Development of mathematical models of lateral flow membrane bioanalytical systems and characterization of the regularities of their functioning

Lateral flow membrane bioanalytical (immunochromatographical) systems have become the most widespread tool for nonlaboratory (point-of-care) analyses. However, the theory of their functioning has been developed only for a few special cases. As such, the aim of this study is to create mathematical models to predict the general regularities of the functioning of immunochromatographical systems. Analytical models of immunochromatography for competitive and “sandwich” schemes of analysis have been developed. The necessary approximations are formulated to allow researchers to solve systems of kinetic differential equations in explicit form. The proposed simplifications are adequate for the conditions under which real analytical reactions occur. Thanks to the application of the nonnumerical approach, general solutions are obtained by way of formulas that demonstrate the dependences of the systems’ functioning, such as the influence of the concentration and affinity of immune reactants on the calibration curve. The proposed models make it possible to evaluate the impact of various factors on the parameters of immunochromatographic analysis.