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J Appl Physiol 87: 1973-1980, 1999;
8750-7587/99 $5.00
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Vol. 87, Issue 5, 1973-1980, November 1999

MODELING IN PHYSIOLOGY
Modeling expiratory flow from excised tracheal tube laws

Nikolai Aljuri, Lutz Freitag, and José G. Venegas

Department of Anesthesia (Bio-Engineering), Massachusetts General Hospital, Harvard Medical School, Boston, Massachusetts 02114; and Ruhrlandklinik Essen, Essen, Germany

Flow limitation during forced exhalation and gas trapping during high-frequency ventilation are affected by upstream viscous losses and by the relationship between transmural pressure (Ptm) and cross-sectional area (Atr) of the airways, i.e., tube law (TL). Our objective was to test the validity of a simple lumped-parameter model of expiratory flow limitation, including the measured TL, static pressure recovery, and upstream viscous losses. To accomplish this objective, we assessed the TLs of various excised animal tracheae in controlled conditions of quasi-static (no flow) and steady forced expiratory flow. Atr was measured from digitized images of inner tracheal walls delineated by transillumination at an axial location defining the minimal area during forced expiratory flow. Tracheal TLs followed closely the exponential form proposed by Shapiro (A. H. Shapiro. J. Biomech. Eng. 99: 126-147, 1977) for elastic tubes: Ptm = Kp [(Atr/Atr0)-n - 1], where Atr0 is Atr at Ptm = 0 and Kp is a parametric factor related to the stiffness of the tube wall. Using these TLs, we found that the simple model of expiratory flow limitation described well the experimental data. Independent of upstream resistance, all tracheae with an exponent n < 2 experienced flow limitation, whereas a trachea with n > 2 did not. Upstream viscous losses, as expected, reduced maximal expiratory flow. The TL measured under steady-flow conditions was stiffer than that measured under expiratory no-flow conditions, only if a significant static pressure recovery from the choke point to atmosphere was assumed in the measurement.

flow limitation; tracheal cross-sectional area and collapse; wave speed


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