Biorheology

Stress relaxation analysis was used to measure mechanical properties of the cell wall. Although a pre-extension period is needed to give the initial stress or strain to a cell wall specimen in the experiments, studies reported in literature have assumed its length to be zero. Thus, the parameters obtained may not represent characteristic properties of the cell wall, which vary depending upon the pre-extension conditions. A mathematical formulation for stress relaxation with consideration for pre-extension was established by introducing a correction factor K in order to obtain parameters which represent characteristic mechanical properties of the cell wall. The validity of this treatment was examined by comparing the calculated values with experimental data.

The stress relaxation parameters T o , T m , b, and c vary depending upon the pre-extension rate when a cell wall specimen is stretched using a tensile tester. The effect of the pre-extension rate on the stress relaxation parameters of pea epidermal cell wall was investigated using a newly established equation. The change in the parameters due to the pre-extension rate can be corrected by the equation qualitatively and approximately quantitatively. The newly established equation appears to validly express the stress relaxation process with consideration for the pre-extension rate and the parameters T o k , T m k , b k , c k and K in the equation seem to represent the characteristic mechanical properties of the cell wall, although the parameters T o , T m , b, and c are valid for practical use to analyze the auxin effect on the mechanical properties of the cell wall.

When the cell wall of pea epidermis is extended and returned at a fixed rate, the stress-strain curves form a hysteresis loop. The mechanical properties of the pea epidermal cell wall in a constant rate experiment can be simulated by a model consisting of an infinite number of Maxwell elements and a single spring in parallel with them, as in stress relaxation experiments. The mathematical formulation for a constant rate experiment is closely related to that for a stress relaxation experiment through its constant parameters.

In a constant rate experiment, auxin pretreatment increases strain at a small stress. The effect of auxin on the stress-strain curve in the constant rate experiment is qualitatively and quantitatively reproduced well by the constant parameters representing the effect of auxin on the stress-time curve in the stress relaxation experiment.

A study of blood and plasma viscosities and of aggregation of red cells in 125 patients with malignant melanoma indicated that patients who died subsequently of metastasis showed a significant elevation of plasma viscosity and of aggregation of red cells. Plots of plasma viscosity or of aggregation of red cells against the time interval between test and subsequent death showed significant and negative correlations. Plots of plasma viscosity against globulin level, and plots of aggregation of red cells against albumin/fibrinogen ratio, showed significant differences between slopes of linear regressions for the survivors and for the deceased group.

Platelet diffusivity in flowing blood was measured using data from a deposition experiment on a subendothelial surface in a laminar flow chamber with aid of a theoretical estimation of platelet flux based on Leveque equation. Values of diffusivity range between 0.3 and 3.5×10⁻⁷ cm² sec⁻¹ for shear rates varying between 50 and 550 sec⁻¹ and for a series of hematocrits (20, 40, 60).

A convective-diffusive theory of the enhancement of diffusivity due to red cell rotational motion is then developed to quantitatively analyse the dependence of diffusivity on both shear rate and hematocrit.

Viscosity of Poiseuille flow of a fluid with couple stress has been studied in this paper. The analytic expression of the viscosity of couple stress fluid has been obtained in the form of modified Bessel’s functions of the order of zero and one. Since it is a complicated function of the couple stress parameters α and η, the numerical values of the relative viscosity η r have been computed for various values of α and η. These theoretical results are compared with other theoretical and experimental results on blood flow and suspension flows with 40% concentration. For the quick calculation of η r two simple approximate formulas have been obtained. The values of η r obtained from the exact formula and the approximate formulas are compared and it is found that they are in good agreement (within 6% error). The variation of η r (exact and approximate) with α and η is shown graphically which clearly indicates the existence of a discontinuity in the relative viscosity and the velocity at point (α = 0.0 and η = 1.0). The most important conclusions of this analysis are: (i) the conditions for the existence of Fahraeus-Lindquist effect in a tube flow have been obtained; (ii) Up to this date, only velocity profiles have been used to determine the values of α and η (η chosen arbitrarily); here it is shown that by using the experimental velocity profiles and relative viscosity both the couple stress parameters can be determine quite accurately (η no longer chosen arbitrarily). Finally, some biological implications of this theoretical investigation have been indicated.