Theoretical study of diffusional release of a dispersed solute from a hollow cylindrical polymeric matrix

Document Type : Article


Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran


An exact solution for the release kinetic of a solute from inside a hollow cylindrical polymeric matrix into an infinite medium has been developed, when the initial concentration of the solute (A) is greater than the solubility limit (Cs). A combination of analytical and numerical methods was used to calculate the solute concentration profile and the release rate. The model was developed for two different strategies: 1) the release medium is flowing through the hollow cylinder in which boundary layer may be neglected, 2) the release medium inside the hollow cylinder is stagnant and the boundary layer should be considered. The results indicated that the release profiles were close to the constant release rate after a typical burst release. Also, the release profile from a solid cylindrical matrix and a hollow cylinder was compared. The results indicated that the hollow cylindrical matrix is a promising carrier when zero-order release is desirable. The present model demonstrates the potential of the hollow cylindrical matrix as a suitable geometry for sustained drug delivery systems.


[1]    Kim, S. W., Petersen, R. V., and Feijen, J., "Polymeric drug delivery systems," Drug Design, vol. 10, pp. 193-250, 2016.
[2]    Wen, N., Dong, Y., Song, R., et al., "Zero-order release of gossypol improves its antifertility effect and reduces its side effects simultaneously," Biomacromolecules, vol. 19, pp. 1918-1925, 2018, DOI: 10.1021/acs.biomac.7b01648.
[3]    Feng, L., Milner, D. J., Xia, C., et al., "Xenopus laevis as a novel model to study long bone critical-size defect repair by growth factor-mediated regeneration," Tissue Engineering Part A, vol. 17, pp. 691-701, 2010.
[4]    Moioli, E. K., Clark, P. A., Xin, X., et al., "Matrices and scaffolds for drug delivery in dental, oral and craniofacial tissue engineering," Advanced drug delivery reviews, vol. 59, pp. 308-324, 2007.
[5]    Geris, L., Andreykiv, A., Van Oosterwyck, H., et al., "Numerical simulation of tissue differentiation around loaded titanium implants in a bone chamber," Journal of biomechanics, vol. 37, pp. 763-769, 2004.
[6]    Shim, J.-H., Kim, S. E., Park, J. Y., et al., "Three-dimensional printing of rhBMP-2-loaded scaffolds with long-term delivery for enhanced bone regeneration in a rabbit diaphyseal defect," Tissue Engineering Part A, vol. 20, pp. 1980-1992, 2014.
[7]    Koons, G. L. and Mikos, A. G., "Progress in three-dimensional printing with growth factors," Journal of Controlled Release, vol. 295, pp. 50-59, 2019.
[8]    Huang, Y. C. and Yang, Y. T., "Effect of basic fibroblast growth factor released from chitosan–fucoidan nanoparticles on neurite extension," Journal of tissue engineering and regenerative medicine, vol. 10, pp. 418-427, 2016.
[9]    Tarafder, S., Gulko, J., Kim, D., et al., "Effect of dose and release rate of CTGF and TGFβ3 on avascular meniscus healing," Journal of Orthopaedic Research®, 2019.
[10]    Carr, E. J. and Pontrelli, G., "Modelling mass diffusion for a multi-layer sphere immersed in a semi-infinite medium: application to drug delivery," Mathematical biosciences, vol. 303, pp. 1-9, 2018.
[11]    Abdekhodaie, M. and Cheng, Y.-L., "Diffusional release of a dispersed solute from a spherical polymer matrix," Journal of Membrane Science, vol. 115, pp. 171-178, 1996.
[12]    Higuchi, T., "Mechanism of sustained‐action medication. Theoretical analysis of rate of release of solid drugs dispersed in solid matrices," Journal of pharmaceutical sciences, vol. 52, pp. 1145-1149, 1963.
[13]    Jahromi, A. K., Shieh, H., and Saadatmand, M., "Theoretical study of diffusional release of a dispersed solute from cylindrical polymeric matrix: A novel configuration for providing zero-order release profile," Applied Mathematical Modelling, vol. 73, pp. 136-145, 2019.
[14]    Ibarra, J. C., Helbling, I. M., and Luna, J. A., "Mathematical modeling of drug delivery from cylindrical implantable devices," Mathematical Methods in the Applied Sciences, vol. 37, pp. 2677-2688, 2014.
[15]    Baker, R. and Lonsdale, H., "Div. of Organic Coatings and Plastics Preprints," ACS, vol. 3, p. 229, 1976.
[16]    Paul, D. R. and McSpadden, S., "Diffusional release of a solute from a polymer matrix," Journal of Membrane Science, vol. 1, pp. 33-48, 1976.
[17]    Lee, P., "Diffusional release of a solute from a polymeric matrix—approximate analytical solutions," Journal of membrane science, vol. 7, pp. 255-275, 1980.
[18]    Lee, P., "Controlled drug release from polymeric matrices involving moving boundaries," in Controlled Release of Pesticides and Pharmaceuticals, ed: Springer, 1981, pp. 39-48.
[19]    Langer, R., Hsieh, D. S., Rhine, W., et al., "Control of release kinetics of macromolecules from polymers," Journal of Membrane Science, vol. 7, pp. 333-350, 1980.
[20]    Zhou, Y. and Wu, X., "Finite element analysis of diffusional drug release from complex matrix systems. I.: Complex geometries and composite structures," Journal of controlled release, vol. 49, pp. 277-288, 1997.
[21]    Khamene, Z. M. and Abdekhodaie, M. J., "Diffusional release of a dispersed solute from a cylindrical polymeric matrix into an infinite external volume," Applied Mathematics and Computation, vol. 259, pp. 676-685, 2015.
[22]    Wazwaz, A.-M., Partial differential equations and solitary waves theory: Springer Science & Business Media, 2010.