Modeling Diffusivity Through Alginate-Based Microfibers: A Comparison of Numerical and Analytical Models Based on Empirical Spectrophotometric Data

Abstract: The study of mass transport across hollow and solid 3D microfibers to study metabolic profiles is a key aspect of tissue engineering approach. A new modified numerical mathematical model based on Fickian equations in cylindrical coordinates has been proposed for determining the membrane diffusivity of 2% (w/v) alginate-based stents cross-linked with 10% CaCl 2 . Based on the economical and direct spectrophotometric measurements, using this model, inward diffusivities ranging from 5.2x10 -14 m 2 /s 2.93x10 -12 m 2 /s were computed for solutes with Stokes radii ranging between 0.36 to 3.5 nm, diffusing through bare alginate and alginate-chitosan-alginate microfibers. In parallel an analytical solution to the cylindrical Fickian equation was derived to validate the numerical solution using experimental diffusion data from a solid stent. Excellent agreement was found between the numerical and analytical models with a maximum calculated residual value of 4%. Using these models, a flexible computational platform is proposed to conduct custom diffusion and MW cut-off characterization across micro-porous microfibers not limited to alginate in composition.