title: Comparison of artificial neural network and multiple linear regression in the optimization of formulation parameters of leuprolide acetate loaded liposomes.
abstract: OBJECTIVE
  We planned to optimize the effect of formulation variables on the percent drug entrapment (PDE) of the liposomes encapsulating leuprolide acetate by reverse phase evaporation method using Artificial neural network (ANN) and Multiple linear regression (MLR).
  
  
  METHODS
  Twenty seven formulations were prepared based on 3x3 factorial design. The volume of aqueous phase (X(1)), HSPC/DSPG [negative charge] (X(2)), and HSPC/Cholesterol (X(3)) were selected as the causal factors. Potential variables such as concentration of lipid: drug and hydration medium were kept constant in experimental design. The PDE (dependent variable) and the transformed values of independent variables were subjected to multiple regression analysis to establish a second order polynomial equation (full model). A set of PDE and causal factors was used as tutorial data for the ANN and fed into a computer. The feed forward back propagation (bp) method was optimized. The ANN model and MLR were validated for accurate prediction of PDE.
  
  
  RESULTS
  To simplify the polynomial equation, F-statistic was applied to reduce polynomial equation (reduced model) by neglecting non-significant (P<0.05) terms. The reduced polynomial equation was used to plot three two-dimensional contour plots at fixed levels of -1, 0 and 1 of the variable X(3) to obtain various combination values of the two other independent variables (X(1) and X(2)) at predetermined PDE. The root mean square value of the trained ANN model by feed forward bp method was 0.0000354, which indicated that the optimal model was reached. The optimization methods developed by both ANN and MLR were validated by preparing another six liposomal formulations. The predetermined PDE (from ANN and MLR) and the experimental data were compared with predicted data by paired "t" test, no statistically significant difference was observed. ANN showed less error compared to MLR.
  
  
  CONCLUSIONS
  These findings demonstrate that the ANN model provides more accurate prediction and is quite useful in the optimization of pharmaceutical formulations when compared to multiple regression analysis method. The normalized error (NE) value observed with the optimal ANN model was 0.0211 while it was 0.0658 for the full model in the case of second-order polynomial equation composed of the combination of causal factors (X(1), X(2) and X(3)). Thus the derived equation, contour plots and ANN helps in predicting the values of the independent variables for maximum PDE in the preparation of leuprolide acetate liposomes by reverse phase evaporation technique.
authors.affiliation: New Drug Delivery Systems Laboratory, Pharmacy Department, M.S. University of Baroda, Vadodara, India.
authors.forename: N
authors.initials: N
authors.lastname: Arulsudar
authors.forename: N
authors.initials: N
authors.lastname: Subramanian
authors.forename: R S R
authors.initials: RS
authors.lastname: Muthy
mesh_terms: D002626:Chemistry, Pharmaceutical; D016729:Leuprolide / Q000737:chemistry*; D016014:Linear Models; D008081:Liposomes; D016571:Neural Networks, Computer
chemical_list: D008081:Liposomes; D016729:Leuprolide