Biorheology

Specimens of bave (undegummed silk thread) were collected from cocoons of various origins of parent silkworm races, such as Japanese, Chinese, European, Korean and tropical origins, and from as many races as possible. An apparatus was set up to measure the dynamic elastic modulus of these specimens. In all the categories of the races tested, the elastic modulus was linearly related to the size of bave, regardless of the portion of cocoon layer from which the specimens were taken. This correlation was concluded to be universal to the silk thread of Bombyx mori L. species; however, values of the regression coefficient and of the elastic modulus were susceptible to the origin of silkworm races, depending on whether they were native or improved.

The effects of the deformation of red blood cells on non-Newtonian viscosity of a concentrated red cell suspension are investigated theoretically. To simplify the problem an elastic spherical shell filled with an incompressible Newtonian fluid is considered as a model of a normal red cell. The equation of the surface of the shell suspended in a steady simple shear flow is calculated on the assumption that the deformation from a spherical shape is very small. The relative viscosity of a concentrated suspension of such particles is obtained based on the “free surface cell” method proposed by Happel. It is shown that the relative viscosity decreases as the shear rate increases.

The intensity of light scattering by blood in a tube of diameter 0.26 cm was measured with an apparatus devised by us at different angles on an incident cross-sectional plane. Changes in angular distribution of light intensity associated with hemolysis, and changes in hematocrit (Ht), red blood cell (RBC) swell ing, and flow rate were plotted on polar coordinates. The dyssymmetry index, defined as the ratio of the intensity of light at 45° to that at 135°, was used to characterize the shape of the diagrams of light scattering. The index decreased with Ht, flow rate, but increased with RBC swelling. It is concluded that light scattering by blood requires intactness of the RBC membrane. Even when the cell membrane is intact, light scattering is subject to changes with the flow rate of blood, presumably due to RBC aggregation.

Complex Young’s modulus of blend gels of gelatin and kappa-carrageenan or agarose has been measured in order to clarify the protein-polysaccharide interaction in biological systems. The mixture of gelatin and kappa-carrageenan showed phase separation in the intermediate volume fraction of gelatin, and it formed a homogeneous gel when the volume fraction of gelatin is very large or very small. Since the dynamic Young’s modulus for blend gels of kappa-carrageenan and gelatin was larger than the calculated one from a theory for dispersed systems, some structural reinforcing must occur. The mixture of agarose and gelatin showed the inverse tendency. It was concluded that the role of electrolytic groups was dominant in dilute gels, while molecular entanglement became more important in concentrated gels.

Steady flows and pulsatile flows of a Newtonian fluid through a channel with a rectangular hump were numerically studied as a two-dimensional model of blood flow in a constricted artery. From the numerical calculation, it was shown that one of the hydrodynamic causes of endothelial lesion of artery and post-stenotic dilatation can be found in the large temporal variation of shear stress behind a constricted portion of artery. Local maximum of the pressure there can be seen as secondary factor for the post-stenotic dilatation.

The complex viscosity η ∗ has been measured of bovine red blood cells suspended in a medium of isotonic NaCl solutions including dextran and buffered with potassium phosphate at pH 7.0. A multiple lumped resonator apparatus was used at the frequencies of 144, 572, 1491, 3742, and 8026 Hz at 20.0°C. Due to the high molecular weight of dextran the medium also exhibited some viscoelasticity η s ∗ . So we adopted the complex specific viscosity η sp ∗ = ( η ∗ − η s ∗ ) / | η s ∗ | . At 20.0°C η sp ∗ decreased with the frequency where the hematocrit was 0.233 and η_s 0.34 poise. The measurements were made for the medium with different viscosity at 5.0°C and 25.0°C. The results are compared with the theory of elastic shells.

The static and dynamic viscoelastic properties were studied of longitudinal and circumferential strips excised from various large veins of dogs. The mechanical behavior in longitudinal direction could be regarded as elastic, while that in circumferential direction was highly viscoelastic. No distinct regionality was observed in either of the longitudinal and the circumferential groups. Noradrenaline and papaverine did not alter the elastic behavior of the longitudinal strips. In circumferential strips, however, noradrenaline caused a considerable decrease in stress relaxation and some steepening in the slope of the upper limb of hysteresis loop. Papaverine did not affect the circumferential characteristics. These findings suggest the dominant contribution of smooth muscle tone to the circumferential characteristics of venous walls. Pretreatment with formic acid abolished the occurrence of stress relaxation in circumferential direction but produced no change in the longitudinal behavior. This indicates that elastin fibers may be a principal determinant of the elastic behavior in longitudinal direction and that a residual tension observed in stress-relaxation tests of circumferential strips may be due to stretched elastin fibers. The elastic moduli of elastase pretreated venous walls were in the order of 10⁸ dynes/cm², about 1000 times higher than those of the control. Accordingly, collagen fibers seemed not to play any appreciable role in the rheological behavior of venous walls under physiological conditions. This inference was supported by histological observations of venous walls under unstretched and stretched states. Models were proposed in regard to the architecture of the fibrous elements in the venous walls.

A flow of a highly concentrated latex suspension around a solid body in a thin layer between two parallel glass plates was observed by an optical microscope. A clear region, where suspended particles were rare, appeared near the rear stagnation point of the body. A model for. explaining this phenomenon is proposed, in which the area of the clear region depends on an average size of aggregates of suspended particles. A possibility is suggested to use this phenomenon for measuring aggregate size in concentrated suspensions.

In order to consider the effect of membrane fluidity upon the mechanical property of biological cell suspensions, we have calculated the complex intrinsic viscosity [ η ∗ ] = [ η ′ ] − i [ η ″ ] of spherical shell structures with material incompressibility in suspension as a function of the dimensionless frequency x = ω η ′ a / γ ′ together with the parameters of h m = η m / η ′ , g = γ / γ ′ , h = η / η ′ , δ = d / a , where a is the radius of the cell, d is the width of the membrane, η, η_m, and η ′ are the viscosities of the medium, of the membrane and of the internal region of the cell, γ and γ ′ the surface tensions at the outer and the inner side of the membrane respectively, and w the angular frequency. The result is simply represented by two dispersions as follows: [ η ∗ ] / [ η ] = A 1 + B 1 / ( 1 + i ω τ 1 ) + B 2 / ( 1 + i ω τ 2 ) . Here i is the imaginary unit, A 1 = 2 ( 1 − h ) / ( 2 + 3 h ) + O ( δ ) , B 1 = 3 h / ( 5 + 5 h ) + O ( δ ) , B 2 = h ( 19 + 16 h ) / { 5 ( 1 + h ) ( 2 + 3 h ) } + O ( δ ) , τ 1 = { ( 5 / 24 ) ( 1 + h ) ( 1 + 1 / g ) δ − 2 + O ( δ − 1 ) } a η ′ / γ ′ , τ 2 = [ ( 2 + 3 h ) ( 19 + 16 h ) / 40 ( 1 + h ) ( 1 + g ) + O ( δ ) ] a η ′ / γ ′ and [ η ] = ( 5 / 2 ) { 96 h m g + 32 g ( 5 + 5 h − 12 h m ) δ + O ( δ 2 ) } / { 96 h m g + 32 g ( 5 + 2 h − 12 h m ) δ + O ( δ 2 ) } .

Using a rheoscope, combined with a TV image analyzer and a computer, the effects of immunoglobulins and IgG-fragments on the process of human erythrocyte aggregation were determined. The immunoglobulins accelerated the aggregation; the effect increased with their molecular weight, i.e., IgG ≃ γ-globulin < IgA < IgM. An empirical relationship, expressing the dependence on the immunoglobulin concentrations, was proposed. F(ab′)₂-fragment accelerated the aggregation, more effectively than IgG, while Fab- and Fc-fragments did not. Therefore, two Fab-portions are presumably needed to form the aggregates, and the flexibility between two Fab-portions may be important.

A case of multiple myeloma showed an increased aggregation, due to the increased myeloma protein.

An entire settling curve for whole blood is derived theoretically based upon Chien’s expression for the viscosity of whole blood at hematocrits in excess of 40%. This problem was already studied by Puccini et ale in 1977. The aim of this note lies in correcting a mistake found in their treatment of a differential equation. The functional form of the entire settling curve differs, of course, from that obtained by them. It is shown that the settling curve is governed by only two parameters. The comparison of our theoretical formula with experimental data is left for our future task. It is suggested that the meniscus will be curved in close neighborhood of the glass wall due to the fluid mechanical influence of the wall. The effect of the aggregation of red cells will also be taken into account in future.

A purpose of the present study is to make an artificial rouleau of bovine red blood cells which is not capable of rouleau formation under physiological condition. Rheological behaviors of bovine blood forming artificial rouleaux were examined. The modification of cell surface by enzyme trypsin induced rouleau formation, whereas the modification of cell surface by neuraminidase did not cause any aggregate formation. The drastic elevation of the fibrinogen content in bovine red blood cells suspension also brought about the formation of rouleau. The value of dynamic rigidity modulus G′ of bovine red blood cells in saline solution containing high concentration of fibrinogen is somewhat smaller than that of trypsin treated bovine red blood cells in plasma. The value of G′ of trypsin treated bovine red blood cells in plasma first increased to a maximum value and then decreased with the time. It is supposed that the removal of macromolecules from the cell surface facilitates the mutual approach of cells and causes the formation of rouleau which seems to be the same as that of human and horse bloods.

Sheep hemolysate-loaded liposomes were prepared by a modified interfacial deposition technique. The mean diameter of the liposomes was estimated to be about 310 nm. Sheep hemolysate-loaded liposomes were called artificial red blood cells (ARBC). The flow properties of the ARBC suspension (pH 7.4) were measured with a concentric cylinder-type rotational viscometer at low shear rates and were compared with those of sheep red blood cell (SRBC) suspension (pH 7.4). It was revealed that the flow type of the ARBC suspension (pH 7.4) was of pseudoplastic as in the case of SRBC suspension (pH 7.4). The relative viscosity of the ARBC suspension as a function of particle concentration in the medium was linear and fitted fairly well with the Einstein equation. However, the relative viscosity of SRBC suspension was increased more gradually with increasing particle concentration, and was well presented by the Brinkman equation as a function of particle concentration for concentrated suspensions. It was suggested that this would be due to the difference in particle-particle interaction between the two types of suspensions. The flow properties of the mixed suspensions of the ARBC and SRBC in the suspending medium (pH 7.4) with and without dextran were measured. It was revealed that the relative viscosity of the mixed suspension is reduced with increasing mixing ratio of the ARBC in the suspension, suggesting that the flow properties of the mixed suspension of the ARBC and SRBC are dependent on the ARBC rather than dextran.

The supply of oxygen to tissue from capillaries may be influenced by hemorheological factors. A hemorheological model is developed for elucidating which factors play a major role in the oxygen transport to tissue. For a capillary tissue unit, a modified cylindrical model of Krogh is used. For blood, two fluids model of red blood cells (RBCs) and plasma is used where hemoglobin release effect is included. Non-equilibrium flows as well as equilibrium flows are examined for various parameters (total flow Q or RBC velocity Vr, discharge hematocrit Hd and capillary hematocrit Hc). In equilibrium flow, Hd and Q determine the oxygen transport. In non-equilibrium flow, Hc also becomes important. Especially, hemoglobin release effect becomes significant in low Hc flow, which affects the area of lethal region in tissue.

Effects of high osmotic media on the shape and deformability of RBC were examined for determining increasing factors of blood viscosity. Dog blood and Urographin (a hypertonic contrast medium) were used; the plasma osmolality was changed by urografin suspended in blood. The viscosity was measured for normal RBC and glutaraldehyde-treated RBC suspensions with a cell volume concentration. The RBC deformability was evaluated from the difference in viscosity between the two suspensions. It was shown that normal RBC suspension increased the viscosity with increase in osmolality at high shear rate; hardened RBC suspension decreased the viscosity with increase in osmolality. It was concluded that the RBC deformability decreased with increasing osmolality.

Dependence of the viscosity of milks on the bore-size of capillary viscometer has been studied at 25°C. Viscosity measurements were carried out with a Maron-Belner type low shear capillary viscometer with various capillary radii (0.0190–0.076 cm) within the shear stress range of 0.2–30 dynes/cm² at the capillary wall. Each milk showed non-Newtonian flow behavior and dependence on the size of the capillary. The viscosity of human fresh milk and cow’s fresh milk decreased with the decreases in the capillary bore-size within the range of shear stress studied, and the viscosity of homogenized milk, although similar phenomena as above were Observed in higher shear stress, decreased with the decrease in the capillary bore-size at the range of lower shear stress.

The difference in characteristics of capillary bore-size dependence on viscosity may be attributed to the difference in the behavior of fat droplets existing near the wall at which thermal motion of fat droplets will be hindered by the existence of capillary wall. The results were represented by the modified Ree-Eyring generalized flow formula for a flow system containing one Newtonian flow unit and one non-Newtonian flow unit which included additional terms dependent on the capillary bore-size. The viscosity equation suitable for analysing the dependence of viscosity on the capillary bore-size at entire ranges of rate of shear, was derived by assuming the wall layer. Composed of double layers (of thickness d_o and d_i - d_o) in the flowing liquid in capillary tube, and by combining this equation with the modified Ree-Eyring equation, the values of d_o and d_i were calculated.

A Maxwell-type equation, which involves both time-dependent viscosity η ( t ) and elastic modulus G ( t ) is proposed as governing the shear stress difference σ ′ = σ − σ y , where σ and σ y are total and yield shear stresses respectively.

A (reaction kinetics) equation for a structure variable λ is written which describes the evolution of blood structure (network ⇄ rouleau ⇄ RBC) in stress formation and stress relaxation measurements and which also depends on the (constant) applied shear rate γ ˙ 1 . The time dependent viscosity is assumed to involve the solution λ ( t , γ ˙ 1 ) of the rate equation in the same manner than its equilibrium value λ e q ( γ ˙ 1 ) enters in a viscosity equation η ( λ e q ) yet proposed by one of the authors. A simple relation G ( λ ) completes the structural description.

General solutions σ ( t ) of the Maxwell-type equation are discussed in the case of stress relaxation (after the cessation of steady flow) and stress formation (under constant shear rate). Especially, the latter exhibits the well-known “overshoot” behavior. Moreover, the long time behavior of the former allows the quantification of the yield shear stress. Lastly one example of application to blood measurements is discussed.

For the purpose to observe the possible vessel wall damage by deionization of the related anionic groups the perfusion test of rat kidney and aorta with cationic iron colloid particles and the injection experiments with albumin-poly-L-lysine complex were carried out. By staining the fixed tissue sections with the cationic iron colloid at pH 7.3 the ionized anionic sites on vessel walls have been demonstrated histochemically. The perfusion test of living tissue with the cationic iron colloid induced the desquamation of the endothelial cells. The perfused colloid particles were adsorbed to the whole endothelial cell surfaces facing to luminal and subliminal sides. Albumin-poly-L-lysine complex injected into vein deposited in the subendothelial spaces of glomerular capillaries through the endothelial cell layer having the well-kept anionic barriers. Discussion was made on possible damage of vessels due to the deionization of anionic groups of endothelial cells and serum proteins by general cationic molecules.

The method of the tangent simple systems is applied to the study of the viscoelastic behaviour of human blood in unstationary flow for rectangular steps and triangular ramps of shear rate. The tangent systems we utilize, Maxwell liquids, enable us to determine, at every point of the rheograms, apparent instantaneous values of retardation or relaxation time, viscosity coefficient and elasticity modulus of the studied blood samples, and to plot the curves of variation of these parameters as a function of flow duration. A qualitative interpretation of the results is proposed from data on the aggregation-disaggregation kinetics of red blood cells. Examples are given for samples of normal and pathological bloods.

We studied the effects of expectorants (mucolytic agents) in vivo on the relaxation behavior of sputum viscoelasticity. Seven female and thirty-three male patients (56.8 ± 19.3 yrs, range: 21 to 82 years old) with a chronic pulmonary disease except bronchial asthma were studied. They were randomly put into the control group or a group which would be given oral treatments with an expectorant for a week after a one week washout period. The groups were as follows: Group I ( n = 8 ), control; Group II ( n = 7 ), Bromhexine hydrochloride 24 mg per day; Group III ( n = 10 ), Ambroxol 90 mg per day; Group IV ( n = 9 ) α - Chymotrypsin buccle 100 ch.u. per day; Group V ( n = 6 ), Serratiopeptidase 30 mg per day. In Groups IV & V, frequency dependence of sputum viscoelasticity at the range of ω = 10 − 3 to 10 − 0 rad.sec⁻¹ were clearly changed after the treatments, and the magnitude of the relaxation and its main relaxation time were significantly increased. On the other hand, in Groups I, II & III, no significant changes of the frequency dependences were observed. These findings suggest that proteolytic enzymes administered orally work on the molecular structure of sputum, and break down their linkages between subunits of the structure.

When viscoelasticity is measured with an oscillating capillary rheometer, the density of the fluid under study is an influencing factor (inertia). In the particular case of blood rheology hematocrit is also of interest. It can be measured more exactly on the basis of the density of blood and blood plasma than by conventional methods using a hematocrit centrifuge or Coulter counter, as these give too high readings when there is an increased tendency towards erythrocyte aggregation and reduced erythrocyte flexibility. Due to the double significance of blood density for blood viscoelasticity, an oscillating capillary rheometer and a new type of density-measuring device were attached to a computer in such a way that simultaneous evaluation is possible. The density-measuring device is a U-tube that is set into oscillation electronically. The duration of the oscillation is an indication of the density of the fluid in the U-tube.

Hemorheological studies were made on surface layers of solutions of highly purified human fibrinogen, to which low molecular weight (LMW) heparins, as well as chondroitins A, Band C were added. The surface viscous ( η s ′ ) and elastic ( G s ) moduli of these fibrinogen systems were measured with a modified Weissenberg Rheogoniometer. Our findings show that n s ′ and G s of these heparin-fibrinogen and chondroitin-fibrinogen surface systems were markedly decreased as compared to the fibrinogen control. Heparin of MW 4400 exhibited about 30 per cent decrease, while heparins of MW 5300 and 5900 had decreases of approximately 75 per cent in n s ′ and G s . The three chondroitins A, Band C were found to reduce the n s ′ and G s by about 40 per cent. The surface layers of fibrinogen, which are surface gels, constitute the clotting of fibrinogen without thrombin participation. Such so-called ‘fibrinogenin’ formation is considered by Copley to initiate thrombosis. The LMW heparins and the chondroitins tested, which we found to inhibit fibrinogen formation, may therefore be expected to act as anti thrombotic agents. Thus, LMW heparins and chondroitins A, Band C may play important roles in the prevention of thrombosis.

Hydroxyethyl starch (RES) has often been used as a plasma expander, but questions still remain concerning the mechanism by which it produces changes in the rheological properties of blood and erythrocyte (RBC) suspensions under various flow conditions. The present investigation has shown that the dynamic viscosity of RES (232,000 and 565,000 daltons) solutions rises in a nonlinear fashion with increasing HES concentration, and for a given concentration of HES exhibits Newtonian behavior at shear rates between 0.15 to 124 ⁻¹. At low (< 0.9 ⁻¹) shear rates the apparent viscosity of a 40% RBC suspension increases with lower concentrations of HES because of RBC aggregation. At higher concentrations of RES, increases in suspension viscosity are due to an increase in the viscosity of the continuous phase since the RBC are largely disaggregated. At high (> 36 sec⁻¹) shear rates the relative viscosity ( η / η 0 ) of RBC suspensions slowly decreases with increasing HES concentration. At low shear rates η / η 0 increases and then decreases with increasing RES concentration. Evidence of the concentration-dependent effects of RES on RBC aggregation is provided not only by the viscometric analysis but also from measurements of erythrocyte sedimentation rate (ESR) and the zeta sedimentation ratio (ZSR). HES is a more potent aggregating agent in phosphate buffered saline (PBS) than it is in plasma. Polymer size has only a slight effect on the extent of RBC aggregation produced, but does have a significant effect on the concentration of polymer at which maximum aggregation occurs. The viscosity-corrected electrophoretic mobility of RBC in HES rises monotonically with the concentration of HES in the suspending medium. Decreases in the extent of RBC aggregation with increasing polymer concentrations probably result from an increase in the electrostatic repulsive forces between the cells.

Separation flow through matrices or membranes is generally characterized by three phenomenological coefficients. Of these the hydraulic permeability L_p and the reflection coefficient σ are the most commonly discussed. Their theoretical interpretation is much aided by the use of friction coefficients f ˆ ℓ m defined to characterize the relative interaction in flow of the thermodynamic component ℓ in its movement past m. It is shown that this definition can be further simplified and that as a result simplified expressions notably for L_p result.