Mathematical Modelling for the Diffusional Release of a Dispersed Solute from a Cylindrical Polymer Matrix into Finite External Volume
ABSTRACT
An exact solution has been obtained for the release kinetics of a solute from a cylindrical non-erodible polymeric matrix into a finite external volume when the initial solute loading is greater than the solubility limit in the matrix. The moving boundary solution is derived based on the combination of variable method. The formulas of the moving boundary and the fractional solute release are given. The moving boundary and the fractional solute release profiles have been calculated at various solute loading levels and different external volumes. The obtained results show that as the external fluid volume increases, the fractional release at any time and the maximum fractional release increase. In addition, for a given external volume, as initial drug loading increases, the fractional release at any time decreases.
An exact solution has been obtained for the release kinetics of a solute from a cylindrical non-erodible polymeric matrix into a finite external volume when the initial solute loading is greater than the solubility limit in the matrix. The moving boundary solution is derived based on the combination of variable method. The formulas of the moving boundary and the fractional solute release are given. The moving boundary and the fractional solute release profiles have been calculated at various solute loading levels and different external volumes. The obtained results show that as the external fluid volume increases, the fractional release at any time and the maximum fractional release increase. In addition, for a given external volume, as initial drug loading increases, the fractional release at any time decreases.
KEYWORDS
Diffusional Release Kinetics; Exact Solution; Finite External Volume; Mathematical Modeling
Diffusional Release Kinetics; Exact Solution; Finite External Volume; Mathematical Modeling
Cite this paper
T. Shefeeq and N. Ahmad, "Mathematical Modelling for the Diffusional Release of a Dispersed Solute from a Cylindrical Polymer Matrix into Finite External Volume," Applied Mathematics, Vol. 3 No. 1, 2012, pp. 34-38. doi: 10.4236/am.2012.31006.
T. Shefeeq and N. Ahmad, "Mathematical Modelling for the Diffusional Release of a Dispersed Solute from a Cylindrical Polymer Matrix into Finite External Volume," Applied Mathematics, Vol. 3 No. 1, 2012, pp. 34-38. doi: 10.4236/am.2012.31006.
References
[1] J. Siepmann, H. Kranz, R. Bodmeier and N. A. Peppas, “HPMC-Matrices for Controlled Drug Delivery: A New Model Combining Diffusion, Swelling and Dissolution Mechanisms and Predicting the Release Kinetics,” Pharmaceutical Research, Vol. 16, No. 11, 1999, pp. 1748-1756. doi:10.1023/A:1018914301328 [2] J. Crank, “Mathematics of Diffusion,” 2nd Edition, Oxford University Press, Oxford, 1975. [3] T. Higuchi, “Rate of Release of Medicaments from Ointment Bases Containing Drugs in Suspension,” Journal of Pharmaceutical Sciences, Vol. 50, No. 10, 1961, pp. 874-875. doi:10.1002/jps.2600501018 [4] T. Higuchi, “Mechanism of Sustained-Action Medication. Theoretical Analysis of Solid Drugs Dispersed in Solid Matrices,” Journal of Pharmaceutical Sciences, Vol. 52, No. 12, 1963, pp. 1145-1149. doi:10.1002/jps.2600521210 [5] D. R. Paul and S. K. McSpadden, “Diffusional Release of a Solute from a Polymer Matrix,” Journal of Membrane Science, Vol. 1, 1976, pp. 33-48. doi:10.1016/S0376-7388(00)82256-5 [6] P. I. Lee, “Diffusional Release of a Solute from a Polymeric Matrix. Approximate Analytical Solution,” Journal of Membrane Science, Vol. 7, No. 3, 1980, pp. 255-275. doi:10.1016/S0376-7388(00)80472-X [7] M. J. Abdekhodai and Y.-L. Cheng, “Diffusional Release of a Dispersed Solute from a Spherical Polymer Matrix,” Journal of Membrane Science, Vol. 115, No. 2, 1996, pp. 171-178. doi:10.1016/0376-7388(96)00018-X [8] M. J. Abdekhodai and Y.-L. Cheng, “Diffusional Release of a Dispersed Solute from a Dispersed solute from a Planar and Spherical Matrices into Finite External Volume,” Journal of Controlled Release, Vol. 43, No. 2-3, 1997, pp. 175-182. doi:10.1016/S0168-3659(96)01482-4 [9] Y. Zhou and X. Y. Wu, “Theoretical Analysis of Dispersed-Drug Release from Planar Matrices with a Boundary Layer in a Finite Medium,” Journal of Controlled Re- lease, Vol. 84, No. 1-2, 2002, pp. 1-13. doi:10.1016/S0168-3659(02)00263-8 [10] Y. Zhou and X. Y. Wu, “Modeling and Analysis of Dispersed-Drug Release into a Finite Medium from Sphere Ensembles with a Boundary Layer,” Journal of Controlled Release, Vol. 90, No.1, 2003, pp. 23-26. doi:10.1016/S0168-3659(03)00128-7 [11] Y. Zhou, J. S. Chu, T. Zhou and X. Y. Wu, “Modeling of Dispersed-Drug Release from Two-Dimensional Matrix Tablets,” Biomaterials, Vol. 26, No. 8, 2005, pp. 945-952. doi:10.1016/j.biomaterials.2004.03.034 [12] Y. Zhou, J. S. Chu, J. X. Li and X. Y. Wu, “Theoretical Analysis of Release Kinetics of Coated Tablets Containing Constant and Non-Constant Drug Reservoirs,” International Journal of Pharmaceutics, Vol. 385, No. 1-2, 2010, pp. 98-103. doi:10.1016/j.ijpharm.2009.10.039 [13] I. M. Helbling, J. C. D. Ibarra, J. A. Luna, M. I. Cabrera and R. J. A. Grau, “Modeling Dispersed-Drug Delivery from Planar Polymeric Systems: Optimizing Analytical Solutions,” International Journal of Pharmaceutics, Vol. 400, No. 1-2, 2010, pp. 131-137. doi:10.1016/j.ijpharm.2010.08.043
[1] J. Siepmann, H. Kranz, R. Bodmeier and N. A. Peppas, “HPMC-Matrices for Controlled Drug Delivery: A New Model Combining Diffusion, Swelling and Dissolution Mechanisms and Predicting the Release Kinetics,” Pharmaceutical Research, Vol. 16, No. 11, 1999, pp. 1748-1756. doi:10.1023/A:1018914301328 [2] J. Crank, “Mathematics of Diffusion,” 2nd Edition, Oxford University Press, Oxford, 1975. [3] T. Higuchi, “Rate of Release of Medicaments from Ointment Bases Containing Drugs in Suspension,” Journal of Pharmaceutical Sciences, Vol. 50, No. 10, 1961, pp. 874-875. doi:10.1002/jps.2600501018 [4] T. Higuchi, “Mechanism of Sustained-Action Medication. Theoretical Analysis of Solid Drugs Dispersed in Solid Matrices,” Journal of Pharmaceutical Sciences, Vol. 52, No. 12, 1963, pp. 1145-1149. doi:10.1002/jps.2600521210 [5] D. R. Paul and S. K. McSpadden, “Diffusional Release of a Solute from a Polymer Matrix,” Journal of Membrane Science, Vol. 1, 1976, pp. 33-48. doi:10.1016/S0376-7388(00)82256-5 [6] P. I. Lee, “Diffusional Release of a Solute from a Polymeric Matrix. Approximate Analytical Solution,” Journal of Membrane Science, Vol. 7, No. 3, 1980, pp. 255-275. doi:10.1016/S0376-7388(00)80472-X [7] M. J. Abdekhodai and Y.-L. Cheng, “Diffusional Release of a Dispersed Solute from a Spherical Polymer Matrix,” Journal of Membrane Science, Vol. 115, No. 2, 1996, pp. 171-178. doi:10.1016/0376-7388(96)00018-X [8] M. J. Abdekhodai and Y.-L. Cheng, “Diffusional Release of a Dispersed Solute from a Dispersed solute from a Planar and Spherical Matrices into Finite External Volume,” Journal of Controlled Release, Vol. 43, No. 2-3, 1997, pp. 175-182. doi:10.1016/S0168-3659(96)01482-4 [9] Y. Zhou and X. Y. Wu, “Theoretical Analysis of Dispersed-Drug Release from Planar Matrices with a Boundary Layer in a Finite Medium,” Journal of Controlled Re- lease, Vol. 84, No. 1-2, 2002, pp. 1-13. doi:10.1016/S0168-3659(02)00263-8 [10] Y. Zhou and X. Y. Wu, “Modeling and Analysis of Dispersed-Drug Release into a Finite Medium from Sphere Ensembles with a Boundary Layer,” Journal of Controlled Release, Vol. 90, No.1, 2003, pp. 23-26. doi:10.1016/S0168-3659(03)00128-7 [11] Y. Zhou, J. S. Chu, T. Zhou and X. Y. Wu, “Modeling of Dispersed-Drug Release from Two-Dimensional Matrix Tablets,” Biomaterials, Vol. 26, No. 8, 2005, pp. 945-952. doi:10.1016/j.biomaterials.2004.03.034 [12] Y. Zhou, J. S. Chu, J. X. Li and X. Y. Wu, “Theoretical Analysis of Release Kinetics of Coated Tablets Containing Constant and Non-Constant Drug Reservoirs,” International Journal of Pharmaceutics, Vol. 385, No. 1-2, 2010, pp. 98-103. doi:10.1016/j.ijpharm.2009.10.039 [13] I. M. Helbling, J. C. D. Ibarra, J. A. Luna, M. I. Cabrera and R. J. A. Grau, “Modeling Dispersed-Drug Delivery from Planar Polymeric Systems: Optimizing Analytical Solutions,” International Journal of Pharmaceutics, Vol. 400, No. 1-2, 2010, pp. 131-137. doi:10.1016/j.ijpharm.2010.08.043