Analysis of kinetics of light scattering by cell suspection during aggregation: mathematical modeling of platelet disaggregation

Abstract

Background. Molecular mechanisms of platelet aggregation are actively studied by methods of molecular cell biology, biochemistry, applied physics, but the problem of modeling the dynamics of this process remains open. Mathematical modeling allows to establish quantitative indicators of aggregation kinetics, to analyze the results of scientific research and testing of blood samples in everyday medical practice. Known mathematical models of spontaneous reversible and irreversible platelet aggregation in a shear flow of different intensity are not suitable for analysis of data obtained by the most common laboratory method - light transmission aggregometry. Objectives. The aim of the work was to create a mathematical model of platelet aggregation that can adequately describe the reversible cell aggregation, in particular the disaggregation of platelets in suspension. Materials and methods. A mathematical model of induced platelet aggregation has been developed. The kinetic constants of the model were optimized by experimentally determined average platelet counts in the aggregate measured by light scattering. Kinetic curves of light scattering of platelet suspension during aggregation induced by physiological agonist ADP were obtained using a laser analyzer of platelet aggregation ALAT-2 "Biola". Results. The proposed mathematical model is suitable for modeling reverse aggregation of platelets due to taking into account the inactivation of cells using the time dependence and correction of the disaggregation term. Conclusions. The developed mathematical model complements the models of the dynamics of irreversible platelet aggregation and allows to analyze reversible aggregation. The model satisfactorily describes the experimental time dependences of the size of platelet aggregates obtained by light transmission aggregometry. The introduced additional parameter and the method of setting the term corresponding to inactivation have a much smaller effect on the dependences than the kinetic constants. Calculated by model and optimized according to experimental data at different temperatures rate constants allow to calculate the activation energies of the aggregation process. When using light transmission aggregometry data to optimize the model parameters, it is advised to pre-smooth the input data to remove noise caused by the inhomogeneity of the suspension.