Quantification of Platelet Aggregation by Mathematical Model of the Chemical Kinetics

Abstract

We developed a mathematical model for quantifying the progress of platelet aggregation by applying the chemical kinetic theory. We established a linear inverse problem to obtain a reaction rate constant matrix which is related to the progress of aggregation. The matrix was obtained from the time series data of the numbers of small, medium, and large aggregates and their subtracted data measured by the time-resolved laser scattering method (TRLSM). The algorithm for solving the inverse problem was developed by employing the Moore-Penrose generalized inverse matrix with the singular value decomposition technique. We analyzed the experimental data with our model to investigate (1) the dependence of the ADP-induced aggregation in platelet rich plasma (PRP) on the concentration of ADP, and (2) the mechanism of aggregate formation induced by 3 different agonists, ADP, epinephrine, and collagen. The results suggested the applicability of the proposed method to quantify the progress of the platelet aggregation using classification by mechanism of aggregate formation.