A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems

Mustafa Gülsu; Yalçın Öztürk; Aydan Gülsu

doi:10.17100/nevbiltek.210873

A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems

Year 2013, Volume: 2 Issue: 2, 56 - 64, 22.01.2014

Mustafa Gülsu , Yalçın Öztürk , Aydan Gülsu

https://doi.org/10.17100/nevbiltek.210873

Cited By: 1

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.

Keywords

Drug release systems, higuchi law, power law, collocation method.

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

İlaç Salım Sistemleri için Modifiye Epidemiyolojik Modelin Sayısal Çözümü

Year 2013, Volume: 2 Issue: 2, 56 - 64, 22.01.2014

Mustafa Gülsu , Yalçın Öztürk , Aydan Gülsu

https://doi.org/10.17100/nevbiltek.210873

Cited By: 1

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.

Keywords

İlaç salım sistemleri, higuchi modeli, güç modeli, sıralama metodu

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	Mustafa Gülsu Yalçın Öztürk Aydan Gülsu
Publication Date	January 22, 2014
Published in Issue	Year 2013 Volume: 2 Issue: 2

Cite

APA	Gülsu, M., Öztürk, Y., & Gülsu, A. (2014). A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems. Nevşehir Bilim Ve Teknoloji Dergisi, 2(2), 56-64. https://doi.org/10.17100/nevbiltek.210873
AMA	Gülsu M, Öztürk Y, Gülsu A. A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems. Nevşehir Bilim ve Teknoloji Dergisi. January 2014;2(2):56-64. doi:10.17100/nevbiltek.210873
Chicago	Gülsu, Mustafa, Yalçın Öztürk, and Aydan Gülsu. “A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems”. Nevşehir Bilim Ve Teknoloji Dergisi 2, no. 2 (January 2014): 56-64. https://doi.org/10.17100/nevbiltek.210873.
EndNote	Gülsu M, Öztürk Y, Gülsu A (January 1, 2014) A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems. Nevşehir Bilim ve Teknoloji Dergisi 2 2 56–64.
IEEE	M. Gülsu, Y. Öztürk, and A. Gülsu, “A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems”, Nevşehir Bilim ve Teknoloji Dergisi, vol. 2, no. 2, pp. 56–64, 2014, doi: 10.17100/nevbiltek.210873.
ISNAD	Gülsu, Mustafa et al. “A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems”. Nevşehir Bilim ve Teknoloji Dergisi 2/2 (January 2014), 56-64. https://doi.org/10.17100/nevbiltek.210873.
JAMA	Gülsu M, Öztürk Y, Gülsu A. A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems. Nevşehir Bilim ve Teknoloji Dergisi. 2014;2:56–64.
MLA	Gülsu, Mustafa et al. “A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems”. Nevşehir Bilim Ve Teknoloji Dergisi, vol. 2, no. 2, 2014, pp. 56-64, doi:10.17100/nevbiltek.210873.
Vancouver	Gülsu M, Öztürk Y, Gülsu A. A Numerical Approach for Solving Modified Epidemiological Model for Drug Release Systems. Nevşehir Bilim ve Teknoloji Dergisi. 2014;2(2):56-64.