A Holographic-Type Model in the Description of Polymer–Drug Delivery Processes

Abstract

A unitary model of drug release dynamics is proposed, assuming that the polymer–drug system can be assimilated into a multifractal mathematical object. Then, we made a description of drug release dynamics that implies, via Scale Relativity Theory, the functionality of continuous and undifferentiable curves (fractal or multifractal curves), possibly leading to holographic-like behaviors. At such a conjuncture, the Schrödinger and Madelung multifractal scenarios become compatible: in the Schrödinger multifractal scenario, various modes of drug release can be “mimicked” (via period doubling, damped oscillations, modulated and “chaotic” regimes), while the Madelung multifractal scenario involves multifractal diffusion laws (Fickian and non-Fickian diffusions). In conclusion, we propose a unitary model for describing release dynamics in polymer–drug systems. In the model proposed, the polymer–drug dynamics can be described by employing the Scale Relativity Theory in the monofractal case or also in the multifractal one.

Keywords

• drug delivery
• fractal/multifractal curves
• Schrödinger and Madelung scenarios
• multifractal diffusion laws
• nanomedicine