Predicting the tabletability of binary powder mixtures from that of individual components

Abstract

Predicting the tabletability, i.e., the relationship between tensile strength and compaction pressure, of powder mixtures based on that of pure materials would streamline tablet formulation development, saving both time and materials. This would be a significant step toward achieving digital tablet formulation design. The recently derived Vreeman-Sun tabletability equation enables the mathematical description of tabletability data using three parameters: $σ_{m a x}$ , $α$ , and $β$ . Therefore, tabletability prediction is reduced to predicting these three tabletability parameters. In this work, we developed a strategy to predict mixture tabletability parameters based on those of the individual components, employing an appropriate mixing rule. Using materials with diverse mechanical properties, we demonstrate that the power-law mixing rule overall outperforms both the linear and harmonic mixing rules in predicting mixture tabletability parameters, leading to excellent agreement with experimental tabletability profiles.

Introduction

Tablets are a widely used oral solid dosage forms for delivering small-molecule drugs to achieve local and systemic therapeutic effects. Their cost-effective manufacturing, high patient compliance, and excellent stability make them the preferred choice for drug development (Arshad et al., 2021). Tablet formulation development involves optimizing both composition and manufacturing process parameters. The active pharmaceutical ingredient (API) is the primary component responsible for therapeutic efficacy. However, APIs are frequently combined with other tablet excipients, such as binders, diluents, disintegrants, and other processing aids, to enhance manufacturability and ensure the desired tablet properties, including mechanical integrity, stability, uniformity, and bioavailability.

Tablet compression is a critical unit operation in tablet manufacturing, where powder is compacted into an intact tablet. Processing parameters such as compaction pressure, turret speed, feeder speed, and dosing level can significantly influence key tablet properties (Patel et al., 2006). Among these, tablet tensile strength is crucial for ensuring structural integrity during processes, such as packaging, transport, and coating. Optimizing formulation composition and processing parameters is therefore essential to achieve sufficient tensile strength (Sun, 2011). Current formulation strategies often rely on empirical approaches, sometime supplemented by design of experiments. In contrast, the ability to predict tablet tensile strength based on a given formulation composition would facilitate a more efficient, digital approach to formulation design.

Powder compaction properties have traditionally been analyzed using two key relationships: powder compressibility, defined as porosity (ε) versus compaction pressure (P), and powder compactibility, defined as tablet tensile strength (σ) versus compact porosity. Consequently, models for predicting the compaction behavior of mixtures have mainly focused on these two aspects (Berkenkemper et al., 2023; Busignies et al., 2006a, 2006b; Patel and Bansal, 2011; Paul et al., 2022; Paul and Sun, 2017; Polak et al., 2024; Wang et al., 2021; Wünsch et al., 2022). Wu et al. proposed a linear mixing model to predict the exponential compactibility constants of binary mixtures based on the pure constituent materials (Wu et al., 2005). This model was later extended to predict the tensile strength of ternary and four-component blends, demonstrating visually acceptable accuracy compared to the experimental data (Wu et al., 2006). Michrafy et al. employed a similar approach, combining linear and power mixing models to predict the compactibility of binary mixtures (Michrafy et al., 2007). However, the optimal model varied across different binary mixture systems, making it challenging to generalize the approach to more complex systems. Etzler et al. proposed a mixing model similar to Wu et al., attributing mixture compactibility to surface adhesion and predicting mixture parameters using a power law model weighted by volume fraction (Etzler et al., 2011).

Given the critical importance of tabletability, defined as tablet tensile strength as a function of compaction pressure (Joiris et al., 1998), in tablet manufacturing, accurately predicting the tabletability of mixtures is essential. Reynolds et al. proposed a multi-step method for this purpose by 1) predicting mixture compressibility using the Gurnham compressibility equation and volumetric additivity (Busignies et al., 2012; Gurnham and Masson, 1946; Zhao et al., 2006); 2) predicting mixture compactibility using the Ryshkewitch-Duckworth equation and a geometric mean rule (Duckworth, 1953; Etzler et al., 2011; Ryshkewitch, 1953); and 3) generating a tabletability profile by plotting tensile strength against compaction pressure based on the predicted compressibility and compactibility (Reynolds et al., 2017). However, this indirect approach requires porosity normalization and often exhibits poor predictive accuracy outside the experimental data range, e.g., underestimating at low compaction pressure and overestimating at high compaction pressures (Reynolds et al., 2017). Thus, a more robust and straightforward method for predicting the tabletability of a mixture is needed. This is now possible due to the availability of a mathematical relationship that quantitatively describe tabletability (Vreeman and Sun, 2022a). The tabletability equation (Eq. (1)) is a double exponential function that characterizes an asymmetric sigmoidal curve (Vreeman and Sun, 2022a).

(1) Equation (1) includes three material-specific parameters, and , which represent the maximum achievable tensile strength, the curve shift along the pressure axis, and a parameter related to powder plasticity, respectively (Vreeman and Sun, 2022a, 2025). The availability of the tabletability equation enables the prediction of mixture tabletability estimating its parameters based on the properties of individual components and an appropriate mixing model. In this study, we evaluate the feasibility of three generalizable mixing models (linear, power, and harmonic) for predicting the tabletability of binary mixtures composed of materials with diverse mechanical properties.

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Materials

Microcrystalline cellulose (MCC; Avicel PH 102 and Avicel PH 200, DuPont, Wilmington, DE), hydroxypropyl methylcellulose (HPMC; K100M DC, Ashland), Kollidon VA64 (KOL; BASF, Ludwigshafen, Germany), Starch (ST; 1500, Colorcon, Netherlands), lactose monohydrate (LM, Pharmatose 350M and 110M, DFE Pharma, Klever Strasse, Germany), lactose anhydrous (LA; Supertab 24AN, DFE Pharma, Klever Strasse, Germany), mannitol (MN; Pearlitol 400DC and 200SD, Roquette America Inc., Keokuk, IA), dicalcium phosphate anhydrous (DCPA; Emcompress, JRS Pharma, Patterson, NY), and theophylline anhydrate (TH; BASF, Ludwigshafen, Germany) were used as received.

Vedant Girish Bhagali, Gerrit Vreeman, Aakash Hasabnis, Changquan Calvin Sun, Predicting the tabletability of binary powder mixtures from that of individual components, European Journal of Pharmaceutical Sciences, 2025, 107151, ISSN 0928-0987, https://doi.org/10.1016/j.ejps.2025.107151.