Fractional kinetics in drug absorption and disposition processes

Area of Science:

• Pharmacokinetics and Drug Development
• Mathematical Modeling
• Nonlinear Dynamics

Background:

• Anomalous kinetics in drug processes often exhibit non-exponential behavior, typically described by power-laws.
• Existing models may struggle to accurately represent data across all time scales.

Purpose of the Study:

• To explore fractional order differential equations for analyzing anomalous drug kinetics.
• To derive and apply fractional equivalents of zero- and first-order processes.

Main Methods:

• Derivation of fractional zero-order (power-law) and first-order (Mittag-Leffler function) processes.
• Application of these models to drug dissolution and disposition datasets.
• Fitting fractional models to in vivo dissolution curves and pharmacokinetic data with power-law tails.

Main Results:

• The fractional first-order process, a Mittag-Leffler function, effectively models data at both early (stretched exponential) and late (power-law) times.
• Successful fitting of the fractional dissolution model to literature data.
• The proposed pharmacokinetic model accurately described data exhibiting power-law terminal phases.
• The Mittag-Leffler function offers advantages over empirical power-laws, particularly near time zero.

Conclusions:

• Fractional kinetics provides an elegant and scientifically valid approach for describing anomalous drug kinetics.
• The proposed fractional models demonstrate superior performance compared to traditional methods for datasets with non-exponential behavior.
• This framework has broad applicability in analyzing complex drug release and disposition profiles.