Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012, Article ID 653720, 26 pages
http://dx.doi.org/10.1155/2012/653720
Research Article

Nonlinearities in Drug Release Process from Polymeric Microparticles: Long-Time-Scale Behaviour

1Department of Natural and Synthetic Polymers, Faculty of Chemical Engineering and Environmental Protection, “Gheorghe Asachi” Technical University of Iasi, Prof. Dr. Docent Dimitrie Mangeron Road, No. 73, 700050 Iasi, Romania
2Department of Physics, Faculty of Machine Manufacturing and Industrial Management, “Gheorghe Asachi” Technical University of Iasi, Prof. Dr. Docent Dimitrie Mangeron Road, No. 59A, 700050 Iasi, Romania
3Department of Materials Engineering and Industrial Security, Faculty of Materials Science and Engineering, “Gheorghe Asachi” Technical University of Iasi, Prof. Dr. Docent Dimitrie Mangeron Road, No. 59A, 700050 Iasi, Romania
4Department of Technology of Information, Mathematics and Physics, Faculty of Letters and Sciences, Petroleum-Gas University of Ploiesti, Bucuresti Boulevard, No. 39, 100680 Ploiesti, Romania
5Physics Department, “Al. I. Cuza” University, Carol I Road, No. 11, 700506 Iasi, Romania
6Lasers, Atoms and Molecules Physics Laboratory, University of Science and Technology, Villeneuve d’Ascq, 59655 Lille, France

Received 4 May 2012; Revised 8 July 2012; Accepted 20 July 2012

Academic Editor: Zhiwei Gao

Copyright © 2012 Elena Simona Bacaita et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. J. Shukla and J. C. Price, “Effect of drug loading and molecular weight of cellulose acetate propionate on the release characteristics of theophylline microspheres,” Pharmaceutical Research, vol. 8, no. 11, pp. 1396–1400, 1991. View at Google Scholar · View at Scopus
  2. N. M. Najib, M. Suleiman, and A. Malakh, “Characteristics of the in vitro release of ibuprofen from polyvinyl pyrrolidone solid dispersions,” International Journal of Pharmaceutics, vol. 32, no. 2-3, pp. 229–236, 1986. View at Google Scholar · View at Scopus
  3. F. J. Wang and C. H. Wang, “Etanidazole-loaded microspheres fabricated by spray-drying different poly(lactide/glycolide) polymers: effects on microsphere properties,” Journal of Biomaterials Science, vol. 14, no. 2, pp. 157–183, 2003. View at Publisher · View at Google Scholar · View at Scopus
  4. J. M. Bezemer, R. Radersma, D. W. Grijpma, P. J. Dijkstra, C. A. Van Blitterswijk, and J. Feijen, “Microspheres for protein delivery prepared from amphiphilic multiblock copolymers 2,” Journal of Controlled Release, vol. 67, no. 2-3, pp. 249–260, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. G. Crotts, H. Sah, and T. G. Park, “Adsorption determines in-vitro protein release rate from biodegradable microspheres: quantitative analysis of surface area during degradation,” Journal of Controlled Release, vol. 47, no. 1, pp. 101–111, 1997. View at Publisher · View at Google Scholar · View at Scopus
  6. H. Robson, D. Q. M. Craig, and D. Deutsch, “An investigation into the release of cefuroxime axetil from taste-masked stearic acid microspheres—III. The use of DSC and HSDSC as means of characterising the interaction of the microspheres with buffered media,” International Journal of Pharmaceutics, vol. 201, no. 2, pp. 211–219, 2000. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Siepmann, N. Faisant, J. Akiki, J. Richard, and J. P. Benoit, “Effect of the size of biodegradable microparticles on drug release: experiment and theory,” Journal of Controlled Release, vol. 96, no. 1, pp. 123–134, 2004. View at Publisher · View at Google Scholar · View at Scopus
  8. P. Borgquist, A. Körner, L. Piculell, A. Larsson, and A. Axelsson, “A model for the drug release from a polymer matrix tablet-effects of swelling and dissolution,” Journal of Controlled Release, vol. 113, no. 3, pp. 216–225, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. B. Narasimhan and N. A. Peppas, “Molecular analysis of drug delivery systems controlled by dissolution of the polymer carrier,” Journal of Pharmaceutical Sciences, vol. 86, no. 3, pp. 297–304, 1997. View at Publisher · View at Google Scholar · View at Scopus
  10. I. Katzhendler, A. Hoffman, A. Goldberger, and M. Friedman, “Modeling of drug release from erodible tablets,” Journal of Pharmaceutical Sciences, vol. 86, no. 1, pp. 110–115, 1997. View at Google Scholar · View at Scopus
  11. C. Raman, C. Berkland, K. Kim, and D. W. Pack, “Modeling small-molecule release from PLG microspheres: effects of polymer degradation and nonuniform drug distribution,” Journal of Controlled Release, vol. 103, no. 1, pp. 149–158, 2005. View at Publisher · View at Google Scholar · View at Scopus
  12. R. S. Harland, C. Dubernet, J. P. Benoit, and N. A. Peppas, “A model of dissolution-controlled, diffusional drug release from non-swellable polymeric microspheres,” Journal of Controlled Release, vol. 7, no. 3, pp. 207–215, 1988. View at Google Scholar · View at Scopus
  13. M. I. Cabrera, J. A. Luna, and R. J. A. Grau, “Modeling of dissolution-diffusion controlled drug release from planar polymeric systems with finite dissolution rate and arbitrary drug loading,” Journal of Membrane Science, vol. 280, no. 1-2, pp. 693–704, 2006. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Higuchi, “Mechanism of sustained-action medication. Theoretical analysis of rate released of solid drugs dispersed in solid matrices,” Journal of Pharmaceutical Sciences, vol. 52, no. 12, pp. 1145–1149, 1963. View at Google Scholar
  15. B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Co., San Francisco, Calif, USA, 1982. View at Zentralblatt MATH
  16. D. Stauffer and H. E. Stanley, From Newton to Mandelbrot, Academic Press, New York, NY, USA, 1996.
  17. G. V. Kozlov and G. E. Zaikov, Fractals and Local Order in Polymeric Materials, Nova Science, New York, NY, USA, 2001.
  18. V. U. Novikov and G. V. Kozlov, “Structure and properties of polymers in terms of the fractal approach,” Russian Chemical Reviews, vol. 69, no. 6, pp. 523–549, 2000. View at Publisher · View at Google Scholar · View at Scopus
  19. P. L. Ritger and N. A. Peppas, “A simple equation for desciption of solute release I. Fickian and non-Fickian release from non-swellable devices in the form of slabs, spheres, cylinders or discs,” Journal of Controlled Release, vol. 5, no. 1, pp. 23–36, 1987. View at Google Scholar · View at Scopus
  20. N. A. Peppas and J. J. Sahlin, “A simple equation for the description of solute release—III. Coupling of diffusion and relaxation,” International Journal of Pharmaceutics, vol. 57, no. 2, pp. 169–172, 1989. View at Publisher · View at Google Scholar · View at Scopus
  21. T. Alfrey, E. F. Gurnee, and W. G. Lloyd, “Diffusion in glassy polymers,” Journal of Polymer Science Part C, vol. 12, pp. 249–261, 1966. View at Google Scholar
  22. S. Popescu, Actual Issues in the Physics of Self-Structured Systems, Tehnopress, Iasi, Romania, 2003.
  23. K. Kosmidis, P. Argyrakis, and P. Macheras, “Fractal kinetics in drug release from finite fractal matrices,” Journal of Chemical Physics, vol. 119, no. 12, pp. 6373–6377, 2003. View at Publisher · View at Google Scholar · View at Scopus
  24. R. Villalobos, S. Cordero, A. Maria Vidales, and A. Dominguez, “In silico study on the effects of matrix structure in controlled drug release,” Physica A, vol. 367, pp. 305–318, 2006. View at Publisher · View at Google Scholar · View at Scopus
  25. R. Villalobos, A. M. Vidales, S. Cordero, D. Quintanar, and A. Dominguez, “Monte carlo simulation of diffusion-limited drug release from finite fractal matrices,” Journal of Sol-Gel Science and Technology, vol. 37, no. 3, pp. 195–199, 2006. View at Publisher · View at Google Scholar · View at Scopus
  26. R. Villalobos, A. Dominguez, A. Ganem, A. M. Vidales, and S. Cordero, “One-dimensional drug release from finite Menger sponges: in silico simulation,” Chaos, Solitons and Fractals, vol. 42, no. 5, pp. 2875–2884, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. P. Costa and J. M. Sousa Lobo, “Modeling and comparison of dissolution profiles,” European Journal of Pharmaceutical Sciences, vol. 13, no. 2, pp. 123–133, 2001. View at Publisher · View at Google Scholar · View at Scopus
  28. L. Nottale, Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity, World Scientific Publishing, Singapore, 1993.
  29. L. Nottale, Scale Relativity and Fractal Space-Time—A New Approach to Unifying Relativity and Quantum Mechanics, Imperial College Press, London, UK, 2011.
  30. L. Nottale, “Fractals and the quantum theory of space time,” International Journal of Modern Physics A, vol. 4, no. 19, pp. 5047–5117, 1989. View at Google Scholar
  31. N. A. Peppas, “Analysis of Fickian and non-Fickian drug release from polymers,” Pharmaceutica Acta Helvetiae, vol. 60, no. 4, pp. 110–111, 1985. View at Google Scholar · View at Scopus
  32. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Butterworth Heinemann, Oxford, UK, 2nd edition, 1987.
  33. J. F. Gouyet, Physique et Structures Fractals, Masson, Paris, France, 1992.
  34. M. S. El Naschie, O. E. Rössler, and I. Prigogine, Quantum Mechanics, Diffusion and Chaotic Fractals, Elsevier, Oxford, UK, 1995.
  35. P. Weibel, G. Ord, and O. E. Rösler, Space Time Physics and Fractality, Springer, Dordrecht, The Netherlands, 2005.
  36. M. Agop, N. Forna, I. Casian-Botez, and C. Bejenariu, “New theoretical approach of the physical processes in nanostructures,” Journal of Computational and Theoretical Nanoscience, vol. 5, no. 4, pp. 483–489, 2008. View at Google Scholar · View at Scopus
  37. I. Casian-Botez, M. Agop, P. Nica, V. Paun, and G. V. Munceleanu, “Conductive and convective types behaviors at nano-time scales,” Journal of Computational and Theoretical Nanoscience, vol. 7, no. 11, pp. 2271–2280, 2010. View at Publisher · View at Google Scholar · View at Scopus
  38. S. Bacaita, C. Uritu, M. Popa, A. Uliniuc, C. Peptu, and M. Agop, “Drug release kinetics from polymer matrix through the fractal approximation of motion,” Smart Materials Research, vol. 2012, Article ID 264609, 8 pages, 2012. View at Publisher · View at Google Scholar
  39. D. Magop, S. Bacaita, C. Peptu, M. Popa, and M. Agop, “Non-differentiability at mesoscopic scale in drug release processes from polymer microparticles,” Materiale Plastice, vol. 49, no. 2, pp. 101–105, 2012. View at Google Scholar
  40. F. Bowman, Introduction to Elliptic Functions: With Applications, Dover, New York, NY, USA, 1961.
  41. M. Toda, Theory of Nonlinear Lattices, Springer, Berlin, Germany, 1989.
  42. A. J. Lichtenberg, Phase-Space Dynamics of Particle, John Wiley and Sons, New York, NY, USA, 1969.