Interaction of oscillatory and steady turbulent flows in airway tubes during impedance measurement

Measurement of input respiratory impedance is carried out by superimposing forced oscillations on spontaneous breathing. The latter thus acts as a quasi-steady unidirectional flow component, with effects on the measured impedance that are habitually neglected (linearity assumption). We examined the validity of that assumption in the case of a turbulent steady flow. We tested the validity of a fluid dynamics criterion previously proposed in water channel experiments for gas flow in a tube. This criterion states that oscillatory and continuous turbulent flow may or may not interact if the Stokes boundary layer (ls) is embedded within the viscous sublayer (lv), i.e., if lS+ = lS/lv < or = 10, implying Re7/8 < or = (100 alpha/square root of 2), for a fully developed hydraulically smooth turbulent flow in a tube (where alpha is Womersley parameter and Re is Reynolds number of the steady-flow component). Experiments were performed in long rigid circular and semicircular tubes by superimposing two independent well-defined flows: 1) laminar oscillatory flow obeying the linear transmission line model (frequency = 1.5-250 Hz, i.e., alpha = 6-80) and 2) fully developed turbulent flow characterized by Blasius resistance formula (Re = 3,000-16,000). Confirming the validity of the criterion above, we found that the real and the imaginary parts of the long-tube impedance did not differ from those measured in the absence of a steady-flow component, provided lS+ < or = 10. On the contrary, the real parts measured with and without the continuous component differed greatly as soon as lS+ > 10, both for circular and semicircular tubes and for outward as well as inward steady flows. We concluded that the proposed criterion is pertinent for predicting appropriate oscillation frequency for a given rate of spontaneous flow, such that oscillatory and turbulent flows do not interact. Application of the forced oscillation measurement technique during spontaneous breathing requires use of a range of oscillatory frequencies higher than the frequency range classically used during apnea.