Fractional kinetics in multi-compartmental systems
Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we ext...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Dokoumetzidis, Aristides [verfasserIn] Magin, Richard [verfasserIn] Macheras, Panos [verfasserIn] |
|---|
| Format: |
E-Artikel |
|---|---|
| Sprache: |
Englisch |
| Erschienen: |
2010 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Journal of Pharmacokinetics and Biopharmaceutics - Kluwer Academic Publishers-Plenum Publishers, 1973, 37(2010), 5 vom: 01. Okt., Seite 507-524 |
|---|---|
| Übergeordnetes Werk: |
volume:37 ; year:2010 ; number:5 ; day:01 ; month:10 ; pages:507-524 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10928-010-9170-4 |
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| 520 | |a Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. | ||
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10.1007/s10928-010-9170-4 doi (DE-627)SPR01470921X (SPR)s10928-010-9170-4-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in multi-compartmental systems 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. Compartmental analysis (dpeaa)DE-He213 Numerical solutions (dpeaa)DE-He213 Fractional differential equations (dpeaa)DE-He213 Parameter estimation (dpeaa)DE-He213 Magin, Richard verfasserin aut Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 37(2010), 5 vom: 01. Okt., Seite 507-524 (DE-627)SPR014694166 nnns volume:37 year:2010 number:5 day:01 month:10 pages:507-524 https://dx.doi.org/10.1007/s10928-010-9170-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 37 2010 5 01 10 507-524 |
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10.1007/s10928-010-9170-4 doi (DE-627)SPR01470921X (SPR)s10928-010-9170-4-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in multi-compartmental systems 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. Compartmental analysis (dpeaa)DE-He213 Numerical solutions (dpeaa)DE-He213 Fractional differential equations (dpeaa)DE-He213 Parameter estimation (dpeaa)DE-He213 Magin, Richard verfasserin aut Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 37(2010), 5 vom: 01. Okt., Seite 507-524 (DE-627)SPR014694166 nnns volume:37 year:2010 number:5 day:01 month:10 pages:507-524 https://dx.doi.org/10.1007/s10928-010-9170-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 37 2010 5 01 10 507-524 |
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10.1007/s10928-010-9170-4 doi (DE-627)SPR01470921X (SPR)s10928-010-9170-4-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in multi-compartmental systems 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. Compartmental analysis (dpeaa)DE-He213 Numerical solutions (dpeaa)DE-He213 Fractional differential equations (dpeaa)DE-He213 Parameter estimation (dpeaa)DE-He213 Magin, Richard verfasserin aut Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 37(2010), 5 vom: 01. Okt., Seite 507-524 (DE-627)SPR014694166 nnns volume:37 year:2010 number:5 day:01 month:10 pages:507-524 https://dx.doi.org/10.1007/s10928-010-9170-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 37 2010 5 01 10 507-524 |
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10.1007/s10928-010-9170-4 doi (DE-627)SPR01470921X (SPR)s10928-010-9170-4-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in multi-compartmental systems 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. Compartmental analysis (dpeaa)DE-He213 Numerical solutions (dpeaa)DE-He213 Fractional differential equations (dpeaa)DE-He213 Parameter estimation (dpeaa)DE-He213 Magin, Richard verfasserin aut Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 37(2010), 5 vom: 01. Okt., Seite 507-524 (DE-627)SPR014694166 nnns volume:37 year:2010 number:5 day:01 month:10 pages:507-524 https://dx.doi.org/10.1007/s10928-010-9170-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 37 2010 5 01 10 507-524 |
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10.1007/s10928-010-9170-4 doi (DE-627)SPR01470921X (SPR)s10928-010-9170-4-e DE-627 ger DE-627 rakwb eng Dokoumetzidis, Aristides verfasserin aut Fractional kinetics in multi-compartmental systems 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. Compartmental analysis (dpeaa)DE-He213 Numerical solutions (dpeaa)DE-He213 Fractional differential equations (dpeaa)DE-He213 Parameter estimation (dpeaa)DE-He213 Magin, Richard verfasserin aut Macheras, Panos verfasserin aut Enthalten in Journal of Pharmacokinetics and Biopharmaceutics Kluwer Academic Publishers-Plenum Publishers, 1973 37(2010), 5 vom: 01. Okt., Seite 507-524 (DE-627)SPR014694166 nnns volume:37 year:2010 number:5 day:01 month:10 pages:507-524 https://dx.doi.org/10.1007/s10928-010-9170-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA GBV_ILN_40 AR 37 2010 5 01 10 507-524 |
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Dokoumetzidis, Aristides Magin, Richard Macheras, Panos |
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Elektronische Aufsätze |
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Dokoumetzidis, Aristides |
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10.1007/s10928-010-9170-4 |
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fractional kinetics in multi-compartmental systems |
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Fractional kinetics in multi-compartmental systems |
| abstract |
Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. |
| abstractGer |
Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. |
| abstract_unstemmed |
Abstract Fractional calculus, the branch of calculus dealing with derivatives of non-integer order (e.g., the half-derivative) allows the formulation of fractional differential equations (FDEs), which have recently been applied to pharmacokinetics (PK) for one-compartment models. In this work we extend that theory to multi-compartmental models. Unlike systems defined by a single ordinary differential equation (ODE), considering fractional multi-compartmental models is not as simple as changing the order of the ordinary derivatives of the left-hand side of the ODEs to fractional orders. The latter may produce inconsistent systems which violate mass balance. We present a rationale for fractionalization of ODEs, which produces consistent systems and allows processes of different fractional orders in the same system. We also apply a method of solving such systems based on a numerical inverse Laplace transform algorithm, which we demonstrate that is consistent with analytical solutions when these are available. As examples of our approach, we consider two cases of a basic two-compartment PK model with a single IV dose and multiple oral dosing, where the transfer from the peripheral to the central compartment is of fractional order α < 1, accounting for anomalous kinetics and deep tissue trapping, while all other processes are of the usual order 1. Simulations with the studied systems are performed using the numerical inverse Laplace transform method. It is shown that the presence of a transfer rate of fractional order produces a non-exponential terminal phase, while multiple dose and constant infusion systems never reach steady state and drug accumulation carries on indefinitely. The IV fractional system is also fitted to PK data and parameter values are estimated. In conclusion, our approach allows the formulation of systems of FDEs, mixing different fractional orders, in a consistent manner and also provides a method for the numerical solution of these systems. |
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Fractional kinetics in multi-compartmental systems |
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