Rheological aspects of red blood cell aggregation

Simultaneous Determination of Human Erythrocyte Deformability and Adhesion Energy: A Novel Approach Using a Microfluidic Chamber and the "Glass Effect"

The simultaneous determination of adhesion and deformability parameters of erythrocytes was carried out through a microfluidic device, which uses an inverted optical microscope with new image acquisition and analysis technologies. Also, an update of the models describing erythrocyte adhesion and deformation was proposed. Measurements were carried out with red blood cells suspended in saline solution with human serum albumin at different concentrations. Erythrocytes adhered to a glass surface were subjected to different low shear stress (from 0.04 to 0.25 Pa), causing cellular deformation and dissociation. The maximum value obtained of the erythrocyte deformability index was 0.3, and that of the adhesion energy per unit area was 1.1 × 10^-6 Pa m, both according to previous works. The obtained images of RBCs adhered to glass reveal that the adhesion is stronger in a single point of the cell, suggesting a ligand migration that concentrates the adhesion in a "spike-like tip" in the cell. Moreover, adhesion energy results indicate that the energy required to separate erythrocytes in media with a lower albumin concentration is greater. Both results could be explained by the mobility of membrane receptors.

Computational fluid dynamic simulation of aggregation of deformable cells in a shear flow

We present computational fluid dynamic (CFD) simulation of aggregation of two deformable cells in a shearflow. This work is motivated by an attempt to develop computational models of aggregation of red blood cells (RBCs). Aggregation of RBCs is a major determinant of blood viscosity in microcirculation under physiological and pathological conditions. Deformability of the RBCs plays a major role in determining their aggregability. Deformability depends on the viscosity of the cytoplasmic fluid and on the rigidity of the cell membrane, in a macroscopic sense. This paper presents a computational study of RBC aggregation that takes into account the rheology of the cells as well as cell-cell adhesion kinetics. The simulation technique considered here is two dimensional and based on the front tracking/immersed boundary method for multiple fluids. Results presented here are on the dynamic events of aggregate formation between two cells, and its subsequent motion, rolling, deformation, and breakage. We show that the rheological properties of the cells have significant effects on the dynamics of the aggregate. A stable aggregate is formed at higher cytoplasmic viscosity and membrane rigidity. We also show that the bonds formed between the cells change in a cyclic manner as the aggregate rolls in a shearflow. The cyclic behavior is related to the rolling orientation of the aggregate. The frequency and amplitude of oscillation in the number of bonds also depend on the rheological properties.

Novel method for measurement of medium size arterial lumen area with an impedance catheter: in vivo validation

There is no doubt that the transformation of a cardiac catheter into a conductance catheter that allows reliable and accurate assessment of lumen cross-sectional area (CSA) will provide a powerful diagnostic and treatment tool for the invasive cardiologist. The objective of this study was to develop a method based on the impedance catheter that allows accurate and reproducible measurements of CSA for medium size vessels (e.g., coronary, femoral, and carotid arteries). Two solutions of NaCl (0.5% and 1.5%) with known conductivities were injected directly into the lumen of the artery in eight swine. We showed that the CSA can be determined analytically from two Ohm's law-type algebraic equations that account for the parallel conductance of the current into the surrounding tissue. Excellent agreement was found between the conductance catheter with the proposed two-injection method and B-mode ultrasound (US). The root mean square error for the impedance measurements was 4.8% of the mean US diameter. The repeatability of the technique was assessed with duplicate measurements. The mean of the difference between the two measurements was nearly zero, and the repeatability coefficient was within 2.4% of the mean of the two measurements. The validated method was used to assess the degree of acute vasodilatation of the vessel in response to flow overload.

Measurement of Coronary Lumen Area Using an Impedance Catheter: Finite Element Model and in Vitro Validation

The measurement of coronary lumen cross-sectional area (CSA) is important for coronary physiology and cardiology. The general objective of this study is to develop an accurate and reproducible method to measure the lumen CSA of left anterior descending (LAD) artery using an impedance or conductance catheter. The conductance catheter technique is based on a cylindrical model of the chamber of interest. The first aim of this study was to validate the assumptions of the cylindrical model using a finite-element analysis (FEA) of the conductance catheter in the lumen of the vessel that takes into account the conductance of current through the vessel wall and surrounding tissue (parallel conductance, Gp). The FEA was used to determine the heterogeneity of potential and electrical fields and to optimize the design of the catheter relative to the diameter of the vessel. An optimum relationship between vessel and catheter diameter was obtained based on FEA. The second aim was to validate the in vitro CSA of LAD artery obtained from the conductance catheter method using A-mode ultrasound (US). The present study offers a novel approach to correct for the Gp that involves the injection of two solutions of NaCl (0.5% and 1.5%) with known conductivities directly into the lumen of the coronary artery in a porcine heart. In six hearts obtained from a slaughterhouse, we showed that the CSA and Gp can be determined analytically from two Ohm's law-type algebraic equations (cylindrical model) that account for the parallel conductance. The mean difference in diameter between the conductance catheter using the proposed two-injection method and U.S. was -0.02. The root mean square error for the impedance measurements was 2.8% of the mean US diameter. The future application of this technique to the in vivo condition is discussed.

Evaluation of the energy of red blood cell agglutination by monoclonal antibodies

The knowledge of the energy involved in cell-cell interactions has significant implications in biological and medical sciences. Red blood cells (RBC) become mutually adhered when specific (agglutinins) or nonspecific macromolecules bind adjacent cells in an irreversible or reversible form. Flow chamber technique with digital image processing was successfully applied to determine the partial separation, by shear stress, of two RBC agglutinated face to face (doublet) by specific monoclonal antibodies (MAb) and also to evaluate the shear stress required to attain this separation. The work done in separating adhered cells is then easily calculated and serves to evaluate the antibody affinity. In this work, this technique was applied to evaluate the affinity of a monoclonal antibody specific to the blood group A antigen. The specific disaggregation energy gamma (i.e., the work done by the shear stress) required to disrupt a unit of adhered membrane areas between agglutinated cells was calculated. On play back of the image analysis, measurements were taken to determine the force applied to the doublet and the relative separation between both RBC. Values of gamma(d) (from 2.70 to 4.61 x 10(-9) N/cm) were found to be proportional to the density (D = 27 to 55 molecules/microm(2)) of MAb molecules bound on the RBC membrane.

[Rheologic study of the dissociation reaction of erythrocyte immunologic agglutinates: application to subgroup A erythrocytes]

Red blood cell Agglutinates can be dissociated by providing enough energy which may be supplied by shear stress in a viscometer. In this paper a new technique is proposed to determine dissociation parameters of erythrocyte immunological agglutinates by using a laser backscattering method. Backscattered light intensity increases during the process of agglutinate dissociation when a controlled shear stress in a transparent Couette viscometer is applied. The obtained curves of dissociation can be fitted by an exponential function. A numerical integration of the dissociation curves allows us to obtain a parameter associated to the energy used in the dissociation process. A satisfactory differentiation of erythrocyte sub-groups Al, Az, A,B and Am has been carried out using this technique.

Influence of polymer concentration and molecular weight and of enzymic glycocalyx modification on erythrocyte interaction in dextran solutions

Erythrocytes adhere to each other when suspended in supra-threshold concentrations of dextran of molecular mass of 40 kD or greater. The plasma membranes are parallel to each other over the entire length of the contact seam at the lower effective polymer concentrations. When cells are pretreated with the proteolytic enzyme pronase or the sialidase neuraminidase the membranes are not parallel but make contact at spatially periodic locations along the membrane surface. Pronase induced reduction of cell electrophoretic mobility rapidly reaches a limiting value. Nevertheless, prolonged pre-exposure to enzyme leads to a continuing reduction in contact separations. This result taken with the observation that, for equal loss of electrophoretic mobility, a shorter contact separation results from pronase rather than neuraminidase pre-treatment implies that a non-electrostatic consequence of pronase pre-treatment dominates membrane interaction in the experimental regimes examined here. The average lateral contact separation for different enzyme regimes lay in the range 3.3 microns to a limiting lower value of about 0.7 micron. There was a good correlation between the logarithm of a contact separation index (the approach of separation distance to its limiting value) against the logarithm of a derived index related to net attractive interaction for a wide range of experimental conditions. Treatments which increased attraction or decreased repulsion (e.g. increased dextrans concentration or enzyme pre-treatment) lead to shorter lateral contact separation. This result is qualitatively consistent with the predicted behaviour for the dominant wavelength arising from interfacial instability of a thin aqueous film between adjacent membranes.

A thermodynamic and biomechanical theory of cell adhesion. Part I: General formulism

The equilibrium thermodynamics calculus of cell adhesion developed by Bell et al. (1984, Biophys. J. 45, 1051-1064) has been extended to the general non-equilibrium case. In contrast to previous models which could only compute the end results of equilibrium states, the present theory is able to calculate the kinetic process of evolution of adhesion, which may or may not approach towards equilibrium. Starting from a basic constitutive hypothesis for Helmholtz free energy, equations of balance of normal forces, energy balance at the edge of the contact area and rate of entropy production are derived using an irreversible thermodynamics approach, in which the restriction imposed by the Second Law of Thermodynamics takes the place of free energy minimization used by Bell et al. (1984). An explicit expression for adhesion energy density is derived for the general transient case as the difference of the usable work transduced from chemical energy liberation from bond formation of specific crosslinking molecules and the repulsive potential of non-specific interactions. This allows the energy balance to be used as an independent boundary equation rather than a practical way of computing the adhesion energy. Jump conditions are obtained from the conservation of crosslinking molecules across the edge of adhesion region which is treated as a singular curve. The bond formation and lateral motion of the crosslinking molecules are assumed to obey a set of reaction-diffusion equations. These equations and the force balance equation within the contact area, plus the jump conditions and the energy balance equation at the edge form a well-posed moving boundary problem which determines the propagation of the adhesion boundary, the separation distance between the two cell membranes over the contact area as well as the distributions of the crosslinking molecules on the cell surfaces. The behavior of the system depends on the relative importance of virtual convection, lateral diffusion and bond formation of the crosslinking molecules at the edge of the adhesion region, according to which two types of rate limiting cases are discussed, viz, reaction-limited and diffusion-limited processes.