Conditions for equivalence of gas exchange in series and parallel models of the lung.

The Fick principle was applied to series and parallel compartmental lung models to determine whether conditions existed under which their differentiation was theoretically possible. Respiratory and inert gases were examined under assumptions of steady-state gas exchange, continuous ventilation and bloodflow, perfect mixing within each compartment and alveolar-endcapillary diffusion equilibration. Algebraic analyses allowing broad generalizations were possible for inert gases but not for O2 and CO2, for which numerical methods were required. For trace amounts of inert gases present in venous blood but absent from inspired air, a given series model always had an exact parallel equivalent. When inert gases were then inspired, equivalence was lost if more than one 'resident' gas (inert or respiratory) was soluble, but the discrepancies were two orders of magnitude smaller than current experimental errors in inert gas measurements. Consequently, steady-state trace inert gas exchange cannot in practice be used to differentiate series from parallel models, but by the same token, if series gas exchange occurs, equivalent parallel analysis is possible.