Model of gas transport during high-frequency ventilation

We analyze gas exchange during high-frequency ventilation (HFV) by a stochastic model that divides the dead space into N compartments in series where each compartment has a volume equal to tidal volume (V). We then divide each of these compartments into alpha subcompartments in series, where each subcompartment receives a well-mixed concentration from one compartment and passes a well-mixed concentration to another in the direction of flow. The number of subcompartments is chosen on the basis that 1/alpha = (sigma t/-t)2, where -t is mean transit time across a compartment of volume, and sigma t is standard deviation of transit times. If (sigma t/-t)D applies to the transit times of the entire dead space, the magnitude of gas exchange is proportional to (sigma t/-t)D, frequency, and V raised to some power greater than unity in the range where V is close to VD. When V is very small in relation to VD, gas exchange is proportional to (sigma t/-t)2D, frequency, and V raised to a power equal to either one or two depending on whether the flow is turbulent or streamline, respectively. (sigma t/-t)D can be determined by the relation between the concentration of alveolar gas at the air outlet and volume expired as in a Fowler measurement of the volume of the dead space.