Journal of Applied Physiology, Vol 51, Issue 5 1287-1293, Copyright © 1981 by American Physiological Society
Gas mixing by cardiogenic oscillations: a theoretical quantitative analysis
A. S. Slutsky
A quantitative theoretical model of the enhanced gas mixing secondary to
cardiogenic oscillations is presented based on the concept of augmented gas
transport within the tracheobronchial tree (Science 209: 609, 1980). The
model assumes "well-mixed" flow in the upper airways with the enhanced
mixing described by Deff = Dmol + K . ud, where Deff is the effective
diffusivity; Dmol, the molecular diffusivity: K, a constant; u, the
root-mean-square flow; and d, the airway diameter. In the smaller airways
on analysis based on Taylor laminar dispersion is used described by Deff =
Dmol + (1/192) (ud)2/Dmol. The model predicts that, in dogs, cardiogenic
oscillations should enhance gas mixing about 10-fold depending on the flow
rates generated by the heart. Other predictions are that the augmentation
of gas mixing should be greater 1) at lower lung volumes, 2) with sulfur
hexafluoride vs. helium or air, 3) after peripheral airway dilation, and 4)
after central airways constriction. Theoretical predictions are very close
to published experimental results where available. This model should help
in the development of mathematical models of gas mixing within the lungs
that will include the contribution of cardiogenic oscillations.
