Biorheology

Blood flow through narrow tubes has been studied by two theoretical models, viz., sigma phenomenon and marginal zone theory. The analysis for the latter model, developed by the author elsewhere, has been used to obtain the marginal zone thickness; the sigma phenomenon theory for the flow of couple stress fluid has been developed here. It is found that the marginal zone thickness ε and the thickness of the unsheared laminae δ are very complicated functions of tube radius. Therefore, to get some insight into their relation with tube radius, the approximate expressions of ε and δ have been obtained. These approximate expressions of ε and δ contain their corresponding expressions for Newtonian fluids, given by Haynes analysis, as their limiting cases. A comparison of the theoretically predicted numerical values of ε and δ, obtained from the present and Haynes analysis, with the experimental values shows that the results obtained by the present analysis are in better agreement with the experimental results than those obtained by Haynes analysis. In contrast to Haynes conclusion (ε and δ are independent of tube radius), it is found that both the analyses (present and Haynes) indicate the dependence of the value of ε and δ on the tube radius. Further, it appears that ε in comparison to δ is a weaker function of tube radius. It is of interest to note that the nature of the variation of ε with tube radius in experiments is opposite to the one obtained from both the analyses. The reasons for this discrepancy are not clear. Finally, some physiological implications of the present analysis have been cited.

When the function ϕ(K, A; B) is defined by the equation ϕ ( K , A ; B ) = B ( 1 + A B ) 1 + B − K A the stress-relaxation process at a fixed strain has been represented in the previous papers of this series as follows: S = b k · ln ϕ ( K , t p ; t + T mk ) ϕ ( K , t p ; t + T ok ) + c k where S is stress, t_p is pre-extension time, and the parameters T_ok, T_mk, b_k, c_k, and K are constants. As we have reported, the parameters T_ok, T_mk, b_k, and c_k can be defined physically. However, the physical meaning of the parameter K has remained unclear. This study leads to the conclusion that parameter K can be defined as being equal to the pre-extension time, t_p, in the stress-relaxation experiment. Thus, the stress-relaxation curve and the effect of auxin pretreatment on a hysteresis loop in a stress-strain curve at a constant rate could be represented well by the calculated values.

Known methods for the measurement of blood rheologic properties are usually too slow for fast screening purposes under clinical conditions. The correlation between the molecular mobility of solvent water molecules in aqueous protein solutions and the nuclear magnetic relaxation rate has been well established. In addition the closely related dynamics of molecular exchange between solvent water and the water attached to the surface of the protein chains provide a dominant contribution to the nuclear magnetic relaxation. Since nuclear magnetic relaxation rate measurements can be done within seconds and purely electro-magnetically without physical contact with the sample, they are proposed as a test method for the microdynamics in biological liquid systems. The clinical significance of blood plasma spin relaxation rates has therefore been tested on plasma samples of 260 patients and test persons with an easy to operate computerized NMR-apparatus. The correlation with the corresponding plasma viscosity values proved to be sufficient for the establishment of a critical value for 1/T₂ indicating pathological conditions.

Dynamic viscoelastic properties were determined during the progress of plasma coagulation using a Weissenberg Rheogoniometer. A simple kinetic model was employed to describe the network formation phase of coagulation following recalcification of normal plasma. Rheological data obtained with pathological plasma samples (with Factor VIII and Factor IX deficiencies) indicated a delay in the initiation of clot formation and a slower initial fibrin polymerization rate. The computed ‘rate constant’ gave significantly different values for normal and hemophilic plasma clotting systems. No change was found in the final maximum elastic modulus attained, indicating network formation, though slow, eventually was complete and the final structure was unaltered.

The purpose of this study is to explore the effect of the branch-to-trunk area ratio upon the tendency of flow to become turbulent in symmetrically branched tubes. Velocity was measured with a laser Doppler anemometer in glass tubes which branched at 70° from a 25 mm diameter trunk. The branch-to-trunk area ratio of branches studied was .4, .6, .8, 1.0, 1.2, and 1.4. For branch-to-trunk area ratios of .4 to .8, the critical Reynolds number in the trunk at which the transition to turbulence in the branch occurred was relatively constant at approximately 2100. As the branch-to-trunk area ratio increased beyond .8, the critical Reynolds number decreased until, at a ratio of 1.4, the critical Reynolds number was 1200. Since the Reynolds number of transition in the trunk was found to be 2100, it is apparent that a branch-to-trunk area ratio of 1.4 caused a prominent reduction of the critical Reynolds number in the system. A branch-to-trunk area ratio less than .8 had no effect. The velocity profiles at a branch-to trunk area ratio of .4 showed acceleration of velocity in the branch; while at an area ratio of 1.4, the velocity was shown to decelerate. This explains the tendency for flow to be unstable in branches with area ratios greater than one. These observations suggest that the branch-to-trunk area ratio usually observed in patients at the aortic bifurcation is such that laminar flow is promoted.

In the present analysis, a two-fluid model for blood flow through small diameter tubes has been studied. This model essentially consists of a core region (suspension of red cells, etc.), assumed to be a micropolar fluid, and a peripheral plasma layer (Newtonian fluid). It is proposed that the coefficient of Viscosity in the core region may be considered as the shear viscosity of blood. Using the boundary conditions proposed by Ariman et al. and Bugliarello and Sevilla, analytical expressions for flow velocity, cell rotational velocity and effective viscosity have been obtained. Variation of velocity profile shows that the results obtained are in better agreement with the experimental results. A critical study of Ariman et ale model and other existing two-fluids models has been presented. The values of effective viscosity for different tube diameters have been computed from Ariman et ale model and from the present model. On comparing, it is found that the results obtained from the present analysis exhibit Fahraeus-Lindquist effect, whereas the Ariman et al. model does not show this effect.

The process of substance diffusion in tissue with nonlinear consumption of Michaelis-Menten type is described analytically. Formulas are derived describing the substance concentration profile in the capillary and in the tissue on condition that concentration several times exceeds the Michaelis-Menten constant in value. The model takes into consideration the finite substance permeability through the capillary wall and substance diffusion into the tissue only in the radial direction.

Nous avons étudié le comportement rhéologique de suspensions sanguines en fonction du temps de conservation (21 jours) et de la solution de conservation (ACD, CPD et CPD-Adénine). Nous avons utilisé pour cette étude un viscosimètre à cylindres coaxiaux. Nos résultats ont permis de montrer que la viscosité augmente régulièrement au cours de la conservation, que cette augmentation est toujours plus importante aux faibles valeurs du gradient de vitesse et qu’elle est indépendante de la solution de conservation. D’autres mesures ont permis de cons tater que, au cours du stockage, il n’apparaissait aucune variation de la viscosité du plasma, de la concentration moyenne en hémoglobine et du volume globulaire moyen. Enfin nous avons pu cons tater que des globules rajeunis par incubation dans une solution PIGPA ont un comportement rhéologique proche de celui des globules rouges fraîchement prélevés, et ceci pour toutes les valeurs du gradient de vitesse utilisées.

The osmotic pressure of proteoglycans extracted from human hip, knee and intervertebral disc cartilage and from bovine nasal cartilage, and of chondroitin sulphate was measured by equilibrium dialysis against solutions of polyethylene glycol in 0.15M NaCl and 1.5M NaCl. The osmotic pressure of the proteoglycans at concentrations found in these cartilaginous tissues, viz. 0.08–0.35 meq/gH₂O, was found to lie in the range 0.3–3.5 atm. Molecular size and degree of aggregation were found to have no measurable influence on the value of osmotic pressure. The “Donnan” osmotic pressure was by far the major component; under physiological conditions, not more than 15 per cent of the total osmotic pressure resulted from excluded volume effects.

In this investigation, the erythrocyte sedimentation rate was studied in inclined tubes. Two parameters were included which make this work different from any previous research on this subject. First, the actual rate of settling was measured with an automatic sedimentimeter and second, the settling tubes were rotated along their long axis with constant angular velocity. The results in both the vertical and inclined tubes could be expressed in terms of a simple mathematical equation. It was also observed that the rotation of the inclined tubes practically negates the effect of the inclination.

Simultaneous measurement of apparent viscosity and mean tube hematocrits have been made at various shear rates for the flow of red blood cell suspensions through glass capillaries with diameters in the range 30 to 500 microns. Two types of red blood cell (RBC) suspensions, namely normal and heated RBC suspensions, have been used in the investigation to study the effect of erythrocyte deformability. The effect of heating on the shape and size of erythrocytes was studied through scanning electron microscopy. The hematocrit of the suspensions ranged from 5 to 65 % in the large tubes whereas in the smaller tubes it was maintained around 40 % for both the suspensions. Experimental results on the apparent viscosity and hematocrit defect for normal RBC suspensions are found to be in good agreement with the published data in literature. The decreased deformability of the heated erythrocytes resulted in an increase in the apparent viscosity as measured in all the tubes. However, the extent of this increase was observed to depend on tube diameter, the effect being more pronounced in smaller tubes. Further, the hematocrit defect in the heated RBC suspensions was found to be less than that for the normal RBC suspensions under comparable flow conditions.