Simplified Bateman equation where Ka=Ke

Dear fellow NMusers, My previous submission to the forum had Word equations, and I think the email server choked on that so I'm submitting a new text-only version :-) I've been going insane trying to search for a reference to which I assumed was a very common equation. It is the simplification of a Bateman function where absorption cannot be distinguished from elimination, resulting in system breakdown. The consequence however is a very useful equation governed only by Cmax and Tmax. The Bateman function describes the biexponential equation associated with a kinetic system with first order absorption and linear elimination [1,2]: C(Time)=(F*Dose*Ka/(V*(Ka-Ke)))*(exp(-Ke*Time)- exp(-Ka*Time)) In the case where Ka and Ke cannot be distinguished (Ka=Ke=K), this biexponential equation breaks down to a single exponential equation (see Eqn 25 in Garret [1] or Eqn 2 in Bialer [2]) C(Time)=(F*Dose*K*Time/V)*(exp(-K*Time)) For this equation, Tmax can be derived to be given by 1/K and Cmax is given by F*Dose/(V*e) where e is the base of natural logarithms (see Eqn 26 and 27 in Garret [1] or Eqn 3 and 4 in Bialer [2]). Substituting K by 1/Tmax and V by F*Dose/(Cmax*e) gives: C(Time)=(Cmax*e*Time/Tmax)*(exp(-Time/Tmax)) Extremely useful for describing disease progression profiles, and I assumed it to be widely know. Perhaps it still is, but then someone must have published it somewhere: can anyone help me out? Cheers and thanks, Rik [1] Garrett ER. The Bateman function revisited: a critical reevaluation of the quantitative expressions to characterize concentrations in the one compartment body model as a function of time with first-order invasion and first-order elimination. J Pharmacokinet Biopharm (1994) 22(2):103-128. [2] Bialer M. A simple method for determining whether absorption and elimination rate constants are equal in the one-compartment open model with first-order processes. J Pharmacokinet Biopharm (1980) 8(1):111-113 Rik Schoemaker, PhD Occams Coöperatie U.A. Malandolaan 10 1187 HE Amstelveen The Netherlands http://www.occams.com +31 20 441 6410 mailto:[email protected]