On the use of the Weibull function for the discernment of drug release mechanisms
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:where 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):where 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 functionwhere 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.
References (38)
- et al.
Non-linear mixed effects models for the evaluation of dissolution profiles
Int. J. Pharm.
(2002) - et al.
Dissolution and diffuse reflectance characteristics of coated theophylline particles
Int. J. Pharm.
(1997) - et al.
Translocation of drug particles in HPMC matrix gel layer: effect of drug solubility and influence on release rate
J. Control. Release
(2001) - et al.
Solubility effects on drug transport through pH-sensitive, swelling-controlled release systems: transport of theophylline and metoclopramide monohydrochloride
J. Control. Release
(1995) - et al.
On the employment of λ carrageenan in a matrix system. III. Optimization of λ carrageenan-HPMC hydrophilic matrix
J. Control. Release
(1998) - et al.
Comparison of dissolution profiles or ibuprofen pellets
J. Control. Release
(2003) An alternative method to the evaluation of similarity factor in dissolution testing
Int. J. Pharm.
(2001)- et al.
Modeling and comparison of dissolution profiles
Eur. J. Pharm. Sci.
(2001) - et al.
Fronts movement as a useful tool for hydrophilic matrix release mechanism elucidation
Int. J. Pharm.
(2000) - et al.
Importance of drug type, tablet shape, and added diluents on drug release kinetics from hydroxypropylmethylcellulose matrix tablets
Int. J. Pharm.
(1987)