Kinetics of rouleau formation. I. A mass action approach with geometric features

In the presence of certain macromolecules, such as fibrinogen, immunoglobulin, dextran, and polylysine, erythrocytes tend to aggregate and form cylindrical clusters called "rouleaux" in which cells resemble coins in a stack. The aggregates may remain cylindrical or they may branch, forming tree, and networklike structures. Using the law of mass action and notions from polymer chemistry, we derive expressions describing the kinetics of the early phase of aggregation. Our models generalize work initiated by Ponder in 1927 who used the Smoluchowski equation to predict the concentration of rouleaux of different sizes. There are two novel features to our generalization. First, we allow erythrocytes that collide near the end of a stack of cells to move to the end of the cylinder and elongate it. Second, we incorporate geometric information into our models and describe the kinetics of branched rouleau formation. From our models we can predict the concentration of rouleaux with n cells and b branches, the mean number of cells per rouleau, the mean number of branches per rouleau, and the average length of a branch. Comparisons are made with the available experimental data.