Using a four-compartment closed model to describe inhalation of vaporised ethanol on 1-14C-pyruvate kinetics in mice

A four-compartment closed model was set up by means of a system of differential equations. A completely analytical solution of the four-compartment closed model was found by means of Laplace transform and Cramer's rule. 1-14C-pyruvate kinetics were studied in mice without and with inhalation of vaporised ethanol. The 1-14C-pyruvate kinetics were modelled by the four-compartment closed model, i.e. injected site, blood, 14CO2 expired in air, and 14C eliminated in urine. The kinetic parameters were estimated using the analytical solution of the four-compartment closed model to fit expired 14CO2 and 14C eliminated in urine simultaneously. Although the results showed that the inhalation of vaporised ethanol increased the expired 14CO2, the compartmental analysis revealed that the increase of expired 14CO2 is mainly attributed to increased 1-14C-pyruvate transmembrane process. The developed model is useful for toxicokinetic analysis when blood is not easy to obtain. Moreover, the developed model can also be used to model two compartments as urine and faeces when the toxin is not eliminated through air.