Practice May Be More Difficult than Theory |
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For at least 35 years, it has been understood that ventilatory oscillations having a period of a few to several tens of breaths could arise from the feedback nature of the respiratory chemical control system (1), and much emphasis has been placed on assessing the "loop gain" of this system. Because it is difficult to measure all of the physiological factors that influence whether such oscillations will occur, various investigators have endeavored to develop predictive methods based on either simplified models of the chemical feedback system or model-based interpretations of simple experimental tests (2-4). A desirable objective has always been to make such predictions by applying data from spontaneous breathing to a simple model, because such a method may have clinical usefulness. The article by Van den Aardweg and Karemaker (5) in this issue of the American Journal of Respiratory and Critical Care Medicine (pp. 1041-1047) takes a significant step in this direction. In this paper, the authors apply standard frequency-domain analyses to identify coherent (i.e., correlated) oscillations in end-tidal carbon dioxide tension (PETCO2) and mean inspiratory flow (VI/TI). Through the accompanying analysis of a simplified model of chemoreflex control of respiration, they conclude: (1) that these correlations reflect responses of the chemoreflex feedback system to (uncorrelated) noisy disturbances of these two variables; and (2) that an index of loop gain can be estimated from the squared coherence between the above two variables during spontaneous breathing.
The conclusion that noise disturbances to arterial CO2 levels could drive fluctuations in ventilation has been inferred from the presence of breath-to-breath correlations in respiratory cycle variables (6-8) and was shown experimentally by Modarreszadeh and coworkers (9) for spontaneous breathing in hyperoxia. The present paper by Van den Aardweg and Karemaker (5) extends the latter finding to room air breathing and also quantifies the relationship between PETCO2 and VI/TI at the frequencies of highest correlation and demonstrates that these data are reasonably compatible with their model. Thus, the paper presents another demonstration that random disturbances to arterial CO2 (including those caused by ventilation itself) are sensed by chemoreceptors and are responsible for part of the breath-to-breath variability of mean inspiratory flow and minute volume. That is, the properties of the chemoreflex control system can affect both pronounced oscillations and "noisy" fluctuations in respiratory pattern.
It should be noted that the model of the present paper ignores the contributions of chemical feedback via venous return; therefore, its description of very slow dynamics will be
incomplete. It also ignores the effects of fluctuations in PETO2
mediated via peripheral chemoreceptors, which limits its accuracy in hypoxia and, to some extent, in normoxia. Control of
the upper airway also is not included (10). The reported difference in relative occurrence of oscillations in hyperoxia compared with normoxia (5) may be consistent with physiological
expectations, but this finding may be an artifact of the shorter
data records in hyperoxia (see following paragraph). Another
general concern is that the "frequency" of oscillation may not
remain constant
for example, if cardiac output also is fluctuatingand thus the "peak" in the spectra may be spread
across a frequency range and not be detected. I also would
have preferred to estimate the mean value of VI/TI by averaging these values rather than by dividing the average VI by
the average TI.
Proper estimation of squared coherence, using methods based on the discrete fourier transform, requires careful attention to issues such as variance and bias of the estimate and frequency resolution. The high variance and bias of the coherence estimate necessitate the use of averaging methods, and the authors used smoothing in the frequency domain (see online article notes by Drs. Van den Aardweg and Karemaker [Part I]). Clearly, this averaging was sufficient to permit detection of nonzero squared coherence at some frequencies. The estimated squared coherence, however, is biased toward a value of one when nonparametric spectra are used, and this bias (and also the variance) is inversely related to the amount of averaging. In hyperoxia, where the data records averaged only 225 breaths, bias might have been significant and the increased variance (relative to normoxia) might have obscured some nonzero coherence. The authors might have addressed these issues through the use of surrogate data (or bootstrap) methods or by comparing analyses of short and long data records from their model.
The conclusion that respiratory variability contains information about chemoreflex properties is not new, but the proposed model presents new relationships from which to extract parameters related to chemoreflex properties. The terminology used in this paper (and its online supplement) sometimes appears different from similar nomenclature in the literature. In particular, the phrase "loop gain" is not the product of open-loop feedforward and feedback gains, as in the historical context. That this is so may be seen by assuming that chemoreflex sensitivity is zero. In the historical context, loop gain should also be zero, but in the present formulation it is not (Equation C23 in the online data supplement to the article by Van den Aardweg and Karemaker). The approach in the current article indeed captures the correlations in the data between PETCO2 and VI/TI when the chemoreflex loop is closed, and the "gain" terms in Equation C31 are apparent gains in the presence of feedback and two noise sources (see online article notes [Part II]). (The relationship between these gains and the squared coherence shown in this equation is the basis of a well-known approach for estimating coherence.) Although one can derive a mathematical relationship between the two definitions of loop gain, they are based on different concepts and their practical equivalence needs to be demonstrated.
Notwithstanding these concerns, the paper illustrates the synergism possible from blending experimental and computational approaches to obtain insights about natural functions of complex physiological systems. There is great potential in the combination of simple experimental measurements with data interpretation via a rigorously simplified mathematical model, and the authors have taken a significant step toward developing a useful index of chemoreflex loop stability. Its relationship to other approaches awaits further analysis and testing.
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This article has been cited by other articles:
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  M. J. Tobin Sleep-Disordered Breathing, Control of Breathing, Respiratory Muscles, and Pulmonary Function Testing in AJRCCM 2002 Am. J. Respir. Crit. Care Med., February 1, 2003; 167(3): 306 - 318. [Full Text] [PDF]
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