By Jean-Maurice Vergnaud, Iosif-Daniel Rosca

Writing for pharmacology researchers and practitioners in medication or pharmacology, Vergnaud (materials and chemical engineering, U. de Saint-Etienne, France) and Rosca (polymer Chemistry and expertise, Polytechnic U., Bucharest, Romania) clarify mathematical modeling to correlate in-vitro and in-vivo controlled-release drug dosage types. They current equipment for calculating the profiles of plasma degrees acquired with controlled-release dosage types, and supply examples and case stories to demonstrate the innovations. The grasp curves they current use dimensionless numbers in repeated doses, both for the time or for the plasma drug focus, and so could be utilized to any drug with a linear pharmacokinetics.

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Fm Page 15 Friday, April 15, 2005 2:37 PM 2 Intravenous Administration NOMENCLATURE AUC0−−T, AUCT − 2 T Area under the curve up to time T, between T and 2T, respectively. C0 Initial free drug concentration in the blood corresponding with the dose injected. 5 , respectively. Cnmax, Cnmin Drug concentration at the nth peak, at the nth trough, respectively. C∞ Free drug concentration in the blood, under steady state with infusion. Ct i Plasma drug concentration at time ti . Dose Amount of drug delivered intravenously in the blood.

5 = 6 h; θ = 3. 3, showing precisely the effect of the time interval between successive doses on the proﬁle of the drug concentration in the blood. 3), the following conclusions can be drawn: • The interval of time between successive oral doses plays an important role, acting especially upon the values of the peaks and troughs. fm Page 44 Friday, April 15, 2005 2:39 PM 44 Assessing Bioavailability of Drug Delivery Systems • • • • The time elapsed between two successive peaks slightly increases from the second dose to the next, ﬁnally reaching the value selected for the time interval between each dose.

Constant doses associated with the constant concentrations equal to C0 . 3. The second and subsequent doses are 20% larger than the first dose. 24, the concentration of the free drug in the blood is proportional to the rate of infusion and inversely proportional to both the rate constant of elimination and the apparent volume of distribution. 6 Master curve for the profile of blood concentration obtained during intravenous C infusion at constant rate Cθ = f (θ ) with θ = t t and C∞ = k UV . 6, a master curve is obtained by plotting the concentration at any time Cθ as a fraction of the asymptotical value of this concentration C∞ in terms of the dimensionless time.