2003 - Macheras - A Reappraisal of Drug Release Laws Using Monte Carlo Simulations - The Prevalence

2003 - Macheras - A Reappraisal of Drug Release Laws Using Monte Carlo Simulations - The Prevalence

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A Reappraisal of Drug Release Laws Using Monte Carlo Simulations: The Prevalence of the Weibull Function Kosmas Kosmidis, 1 Panos Argyrakis, 1 and Panos Macheras 2,3 Received December 24, 2002; accepted March 31, 2003 Purpose. To verify the Higuchi law and study the drug release from cylindrical and spherical matrices by means of Monte Carlo computer simulation. Methods. A one-dimensional matrix, based on the theoretical as- sumptions of the derivation of the Higuchi law, was simulated and its time evolution was monitored. Cylindrical and spherical three- dimensional lattices were simulated with sites at the boundary of the lattice having been denoted as leak sites. Particles were allowed to move inside it using the random walk model. Excluded volume in- teractions between the particles was assumed. We have monitored the system time evolution for different lattice sizes and different ini- tial particle concentrations. Results. The Higuchi law was verified using the Monte Carlo tech- nique in a one-dimensional lattice. It was found that Fickian drug release from cylindrical matrices can be approximated nicely with the Weibull function. A simple linear relation between the Weibull func- tion parameters and the specific surface of the system was found. Conclusions. Drug release from a matrix, as a result of a diffusion process assuming excluded volume interactions between the drug molecules, can be described using a Weibull function. This model, although approximate and semiempirical, has the benefit of providing a simple physical connection between the model parameters and the system geometry, which was something missing from other semiem- pirical models. KEY WORDS: drug release; Monte Carlo simulations; power law; Weibull function. INTRODUCTION The modeling of drug release from delivery systems is important for our understanding and elucidation of the trans- port mechanisms and allows the prediction of the effect of the device design parameters on the drug release rate. Hence, the development of new pharmaceutical products is highly facili- tated because the desirable release kinetics can be predicted in advance and thus be better achieved. Despite the complex- ity of the phenomena involved in drug release mechanisms, the mathematical models commonly used to describe the ki- netics of drug release from a large variety of devices are two simple expressions, the Higuchi law and the power law. The Higuchi law (1) states that M t = A D 2 c o c s t ( 1 ) where M t is the cumulative amount of drug released at time t , A is the surface area of the controlled release device exposed to the release medium, D is the drug diffusivity, and c o and c s are the initial drug concentration and the drug solubility, re- spectively. This law is valid for systems where the drug con- centration is much higher than the drug solubility.
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  • Summer '19
  • Britto
  • The Land, Monte Carlo method, Computer simulation, Monte Carlo methods in finance, Weibull distribution

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