Modeling And Analyzing Of The Pharmacokinetics Based On Fractional Calculus

Compartmental analysis initially developed from studies of the uptake anddistribution of radioactive tracers, but today it plays a fundamental role in many parts ofmedicine, bioengineering and environmental science. The specialized fields ofpharmacokinetics and pharmacology, for example, rely on compartmental models topredict the safe and most effective way to administer drugs. In its classicalversion,compartmental analysis is based on mathematical models, typically in the formof systems of ordinary differential equations, that are widely used to characterize the timeof uptake/elimination of a drug.With the rapid development of science and deeper research, people have found thata lot of drugs process and pharmacokinetics of biological systems are based on theanomalous diffusion, which cannot be accurately fitted with the traditional model for theexperimental data. fractional calculus applied to the pharmacokinetic modeling can bettercharacterize the nature of memory and hereditary of biological systems and drug process,in particular one exhibit anomalous diffusion and the phenomenon of power-lawdistribution. The model can be achieved by adjust the parameters to accurately fit. So thispaper mainly used fractional calculus to conduct research on pharmacokinetics model.Firstly, according to the three common drug administrations routes (intravenousinjection, intravenous infusion, oral administration), the specific ordinary differentialequations describing the process of pharmacokinetics are introduced.Secondly, in this paper, the reasons, modeling operations and the effect of thefractional calculus pharmacokinetics model are summarized, and analytical&numericalsolutions of the compartment model simulation analysis are also presented. Finally, a brief introduction to the fractal pharmacokinetics, stochasticpharmacokinetics was presented in this paper, as well as the comparison of the threemodels.