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Loop Gain in Ventilation

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Loop Gain in Apnea

Gaining Control or Controlling the Gain?

Matthew T. Naughton ,

Source: https://www.atsjournals.org/doi/full/10.1164/rccm.200909-1449ED


As sleep-related breathing disorders remain a major public health concern (1), a greater understanding of the pathogenesis is required to develop and improve therapeutic options. In the late 1970s, it became known that ventilation during non-REM sleep was critically dependent upon Pco2 levels (2). In the early 1980s, loop gain, an engineering term used to define the sensitivity of a variable system entered our parlance (3). Loop gain incorporated the “gains” of a controller, a plant, and the feedback between the two. Loop gain could be calculated as the ratio of the size of a response to the size of a disturbance, where a ratio of less than 1 would predict a reduction in amplitude and stability of the system whereas a ratio greater than 1 would predict an increase in amplitude and progressive instability.

With ventilation, loop gain can be considered as a ratio of the controller gain (i.e., ventilatory response to CO2), the plant gain (i.e., blood gas response to a change in ventilation), and feedback gain (i.e., the speed [cardiac output] of feedback signal [CO2] back to the controller). Under normal non-REM sleep conditions, small (<2 mm Hg) changes in Pco2 are promptly recognized by the chemoreceptors, maintaining stable ventilation. This tightly controlled, and rapidly responsive, negative feedback system between the brain and the lungs allows for stable ventilation with miniscule changes in CO2 levels. These oscillating Pco2 levels stay comfortably within a CO2 reserve of approximately 5 mm Hg (i.e., the difference between eupnea and apnea Pco2 thresholds).

CPAP-emergent CSA occurs during the initial nights of CPAP in up to 15% of patients with OSA, with near complete abolition after 2 to 3 months of CPAP (9). Given the current study (4), it is likely that CPAP-emergent CSA is associated with a loop gain greater than 1 and a narrow CO2 reserve. The immediate resolution of upper airway obstruction with CPAP revealing an underlying CSA indicates an increased loop gain due to heightened controller gain. Salloum's results confirm that ventilatory responses are elevated in untreated OSA and fall with CPAP over a few weeks (10). A 60% reduction in ventilatory response toward normal was recently reported in a 10-month CPAP trial in an older (mean 47 yr) and more obese (mean BMI, 39 kg/m2) OSA population (11). This effect may be due to the withdrawal of hypoxemia and attenuated ventilatory response.

With CPAP, acute lung inflation may, by reflex, cause CSA. However, in the long term, increased lung volume should reduce plant gain. In heart failure, CSA and OSA coexist due to controller, plant, and feedback gains plus upper airway instability (12). Controller gain is increased due mainly to heart failure–related dysfunctional autonomic control (5). Plant gain is increased due to restrictive ventilatory defect related to heart failure (13). Finally, the feedback from plant to controller is delayed (from ∼10 to 30 s), predisposing to oscillating long cycle length apneas and hyperpneas (7). In heart failure, compared with stable ventilation, CSA is associated with a narrow CO2 reserve (15) and an increased ventilatory response to CO2 at rest (5) and with exercise (6). CPAP over 1 to 3 months attenuates the apnea-hypopnea index thus suggesting dampening of loop gain (15). The study by Salloum (4) assists in understanding the mechanisms responsible for such effects. Prevailing awake Pco2 levels rise with CPAP therapy (12), suggesting an attenuated controller gain. Feedback gain (i.e., greater cardiac output) may improve with CPAP, although this may not always be the case, especially in the setting of severe end-stage and long-standing cardiomyopathy. Finally, and possibly most importantly, CPAP may attenuate plant gain through lung inflation to overcome restricted lung volume. CPAP has been shown to reduce plant gain and attenuate CSA induced by hyperoxia in newborn lambs (8), supporting this concept, and challenging the hypotheses of Salloum (4).

In Salloum's study, the narrow CO2 reserve (2.2 mm Hg) in OSA (4) doubled (1.9–3.7 mm Hg) with CPAP, compared with controls (4.5 mm Hg). Comparatively, canine CO2 reserve was reported to be 5 mm Hg, and became wider with metabolic acidosis induced by acetazolamide (6.7 mm Hg) and peripheral chemoreceptor stimulation with almitrine (5.9 mm Hg), whereas it was narrowed with metabolic alkalosis with sodium bicarbonate (−3.7 mm Hg) and hypoxia (4.1 mm Hg), thus predisposing to unstable or periodic breathing (16). Similarly, in humans with heart failure, CO2 reserves were narrowed with CSA compared with no CSA (2.8 vs. 5.7 mm Hg) (14).

Salloum's study (4) suggests that CPAP does more than simply splint open an upper airway (and provide an apnea-hypopnea index of zero!). In clinical practice, we know that CPAP-emergent CSA may occur and then attenuate over the subsequent 1 to 3 months. In such cases, one should consider incorporating outcome variables, in addition to the apnea-hypopnea index, such as apnea-hyperpnea cycle length, sleep quality and quantity, heart rate, and oxygen levels. Moreover, once loop gain is normalized, consideration should be given to alter positive pressure level and perhaps to reassess residual sleep-related breathing disorders.

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