A general dimensionless equation of gas transport by high-frequency ventilation

To identify a general relationship between eucapnic oscillatory flow (Vosc) and frequency (f) in high-frequency ventilation (HFV), we searched the literature for eucapnic HFV data in different mammalian species. We found suitable results for rat, rabbit, monkey, dog, human, and horse, which we expressed in terms of two dimensionless variables, Q = Vosc/Va and F = f/(VA/VD), with VA the alveolar ventilation and VD the volume of the conducting airways. The experimental HFV data define the linear regression equation in Q = 0.54 In F + 0.92 (R = 0.94). Krogh's equation for conventional ventilation (CV), Vosc = VA + fVD, in dimensionless terms becomes Q = 1 + F, which is valid for low F. The intersection of the CV and HFV equations at F = 5.0 defines a transition frequency, ft = 5.0 (VA/VD). At that point the alveolar ventilation per breath, VA/f, represents 20% of VD, and tidal volume (VT) equals 1.20 VD. For eucapnia ft ranges from 5.9 Hz in the rat to 0.9 Hz in the dog. The dimensional form of our HFV equation, VA = 0.13 (VT/VD)1.2 (VTf) is very similar to other empirical equations reported for dogs in noneucapnic settings. Therefore the dimensionless equation should also be valid within a species at noneucapnic settings.