A nonlinear two compartmental fractional derivative model

This study presents a new nonlinear two compartmental model and its application to the evaluation of valproic acid (VPA) pharmacokinetics in human volunteers after oral administration. We have used literature VPA concentrations. In the model, the integer order derivatives are replaced by derivatives...

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Bibliographic Details
Published in:European journal of drug metabolism and pharmacokinetics 2011-12, Vol.36 (4), p.189-196
Main Authors: POPOVIC, Jovan K, DOLICANIN, Diana, RAPAIC, Milan R, POPOVIC, Stevan L, PILIPOVIC, Stevan, ATANACKOVIC, Teodor M
Format: Article
Language:English
Subjects:
Biological and medical sciences
Biomedical and Life Sciences
Biomedicine
Computer Simulation
Human Physiology
Humans
Medical Biochemistry
Medical sciences
Models, Biological
Nonlinear Dynamics
Original Paper
Pharmaceutical Sciences/Technology
Pharmacology. Drug treatments
Pharmacology/Toxicology
Pharmacy
Valproic Acid - pharmacokinetics
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Summary:This study presents a new nonlinear two compartmental model and its application to the evaluation of valproic acid (VPA) pharmacokinetics in human volunteers after oral administration. We have used literature VPA concentrations. In the model, the integer order derivatives are replaced by derivatives of real order often called fractional order derivatives. Physically that means that the history (memory) of a biological process, realized as a transfer from one compartment to another, is taken into account with the mass balance conservation observed. Our contribution is the analysis of a specific nonlinear two compartmental model with the application in evaluation of VPA pharmacokinetics. The agreement of the values predicted by the proposed model with the values obtained through experiments is shown to be good. Thus, pharmacokinetics of VPA after oral application can be described well by a nonlinear two compartmental model with fractional derivatives of the same order proposed here. Parameters in the model are determined by the least-squares method and the particle swarm optimization (PSO) numerical procedure is used. The results show that the nonlinear fractional order two compartmental model for VPA pharmacokinetics is superior in comparison to the classical (integer order) linear two compartmental model and to the linear fractional order two compartmental model.
ISSN:0378-7966
2107-0180
DOI:10.1007/s13318-011-0057-6