Introduction: Electrospun 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[1],[2]. Bioactive macromolecules such as growth factors have also been incorporated in the electrospun fibers to promote cell growth and differentiation[3],[4]. It is important to understand and control the release rate of these macromolecules[5].
The objective of this study is to develop a stochastic simulation method to model the diffusive behaviors of macromolecules encapsulated in electrospun fibers.
Methods: For a given sample of electrospun fibers with macromolecules encapsulated, a region of interest consists of N fibers, with di and Li denoting the diameter and the length of the ith fiber. These quantities can be generated based on a statistical distribution determined from electrospun fiber samples via imaging analysis. For the ith fiber, the Fick’s diffusion equation is used to solve for the diffusion of encapsulated molecules. Assuming the ith fiber has a cylindrical shape, the diffusion equation and the initial and boundary conditions are given in Eq.1 The corresponding solutions for concentration and total mass in the ith fiber (Eq. 2) are based on initial concentration C0, diffusion constant D, Bessel function J of zeroth order, and αm0 where J0 equals zero for integer m.
Once the concentration of molecules in individual fibers is determined, one can determine the overall diffusion behavior for a given region with random fibers distributed via stochastic simulation. Subsequently, statistical characterization can be performed based on the results of a set of random generated regions.
The model can also be applied applied to macromolecules encapsulated in microspheres by solving the diffusion equation in a spherical coordinate system.
Results: MATHEMATICA was used to implement the developed method and numerical simulations were conducted to demonstrate the applicability of the method for both randomly distributed fibers and microspheres. Based on the diameter and length distribution data for a set of ES PEO/alginate fibers, numerical results were obtained for 20 random generated regions. Figure 1 shows the mean concentration decreases with respect to time based on results.
The same stochastic analysis was applied to random microsphere regions was overlaid with interpolated literature data[5]. Figure 2 shows that the model prediction matches well with experimental data.
Figure 1. Mean concentration in stochastic analysis of twenty random regions with ± 1 standard deviation at D=1x10-10 cm2/s
Figure 2. Percent mass diffused in microspheres with varying radii at D = 3.5x10-9 cm2/day. The experimental data are from [5].
Conclusion: A stochastic simulation method has been developed and implemented in MATHEMATICA. The method allows for examining how multiple factors affect the diffusion behavior of encapsulated macromolecules. Comparison with experimental data from the literature demonstrates the applicability of the developed method. Currently, we are collecting data for the diffusion of macromolecule encapsulated in electrospun fibers to validate and fine tune the developed methods.
References:
[1] A. Baji, Y.-W. Mai, S.-C. Wong, M. Abtahi and P. Chen, “Electrospinning of polymer nanofibers: Effects on oriented morphology, structures and tensile properties”, Composites Science and Technology, p. 16, 2010
[2] P. D Dalton, N. T. Joergensen, J. Groll, and M. Moeller, “Patterned melt electrospun substrates for tissue engineering”, Biomedical Materials, Vol. 3, 2008
[3] G. Tetteh, A.S. Khan, R.M. Delaine-Smith, G.C. Reilly, and I.U. Rehman, “Electrospun polyurethane/hydroxyapatite bioactive Scaffolds for bone tissue engineering: The role of solvent and hydroxyapatite particles”, Journal of the Mechanical Behavior of Biomedical Materials, Volume 39, November 2014, Pages 95-110
[4] Sill, T. J., and von Recum, H. A. (2008). “Electrospinning: applications in drug delivery and tissue engineering”. Biomaterials, 29(13), 1989-2006.
[5] A. Bertz, S. Wöhl-Bruhn, S. Miethe, B. Tiersch,, J. Koetz, J., M. Hust, and H. Menzel, (2013). “Encapsulation of proteins in hydrogel carrier systems for controlled drug delivery: Influence of network structure and drug size on release rate”. Journal of biotechnology, 163(2), 243-249.