Empirical modeling of the fine particle fraction for carrier-based pulmonary delivery formulations

Abstract

In vitro study of the deposition of drug particles is commonly used during development of formulations for pulmonary delivery. The assay is demanding, complex, and depends on: properties of the drug and carrier particles, including size, surface characteristics, and shape; interactions between the drug and carrier particles and assay conditions, including flow rate, type of inhaler, and impactor. The aerodynamic properties of an aerosol are measured in vitro using impactors and in most cases are presented as the fine particle fraction, which is a mass percentage of drug particles with an aerodynamic diameter below 5 μm. In the present study, a model in the form of a mathematical equation was developed for prediction of the fine particle fraction. The feature selection was performed using the R-environment package "fscaret". The input vector was reduced from a total of 135 independent variables to 28. During the modeling stage, techniques like artificial neural networks, genetic programming, rule-based systems, and fuzzy logic systems were used. The 10-fold cross-validation technique was used to assess the generalization ability of the models created. The model obtained had good predictive ability, which was confirmed by a root-mean-square error and normalized root-mean-square error of 4.9 and 11%, respectively. Moreover, validation of the model using external experimental data was performed, and resulted in a root-mean-square error and normalized root-mean-square error of 3.8 and 8.6%, respectively.

Keywords: deposition modeling; empirical modeling; feature selection; fine particle fraction; genetic programming; pulmonary delivery.

Figure 1

Scheme of work. Abbreviations: 3D, three-dimensional; SEM, scanning electron microscope; API, active pharmaceutical ingredient.

Figure 2

General structure of created models.

Figure 3

Observed versus predicted plot for model created with the genetic programming method. Abbreviation: FPF, fine particle fraction.

Figure 4

Response surfaces for predicted FPF and variables. Notes: (A) Drug lipophilicity (logP) and carrier surface properties (Rsk). (B) Drug content in formulation (%) and flow rate (L/min). Abbreviations: FPF, fine particle fraction; Rsk, skewness of the assessed profile.

Figure 5

Plots and Rsk values for various surfaces. Notes: (A) Rsk =1.4, (B) Rsk =1.5, (C) Rsk = −0.18, (D) Rsk =0.08. Abbreviations: Rsk, the skewness of the assessed profile; Z-depth(pixel), distance.

Figure 6

Scanning electron micrograph of hydroxyapatite carrier for additional formulation.