An Adjusted Pharmacokinetic Equation for Predicting Drug Levels In Vivo Based on In Vitro Square Root of Time Release Kinetics

Abstract

An adjusted pharmacokinetic equation that predicts in vivo plasma drug profiles for controlled release (CR) dosage forms having square root of time drug release kinetics has been derived. The CR hydrogel tablets containing hydroxypropyl methylcellulose (HPMC) were formulated with theophylline and Fast Flo® lactose, to produce tablets with HPMC K100MP content of 30% w/w. Plasma profiles in vivo were determined from four male beagle dogs. Tablet gel strength (Γ) was measured as previously reported. Results show drug release in vitro follows square root of time kinetics for the formulation in all media (purified H₂O, 0.1 N HCl, and pH 6.8 phosphate buffer). The Γ values were not significantly different (p>0.05) among the tablets in different dissolution media, with absolute values in DI H₂O of 6600 erg/cm³, which is above the minimum threshold value of Γ (≈6000 erg/cm³) needed for acceptable in vitro/in vivo correlation. Comparison of predicted and observed plasma profiles in vivo, using the adjusted square root pharmacokinetic equation, showed a better fit of the overall pattern and absolute values of the in vivo data as compared to equations that assume first- or zero-order drug release from the HPMC based tablets. The adjusted square root pharmacokinetic equation can serve as a valuable aid in the design of formulations to yield a desired plasma profile in vivo and provides supporting evidence to the mechanism of drug release in vitro.

Keywords:

• Pharmacokinetic equation
• Square root of time kinetics
• Hydrogel tablet
• Controlled release
• In vitro/in vivo correlation
• Gel strength
• Hydroxypropyl methylcellulose
• Beagle dog
• Theophylline
• Rheology