A Multiscale Model for Solute Diffusion in Hydrogels

The number of biomedical applications of hydrogels is increasing rapidly on account of their unique physical, structural, and mechanical properties. The utility of hydrogels as drug delivery systems or tissue engineering scaffolds critically depends on the control of diffusion of solutes through the hydrogel matrix. Predicting or even modeling this diffusion is challenging due to the complex structure of hydrogels. Currently, the diffusivity of solutes in hydrogels is typically modeled by one of three main theories proceeding from distinct diffusion mechanisms: (i) hydrodynamic, (ii) free volume, and (iii) obstruction theory. Yet, a comprehensive predictive model is lacking. Thus, time and capital-intensive trial-and-error procedures are used to test the viability of hydrogel applications. In this work, we have developed a model for the diffusivity of solutes in hydrogels combining the three main theoretical frameworks, which we call the multiscale diffusion model (MSDM). We verified the MSDM by analyzing the diffusivity of dextran of different sizes in a series of poly(ethylene glycol) (PEG) hydrogels with distinct mesh sizes. We measured the subnanoscopic free volume by positron annihilation lifetime spectroscopy (PALS) to characterize the physical hierarchy of these materials. In addition, we performed a meta-analysis of literature data from previous studies on the diffusion of solutes in hydrogels. The model presented outperforms traditional models in predicting solute diffusivity in hydrogels and provides a practical approach to predicting the transport properties of solutes such as drugs through hydrogels used in many biomedical applications.