Elsevier

Powder Technology

Volume 383, May 2021, Pages 115-130
Powder Technology

Novel algorithm elucidating the tablet dividing mechanism in scored tablets and its experimental verification

https://doi.org/10.1016/j.powtec.2021.01.035Get rights and content

Highlights

  • Novel algorithm is derived for calculating crack occurrence probability.

  • The algorithm is based on fracture mechanics and statistical mechanics.

  • Stress distribution is essential for calculating crack occurrence probability.

  • Reproducibility of dividing tablet is quantitatively predicted by the proposed algorithm.

Abstract

Scored tablets are produced to facilitate easy and uniform division of tablets. One of the most critical quality attributes of the scored tablet is its dividing uniformity. To clarify the tablet dividing mechanism, we proposed a novel algorithm on the basis of fracture and statistical mechanics. Powder formulations composed of microcrystalline cellulose, cornstarch, and lactose were prepared to realize tablets with different score line shapes. As a result, the probability of cracks in the tablet and the dividing uniformity were well estimated. The dividing uniformity was observed to be more sensitive to changes in the formulation factors rather than the shape of the score line. The proposed algorithm demonstrated that the variation in the crack initiation threshold originating from the formulation factors was more significant than that of the stress concentration on the basis of the shape of the score line.

Introduction

Scored tablets are produced to enable easy and uniform division of tablets. Because the internal stress is concentrated at the deepest tip of the score line when a bending force is loaded from the outside of the tablets, the mechanical properties of the tablets may change as a function of the formulation factors as well as the score line shapes. Therefore, the ease and uniformity of division are crucial quality attributes of the scored tablets. Regarding the dividing uniformity, McDevitt et al. reported that more than 10% of weight deviation between the two pieces of tablet halves had been observed in over 40% of commercial products [1]. The article clarified that dividing the tablet along the score line was often difficult, resulting in poor reproducibility. Vooren et al. demonstrated that force loading from the back of the scored face, as in the three-point bending test, resulted in the most uniform division of the scored tablet [2]. To date, personal skills and expertise dependent on relevant patients are still necessary for improving the dividing uniformity of scored tablets. A numerical approach via the finite element method (FEM) has also been reported to evaluate the mechanism of the breaking phenomena of scored tablets. For instance, Podczeck et al. reported that the stress distribution significantly changed with a change in the direction of the score line toward the force loading axis from the outside in the case of diametral compression [3]. A strong tensile stress was generated on the score line when the direction of the force loading axis was similar to that of the score line. Meanwhile, to elevate the angle between the score line and loading axis from 0° to 45°, the tensile stress was unevenly distributed along the score line when the test tablet was rotated. A similar tendency was observed in the three-point bending test [4]. Okada et al. demonstrated that the maximum principal stress, which was generated at the tip of the score line, was negatively correlated with the breaking strength in the scored tablets. They also found that the higher maximum principal stress at the score line resulted in better dividing uniformity [5]. Cracks in tablets may cause tableting failures such as capping and lamination; therefore, more studies have been conducted using numerical analysis rather than scored tablets. Furukawa et al. demonstrated a tableting condition in which capping failure was evoked. They employed the combined simulation techniques of a powder compression process based on a three-dimensional Drucker–Prager cap model and diametral compression [6]. Consequently, it was verified that capping was induced under the condition that plastic strain was generated in the central part of the tablets based on the diametral compression. Mazel et al. also demonstrated that the tensile stress remaining in the central part of tablets was a risk factor for lamination failure [7]. These findings suggest that FEM simulation could provide considerable knowledge on crack initiation and the direction of crack propagation in tablets. Further, Croquelois et al. reported that the value of the stress concentration factor increased with an increase in the diameter of the circular hole prepared in advance in the central part of the tablet [8]. It is likely that a deeper score line increases the stress concentration at its tip; however, there is no mention of the influence of stress concentration in dividing uniformity. Many other studies have been conducted to verify the mechanical properties of tablets using numerical analysis [[9], [10], [11], [12], [13]]; however, the mechanical properties of scored tablets are yet to be fully confirmed. Therefore, we attempted to derive a novel algorithm for clarifying the dividing mechanism of scored tablets. A probability theory based on statistical mechanics was introduced into the algorithm, considering the deterioration of the reproducibility of generating cracks in the scored tablet. Powder formulations containing microcrystalline cellulose (MCC), cornstarch (CS), and lactose (LAC) as excipients were prepared to make scored tablets with various score lines. A three-point bending test was conducted on the test tablets to determine the dividing uniformity. Further, the generation of various stresses in all the scored tablets was simulated using the FEM, and the predominant stress was identified. Finally, we estimated the probability of cracks in the tablet and subsequently the dividing uniformity. The proposed algorithm was verified as a response surface of the dividing uniformity, which was obtained from both the three-point bending test and the FEM. The response surfaces plotted using the experimental data were compared with those simulated via the FEM. Further, the initiation position and probability of the cracks simulated via the FEM were evaluated using experimental data from the three-point bending test.

Section snippets

Algorithm for estimating the dividing characteristics

Cracks of any shape can generate anywhere in the scored tablet when there are no constraints subjected to the crack initiation and shape. For instance, it can be assumed that a crack propagates via the shortest path from the deepest part of the scored line to the tablet bottom—that is, the crack dividing the tablet into two equal pieces. Sometimes, a crack may propagate in a zigzag manner at a position apart from the score line. Although it is not realistic, a crack may be generated with a

Materials

LAC (Tabletose® 80) was purchased from Meggre Japan Co., Ltd. (Tokyo, Japan). CS (Graflaw® M) was purchased from Nippon Starch Chemical Co., Ltd. (Osaka, Japan). MCC (CEOLUS® PH-101) was purchased from Asahi Kasei Chemicals Corporation (Tokyo, Japan). Polyvinylpyrrolidone K-90 (PVP K-90) and magnesium stearate (Mg-St; plant-derived) were purchased from Wako Pure Chemical Industries, Ltd. (Osaka, Japan). Additionally, all reagents used were of the same batch.

Design of experiments

An extreme vertices design composed

Powder physical property value

The powder physical property values including the SFE, E, E0 and ν are summarized in Table 4, Table 5, Table 6, respectively.

A positive correlation was observed between E and E0, although the values did not match well. Because E0 is the value calculated from the compression process of flat tablets, and E is the value obtained from the diametral compression of scored tablets, the stress remaining in the scored tablet varies depending on the score shape. It was deduced that the two values did not

Effect of score line shape

In both the experimental and estimated results, the shallower score line resulted in poor dividing uniformity. Stress concentration is generated at the deepest part of the score line, and the stress concentration factor (Kt) can be defined, considering an ellipse equivalent to the score line shape (Fig. 11) [27,28]. The minor axis (a) and major axis (b) of the equivalent ellipse are given asa=ktanθ1+tan2θ1b=dk=d2ρcosθ2dρ1sinθ2,where k is the constant calculated from the score line

Conclusion

In this study, nine types of scored tablets with different scored shapes were prepared for each of ten formulations with different quantities of MCC, LAC, and CS. A three-point bending test was conducted to measure the dividing uniformity. Meanwhile, a FEM simulation was performed for each of the scored tablets, and the probability of crack generation for each was predicted. Furthermore, the dividing uniformity of the scored tablets was calculated. In both the experimental and simulation

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Number JP17K08252.

References (28)

Cited by (4)

1

Present address: Department of CMC Research Laboratory, Kyorin Pharmaceutical Co., Ltd., 1848, Nogi, Nogi-machi, Shimotsuga-gun, Tochigi, 329-0114, Japan.

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