Year 2013,
Volume: 2 Issue: 2, 56 - 64, 22.01.2014
Abstract
The mathematical modeling of drug release systems
has a significant potential to facilitate product development and to help
understanding complex pharmaceutical dosage forms. The findings of the modeling studies can help control some
of the parameters to obtain the
desired release performance.
In this article, we have introduced a Chebyshev collocation method, which is
based on collocation method for solving initial-boundary value problem
describing the Higuchi and power law.
References
- Higuchi T., “Rate of release of medicaments from ointment bases containing drugs in suspension” J. Pharm. Sci., 50, 874–875, 1961
- Pillai O., Dhanikula A. B., Panchagnula R.,”Drug delivery: an odyssey of 100 years” Current Opinion in Chemical Biology 5, 439–446, 2001
- Cartensen T., J., “Modeling and data treatment in the pharmaceutical sciences” Technomic Publishing Co. Inc., Lancaster, Basel, 1996
- Israel G., “In Modelli Matematici nelle Scienze Biologiche” P. ed. Edizioni Quattro Venti, Urbino, 1998
- Peppas N. A., “Analysis of Fickian and non-Fickian drug release from polymers”, Pharm. Acta Helv., 60, 110–111, 1985
- Ritger P. L., Peppas N. A., “A simple equation for description of solute release I. Fickian and non-Fickian release from nonswellable devices in the form of slabs spheres, cylinders or discs” J. Control. Release 5, 23–36, 1987.
- Ritger P. L., Peppas N. A., “A simple equation for description of solute release II. Fickian and anomalous release from swellable devices” J. Control. Release, 5, 37–42, 1987
- Siepmann J., Peppas N. A., “Modeling of drug release from delivery systems based on hydroxypropyl methylcellulose” Adv. Drug Deliv. Rev., 48, 139–157, 2001.
- Gao P., Nixon P. R., Skoug J. W., “Diffusion in HPMC gels. II. Prediction of drug release rates from hydrophilic matrix extended- release dosage forms” Pharm. Res. 12, 965–971, 1995
- Peppas N. A., Gurny R., Doelker E., Buri P., “Modelling of drug diffusion through swellable polymeric systems” J. Membr. Sci., 7, 241–253, 1980.
- Weibull W., “A statistical distribution of wide applicability” J. Appl. Mechan. 18, 293 –297, 19 Sahte P. M., Song Y. T., Shah V. P., “In-vitro dissolution profile comparison: statistics and analysis, model dependent approach” Pharm. Res. 13, 1799–1803, 1996
- Kosmidis K., Argyrakis P., Macheras P., “A Reappraisal of drug release laws using Monte Corlo simulations: the prevalence of the Weibull function” Pharm Res. 20(7), 988-95, 2003
- Gülsu M., Öztürk Y., Sezer M., “A new collocation method for solution of mixed linear integrodifferential-difference equations” Appl. Math. Comp., 216, 2183-2198, 2010
- Gülsu M., Öztürk Y., Sezer M., “Numerical approach for solving Volterra integro differential equations with piecewise intervals” J. Avdan. Research Appl. Math. 4(1), 23-37, 2012
- Gülsu M., Öztürk Y., Sezer M., “Approximate solution of the singular-perturbation problem on Chebyshev-Gauss grid” J. Avdan. Research Diff. Equa. 3(1), 1-13, 2012
- Öztürk Y., Gülsu M., “Approximate solution of linear generalized pantograph equations with variable coefficients on Chebyshev-Gauss grid” J. Avdan. Research Scie. Comp. 4(1), 36-51, 2012
- Gülsu M., Öztürk Y., Sezer M., “On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials” Appl. Math. Comp. 217, 4827-4833, 2011
- Body J., P., “Chebyshev and fourier spectral methods” University of Michigan, New York, 2000 Mason J., M., Handscomb D., S., “Chebyshev polynomials” Chapman and Hall/CRC, New York, 2003
Year 2013,
Volume: 2 Issue: 2, 56 - 64, 22.01.2014
Abstract
İlaç salım sistemlerinin matematiksel modellemesi
ürün geliştirme ve karmaşık farmasötik
dozaj formları anlama kolaylığı
sağlamada önemli bir potansiyele sahiptir. Modelleme
çalışmaları bulguları, bazı parametrelerin kontrolü, istenilen salım
performanslarının elde edilmesine yardımcı olmaktadır. Bu makalede Chebyshev
sıralama metodu ile taşıyıcı sistemlerden ilaç salım modeli Higuchi ve güç
modeli için nümerik sonuçlar verilmiştir.
References
- Higuchi T., “Rate of release of medicaments from ointment bases containing drugs in suspension” J. Pharm. Sci., 50, 874–875, 1961
- Pillai O., Dhanikula A. B., Panchagnula R.,”Drug delivery: an odyssey of 100 years” Current Opinion in Chemical Biology 5, 439–446, 2001
- Cartensen T., J., “Modeling and data treatment in the pharmaceutical sciences” Technomic Publishing Co. Inc., Lancaster, Basel, 1996
- Israel G., “In Modelli Matematici nelle Scienze Biologiche” P. ed. Edizioni Quattro Venti, Urbino, 1998
- Peppas N. A., “Analysis of Fickian and non-Fickian drug release from polymers”, Pharm. Acta Helv., 60, 110–111, 1985
- Ritger P. L., Peppas N. A., “A simple equation for description of solute release I. Fickian and non-Fickian release from nonswellable devices in the form of slabs spheres, cylinders or discs” J. Control. Release 5, 23–36, 1987.
- Ritger P. L., Peppas N. A., “A simple equation for description of solute release II. Fickian and anomalous release from swellable devices” J. Control. Release, 5, 37–42, 1987
- Siepmann J., Peppas N. A., “Modeling of drug release from delivery systems based on hydroxypropyl methylcellulose” Adv. Drug Deliv. Rev., 48, 139–157, 2001.
- Gao P., Nixon P. R., Skoug J. W., “Diffusion in HPMC gels. II. Prediction of drug release rates from hydrophilic matrix extended- release dosage forms” Pharm. Res. 12, 965–971, 1995
- Peppas N. A., Gurny R., Doelker E., Buri P., “Modelling of drug diffusion through swellable polymeric systems” J. Membr. Sci., 7, 241–253, 1980.
- Weibull W., “A statistical distribution of wide applicability” J. Appl. Mechan. 18, 293 –297, 19 Sahte P. M., Song Y. T., Shah V. P., “In-vitro dissolution profile comparison: statistics and analysis, model dependent approach” Pharm. Res. 13, 1799–1803, 1996
- Kosmidis K., Argyrakis P., Macheras P., “A Reappraisal of drug release laws using Monte Corlo simulations: the prevalence of the Weibull function” Pharm Res. 20(7), 988-95, 2003
- Gülsu M., Öztürk Y., Sezer M., “A new collocation method for solution of mixed linear integrodifferential-difference equations” Appl. Math. Comp., 216, 2183-2198, 2010
- Gülsu M., Öztürk Y., Sezer M., “Numerical approach for solving Volterra integro differential equations with piecewise intervals” J. Avdan. Research Appl. Math. 4(1), 23-37, 2012
- Gülsu M., Öztürk Y., Sezer M., “Approximate solution of the singular-perturbation problem on Chebyshev-Gauss grid” J. Avdan. Research Diff. Equa. 3(1), 1-13, 2012
- Öztürk Y., Gülsu M., “Approximate solution of linear generalized pantograph equations with variable coefficients on Chebyshev-Gauss grid” J. Avdan. Research Scie. Comp. 4(1), 36-51, 2012
- Gülsu M., Öztürk Y., Sezer M., “On the solution of the Abel equation of the second kind by the shifted Chebyshev polynomials” Appl. Math. Comp. 217, 4827-4833, 2011
- Body J., P., “Chebyshev and fourier spectral methods” University of Michigan, New York, 2000 Mason J., M., Handscomb D., S., “Chebyshev polynomials” Chapman and Hall/CRC, New York, 2003
There are 18 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Matematik |
| Authors | |
| Publication Date | January 22, 2014 |
| Published in Issue | Year 2013 Volume: 2 Issue: 2 |
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Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
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https://doi.org/10.25092/baunfbed.320025
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