Gas mixing by cardiogenic oscillations: a theoretical quantitative analysis

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Abstract
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.