Water insoluble polymers such as the acrylate methacrylates have been frequently applied on drug microparticles to obtain controlled release^1,2 . The resulting microcapsules are invariably inhomogeneous with respect to either the distribution of particle size, shape, nature of the wall (coating) material and/or wall thickness. A polydisperse system is therefore an ensemble of such inhomogeneously distributed particles. The release profile of an ensemble is dependent on the release characteristic of the individual (component) particles, and hence the particle distribution which may therefore be predetermined by computer simulation to optimize drug release³.

The important parameters which define the release profile of a microencapsulated drug are the rate order kinetic, the diffusion coefficient, the maximum release, m_∞ and the time to attain it, t_∞. Whereas the ensemble of microcapsules invariably displays a first order rate kinetic the single (component) microcapsules display a zero order rate profile^3-7. The individual particles were found to be inhomogeneous in the distribution of the release parameters, m_∞ and t_∞. Consequently summation of the individual releases from the single particles will give a cumulative release curve of he first order type, which was confirmed experimentally^3,4 . The individual releases are additive only under a sink condition such that the release from the individual particles are independent of each other. This finding provides a basis for predicting the release profile of an ensemble of a given particle distribution. In the previous studies^{3, 4}, the release data on several single particles of various sizes and weights were first determined empirically and the data subsequently used to simulate the release profiles of the ensembles, which is tedious. In the first part of this report we showed that the release profiles of the single particles could be simulated applying certain derived mathematical models⁸. Also the previous study³ was modelistic in design as one particle each of different sizes and weights were randomly selected to constitute the ensemble. In the present study the model was applied to an actual polydisperse system of an accidental particle distribution.

Modelling

Details of the derivation of the mathematical models for the simulation of the drug release profiles of the single particles of aspirin of an orthorhombic shape have been presented elsewhere in a recent publication⁸. The model allowed the estimation of the parameters m_∞, t_∞ and mt (the amount released at time intervals, t) from each particle in the distribution. In the case of the single crystals only the simulated amount of drug that would be released at the transition point from zero to first order release was designated as m1 and the time to attain it as t₁⁸. The data are used here to simulate drug release from the ensembles based on the model:

where Mt is the cumulative release from the ensemble in time t, ni is the number of particles each of size i distributed between the 1^st and the N^th term which in the system studied were 0.3 mm and 1.4 mm respectively (i.e. the particle size range), mi(t) is the individual release from each particle in time, t. The maximum value of mi(t) is predetermined as the calculated m_∞ of that particle achieved in time, t_∞. This model assumes that under sink conditions the release from individual particles in the ensemble would be independent of each other and therefore additive.

An aspect which was not considered in the first part of this study⁸ is the development of mathematical models for the simulation of the release profiles of single microcapsules at different wall thicknesses. The published values of m_∞ and t_∞ relate to single microcapsules of wall thickness, 11 µm⁸. Values of these parameters at other wall thicknesses e.g. 27 µm were estimated in the present study from the modified Fick equation, applicable to drug release from microcapsules⁹, thus:

where K is the proportionality constant for mass transfer through a wall barrier of thickness, L; m is the mass transferred in time, t. At the point of maximum release m = _∞ and t = t_∞ in equation 2. Thus the maximum release m_∞(1) and m_∞(2) of two microcapsules of same core weight but of different wall thicknesses, L1 and L2 respectively, can be compared by the ratios:

These expressions are based on the inverse relationship between m_∞ and L and the direct relationship between m_∞ and t_∞, (equation 2) since the m_∞ and t_∞ values of microcapsules of wall thickness 11 µm (represented by L1) were already known ⁸ the corresponding values for microcapsules of same core weight but of wall thickness 27 µm (represented by L2) were easily computed. The simulated values were used to compute the release profile of the ensembles.

Materials and Methods

Aspirin crystals (Synopharm Ltd., Germany) were selected as the core material primarily because of the ease of their microencpsulation by spray coating methods, thus obviating the need for preliminary pelletization, as would be the case with a fine powder. The particles were mainly orthorhombic with size range 0.3 to 1.4 mm; the most frequent size was 0.7 to 0.8 mm (frequency, 70%)⁸. The frequency - size distribution in a sample of the aspirin crystals (100 mg) is given in Table 1 a, b. Acetone (analar grade, BDH Poole, England) was used as solvent in the preparation of the polymeric coating fluid, while dibutylphthalate (reagent grade, BDH) was used as plasticizer.

Microencapsulation technique

The polymer films were applied on the aspirin crystals by a spray coating method, details of the technique have been described elsewhere⁸. Resulting microcapsules were of coating thickness 11 and 27 µm. The cores (i.e. the aspirin crystals) varied in size, 0.3 to 1.4 mm.

Determination of drug release

The procedure for single particles has been described earlier⁸. To determine release from the ensembles, a sample of the crystals or the microcapsules (100 mg) was placed in 1000 ml water in a conical flask and stoppered. The flask was mounted on a shaker bath which was agitated 50 rev. min ^{- 1} and maintained at a temp. 37 °C. At predetermined time intervals 3 min (crystals) or 30 min (microcapsules) samples (2ml) were withdrawn from the leaching fluid with a pipette fitted with a cotton wool plug. The samples were analyzed with a spectrophotometer (Hitachi U - 1100, Tokyo, Japan) at λ_max 267 nm. Each experiment was carried out in triplicate and the mean results reported. The cumulative amounts of drug released were plotted against time and from the curves the values of m_∞ and t_∞ were obtained

Simulation of drug release

A computer program, GW-BASIC (Microsoft Corporation, USA) was employed in the simulation. The computation was based on equation 2 which was built into the program. Values of the release parameters, mt, m1, t1, m_∞, t_∞, of the single particles which are needed for the simulation of the cumulative release of the ensembles have been published earlier⁸, except the data on single microcapsules of wall thickness of 27 µm which are presented in the present report in Figure 2b.

To obtain the simulated release from particles of each size fraction, the individual release at a particular time interval from a single particle of a given size was multiplied by the number of particles of that size represented by nimi(t) in equation 1. These were in turn summed up at each time scale and for the various time intervals to obtain the cumulative release curves. The system simulated was the accidental distribution of particles in a 100 mg samples (Table 1 a, b). For the ensembles of the crystals the results are presented in Table 1 a, b. The cumulative release data were plotted versus time and from the curves the values of m_∞ and t_∞ were obtained.

Determination of the rate order of release

Most drug delivery systems release their drug content by either zero or first order rate kinetic. Consequently in the present study, the cumulative release data on the ensembles were analyzed on the basis of zero or first order rate kinetic. The release was considered to follow a particular kinetic if the correlation coefficient was ≥0.90.

Validation of the models

The models employed in the simulation were considered valid if the observed results were in the same order of magnitude as the simulated data. The data were compared by means of a proportional difference given by:

The parameters compared were the correlation coefficient, r, for the rate order of release, m_∞ and t_∞ which define the release profiles of the ensembles. The proportional difference is a measure of the % deviation of the empirical from the simulated data. The results are presented in Table 2. The simulation was considered valid if the % deviation of the observed from the simulated data were within ± 20%.

Results

Simulated release data on the single particles

The release curves of the single crystals already published earlier⁸ are represented here (Figure 1), as the data would contribute to the understanding of how the release data in Table 1 a, b were generated. As noted in the previous report the curves fitted into an initial zero order followed by a first order release profile. The linear portion of the plot represents the zero order flux and the curved portion the first order phase.

The release data on the single microcapsules are presented in Figure 2. The data generally fitted into a zero order release profile. An increase in wall thickness from 11 to 27 mm brought about a profound decrease in the maximum release, m_∞ while the time to attain it, t_∞ increased considerably (compare Figures 2A and 2B).

These parameters also varied with core weight or size. This means that the point of maximum release (the extent and duration) can be controlled by variation in the microcapsule core weight and/or the wall thickness.

Simulated cumulative release profiles of the ensembles

The releases from particles of each size fraction of the crystals (taking into account the release from each particle (Figure 1) and the number of particles of each size) are presented in Table 1 a, b, from which the cumulative curve of the crystals was obtained; the curves for the two sets of ensembles of the microcapsules were similarly deduced. The cumulative curves of the three sets of ensembles are shown in Figure 3. The points for maximum release (m_∞, and t_∞) were obtained from these curves; the values are given in Table 2. The release profiles (Figure 3) generally fitted into an initial zero order flux followed by a first order release, as was the case with the single crystals (Figure 1). The evidence which suggests this profile for the ensembles is that the linear correlation coefficient was generally ≥ 0.95 when the data were analyzed on the basis of an initial zero oerder plot (up to 90% release) followed by first order plot for the remaining portion up to the maximum release. The correlation index fell below 0.8 when the data were analyzed entirely either as a zero order or as a first order plot.

Empirical release profiles of the ensembles: The curves are presented in Figure 4. The profiles are in many respects similar to the simulated curves for the ensembles (Figure 3). The observed m_∞ and _∞ values are presented in Table 2; they differed from the simulated values by a maximum of ± 22% (Table 2). The simulation predicted a decrease in m_∞ from 48 to 18 µg and an increase in t_∞ from 150 to 340 min during increase in wall thickness from 11 to 27 µm. The actual change in m_∞ was 58 to 22 µg and in t_∞, 120 to 280 min. These results lend credence to the models used in the simulation.

Discussion

This study has shown that the release profile of a polydisperse multiparticulate system can be reliably deduced from its particle distribution and the release profiles of the individual (component) particles in the distribution. Hence, the particle distribution may be predetermined in simulation studies to optimize drug release. The release parameters (m_∞ and t_∞) of the single particles can be theoretically derived which provides a rationale basis for the selection of the particles in the simulation process.

Acknowledgement

The authors wish to thank Prof. R. Groning of the Institute for Pharmaceutical Technology, University of Munster, Germany for his technical assistance and DAAD, Germany for the part funding of this research.

References