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Matrix type controlled release systems II. Percolation effects in non-swellable matrices
PHARMACEUTICA ACTAHELVETIAE ELSEVIER
Pharmaceutica Acta Helvetiae 68 (1993) 25-33
Matrix type controlled release systems II. Percolation effects in non-swellable matrices J.D. B o n n y 1, H. L e u e n b e r g e r * School of Pharrnacy, University of Basel, Totengaesslein 3, CH-4051 Basel, Switzerland
Abstract Two types of non-swellable matrix tablets were prepared by compressing binary mixtures of the water-soluble model drug caffeine with either ethyl cellulose (EC) as an inert, or hydrogenated castor oil (HCO) as a lipophilic matrix-forming excipient. The drug content in the tablets was varied from 10% to 95% (weight/weight). The drug release was measured from both flat sides of the tablets separately by a rotating-disk method. At the same drug loading, the tablet side having faced the upper punch during single-punch compaction showed a slower release rate than the opposite side, which can probably be attributed to differences in compaction pressure as well as in drug distribution between upper and lower side. Additionally, the drug release from the entire tablets was determined in a flow-through cell. From the dissolution data the percolation thresholds of the matrix systems were calculated according to a previously published method. The lower percolation threshold, expressed as total porosity of the completely leached matrix, ranged between 0.30 and 0.36, which can be explained by site percolation on a three-dimensional lattice of isomeric particles of drug and matrix substance. The upper percolation threshold, expressed as critical volume fraction of the matrix substance, was about 0.30 for the EC-matrices, but only 0.06 for the HCO-matrices. The latter shift to a very low percolation threshold may be attributed to the different particle sizes of matrix and active substance. A comparison of the drug release profiles determined in the flow-through cell shows the different behaviour of the two matrices with increasing drug loadings. Based on the concepts of percolation theory, the reasonable range of mixing ratios of drug and matrix substance yielding an optimal dissolution behaviour has to be evaluated, offering the possibility of a more rational dosage form design.
Key words: Percolation theory; Percolation threshold; Binary mixtures; Drug release; Inert matrix; Lipophilic matrix
I. Introduction
In a previous publication (Bonny and Leuenberger, 1991) the concepts of percolation theory were applied to the diffusion of a drug out of a matrix. It was demonstrated that in the binary system consisting of the drug and the matrix-forming excipient two percolation thresholds can be determined, i.e. distinct mixing ratios of the two components at which changes in the drug release kinetics occur. The lower percolation threshold Pct corresponds to a critical porosity e c of the matrix, below which the drug is mainly encapsulated, resulting in an incomplete release. The upper
* Corresponding author. 1 Present address: Nippon Roche Research Center, 200 Kajiwara, Kamakura, Kanagawa Pref., 247, Japan.
percolation threshold Pc2, however, represents the critical volume fraction of matrix substance .which is required to ensure the integrity of the matrix during drug release. Provided that the drug release from a matrix follows the square-root-of-time law of Higuchi (1963), a plot of the cumulative amount Q of drug released per unit surface area versus the square root of the time t will give a straight line with slope b. By investigating the release behaviour of a matrix at different drug loadings, i.e. different total matrix porosities e, the critical porosity e c can be calculated according to the following equation for the apparent or observed diffusion coefficient D of the drug in the porous matrix (Bonny and Leuenberger, 1991): b2 o
=
Cs(2A
0031-6865/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved SSDI: 0 0 3 1 - 6 8 6 5 ( 9 3 ) E 0 0 0 9 - 6
-eCs)
= XDo(
-
(1)
26
J.D. Bonny, 1t. Leuenberger / Pharmaceutica Acta Heh,etiae 68 (1993) 25-33
Or by means of the previously introduced tablet property/3 (Bonny and Leuenberger, 1991):
2.
Materials
and
methods
2.1. Materials [3
V~
_ eCs
~XDoC s ( e - ec)
(2)
with D O = diffusion coefficient of the drug in the permeating fluid b = s l o p e of the regression line in a plot of Q versus v~C s = solubility of the drug in the permeating fluid A = concentration of the dispersed drug in the tablet x D o = scaling factor e = total porosity of the matrix (due to air as well as drug) ec = critical porosity of the matrix, i.e. lower percolation threshold Pc1 In the first part of this work (Bonny and Leuenberger, 1991), matrix tablets composed of caffeine and ethyl cellulose were p r e p a r e d and the drug release from the tablet side, which was orientated towards the lower punch during single-punch compaction, was measured with a rotating-disk method. From the dissolution data the critical porosity e c was calculated according to Eqs. 1 and 2. The u p p e r percolation threshold or critical volume fraction of the matrix could be estimated based on the change of the dissolution kinetics from matrix-controlled (v~--law) to zero-order drug release. The aims of this second part of the work are as follows: Additional investigation of the dissolution from the tablet side orientated towards the u p p e r punch during the compaction process. Determination of the percolation thresholds in a lipophilic matrix. Significance of the percolation thresholds for the development of non-swellable matrix type controlled release systems.
Granular anhydrous caffeine was chosen as a water-soluble model drug and two non-swellable matrix-forming excipients were selected. According to the classification of Buri (1987), ethyl cellulose (EC) is considered as an inert, and hydrogenated castor oil ( H C O ) as lipophilic matrix substance. The origin of the substances as well as their mean particle sizes and true densities are compiled in Table 1. The solubility C s of the caffeine in the chosen dissolution medium (distilled water of 37°C) has previously (Bonny and Leuenberger, 1991, 1993) been determined as 38.0 + 0.4 m g / c m 3 and the diffusion coefficient D O as (5.4 _+ 0.2). 10 -6 cm2/s. Before further use, all substances were conditioned for at least 1 week at 4 5 - 5 0 % relative humidity at room t e m p e r a t u r e (20 _+ 2°C). 2.2. Methods
All matrix tablets were p r e p a r e d by uniaxial direct compression of the binary powder mixtures at a force of 16 kN as previously described for the matrices of ethyl cellulose (Bonny and Leuenberger, 1991), yielding round and flat tablets with a diameter of 11 m m and a weight of 400 + 1 mg. For the m e a s u r e m e n t of the intrinsic dissolution rate, the previously described rotating-disk method (Bonny and Leuenberger, 1991) was used as well. The flat tablet side facing the lower punch during compaction is termed as bottom side, its opposite as top side. Some of the matrix surfaces were examined in a scanning electron microscope (SEM) after dissolution testing. For that purpose specimens were air-dried, mounted with silver paint on an aluminium stub, sput-
Table 1 Mean particle size and true density of the substances used Substance Granular anhydrous caffeine Ethyl cellulose (EC) Hydrogenated castor oil (HCO)
Trade name
Ethocel ® 7 mPas Cutina ® HR
Source Sandoz Pharma AG, CH-Basel Fluka AG, CH-Buchs Sandoz Pharma AG, CH-Basel
Mean particle size (/~m)
(g/cm3)
True density
387
1.42
302
1.26
30
1.02
.I.D. Bonny, H. Leuenberger / Pharmaceutica Acta Heluetiae 68 (1993) 25-33
tered with 20 nm of gold (Sputter Coater SCD 030, Balzers, Liechtenstein) and finally observed and photographed in a SEM 515 (Philips, Eindhoven, Netherlands) at an accelerating voltage of 5 kV. For dissolution testing in the flow-through cell the apparatus mentioned in Usteri et al. (1990) with the same tablet cells (diameter 22.6 mm) was used. Distilled water of 37°C as a dissolution medium was pumped through the cells at a flow rate of 25 ml/min. The total volume of the medium used ranged between 1 1 and 3 1 depending on the drug content of the dosage form. Thus, on the one hand sink conditions were maintained in all tests and on the other hand, the spectrophotometric assay of the drug released was possible without any further dilution at a wavelength of 272 nm.
versus the square root of the time, Fig. 1 also expresses that up to caffeine loadings of about 60% (w/w) the release rate from the bottom side is faster than from the top side of the matrices. This difference can be attributed on the one hand to a higher caffeine concentration in the region of the bottom side of the tablet, resulting from the manual filling of the weighed amount of powder mixture into the die. On the other hand a higher degree of compaction in the area proximate to the upper punch, which reduces t h e local porosity of the compact, also decreases the release rate. This second assumption is confirmed by the work of Train (1956), who extensively studied differences in porosity or relative density within a powder compact. Thus, differences in drug distribution and compaction pressure can both reduce the total porosity of the matrix in the vicinity of the upper punch and consequently lead to a slower drug release from the top side. As explained in the previous part (Bonny and Leuenberger, 1991), the caffeine loadings taken into account for the calculation of the critical porosity e c according to Eq. 2 are those yielding release profiles which can adequately be described by the v~--law and which are furthermore in good agreement with the applied scaling laws of percolation theory. Based on these criteria, the data of the top side were evaluated in the range of caffeine loading,s from 30% to 50% (w/w) resulting in a critical porosity e c of 0.32 + 0.01. For the bottom side the corresponding range was 3555% (w/w) leading to a critical porosity e c of 0.35 + 0.01 (Bonny and Leuenberger, 1991). Concerning the upper percolation threshold Pc2, the change in the
3. Results and discussion
3.1. Matrices of ethyl cellulose The evaluation of the dissolution data from the bottom side of the EC-matrices has been described in detail in Bonny and Leuenberger (1991). The same method was used to calculate the tablet property /3 according to Eq. 2 from the dissolution data of the top side. For comparison, the values of /3 for both tablet sides and caffeine loadings from 20% to 65% (w/w) are shown in Fig. 1. As the tablet property/3 is proportional to the slope b obtained in a plot of the amount of drug released
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POROSITY Fig. 1. Plot of the tablet property 13 versus the total porosity e for the bottom side ( • ) and the top side ( • ) of EC-matrices. The solid lines represent the regression lines of the evaluated ranges.
,I.D. Bonny, H. Leuenberger / Pharmaceutica Acta Heluetiae 68 (1993) 25-33
28
dissolution kinetics from matrix-controlled to zeroorder release occurred at caffeine loadings between 70% and 80% (w/w) in case of the top side as well as in case of the bottom side, i.e. the upper percolation threshold Pc2 is above 70% (w/w) of caffeine, which corresponds to a volume fraction of the matrix substance smaller than 0.29. The found percolation thresholds expressed as critical volume-to-volume ratios of the pore system (i.e. the critical porosity e c) and the matrix substance, respectively, are both in good agreement with the theoretical site percolation threshold of 0.312 in a simple cubic lattice. As a rough model, it can be assumed that the particles of caffeine as well as those of ethyl cellulose are sites on the same cubic lattice. The comparable magnitude of the particle sizes of the two substances also supports this assumption. In the model of the "ant in the labyrinth", on which the present approach is based (Bonny and Leuenberger, 1991), the caffeine particles would represent the "occupied sites", i.e. accessible sites, on the lattice which have to form a continuous network to enable a satisfactory drug release, while the remaining sites containing ethyl cellulose particles would be termed as "unoccupied (by caffeine)", i.e. inaccessible, because diffusing drug particles cannot move into the matrix substance. Approaching the critical mixing ratio termed as upper percolation threshold, the matrix substance is the component reaching a critical volume ratio below which no more coherent network can be formed, leading to tablet disintegration.
Table 2 Porosity and drug concentration of the matrix tablets prepared from ethyl cellulose (EC) and hydrogenated castor oil (HCO), respectively Drug content (in % w / w ) 10 20 30 35 40 45 50 55 60 65 70 80 90 95
EC-matrices e0
e
0.134 0.212 0.128 0.286 0.121 0.363 0.118 0.403 0.116 0.444 0.109 0.484 0.110 0.528 0.106 0.571 0.103 0.615 0.098 0.660 0.099 0.707 0.092 0.800 0.088 0.899 notinvestigated
HCO-matrices A
eo
e
A
0.110 0.225 0.344 0.405 0.466 0.532 0.594 0.660 0.727 0.798 0.863 1.006 1.151
0.030 0.033 0.034 0.031 0.034 0.037 0.040 0.041 0.043 0.047 0.047 0.055 0.061 0.068
0.102 0.180 0.261 0.301 0.347 0.394 0.441 0.489 0.539 0.592 0.644 0.756 0.874 0.936
0.102 0.209 0.323 0.384 0.444 0.506 0.570 0.637 0.705 0.773 0.848 0.996 1.155 1.233
e o = initial tablet porosity (due to air). e = total porosity of matrix (due to air and drug content). A = concentration of dispersed drug in tablet in g / c m 3.
3.2. Matrices of hydrogenated castor oil The HCO-matrices were prepared at the same maximum compression force of 16 kN as the previously discussed EC-matrices. The initial and total porosities and the concentrations of drug within the prepared HCO-matrices are summarized in Table 2 and compared to the previously reported (Bonny and Leuenberger, 1991) properties of the corresponding EC-
0.20 0.18 t
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95%
0.16
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s
Fig. 2. Cumulative amounts of caffeine released in g / c m 2 as a function of time from the bottom side of HCO-matrices and pure caffeine tablets, respectively, containing 30% to 100% ( w / w ) of caffeine (means of three tablets per drug loading).
J.D. Bonny, H. Leuenberger / Pharmaceutica Acta Helvetiae 68 (1993) 25-33
matrices. The drug release profiles from the bottom side of the HCO-matrices with caffeine loadings between 30% and 95% ( w / w ) as well as from pure caffeine compacts are shown in Fig. 2. As in the preceding part (Bonny and Leuenberger, 1991), only values of the amount released Q up to 50% of the total dose were taken into account to allow the application of the v~-law. The dissolution data from the tablets containing 10% and 20% ( w / w ) of caffeine were not evaluated because they were poorly reproducible due to the very small amount of drug released (maximum 1.4 mg after 12 h). The other dissolution profiles were evaluated like the EC-matrices in (Bonny and Leuenberger, 1991), i.e. fitted by regression analysis to the two models Q(t) = a + bv~ and Q(t) at t k. The results and derived values of the apparent diffusion coefficient D and the tablet property/3 according to Eqs. 1 and 2, respectively, are compiled in Table 3. The dissolution data from the top side of the HCO-
29
matrices were treated in the same way and confirmed the tendency of a slower drug release from the top side as observed for the EC-matrices. The values of the slope b obtained by fitting the dissolution data to the v~--law ranged between 0.085. 10 -3 and 1.56.10 -3 g . c m - 2 . s -1/2 for the ECmatrices with drug loadings from 30% to 70% ( w / w ) (Bonny and Leuenberger, 1991), while the HCOmatrices at the same loadings show clearly lower values of b between 0.009-10 -3 and 0.320" 10 -3 g. cm -2. s-1/2. The slower drug release from the HCO-matrices can be attributed on one side to the lower total porosity e at the same drug content (see Table 2) and on the other side mainly to differences in the pore structures. While the fine and very plastic HCO-particles lead to an almost quantitative coating of the caffeine particles leaving only narrow connecting channels, the embedment of the drug by the EC-particles is less complete and allows the generation of wider pores (Bonny and
Fig. 3. SEM-micrographs of matrix tablets with an initial caffeine content of 40% ( w / w ) after 12 h of dissolution testing by rotating-disk method. The bottom side of the tablets is shown on the left, the top side on the right (1 bar corresponds to 1 ram). (a) Matrices of ethyl cellulose (top). (b) Matrices of hydrogenated castor oil (bottom).
J.D. Bonny, tt. Leuenberger / Pharmaceutica Acta tteh:etiae 68 (1993) 25-33
30
Table 3
The dissolution kinetics observed from the HCOmatrices considered over the whole range of drug loadings are somewhat different from those of the EC-matrices. In the actual case of hydrogenated castor oil, Table 3 shows an excellent conformity with the Ct-law or exponents k between 0.45 and 0.64 for all drug loadings up to 95% (w/w), while the EC-matrices with drug loadings of 10% and 20% (w/w) yielded exponents k of 0.17 and 0.27, respectively, indicating so-called anomalous diffusion (Bonny and Leuenberger, 1991). Therefore the lower percolation threshold Pcl or critical porosity e c of the HCO-matrices cannot directly be estimated from the changing values of k as was possible for the EC-matrices. A distinct change in the dissolution behaviour takes place only at drug loadings higher than 95% (w/w) indicating the upper percolation threshold Pc2 at a low volume fraction of the matrix substance. Although the exponents k listed in Table 3 do not point at the lower percolation threshold, the same evaluation as for the EC-matrices using the tablet property fl was performed (see Fig. 4). The critical porosity e c was calculated according to Eq. 2 by nonlinear regression analysis taking into account a certain range of caffeine loadings. The considered ranges and the resulting percolation thresholds are summarized in Table 4 and compared to the corresponding data of the EC-matrices. The critical porosities e c of the HCO-matrices are in about the same range as those of the EC-matrices, indicating also a simple cubic lattice as a rough model.
Evaluation of dissolution data from the bottom side of the HCOmatrices Drug content 30 35 40 45 50 55 60 65 70 80 90 95 100
Q(t)=a+bCt
Q(t)~t k
b
r2
k
r2
D
0.009 0.037 0.058 0.076 0.082 0.123 0.177 0.219 0.320 0.488 0.804 1.59 5.14
0.9959 0.9935 0.9956 0.9984 0.9989 0.9874 0.9964 0.9960 0.9967 0.9966 0.9981 0.9987 0.9716
0.46 0.60 0.53 0.59 0.48 0.48 0.48 0.45 0.48 0.48 0.52 0.64 1.11
0.9956 0.9886 0.9944 0.9948 0.9988 0.9824 0.9941 0.9958 0.9964 0.9969 0.9962 0.9921 > 0.9999
0.0032 0.0469 0.101 0.153 0.158 0.319 0.589 0.834 1.62 3.19 7.48 27.5 271
0.011 0.042 0.062 0.076 0.078 0.110 0.150 0.178 0.248 0.348 0.533 1.02 3.21
Drug content in % ( w / w ) . b = s l o p e in 10 3 g-cm 2.s i/2. k = dimensionless exponent, r e = squared correlation coefficient. D = apparent diffusion coefficient in 10 6 cm2/s. /3 = tablet property in 10 3 gWZ.cm 1/2. s we.
Leuenberger, 1993) as demonstrate the SEM-micrographs in Fig. 3. The micrographs, all taken at the same magnification, clearly show the different pore widths and the structural differences between the two matrix surfaces after the dissolution test. Furthermore, they support the assumption that more pores are formed on the bottom side than on the top side. The crystals visible particularly on the HCO-matrices consist of caffeine crystallized during the drying of the tablets.
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POROSITY Fig. 4. Plot of the tablet property/3 versus the total porosity e for the bottom side (11) and the top side ( A ) of HCO-matriees. The solid lines represent the regression lines of the evaluated ranges.
J.D. Bonny, H. Leuenberger/ Pharmaceutica Acta Helvetiae 68 (1993) 25-33
This finding supports the assumption that the lattice type is mainly determined by the caffeine particles, while the matrix substance is capable to fill up the sites not occupied by the caffeine. However, because of the lower initial porosities e 0 of the HCO-matrices the values of e c correspond to higher caffeine loadings than in the case of the EC-matrices. Assuming that the value of the critical porosity ec was determined with a sufficiently high precision, the drug dissolution behaviour of the HCO-matrices still follows vrf-kinetics below the percolation threshold, e.g. for a drug loading of 30% (w/w). This fact might be explained by a diffusion across the lipophilic matrix. However, this would require a certain solubility of the drug in the matrix substance which could not be demonstrated. On the other hand, SEM-micrographs of the matrices with only 10% (w/w) of caffeine (Bonny, 1992) showed a few small openings of pores, indicating a diffusional release through "water-filled pores" and not across the matrix. One possible explanation, why anomalous diffusion with an exponent of about 0.2 (Bonny and Leuenberger, 1991) could not be observed in case of the HCO-matrices, might be given by the percolation theory itself. According to Stauffer and Aharony (1992) anomalous diffusion can be observed for the "ant in the labyrinth" for long times right at the percolation threshold. In the vicinity of the threshold the situation is slightly different and anomalous diffusion will be found only for times much smaller than a characteristic time tchar. For times much longer than tchar either normal diffusion with Q(t) o~x/-f (for drug loading above Pc1) or diffusion over a constant distance, i.e. Q(t)= const. (for drug loadings below
Pc1), will occur. This time tchar decreases with increasing distance from the percolation threshold according to a scaling law and is among others proportional to the square of the correlation length ~, i.e. the mean distance between two sites belonging to the same cluster (Stauffer and Aharony, 1992). Due to the intense embedment of the caffeine particles leading to a lower initial porosity of the HCO-matrices, it can be assumed that at the same drug loading the correlation length in the HCO-matrices is shorter than in the EC-matrices. Consequently, the time tchar for the diffusion from the HCO-matrices is also shorter and, in contrast to the EC-matrices, anomalous diffusion might not be discovered by evaluating the dissolution data over the whole test period of 12 h. However, also a separate evaluation of the initial phase of the dissolution profile did not show a deviation from xff-kinetics towards anomalous diffusion with an exponent k of about 0.2. Furthermore, the predicted constant value of Q(t) for drug loadings below Pc~ was not achieved during the dissolution time of 12 h. So it is assumed that there is another reason for not observing anomalous diffusion in the case of the HCO-matrices. In contrast to the infinitely large lattices, which are the theoretical basis for the concepts of percolation theory, in the performed experiments effects at the surface of the matrices cannot be neglected. The appearance of x//-kinetics can be due to normal diffusion of the drug substance located in proximate caffeine clusters connected directly to the tablet surface. Because of the narrow pores in the HCO-matrices the dissolution of the drug in these accessible clusters takes much more time than in case of the EC-matrices and might therefore mask
Table 4 Percolation thresholds of the investigated EC-matrices and HCO-matrices
a. Estimation of Pcl From bottom side dissolution: Evaluated range of drug loadings Squared correlation coefficient Critical porosity e c Approx. drug loading corresponding to e c From top side dissolution: Evaluated range of drug loadings Squared correlation coefficient Critical porisity e c Approx. drug loading corresponding to e c b. Estimation of Pc2 Drug loadings leading to disintegration Corresponding volume fractions of matrix substance
31
EC-matrices
HCO-matrices
35-55% (w / w) 0.9867 0.35_+0.01 28% (w/w)
50-80% (w / w) 0.9877 0.36+_0.01 41% (w / w )
30-50% (w / w) 0.9948 0.32_+0.01 24% (w / w)
45-65% (w / w) 0.9944 0.30_+0.01 35% (w / w)
>70%(w/w) < 0.29
>95 (w/w) < 0.06
J.D Bonny, H. Leuenberger/ Pharmaceutica Acta Heluetiae 68 f'1993) 25-33
32
mensional lattice. However, it can be taken for granted that the fine particles of hydrogenated castor oil (mean diameter 30/xm) adhere to the coarser caffeine particles (mean diameter 387/xm), comparable to the formation of so-called ordered powder mixtures (Hersey, 1975; Yeung and Hersey, 1979). Because of the interaction between the two components, the lattice sites are no more occupied at random. In that case the percolation process is defined as a correlated percolation (Stauffer et al., 1982) and is capable to explain such low percolation thresholds. Another approach is to imagine a lattice where the lattice distance is determined by the size of the smaller HCO-particles so that a larger caffeine particle cannot occupy one individual
any anomalous diffusion during the whole test time. The upper percolation threshold Pc2 was found at the high drug loading of 95% (w/w), which means that even in concentrations as low as 5% (w/w) the matrix substance hydrogenated castor oil can still form a coherent network. This percolation threshold corresponds to a critical volume fraction smaller than 0.06. Such low percolation thresholds have also been reported before, e.g. by Ehrburger et al. (1990) for the conductivity of a powder bed of very fine carbon black and by Hastedt and Wright (1990) in the work mentioned in the preceding part (Bonny and Leuenberger, 1991). These small critical volume fractions cannot be explained by the random site percolation in a three-di-
80
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540
600
660
720
Fig. 5. Drug release (in percent of the dose) in the flow-through cell from non-swellable matrix tablets containing 10% to 95% ( w / w ) of caffeine (all data are m e a n s of 3 tablets). (a) Matrices of ethyl cellulose. (b) Matrices of hydrogenated castor oil.
J.D. Bonny, H. Leuenberger / Pharmaceutica Acta Helvetiae 68 (1993) 25-33
site, but already forms a cluster. Obviously, such a situation implies also a model of correlated percolation.
4. Conclusions In Fig. 5 the dissolution profiles of the two matrix types measured in the flow-through cell are summarized. To allow a direct comparison of the wide range of investigated drug loadings the amounts of drug released are plotted in percent of the dose. For both types of non-swellable matrices the release rate clearly increases with increasing drug loading, but as previously mentioned, at the same mixing ratio the HCOmatrices show a much slower release rate than the EC-matrices. According to the data in Table 4, bicoherent systems can be assumed for caffeine loadings between 30% and 70% (w/w) and 45% to 95% (w/w) for the ECmatrices and the HCO-matrices, respectively. Thus, the dissolution profiles in Fig. 5 measured over a period of 12 h indicate that the presence of a bicoherent system cannot guarantee a quantitative release of the drug within an adequate period of time in vivo, e.g. during a transit time of about 6 to 8 h effective for the absorption process. The EC-matrices with 40% (w/w) of caffeine showed an in vitro release of only 37% after 8 h and drug loadings of at least 60% (w/w) are required to achieve a release of more than 80% in 8 h. Using the lipophilic matrix hydrogenated castor oil a comparable release rate can only be achieved with a drug content of 90% (w/w). Using the concept of the two percolation thresholds in the matrices, the possible range of mixing ratios of drug and matrix substance can be restricted, giving a basis for a more rational design of dosage forms. Additionally it must be taken into account that the drug content should not be raised completely up to the upper percolation threshold in order to ensure the mechanical stability of the matrix. Finally, only a narrow range of mixing ratios will remain, which yield an almost complete drug release in vivo without the danger of an uncontrollable disintegration of the matrix.
33
Acknowledgements One of us, J.D.B., acknowledges Nippon Roche K.K., Japan, for the granted postdoctoral fellowship, during which the present paper based on data collected at the University of Basel could be completed. We would like to thank Prof. Dr. R. Guggenheim and his co-workers at the SEM-laboratory of the University of Basel for the preparation of the photographs and Prof. Dr. M. Kolb from the "Ecole Polytechnique" in Palaiseau (France) for the discussions on percolation theory. Sandoz Pharma is acknowledged for supplement of drug substance and excipients.
References Bonny, J.D. (1992) Wirkstoffreisetzung aus Matrix-Retardformen: Die Bedeutung der fraktalen Geometrie und der Perkolationstheorie. Ph.D. Thesis, University of Basel. Bonny, J.D. and Leuenberger, H. (1991) Matrix type controlled release systems. I. Effect of percolation on drug dissolution kinetics. Pharm. Acta Helv. 66, 160-164. Bonny, J.D. and Leuenberger, H. (1993) Determination of fractal dimensions of matrix-type solid dosage forms and their relation with drug dissolution kinetics. Eur. J. Pharm. Biopharm. 39, 31-'37. Buri, P. (1987) D6finition et classification des syst~mes matriciels. STP Pharma 3, 193-199. Ehrburger-Dolle, F., Misono, S. and Lahaye, J. (1990) Percolation dans les poudres de noir de carbone. Textes des Communications, Journ6e d'Etudes de la Soci6t6 des Electriciens et de Electroniciens, Paris, pp. 197-204. Hastedt, J.E. and Wright, J.L. (1990) Diffusion in porous materials above the percolation threshold. Pharm. Res. 7, 893-901. Hersey, J.A. (1975) Ordered mixing: A new concept in powder mixing practice. Powder Technol. 11, 41-44. Higuchi, T. (1963) Mechanism of sustained-action medication-theoretical analysis of rate of release of solid drugs dispersed in solid matrices. J. Pharm. Sci. 52, 1145-1149. Stauffer, D. and Aharony, A. (1992) Introduction to Percolation Theory, 2nd edition. Taylor & Francis, London, pp. 115-122. Stauffer, D., Coniglio, A. and Adam, M. (1982) Gelation and critical phenomena. Adv. Polym. Sci. 44, 103-155. Train, D. (1956) An investigation into compaction of powders. J. Pharm. Pharmacol. 8, 745-761. Usteri, M., Bonny, J.D. and Leuenberger, H. (1990) Fractal dimension of porous solid dosage forms. Pharm. Acta Helv. 65, 55-61. Yeung, C.C. and Hersey, J.A. (1979) Ordered powder mixing of coarse and fine particulate systems. Powder Technol. 22, 127-133.
Pharmaceutica Acta Helvetiae 68 (1993) 25-33
Matrix type controlled release systems II. Percolation effects in non-swellable matrices J.D. B o n n y 1, H. L e u e n b e r g e r * School of Pharrnacy, University of Basel, Totengaesslein 3, CH-4051 Basel, Switzerland
Abstract Two types of non-swellable matrix tablets were prepared by compressing binary mixtures of the water-soluble model drug caffeine with either ethyl cellulose (EC) as an inert, or hydrogenated castor oil (HCO) as a lipophilic matrix-forming excipient. The drug content in the tablets was varied from 10% to 95% (weight/weight). The drug release was measured from both flat sides of the tablets separately by a rotating-disk method. At the same drug loading, the tablet side having faced the upper punch during single-punch compaction showed a slower release rate than the opposite side, which can probably be attributed to differences in compaction pressure as well as in drug distribution between upper and lower side. Additionally, the drug release from the entire tablets was determined in a flow-through cell. From the dissolution data the percolation thresholds of the matrix systems were calculated according to a previously published method. The lower percolation threshold, expressed as total porosity of the completely leached matrix, ranged between 0.30 and 0.36, which can be explained by site percolation on a three-dimensional lattice of isomeric particles of drug and matrix substance. The upper percolation threshold, expressed as critical volume fraction of the matrix substance, was about 0.30 for the EC-matrices, but only 0.06 for the HCO-matrices. The latter shift to a very low percolation threshold may be attributed to the different particle sizes of matrix and active substance. A comparison of the drug release profiles determined in the flow-through cell shows the different behaviour of the two matrices with increasing drug loadings. Based on the concepts of percolation theory, the reasonable range of mixing ratios of drug and matrix substance yielding an optimal dissolution behaviour has to be evaluated, offering the possibility of a more rational dosage form design.
Key words: Percolation theory; Percolation threshold; Binary mixtures; Drug release; Inert matrix; Lipophilic matrix
I. Introduction
In a previous publication (Bonny and Leuenberger, 1991) the concepts of percolation theory were applied to the diffusion of a drug out of a matrix. It was demonstrated that in the binary system consisting of the drug and the matrix-forming excipient two percolation thresholds can be determined, i.e. distinct mixing ratios of the two components at which changes in the drug release kinetics occur. The lower percolation threshold Pct corresponds to a critical porosity e c of the matrix, below which the drug is mainly encapsulated, resulting in an incomplete release. The upper
* Corresponding author. 1 Present address: Nippon Roche Research Center, 200 Kajiwara, Kamakura, Kanagawa Pref., 247, Japan.
percolation threshold Pc2, however, represents the critical volume fraction of matrix substance .which is required to ensure the integrity of the matrix during drug release. Provided that the drug release from a matrix follows the square-root-of-time law of Higuchi (1963), a plot of the cumulative amount Q of drug released per unit surface area versus the square root of the time t will give a straight line with slope b. By investigating the release behaviour of a matrix at different drug loadings, i.e. different total matrix porosities e, the critical porosity e c can be calculated according to the following equation for the apparent or observed diffusion coefficient D of the drug in the porous matrix (Bonny and Leuenberger, 1991): b2 o
=
Cs(2A
0031-6865/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved SSDI: 0 0 3 1 - 6 8 6 5 ( 9 3 ) E 0 0 0 9 - 6
-eCs)
= XDo(
-
(1)
26
J.D. Bonny, 1t. Leuenberger / Pharmaceutica Acta Heh,etiae 68 (1993) 25-33
Or by means of the previously introduced tablet property/3 (Bonny and Leuenberger, 1991):
2.
Materials
and
methods
2.1. Materials [3
V~
_ eCs
~XDoC s ( e - ec)
(2)
with D O = diffusion coefficient of the drug in the permeating fluid b = s l o p e of the regression line in a plot of Q versus v~C s = solubility of the drug in the permeating fluid A = concentration of the dispersed drug in the tablet x D o = scaling factor e = total porosity of the matrix (due to air as well as drug) ec = critical porosity of the matrix, i.e. lower percolation threshold Pc1 In the first part of this work (Bonny and Leuenberger, 1991), matrix tablets composed of caffeine and ethyl cellulose were p r e p a r e d and the drug release from the tablet side, which was orientated towards the lower punch during single-punch compaction, was measured with a rotating-disk method. From the dissolution data the critical porosity e c was calculated according to Eqs. 1 and 2. The u p p e r percolation threshold or critical volume fraction of the matrix could be estimated based on the change of the dissolution kinetics from matrix-controlled (v~--law) to zero-order drug release. The aims of this second part of the work are as follows: Additional investigation of the dissolution from the tablet side orientated towards the u p p e r punch during the compaction process. Determination of the percolation thresholds in a lipophilic matrix. Significance of the percolation thresholds for the development of non-swellable matrix type controlled release systems.
Granular anhydrous caffeine was chosen as a water-soluble model drug and two non-swellable matrix-forming excipients were selected. According to the classification of Buri (1987), ethyl cellulose (EC) is considered as an inert, and hydrogenated castor oil ( H C O ) as lipophilic matrix substance. The origin of the substances as well as their mean particle sizes and true densities are compiled in Table 1. The solubility C s of the caffeine in the chosen dissolution medium (distilled water of 37°C) has previously (Bonny and Leuenberger, 1991, 1993) been determined as 38.0 + 0.4 m g / c m 3 and the diffusion coefficient D O as (5.4 _+ 0.2). 10 -6 cm2/s. Before further use, all substances were conditioned for at least 1 week at 4 5 - 5 0 % relative humidity at room t e m p e r a t u r e (20 _+ 2°C). 2.2. Methods
All matrix tablets were p r e p a r e d by uniaxial direct compression of the binary powder mixtures at a force of 16 kN as previously described for the matrices of ethyl cellulose (Bonny and Leuenberger, 1991), yielding round and flat tablets with a diameter of 11 m m and a weight of 400 + 1 mg. For the m e a s u r e m e n t of the intrinsic dissolution rate, the previously described rotating-disk method (Bonny and Leuenberger, 1991) was used as well. The flat tablet side facing the lower punch during compaction is termed as bottom side, its opposite as top side. Some of the matrix surfaces were examined in a scanning electron microscope (SEM) after dissolution testing. For that purpose specimens were air-dried, mounted with silver paint on an aluminium stub, sput-
Table 1 Mean particle size and true density of the substances used Substance Granular anhydrous caffeine Ethyl cellulose (EC) Hydrogenated castor oil (HCO)
Trade name
Ethocel ® 7 mPas Cutina ® HR
Source Sandoz Pharma AG, CH-Basel Fluka AG, CH-Buchs Sandoz Pharma AG, CH-Basel
Mean particle size (/~m)
(g/cm3)
True density
387
1.42
302
1.26
30
1.02
.I.D. Bonny, H. Leuenberger / Pharmaceutica Acta Heluetiae 68 (1993) 25-33
tered with 20 nm of gold (Sputter Coater SCD 030, Balzers, Liechtenstein) and finally observed and photographed in a SEM 515 (Philips, Eindhoven, Netherlands) at an accelerating voltage of 5 kV. For dissolution testing in the flow-through cell the apparatus mentioned in Usteri et al. (1990) with the same tablet cells (diameter 22.6 mm) was used. Distilled water of 37°C as a dissolution medium was pumped through the cells at a flow rate of 25 ml/min. The total volume of the medium used ranged between 1 1 and 3 1 depending on the drug content of the dosage form. Thus, on the one hand sink conditions were maintained in all tests and on the other hand, the spectrophotometric assay of the drug released was possible without any further dilution at a wavelength of 272 nm.
versus the square root of the time, Fig. 1 also expresses that up to caffeine loadings of about 60% (w/w) the release rate from the bottom side is faster than from the top side of the matrices. This difference can be attributed on the one hand to a higher caffeine concentration in the region of the bottom side of the tablet, resulting from the manual filling of the weighed amount of powder mixture into the die. On the other hand a higher degree of compaction in the area proximate to the upper punch, which reduces t h e local porosity of the compact, also decreases the release rate. This second assumption is confirmed by the work of Train (1956), who extensively studied differences in porosity or relative density within a powder compact. Thus, differences in drug distribution and compaction pressure can both reduce the total porosity of the matrix in the vicinity of the upper punch and consequently lead to a slower drug release from the top side. As explained in the previous part (Bonny and Leuenberger, 1991), the caffeine loadings taken into account for the calculation of the critical porosity e c according to Eq. 2 are those yielding release profiles which can adequately be described by the v~--law and which are furthermore in good agreement with the applied scaling laws of percolation theory. Based on these criteria, the data of the top side were evaluated in the range of caffeine loading,s from 30% to 50% (w/w) resulting in a critical porosity e c of 0.32 + 0.01. For the bottom side the corresponding range was 3555% (w/w) leading to a critical porosity e c of 0.35 + 0.01 (Bonny and Leuenberger, 1991). Concerning the upper percolation threshold Pc2, the change in the
3. Results and discussion
3.1. Matrices of ethyl cellulose The evaluation of the dissolution data from the bottom side of the EC-matrices has been described in detail in Bonny and Leuenberger (1991). The same method was used to calculate the tablet property /3 according to Eq. 2 from the dissolution data of the top side. For comparison, the values of /3 for both tablet sides and caffeine loadings from 20% to 65% (w/w) are shown in Fig. 1. As the tablet property/3 is proportional to the slope b obtained in a plot of the amount of drug released
1.0 ('4 \
0.9
7
0.8
i--i i
--
65%
..../£'//
%
0.7
.//" //:
0.8
/ Jt 55% ../. ./'./'F-it Bottom "',li'"
-
\ ,,-i
0.5
?
0.4
27
45%~//"~
Side
Fit Top Side
0.3 i 30% 0.1
......
20%
:::::i:::::::Z~
0.0 0.25
0.30
0.35
I 0.40
I 0.45
I 0.50
I 0.55
I O.CO0
l 0.05
I 0.70
POROSITY Fig. 1. Plot of the tablet property 13 versus the total porosity e for the bottom side ( • ) and the top side ( • ) of EC-matrices. The solid lines represent the regression lines of the evaluated ranges.
,I.D. Bonny, H. Leuenberger / Pharmaceutica Acta Heluetiae 68 (1993) 25-33
28
dissolution kinetics from matrix-controlled to zeroorder release occurred at caffeine loadings between 70% and 80% (w/w) in case of the top side as well as in case of the bottom side, i.e. the upper percolation threshold Pc2 is above 70% (w/w) of caffeine, which corresponds to a volume fraction of the matrix substance smaller than 0.29. The found percolation thresholds expressed as critical volume-to-volume ratios of the pore system (i.e. the critical porosity e c) and the matrix substance, respectively, are both in good agreement with the theoretical site percolation threshold of 0.312 in a simple cubic lattice. As a rough model, it can be assumed that the particles of caffeine as well as those of ethyl cellulose are sites on the same cubic lattice. The comparable magnitude of the particle sizes of the two substances also supports this assumption. In the model of the "ant in the labyrinth", on which the present approach is based (Bonny and Leuenberger, 1991), the caffeine particles would represent the "occupied sites", i.e. accessible sites, on the lattice which have to form a continuous network to enable a satisfactory drug release, while the remaining sites containing ethyl cellulose particles would be termed as "unoccupied (by caffeine)", i.e. inaccessible, because diffusing drug particles cannot move into the matrix substance. Approaching the critical mixing ratio termed as upper percolation threshold, the matrix substance is the component reaching a critical volume ratio below which no more coherent network can be formed, leading to tablet disintegration.
Table 2 Porosity and drug concentration of the matrix tablets prepared from ethyl cellulose (EC) and hydrogenated castor oil (HCO), respectively Drug content (in % w / w ) 10 20 30 35 40 45 50 55 60 65 70 80 90 95
EC-matrices e0
e
0.134 0.212 0.128 0.286 0.121 0.363 0.118 0.403 0.116 0.444 0.109 0.484 0.110 0.528 0.106 0.571 0.103 0.615 0.098 0.660 0.099 0.707 0.092 0.800 0.088 0.899 notinvestigated
HCO-matrices A
eo
e
A
0.110 0.225 0.344 0.405 0.466 0.532 0.594 0.660 0.727 0.798 0.863 1.006 1.151
0.030 0.033 0.034 0.031 0.034 0.037 0.040 0.041 0.043 0.047 0.047 0.055 0.061 0.068
0.102 0.180 0.261 0.301 0.347 0.394 0.441 0.489 0.539 0.592 0.644 0.756 0.874 0.936
0.102 0.209 0.323 0.384 0.444 0.506 0.570 0.637 0.705 0.773 0.848 0.996 1.155 1.233
e o = initial tablet porosity (due to air). e = total porosity of matrix (due to air and drug content). A = concentration of dispersed drug in tablet in g / c m 3.
3.2. Matrices of hydrogenated castor oil The HCO-matrices were prepared at the same maximum compression force of 16 kN as the previously discussed EC-matrices. The initial and total porosities and the concentrations of drug within the prepared HCO-matrices are summarized in Table 2 and compared to the previously reported (Bonny and Leuenberger, 1991) properties of the corresponding EC-
0.20 0.18 t
I100%
95%
0.16
90%
0.14 c~E 0.12
o~ 0.10 .c_ 0.08
80%
0
70%
0.06 65% 60%
0.04
55% o.o2
~,~
-
v
.
A
0.00 0.0
3.6
7.2
5%
30% 35% 10.8 14.4 18.0 21.6 25.2 28.8 32.4 36.0 39.6 43.2 TIME in 103
s
Fig. 2. Cumulative amounts of caffeine released in g / c m 2 as a function of time from the bottom side of HCO-matrices and pure caffeine tablets, respectively, containing 30% to 100% ( w / w ) of caffeine (means of three tablets per drug loading).
J.D. Bonny, H. Leuenberger / Pharmaceutica Acta Helvetiae 68 (1993) 25-33
matrices. The drug release profiles from the bottom side of the HCO-matrices with caffeine loadings between 30% and 95% ( w / w ) as well as from pure caffeine compacts are shown in Fig. 2. As in the preceding part (Bonny and Leuenberger, 1991), only values of the amount released Q up to 50% of the total dose were taken into account to allow the application of the v~-law. The dissolution data from the tablets containing 10% and 20% ( w / w ) of caffeine were not evaluated because they were poorly reproducible due to the very small amount of drug released (maximum 1.4 mg after 12 h). The other dissolution profiles were evaluated like the EC-matrices in (Bonny and Leuenberger, 1991), i.e. fitted by regression analysis to the two models Q(t) = a + bv~ and Q(t) at t k. The results and derived values of the apparent diffusion coefficient D and the tablet property/3 according to Eqs. 1 and 2, respectively, are compiled in Table 3. The dissolution data from the top side of the HCO-
29
matrices were treated in the same way and confirmed the tendency of a slower drug release from the top side as observed for the EC-matrices. The values of the slope b obtained by fitting the dissolution data to the v~--law ranged between 0.085. 10 -3 and 1.56.10 -3 g . c m - 2 . s -1/2 for the ECmatrices with drug loadings from 30% to 70% ( w / w ) (Bonny and Leuenberger, 1991), while the HCOmatrices at the same loadings show clearly lower values of b between 0.009-10 -3 and 0.320" 10 -3 g. cm -2. s-1/2. The slower drug release from the HCO-matrices can be attributed on one side to the lower total porosity e at the same drug content (see Table 2) and on the other side mainly to differences in the pore structures. While the fine and very plastic HCO-particles lead to an almost quantitative coating of the caffeine particles leaving only narrow connecting channels, the embedment of the drug by the EC-particles is less complete and allows the generation of wider pores (Bonny and
Fig. 3. SEM-micrographs of matrix tablets with an initial caffeine content of 40% ( w / w ) after 12 h of dissolution testing by rotating-disk method. The bottom side of the tablets is shown on the left, the top side on the right (1 bar corresponds to 1 ram). (a) Matrices of ethyl cellulose (top). (b) Matrices of hydrogenated castor oil (bottom).
J.D. Bonny, tt. Leuenberger / Pharmaceutica Acta tteh:etiae 68 (1993) 25-33
30
Table 3
The dissolution kinetics observed from the HCOmatrices considered over the whole range of drug loadings are somewhat different from those of the EC-matrices. In the actual case of hydrogenated castor oil, Table 3 shows an excellent conformity with the Ct-law or exponents k between 0.45 and 0.64 for all drug loadings up to 95% (w/w), while the EC-matrices with drug loadings of 10% and 20% (w/w) yielded exponents k of 0.17 and 0.27, respectively, indicating so-called anomalous diffusion (Bonny and Leuenberger, 1991). Therefore the lower percolation threshold Pcl or critical porosity e c of the HCO-matrices cannot directly be estimated from the changing values of k as was possible for the EC-matrices. A distinct change in the dissolution behaviour takes place only at drug loadings higher than 95% (w/w) indicating the upper percolation threshold Pc2 at a low volume fraction of the matrix substance. Although the exponents k listed in Table 3 do not point at the lower percolation threshold, the same evaluation as for the EC-matrices using the tablet property fl was performed (see Fig. 4). The critical porosity e c was calculated according to Eq. 2 by nonlinear regression analysis taking into account a certain range of caffeine loadings. The considered ranges and the resulting percolation thresholds are summarized in Table 4 and compared to the corresponding data of the EC-matrices. The critical porosities e c of the HCO-matrices are in about the same range as those of the EC-matrices, indicating also a simple cubic lattice as a rough model.
Evaluation of dissolution data from the bottom side of the HCOmatrices Drug content 30 35 40 45 50 55 60 65 70 80 90 95 100
Q(t)=a+bCt
Q(t)~t k
b
r2
k
r2
D
0.009 0.037 0.058 0.076 0.082 0.123 0.177 0.219 0.320 0.488 0.804 1.59 5.14
0.9959 0.9935 0.9956 0.9984 0.9989 0.9874 0.9964 0.9960 0.9967 0.9966 0.9981 0.9987 0.9716
0.46 0.60 0.53 0.59 0.48 0.48 0.48 0.45 0.48 0.48 0.52 0.64 1.11
0.9956 0.9886 0.9944 0.9948 0.9988 0.9824 0.9941 0.9958 0.9964 0.9969 0.9962 0.9921 > 0.9999
0.0032 0.0469 0.101 0.153 0.158 0.319 0.589 0.834 1.62 3.19 7.48 27.5 271
0.011 0.042 0.062 0.076 0.078 0.110 0.150 0.178 0.248 0.348 0.533 1.02 3.21
Drug content in % ( w / w ) . b = s l o p e in 10 3 g-cm 2.s i/2. k = dimensionless exponent, r e = squared correlation coefficient. D = apparent diffusion coefficient in 10 6 cm2/s. /3 = tablet property in 10 3 gWZ.cm 1/2. s we.
Leuenberger, 1993) as demonstrate the SEM-micrographs in Fig. 3. The micrographs, all taken at the same magnification, clearly show the different pore widths and the structural differences between the two matrix surfaces after the dissolution test. Furthermore, they support the assumption that more pores are formed on the bottom side than on the top side. The crystals visible particularly on the HCO-matrices consist of caffeine crystallized during the drying of the tablets.
0.6
m
90~
\
.."
i O.5 (.0 ('4 \
V 0.4
J
E
80%
(,,I£3 o')
0
..u.:::' ~:(:; ./..'-
..Y
F'it B o t t o m
S.
~ ~ : : " 0.3
70
0.2
65~/.~
~
Fit Top Side
¢' -
--
ol
ss~ so~
0.0 0.20
~ ~ : ~ . - -. . ~ _...,...L
~" S::~ ~
, ~IF::::::'"~..~I
0.30
,
0.40
I
0.50
,
I
0.60
,
I
0.70
,
I
0.80
,
I
0.90
POROSITY Fig. 4. Plot of the tablet property/3 versus the total porosity e for the bottom side (11) and the top side ( A ) of HCO-matriees. The solid lines represent the regression lines of the evaluated ranges.
J.D. Bonny, H. Leuenberger/ Pharmaceutica Acta Helvetiae 68 (1993) 25-33
This finding supports the assumption that the lattice type is mainly determined by the caffeine particles, while the matrix substance is capable to fill up the sites not occupied by the caffeine. However, because of the lower initial porosities e 0 of the HCO-matrices the values of e c correspond to higher caffeine loadings than in the case of the EC-matrices. Assuming that the value of the critical porosity ec was determined with a sufficiently high precision, the drug dissolution behaviour of the HCO-matrices still follows vrf-kinetics below the percolation threshold, e.g. for a drug loading of 30% (w/w). This fact might be explained by a diffusion across the lipophilic matrix. However, this would require a certain solubility of the drug in the matrix substance which could not be demonstrated. On the other hand, SEM-micrographs of the matrices with only 10% (w/w) of caffeine (Bonny, 1992) showed a few small openings of pores, indicating a diffusional release through "water-filled pores" and not across the matrix. One possible explanation, why anomalous diffusion with an exponent of about 0.2 (Bonny and Leuenberger, 1991) could not be observed in case of the HCO-matrices, might be given by the percolation theory itself. According to Stauffer and Aharony (1992) anomalous diffusion can be observed for the "ant in the labyrinth" for long times right at the percolation threshold. In the vicinity of the threshold the situation is slightly different and anomalous diffusion will be found only for times much smaller than a characteristic time tchar. For times much longer than tchar either normal diffusion with Q(t) o~x/-f (for drug loading above Pc1) or diffusion over a constant distance, i.e. Q(t)= const. (for drug loadings below
Pc1), will occur. This time tchar decreases with increasing distance from the percolation threshold according to a scaling law and is among others proportional to the square of the correlation length ~, i.e. the mean distance between two sites belonging to the same cluster (Stauffer and Aharony, 1992). Due to the intense embedment of the caffeine particles leading to a lower initial porosity of the HCO-matrices, it can be assumed that at the same drug loading the correlation length in the HCO-matrices is shorter than in the EC-matrices. Consequently, the time tchar for the diffusion from the HCO-matrices is also shorter and, in contrast to the EC-matrices, anomalous diffusion might not be discovered by evaluating the dissolution data over the whole test period of 12 h. However, also a separate evaluation of the initial phase of the dissolution profile did not show a deviation from xff-kinetics towards anomalous diffusion with an exponent k of about 0.2. Furthermore, the predicted constant value of Q(t) for drug loadings below Pc~ was not achieved during the dissolution time of 12 h. So it is assumed that there is another reason for not observing anomalous diffusion in the case of the HCO-matrices. In contrast to the infinitely large lattices, which are the theoretical basis for the concepts of percolation theory, in the performed experiments effects at the surface of the matrices cannot be neglected. The appearance of x//-kinetics can be due to normal diffusion of the drug substance located in proximate caffeine clusters connected directly to the tablet surface. Because of the narrow pores in the HCO-matrices the dissolution of the drug in these accessible clusters takes much more time than in case of the EC-matrices and might therefore mask
Table 4 Percolation thresholds of the investigated EC-matrices and HCO-matrices
a. Estimation of Pcl From bottom side dissolution: Evaluated range of drug loadings Squared correlation coefficient Critical porosity e c Approx. drug loading corresponding to e c From top side dissolution: Evaluated range of drug loadings Squared correlation coefficient Critical porisity e c Approx. drug loading corresponding to e c b. Estimation of Pc2 Drug loadings leading to disintegration Corresponding volume fractions of matrix substance
31
EC-matrices
HCO-matrices
35-55% (w / w) 0.9867 0.35_+0.01 28% (w/w)
50-80% (w / w) 0.9877 0.36+_0.01 41% (w / w )
30-50% (w / w) 0.9948 0.32_+0.01 24% (w / w)
45-65% (w / w) 0.9944 0.30_+0.01 35% (w / w)
>70%(w/w) < 0.29
>95 (w/w) < 0.06
J.D Bonny, H. Leuenberger/ Pharmaceutica Acta Heluetiae 68 f'1993) 25-33
32
mensional lattice. However, it can be taken for granted that the fine particles of hydrogenated castor oil (mean diameter 30/xm) adhere to the coarser caffeine particles (mean diameter 387/xm), comparable to the formation of so-called ordered powder mixtures (Hersey, 1975; Yeung and Hersey, 1979). Because of the interaction between the two components, the lattice sites are no more occupied at random. In that case the percolation process is defined as a correlated percolation (Stauffer et al., 1982) and is capable to explain such low percolation thresholds. Another approach is to imagine a lattice where the lattice distance is determined by the size of the smaller HCO-particles so that a larger caffeine particle cannot occupy one individual
any anomalous diffusion during the whole test time. The upper percolation threshold Pc2 was found at the high drug loading of 95% (w/w), which means that even in concentrations as low as 5% (w/w) the matrix substance hydrogenated castor oil can still form a coherent network. This percolation threshold corresponds to a critical volume fraction smaller than 0.06. Such low percolation thresholds have also been reported before, e.g. by Ehrburger et al. (1990) for the conductivity of a powder bed of very fine carbon black and by Hastedt and Wright (1990) in the work mentioned in the preceding part (Bonny and Leuenberger, 1991). These small critical volume fractions cannot be explained by the random site percolation in a three-di-
80
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660
720
Fig. 5. Drug release (in percent of the dose) in the flow-through cell from non-swellable matrix tablets containing 10% to 95% ( w / w ) of caffeine (all data are m e a n s of 3 tablets). (a) Matrices of ethyl cellulose. (b) Matrices of hydrogenated castor oil.
J.D. Bonny, H. Leuenberger / Pharmaceutica Acta Helvetiae 68 (1993) 25-33
site, but already forms a cluster. Obviously, such a situation implies also a model of correlated percolation.
4. Conclusions In Fig. 5 the dissolution profiles of the two matrix types measured in the flow-through cell are summarized. To allow a direct comparison of the wide range of investigated drug loadings the amounts of drug released are plotted in percent of the dose. For both types of non-swellable matrices the release rate clearly increases with increasing drug loading, but as previously mentioned, at the same mixing ratio the HCOmatrices show a much slower release rate than the EC-matrices. According to the data in Table 4, bicoherent systems can be assumed for caffeine loadings between 30% and 70% (w/w) and 45% to 95% (w/w) for the ECmatrices and the HCO-matrices, respectively. Thus, the dissolution profiles in Fig. 5 measured over a period of 12 h indicate that the presence of a bicoherent system cannot guarantee a quantitative release of the drug within an adequate period of time in vivo, e.g. during a transit time of about 6 to 8 h effective for the absorption process. The EC-matrices with 40% (w/w) of caffeine showed an in vitro release of only 37% after 8 h and drug loadings of at least 60% (w/w) are required to achieve a release of more than 80% in 8 h. Using the lipophilic matrix hydrogenated castor oil a comparable release rate can only be achieved with a drug content of 90% (w/w). Using the concept of the two percolation thresholds in the matrices, the possible range of mixing ratios of drug and matrix substance can be restricted, giving a basis for a more rational design of dosage forms. Additionally it must be taken into account that the drug content should not be raised completely up to the upper percolation threshold in order to ensure the mechanical stability of the matrix. Finally, only a narrow range of mixing ratios will remain, which yield an almost complete drug release in vivo without the danger of an uncontrollable disintegration of the matrix.
33
Acknowledgements One of us, J.D.B., acknowledges Nippon Roche K.K., Japan, for the granted postdoctoral fellowship, during which the present paper based on data collected at the University of Basel could be completed. We would like to thank Prof. Dr. R. Guggenheim and his co-workers at the SEM-laboratory of the University of Basel for the preparation of the photographs and Prof. Dr. M. Kolb from the "Ecole Polytechnique" in Palaiseau (France) for the discussions on percolation theory. Sandoz Pharma is acknowledged for supplement of drug substance and excipients.
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