A fractal model for erythrocyte sedimentation

The erythrocyte sedimentation test is a useful tool for studying the biophysical properties of red blood cells (RBCs) and the interactions between RBCs and bridging macromolecules in the suspending fluid. In our previous model of erythrocyte sedimentation formulated on the basis of a logistic growth equation of population dynamics (Kuo et al., 1989), the sedimentation rate constant, r, was assumed to be an intrinsic constant characteristic of the interaction between RBCs and bridging macromolecules in the suspending fluid. By analyzing the time dependence of r in that model, however, it was found that r depends on the sedimentation time, t. There is a power law relation between r(t) and t; the rate "constant" is therefore an effective kinetic rate constant rather than a true constant. The realization that r is an effective kinetic rate constant allowed the introduction of a power law function r(t) into the formalism of erythrocyte sedimentation. Doing so yielded a new model with the following capacities: (a) The skew-symmetric sedimentation curves can be modeled; (b) the experimental data can be fitted better with the new sedimentation equations; (c) a fractal dimension, D, and a new rate constant, k, can be defined; (d) the tendency for a certain amount of plasma to be trapped inside the rouleau network, xi, can be accounted for. The D, k, xi, and other parameters can be used in the analysis of RBC interactions mediated by bridging macromolecules.