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We measured the electric current dependence of sedimentation curves of swine erythrocytes in a saline solution at the volume fraction of erythrocytes H = 0.091 and 0.220. The sedimentation curve fitted well to the exponential type equation l = a[1-exp(-bt)] at the upward initial electric current I0 = 0.50 mA, 1.01 mA and 1.50 mA, where l is the length of the medium layer at time t, and a and b are phenomenological parameters. The initial slope v0 of sedimentation curve was enhanced from 0.68 mm/hr at I0 = 0 mA to 2.85 mm/hr, 3.87 mm/hr and 5.50 mm/hr at I0 = 0.50 mA, 1.01 mA and 1.50 mA, respectively, for H = 0.220. We also made sedimentation measurements of erythrocytes in their own plasma at H = 0.220 and 0.316. Sedimentation curves coincided with the sigmoidal type equation l = l infinity/[1 + (t50/t)beta] at I0 = 0 mA and 0.50 mA, where l infinity is l at t----infinity, t50 is the time when the plasma level falls to l infinity/2 and beta is a constant. The maximum slope vmax of sedimentation curve increased from 13.29 mm/hr at I0 = 0 mA to 18.65 mm/hr at I0 = 0.50 mA for H = 0.220.

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 al. 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 new physical theory of erythrocyte sedimentation is proposed. Various assumptions underlying Stokes' formula are first criticized. An explicit formula is proposed, taking into account some of the results of recent experimental investigations including the effect of upward flow of plasma and the time course of growth of aggregates. It is generally shown that the sedimentation curve without aggregation never becomes a sigmoid. Our formula is applicable to the increased ESR due to the aggregation of erythrocytes. The sedimentation velocity depends not only on the hematocrit and the ultimate size of the aggregates, but also on the retardation time of the growth of aggregates in conformity with the experimental result of Kernick et al.

We have measured volume fraction dependence of the sedimentation curve of swine erythrocytes in a physiological saline solution at 10 degrees C, 20 degrees C, 30 degrees C and 40 degrees C. The sedimentation curves were found to consist of initial constant velocity region and final plateau region at the lower temperatures of 10 degrees C and 20 degrees C, while modified S-shaped curves were observed at the higher temperatures of 30 degrees C and 40 degrees C. The volume fraction dependence of the initial slope v of the sedimentation curve was fitted well to the following exponential type equation at all the temperatures: v = vs,exp (1 - H)exp[-(BH + CH2)] where vs,exp is the velocity in infinite dilution corresponding to the Stokes velocity and H is the volume fraction of erythrocytes. The volume fraction dependence of the relative velocity v/vs,exp was in close agreement with a semi-empirical equation derived for slurrys in the field of chemical engineering at the lower temperatures, while a small deviation between the observed and calculated curves was found at the higher temperatures. The volume fraction dependence of v at 20 degrees C was also analyzed on a theory recently developed by Oka. The explicit functional form of the medium up-flow factor phi (H) and the deformability factor f in the theory were determined using the experimental data.

Employing the optimality principle, we attempted to predict the effects of non-Newtonian blood and the metabolic states of individual vessel segments on the optimum vascular design. Our results implied that irrespective of the vessel caliber, the optimum flow rate of non-Newtonian blood through a cylindrical vessel is less than that of Newtonian blood by not more than some 12-13%, even though the non-Newtonian nature is within the pathologically-realistic highest range. Non-Newtonian blood does not exert the slightest degree of influence on the optimum geometry of the vascular bifurcation. In contrast, as the metabolic state of the vessel wall overwhelms that of the blood, the optimum flow through the cylindrical vessel becomes markedly increased: the optimum relative caliber of the branch of the bifurcation decreases and the optimum branching angle increases.

We have measured the sedimentation curves of swine erythrocytes in a physiological saline solution in inclined glass tubes. The curves are well fitted to the exponential type equation l = a[1 - exp(-bt)] for the tilt angle theta in the range of theta less than 80 degrees and hematocrits from 10 to 50%, where l and t are the medium length along the tube and the elapsed time from the sample injection, respectively. The coefficient a increases with theta and b is proportional to sin theta. The erythrocyte sedimentation rate ESR(theta) = (d l/dt)t----0 determined from the above empirical equation increases with the increase in sin theta roughly linearly. The experimental results are discussed with reference to the Ponder-Nakamura-Kuroda theory and some recent theories.

Erythrocyte sedimentation rate was measured in a physiological saline solution as a function of both the tube diameter d and the initial suspension length iota 0. All the sedimentation curves in the vertical tubes were found to overlap over the range 1 mm less than d less than 7 mm and 100 mm less than iota 0 less than 330 mm, within the precision of 8 %. The sedimentation curves in the tilted tubes fit well to an exponential equation of iota = a [1 - exp (-bt)], where iota and t are the medium length along the tube and the elapsed time from sample injection respectively: At fixed tilt angle theta and iota 0, a was roughly constant and b was roughly proportional to l/d, while at fixed theta and d, a was linearly proportional to iota 0 and b was constant. The initial slope ESR (theta) = (d iota/dt) t----0 = ab was represented by a unique straight line as a function of iota 0/d for each fixed tilt angle. The experimental results were compared with some recent theories.

The optimal geometry of the vascular bifurcation is interpreted on the basis of the principle of minimum work. We consider the energy expenditure due to the viscosity of blood, and that for maintaining the metabolic states of the blood cells and of the vessel wall. It is shown that the optimal radii of the stem and branch vessels and the optimal branching angle are related to two parameters which represent the morphologic and metabolic states of the blood and the vessel wall. In the special case of symmetrical bifurcation, it was found that as the metabolic demand of the vessel wall becomes more apparent when compared with that of the blood, the branch radius relative to that of the stem takes values of from 0.794 down to 0.758 minimally, and the angle from 37.5 degrees up to 48.7 degrees maximally with respect to the direction of the stem.