Dynamics of Gaseous Uptake in the Lungs: The Concentration and Second Gas Effects

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Abstract
A one-compartment, continuous-time model is proposed for the investigation of dynamic gas exchange in the lungs. The dynamics of the alveolar gas concentrations (state variables, xi) are demonstrated to be critically determined by, among other things, the blood-gas partition coefficients and the inspired concentrations (inputs, ui) of the component gases. The model has a bilinear structure which, when sibjected to a step input, can be exactly linearized. It is shown that the eigenvalues of the system are all real and negative, and can be simultaneously maximized if the most soluble gas of the inspirate alone is inhaled (i. e., the system becoming minimally stable). The normalized state response (xg/uj) corresponding to this input exhibits the greatest steady-state excursion, albeit with the slowest kinetics, so that the response xi/Ui rises most rapidly. Furthermore, this input-dependent effect extends also to the uptake kinetics of all other gases in the inspirate. Our investigations suggest that it can be ascribed primarily to an increase in the ratio of inspired-to-expired ventilation. These analytical predictions are further supported by simulation studies, and correspond closely with independent experimental observations. These results are consistent with, and provide a quantitative account for, the experimental observations generally known as the concentration and second gas effects.