Mathematical modelling of preparation of acyclovir liposomes: reverse phase evaporation method

The aim of this study was to derive simple reduced second order polynomial equation for constructing contour plots to obtain predetermined % drug entrapment (PDE) within liposomes of acyclovir (ACY) when prepared by reverse phase evaporation (REV) method using technique of three variables at three levels (3(3)) factorial design.

Three independent variables selected were volume of organic phase (x(1)), volume of aqueous phase (x(2)), and Drug/Phosphatidylcholine (PC) /Cholesterol (CHOL) in molar ratio (x(3)). Based on factorial design, twenty-seven batches of ACY liposomes were prepared by REV method. Prepared liposomal batches were evaluated for size, lamellarity, and PDE. The PDE (dependent variable) and the transformed values of independent variables were subjected to multiple regressions to establish a second order polynomial equation (full model). To simplify the equation, F-statistic was applied to reduce polynomial equation (reduced model) by neglecting nonsignificant (p>0.05) terms. The coefficient value for independent variable, Drug/PC/CHOL in molar ratio (x(3)) was found to be maximum (b(3) = 2.52) and hence the variable x(3) was considered to be a major contributing variable for PDE within liposomes by REV method. The reduced polynomial equation was used to plot three two-dimensional contour plots at a fixed levels of -1, 0 and 1 of major contributing variable (x(3)) to obtain various combinations of values of two other independent variables (x(1) & x(2)) at predetermined PDE. The conformity of the established equation was checked by preparing three batches three times taking values of the independent variables from the contour plots for prefixed value of PDE.

Prefixed PDE value taken for designing the experiment and results obtained experimentally were compared using student 't' test and difference between experimentally obtained and theoretically calculated values of PDE was found to be statistically nonsignificant (p>0.05).

Findings of this study establishes the role of the derived equation and plotted contour plots in predicting the values of independent variables for preparation of ACY liposomes by REV method having predetermined PDE.