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

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[…] The database was acquired from the literature. Scientific articles were scanned and included in the analysis based on the following criteria: detailed information about drug and carrier (name and particle size); availability of an SEM image of the carrier; and description of assay conditions (flow rate, impactor and inhalator type).After review of approximately 800 papers from the Scopus and PubMed databases, eleven met the inclusion criteria. The created database contained information about FPF for three various impactors, ie, the ACI, the next-generation impactor, and the multi-stage liquid impinger. A detailed list of the source publications is included in Table S1. Formulations were composed of five different types of substances as carriers, ie, trehalose, mannitol, lactose, erythritol, and hydroxyapatite. Based on the SEM pictures of carriers, 13 variables describing surface properties were calculated, including the arithmetical mean deviation, root mean square deviation, skewness of the assessed profile (Rsk), kurtosis of the assessed profile, lowest valley, highest peak, total height of the profile, average height of an unleveled surface, mean polar facet orientation, variation of the polar facet orientation, direction of azimuthal facets, mean resultant vector, and surface area. The carrier shape analysis was performed based on SEM pictures using ImageJ, as described in the section on surface and shape analysis. The procedure resulted in six parameters describing the shape of carriers: the circularity, longest distance between two points (Feret), angle between the Feret’s diameter and a line parallel to the x axis of the image (FeretAngle), minimum caliper diameter (MinFeret), ratio between particle height and particle width, and roundness. The database contained information about formulations composed of nine active pharmaceutical ingredients (API), ie, salbutamol, budesonide, ciprofloxacin, cyclosporine A, disodium cromoglycate, fluticasone propionate, formoterol fumarate, ipratropium bromide, and salmeterol. The chemical structure and properties of the drug molecules were encoded by chemical descriptors computed using Marvin cxcalc plugin, UK (version 6.1; ChemAxon, Budapest, Hungary) based on three-dimensional optimized structures. Moreover, the mass percentage of API in the formulation, the carrier, and the API particle size distribution, inhaler device type (Novolizer®, Aerolizer®, Rotahaler®, powder dispatchment tube, SetA, SetD), flow rate (L/min) during the experiment, were included according to data found in the articles. The complete structure of the database is shown in and the full database is available in Table S2. Overall, there were 91 data records with 136 variables. The FPF was the only dependent variable and the other 135 input variables contained information about the carrier, drug, and assay conditions. The data set was processed to reduce the size of the input vector and to split data according to the 10-fold cross-validation method to check the generalization ability of the models created and simulate their real application to predict in vitro deposition for new formulations and unknown conditions. [...] For modeling purposes, two rule-based systems were used, ie, “randomForest” and “Cubist”. The first one creates models based on a forest of decision trees using random inputs. The following parameters were used during the modeling process: automatic selection number of variables, maximum number of nodes set as 1,000, and number of trees set from 1 to 100. Cubist also creates regression models in a manner of decision trees, but it introduces linear equations at their terminate branches. During the modeling process, the maximum number of rules was fixed at 100, and the number of committees was set from one to 100. The extrapolation parameter, which controls the estimation ability of created models beyond the original observation range, was set to 100. The sample parameter, which is a percentage of the randomly selected data set for model building, was established at zero, which means that no data subsampling was employed and all the models were built on the complete data sets available for each run. […]

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