Determination of rate-constants as a method to describe passive expiration

To describe the relaxed expiration by a two-compartment model, we introduced a gas/energy transfer between the lung compartment (V ₁) and a second one (V ₂). If V ₂ were a real volume, the rate-constants (i.e. the flow/volume ratios) of the compartments would describe a real gas-exchange. Alternatively, if a viscoelastic behaviour of the lung or an energy-exchange between compartments was simulated, V ₂ would become a "pseudo-volume". We studied nine mechanically ventilated subjects. Changes in volume were transduced by respiratory inductive plethysmography. The rate-constants were assumed (together with the initial volumes of the compartments) as parameters to fit the total volume [V ₁(t)+V ₂(t)]. Once the best fitting was performed using these "physiological" parameters, the system was directly identified and the compartments were independently analysed. The time profile of the second compartment showed a maximum that depended on the value of the rate-constants. Appropriate tests confirmed the reliability of our procedure. In conclusion, our analysis demonstrated that the energy/volume of the second compartment may increase at the beginning of expiration and then decrease, showing a maximum, even though the total curve can only be a decreasing one. In other words, the slowing down of the curve representing expiratory volume is due not only to the longer emptying of the second compartment, but also to the interaction between the two compartments. As presently proposed, this interaction can be represented by either a gas exchange between two actual volumes, or a mechanical energy transfer between the lung and the tissue compartment.