A Finite Element Method for Modeling Diffusion and Drug Release from Nanocellulose/Nanoporous Silicon Composites

Background and Objective: A previous study investigated the in vitro release of methylene blue (MB), a widely used cationic dye in biomedical applications, from nanocellulose/nanoporous silicon (NC/nPSi) composites under conditions simulating body fluids. The results showed that MB release rates varied significantly with the nPSi concentration in the composite, highlighting its potential for controlled drug delivery. To further analyze the relationship between diffusion dynamics and the MB concentration, this study developed a finite element (FE) method to solve Fick's equations governing the drug delivery system. Methods: Release profiles of MB from NC/nPSi composites with varying nPSi concentrations (0%, 0.1%, 0.5%, and 1.0%) were experimentally measured in triplicate using phosphate-buffered saline (PBS) at 37 °C, pH 7.4, and 100 rpm. Mathematical models incorporating linear and quadratic dependencies of the diffusion coefficient on the MB concentration were developed and tested using the FE method. Model parameters were refined by minimizing the error between simulated and experimental MB release profiles. Results: The proposed FE method closely matched experimental data, validating its accuracy and robustness in simulating the diffusion and release processes. Conclusions: This study emphasizes the significant impact of the nPSi concentration on enhancing release control and highlights the importance of material composition in designing drug delivery systems. The findings suggest that the FE method can be effectively applied to model other complex systems, paving the way for advancements in precision drug delivery and broader biomedical applications.