A new approach to the compartmental analysis in pharmacokinetics: fractional time evolution of diclofenac

Abstract

This study presents a new two compartmental model and its application to the evaluation of diclofenac pharmacokinetics in a small number of healthy adults, during a bioequivalence trial. In the model the integer order derivatives are replaced by derivatives of real order often called fractional order derivatives. Physically that means that a history (memory) of a biological process, realized as a transfer from one compartment to another one with the mass balance conservation, is taken into account. This kind of investigations in pharmacokinetics is founded by Dokoumetzidis and Macheras through the one compartmental models while our contribution is the analysis of multi-dimensional compartmental models with the applications of the two compartmental model in evaluation of diclofenac pharmacokinetics. Two experiments were preformed with 12 healthy volunteers with two slow release 100 mg diclofenac tablet formulations. The agreement of the values predicted by the proposed model with the values obtained through experiments is shown to be good. Thus, pharmacokinetics of slow release diclofenac can be described well by a specific two compartmental model with fractional derivatives of the same order. 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 fractional order two compartmental model for diclofenac is superior in comparison to the classical two compartmental model. Actually this is true in general case since the classical one is a special case of the fractional one.

Controlled Drug Administration by a Fractional PID

“…The designed controller not only has a high gain margin but also exhibits excellent behaviour with respect to noise rejection in the closed loops and attenuation of externally applied disturbances. The proposed control approach is a good candidate for the control of other drugs that follow such fractionalorder dynamics such as Mibefradil (Fuite et al [2002]) or Diclofenac (Popović et al [2010]). …”

“…In practice, non-linearities, anomalous diffusion, fractional-order kinetics, diffusion accross fractal manifolds, synergetic and competitive action and a great many other factors render this approach not applicable (see Dokoumetzidis and Macheras [2008]). Recently, a significant number of relevant publications has emerged; see Popović et al [2012], Verotta [2010a,b], Pereira [2010], Dokoumetzidis et al [2010b], Popović et al [2010].…”

Relation between fractional order models and diffusion in the body

“…Compartmental models for pharmacokinetics (PK) have been generalized using fractional calculus in order to extend the systems to the form of fractional-order differential equations (Dokoumetzidis and Macheras (2009);Popovic et al (2010)). PK can be defined as the study of drug disposition in the body and it focuses on drug plasma (blood) amount changes.…”

“…The first compartment represents the place where the drug is applied (plasma) and the second compartment represents the target organ (muscle). The basic idea behind this model can be used to model the diffusion process in the human body by a multi-compartmental model (Dokoumetzidis and Macheras (2009);Popovic et al (2010); Copot et al (2013)). The model is formulated while maintaining the mass balance principles.…”

Validation of Individual Non-Linear Predictive Pharmacokinetic Parameters in a Rabbit Phenytoin Model

“…Individualized components are k, λ, X, Y. All parameters for model are determined through the least square numerical procedure described earlier [18]. The optimal model parameters are those for which the mean square error value is minimal.…”