Mathematical Modeling of Drug Diffusion in Bioengineered Scaffolds for Tissue Regeneration

Abstract

Localized and targeted controlled drug delivery using bioengineered scaffolds offers a promising concept in tissue engineering and regenerative medicine, in that, therapeutic molecules, including growth factors, proteins, and small-molecule drugs, can be released at the tissue-repair site on-command. The key to designing scaffolds is a clear comprehension of the processes underlying drug release, which can depend on the complicated relationship between scaffold porosity, degradation dynamics and drug-matrix binding phenomena. To overcome this issue, the current study constructs a detailed mathematical modeling framework that combines multi-scale diffusion equations, multi-scale porosity evolution driven by degradation, and nonlinear binding kinetics to determine reliably drug release of polymeric scaffolds. The governing equations are Fickian with time-dependent effective diffusivity to include effects due to the scaffold microarchitecture and degradation and binding terms modeling reversible polymer-drug interactions. Finite element methods (FEM) were applied to numerical simulations in COMSOL Multiphysics, and geometry of scaffolds were computed as porous cylindrical structures with sink boundary conditions which are physiologically relevant. The parametric analysis examined the effect of scaffold porosity, degradation rate, tortuosity, and binding constants on cumulative drug release during a 30-day cumulative drug release. Findings have revealed that increasing porosity contributes to a faster release rate with increase in effective diffusivity but the over-increase in porosity results in early burst release which causes loss of scaffold integrity. On the other hand, controlled degradation increased release time by progressively opening porosity without disrupting mechanical stability and nonlinear binding interaction dramatically decreased release time, allowing persistent therapeutic residence. Experimental datasets of literature on PLGA-based scaffolds were compared against model predictions and found to match well with a deviation of not more than 10 percent. Here, it is pointed out that mathematical modeling is an effective predictive method to design scaffolds with specific drug release kinetics, easier therapeutic approaches in tissue regeneration and future scaffold development in clinical translation.