New data and mathematical model of erythrocyte sedimentation.

The known models do not provide satisfactory description of the erythrocyte sedimentation kinetics. Experimental data have shown that erythrocyte sedimentation rate (ESR) depends on (i) hematocrit (H); (ii) aggregation degree; (iii) height of the liquid column (h(o)); (iv) the state of the capillary inner surface and (v) diameter of the capillary (D). The latter dependence is very strong at D similar to 1 mm. Such an effect is due to a notable influence of rubbing forces on the sedimentation process at small D. Significant scatter of the ESR data for a variety of healthy donors may be due to non-standard laboratory capillaries. In this work, a mathematical model has been developed for the case of D>4 mm, the contribution of friction being negligible. According to experimental data, the dependence of the initial ESR value (v(o)) on H is hyperbolic at H --> 1 and linear at H --> 0: v(o)=2gR(2) Delta rho(1-H)/9 eta(H), where g=9.8 m/s(2), R is the average erythrocyte radius, Delta rho is the difference between specific densities of erythrocytes and the medium, eta(H)=eta(o) (1+alpha H-2) is the viscosity of erythrocyte suspension at H<0.4, eta(o) is the medium viscosity. A kinetic equation has been derived describing the time dependence of height of erythrocytes column, h: h-h(o)+Hh(o)(1+alpha)1n((h-Hh(o))/h(o)(1-H))=At,A=2gR(2) Delta rho/9 eta(o). The equation is in a good agreement with experimental data.