Correspondence  |   December 1995
Volumetric Capnography and Lung Growth in Children: A Simple Model Validated
Article Information
Correspondence   |   December 1995
Volumetric Capnography and Lung Growth in Children: A Simple Model Validated
Anesthesiology 12 1995, Vol.83, 1377-1379. doi:
Anesthesiology 12 1995, Vol.83, 1377-1379. doi:
To the Editor: I read with interest the paper by Ream et al. 1in which the slopes of the alveolar plateaus of volumetric capnograms (phase III slopes) were studied in a series of children of various ages whose lungs were mechanically ventilated. Their finding that, as children grow, the normalized slope diminishes in a way that is predicted by the "single path" lung model with stratified inhomogeneity is presented as evidence in support of this hypothesis. Inspection of the plots of normalized slope versus age or weight reveals a seemingly hyperbolic relationship, so it is not clear why the authors chose to use quadratic regression analysis to describe it. The coefficients of the squared terms in these quadratic functions are so small as to render them effectively linear. The quoted R2values add no weight to the closeness of fit of the data to the model because the relationship is unlikely to be linear.
To paraphrase the theory proposed by the authors, the phase III slope represents the longitudinal carbon dioxide tension gradient within the acinar airway caused by continued carbon dioxide evolution. This gradient is the driving force behind diffusive carbon dioxide flux at the interface between the FRC gas and tidal gas and is inversely proportional to its cross-sectional area. As the cross-sectional area of this interface increases with lung growth, the diffusional resistance is reduced, and the longitudinal carbon dioxide tension gradient (and hence phase III slope) is diminished in a way predicted by Fick's law of diffusion.
Although I do not wish to cast excessive doubt on this hypothesis, I would submit that these data are equally compatible with a much simpler model of the lung, i.e., that of the single alveolus. This assertion is supported by the following derivation of an expression for the phase III slope, assuming that the lung is a single homogeneous alveolus.
The phase III slope, dF/dV, measured at the mouth is a compound function of the rate of rise of FCO2in the alveolus (dFA/dt) and the rate of delivery of this gas from the alveolar compartment to the mouth (dVA/dt), where VAis the volume of the alveolar unit. Hence:.
The calculation of instantaneous values of this function is complicated by the fact that the appropriate values of dFA/dt and dV sub A/dt are not contemporaneous but are separated by the deadspace transit time. However, as we are considering mean values over the whole expiratory breath, we can simplify this to:letting the bar embellishment denote mean values, we have:where VTis tidal volume, and tcis expiratory time.
The rate of rise of FAin expiration can be derived as follows 2: The total volume of carbon dioxide in the alveolar compartment is FA*symbol* VA. The rate of change of carbon dioxide in the alveolar compartment is:. In accordance with the conservation of mass, this must equal the algebraic sum of the rates of carbon dioxide entry into the alveolar compartment (v with dotCOsub 2) and the rate of carbon dioxide egress via the airway in expiration (FA*symbol* dVA/dt). Combining this with gives:. Averaged over the whole expiratory breath (in the steady state), this approximates to:where V with dotCO2is the whole body carbon dioxide production rate, and FRC + VT/2 is the average lung volume (with respect to volume) over the whole of expiration. By combining and , we have:. V with dotCO2can be expressed as f *symbol* VT*symbol* FEwith bar (where f is respiratory frequency (min sup -1), and FEis mixed expiratory FCO2), which, when substituted into , yields:.
The authors define "normalized" slope as the true slope divided by mixed FCO2(FEwith bar). Therefore, . Because the inspiratory times are stated as 1 s, we have:. The values for ventilatory frequency are stated as being between 8 and 15 min sup -1, and if a midway value of 11 is chosen, we have:.
It is now apparent that the relationship between normalized slope and FRC is a (not quite purely rectangular) hyperbola. The relationship between normalized slope and body weight can be plotted by substituting values for FRC at various body weights from Cotes' nomogram 3(correcting for changes under anesthesia 4) and values for V sub T, which were stated as either 8.5 or 12.5 ml *symbol* kg sup -1, into . This plot of normalized slope versus body weight is shown in 1along with the authors' data points (for VT, 8.5 ml *symbol* kg sup -1) transcribed approximately from their figure.

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It appears that the observed relationship between normalized slope and the various morphologic parameters can be explained by consideration of a single homogeneous alveolus whose volume increases (almost linearly) as the child grows. This does not involve invoking theories regarding sequential emptying, diffusive pendelluft, or the cross-sectional area of the FRC: VTinterface. I do not wish to speculate as to which of the many hypothetical models pertain, but my point is that any experimental evidence that claims to support one theory while supporting another equally well cannot be regarded as supporting either definitively.
Andrew D. Farmery, B.Sc., M.B., F.R.C.A., Department of Anaesthesia, Addenbrooke's Hospital, Hills Road, Cambridge CB2 2QQ United Kingdom.
Ream RS, Schreiner MS, Neff JD, McRae KM, Jawad AF, Scherer PW, Neufeld GR: Volumetric capnography in children. ANESTHESIOLOGY 82:64-73, 1995.
Edwards AD, Jennings SJ, Newstead CG, Wolff CB: The effect of increased lung volume on the expiratory rate of rise of carbon dioxide tension in normal man. J Physiol 344:81-88, 1983.
Cotes JE: Lung Function. 3rd edition. Oxford, Blackwell Scientific, 1975, pp 345-353.
Nunn JF: Applied Respiratory Physiology. 2nd edition. Stoneham, Butterworths, 1977, p 68.