Electrospun(ES) fibers made of biocompatible polymers have been used as scaffolds in tissue engineering due to the potential to mimic the fibrous environment found in the extracellular matrix of biological tissue. Bioactive macromolecules such as growth factors have also been incorporated in the electrospun fibers to promote cell growth and differentiation. Therefore, it is critical to understand and control the release rate of the bioactive molecules. This paper presents the development of a stochastic simulation method to model the diffusive behaviors of macromolecules encapsulated in electrospun fibers. Specifically, a given ES fiber sample is represented by a set of random fibers with total fiber number denoted as N. Each fiber in the set is assumed as a cylinder and has a randomly assigned diameter and length, these parameters are based on statistical distributions determined from physical fiber samples. The Fick's diffusion equation is used to solve the concentration of encapsulated macromolecules in the fiber due to diffusion. Upon obtaining the solution of the concentration of molecules in individual fibers, one can determine the overall diffusion behavior for a given sample with random fibers distributed. A subsequent statistical characterization can be performed based on the results of a set of random generated samples. Moreover, the developed method can be applied to the diffusion of macromolecules encapsulated in microspheres. The developed method was implemented in MATHEMATICA. As an example, the ES fiber samples were generated via electrospinning alginate and poly(ethylene oxide) (PEO) blend polymer aqueous solution (1:1 ratio, 3% w/v), and FITC-dextran was mixed in the polymer solution to enable fluorescent image analysis. The fiber diameter, length and number of fibers were determined based on the fluorescent images of fiber samples. Parametric study was conducted to examine how the diffusive behavior of encapsulated macromolecules is affected by the fiber diameters, total number of fibers, diffusion constants, and boundary conditions. Furthermore, the stochastic analyses were conducted for cases of the diffusion of macromolecules encapsulated in microspheres. The model predictions agree well with the experimental data obtained from the literature.
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