Development of a methodological approach to determine regression equations in the study of the technology for manufacturing tablets based on quercetin




quantitative effect of excipients; three-factor mathematical model; dependent mixture factors; identification algorithm


When developing the technology of tablets and tablet masses one of the tasks is to determine the amounts of excipients required to obtain pharmaco-technological quality indicators that meet the requirements of the State Pharmacopoeia
of Ukraine (SPhU).

Aim. To develop an algorithm for determining the type of three-factor mathematical models with dependent variables.

Materials and methods. The study object was experimental observations of the quantitative effect of excipients in the tablet composition based on a solid dispersion of quercetin on the pharmacopeial characteristics of this dosage form, in particular on its flowability. The experimental data were processed by the planned experiment using Mathcad 15 and MS Excel software according to the algorithm proposed.

Results and discussion. It has been found that the identification of mathematical models in pharmaceutical studies with three dependent factors, which total value is determined by the quantitative composition of the dosage form
and fixed at a certain level, is difficult to perform due to the difficulty of interpreting the multiple regression parameters as characteristics of factors in isolation through their correlability. It has been proven that the replacement of variables
leads to the determination of a mathematical model that does not reveal the mechanism of the factors’ action and is a static description of their overall impact on the indicator studied.

Conclusions. As a result of the research conducted, regression equations were found to determine the effect of the amount of these excipients on the tablet flowability. It has been found that the most influential role in determining the target in the factor space studied is played by the interaction of factors. The algorithm for determining the mathematical description of the dependence with three variables has been proposed. Based on the fact that the research is conditioned by strict conditions in the quantitative composition, the chosen mathematical model of the dependence of the quadratic equation with two factors, for which there are limitations, has no correlation. The model determined is characterized by the possibility of providing the graphical interpretation and simplification of analysis and can be used for forecasting and optimization.

Author Biographies

O. V. Kutova, National University of Pharmacy of the Ministry of Health of Ukraine

Сandidate of Engineering Science (Ph.D.), associate professor of the Department of  Technologies  of Pharmaceutical Preparations 

I. V. Kovalevska, National University of Pharmacy of the Ministry of Health of Ukraine

Doctor of Pharmacy (Dr. habil.), associate professor of the Department of Industrial Technology of Drugs

N. V. Demchenko , National University of Pharmacy of the Ministry of Health of Ukraine

Candidate of Economics (Ph.D.), Associate Professor of the Organization and Economics of Pharmacy Department


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Technology of Medicines