On the dilemma of fractal or fractional kinetics in drug release studies: A comparison between Weibull and Mittag-Leffler functions

TL;DR

This paper compares Weibull and Mittag-Leffler functions for modeling drug release, showing both fit well up to 85% release but overestimate at later stages, highlighting the strengths and limitations of fractal and fractional kinetics models.

Contribution

It provides a comparative analysis of Weibull and Mittag-Leffler functions in drug release modeling using both simulated and real data.

Findings

Both models fit data up to 85% release

Models overestimate remaining particles at later times

Comparison highlights strengths and limitations of each approach

Abstract

We compare two of the most successful models for the description and analysis of drug release data. The fractal kinetics approach leading to release profiles described by a Weibull function and the fractional kinetics approach leading to release profiles described by a Mittag-Leffler function. We used Monte Carlo simulations to generate artificial release data from euclidean and fractal substrates. We have also used real release data from the literature and found that both models are capable in describing release data up to roughly $85\% $ of the release. For larger times both models systematically overestimate the number of particles remaining in the release device.