Comparison of multi-linear regression, particle swarm optimization artificial neural networks and genetic programming in the development of mini-tablets

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Abstract

In the present study, the preparation of pharmaceutical mini-tablets was attempted in the framework of Quality by Design (QbD) context, by comparing traditionally used multi-linear regression (MLR), with artificially-intelligence based regression techniques (such as standard artificial neural networks (ANNs), particle swarm optimization (PSO) ANNs and genetic programming (GP)) during Design of Experiment (DoE) implementation. Specifically, the effect of diluent type and particle size fraction for three commonly used direct compression diluents (lactose, pregelatinized starch and dibasic calcium phosphate dihydrate, DCPD) blended with either hydrophilic or hydrophobic flowing aids was evaluated in terms of: a) powder blend properties (such as bulk (Y1) and tapped (Y2) density, Carr’s compressibility index (Y3, CCI), Kawakita’s compaction fitting parameters a (Y4) and 1/b (Y5)), and b) mini-tablet’s properties (such as relative density (Y6), average weight (Y7) and weight variation (Y8)). Results showed better flowing properties for pregelatinized starch and improved packing properties for lactose and DPCD. MLR analysis showed high goodness of fit for the Y1, Y2, Y4, Y6 and Y8 with RMSE values of Y1 = 0.028, Y2 = 0.032, Y4 = 0.019, Y6 = 0.015 and Y8 = 0.130; while for rest responses, high correlation was observed from both standard ANNs and GP. PSO-ANNs fitting was the only regression technique that was able to adequately fit all responses simultaneously (RMSE values of Y1 = 0.026, Y2 = 0.022, Y3 = 0.025, Y4 = 0.010, Y5 = 0.063, Y6 = 0.013, Y7 = 0.064 and Y8 = 0.104).

Introduction

Mini-tablets, described as tablets with a diameter of 3 mm or smaller, are emerging as a promising platform exhibiting several advantages not only over the conventional single unit dosage forms but even over other multiple-unit dosage systems, like pellets or granules (Lennartz and Mielck, 1998, Stoltenberg and Breitkreutz, 2011). Their advantageous performance involves reduced risk of dose dumping, faster gastric emptying, higher dispersion in the GI tract with lower toxicity and irritation risks, better localization and less variable bioavailability (Aleksovski et al., 2015, Asghar and Chandran, 2006). Mini-tablets can also be considered as patient-centered oral dosage forms offering a novel approach to pediatric, geriatric or personalized drug delivery with flexible dosing and easy combination of different dose units (having either different API release profiles or chemically incompatible APIs) (Bredenberg et al., 2003, Drumond et al., 2017, Klingmann, 2017, Page et al., 2016, Preis, 2015).

Although mini-tablets can be easily prepared by simple processing methods, such as direct compression, many challenges should be addressed during manufacturing to meet crucial requirements, such as tablet weight and content uniformity. Due to the small tablets’ size and die orifice’s dimensions, appropriate excipients should be selected and the critical material attributes (CMAs) should be carefully controlled in order to ensure the critical quality attributes (CQAs) which optimize the final product’s characteristics and avoid possible process-related defects (i.e. tooling damage etc.) (Aleksovski et al., 2015). Powder particle size, as well as flow and packing properties are among the most significant properties to be considered during mini-tablet processing (Tissen et al., 2011). By designing mixtures with good powder flow properties, a homogenous and consistent die filling can be achieved that, in turn, can lead to increased process efficacy (i.e. mini-tablets with low weight variation and subsequently excellent dosing accuracy). As the weight variation tolerance is smaller compared to regular tablets, a more stringent control of these mini-tablet CMAs is required.

Additionally, the lack of sufficient understanding regarding the interactions occurring among powder fundamental (particle size) and derived (flowability) properties during mini-tableting (Kachrimanis et al., 2003) necessitates the implementation of a systematic experimentation suggested by the Quality by Design (QbD) approach (Mohammed et al., 2015). QbD, according to ICH Q8 and Q9 guidelines, should be applied in order to guide the pharmaceutical formulation development for ensuring robustness and quality of the developing product/process. During QbD implementation CMAs are identified as significant variables which are then assessed on how they influence the CQAs of the final product. A design space is obtained as the range of formulation/process variables providing the desired quality attributes (Gyulai et al., 2018, Patwardhan et al., 2015).

In order to establish the above-mentioned relation (i.e. construction of a design space and, in a further step, establishment of a control strategy), design of experiments (DoE) with the aid of multi-linear-regression (MLR) is generally applied (Hales et al., 2017, Iurian et al., 2017). An alternative approach, selected when improved model’s generalizing ability is desired, is to combine DoE with artificial intelligence (AI) based regression techniques, such as artificial neural networks (ANNs) and genetic programming (GP) (Barmpalexis et al., 2018a, Barmpalexis et al., 2011, Barmpalexis et al., 2010). ANNs used as multivariate regression tools are intelligent nonlinear systems built to loosely simulate the functions of the human brain (Aleksić et al., 2014, Barmpalexis et al., 2018b, Krajisnik et al., 2014, Shirazian et al., 2017). Compared to earlier standard algorithms used for ANN training, new biologically inspired algorithms (BIAs) may show improved performance in solving complex optimization/regression problems as they can explore more easily big multimodal and non-continuous search spaces. Such an algorithm is swarm-based intelligence, in which a specific property of a studied system, composed of unintelligent agents with limited individual capabilities, exhibits an intelligent collective behavior (Beni and Wang, 1993, Elragal, 2009, Garro and Vazquez, 2015, Shen et al., 2006). Additionally, another AI methodology used successfully in multivariate regression problems is the implementation of an evolutionary algorithm known as GP. In GP, computer programs (or mathematical operations) are encoded as a set of genes that are then modified (evolved) based on Darwin’s Natural Selection theory (Güres et al., 2012, Koza, 1994). The use of such AI regression approaches in combination with DoE may show enhanced fitting performance (i.e. superiority) compared to MLR or logistic regression techniques (and hence, a more precise/safe design space or control strategy can be constructed during QbD-based product development) due to the fact that they: 1) require less formal statistical training to develop, 2) can implicitly model more complex nonlinear relationships between independent and dependent variables, 3) can detect “hidden” (to MLR) interactions between input and output variables (i.e. factors and responses), and 4) can show increased adaptability by embedding multiple training approaches (such as swarm-based intelligence with ANNs) (Tu, 1996). Furthermore, the use of AI-based techniques (such as ANNs) in combination with traditionally applied multivariate analysis tools (such as principal component analysis, PCA), may help in the establishment of more accurate multivariate product specifications (i.e. product performance CQAs assessed on several attributes).

In a previous series of works, the effect of cylindrical orifice dimensions (length and diameter), along with powder particle characteristics (size, aspect ratio, roundness and convexity) and packing properties (true, bulk and tapped density) on the flow-rate of three commonly used pharmaceutical direct compression diluents (lactose, dibasic calcium phosphate dihydrate and pregelatinised starch) were investigated; while standard back-propagation feed-forward ANNs were used to model the effect of micromeritics properties on powder flow (Kachrimanis et al., 2003, Kachrimanis et al., 2005). Results showed that as the diameter of the orifice decreases (from 4 to 2 mm), powder flow rate decreases, suggesting that serious flow-related problems may occur during compression of small (∼2 mm) mini-tablets. Hence, in order to increase mini-tableting process robustness, it is important to incorporate flowing aid components (glidants) and to evaluate their synergistic or antagonistic effect on powder flow properties.

Therefore, in the present study (conducted in the general-context of QbD) DoE was combined, for the first time, with modern AI regression techniques (such as PSO ANNs) in an attempt to evaluate the effect of several CMAs during the preparation of small (∼2 mm) pharmaceutical mini-tablets. Specifically, the effect of Lactose, Starch 1500 and DCPD mixture size fractions blended with two colloidal silica dioxides (a hydrophobic and a hydrophilic) on several micromeritic and mini-tablets properties was evaluated via DoE, while MLR modelling was compared to standard backpropagation ANNs, PSO ANNs and GP.

Section snippets

Materials

Three commonly used direct compression diluents, namely lactose (Lactose DCL 21, DMV International, Veghel, The Netherlands), pregelatinized starch (Starch 1500, Colorcon Ltd., Orpington, UK) and dibasic calcium phosphate dihydrate (DCPD, Emcompress®, Edward Mendell, NY, USA) were tested. Additionally, two derivatives of colloidal silicon dioxide having different lipophilicity, i.e. the hydrophilic Aerosil (200 Pharma) and hydrophobic, cohesive Aerosil (R972V), both obtained from BASF

Diluent/glidant blend properties

Table 1 summarizes the bulk and tapped densities along with the CCI values and the Kawakita’s regression parameters, for the examined diluent/glidant blends. Bulk density results varied from 0.778 g/mL (Run F17) to 0.652 g/mL (Runs F22 and F31), while tapped density varied from 0.915 g/mL (Run 18) to 0.767 g/mL (Run F24). Also, CCI values varied from 10.09% (Run F15) to 19.42% (Run F31), while Kawakita’s regression parameter a varied from 0.194 (Run F13 and F31) to 0.112 (Run F3), and 1/b from

MLR

ANOVA results indicated that the type of diluent (factor X5) exerts a significant main effect on all selected responses, followed by factor X4 (glidant addition) which had a significant effect in all responses except Y8 (weight variation). Additionally, factor X3 was identified as insignificant in all main and interaction effect parameters, indicating that the use of large diluent particles did not result in any statistically significant change. Small size diluent particles (X1) showed a

Conclusions

Starch 1500 mixtures exhibited improved powder flow rates through a 2 mm orifice compared to Lactose and DPCD in all tested diluent size fractions. DoE statistical analysis revealed that the addition of flowing aids (either hydrophilic or hydrophobic) results in a significant improvement of all diluent flowing properties, while Lactose and DPCD showed better packing properties (expressed by Kawakita’s regression parameters a and 1/b) compared to pregelatinized starch. Furthermore, compression

Funding sources

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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