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Contents lists available at ScienceDirect
European Journal of Pharmaceutics and Biopharmaceutics journal homepage: www.elsevier.com/locate/ejpb
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Research Paper
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A new tablet brittleness index
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Xingchu Gong a,b, Changquan Calvin Sun b,⇑ a b
Pharmaceutical Informatics Institute, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, PR China Pharmaceutical Materials Science and Engineering Laboratory, Department of Pharmaceutics, University of Minnesota, Minneapolis, MN, USA
a r t i c l e
i n f o
Article history: Received 1 October 2014 Revised 24 February 2015 Accepted in revised form 1 April 2015 Available online xxxx Keywords: Brittleness Friability Tablet Elastic deformation Strain Powder technology
a b s t r a c t Brittleness is one of the important material properties that influences the success or failure of powder compaction. We have discovered that the reciprocal of diametrical elastic strain at fracture is the most suitable tablet brittleness indices (TBIs) for quantifying brittleness of pharmaceutical tablets. The new strain based TBI is supported by both theoretical considerations and a systematic statistical analysis of friability data. It is sufficiently sensitive to changes in both tablet compositions and compaction parameters. For all tested materials, it correctly shows that tablet brittleness increases with increasing tablet porosity for the same powder. In addition, TBI increases with increasing content of a brittle excipient, lactose monohydrate, in the mixtures with a plastic excipient, microcrystalline cellulose. A probability map for achieving less than 1% tablet friability at various combinations of tablet tensile strength and TBI was constructed. Data from marketed tablets validate this probability map and a TBI value of 150 is recommended as the upper limit for pharmaceutical tablets. This TBI can be calculated from the data routinely obtained during tablet diametrical breaking test, which is commonly performed for assessing tablet mechanical strength. Therefore, it is ready for adoption for quantifying tablet brittleness to guide tablet formulation development since it does not require additional experimental work. Ó 2015 Published by Elsevier B.V.
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1. Introduction Brittleness is one of the important material properties that determines the deformation and fracture of tablets under stress. Tablets of highly brittle materials tend to have more defects because of their lower ability to accommodate stress during tablet production, storage, transportation, and handling. This is shown as the propensity of these tablets to easy chipping, high friability, and generation of hidden defects [1]. On the other hand, tablets from very plastic materials tend to loss tabletability after dry or wet granulation processes [2–5]. When a bilayer tablet consisting of two layers with very different brittleness is diametrically compressed, the more brittle layer tends to fracture more easily leading to a unique breakage mode [6]. These problems can be minimized or even eliminated by maintaining a balanced tablet brittleness through appropriate choice of excipients in the formulation [7]. However, the effective design of a formulation with balanced brittleness and ductility requires a reliable method for quantifying tablet brittleness. Outside of the pharmaceutical arena, material brittleness is usually quantified using an empirical index that correlates with ⇑ Corresponding author at: 9-127B Weaver-Densford Hall, 308 Harvard Street S.E., Minneapolis, MN 55455, USA. Tel.: +1 612 624 3722; fax: +1 612 626 2125. E-mail address: [email protected] (C.C. Sun).
performance of importance. In geotechnical engineering, brittleness of rocks is usually assessed by penetration rate index or drilling rate index [8,9], because they correlate well with the brittle fracture propensity of rocks. This approach, although empirical, has been widely adopted in the geoengineering field because of its practicality and effectiveness in assessing brittleness of rocks. A similar approach has also been used to quantify brittleness of dental ceramics using a chipping factor, which quantifies the propensity to chipping at the edges [10]. Hucka and Das [11] comprehensively summarized methods for measuring brittleness. Five common approaches to obtain brittleness of rocks are based on strain, reversible energy, Mohr’s envelope, strength ratio, and special tests [12]. The special tests include impact test [13], indentation test [14,15], and punch penetration test [8]. Because of the unique specimen shape requirement for performing test, approaches based on Mohr’s envelope and strength ratio are not applicable for tablets. However, the approaches based on strain, reversible energy, and special tests can possibly be adopted for determining tablet brittleness. These have been explored in this work. In an effort to quantify brittleness of pharmaceutical materials, a brittle fracture index (BFI) was proposed by comparing tensile strength of tablets with and without a central hole [16–18]. Despite the initial promise and enthusiastic adoption of BFI in pharmaceutical research [19,20], its usefulness was questioned in
http://dx.doi.org/10.1016/j.ejpb.2015.04.007 0939-6411/Ó 2015 Published by Elsevier B.V.
Please cite this article in press as: X. Gong, C.C. Sun, A new tablet brittleness index, Eur. J. Pharm. Biopharm. (2015), http://dx.doi.org/10.1016/ j.ejpb.2015.04.007
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light of the finding that BFI did not vary in a systematic manner with composition [21]. This is related, at least partially, to the fact that BFI does not sufficiently discriminate among materials with brittleness in the middle range of the 0 – 1 scale where most materials lie. BFI was further challenged on the basis that the tensile strength of a compact with a central hole cannot be calculated using the same equation for an intact tablet because of the different stress distributions in the two types of tablets [22]. Practically speaking, making tablets with a central hole is challenging because it requires either the use of special punches when making the tablets or drilling post tablet compression. In a recent effort to improve the technique for quantifying brittleness, Sönnergaard proposed a new brittle-ductile index (BDI) for compacted cylindrical tablets based on the work of failure (WOF) and maximum breaking force (Fmax) [23], as shown in Eq. (1):
BDI ¼ 100
WOF 2 F max D
ð1Þ
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where D is the diameter of the tablet. The term, 2WOF/Fmax, in Eq. (1) is used to approximate the displacement required to fracture the tablet because of the experimental difficulty in directly determining the initial point of contact between the platen and tablet [23]. Unlike BFI, BDI values do vary in a more systematic manner with changes in composition of a mixture consisting of plastic and brittle materials [23]. This approach yields a reasonable estimate of the maximum diametrical strain in a tablet for brittle materials, such as lactose. However, errors are expected for pharmaceutical tablets that exhibit substantial plastic deformation leading to the tablet fracture because of work due to irreversible plastic deformation that should have not been included for characterizing brittle fracture behavior, which is, elastic by definition. For this reason, the relationship between WOF and force is actually not strictly linear [23]. To alleviate this problem, WOF was plotted against Fmax of tablets prepared under different pressures [23] and the slope of the line, a, is used to calculate BDI using Eq. (2):
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BDI ¼ 100
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127
2a D
ð2Þ
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The application of Eq. (2) implies that tablet fracture behavior is independent of tablet porosity, which varies when the compaction pressure changes. This assumption is, however, inconsistent with both theoretical expectations and practical observations. Qualitative observations suggest that tablets with high porosity or made from brittle materials are usually more brittle. For example, porous tablets (prepared at a low pressure) of relatively plastic hydroxypropyl cellulose (HPC) fracture during diametrical compression but a denser HPC tablet (prepared under a high pressure) yields without fracture during the same test. Therefore, a measurement of brittleness of a tablet should not be assumed to be a reliable descriptor of the brittleness of the material and a clear distinction between brittleness of a material and that of a tablet needs to be made. In addition to the problems discussed above, both BFI and BDI were developed without being validated against a tablet property known to correlate with brittleness. In absence of such validation, the application of BFI and BDI requires caution. Inspired by the successful approaches in quantifying the brittleness of the rocks and dental ceramics, we set out to identify a new tablet brittleness index (TBI) that most strongly correlates to tablet friability, a tablet property with recognized linkage to tablet brittleness. Unlike BFI and BDI, TBI quantifies brittleness of individual tablets; regardless, they are made from the same powder or not.
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1.1. Theoretical considerations
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In the most rigorous sense, brittleness determination is suitable only for an elastically deforming body, which is represented by the
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line oa in Fig. 1. In this case, the strain at the fracture point is used to quantify brittleness of the specimen. A smaller strain at the fracture point corresponds to a more brittle specimen. However, most pharmaceutical materials have some degree of ductility. Hence, the specimen undergoes some degree of plastic deformation before it fractures (curve obcd in Fig. 1). The non-linear strain immediately before the peak force corresponds to the buildup of stress that is required for the crack to grow within the specimen to eventually split it. For more ductile materials, such as those shown in oe, the non-linear strain before breakage is longer. In the situations similar to obcd and oe, the strain that should be used to quantify brittleness of the specimen is difficult to define. In this work, we adopt the more conservative approach by using the strain at the elastic limit, i.e., the point of initial deviation from linearity instead of the point of maximum force, to quantify brittleness. Curves shown in Fig. 1 are usually obtained using specimens with a standard shape, e.g., dumb bell shaped bar, in the strength test (either compressive or tensile). However, such a specimen is rarely relevant to pharmaceutical tablets. On the other hand, cylindrical tablets studied by the Brazilian test [24–26], or diametrical breaking test, are commonly used for calculating tablet tensile strength. It will be very efficient if we can calculate TBI using data collected in this test. Under this test configuration, a generic force– displacement curve, as shown in Fig. 2, is usually obtained. This curve differs from those in Fig. 1 mainly in the appearance of a brief non-linear part of the curve, OA, before linear segment AB. This non-linear portion is because of the initially very high local stress due to the line contact (very small contact area) between the tablet and the platens despite the small loading force. The high local stress exceeds the elastic limit of the specimen and induces local plastic deformation. At this stage, the elastic deformation of the entire tablet is negligible since the overall force is still low. However, the plastic deformation increases contact area between the tablet and platens, which quickly lowers the stress at the contact to below the elastic limit. Beyond point A, the tablet undergoes mainly elastic deformation, which is shown as the linear portion, AB, in the curve. The part BC is due to the birth and propagation of cracks in the tablet until sufficient elastic energy is built up to eventually split the tablet. In this work, we have considered as many brittleness indices as we can find in a literature search. In the strain based approach, 4 possible brittleness indices (B1 to B4) can be defined from data shown in Fig. 2 (Appendix 1). Here, B1 is the same form as the index defined by Sönnergaard [23]. The adoption of Yagiz’s brittleness index [8], Fmax/displacement, generates four more possible brittleness indices, denoted by B5 to B8. In the energy based approach, compression force was applied diametrically without breaking the tablet so that both the loading (OABC) and the unloading (CD) curves can be obtained (Fig. 3). From the force–displacement curves shown in Fig. 3, one can
Fig. 1. Stress–strain curve of materials using specimens with uniform width. (oa: brittle material; obcd: brittle-ductile material; oe: ductile material).
Please cite this article in press as: X. Gong, C.C. Sun, A new tablet brittleness index, Eur. J. Pharm. Biopharm. (2015), http://dx.doi.org/10.1016/ j.ejpb.2015.04.007
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Fmax
C B
Fo rc e
A O
A’
B’
C’
Displacement
Fig. 2. A generic force–displacement curve during the diametrical compression test of pharmaceutical tablets. Segment AB is linear.
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obtain two possible brittleness indices, B9 (obtained by dividing the area under the unloading curve, i.e., the elastic energy, by the total energy during loading) and B10 (elastic energy divided by the plastic energy between the loading and unloading curves). In the indentation approach, the flat face of the tablet was penetrated with a spherical indenter until the tablet breaks to obtain force– displacement curves similar to that shown in Fig. 2. Therefore, 8 brittleness indices, B11–B18 (Appendix 1), can be obtained in the indentation approaches similar to B1–B8 obtained from the Brazilian test. In total, we have 18 possible brittleness indices to evaluate. To select the most suitable TBI from the 18 candidates (Appendix 1), we rely on tablet friability because it is known to strongly correlate with tablet brittleness [27].
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2. Materials and methods
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2.1. Materials
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Microcrystalline cellulose (MCC, Avicel PH101, Lot: P108819435) was received from FMC Biopolymer (Philadelphia, PA). a-Lactose monohydrate (LM, Batch: 025K0043), hydroxypropyl cellulose (HPC, Batch: 07413KH), and polyvinyl pyrrolidone (PVP, Batch: 125K0151) were purchased from Sigma– Aldrich (St Louis, Mo). Dibasic calcium phosphate dihydrate (DCPD, Lot: 7072X) was obtained from JRS PHARMA (Rosenberg,
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Germany). Magnesium stearate was received from Mallinckrodt (St Louis, MO). Magnesium chloride hexahydrate (Lot: 132231) was purchased from Fisher Scientific (Fair Lawn, NJ).
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2.2. Methods
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Powders of MCC, HPC, PVP, LM, DCPD, and binary mixtures of LM and MCC were mixed with 0.5% (wt%) magnesium stearate. In the mixtures, the weight ratios of LM to MCC were 3:1, 1:1, and 1:3. All powders were equilibrated at a relative humidity (RH) of 32% for more than 48 h in a desiccator before compaction. Powders were manually filled into a tableting die and compressed at predetermined pressures using flat-faced round tooling (8 mm diameter) on a universal material testing machine (Model 1485, Zwick, Germany). Compression speed was 2 mm/min. Cylindrical tablets were allowed to relax overnight in the 32% RH chamber before further characterization. For the determination of strain based TBI, tablets were fractured diametrically using a Texture Analyzer (TA-XT2i, Texture Technologies Corp., NY, USA) at a testing speed of 0.02 mm/s without using trigger force to initiate data collection. Maximum breaking force, tablet diameter, and tablet thickness were used to calculate tensile strength, r (MPa), according to Eq. (3) [24]:
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r¼
2F 106 pDT
ð3Þ
where F is the breaking force (N), D is the tablet diameter (m), and T is the thickness of tablet (m). For the determination of energy based brittleness indices, tablets were tested diametrically using the Texture Analyzer. The maximum force is set to 75% of Fmax to avoid tablet breakage and allow the collection of tablet recovery data. The tip was withdrawn immediately after the maximum force was achieved. The indentation approach for brittleness determination was also carried out by pressing a spherical tip (TA-8A, diameter of 1/800 ) into a tablet at a testing speed of 0.02 mm/s until the tablet fractures. No trigger force was used so that baseline data were collected as soon as the indenter moved down. Tablet friability (percentage of weight loss after being dropped for 100 times from a fixed height) was determined with an expedited method using a standard friabilator (F-2, Pharma Alliance, London, UK) operated at 25 rpm for 4 min [27]. All the determinations were carried out in triplicate. The tensile strength of marketed tablets was calculated using equations appropriate to their shapes. For convex tablets, Eq. (4) was applied [28] as follows:
1 10F t t W r ¼ 2 2:84 0:126 þ 3:15 þ 0:01 D W D pD
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ð4Þ
where t is the overall tablet thickness and W is the central cylinder thickness. Tensile strength of concave tablets was calculated using Eq. (5) [29]:
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r¼
Fig. 3. Force–displacement diagram in energy based approach (O, starting point of displacement; A, the starting point of tablet elastic deformation; B, the ending point of tablet elastic deformation; C, the maximum force point; A0 , B0 , and C0 are corresponding displacement of A, B, and C, respectively).
0:0296F þ 0:258 1:99 106
ð5Þ
For oblong convex tablets and modified rectangle tablets, Eq. (2) was applied to estimate the tensile strength. Since conventional pycnometry cannot determine the true density values of water-containing powders, the true densities of PVP and HPC were obtained using the regression method described by Sun [30,31]. The true densities of MCC, LM and DCPD were taken from the literature [32,33]. The true densities of the mixtures of LM and MCC were calculated from the true densities of individual powders and the weight fraction. All true density values are listed in Table S1.
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2.3. Determination of elastic strain using the first derivative method
3. Results and discussion
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3.1. Tablet tensile strength and friability
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Tablet tensile strength increases as compaction pressure increases for all materials (Fig. S2), which is in agreement with the literature results [34,35]. Tabletability of the LC–MCC mixtures is higher when more MCC is present. Tablet tensile strength decreases when porosity increases for all systems (Fig. S3). Porosity of MCC tablet spans a wider range and covers higher values than other tablets because of the much lower pressures employed to prepare them. Higher pressures result in very strong MCC tablets, which yields zero friability. They are, therefore, unfit for selecting the most suitable TBI based on friability. For all materials, friability decreases as compaction pressure increases (Fig. 4). When the pressure is comparable, the friability of MCC tablets is the lowest. The friability of LM-MCC tablets increases as LM content increases. Finally, DCPD tablets show largest friability when the compaction pressure is similar.
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To calculate TBI based on strain approach and indentation approach, it is required to determine the displacement length corresponding to the linear segment of the force–displacement curve in Fig. 2. To achieve this, the contribution of system deflection to the measured displacement value was first removed. Otherwise, large errors may be introduced in the calculation of strain especially for tablets that break at a high force. The corrected line was then smoothed using a moving average method with the span of 99. The corresponding first derivative of the smoothed displacement was then obtained using Matlab (R2010b, Version 7.13, MathWorks, USA), with the first 50 and last 50 points excluded. The line segment with first derivative values between 70% and 100% of the maximum value was taken as the linear part of the line AB in Fig. 2. The positions of A0 and B0 were then determined. The length of A0 B0 increases as the inclusion criterion for linear portion is relaxed. We chose the cutoff value of 70% because the changes in the lengths of A0 B0 are generally small when the inclusion criterion is further relaxed (Fig. S1).
3.2. Identification of the best TBI
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2.4. Selection of the best brittleness index
The statistical analyses of tablet friability, tensile strength, and all possible TBIs led to the clear identification of the index, B20 = 1/elastic strain, as the most suitable TBI (see Appendix II for details). For this TBI, friability calculated from Eq. (8) is in excellent agreement with the experimentally determined friability (Fig. 5) as follows:
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Because tablet friability highly relates to tablet brittleness, the first step in screening for the best TBI was carried out based on the Pearson correlation coefficient (r) between friability data and 18 TBI candidates. In this exercise, different forms of all 18 TBI candidates and friability data of LM, MCC, and DCPD tablets were used to make sure the best correlation can be identified. These included logarithmic form, square root form, quadratic form, and reciprocal form in addition to the original form of each variable. A total of 450 combinations between TBI and friability (18 5 5) were tested for each of all materials. For each combination, the form of TBI that yields the highest correlation with friability among the 18 candidates was identified based on their absolute r values. An absolute r value more than 0.8 qualified the pair of TBI and friability for more detailed analysis in the second stage of screening that also considers the contributions from tablet tensile strength. In the second stage of screening, we correlated friability with both tensile strength and TBI identified in first stage using Eq. (6). This was done with the expectation that tablet friability is affected by both brittleness and mechanical strength of tablets.
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Y ¼ a0 þ a1 X 1 þ a2 X 2
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where Y represents friability data (in original form, logarithmic form, square root form, quadratic form, and reciprocal form); X1 and X2 tensile strength and TBI (also in the five mathematical forms), respectively; and a0, a1 and a2 are constants. The equations with determination coefficient (R2) higher than 0.95 for the entire data set were accepted for further testing in the third stage. In the third step, the lead equations identified in the second step were used to predict the friability of tablets prepared from three MCC–LM mixtures at different pressures. Average absolute deviation (AAD) values between experimental results and calculated friability were calculated using Eq. (7):
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ð6Þ
P AAD ¼
jFriExp FriCal j 100% NED
ð7Þ
where ‘‘Fri’’ is friability; subscripts ‘‘Exp’’ and ‘‘Cal’’ refer to experimental and calculated results, respectively; and NED is the number of experimental points. The form of TBI in the equation that yielded the most accurate friability, or smallest AAD, was identified as the best brittleness index. All calculations were performed using Matlab.
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lnðFriabilityÞ ¼ 0:2211 1:004 lnðTensile strengthÞ þ 0:004792 TBI
ð8Þ
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Since this TBI is based on the dimensionless elastic strain when a tablet was deformed diametrically, it has a clear physical meaning. A tablet that sustains shorter elastic strain to fracture is more brittle and corresponds to a larger TBI value.
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3.3. Factors that influence TBI
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The relationship between TBI and compaction pressure for six materials is shown in Fig. 6. When compaction pressure is low, TBI decreases noticeably as compaction pressure increases for a given material. However, the dependence on pressure is little in high pressure region. This is likely because the higher pressure only slightly reduces tablet porosity once tablet porosity is close to zero. Hence, the impact of pressure variation on tablet structure and property is negligible. It is also clear from Fig. 6 that TBI values vary significantly with material. For example, the TBI values of LM
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100 MCC DCPD LM
Friability (%)
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MCC:LM=1:3 MCC:LM=1:1 MCC:LM=3:1
10
1
0.1
0
40
80
120
160
200
Pressure (MPa) Fig. 4. Dependence of tablet friability on pressure.
Please cite this article in press as: X. Gong, C.C. Sun, A new tablet brittleness index, Eur. J. Pharm. Biopharm. (2015), http://dx.doi.org/10.1016/ j.ejpb.2015.04.007
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400 MCC LM DCPD
15
350
12
250
9
200 150
6
100
LM:MCC=3:1 LM:MCC=1:1 LM:MCC=1:3
3 0
MCC DCPD LM MCC:LM=1:3 MCC:LM=1:1 PVP HPC MCC:LM=3:1
300
TBI
Experimental friability (%)
18
0
3
6
9
12
15
50 0
0.08 0.16 0.24 0.32 0.40 0.48 0.56
18
Calculated friability (%)
Tablet porosity Fig. 7. The relationships between TBI and tablet porosity for different materials.
Fig. 5. Comparison between experimentally obtained friability and friability calculated from Eq. (8).
400 LM:MCC=1:3 LM:MCC=1:1 LM:MCC=3:1
350
MCC LM DCPD
increasing tensile strength. The latter assumption is supported by Fig. 8, which shows the friability decreases sharply with decreasing TBI. This result shows the potential of the new TBI to quantitatively describe problems related to tablet brittleness that have not been well understood.
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3.5. Probability map based on tensile strength and TBI
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The Bayesian modeling, Monte-Carlo simulation, and bootstrapping techniques have seen more recent applications in calculating probability based design space [37]. Using the Z-test, residuals in the regression of Eq. (8) are found to follow a normal distribution (p = 0.9999) with a standard deviation value of 0.274 and an average of zero. Based on Eq. (8), we can now construct a friability map that details the probability of attaining 61% friability for any combinations between tensile strength and TBI using the Debrus method [38]. Random residual values following a normal distribution with an average value of 0 and standard deviation value of 0.274 were generated. For each combination of tensile strength and TBI, a total of 10,000 residual values were generated to obtain an accurate distribution of friability, from which the probability of tablets with friability 61% was calculated and is shown in Fig. 9. The probability of reaching 61% friability is higher at either higher tensile strength or lower TBI. LM tablet is too brittle to reach the high probability region, unless very strong tablets of LM can be made. By adding MCC to LM, the tablets move toward higher probability region (left upper corner of the map) of meeting the friability criterion when tablet tensile strength is kept the same. For plastic MCC, increasing tensile strength effectively brings tablets into the region where 61% friability is guaranteed. This indicates that increasing compaction pressure, which increases tablet tensile
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250 200 150 100 50 0
30
60
90
120
150 200
Pressure (MPa) Fig. 6. The relationships between TBI and compaction pressure for different materials.
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and DCPD are much higher than that of MCC. This is in agreement with the accepted notion that LM and DCPD are brittle materials while MCC is ductile. For tablets from MCC–LM mixture, TBI increases when MCC content decreases. The dependence of brittleness on composition has been qualitatively utilized to address long standing problems in tablet formulation and manufacturing. For example, overgranulation in high shear wet granulation and loss of tabletability in dry granulation can be overcome by incorporating more brittle excipients to promote fracture of granules during tableting [2–5]. On the other hand, the incorporation of ductile MCC helps to reduce the ejection force that is commonly observed for brittle materials, such as LM and DCPD. Such efforts can now be more effective with quantitative information on material brittleness available. As a tablet property, tablet brittleness is expected to be a function of both intrinsic material property and tablet structure [36]. Fig. 7 shows that TBI generally increases as porosity increases for a given material. However, the dependence of TBI on porosity is weaker for more ductile materials, such as PVP, HPC, MCC, and LM–MCC mixtures. The lower sensitivity to tablet porosity is consistent with the higher ability of more ductile materials to alleviate stress during tablet deformation.
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3.4. Impact of tensile strength and TBI on tablet friability
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During the search for the most suitable TBI, we assumed both tablet tensile strength and brittleness are significant factors that affect tablet friability. The former assumption is supported by Fig. A1, which shows the friability decreases sharply with
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100
Friability (%)
TBI
300
10
MCC DCPD LM MCC:LM=1:3 MCC:LM=1:1 MCC:LM=3:1
1
0.1
50
100
150
200
250
300
350
400
TBI Fig. 8. The relationships between TBI and friability.
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Fig. 9. The effects of TBI and tensile strength on the probability of a tablet to attain lower than 1% tablet friability. (The solid dots are marketed tablets with TBI value less than 150; Open dots are marketed tablets with TBI value higher than 150; Lines refer to compressed cylindrical tablets of different materials.)
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strength, is an effective way to reduce friability for plastic materials. However, for brittle materials, such as lactose, increasing pressure does not effectively eliminate the high friability problem because LM tablet tensile strength does not reach the tensile strength required for meeting the friability criterion (Fig. A3). For powders such as LM, the more effective approach to address friability problem is to incorporate plastic materials to simultaneously reduce TBI and increase tensile strength, as shown by the LM–MCC mixtures. It should be noted that Fig. 9 is obtained from the experimental data collected from cylindrical tablets. Relationships for friability, tensile strength, and TBI for tablets with different size and shape will be different from Fig. 9. The magnitude of difference depends on the effect of tablet size and shape on friability. In general, this map is stricter on the tensile strength and brittleness required for 61% friability because it is based on friability data from cylindrical tablets, which has been shown to have higher friability than bevel edged, oval, and likely other tablet shapes commonly used in commercial tablets [27]. In Fig. 9, the region covering probability between 0.2 and 0.8 is very narrow. This means that the probability changes sharply in this region. Based on the data, we suggest that TBI value of 150 or lower is sufficiently ductile to avoid unacceptable tablet friability. When TBI is 150, corresponding tensile strength is approximately 2 MPa in order to attain less than 1% friability with a probability of 0.95. To check the applicability of this friability map, we determined TBI and tensile strength of 30 marketed tablets. The results are summarized in Table S2 and plotted in Fig. 9. The TBI values vary from 38.6 to 278.3 with 25 of them less than 150. The tensile strength varies in the range of 0.6–4.0 MPa. Five commercial tablets (open circles in Fig. 9) with TBI values higher than 150 also have relatively low tensile strength (
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Contents lists available at ScienceDirect
European Journal of Pharmaceutics and Biopharmaceutics journal homepage: www.elsevier.com/locate/ejpb
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Research Paper
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A new tablet brittleness index
7 8 9 11 10 12 1 8 4 2 15 16 17 18 19 20 21 22 23 24 25 26 27
Xingchu Gong a,b, Changquan Calvin Sun b,⇑ a b
Pharmaceutical Informatics Institute, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, PR China Pharmaceutical Materials Science and Engineering Laboratory, Department of Pharmaceutics, University of Minnesota, Minneapolis, MN, USA
a r t i c l e
i n f o
Article history: Received 1 October 2014 Revised 24 February 2015 Accepted in revised form 1 April 2015 Available online xxxx Keywords: Brittleness Friability Tablet Elastic deformation Strain Powder technology
a b s t r a c t Brittleness is one of the important material properties that influences the success or failure of powder compaction. We have discovered that the reciprocal of diametrical elastic strain at fracture is the most suitable tablet brittleness indices (TBIs) for quantifying brittleness of pharmaceutical tablets. The new strain based TBI is supported by both theoretical considerations and a systematic statistical analysis of friability data. It is sufficiently sensitive to changes in both tablet compositions and compaction parameters. For all tested materials, it correctly shows that tablet brittleness increases with increasing tablet porosity for the same powder. In addition, TBI increases with increasing content of a brittle excipient, lactose monohydrate, in the mixtures with a plastic excipient, microcrystalline cellulose. A probability map for achieving less than 1% tablet friability at various combinations of tablet tensile strength and TBI was constructed. Data from marketed tablets validate this probability map and a TBI value of 150 is recommended as the upper limit for pharmaceutical tablets. This TBI can be calculated from the data routinely obtained during tablet diametrical breaking test, which is commonly performed for assessing tablet mechanical strength. Therefore, it is ready for adoption for quantifying tablet brittleness to guide tablet formulation development since it does not require additional experimental work. Ó 2015 Published by Elsevier B.V.
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1. Introduction Brittleness is one of the important material properties that determines the deformation and fracture of tablets under stress. Tablets of highly brittle materials tend to have more defects because of their lower ability to accommodate stress during tablet production, storage, transportation, and handling. This is shown as the propensity of these tablets to easy chipping, high friability, and generation of hidden defects [1]. On the other hand, tablets from very plastic materials tend to loss tabletability after dry or wet granulation processes [2–5]. When a bilayer tablet consisting of two layers with very different brittleness is diametrically compressed, the more brittle layer tends to fracture more easily leading to a unique breakage mode [6]. These problems can be minimized or even eliminated by maintaining a balanced tablet brittleness through appropriate choice of excipients in the formulation [7]. However, the effective design of a formulation with balanced brittleness and ductility requires a reliable method for quantifying tablet brittleness. Outside of the pharmaceutical arena, material brittleness is usually quantified using an empirical index that correlates with ⇑ Corresponding author at: 9-127B Weaver-Densford Hall, 308 Harvard Street S.E., Minneapolis, MN 55455, USA. Tel.: +1 612 624 3722; fax: +1 612 626 2125. E-mail address: [email protected] (C.C. Sun).
performance of importance. In geotechnical engineering, brittleness of rocks is usually assessed by penetration rate index or drilling rate index [8,9], because they correlate well with the brittle fracture propensity of rocks. This approach, although empirical, has been widely adopted in the geoengineering field because of its practicality and effectiveness in assessing brittleness of rocks. A similar approach has also been used to quantify brittleness of dental ceramics using a chipping factor, which quantifies the propensity to chipping at the edges [10]. Hucka and Das [11] comprehensively summarized methods for measuring brittleness. Five common approaches to obtain brittleness of rocks are based on strain, reversible energy, Mohr’s envelope, strength ratio, and special tests [12]. The special tests include impact test [13], indentation test [14,15], and punch penetration test [8]. Because of the unique specimen shape requirement for performing test, approaches based on Mohr’s envelope and strength ratio are not applicable for tablets. However, the approaches based on strain, reversible energy, and special tests can possibly be adopted for determining tablet brittleness. These have been explored in this work. In an effort to quantify brittleness of pharmaceutical materials, a brittle fracture index (BFI) was proposed by comparing tensile strength of tablets with and without a central hole [16–18]. Despite the initial promise and enthusiastic adoption of BFI in pharmaceutical research [19,20], its usefulness was questioned in
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Please cite this article in press as: X. Gong, C.C. Sun, A new tablet brittleness index, Eur. J. Pharm. Biopharm. (2015), http://dx.doi.org/10.1016/ j.ejpb.2015.04.007
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light of the finding that BFI did not vary in a systematic manner with composition [21]. This is related, at least partially, to the fact that BFI does not sufficiently discriminate among materials with brittleness in the middle range of the 0 – 1 scale where most materials lie. BFI was further challenged on the basis that the tensile strength of a compact with a central hole cannot be calculated using the same equation for an intact tablet because of the different stress distributions in the two types of tablets [22]. Practically speaking, making tablets with a central hole is challenging because it requires either the use of special punches when making the tablets or drilling post tablet compression. In a recent effort to improve the technique for quantifying brittleness, Sönnergaard proposed a new brittle-ductile index (BDI) for compacted cylindrical tablets based on the work of failure (WOF) and maximum breaking force (Fmax) [23], as shown in Eq. (1):
BDI ¼ 100
WOF 2 F max D
ð1Þ
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where D is the diameter of the tablet. The term, 2WOF/Fmax, in Eq. (1) is used to approximate the displacement required to fracture the tablet because of the experimental difficulty in directly determining the initial point of contact between the platen and tablet [23]. Unlike BFI, BDI values do vary in a more systematic manner with changes in composition of a mixture consisting of plastic and brittle materials [23]. This approach yields a reasonable estimate of the maximum diametrical strain in a tablet for brittle materials, such as lactose. However, errors are expected for pharmaceutical tablets that exhibit substantial plastic deformation leading to the tablet fracture because of work due to irreversible plastic deformation that should have not been included for characterizing brittle fracture behavior, which is, elastic by definition. For this reason, the relationship between WOF and force is actually not strictly linear [23]. To alleviate this problem, WOF was plotted against Fmax of tablets prepared under different pressures [23] and the slope of the line, a, is used to calculate BDI using Eq. (2):
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BDI ¼ 100
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127
2a D
ð2Þ
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The application of Eq. (2) implies that tablet fracture behavior is independent of tablet porosity, which varies when the compaction pressure changes. This assumption is, however, inconsistent with both theoretical expectations and practical observations. Qualitative observations suggest that tablets with high porosity or made from brittle materials are usually more brittle. For example, porous tablets (prepared at a low pressure) of relatively plastic hydroxypropyl cellulose (HPC) fracture during diametrical compression but a denser HPC tablet (prepared under a high pressure) yields without fracture during the same test. Therefore, a measurement of brittleness of a tablet should not be assumed to be a reliable descriptor of the brittleness of the material and a clear distinction between brittleness of a material and that of a tablet needs to be made. In addition to the problems discussed above, both BFI and BDI were developed without being validated against a tablet property known to correlate with brittleness. In absence of such validation, the application of BFI and BDI requires caution. Inspired by the successful approaches in quantifying the brittleness of the rocks and dental ceramics, we set out to identify a new tablet brittleness index (TBI) that most strongly correlates to tablet friability, a tablet property with recognized linkage to tablet brittleness. Unlike BFI and BDI, TBI quantifies brittleness of individual tablets; regardless, they are made from the same powder or not.
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1.1. Theoretical considerations
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In the most rigorous sense, brittleness determination is suitable only for an elastically deforming body, which is represented by the
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line oa in Fig. 1. In this case, the strain at the fracture point is used to quantify brittleness of the specimen. A smaller strain at the fracture point corresponds to a more brittle specimen. However, most pharmaceutical materials have some degree of ductility. Hence, the specimen undergoes some degree of plastic deformation before it fractures (curve obcd in Fig. 1). The non-linear strain immediately before the peak force corresponds to the buildup of stress that is required for the crack to grow within the specimen to eventually split it. For more ductile materials, such as those shown in oe, the non-linear strain before breakage is longer. In the situations similar to obcd and oe, the strain that should be used to quantify brittleness of the specimen is difficult to define. In this work, we adopt the more conservative approach by using the strain at the elastic limit, i.e., the point of initial deviation from linearity instead of the point of maximum force, to quantify brittleness. Curves shown in Fig. 1 are usually obtained using specimens with a standard shape, e.g., dumb bell shaped bar, in the strength test (either compressive or tensile). However, such a specimen is rarely relevant to pharmaceutical tablets. On the other hand, cylindrical tablets studied by the Brazilian test [24–26], or diametrical breaking test, are commonly used for calculating tablet tensile strength. It will be very efficient if we can calculate TBI using data collected in this test. Under this test configuration, a generic force– displacement curve, as shown in Fig. 2, is usually obtained. This curve differs from those in Fig. 1 mainly in the appearance of a brief non-linear part of the curve, OA, before linear segment AB. This non-linear portion is because of the initially very high local stress due to the line contact (very small contact area) between the tablet and the platens despite the small loading force. The high local stress exceeds the elastic limit of the specimen and induces local plastic deformation. At this stage, the elastic deformation of the entire tablet is negligible since the overall force is still low. However, the plastic deformation increases contact area between the tablet and platens, which quickly lowers the stress at the contact to below the elastic limit. Beyond point A, the tablet undergoes mainly elastic deformation, which is shown as the linear portion, AB, in the curve. The part BC is due to the birth and propagation of cracks in the tablet until sufficient elastic energy is built up to eventually split the tablet. In this work, we have considered as many brittleness indices as we can find in a literature search. In the strain based approach, 4 possible brittleness indices (B1 to B4) can be defined from data shown in Fig. 2 (Appendix 1). Here, B1 is the same form as the index defined by Sönnergaard [23]. The adoption of Yagiz’s brittleness index [8], Fmax/displacement, generates four more possible brittleness indices, denoted by B5 to B8. In the energy based approach, compression force was applied diametrically without breaking the tablet so that both the loading (OABC) and the unloading (CD) curves can be obtained (Fig. 3). From the force–displacement curves shown in Fig. 3, one can
Fig. 1. Stress–strain curve of materials using specimens with uniform width. (oa: brittle material; obcd: brittle-ductile material; oe: ductile material).
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Fmax
C B
Fo rc e
A O
A’
B’
C’
Displacement
Fig. 2. A generic force–displacement curve during the diametrical compression test of pharmaceutical tablets. Segment AB is linear.
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obtain two possible brittleness indices, B9 (obtained by dividing the area under the unloading curve, i.e., the elastic energy, by the total energy during loading) and B10 (elastic energy divided by the plastic energy between the loading and unloading curves). In the indentation approach, the flat face of the tablet was penetrated with a spherical indenter until the tablet breaks to obtain force– displacement curves similar to that shown in Fig. 2. Therefore, 8 brittleness indices, B11–B18 (Appendix 1), can be obtained in the indentation approaches similar to B1–B8 obtained from the Brazilian test. In total, we have 18 possible brittleness indices to evaluate. To select the most suitable TBI from the 18 candidates (Appendix 1), we rely on tablet friability because it is known to strongly correlate with tablet brittleness [27].
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2. Materials and methods
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2.1. Materials
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Microcrystalline cellulose (MCC, Avicel PH101, Lot: P108819435) was received from FMC Biopolymer (Philadelphia, PA). a-Lactose monohydrate (LM, Batch: 025K0043), hydroxypropyl cellulose (HPC, Batch: 07413KH), and polyvinyl pyrrolidone (PVP, Batch: 125K0151) were purchased from Sigma– Aldrich (St Louis, Mo). Dibasic calcium phosphate dihydrate (DCPD, Lot: 7072X) was obtained from JRS PHARMA (Rosenberg,
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3
Germany). Magnesium stearate was received from Mallinckrodt (St Louis, MO). Magnesium chloride hexahydrate (Lot: 132231) was purchased from Fisher Scientific (Fair Lawn, NJ).
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2.2. Methods
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Powders of MCC, HPC, PVP, LM, DCPD, and binary mixtures of LM and MCC were mixed with 0.5% (wt%) magnesium stearate. In the mixtures, the weight ratios of LM to MCC were 3:1, 1:1, and 1:3. All powders were equilibrated at a relative humidity (RH) of 32% for more than 48 h in a desiccator before compaction. Powders were manually filled into a tableting die and compressed at predetermined pressures using flat-faced round tooling (8 mm diameter) on a universal material testing machine (Model 1485, Zwick, Germany). Compression speed was 2 mm/min. Cylindrical tablets were allowed to relax overnight in the 32% RH chamber before further characterization. For the determination of strain based TBI, tablets were fractured diametrically using a Texture Analyzer (TA-XT2i, Texture Technologies Corp., NY, USA) at a testing speed of 0.02 mm/s without using trigger force to initiate data collection. Maximum breaking force, tablet diameter, and tablet thickness were used to calculate tensile strength, r (MPa), according to Eq. (3) [24]:
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r¼
2F 106 pDT
ð3Þ
where F is the breaking force (N), D is the tablet diameter (m), and T is the thickness of tablet (m). For the determination of energy based brittleness indices, tablets were tested diametrically using the Texture Analyzer. The maximum force is set to 75% of Fmax to avoid tablet breakage and allow the collection of tablet recovery data. The tip was withdrawn immediately after the maximum force was achieved. The indentation approach for brittleness determination was also carried out by pressing a spherical tip (TA-8A, diameter of 1/800 ) into a tablet at a testing speed of 0.02 mm/s until the tablet fractures. No trigger force was used so that baseline data were collected as soon as the indenter moved down. Tablet friability (percentage of weight loss after being dropped for 100 times from a fixed height) was determined with an expedited method using a standard friabilator (F-2, Pharma Alliance, London, UK) operated at 25 rpm for 4 min [27]. All the determinations were carried out in triplicate. The tensile strength of marketed tablets was calculated using equations appropriate to their shapes. For convex tablets, Eq. (4) was applied [28] as follows:
1 10F t t W r ¼ 2 2:84 0:126 þ 3:15 þ 0:01 D W D pD
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ð4Þ
where t is the overall tablet thickness and W is the central cylinder thickness. Tensile strength of concave tablets was calculated using Eq. (5) [29]:
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r¼
Fig. 3. Force–displacement diagram in energy based approach (O, starting point of displacement; A, the starting point of tablet elastic deformation; B, the ending point of tablet elastic deformation; C, the maximum force point; A0 , B0 , and C0 are corresponding displacement of A, B, and C, respectively).
0:0296F þ 0:258 1:99 106
ð5Þ
For oblong convex tablets and modified rectangle tablets, Eq. (2) was applied to estimate the tensile strength. Since conventional pycnometry cannot determine the true density values of water-containing powders, the true densities of PVP and HPC were obtained using the regression method described by Sun [30,31]. The true densities of MCC, LM and DCPD were taken from the literature [32,33]. The true densities of the mixtures of LM and MCC were calculated from the true densities of individual powders and the weight fraction. All true density values are listed in Table S1.
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2.3. Determination of elastic strain using the first derivative method
3. Results and discussion
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3.1. Tablet tensile strength and friability
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Tablet tensile strength increases as compaction pressure increases for all materials (Fig. S2), which is in agreement with the literature results [34,35]. Tabletability of the LC–MCC mixtures is higher when more MCC is present. Tablet tensile strength decreases when porosity increases for all systems (Fig. S3). Porosity of MCC tablet spans a wider range and covers higher values than other tablets because of the much lower pressures employed to prepare them. Higher pressures result in very strong MCC tablets, which yields zero friability. They are, therefore, unfit for selecting the most suitable TBI based on friability. For all materials, friability decreases as compaction pressure increases (Fig. 4). When the pressure is comparable, the friability of MCC tablets is the lowest. The friability of LM-MCC tablets increases as LM content increases. Finally, DCPD tablets show largest friability when the compaction pressure is similar.
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To calculate TBI based on strain approach and indentation approach, it is required to determine the displacement length corresponding to the linear segment of the force–displacement curve in Fig. 2. To achieve this, the contribution of system deflection to the measured displacement value was first removed. Otherwise, large errors may be introduced in the calculation of strain especially for tablets that break at a high force. The corrected line was then smoothed using a moving average method with the span of 99. The corresponding first derivative of the smoothed displacement was then obtained using Matlab (R2010b, Version 7.13, MathWorks, USA), with the first 50 and last 50 points excluded. The line segment with first derivative values between 70% and 100% of the maximum value was taken as the linear part of the line AB in Fig. 2. The positions of A0 and B0 were then determined. The length of A0 B0 increases as the inclusion criterion for linear portion is relaxed. We chose the cutoff value of 70% because the changes in the lengths of A0 B0 are generally small when the inclusion criterion is further relaxed (Fig. S1).
3.2. Identification of the best TBI
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2.4. Selection of the best brittleness index
The statistical analyses of tablet friability, tensile strength, and all possible TBIs led to the clear identification of the index, B20 = 1/elastic strain, as the most suitable TBI (see Appendix II for details). For this TBI, friability calculated from Eq. (8) is in excellent agreement with the experimentally determined friability (Fig. 5) as follows:
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Because tablet friability highly relates to tablet brittleness, the first step in screening for the best TBI was carried out based on the Pearson correlation coefficient (r) between friability data and 18 TBI candidates. In this exercise, different forms of all 18 TBI candidates and friability data of LM, MCC, and DCPD tablets were used to make sure the best correlation can be identified. These included logarithmic form, square root form, quadratic form, and reciprocal form in addition to the original form of each variable. A total of 450 combinations between TBI and friability (18 5 5) were tested for each of all materials. For each combination, the form of TBI that yields the highest correlation with friability among the 18 candidates was identified based on their absolute r values. An absolute r value more than 0.8 qualified the pair of TBI and friability for more detailed analysis in the second stage of screening that also considers the contributions from tablet tensile strength. In the second stage of screening, we correlated friability with both tensile strength and TBI identified in first stage using Eq. (6). This was done with the expectation that tablet friability is affected by both brittleness and mechanical strength of tablets.
329 331
Y ¼ a0 þ a1 X 1 þ a2 X 2
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where Y represents friability data (in original form, logarithmic form, square root form, quadratic form, and reciprocal form); X1 and X2 tensile strength and TBI (also in the five mathematical forms), respectively; and a0, a1 and a2 are constants. The equations with determination coefficient (R2) higher than 0.95 for the entire data set were accepted for further testing in the third stage. In the third step, the lead equations identified in the second step were used to predict the friability of tablets prepared from three MCC–LM mixtures at different pressures. Average absolute deviation (AAD) values between experimental results and calculated friability were calculated using Eq. (7):
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ð6Þ
P AAD ¼
jFriExp FriCal j 100% NED
ð7Þ
where ‘‘Fri’’ is friability; subscripts ‘‘Exp’’ and ‘‘Cal’’ refer to experimental and calculated results, respectively; and NED is the number of experimental points. The form of TBI in the equation that yielded the most accurate friability, or smallest AAD, was identified as the best brittleness index. All calculations were performed using Matlab.
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lnðFriabilityÞ ¼ 0:2211 1:004 lnðTensile strengthÞ þ 0:004792 TBI
ð8Þ
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Since this TBI is based on the dimensionless elastic strain when a tablet was deformed diametrically, it has a clear physical meaning. A tablet that sustains shorter elastic strain to fracture is more brittle and corresponds to a larger TBI value.
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3.3. Factors that influence TBI
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The relationship between TBI and compaction pressure for six materials is shown in Fig. 6. When compaction pressure is low, TBI decreases noticeably as compaction pressure increases for a given material. However, the dependence on pressure is little in high pressure region. This is likely because the higher pressure only slightly reduces tablet porosity once tablet porosity is close to zero. Hence, the impact of pressure variation on tablet structure and property is negligible. It is also clear from Fig. 6 that TBI values vary significantly with material. For example, the TBI values of LM
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100 MCC DCPD LM
Friability (%)
292
MCC:LM=1:3 MCC:LM=1:1 MCC:LM=3:1
10
1
0.1
0
40
80
120
160
200
Pressure (MPa) Fig. 4. Dependence of tablet friability on pressure.
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400 MCC LM DCPD
15
350
12
250
9
200 150
6
100
LM:MCC=3:1 LM:MCC=1:1 LM:MCC=1:3
3 0
MCC DCPD LM MCC:LM=1:3 MCC:LM=1:1 PVP HPC MCC:LM=3:1
300
TBI
Experimental friability (%)
18
0
3
6
9
12
15
50 0
0.08 0.16 0.24 0.32 0.40 0.48 0.56
18
Calculated friability (%)
Tablet porosity Fig. 7. The relationships between TBI and tablet porosity for different materials.
Fig. 5. Comparison between experimentally obtained friability and friability calculated from Eq. (8).
400 LM:MCC=1:3 LM:MCC=1:1 LM:MCC=3:1
350
MCC LM DCPD
increasing tensile strength. The latter assumption is supported by Fig. 8, which shows the friability decreases sharply with decreasing TBI. This result shows the potential of the new TBI to quantitatively describe problems related to tablet brittleness that have not been well understood.
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3.5. Probability map based on tensile strength and TBI
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The Bayesian modeling, Monte-Carlo simulation, and bootstrapping techniques have seen more recent applications in calculating probability based design space [37]. Using the Z-test, residuals in the regression of Eq. (8) are found to follow a normal distribution (p = 0.9999) with a standard deviation value of 0.274 and an average of zero. Based on Eq. (8), we can now construct a friability map that details the probability of attaining 61% friability for any combinations between tensile strength and TBI using the Debrus method [38]. Random residual values following a normal distribution with an average value of 0 and standard deviation value of 0.274 were generated. For each combination of tensile strength and TBI, a total of 10,000 residual values were generated to obtain an accurate distribution of friability, from which the probability of tablets with friability 61% was calculated and is shown in Fig. 9. The probability of reaching 61% friability is higher at either higher tensile strength or lower TBI. LM tablet is too brittle to reach the high probability region, unless very strong tablets of LM can be made. By adding MCC to LM, the tablets move toward higher probability region (left upper corner of the map) of meeting the friability criterion when tablet tensile strength is kept the same. For plastic MCC, increasing tensile strength effectively brings tablets into the region where 61% friability is guaranteed. This indicates that increasing compaction pressure, which increases tablet tensile
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421 422 423 424
250 200 150 100 50 0
30
60
90
120
150 200
Pressure (MPa) Fig. 6. The relationships between TBI and compaction pressure for different materials.
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and DCPD are much higher than that of MCC. This is in agreement with the accepted notion that LM and DCPD are brittle materials while MCC is ductile. For tablets from MCC–LM mixture, TBI increases when MCC content decreases. The dependence of brittleness on composition has been qualitatively utilized to address long standing problems in tablet formulation and manufacturing. For example, overgranulation in high shear wet granulation and loss of tabletability in dry granulation can be overcome by incorporating more brittle excipients to promote fracture of granules during tableting [2–5]. On the other hand, the incorporation of ductile MCC helps to reduce the ejection force that is commonly observed for brittle materials, such as LM and DCPD. Such efforts can now be more effective with quantitative information on material brittleness available. As a tablet property, tablet brittleness is expected to be a function of both intrinsic material property and tablet structure [36]. Fig. 7 shows that TBI generally increases as porosity increases for a given material. However, the dependence of TBI on porosity is weaker for more ductile materials, such as PVP, HPC, MCC, and LM–MCC mixtures. The lower sensitivity to tablet porosity is consistent with the higher ability of more ductile materials to alleviate stress during tablet deformation.
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3.4. Impact of tensile strength and TBI on tablet friability
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During the search for the most suitable TBI, we assumed both tablet tensile strength and brittleness are significant factors that affect tablet friability. The former assumption is supported by Fig. A1, which shows the friability decreases sharply with
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100
Friability (%)
TBI
300
10
MCC DCPD LM MCC:LM=1:3 MCC:LM=1:1 MCC:LM=3:1
1
0.1
50
100
150
200
250
300
350
400
TBI Fig. 8. The relationships between TBI and friability.
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X. Gong, C.C. Sun / European Journal of Pharmaceutics and Biopharmaceutics xxx (2015) xxx–xxx
Fig. 9. The effects of TBI and tensile strength on the probability of a tablet to attain lower than 1% tablet friability. (The solid dots are marketed tablets with TBI value less than 150; Open dots are marketed tablets with TBI value higher than 150; Lines refer to compressed cylindrical tablets of different materials.)
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strength, is an effective way to reduce friability for plastic materials. However, for brittle materials, such as lactose, increasing pressure does not effectively eliminate the high friability problem because LM tablet tensile strength does not reach the tensile strength required for meeting the friability criterion (Fig. A3). For powders such as LM, the more effective approach to address friability problem is to incorporate plastic materials to simultaneously reduce TBI and increase tensile strength, as shown by the LM–MCC mixtures. It should be noted that Fig. 9 is obtained from the experimental data collected from cylindrical tablets. Relationships for friability, tensile strength, and TBI for tablets with different size and shape will be different from Fig. 9. The magnitude of difference depends on the effect of tablet size and shape on friability. In general, this map is stricter on the tensile strength and brittleness required for 61% friability because it is based on friability data from cylindrical tablets, which has been shown to have higher friability than bevel edged, oval, and likely other tablet shapes commonly used in commercial tablets [27]. In Fig. 9, the region covering probability between 0.2 and 0.8 is very narrow. This means that the probability changes sharply in this region. Based on the data, we suggest that TBI value of 150 or lower is sufficiently ductile to avoid unacceptable tablet friability. When TBI is 150, corresponding tensile strength is approximately 2 MPa in order to attain less than 1% friability with a probability of 0.95. To check the applicability of this friability map, we determined TBI and tensile strength of 30 marketed tablets. The results are summarized in Table S2 and plotted in Fig. 9. The TBI values vary from 38.6 to 278.3 with 25 of them less than 150. The tensile strength varies in the range of 0.6–4.0 MPa. Five commercial tablets (open circles in Fig. 9) with TBI values higher than 150 also have relatively low tensile strength (
