The method for identification of mathematical models in two-factor pharmaceutical research

Abstract

The methodical approach to solving problems of identification of mathematical models of pharmaceutical objects with two dependent quantitative factors has been considered; the total value of them is determined by the quantitative composition of the mixture and is fixed at a definite level.
Aim. To determine the optimal algorithm for processing experimental data using the minimum number of experiments according to the plan 22
to establish an adequate mathematical description of research at the technological stage.
Materials and methods. Such materials as potato starch (quantitative factor x1) and the microcrystalline cellulose solution (quantitative factor x2) were used. The content of excipients should be 54 % of the total mass. Based on a priori data the content of potato starch x1 should be in the range from 45 to 50 % of the total amount (45 ≤ x1 ≥ 50), and x2 characterizes an aqueous solution of microcrystalline cellulose with a concentration in the range from 2 to 5 % (2 ≤ x2 ≥ 5). The least squares method was applied to determine the coefficients of the regression equations. During our research the Mathcad computer environment (MathSoft Ins., USA) was used.
Results. To reduce the number of solutions and make the right decision it is necessary to have a reliable source of information and impose the appropriate restrictions based on a priori data and practical
experience of the researcher.

Conclusions. The studies have shown that to identify mathematical models the analysis of the main
(final) effects of the interaction of factors is effective, it is also expedient to interpret this interaction based
on the interpretation of the dependences of objective functions on each factor provided that the variable is
fixed at the minimum and maximum levels of variation.