Using Loop Gain to Assess Ventilatory Control in Obstructive Sleep Apnea

Michael C. K. Khoo

Biomedical Engineering Department,University of Southern California,Los Angeles, California

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Is obstructive sleep apnea (OSA) predominantly a disorder of abnormal upper airway function or does upper airway collapsibility merely amplify the ventilatory fluctuations that stem from an underlying instability in chemical control? The latter possibility was suggested in both theoretical and experimental studies published almost two decades ago. Using a computer model, Longobardo and colleagues (1) demonstrated that obstructive apnea could be produced during simulated periodic breathing when a dynamic imbalance occurred between ventilatory pump drive and upper airway muscle activity. Onal and Lopata (2) found that patients with OSA who underwent tracheostomy continued to exhibit periodic ventilation during sleep. On the other hand, previous studies of control of breathing had determined that the hypoxic and hypercapnic ventilatory responses in patients with OSA were either depressed or normal (3), suggesting an inherently more stable system. But these tests of chemoresponsiveness were based on measurements conducted during wakefulness under steady state or quasi-steady state conditions. Furthermore, ventilatory control stability depends not only on controller gain, but also on the dynamics of gas exchange as well as the circulatory delays and response lags involved in the process of chemoreflex feedback (4). Thus, the magnitude of feedback control or "loop gain," which incorporates all these factors, provides a more accurate measure of the susceptibility to periodic breathing. But how does one estimate loop gain in sleeping apneics in a relatively nonintrusive manner?

In the present issue of the Journal (pp. 1181-1190), Younes and associates propose an approach that cleverly addresses this problem with a highly practicable technique (5). Two important design features allow this approach to be applied to sleeping subjects with OSA. The first is the stabilization of the upper airways, using continuous positive airway pressure (CPAP), so that the role of fluctuations in upper airway resistance is minimized. The second feature is the application of proportional assist ventilation (PAV) to incrementally increase controller gain until periodic breathing occurs. Linear control theory states that the loop gain must be increased to a value of unity before instability can occur (4, 6). The factor by which the existing loop gain must be increased to produce instability is known, in control parlance, as the "gain margin" (6). Thus, if the original (unperturbed) loop gain is LG and the volume amplification factor required for PAV to initiate periodic breathing is VTAF (which equals the gain margin), we can estimate LG from:

A key finding from the study by Younes and colleagues is that LG was significantly higher in patients with severe OSA compared with patients with milder degrees of sleep-disordered breathing or with normal subjects. This implies that the chemoreflex control of ventilation in OSA is inherently less stable, even when the destabilizing effects of the upper airways have been accounted for. This conclusion is consonant with the results reported recently by Hudgel and coworkers (7), who measured the open-loop and closed-loop responses of awake normal subjects and patients with OSA to randomly modulated changes in inhaled CO₂. The open-loop responses of both groups were similar, indicating similar controller gains. In contrast, the closed-loop responses in OSA were significantly higher and more rapid, suggesting that LG was higher in the patients with OSA relative to the normal subjects. The analysis used by Hudgel did not allow LG to be computed explicitly, but this limitation can be overcome if certain mathematical assumptions are made about the dynamics of gas exchange (8). However, administering randomly changing concentrations of CO₂ and/or hypoxic gas on a breath-to-breath basis to sleeping subjects under CPAP may be technically challenging. The Younes technique is probably easier to implement from a practical standpoint. Nevertheless, a common feature of these recent studies is the emphasis on measuring dynamic open- and closed-loop responses and the inclusion of other factors, aside from controller gain, that are also relevant to system stability.

Notwithstanding the elegance of the Younes approach, there remain some issues that require future resolution. The first is that little attention was paid in this study to determining how LG varied with different sleep stages. Accounting for state differences would allow for more accurate comparisons of LG across individuals or groups. Second, as the authors themselves acknowledge, CPAP can affect system stability through its effects on lung volume, cardiac output, and thoracic compliance. Although there was no significant difference between the optimal CPAP settings in both groups of OSA patients studied, in general one would expect the more severely affected patients to require higher CPAP levels for maintaining upper airway patency. Thus, differences in the applied CPAP levels and the variability with which CPAP affects system stability could contribute to errors in comparing estimates of LG across patients with different CPAP requirements. An important refinement of the technique would be the development of a systematic means for extrapolating estimates of LG measured at the optimal CPAP level to deduce LG in the hypothetical situation of zero CPAP.

Application of PAV itself could affect estimates of LG. The ventilatory assistance provided by PAV reduces the spontaneous drive required to produce a given tidal volume. This decrease in the subject's intrinsic ventilatory drive would also reduce the amount of short-term potentiation, relative to the amount that would have been present without PAV (9). Because short-term potentiation exerts a stabilizing influence (10), it might be surmised that the use of PAV would tend to artificially raise LG. Another limitation of the application of PAV is the possibility that increasing the volume amplification factor to high levels (in subjects who are very stable) would likely provoke arousal, a change in sleep stage, or outright awakening. Estimation of LG from the highest volume amplification factor immediately preceding periodic ventilation also assumes that it was not a transient arousal that precipitated the subsequent unstable breathing pattern.

Finally, it is important to stress that the finding of decreased control stability in subjects with OSA is not sufficient to establish that these patients developed OSA because they were inherently more unstable. It is quite possible that the decreased stability might have been a consequence of the disorder. For instance, it has been demonstrated that short-term potentiation is impaired in awake subjects with OSA relative to normal control subjects (11); this abnormality could well be a consequence of the chronic exposure to nocturnal episodic hypoxia in these patients. A step toward resolving this "which came first, the chicken or the egg" problem would be to determine whether snorers or patients with mild OSA are inherently more unstable than normal control subjects. Future work that could address this question include the application of the powerful Younes approach to larger subject populations (to improve statistical resolution), as well as refinement of the technique to obtain more precise estimates of LG.

	References

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