Kinetics Of Rouleaux Formation Research Articles

A constitutive rheological model for agglomerating blood derived from nonequilibrium thermodynamics

Red blood cells tend to aggregate in the presence of plasma proteins, forming structures known as rouleaux. Here, we derive a constitutive rheological model for human blood which accounts for the formation and dissociation of rouleaux using the generalized bracket formulation of nonequilibrium thermodynamics. Similar to the model derived by Owens and co-workers [“A non-homogeneous constitutive model for human blood. Part 1. Model derivation and steady flow,” J. Fluid Mech. 617, 327–354 (2008)] through polymer network theory, each rouleau in our model is represented as a dumbbell; the corresponding structural variable is the conformation tensor of the dumbbell. The kinetics of rouleau formation and dissociation is treated as in the work of Germann et al. [“Nonequilibrium thermodynamic modeling of the structure and rheology of concentrated wormlike micellar solutions,” J. Non-Newton. Fluid Mech. 196, 51–57 (2013)] by assuming a set of reversible reactions, each characterized by a forward and a reverse rate constant. The final set of evolution equations for the microstructure of each rouleau and the expression for the stress tensor turn out to be very similar to those of Owens and co-workers. However, by explicitly considering a mechanism for the formation and breakage of rouleaux, our model further provides expressions for the aggregation and disaggregation rates appearing in the final transport equations, which in the kinetic theory-based network model of Owens were absent and had to be specified separately. Despite this, the two models are found to provide similar descriptions of experimental data on the size distribution of rouleaux.

Comparison and simulation of different levels of erythrocyte aggregation with pig, horse, sheep, calf, and normal human blood

Erythrocyte aggregation levels in pig, horse, sheep, and calf blood samples were investigated and compared to that of normal human blood. The aggregation kinetics and adhesive forces between red cells, and an index of structure of the aggregates were determined with an erythroaggregameter (Regulest, France) at constant hematocrit (0.40 1/1) and temperature (37 °C). The adhesive forces and the index of structure in pig blood were close to those of normal human blood. The results for horse blood showed a very high level of aggregation kinetics and adhesive forces between red cells. For sheep and calf blood, little erythrocyte aggregation was found. To simulate different levels of red cell hyperaggregation in humans, a volume of horse plasma was replaced by isotonic NaCl in different proportions (5 to 40% V/V). The kinetics of rouleaux formation and especially the adhesive forces between erythrocytes were systematically decreased, while the index of structure was raised with increasing concentrations of isotonic NaCl. By replacing the porcine plasma with isotonic NaCl, normal and hypoaggregating levels of human red cells were simulated. The aggregation kinetics and the adhesive forces were reduced and the index of structure was raised when the concentration of isotonic NaCl was increased. In summary, large differences in the aggregation parameters were found between mammals. This study also showed that different human erythrocyte aggregation levels can be simulated by diluting the concentration of plasma proteins in equine and porcine bloods.

Increased erythrocyte aggregation in insulin-dependent diabetes mellitus and its relationship to plasma factors: A multivariate analysis

Red blood cell aggregation in vitro (kinetics and shear resistance) was studied in 13 healthy controls and 13 type I (insulin-dependent) diabetic patients free of severe degenerative complications who were matched for age, sex, and body mass index. Measurements were performed with a device that analyzes the laser light backscattered by a blood suspension. Both the velocity of rouleau formation and the cohesion of the rouleau network were significantly increased in diabetic patients. Plasma viscosity and whole-blood viscosity measured at low shear rate (0.95 s −1) were also significantly elevated in the diabetic group. Multivariate analyses of the whole population sample and the diabetic patients confirmed the influence of plasma proteins on the kinetics of aggregation. Fibrinogen levels, which were close to normal, affected mainly the shear resistance of the aggregates. Triglyceride and apolipoprotein (apo) B levels and indexes of metabolic control or protein glycation (fasting blood glucose and fructosamine) also appeared to influence markedly both the kinetics of rouleau formation and the cohesion of the rouleau networks. These rheological abnormalities occurred in diabetic patients before the appearance of any severe degenerative complications. We suggest that these rheological abnormalities are linked to plasma or erythrocyte factors, and are not due to angiopathy.

Kinetics of rouleau formation. II. Reversible reactions

Red blood cells aggregate face-to-face to form long, cylindrical, straight chains and sometimes branched structures called rouleaux. Here we extend a kinetic model developed by R. W. Samsel and A. S. Perelson (1982, Biophys. J. 37:493-514) to include both the formation and dissociation of rouleaux. We examine thermodynamic constraints on the rate constants of the model imposed by the principle of detailed balance. Incorporation of reverse reactions allows us to compute mean sizes of rouleaux and straight chain segments within rouleaux, as functions of time and at equilibrium. Using the Flory - Stockmayer method from polymer chemistry, we obtain a closed-form solution for the size distribution of straight chain segments within rouleaux at any point in the evolution of the reaction. The predictions of our theory compare favorably with data collected by D. Kernick , A.W.L. Jay , S. Rowlands , and L. Skibo (1973, Can. J. Physiol. Pharmacol. 51:690-699) on the kinetics of rouleau formation. When rouleaux grow large, they may contain rings or loops and take on the appearance of a network. We demonstrate the importance of including the kinetics of ring closure in the development of realistic models of rouleaux formation.

Theory of long-range coherence in biological systems. I. the anomalous behaviour of human erythrocytes

In this paper, an explicit expression of the interaction potential has been obtained, based on the Fröhlich model of long-range coherence in biological cells. These theoretical expressions are used to correlate with the experimental data obtained from the light scattering and the Brownian motion for the red blood cells (human erythrocytes). The necessary conditions are derived for the formation of rouleaux in human erythrocytes in the presence of long range interactions. The kinetics of rouleaux formation in terms of the properties of the diffusion coefficient has been investigated. It is concluded that both types of experimental data can be interpreted satisfactorily by this model.

Existence and bifurcation theorems for nonlinear elliptic eigenvalue problems on unbounded domains : Achim Bongers, Adam Opel AG, D-609 Russelsheim; Hans-Peter Heinz, Fachbereich Mathematik der Universität Mainz, Sarstr. 21, D-5600 Mainz, West Germany; Tassilo Küpper, Mathematisches Institut der Universitat Köln, Weyertal88, D-5000 Cologne 41, West Germany

Red blood cells aggregate face-to-face to form long, cylindrical, straight chains and sometimes branched structures called rouleaux. Here we extend a kinetic model developed by R. W. Samsel and A. S. Perelson (1982, Biophys. J. 37:493–514) to include both the formation and dissociation of rouleaux. We examine thermodynamic constraints on the rate constants of the model imposed by the principle of detailed balance. Incorporation of reverse reactions allows us to compute mean sizes of rouleaux and straight chain segments within rouleaux, as functions of time and at equilibrium. Using the Flory - Stockmayer method from polymer chemistry, we obtain a closed-form solution for the size distribution of straight chain segments within rouleaux at any point in the evolution of the reaction. The predictions of our theory compare favorably with data collected by D. Kernick , A.W.L. Jay , S. Rowlands , and L. Skibo (1973, Can. J. Physiol. Pharmacol. 51:690–699) on the kinetics of rouleau formation. When rouleaux grow large, they may contain rings or loops and take on the appearance of a network. We demonstrate the importance of including the kinetics of ring closure in the development of realistic models of rouleaux formation.

Kinetics of rouleau formation. I. A mass action approach with geometric features

In the presence of certain macromolecules, such as fibrinogen, immunoglobulin, dextran, and polylysine, erythrocytes tend to aggregate and form cylindrical clusters called "rouleaux" in which cells resemble coins in a stack. The aggregates may remain cylindrical or they may branch, forming tree, and networklike structures. Using the law of mass action and notions from polymer chemistry, we derive expressions describing the kinetics of the early phase of aggregation. Our models generalize work initiated by Ponder in 1927 who used the Smoluchowski equation to predict the concentration of rouleaux of different sizes. There are two novel features to our generalization. First, we allow erythrocytes that collide near the end of a stack of cells to move to the end of the cylinder and elongate it. Second, we incorporate geometric information into our models and describe the kinetics of branched rouleau formation. From our models we can predict the concentration of rouleaux with n cells and b branches, the mean number of cells per rouleau, the mean number of branches per rouleau, and the average length of a branch. Comparisons are made with the available experimental data.

ON SEDIMENTATION AND ROULEAUX FORMATION—II

From this short study of rouleaux formation several points have emerged.The first condition for rouleaux formation, and one which is fulfilled under all but unique circumstances, is that there shall be collisions among the cells. The frequency of these collisions plainly depends on such factors as the movements in the fluid, the number of cells present per unit volume, the viscosity of the fluid, and the size of the cells. The second condition is that the collisions shall result in permanent cohesions. Such cohesions will not occur if the surfaces of the cells are not sticky, if the repulsive forces between the cells are very great, or if the cells collide with one another so that the surfaces which come into contact are small. If, on the other hand, the collisions bring large surfaces into contact, permanent cohesions are likely to occur, for not only are there large surfaces over which the cohesive forces between the cells can act, but separation of these surfaces entails a considerable amount of work.The consideration of these points indicates why cells collect in rouleaux, and not in aggregates of roughly spherical form, for all contacts except those which occur at the ends of the shorter rouleaux are not permanent, whereas all contacts in which the cells are broadside on result in lasting cohesions. To this must be added the fact that discoid cells moved by a fluid orient themselves broadside on, and therefore collisions in this position are encouraged.From the mass of work on the potential difference between the red cells and the suspending fluid, it appears that, if the potential difference be reduced below a certain point, agglutination of the cells occurs, all contacts being permanent, in whatever position they occur. From this may be drawn the deduction that the repulsive forces accompanying this potential difference are sufficient to prevent the permanence of all contacts except those which involve a large extent of surface in connection with which considerable surface and cohesive forces are called into play. Before this explanation is regarded as the correct one, however, it must be shown that those electrolytes, and other substances which reduce the potential difference, do not also increase the stickiness of the cell surfaces. The cases of CaCl2 and MgCl2, which reduce the potential difference and yet do not cause agglutination, and the instance of heated plasma, which increases rouleaux formation without decreasing the potential difference, show how necessary it is to take account of this latter possibility, the importance of which has been clearly recognised by such investigators as Oliver and Barnard and Northrop.As regards the kinetics of rouleaux formation, we have found that a simple equation containing one easily evaluated constant is sufficient to describe the course of the phenomenon under such conditions as are extremely suitable for experimental purposes.This research was carried out under a grant from the Royal Society.