Syoten Oka

Optimality principle in vascular bifurcation

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.

Pressure development in a non-Newtonian flow through a tapered tube.

SummaryThe flow of viscous fluids through a tapered tube is very interesting from the standpoint of blood flow in blood vessels. The taper of the tube is an important factor in the pressure development. In the first place, we have given a brief summary of our theory of the steady convergent flow of non-Newtonian fluids characterized by an arbitrary time-independent flow curve through a slightly tapered tube. Based on our general formula for the flow per unit time, explicit formulae of the pressure gradient are obtained in several cases of non-Newtonian fluids specified by particular flow curves: power law fluid,Bingham body, and the fluid obeyingCassons equation. In all these cases it is shown that the pressure gradient is not constant along the axis but increases with decrease in the radius of the tapered tube. If we neglect quantities of orderα2 (α: angle of taper), then the pressure gradient increases linearly with the distance along the axis of the tube.

Erythrocyte sedimentation rate. I. Volume fraction dependence in saline solution.

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.

Effect of electric field on erythrocyte sedimentation rate. II, dependence on electric current

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.

Erythrocyte sedimentation rate. II: Effects of tilt angle in saline solution

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.

A theory of the pressure distribution in powder in equilibrium in a cylindrical vessel

Abstract A mathematical analysis of the distribution of pressure (vertical stress) in a powder mass filled in a cylindrical vessel is presented, taking into account the variation of pressure with the distance from the axis of the cylinder. The free surface of the powder mass is assumed to be even. It is assumed that vertical stress and horizontal stress are interrelated by Rankines law. From the equilibrium condition of the powder mass a fundamental equation has been derived to determine the pressure as a function of both the depth and the distance from the axis of the cylinder. A solution satisfying the boundary condition at the free surface has been obtained. It contains a number of indeterminate constants and is reduced to Janssens formula, provided that the pressure is independent of the distance from the axis of the cylinder. It is shown that our theory agrees fairly well with the experimental data of Yoshioka .

Circumferential tension in the wall of bent blood vessels

Abstract Applicability of a general formula, derived originally for the circumferential tension in a straight hollow cylindrical tube in equilibrium under constant internal and external pressures, proved to be extended to the equilibrium of a curved tube with arbitrary planar bendings, provided that the circumferential tension is defined as the arithmetic average of tensile forces per unit axial length acting perpendicularly to the section of tube walls cut by a plane passing through the tube axis. It was shown that the formula may be applied to any blood vessel on a plane regardless of its planar bendings, size, and pulsatile movement, in so far as its cross-sectional shape can be assumed to be annular and formed by two concentric circles.

A theoretical study on transcapillary fluid movement

Abstract The prevailing mathematical expression of the Starling hypothesis has proved to involve equivocality and inaccuracy. Assuming that transcapillary flow takes place, following Poiseuilles law, through cylindrical pores perpendicular to the internal surface of a capillary, an improved formula has been derived on the basis of the fact that driving force for filtration and resorption of fluid is equal to the algebraic sum of hydrostatic and colloid osmotic pressures at both sides of the capillary wall. The physical meaning of filtration constant, capillary filtration coefficient and mean capillary pressure are elucidated from the viewpoint of the pore theory. Discussions are given of how the rate of transcapillary fluid movement within a certain amount of a tissue must be dealt with.

Effect of electric field on erythrocyte sedimentation rate. I. Enhancement in saline solution.

In the present paper, the effect of a DC electric field on the swine erythrocytes settling in physiological saline solution in a vertical tube would be investigated. An attempt is made to compare the settling of erythrocytes with and without an electric field, and to present good reproducible data

Erythrocyte sedimentation rate III tube diameter dependence in saline solution

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.