Fractional kinetics in drug absorption and disposition processes
Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differe...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dokoumetzidis, Aristides [verfasserIn] Macheras, Panos [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2009 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of Pharmacokinetics and Biopharmaceutics - Kluwer Academic Publishers-Plenum Publishers, 1973, 36(2009), 2 vom: Apr., Seite 165-178 |
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volume:36 ; year:2009 ; number:2 ; month:04 ; pages:165-178 |
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10.1007/s10928-009-9116-x |
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| 520 | |a Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. | ||
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10.1007/s10928-009-9116-x doi (DE-627)SPR014708639 (SPR)s10928-009-9116-x-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in drug absorption and disposition processes 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. Fractional kinetics (dpeaa)DE-He213 Anomalous kinetics (dpeaa)DE-He213 Power-law (dpeaa)DE-He213 Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 36(2009), 2 vom: Apr., Seite 165-178 (DE-627)SPR014694166 nnns volume:36 year:2009 number:2 month:04 pages:165-178 https://dx.doi.org/10.1007/s10928-009-9116-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 36 2009 2 04 165-178 |
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10.1007/s10928-009-9116-x doi (DE-627)SPR014708639 (SPR)s10928-009-9116-x-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in drug absorption and disposition processes 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. Fractional kinetics (dpeaa)DE-He213 Anomalous kinetics (dpeaa)DE-He213 Power-law (dpeaa)DE-He213 Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 36(2009), 2 vom: Apr., Seite 165-178 (DE-627)SPR014694166 nnns volume:36 year:2009 number:2 month:04 pages:165-178 https://dx.doi.org/10.1007/s10928-009-9116-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 36 2009 2 04 165-178 |
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10.1007/s10928-009-9116-x doi (DE-627)SPR014708639 (SPR)s10928-009-9116-x-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in drug absorption and disposition processes 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. Fractional kinetics (dpeaa)DE-He213 Anomalous kinetics (dpeaa)DE-He213 Power-law (dpeaa)DE-He213 Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 36(2009), 2 vom: Apr., Seite 165-178 (DE-627)SPR014694166 nnns volume:36 year:2009 number:2 month:04 pages:165-178 https://dx.doi.org/10.1007/s10928-009-9116-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 36 2009 2 04 165-178 |
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10.1007/s10928-009-9116-x doi (DE-627)SPR014708639 (SPR)s10928-009-9116-x-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in drug absorption and disposition processes 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. Fractional kinetics (dpeaa)DE-He213 Anomalous kinetics (dpeaa)DE-He213 Power-law (dpeaa)DE-He213 Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 36(2009), 2 vom: Apr., Seite 165-178 (DE-627)SPR014694166 nnns volume:36 year:2009 number:2 month:04 pages:165-178 https://dx.doi.org/10.1007/s10928-009-9116-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 36 2009 2 04 165-178 |
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10.1007/s10928-009-9116-x doi (DE-627)SPR014708639 (SPR)s10928-009-9116-x-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in drug absorption and disposition processes 2009 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. Fractional kinetics (dpeaa)DE-He213 Anomalous kinetics (dpeaa)DE-He213 Power-law (dpeaa)DE-He213 Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 36(2009), 2 vom: Apr., Seite 165-178 (DE-627)SPR014694166 nnns volume:36 year:2009 number:2 month:04 pages:165-178 https://dx.doi.org/10.1007/s10928-009-9116-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 36 2009 2 04 165-178 |
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Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. |
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Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. |
| abstract_unstemmed |
Abstract We explore the use of fractional order differential equations for the analysis of datasets of various drug processes that present anomalous kinetics, i.e. kinetics that are non-exponential and are typically described by power-laws. A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. Fractional kinetics offers an elegant description of anomalous kinetics, with a valid scientific basis, since it has already been applied in problems of diffusion in other fields, and describes well the data. |
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Fractional kinetics in drug absorption and disposition processes |
| url |
https://dx.doi.org/10.1007/s10928-009-9116-x |
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true |
| author2 |
Macheras, Panos |
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Macheras, Panos |
| ppnlink |
SPR014694166 |
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c |
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| doi_str |
10.1007/s10928-009-9116-x |
| up_date |
2024-07-04T02:46:40.212Z |
| _version_ |
1803614893074546688 |
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A fractional differential equation corresponds to a differential equation with a derivative of fractional order. The fractional equivalents of the “zero-” and “first-order” processes are derived. The fractional zero-order process is a power-law while the fractional first-order process is a Mittag–Leffler function. The latter behaves as a stretched exponential for early times and as a power-law for later times. Applications of these two basic results for drug dissolution/release and drug disposition are presented. The fractional model of dissolution is fitted successfully to datasets taken from literature of in vivo dissolution curves. Also, the proposed pharmacokinetic model is fitted to a dataset which exhibits power-law terminal phase. The Mittag–Leffler function describes well the data for small and large time scales and presents an advantage over empirical power-laws which go to infinity as time approaches zero. The proposed approach is compared conceptually with fractal kinetics, an alternative approach to describe datasets with non exponential kinetics. 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7.400819 |