of blood in terms of the behavior of individual red cells. This review describes quantitative theoretical models that relate red cell mechanics to flow properties of blood in capillaries. Red cells often flow in single file in capillaries, and rheological parameters can then be estimated by analyzing the motion and deformation of an individual red cell and the surrounding plasma in a capillary. The analysis may be simplified by using lubrication theory to approximate the plasma flow in the narrow gaps between the cells and the vessels walls. If red cell shapes are assumed to be axisymmetric, apparent viscosities are predicted that agree with determinations in glass capillaries. Red cells flowing in microvessels typically assume nonaxisymmetric shapes, with cyclic "tank-treading" motion of the membrane around the interior. Several analyses have been carried out that take these effects into account. These analyses indicate that nonaxisymmetry and tank-treading do not significantly influence the flow resistance in single-file or two-file flow.     

Red blood cell motion and hematocrit distribution in a deforming capillary

Based on the relation between the red blood cell velocity and the blood velocity of the Fahraeus effect, we analyze the motion of a red blood cell in a deforming capillary to investigate how the ventilatory induced deformation affects the transit of the red blood cell through the pulmonary capillary and changes the hematocrit discharged from the capillary. An analytical solution is also obtained for the case of an infinitesimal deformation. The numerical and analytic solutions demonstrate that the variation in discharge hematocrit is proportional to the change of pulmonary capillary blood volume between the time that the red cell enters and the time that it exits the capillary. We also find that this hematocrit variation could be regarded, in terms of transport, to originate from the mid-section of the capillary.     

Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects

We show theoretically how adenosine 5'-triphosphate (ATP)-induced dynamic dissociations of spectrin filaments (from each other and from the membrane) in the cytoskeleton network of red blood cells (RBC) can explain in a unified manner both the measured fluctuation amplitude as well as the observed shape transformations as a function of intracellular ATP concentration. Static defects can be induced by external stresses such as those present when RBCs pass through small capillaries. We suggest that the partially freed actin at these defect sites may explain the activation of the CFTR membrane-bound protein and the subsequent release of ATP by RBCs subjected to deformations. Our theoretical predictions can be tested by experiments that measure the correlation between variations in the binding of actin to spectrin, the activity of CFTR, and the amount of ATP released.     

Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method

In this paper we develop a lattice Boltzmann algorithm to simulate red blood cell (RBC) behavior in shear flows. The immersed boundary method is employed to incorporate the fluid-membrane interaction between the flow field and deformable cells. The cell membrane is treated as a neo-Hookean viscoelastic material and a Morse potential is adopted to model the intercellular interaction. Utilizing the available mechanical properties of RBCs, multiple cells have been studied in shear flows using a two-dimensional approximation. These cells aggregate and form a rouleau under the action of intercellular interaction. The equilibrium configuration is related to the interaction strength. The end cells exhibit concave shapes under weak interaction and convex shapes under strong interaction. In shear flows, such a rouleau-like aggregate will rotate or be separated, depending on the relative strengths of the intercellular interaction and hydrodynamic viscous forces. These behaviors are qualitatively similar to experimental observations and show the potential of this numerical scheme for future studies of blood flow in microvessels.     

Experimental acute Babesia caballi infections: I. Red blood cell dynamics

Hematological determinations were made on blood samples from six ponies acutely infected with two dosage levels of Babesia caballi (Group 1: divided into two subgroups of three ponies each). Similar determinations were made on blood samples from three premunized ponies given challenge inoculations (Group 2), and three equidae given uninfected red blood cells (Group 3).A trend towards decreases in RBC counts, hemoglobin concentrations, and hematocrits within one to four days after inoculation (AI) was observed in all groups. However, it was marked only in Group 1. In addition, only in Group 1 was there observed a concerted anemia occurring between Days 7 and 16.Those surviving ponies in Group 1 which developed a higher parasitemia between Days 5 and 6 AI (first parasitemia peak) developed a more severe anemia between Days 7 and 16. Ponies which developed parasitemias higher than 40 × 10³ parasitized cells/mm³ at the first parasitemia peak subsequently died.Free bilirubin in Group 1 animals increased immediately after inoculation, and repeatedly exceeded normal ranges until after Day 20 AI when the RBC counts were rising. Similar changes in free bilirubin did not occur in either Groups 2 or 3. Conjugated bilirubin levels did not exceed normal ranges in any of the experimental animals.Active erythrophagocytosis was evident in histological preparations of lymph node, spleen, liver, and lung from ponies which died. Cytosiderin pigment was present in liver parenchyma, and hematin was scattered throughout lymph nodes and spleen.     

Red blood cell magnetophoresis

The existence of unpaired electrons in the four heme groups of deoxy and methemoglobin (metHb) gives these species paramagnetic properties as contrasted to the diamagnetic character of oxyhemoglobin. Based on the measured magnetic moments of hemoglobin and its compounds, and on the relatively high hemoglobin concentration of human erythrocytes, we hypothesized that differential migration of these cells was possible if exposed to a high magnetic field. With the development of a new technology, cell tracking velocimetry, we were able to measure the migration velocity of deoxygenated and metHb-containing erythrocytes, exposed to a mean magnetic field of 1.40 T and a mean gradient of 0.131 T/mm, in a process we call cell magnetophoresis. Our results show a similar magnetophoretic mobility of 3.86 x 10(-6) mm(3) s/kg for erythrocytes with 100% deoxygenated hemoglobin and 3.66 x 10(-6) mm(3) s/kg for erythrocytes containing 100% metHb. Oxygenated erythrocytes had a magnetophoretic mobility of from -0.2 x 10(-6) mm(3) s/kg to +0.30 x 10(-6) mm(3) s/kg, indicating a significant diamagnetic component relative to the suspension medium, in agreement with previous studies on the hemoglobin magnetic susceptibility. Magnetophoresis may open up an approach to characterize and separate cells for biochemical analysis based on intrinsic and extrinsic magnetic properties of biological macromolecules.     

Red blood cell shape and deformability in the context of the functional evolution of its membrane structure

It is proposed that it is possible to identify some of the problems that had to be solved in the course of evolution for the red blood cell (RBC) to achieve its present day effectiveness, by studying the behavior of systems featuring different, partial characteristics of its membrane. The appropriateness of the RBC volume to membrane area ratio for its circulation in the blood is interpreted on the basis of an analysis of the shape behavior of phospholipid vesicles. The role of the membrane skeleton is associated with preventing an RBC from transforming into a budded shape, which could form in its absence due to curvature-dependent transmembrane protein-membrane interaction. It is shown that, by causing the formation of echinocytes, the skeleton also acts protectively when, in vesicles with a bilayer membrane, the budded shapes would form due to increasing difference between the areas of their outer and inner layers.     

Red blood cell membrane defects

We present an overview of the currently known molecular basis of red cell membrane disorders. A detailed discussion of the structure of the red cell membrane and the pathophysiology and clinical aspects of its disorders is reported. Generally speaking, hereditary spherocytosis (HS) results from a loss of erythrocyte surface area. The mutations of most cases of HS are located in the following genes: ANK1, SPTB, SLC4A1, EPB42 and SPTA1, which encode for ankyrin, spectrin beta-chain, the anion exchanger 1 (band 3), protein 4.2 and spectrin alpha-chain, respectively. Hereditary elliptocytosis (HE) reflects a diminished elasticity of the skeleton. Its aggravated form, hereditary pyropoikilocytosis (HPP), implies that the skeleton undergoes further destabilization. The mutations responsible for HE and HPP, lie in the SPTA1 and SPTB gene, and in the EPB41 gene encoding protein 4.1. Allele alpha LELY is a common polymorphic allele, which plays the role of an aggravating factor when it occurs in trans of an elliptocytogenic allele of the SPTA1 gene. Southeast Asian ovalocytosis derives from a change in band 3. The genetic disorders of membrane permeability to monovalent cations required a positional cloning approach. In this respect, channelopathies represent a new frontier in the field. Dehydrated hereditary stomatocytosis (DHS) was shown to belong to a pleiotropic syndrome: DHS + fetal edema + pseudohyperkalemia, which maps 16q23-24. Splenectomy is strictly contraindicated in DHS and another disease of the same class, overhydrated hereditary stomatocytosis, because it increases the risk of thromboembolic accidents.     

Red blood cell dielectrophoresis in axisymmetric fields

Dielectrophoretic velocities of human red blood cells in an axisymmetric field were measured as a function of the applied voltage and the distance from the axis of symmetry. The voltage of the alternating electric field (frequency 2 MHz), applied between two concentric cylindrical metal electrodes (outer and inner radii 0.24 and 1 mm, respectively), was varied up to 19 V. Two kinds of mediums were used: (a) 90% of 2.1% glycine solution and 10% of 5.5% glucose solution and (b) 5.4% sorbitol solution. The results have shown that in both mediums the cell velocities are proportional to the square of the applied voltage and inversely proportional to the cube of the distance from the axis of symmetry, as predicted by the theory. The coefficient of proportionality (dielectrophoretic coefficient) is on the order of 10(-25) A2S4kg-1. It depends on the donor of red blood cells and might be used for diagnostic purposes. These results will be used in future investigations of membrane adhesion, stability and fusion.     

Red blood cell dielectrophoresis in axisymmetric fields

Dielectrophoretic velocities of human red blood cells in an axisymmetric field were measured as a function of the applied voltage and the distance from the axis of symmetry. The voltage of the alternating electric field (frequency 2 MHz), applied between two concentric cylindrical metal electrodes (outer and inner radii 0.24 and 1 mm, respectively), was varied up to 19 V. Two kinds of mediums were used: (a) 90% of 2.1% glycine solution and 10% of 5.5% glucose solution and (b) 5.4% sorbitol solution. The results have shown that in both mediums the cell velocities are proportional to the square of the applied voltage and inversely proportional to the cube of the distance from the axis of symmetry, as predicted by the theory. The coefficient of proportionality (dielectrophoretic coefficient) is on the order of 10⁻²⁵ A²s⁴kg⁻¹. It depends on the donor of red blood cells and might be used for diagnostic purposes. These results will be used in future investigations of membrane adhesion, stability and fusion.     

Red blood cell deformability and the prostaglandins

The effects of Prostaglandin E₁ and Prostaglandin E₂ on the deformability of the human red blood cell have been studied using the glass micropipette method. In the range of concentrations 10^?13 to 10^?5 M, neither PGE₁ nor PGE₂ alters the red cell deformability.     

Red blood cell insulin receptors in health and disease

Contents: Structure and characteristics of erythrocyte insulin receptor. Red blood cell age and insulin receptors. Insulin receptors in human disease states. Obesity. Chronic renal failure. Acanthosis nigricans. Miscellaneous disease states. Insulin receptors in children. Insulin receptors in women during pregnancy. Insulin binding and other hormones. Comparison of biosynthetic insulin, pancreatic human insulin and porcine insulin binding to erythrocytes. Effect of exercise on insulin binding to red blood cells of normal human volunteers. Miscellaneous insulin binding studies. Insulin internalization and degradation. Insulin and erythrocyte metabolism. Summary and conclusion.     

Random transitions,size control,and inheritance in cell population dynamics

A general model of cell population dynamics is derived and analyzed. The model uses the continuous structure variables age and size, and thus distinguishes individual cells with respect to such properties as cycle length and division size. The model allows the occurrence of random transitions as cells progress through the cell cycle, the control of cell size upon cell cycle events, and the inheritance of properties from mother to daughter cells. The concepts of asynchronous exponential growth, α-curves, β-curves, mother-daughter transit time correlations, and sister-sister transit time correlations are formalized. The existence and uniqueness of solutions to the model is proved.     

Red blood cell deformability index in diabetic retinopathy

In order to investigate the relationship between haemorheological disturbances and diabetic microangiopathy we have studied the red blood cell deformability index (RBCD-index) by means of a filtration technique in 69 diabetics, aged 49-83 years, and in 40 non diabetic healthy controls (group A) of respective age and sex. The diabetics were classified into the following groups, according to the findings of a thorough clinical and laboratory investigation. Twenty patients (group B) were free of vascular complications, whereas 9 (group C) suffered from background retinopathy, 27 (group D) background retinopathy and ischaemic cardiopathy or peripheral arterial occlusive disease and 13 (group E) of proliferative retinopathy with diffuse micro- and macroangiopathy. The RBCD-index was significantly (P less than 0.001) decreased in diabetics with retinopathy compared to the diabetic and non diabetic controls. The lowest RBCD-index was observed in diabetics with proliferative retinopathy and in those with diffuse micro- and macrovascular complications (RBCD-index, means +/- SDM ml/min: A 0.68 +/- 0.15; B 0.64 +/- 0.08; C 0.60 +/- 0.08; D 0.49 +/- 0.09; E 0.48 +/- 0.09). These findings suggest that the RBCD is impaired in diabetics with retinopathy, especially in those with severe vascular complications, and that this abnormal rheological behavior of erythrocytes can be found even in the early stages of diabetic microangiopathy.     

Red blood cell galactokinase activity and presenile cataracts

Red blood cell galactokinase activity was measured in 70 patients with cataracts to assess a possible correlation between galactokinase activity levels and risk of cataract development. Among all, 15 patients developed cataracts during the first year of life, 25 patients under the age of 50 and 30 later in life. No cases of total or partial galactokinase deficiency were found. These results, taken together with the absence of cataracts in 9 patients with partial galactokinase deficiency render less certain the cause and effect relationship between partial galactokinase deficiency and the appearance of cataracts.