On the use of the Weibull function for the discernment of drug release mechanisms

https://doi.org/10.1016/j.ijpharm.2005.10.044Get rights and content

Abstract

Previous findings from our group based on Monte Carlo simulations indicated that Fickian drug release from Euclidian or fractal matrices can be described with the Weibull function. In this study, the entire drug release kinetics of various published data and experimental data from commercial or prepared controlled release formulations of diltiazem and diclofenac are analyzed using the Weibull function. The exponent of time b of the Weibull function is linearly related to the exponent n of the power law derived from the analysis of the first 60% of the release curves. The value of the exponent b is an indicator of the mechanism of transport of a drug through the polymer matrix. Estimates for b  0.75 indicate Fickian diffusion in either fractal or Euclidian spaces while a combined mechanism (Fickian diffusion and Case II transport) is associated with b values in the range 0.75 < b < 1. For values of b higher than 1, the drug transport follows a complex release mechanism.

Introduction

The modeling of drug release from delivery systems is important for the understanding and the elucidation of the transport mechanisms. Basically, the mathematical expressions used to describe the kinetics of drug release and the discernment of the release mechanisms are the Higuchi law (Higuchi, 1961) and the Peppas equation or the so-called power law (Ritger and Peppas, 1987, Siepmann and Peppas, 2001). The first approach relies on Eq. (1), which indicates that the fraction of drug released is proportional to the square root of time:MtM=ktwhere k is a constant reflecting formulation characteristics, and Mt and M are cumulative amounts of drug released at time t and infinite time, respectively. The second approach is based on the semi-empirical Eq. (2):MtM=ktnwhere k is the kinetic constant and n is an exponent characterizing the diffusional mechanism. When pure diffusion is the controlling release mechanism, n = 0.5 and Eq. (2) collapses to Eq. (1). Moreover, Eq. (2) also becomes physically realistic for n = 1 since drug release follows swelling controlled release or Case II transport (Siepmann and Peppas, 2001). Both Eqs. (1), (2) are short time approximations (Siepmann and Peppas, 2001, Kosmidis et al., 2003a) of complex exact relationships and therefore their use is confined for the description of the first 60% of the release curve.

Another alternative for the description of release profiles is based on the empirical use of the Weibull functionMtM=1exp(atb)where a and b are constants. Although this function is frequently applied to the analysis of dissolution and release studies (Van Vooren et al., 2001, Adams et al., 2002, Costa et al., 2003, Koester et al., 2004, Varma et al., 2005), its empirical use has been criticized (Costa and Sousa Lobo, 2001a). The criticism is focused on: (i) the lack of a kinetic basis for its use and (ii) the non-physical nature of its parameters (Costa and Sousa Lobo, 2001a). Besides, various attempts have been made to improve its performance (Schreiner et al., 2005) and validate its use (Macheras and Dokoumetzides, 2000, Elkoshi, 1997, Lansky and Weiss, 2003).

Recently, Monte Carlo simulation techniques were used for the study of Fickian diffusion of drug release both in Euclidian and fractal spaces (Kosmidis et al., 2003b, Kosmidis et al., 2003c). It was found that Eq. (3) describes nicely in both cases the entire drug release curve when the drug release mechanism is Fickian diffusion. In the case of release from Euclidian matrices studied by Kosmidis et al. (2003b), the value of the exponent b was found to be in the range 0.69–0.75. In the case of release from the two-dimensional percolation fractal (Kosmidis et al., 2003c) with fractal dimension df = 91/48 the values of b ranged from 0.35 to 0.39. It was shown that the Weibull function arises from the creation of a concentration gradient near the releasing boundaries of the Euclidian matrix (Kosmidis et al., 2003b) or because of the “fractal kinetics” behavior associated with the fractal geometry of the environment (Kosmidis et al., 2003c). The lower value of b in the percolation cluster reflects the slowing down of the diffusion process in the disordered medium. These Monte Carlo simulation results are apparently pointing to a universal law since the Weibull model provides a simple physical connection between the model parameters and the system geometry. Note that Eq. (3) can be approximated by a power law when the product αtb is small. This is evident from a simple series expansion of the exponential term in the right hand side of Eq. (3) (Kosmidis et al., 2003b).

These observations prompted us to use Eq. (3) for the analysis of the entire set of experimental data of controlled release formulations in conjunction with the classical analysis based on Eq. (2) for the first 60% of the release curve. To this end, the entire drug release kinetics of commercially available or prepared controlled release formulations of diltiazem and diclofenac was studied. In addition, published release data for a variety of drugs were re-examined using Eqs. (2), (3) in order to set up a theoretical basis for the discernment of release mechanisms using Eq. (3).

Section snippets

Materials

Hydroxypropylmethylcellulose (Metolose 90 SH 4000, Metolose 90 SH 4000SR, Metolose 90 SH 15000, Metolose 90 SH 100000SR, Shin Etsu) was used as a polymeric excipient. Diclofenac sodium (Sigma Chemical Co.) and Diltiazem hydrochloride (ELPEN) were used as model drugs. Magnesium stearate (BDH) was used as a lubricant.

Manufacture of tablets

Diclofenac sodium was mixed with hydroxypropylmethylcellulose and with 1% of magnesium stearate for 15 min in a powder mixer (WAB Turbula type T2F). Diltiazem hydrochloride was mixed

Results and discussion

Successful fittings were obtained when Eq. (3) was fitted to the entire release curve of the prepared, commercial formulations as well as to literature data. Two typical examples of successful fittings using Eq. (3) are shown in Fig. 1, Fig. 2. Similarly, successful fittings were obtained when Eq. (2) was fitted to the first 60% of the release curve of these formulations (Fig. 1, Fig. 2). An overview of the derived estimates for b and n from the fitting of Eqs. (2), (3) to the data of the

Conclusion

Overall, this study provides experimental evidence for the successful use of the Weibull function in drug release studies. Although the Weibull function has been used empirically for the analysis of release kinetics (Bonferoni et al., 1998, Lin and Cham, 1996, Antal et al., 1997, Van Vooren et al., 2001, Adams et al., 2002, Costa et al., 2003, Koester et al., 2004, Varma et al., 2005), the results of the present study provide a link between the values of b and the diffusional mechanisms of the

Acknowledgement

This work was partly supported by EPEAEK program.

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