This paper deals with the physical and mathematical modelling description of drug release from matrix systems. In the introduction, matrix systems are considered in the wide frame of the controlled release systems and the concept of mathematical model is briefly discussed. Then, matrix structure and topology are matched, analysing the characteristics of the three-dimensional network constituting them. In this context, drug release mechanisms are considered with particular emphasis on the key factors ruling the release kinetics, such as matrix swelling, erosion, drug dissolution (re-crystallisation), drug diffusion, drug - polymer interaction, initial drug distribution and particle size distribution (for powdered matrix systems). The mathematical modelling section firstly considers the empirical and semi-empirical models that have the great advantage of showing analytical solutions. Then, the attention is focused on theoretical approaches regarding matrix swelling equilibrium and kinetics, drug dissolution, drug diffusion, drug - polymer interaction, initial drug distribution and matrix erosion. Finally, release kinetics from polydispersed spherical particles is studied. This review points out the fact that the comprehension of the phenomena ruling drug release from matrix systems is appropriate from both the physical and modelling point of view, although further improvements are always possible and desirable.

Because of its high biocompatibility, bio-degradability, low-cost and easy availability, cellulose finds application in disparate areas of research. Here we focus our attention on the most recent and attractive potential applications of cellulose in the biomedical field. We first describe the chemical/structural composition of cellulose fibers, the cellulose sources/features and cellulose chemical modifications employed to improve its properties. We then move to the description of cellulose potential applications in biomedicine. In this field, cellulose is most considered in recent research in the form of nano-sized particle, i.e., nanofiber cellulose (NFC) or cellulose nanocrystal (CNC). NFC is obtained from cellulose via chemical and mechanical methods. CNC can be obtained from macroscopic or microscopic forms of cellulose following strong acid hydrolysis. NFC and CNC are used for several reasons including the mechanical properties, the extended surface area and the low toxicity. Here we present some potential applications of nano-sized cellulose in the fields of wound healing, bone-cartilage regeneration, dental application and different human diseases including cancer. To witness the close proximity of nano-sized cellulose to the practical biomedical use, examples of recent clinical trials are also reported. Altogether, the described examples strongly support the enormous application potential of nano-sized cellulose in the biomedical field.

A simple relation between pendant groups of polymers in hydrogels is introduced to determine the crosslink density of (complex) hydrogel systems (mixtures of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) modified nanocellulose, alginate, scleroglucan and Laponite in addition of crosslinking agents). Furthermore, the rheological properties and their great potential connection to design complex hydrogel systems with desired properties have been thoroughly investigated. Hydrogel structures governing internal friction and flow resistance were described by the predominant effect of ionic, hydrogen, and electrostatic interactions. The relationship between rheological properties and polymer-polymer interactions in the hydrogel network is explained and expressed in a new mathematical model for determining the crosslink density of (crosslinked) hydrogels based on single or mixture of polymer systems. In the end, the combined used of rheology and low field nuclear magnetic resonance spectroscopy (LF-NMR) for the characterization of hydrogel networks is developed.