ヘモレオロジーに関する二,三の理論的研究

抄録

In this paper are presented some reports of theoretical studies made on hemorheology which is the rheology of blood and blood vessels. The first problem is concerning the influence of the plasmatic zone upon the apparent viscosity of blood in capillaries. If the central core is treated as a Bingham body with the plastic viscosity η_B and the yield value τ_f, the volume of flow per unit time is obtained as follows.
with γ=1-δ/R> and ξ=2L_τf/PR. Here R is the radius, P is the pressure difference between the two cross sections at a distance L, η_p is the viscosity of plasma, and δ is the thickness of the plasmatic zone.
If we neglect small terms of order (δ/R)², then the above equation becomes modified as follows.
It is pointed out that the formula obtained by Bayliss
is not correct.
If we consider that the central core obeys Casson's equation, we get
with ξ=2L τf/PR. η_c is the Casson viscosity and τf is the yield value. If we neglect small terms of order (δ/R)², the above formula is reduced to that derived already by the author.
The second problem is concerned with the elastic tension in thick-walled blood vessels in relation to the law of Laplace. Since some doubts have been expressed in physiological literature about the applicability of the law of Laplace to blood vessels, we have examined closely the elastic tension in the wall from the physical point of view. Let a thick-walled vessel be in equilibrium under the internal pressure p₁ and the external pressure p₂ and let the inner and the outer radius be denoted by r₁', and r₂', respectively. Then the circumferential tension T_c is exactly given by T_c=p₁r₁'-p₂r₂'.
This relationship holds quite well generally, irrespective of whether the blood vessel wall has Hookean or rubber-like elasticity, whether the vessel wall is homogeneous or inhomogeneous, and whether the vessel wall is isotropic or anisotropic. Our formula is reduced to the law of Laplace for thin-walled blood vessels.