A New Approach to the Determination of Ethanol Elimination Rate In Vivo: An Extension of Widmark's Equation

Abstract: In order to provide more experimental data about a single ethanol elimination sequence, tracer amounts of 14C-labelled ethanol were given intravenously in fed and fasted rats into a preexisting pool of unlabelled ethanol. The profiles of the elimination curves of 14C-labelled ethanol were distinctly different from those of unlabelled ethanol. This necessitated the elaboration of a mathematical model based on a two-compartment system, which by using the early distribution phase of the 14C-labelled ethanol and the linear part of the elimination curve of unlabelled ethanol enables the determination of the time-rate constants for distribution of ethanol, K12 and K21 and ethanol elimination rate Q. It is shown that the ratio K21'/(K21' + K12') is “r”, the distribution volume of ethanol in the sense of Widmark, K12' is K12 divided with Va (initial distribution space of ethanol) and K21' is K21 divided with Vb (the peripheral compartment). The mean value ±S.E.M. is 0.57±0.05 for fed rats and 0.49±0.03 for fasted. The slope of the time-concentration curve of ethanol, Widmark's β, is shown to be K12'/(K12'xK21')xQ where Q is ethanol elimination rate. The mean elimination rate is 0.303±0.036 mmol × l−1 × min−1 in fed rats and 0.219±0.015 mmol × l−1 × min.−1 in fasted (P<0.05). It is concluded that we are now able to extend Widmark's equation by an independent determination of the distribution factor “r”.