Hydrogels have attracted much attention for long-term release of biomacromolecules for both tissue engineering and drug delivery. A better understanding of underlying principles in their behavior as biomaterials would be beneficial to the success of their final application. It would be possible with the help of mathematical modeling. In this thesis, effort has been made to (1) develop a theoretical framework to model the degradation behavior of hydrogels prepared by chemical cross-linking of pendant functional groups on long polymer chains and identify the influencing parameters, (2) explain the macromolecular release profile from degradable and non-degradable formulations, and (3) study biomacromolecule distribution within ocular tissues after intravitreal injection of drug bol...[ Read more ]

Hydrogels have attracted much attention for long-term release of biomacromolecules for both tissue engineering and drug delivery. A better understanding of underlying principles in their behavior as biomaterials would be beneficial to the success of their final application. It would be possible with the help of mathematical modeling. In this thesis, effort has been made to (1) develop a theoretical framework to model the degradation behavior of hydrogels prepared by chemical cross-linking of pendant functional groups on long polymer chains and identify the influencing parameters, (2) explain the macromolecular release profile from degradable and non-degradable formulations, and (3) study biomacromolecule distribution within ocular tissues after intravitreal injection of drug bolus and degradable hydrogel depot.

Degradation profiles of these hydrogels can be modeled by tracking the number of small chains between cross-link nodes responsible for the maintaining the network over time and relate it to the macroscopic swelling ratio. Without changing the chemistry of cleavable cross-link nodes, the initial hydrogel composition parameters, including polymer concentration and degree of modification, have significant impact on the swelling profile and the hydrogel lifetime. As hydrogels are formed by a random cross-linking reaction, they bear a heterogeneous microstructure. This feature leads to a multiphase release profile with different slopes from non-degradable formulation, especially when the release duration is over a long time (multiple weeks). In this thesis, the observed multiphase release is explained by applying a lattice-based model with two discrete diffusion coefficients. For three macromolecules, the dual-diffusivity model shows a good agreement with the experimental data over long time. In the degradable hydrogel formulations, macromolecules release depend on the combination of diffusion- and degradation-controlled mechanism. To capture heterogeneity from the mathematical point of view, we apply an initial heterogeneous distribution of diffusion coefficients into the hydrogel network composed of lattice sites. Over the time course of degradation, the diffusion coefficients assigned to the lattices change such that there will be a transition of diffusion coefficients towards higher values. Lastly, a three-dimensional transport model based on the physiology of the rabbit eye is constructed using computational fluid dynamic (CFD) techniques to obtain the spatial-temporal distribution of bevacizumab, an anti-vascular endothelial growth factor protein used to treat the posterior diseases, administered by a bolus injection or a hydrogel depot. The ocular pharmacokinetics of the protein is found to be very sensitive to the hydrodynamic parameters (including the intra ocular pressure and the aqueous flow) as well as transport parameters (such as diffusion coefficients). Superiority of hydrogel over pure drug shot was concluded by observing lower initial peak and higher drug level in vitreous/aqueous after 400 hours post drug administration.