(W0930-05-30) Broad Applicability of a Model for Predicting Tabletability of Mixtures from Those of Individual Components

Purpose: Tablet products must possess sufficient mechanical strength to endure stresses during transportation and handling.1 Therefore, the tabletability, i.e., tablet tensile strength (σ) vs. pressure (P), of a formulation is critical property for developing a tablet product. Traditionally, formulation tabletability has been optimized using a trial-and-error approach, which is time-consuming and material-intensive. Hence, there is a pressing need to establish a predictive tabletability model for material-sparing and efficient tablet formulation, enabling Quality-by-Design. σ=σ_maxexp(αW(-exp(-P/β-1)))  (1) Recently, the Vreeman-Sun equation (Eq. 1) was introduced to describe tabletability.2 The three parameters in Eq. (1), σ_max, α, β, quantify apparent bonding strength, particle rearrangement, and material plasticity, respectively. We hypothesize that the tabletability of a mixture may be predicted by applying a suitable mixing rule to predict the three tabletability parameters of the mixture from those of individual components. In this work, we first evaluated three mixing rules to identify the best predictive model and then validated the model using multiple sets of mixtures of materials exhibiting a wide range of compaction properties. Finally, we investigated the effects of lubrication on performance of the predictive model.

Methods: Model development: The tabletability parameters (σ_max, α, β) of each individual component were obtained by fitting σ vs. P data with the Vreeman-Sun equation. Each of the three parameters of a given mixture (X_m) were predicted from those of individual components (X_n) based on the mixture composition (C_n) using the following three mixing rules:
1) Linear rule: X_m=X₁C₁+X₂C₂+…+X_nC_n
2) Power rule: X_m=X₁C₁×X₂C₂×…×X_nC_n
3) Harmonic rule: X_m=(C₁/X₁+ C₂/X₂+…+C_n/X_n)^-1
The tabletability profile of the mixture was then obtained by evaluating the Vreeman-Sun equation with the predicted parameters. Subsequently, the predicted profiles were compared with the experimental data of corresponding mixtures to assess the performance of different mixing rules. Model assessment: Materials selected in this work are excipients and an API with distinct mechanical properties, including microcrystalline cellulose (MCC, Avicel PH102 (d₅₀ = 100 µm), and PH200 (d₅₀ = 180 µm)), lactose monohydrate (LM, Pharmatose 350M (d₅₀ = 30 µm) and 110M (d₅₀ = 130 µm)), dibasic calcium phosphate anhydrous (DCPA coarse (d₅₀ < 75 µm) and fine (d₅₀ = 150 µm)), hydroxypropyl methylcellulose (HPMC) K100M, polyvinylpyrrolidone (PVP) K30, Crospovidone, magnesium stearate (MgSt), mannitol 50C, calcium carbonate (CC), and theophylline (THEO). Tablets were compressed at pressures ranging from 20 MPa to 450 MPa on a compaction simulator, simulating a Korsch XL 100 press with a dwell time of 103 ms. Tablet tensile strength was calculated from tablet dimensions and maximum breaking force using the standard Fell and Newton method.3

Results: Prediction of the tabletability parameters using the power mixing rule resulted in superior tabletability prediction performance. The linear mixing rule tended to overestimate tabletability while the harmonic mixing rule tended tounderestimate tabletability (see one example in Figure 1). Using 10 sets of binary mixtures (40 mixtures total), which include three common tablet fillers of different particle sizes (MCC, LM and DCPA), other excipients with different tableting properties (PVP, mannitol, and HPMC), and an active pharmaceutical ingredient (THEO), the power rule reasonably predicted the mixture tabletability profiles (Figure 2), suggesting the broad applicability of this approach for mixture tabletability prediction. As tablet formulations often contain more than two components, we investigated the performance of tabletability prediction using the power rule with two ternary mixtures (MCC PH102-LM 110M-THEO and mannitol-HPMC-CC) and a five-component mixture (MCC PH102-LM 350M-HPMC-Crospovidone-THEO). The predicted tabletability of these more complex mixtures closely matched with the experimental data (Figure 3a–3c), affirming the broad applicability of this predictive approach. The widely used tablet lubricant, MgSt, is known to reduce tabletability of formulations. Thus, the applicability of the power mixing model in predicting the tabletability of lubricated mixtures was assessed using MCC PH102-LM 110M mixtures containing 0.5% MgSt, following the same approach as that for unlubricated powders. Here, the lubricated MCC and LM were treated as “pure components” for predicting tabletability of lubricated mixtures. Tabletability of lubricated mixtures was again well predicted (Figure 3d), indicating applicability of the predictive model to lubricated mixtures.

Conclusion: Our results show that, based on the Vreeman-Sun equation, the power mixing rule is robust for predicting the tabletability of mixtures from those of individual components. The predicted mixture tabletability profiles are well-matched with the experimental tabletability for 40 binary mixtures, 2 ternary mixtures, and a five-component mixture with materials exhibiting a wide variety of mechanical properties. Notably, neither internal lubrication by MgSt nor particle size affects the model performance. The highly performing predictive approach represents a significant advancement that may enable material-sparing and expedited development of high-quality tablet products in the pharmaceutical industry.

References: (1) Jain, S. Mechanical Properties of Powders for Compaction and Tableting: An Overview. Pharm. Sci. Technol. Today 1999, 2 (1), 20–31. https://doi.org/10.1016/S1461-5347(98)00111-4.
(2) Vreeman, G.; Sun, C. C. A Powder Tabletability Equation. Powder Technol. 2022, 408, 117709. https://doi.org/10.1016/j.powtec.2022.117709.
(3) Fell, J. T.; Newton, J. M. Determination of Tablet Strength by the Diametral-Compression Test. J. Pharm. Sci. 1970, 59 (5), 688–691. https://doi.org/10.1002/jps.2600590523.

Acknowledgements: CCS thanks the National Science Foundation for support through the Industry University Collaborative Research Center (IUCRC) grant IIP-2137264, Center for Integrated Materials Science and Engineering for Pharmaceutical Products (CIMSEPP).


Figure 1. The predictive performance of the three mixing rules, linear, harmonic, and power, for predicting tabletability parameters compared with experimental mixture tabletability data for a 60-40 (w/w) MCC PH102-LM 110M blend.


Figure 2. Predictive performances of the power law mixing rule for a) MCC PH102–LM 110M, b) MCC PH102–LM 350M, c) MCC PH200–LM 110M, d) MCC PH200–LM 350M, e) MCC PH102–DCPA coarse, f) MCC PH102–DCPA fine, g) MCC PH200–DCPA coarse, h) MCC PH200–DCPA fine, i) PVP–mannitol, and j) HPMC–THEO.


Figure 3. Predictive performance of the power law mixing rule for two ternary mixtures, a) MCC–LM–THEO and b) Mannitol–HPMC–CC, (c) a more complex five-component mixture composed of MCC, LM, HPMC, Crospovidone, and THEO, and (d) lubricated MCC–LM mixtures.