A theoretical mathematical model for assessing diclofenac release from chitosan-based formulations

Abstract

The paper reports a new mathematical model for understanding the mechanism delivery from drug release systems. To do this, two drug release systems based on chitosan and diclofenac sodium salt as a drug model, were prepared by in situ hydrogelation in the presence of salicylaldehyde. The morphology of the systems was analyzed by scanning electron microscopy and polarized light microscopy and the drug release was in vitro investigated into a medium mimicking the in vivo environment. The drug release mechanism was firstly assessed by fitting the in vitro release data on five traditional mathematical model. In the context of pharmacokinetics behavioral analysis, a new mathematical procedure for describing drug release dynamics in polymer-drug complex systems was proposed. Assuming that the dynamics of polymer-drug system's structural units take place on continuous and nondifferentiable curves (multifractal curves), it was showed that in a one-dimensional hydrodynamic formalism of multifractal variables the drug release mechanism is given through synchronous dynamics at a differentiable and non-differentiable scale resolutions.

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan

“…Expanding on the last class of models, new developments have been made, based on Scale Relativity Theory, either in the monofractal dynamics, as in the case of Nottale [23], or in the multifractal dynamics, as in the case of the Multifractal Theory of Motion [24,25]. Our group has recently published in this framework, proving a good match for describing various drug delivery systems [26,27].…”

Theoretical model for the diclofenac release from PEGylated chitosan hydrogels

“…Recently, a new generation of theoretical models has arisen, based on Scale Relativity, either in the monofractal dynamics as in the case of Nottale (Nottale, 2011), or in the multifractal dynamics as is the case for the Multifractal Theory of Motion (Agop et al, 2004;Agop & Murgulet, 2007;Agop et al, 2008;Colotin et al, 2009;Paun et al, 2010;Merches & Agop, 2016;Agop & Paun, 2017;Bujoreanu et al, 2017;Cobzeanu et al, 2017;Irimiciuc et al, 2018Irimiciuc et al, , 2020. In such a context, supposing that, from both structural and functional perspectives, the polymer-drug complex system is assimilated to a multifractal system (Iftime, Dobreci, et al, 2020;Ailincai, Dorobanīu, et al, 2020;Iancu et al, 2020) the wide ranges of drug release dynamics can be described through the movement of the so-called polymer-drug complex system structural units on multifractal curves. Accepting multifractality as a fundamental property in drug release dynamics (and since multifractality is induced through stochasticity (Jackson, 1993;Cristescu, 2008;Mandelbrot, 1982)), the drug release dynamics can be associated to various flow regimes of a stochastic fluid at various scale resolutions (multifractal fluid).…”

“…Then, for a large temporal scale resolution, with respect to the inverse of the highest Lyapunov exponent (Mandelbrot, 1982;Jackson, 1993;Cristescu, 2008), the deterministic trajectories of the polymer-drug system structural units can be replaced by a collection of potential trajectories (virtual trajectories), while the concept of definite trajectories can be replaced by that of probability density. In such a context, a multifractal probability density conservation law will become functional for the drug release dynamics, in the form of a diffusion-type equation at various scale resolutions (multifractal diffusion equations) (Iftime, Dobreci, et al, 2020):…”

“…In a recent paper (Iftime, Dobreci, et al, 2020), operating with Equation (1), it has been shown that specific mechanisms of the release dynamics of the polymer-drug complex system (i.e. Fickian-type diffusion, non-Fickian-type diffusion, degradation of matrix, dissolution of matrix, etc.…”

A Drug Release Mechanism Controlled by Hydrophobic/Hydrophilic Balance of the Matrix. Theoretical and Experimental Perspectives

“…In the following we will build a mathematical model based on the paradigm of a multifractal theory of motion for the analysis of a complex polymer-drug dynamics. Therefore, admitting that from both structural and functional perspectives the polymer-drug complex system is assimilated to a multifractal system [26][27][28][29] the wide ranges of drug release dynamics can be described through the movement of the so-called polymer-drug complex system entities (or structural units) on trajectories that contain nondifferentiability (multifractal curves). Accepting multifractality as a fundamental property in drug release dynamics (and since multifractality is induces through stochasticity [30,31]), the drug release dynamics can be associated to various flow regimes of a stochastic fluid at various scale resolutions.…”