Brownian dynamics simulations in hydrogels using an adaptive time-stepping algorithm

From Microscale to Macroscale: Nine Orders of Magnitude for a Comprehensive Modeling of Hydrogels for Controlled Drug Delivery

Because of their inherent biocompatibility and tailorable network design, hydrogels meet an increasing interest as biomaterials for the fabrication of controlled drug delivery devices. In this regard, mathematical modeling can highlight release mechanisms and governing phenomena, thus gaining a key role as complementary tool for experimental activity. Starting from the seminal contribution given by Flory-Rehner equation back in 1943 for the determination of matrix structural properties, over more than 70 years, hydrogel modeling has not only taken advantage of new theories and the increasing computational power, but also of the methods offered by computational chemistry, which provide details at the fundamental molecular level. Simulation techniques such as molecular dynamics act as a "computational microscope" and allow for obtaining a new and deeper understanding of the specific interactions between the solute and the polymer, opening new exciting possibilities for an in silico network design at the molecular scale. Moreover, system modeling constitutes an essential step within the "safety by design" paradigm that is becoming one of the new regulatory standard requirements also in the field-controlled release devices. This review aims at providing a summary of the most frequently used modeling approaches (molecular dynamics, coarse-grained models, Brownian dynamics, dissipative particle dynamics, Monte Carlo simulations, and mass conservation equations), which are here classified according to the characteristic length scale. The outcomes and the opportunities of each approach are compared and discussed with selected examples from literature.

Mesoscale modelling of environmentally responsive hydrogels: emerging applications

We review recent advances in mesoscale computational modeling, focusing on dissipative particle dynamics, used to probe stimuli-sensitive behavior of hydrogels.

Determination of local diffusion properties in heterogeneous biomaterials

The coupling between structure and diffusion properties is essential for the functionality of heterogeneous biomaterials. Structural heterogeneity is defined and its implications for time-dependent diffusion are discussed in detail. The effect of structural heterogeneity in biomaterials on diffusion and the relevance of length scales are exemplified with regard to different biomaterials such as gels, emulsions, phase separated biopolymer mixtures and chocolate. Different diffusion measurement techniques for determination of diffusion properties at different length and time scales are presented. The interplay between local and global diffusion is discussed. New measurement techniques have emerged that enable simultaneous determination of both structure and local diffusion properties. Special emphasis is given to fluorescence recovery after photobleaching (FRAP). The possibilities of FRAP at a conceptual level is presented. The method of FRAP is briefly reviewed and its use in heterogeneous biomaterials, at barriers and during dynamic changes of the structure is discussed.