American Journal of Respiratory and Critical Care Medicine

The role of chemical control instability in the pathogenesis of obstructive sleep apnea (OSA) is not clear. We studied 32 patients with OSA during sleep while their upper airway was stabilized with continuous positive airway pressure. Twelve patients had repetitive OSA whenever they were asleep, regardless of body position or sleep stage, and were classified as having severe OSA (apnea–hypopnea index [AHI] = 88 ± 19). The remaining 20 patients had sporadic OSA or repetitive OSA for only part of the time (mild/moderate OSA; AHI = 27 ± 16). Susceptibility to periodic breathing (PB) was assessed by gradually increasing controller gain, using proportional assist ventilation. The increase in loop gain (LG) at each assist level was quantified from the ratio of assisted tidal volume (Vt) to the Vt obtained during single-breath reloading tests (Vt amplification factor [VtAF]). Nine of 12 patients with severe OSA developed PB, with recurrent central apneas, whereas only six of 20 patients in the mild/moderate group developed PB (p < 0.02). This difference was observed despite the subjection of the mild/moderate group to greater amplification of LG; the highest values of VtAF in the mild/moderate and severe groups were 2.7 ± 1.0 and 1.9 ± 0.7, respectively (p < 0.01). We conclude that the chemical control system is more unstable in patients with severe OSA than in patients with milder OSA. We speculate that this may contribute to the severity of OSA, at least in some patients.

The syndrome of obstructive sleep apnea (OSA) has a wide spectrum of severity. At one extreme, patients may present with relatively benign, steady snoring punctuated by rare sporadic obstructive events (i.e., hypopnea or apnea). At the other extreme, patients may suffer from repetitive OSA whenever they are asleep, with potentially high morbidity (1). Some patients develop periodic events only when in specific body positions, or sleep stages, or at specific times of night. The reason(s) for these various expressions of OSA among and within individuals is not clear. Conceivably, they may reflect differences in upper airway (UA) anatomy or mechanics, or in arousability (2, 3), among patients and in different sleep conditions. Alternatively, the same UA abnormalities may result in steady snoring or in repetitive OSA depending on the stability of the patient's respiratory control.

It is our hypothesis that patients with severe OSA have an unstable chemical control system. This hypothesis is not new. Periodic breathing (PB) with repetitive central apnea (Cheyne– Stokes breathing [CSB]) was commonly observed after tracheostomy done for treatment of OSA (4, 5). This led Onal and colleagues (5) to postulate that basic instability of respiratory control is essential for the development of severe OSA. This hypothesis was not pursued further, probably because of lack of suitable methodology to assess the extent of instability of chemical control of respiration during sleep in these patients.

We have recently introduced a method to quantitate ventilatory stability during sleep (6, 7). It takes advantage of the ability of proportional assist ventilation (PAV) (8) to augment the ventilatory response to respiratory muscle activation, thereby augmenting the gain of the respiratory controller. Controller gain is one of the most important determinants of ventilatory stability (9-12). In the proposed approach, the level of PAV support, and hence controller gain, is increased in steps until either CSB develops or the patient awakens. Failure of CSB to develop in the face of a severalfold increase in controller gain would reflect a highly stable respiratory control system. Conversely, if CSB develops with minor increases in controller gain, this would reflect a control system that is prone to oscillation.

In the present study we assessed ventilatory stability, using PAV, in patients with OSA after stabilizing their UA with continuous positive airway pressure (CPAP). The results therefore reflect stability of respiratory control in the absence of the confounding influence of variable UA resistance. The results for patients with severe OSA were compared with those for patients with mild/moderate OSA, and the results in both groups were contrasted with those obtained in previous studies of normal sleeping subjects.

Patients referred to the sleep laboratory of our institution for diagnosis of OSA were asked to participate. Thirty-two patients (29 males, and three females) consented to the study. The patients' age was 47 ± 9.5 yr (mean ± SD) and their average body mass index (BMI) was 34.2 ± 5.9.

Patients underwent standard all-night polysomnograph. Monitored studies included a three-lead electroencephalogram (EEG), chin electromyogram (EMG), electrooculogramy (EOG), leg EMG, electrocardiogram (ECG), heart rate (HR), SaO2 , rib cage and abdomen movements (Respitrace; Ambulatory Monitoring, Ardsley, NY), nasal flow (Ultima airflow sensor; Braebon Medical Corp., Kanata, ON, Canada), CO2 concentration at the airway (Datex, Helsinki, Finland), transcutaneous CO2 (Microgas 7640 MKZ; Kontron, Wattford, UK), snoring, and body position. Signals were continuously recorded on a 16-channel polygraph (Grass Instrument Co., Quincy, MA). Scoring of sleep stages, arousal, and respiratory events was done manually from the polygraph record. Sleep stages and arousals were defined according to standard criteria (13, 14). An obstructive apnea was defined as loss of nasal flow accompanied by airway CO2 fluctuations associated with markedly reduced and/or paradoxical respiratory fluctuations in the Respitrace signals for > 10 s. An obstructive hypopnea was defined as a > 50% reduction in both the rib cage and abdominal Respitrace signals or a > 50% reduction in only one of these channels, but accompanied by chest-wall paradoxical motion through most of inspiration, for > 10 s.

CPAP/PAV titration was done either on the same night as polysomnography or on a separate night, depending on whether sufficient information (for clinical purposes) was obtained prior to 3:00 a.m. Titration was made done with a research prototype ventilator built by Respironics (Murrysville, PA), connected to the patient via a nasal mask. This ventilator is capable of delivering CPAP alone or in varying combinations with PAV. It is also equipped with algorithms for estimating total leak flow. A chin strap was applied where necessary, and if the leak was excessive despite the strap, a full face mask was applied. The flow and volume outputs of the ventilator provided estimated patient flow and volume after allowing for leaks. The accuracy of the leak correction was previously verified (6). When the patient was connected to the ventilator, the ventilator output signals corresponding to airway pressure (Paw) and estimated patient flow (V˙) and volume (V) were continuously recorded.

CPAP titration was done first. When the patient was asleep, the CPAP level was increased in steps of 1 to 2 cm H2O until all snoring, chest-wall paradoxical motion, and hypopneas were eliminated and there was no evidence of flow limitation (flat inspiratory flow through most of the inspiratory phase). CPAP titration was repeated when there was a change in body position from supine to lateral, or vice versa.

PAV titration was done during sleep at optimal CPAP. PAV is delivered by applying a pressure assist that is the sum of a flow-related component (flow assist [FA]) and a volume-related component (volume assist [VA]) (8). Ideally, and in order for the proportionality between pressure assist and respiratory muscle pressure (Pmus) to be the same throughout inspiration, it is preferable that FA and VA be the same fraction of the patient's respiratory resistance (R) and elastance (E), respectively. For this reason, the first step in PAV titration was to obtain estimates of resistance and elastance during optimal CPAP. Resistance was determined with a pulse technique described earlier (15). Brief (400-ms) pressure pulses with an amplitude of 3 cm H2O were delivered by using a pulse generator connected to the ventilator. Pulses were delivered at the beginning of inspiration. To calculate resistance, the increase in Paw above CPAP was divided by the increase in flow, measured at the time of peak flow. The validity of this technique was independently established (16). Elastance was determined with the “runaway” method as previously described (15, 17).

The values of resistance and elastance were entered into the ventilator computer. The level of assist was controlled by a “% assist” dial. This determines the percent of resistance and elastance to be used to generate FA and VA, respectively (range: 0 to 99%). The sequence of percent assist applied was 20, 40, 60, 70, 80, 90, and 95% of both resistance and elastance. Following each stepwise increase in which neither PB developed nor awakening occurred, the assist level was kept constant for 3 to 5 min to establish a steady state. Subsequently, the percent assist was decreased to zero (i.e., CPAP only) for one breath (Figure 1) to document the difference between assisted and nonassisted tidal volume (Vt) at the same chemical drive. This procedure was repeated from three to five times over a period of 1 to 2 min. The percent assist was then increased to the next level. This sequence was continued until either PB developed or the patient awakened (brief arousals did not cause a change in protocol). If CSB developed after a stepwise change in the percent assist, the latter was maintained at its existing level until the patient awakened; this typically entailed from three to 10 cycles of observed CSB before the patient woke up. At this point the titration was complete. If the patient awakened without developing CSB, the percent assist was decreased to zero to facilitate resumption of sleep. When sleep resumed, the sequence was reinitiated. However, to increase the likelihood of completing the titration before the next awakening, the levels of assist tested before the last awakening, and which were ineffective in producing CSB, were not repeated. Rather, the level of assist was increased from 0% to the last steady-state level tested over a 1- to 2-min period. Sudden large changes in percent assist were avoided, since they frequently cause awakenings.

When an assist level of 95% was reached without evoking CSB, the level of assist was further increased by increasing the value of elastance assist in steps of 2 cm H2O/L. If a stepwise change in elastance assist resulted in the occurrence of runaway breaths (see the foregoing discussion), it was assumed that patient's elastance did not change from its earlier value. The titration was then terminated. If runaway breaths were not observed as elastance was increased, we assumed that elastance had increased from its previous value, and another steady state was obtained. Step-wise increases in elastance were continued (5 to 7 min each), with single-breath reloading tests at each level, until CSB developed or runaway breaths began appearing. Titration was then deemed to have been complete.

In 21 patients, the increase in lung volume produced by optimal CPAP was determined during periods of CPAP only, by suddenly reducing the CPAP level to 2 cm H2O (the minimum level on the ventilator) at the beginning of an expiratory phase and measuring the reduction in end-expiratory lung volume.

Data Analysis

Severity of OSA was assessed with the apnea–hypopnea index (AHI) without CPAP. Patients were divided into two groups, a severe OSA group, with repetitive OSA under all conditions (n = 12), and a mild/ moderate OSA group (n = 20), with sporadic events or in whom repetitive OSA was observed only intermittently.

The increase in controller gain produced by a given level of PAV assist was assessed from the ratio of assisted Vt to the Vt observed during the single-breath reloading test (Vt amplification factor [VtAF]) (Figure 1). This approach assumes that chemical drive did not systematically change during the first reloaded inspiration relative to the immediately preceding assisted breaths. This is a reasonable assumption, since termination of PAV does not have any mechanical consequence until the onset of the first reloaded inspiration, and the duration of the first reloaded inspiratory phase (∼ 1 s) is too short to be associated with any changes in chemoreceptor Pco 2 or Pco 2. Several steps were taken to minimize the impact of spontaneous variability in Vt on measured VtAF. First, the average of three breaths preceding reloading was used as the numerator of the ratio. Second, from three to five single-breath reloading tests were done at each PAV level, and their VtAF values were averaged. Third, data obtained during rapid eye movement (REM) sleep were not used, since spontaneous variability in Vt is excessive during such sleep and would necessitate many more single-breath reloading tests to obtain reliable VtAF values.

Twelve patients had repetitive OSA whenever they were asleep, whereas 20 patients had intermittent OSA (Table 1). In 12 of the 20 patients in the mild/moderate group, OSA took the form of sporadic apneas or hypopneas, or, at most, of short runs of repetitive OSA superimposed on a background of steady snoring with varying degrees of chest-wall paradoxical motion. In the remaining eight patients in the mild/moderate OSA group, repetitive OSA occurred, but only in the supine position (n = 3), only during REM sleep (n = 2), or both (n = 3). By design, the AHI was significantly higher in the severe OSA group (Table 1). The patients with severe OSA, however, also had a significantly higher BMI and sustained lower values of SaO2 . There was no significant difference in the two groups' CPAP requirement (Table 1).


Severe OSA (n = 12)Mild/Moderate OSA (n = 20)p Value
Age, yr46 ± 947.8 ± 10n.s.
Sex12 M/0 F17 M/3 Fn.s.
BMI, kg/m2 37.8 ± 6.532.1 ± 4.5< 0.005
AHI, min−1 88 ± 1927 ± 16< 0.00001
Min SaO2 , %66 ± 1685 ± 8< 0.0002
CPAP, back, cm H2O15.9 ± 313.8 ± 4n.s.
CPAP, side, cm H2O12.4 ± 510 ± 4n.s.
 Yes9 6< 0.02
VtAF at PB 1.8 ± 0.72.5 ± 0.8< 0.05
Max VtAF 1.9 ± 0.72.7 ± 1.0< 0.01

Definition of abbreviations: AHI = apnea-hypopnea index; BMI = body mass index; CPAP = continuous positive airway pressure; PB = periodic breathing; PVA = proportional assist ventilation; VtAF = tidal volume amplification factor.

CSB was identified visually by the presence of gross fluctuations in Vt with a periodicity consistent with CSB (0.7 to 3.0 cycles/min) (as exemplified in Figure 2B). We did not set a specific threshold (for the amplitude of Vt oscillation) with which to define CSB, since the cycle amplitude did not appear to be graded with level of assist; breathing either showed some random variability (as exemplified in Figures 2A and 3) or was grossly periodic (Figure 2B). In most cases, central apneas were present between cycles. In a few cases, there were no apneas, but Vt at the nadir of the cycle was < 30% of peak Vt. Transition from stable breathing (or breathing with random variability) to gross cycling almost invariably occurred within a few breaths after a stepwise increase in level of assist (Figure 2B).

Arousals were uncommon during CSB. Excluding the final awakening that terminated the PAV run, there were only 22 arousals associated with a total of 212 CSB cycles in the 15 patients who developed CSB (i.e., 10.4%). In virtually all cases the arousals were marginal, barely meeting minimum diagnostic criteria (14). Only one patient had an arousal with each of the CSB cycles (4 cycles in this patient). In the other 14 patients the frequency of arousals ranged from 0% (5 patients) to 28% of CSB cycles. Arousals therefore occurred sporadically when they occurred at all. There were no discernible differences between the ventilatory patterns of cycles associated with or following arousals and those of other cycles.

For every PAV run that terminated in CSB, there were usually many earlier runs that were aborted without CSB because of awakening (see Methods). In no case was the highest assist level reached in these aborted runs higher than the level that ultimately produced CSB. Thus, no patient developed CSB when the assist level was lower than the level that ultimately resulted in CSB, and no patient managed to reach a higher level without developing CSB. This suggests that the level of assist at which CSB develops is consistent in a given experimental condition.

There was a wide range of susceptibility to CSB during the PAV titration. Figure 2 shows an example of the response in a patient with a low threshold for CSB. Figure 2A was obtained from tracings immediately before the appearance of CSB. Single-breath discontinuation of ventilatory assistance was done at the arrow in the figure. There was only a small reduction in Vt, indicating that the VtAF was low (VtAF = 1.3). The level of assist was increased slightly at the arrow in Figure 2B. CSB with central apneas appeared soon after this. By contrast, Figure 3 is an example of the response of a patient who was resistant to CSB. Breathing was essentially nonperiodic even though VtAF was quite high (note the marked reduction in Vt when ventilatory assistance was discontinued for one breath at the arrow in the figure (VtAF = 3.5).

Nine of the 12 patients with severe OSA developed CSB on PAV (Table 1). In these patients, VtAF immediately preceding CSB was relatively low (1.8 ± 0.7). Six of the 20 patients with mild/moderate OSA developed CSB. The VtAF required to induce CSB in these six patients (2.5 ± 0.8) was significantly higher than in the severe OSA group (p < 0.05) (Table 1). The proportion of patients developing CSB was significantly smaller in the mild/moderate OSA group (chi-square test, p < 0.02). This was the case even though, on average, PAV was titrated to a higher level in this group (VtAF 2.7 ± 1.0 versus 1.9 ± 0.7, p < 0.01; Table 1).

In 21 patients the change in FRC upon reducing CPAP from its optimal level (12.5 ± 4.1 cm H2O) to the minimum level of 2.0 cm H2O was 0.44 ± 0.27 L. There was no significant difference between the results (ΔFRC) for the severe and mild/moderate OSA groups (0.46 ± 0.31 L versus 0.42 ± 0.25 L, respectively).

The present study utilized a new approach to assess ventilatory stability: the Vt amplification factor required to induce CSB. Before the specific results of the study can be discussed and interpreted, it is necessary to provide an overview of factors that influence ventilatory stability, and of the role of VtAF in this scheme.

Determinants of Chemical Control Stability

Chemical control of respiration operates in a negative-feedback, closed-loop fashion (Figure 4). At a given metabolic rate, a transient change in ventilation (ΔV˙e) will result in a transient change in alveolar gas tensions (Pa CO2 , Pa O2 ). These changes are sensed by chemoreceptors (CR), resulting in a ventilatory response (ΔV˙e response) that is opposite in direction to the initial perturbation.

Khoo and colleagues (11) were the first to introduce the engineering concept of loop gain (LG) into the analysis of stability of chemical control. LG is a dimensionless index that defines the ratio of ΔV˙e response to ΔV˙e (LG = ΔV˙e response/ΔV˙e). The numerous factors involved in chemical control are conveniently grouped into the following three major categories.

Plant factors. Plant factors (11) are the factors that determine the extent to which gas tensions in mixed pulmonary capillary blood (Pc O2 , Pc CO2 ) will change for a given change in V˙e. The relation between ΔPc CO2 (or ΔPc O2 ) and ΔV˙e is referred to as plant gain (Gp), and is expressed in mm Hg/L/min. Clearly, Gp will be affected by the duration of the change in V˙e (ΔV˙e); the longer a given ΔV˙e is maintained (i.e., the slower the frequency of ΔV˙e), the bigger will be the change in Pc CO2 and Pc O2 . However, for a given duration of ΔV˙e (or cycle frequency), the change in Pc O2 and Pc CO2 is influenced by several factors. The more important of these are listed in Figure 4 (11, 12).

Factors that determine the change in gas tension at the CR for a given change in pulmonary capillary gas tension. Transient changes in Pc CO2 or Pc O2 will delay changes in gas tensions in the immediate vicinity of CR and attenuate their amplitude. The attenuation is the result of mixing of blood leaving the alveoli with a large volume of blood in the thorax and arteries. This blood space acts as a low-pass filter. In the case of central CR, further attenuation occurs because of slow diffusion characteristics in the environment surrounding these receptors (18). This diffusion space also acts as a low-pass filter. The relation between ΔPco 2 (or ΔPo 2) at the CR (ΔPcr CO2 , ΔPcr O2 ) and ΔPc CO2 (or ΔPc O2 ) is referred to here as Gm, signifying the gain change imposed by mixing and diffusion, and is expressed in mm Hg/mm Hg. Not only is the response at the CR attenuated through mixing and diffusion, but, as in the case of all-low pass filters, it is temporally shifted relative to the change at the pulmonary capillary level. The response at the CR is further delayed by the obligate transit times (circulation time) between the pulmonary capillaries and the CR. The total delay (i.e., circulation time plus phase shifts related to mixing and diffusion) determines the cycle duration at which the ventilatory response (ΔV˙e response) will be 180 degrees out of phase with the original perturbation in V˙e. This is of critical importance in determining overall LG (see the subsequent discussion).

Factors that determine the ventilatory response to changes in gas tensions at the CR. These factors determine what is called “controller gain” (11) (Gc, in L/min/mm Hg). Included among these factors are the sensitivity of CR to changes in gas tensions in their immediate vicinity, sensitivity of respiratory centers (RC) to CR output, excitability and integrity of the lower motor neurons supplying the respiratory muscles, and respiratory muscle strength. These, collectively, determine the change in Pmus per unit change in gas tension at the CR (ΔPmus/ΔPcr CO2 ) (Figure 4). Additionally, ΔPmus produces a ventilatory response (ΔV˙e response) whose magnitude is determined by respiratory mechanics (elastance and resistance).

Overall LG

In a sequential process such as chemical control, the overall gain is the mathematical product of the gains at all intermediate steps. Thus; LG = Gp × Gm × Gc. The units cancel out and LG is dimensionless. Because of the presence of gas stores in the lungs (FRC), the plant acts as a low-pass filter and Gp is, necessarily, frequency dependent. Likewise, mixing and diffusion processes act as low-pass filters, and as a result, Gm is frequency dependent. Accordingly, both Gp and Gm decrease as cycling frequency increases. It follows that overall LG is not a fixed number but is frequency dependent (11). The cycling frequency that is relevant to ventilatory stability is that at which the response (ΔV˙e response) is 180 degrees out of phase with the initiating change in V˙e (ΔV˙e). At higher frequencies, LG is smaller and hence irrelevant. At lower frequencies LG is higher, but the response overlaps with the initiating ΔV˙e, and the two (i.e., ΔV˙e response and ΔV˙e) tend to cancel each other out. The frequency at which ΔV˙e response is 180 degrees out of phase with ΔV˙e is determined by the total delay (see the previous discussion of factors that determine the change in gas tension at the CR). If LG at this frequency is > 1.0, the system will cycle at this frequency, since a given ΔV˙e will later result in an opposite change of equal or greater magnitude which, in turn, will be followed by an equal or still greater opposite change in V˙e, and so on. If LG at the critical frequency is < 1, sustained cycling cannot occur, since ΔV˙e response is < ΔV˙e, and this will result in an even smaller secondary response, and so on. In response to a transient change in V˙e, the most that can happen is unsustained cycling of diminishing amplitude.

Breathing does not show important periodic fluctuations in most humans. However, given the multitude of factors that influence LG (Figure 4), and the variability in each of these factors among individuals, it may be expected that underlying LG varies considerably even while breathing is stable. That a wide range of underlying LG exists in normal individuals, breathing regularly has been recently demonstrated (6, 7). It is evident that an individual with high (but < 1) LG is more likely to develop unstable breathing when challenged with an additional destabilizing factor affecting the plant, the delays, or the controller (e.g., a change in FRC or instability of the UA). The corollary of this is that the same derangement may cause one individual to develop clinically significant oscillations, whereas in others breathing would remain stable.

PAV provides an auxiliary pressure source that is proportional to Pmus (Figure 4). It therefore amplifies the pressure output that distends the system in response to respiratory muscle activation. The magnitude of this amplification is given by VtAF. It can be appreciated from Figure 4 that amplification at any level in the motor arm should amplify overall Gc to the same extent, provided that the intervention does not alter the gain at other levels of the controller. The procedure used to obtain VtAF (single-breath reloading) entails an increase in the mechanical load imposed on respiratory muscles. It is theoretically possible that the increased load elicits changes in RC or in spinal motoneuron activity at the same PaCO2 . This, however, is extremely unlikely; several investigators have shown no significant change in respiratory muscle EMG during the first loaded breath (including complete occlusion) in sleeping subjects (19-21). Another consideration is that VtAF describes the amplification produced by PAV at a given Pcr CO2 , whereas Gc describes the slope of the ventilatory response to changes in CR gas tensions. VtAF may not reflect the change in Gc if PAV alters the CR sensitivity to changes in gas tensions or the response of RC to changes in CR output. At the same metabolic rate (V˙co 2), the increase in Gc produced by PAV dictates a reduction in steady-state Pcr CO2 . In fact, with progressive increase in the level of PAV, end-tidal Pco 2 progressively decreases (6, 15) and end-tidal Po2 presumably also increases. These changes may, theoretically, alter CR responsiveness to gas tensions or the RC response to CR output. At maximum PAV assist, however, the steady-state changes in Pet CO2 , and presumably also in a Pet O2 , are in the range of 2 to 3 mm Hg (6, 15). It is very unlikely that this results in a significant change in responsiveness at either site. From this we conclude that VtAF reflects the increase in Gc at the prevailing steady-state gas tensions.

This account relates to the effect of PAV on controller gain (i.e., V˙e response to changes in Pcr CO2 ) above the CO2 apneic threshold. Because the apneic threshold during sleep is normally only a few millimeters of mercury below eupneic PaCO2 (6, 45), the reduction in steady-state PaCO2 produced by PAV, although small (2 to 3 mm Hg at high assist [6]), brings Pcr CO2 closer to the apneic threshold. Thus, when CSB starts because of the increase in LG, central apnea would occur more readily. With respect to overall LG, the closeness of Pcr CO2 to the apneic threshold can be considered a stabilizing factor. This is so because once apnea develops, Gc, and hence overall LG, instantly becomes zero; further reduction in Pcr CO2 , produced by delayed arrival of more hypocapnic blood, has no effect on Ve (i.e., it is not possible to have negative ventilation). Accordingly, although the reduction in steady-state Pcr CO2 produced by PAV increases the likelihood of central apneas once CSB begins, it does not play a role in generating or perpetuating the cycling. CSB develops when LG, in the ventilatory phase, exceeds 1.0.

When PAV assist is increased gradually, as was done in the present study, the point at which CSB is observed represents the point at which overall LG increases from just below 1.0 to just above 1.0. LG at the PAV step immediately preceding CSB (i.e., t − 1) can thus be presumed to be very close to 1.0. Since overall LG = Gp × Gm × Gc, and Gc at t − 1 was amplified by VtAF at t − 1 (i.e., VTAF[−1]), it follows that Gp × Gm × Gc × VtAF [−1] = 1.0. From this, LG without PAV can be estimated as 1/VtAF [−1]. This treatment assumes that PAV does not independently alter Gp or Gm, and that LG (with PAV) at t − 1 is 1.0. In reality, both assumptions involve some errors, but the errors are almost certainly very small and tend to cancel each other out.

For the foregoing reasons, and in view of the various factors that affect Gp and Gm (Figure 4), we feel that the only significant effect of PAV may be a small reduction in Pa CO2 . Because breathing pattern and V˙e are not altered appreciably by PAV (< 5% change in Vt and no change in V˙e [6, 7, 15, 22, 23]), and because the CPAP level was not altered, there is no reason for FRC or for Vd/Vt to change. We estimate the change in mean airway pressure to be no more than 2 cm H2O, even at high levels of PAV support in this setting.* This should have no measurable effect on cardiac output (CO) or circulatory delays (24-27). The change in metabolic rate as a result of unloading respiratory muscles in this clinical setting (i.e., with normalized upper airway) is too small to be measurable (22). There is no reason for PAV to alter the diffusion characteristics in the brain tissue surrounding central CR. End-tidal Pet CO2 (and hence Pa CO2 ) usually decreases by 2 to 3 mm Hg between 0% assist and the highest level (80 to 90%) of assist (6, 15). This corresponds to an approximate 5% reduction in Pa CO2 (i.e., Pa CO2 with a high level of PAV is 0.95 Pa CO2 at 0% assist). According to Khoo and colleagues (28), Gp is directly proportional to the square of Pa CO2 . As a result, Gp at high PAV should be 0.952, or 0.9 of its value at 0% assist.

The small error involved in assuming that Gp did not change as a result of PAV is partly or completely offset by assuming that LG at the PAV step immediately before CSB is 1.0, when in fact it is slightly less than 1.0 (the system is still stable but very close to developing spontaneous oscillation).

In summary, we believe that any errors involved in assuming that PAV did not alter Gp and Gm (almost certainly < 10%) are orders of magnitude smaller than the amplification of LG produced by PAV (300% or more). As a result, we believe that the term 1/VtAF [−1] provides a valid and direct estimate of overall LG in the absence of PAV. This, we believe, is the first time it has been possible to directly determine overall LG under conditions of stable breathing. This approach makes it possible to determine susceptibility to PB under different experimental conditions. The value of 1/VtAF at the step immediately preceding CSB is inversely related to susceptibility to PB. Thus, a value of 0.9 (i.e., VtAF[−1] = 1.1) indicates that a minor change in the gain at any of the many levels in the chemical control loop could precipitate CSB. By contrast, a value of 0.25 (i.e., VtAF[−1] = 4.0) would indicate that major alterations in Gc plant factors, or delays would be necessary to induce repetitive cycling.

Arousals may play an important role in perpetuating cycling (2, 3). We do not believe that this was the case in our study. Arousals occurred infrequently and sporadically when CSB was present, and even when they occurred had no discernible effect on the pattern or amplitude of the cycles. From this we conclude that the CSB observed in this study primarily reflected instability of chemical control.

Susceptibility to PB in OSA

The most important finding in this study was that even with a stabilized UA, patients with severe OSA had a more unstable ventilatory control system than did patients with less frequent OSA. Nine of 12 patients with severe OSA developed CSB with PAV, as compared with six of 20 patients in the mild/ moderate OSA group (p < 0.02). The difference is even more convincing when it is considered that the latter group was subjected to greater Vt amplification (2.7 ± 1.0 versus 1.9 ± 0.7, p < 0.01; Table 1). In earlier studies (6, 7, 29), a total of 30 normal subjects underwent similar PAV titration with a stabilized UA. Despite an average VtAF of 2.4 (range: 1.3 to 5.8), only one subject developed frank CSB with recurrent central apneas. Four subjects developed a waxing and waning ventilatory pattern, without central apneas, at the highest level of ventilatory assistance. Even when these four patients are considered as having developed CSB, the frequency of development of CSB with PAV provocation in sleeping normal subjects was only five of 30. The difference between patients with severe OSA (nine of 12) and normal subjects (five of 30) is highly significant (p < 0.003, chi-square test). The difference between patients with mild/moderate OSA (six of 20) and normal subjects was not significant (p < 0.3).

Hudgel and associates (30) recently compared OSA patients and normal subjects with respect to their dynamic ventilatory response to single-breath increases in inspired CO2 concentration. The OSA patients had a higher dynamic closed-loop response than did the normal subjects. Our results support Hudgel and associates' findings and extend them in several important respects. First, we demonstrated that overall LG is increased in OSA patients. Hudgel and associates (30) did not measure or estimate overall LG. Rather, they reported the ventilatory response to a given change in inspired CO2 concentration or in end-tidal PaCO2 . Accordingly, it is difficult to appreciate from their results how unstable the system is in absolute terms (i.e., the value of overall LG). Second, their subjects were studied while awake, upright, and breathing oxygen. Sleep, body position, and PaO2 have important effects on several determinants of LG. Our study was done during horizontal sleep with room air as the inspired gas. Third, we demonstrated a significant difference in ventilatory stability between patients with severe OSA and those with less severe OSA.

The greater susceptibility to PB in patients with severe OSA can be interpreted in two ways. First, this instability is responsible for or contributes to the greater severity of OSA. Second, differences in severity of OSA are primarily related to differences in UA structure/function; the greater instability of chemical control is not a cause but rather a consequence of severe OSA, or of some other factor that correlates with severity of OSA. Thus, severe OSA may theoretically, and over a long time, increase LG through greater impairment of cardiac function and greater likelihood of hypercapnia and hypoxemia, among other changes. Likewise, the greater instability of chemical control may, theoretically, be due to the higher BMI in severe OSA and the consequent reduction in FRC and Pa O2 . Patients with severe OSA have also been reported to have attenuated short-term potentiation (STP) following ventilatory stimulation (31). A reduced STP should enhance instability through increasing dynamic Gc (12). The CPAP required to eliminate all manifestations of UA dysfunction in our study was not significantly different (Table 1). Had differences in structure/function been the main reason for differences in severity of OSA, one might have expected a higher CPAP requirement in the severe OSA group. This reasoning, however, is very weak. Our data therefore do not permit a definite statement about whether the greater instability of chemical control is an important determinant of severity of OSA in these patients. Further studies are needed to conclusively address this issue. There is, however, sufficient information to make one suspect that the degree of instability that we observed with the use of CPAP will translate into more severe OSA in the absence of CPAP, at least in some patients. This is discussed subsequently.

How May a Higher LG with CPAP Produce Greater AHI Without CPAP?

None of the 32 patients that we studied had spontaneous CSB with CPAP. Thus, LG with CPAP was < 1.0 in all patients. As a result, unless the absence of CPAP is associated with a further increase in LG, a higher LG with CPAP (but < 1.0) need not, by itself, translate into more unstable breathing in the absence of CPAP. In the event that removal of CPAP is associated with additional increases in LG, it may reasonably be expected that, all else being the same, patients who have a higher LG with CPAP will more readily develop oscillatory behavior without CPAP than will those with a lower LG. Thus, for example, if we assume that removal of CPAP results, for one reason or another, in a 50% increase in LG, patients with an LG > 0.7 with CPAP will develop oscillatory behavior without CPAP, whereas those with an LG < 0.7 will not. The relation between LG with CPAP and without CPAP is therefore of considerable relevance to this issue.

Table 2 provides a summary of the qualitative effects of CPAP on various determinants of LG. It is evident that CPAP exerts multiple effects with opposing and at times complex and variable effects on LG. The effect (on LG) of the effect of CPAP on UA resistance is the most complex of these, and it would be useful to consider this separately from the other effects.


VariableChangeEffect on LG
Lung volume↓ (Gp)*
Inspiratory muscle length↓ (Gc)
Pa CO2 ↓ (Gp)
Pa O2 ↓ (Gp)(Gc)
Thoracic blood volume↑ (Gm)
Cardiac output↓ ↔ ↑ ↑ ↔ ↓ (Gp)
Respiratory compliance↓ ↔ ↑ ↓ ↔ ↑ (Gc)
Respiratory resistance↑ ↓ (Gc)

Definition of abbreviations: Gc = controller gain; Gm = mixing and diffusion; Gp = plant gain; LG = loop gain; Pa O2 = alveolar oxygen tension; Pa CO2 = alveolar carbon dioxide tension.

*Terms in brackets denote component(s) of LG being affected.

CPAP exerts several straightforward stabilizing effects. The increase in FRC reduces Gp (11, 12) and shortens inspiratory muscles, which in turn should reduce Gc (less change in pressure output, and hence in V˙e, per unit change in muscle activation [32, 33]). Elimination of the sleep-induced increase in UA resistance results in a lower Pa CO2 (34) and hence in a higher Pa O2 . A lower Pa CO2 is associated with a reduction in Gp (28). A higher Pa O2 results in a lower Gp (less change in SaO2 per unit change in V˙e), and also in a lower Gc (reduced ventilatory response to CO2) (18).

Mitigating these stabilizing influences are the effects of CPAP on thoracic blood volume and possible effects on CO and thoracic compliance. The expected reduction in thoracic blood volume should, by virtue of a smaller mixing pool, cause a greater Gm. This is destabilizing. CPAP decreases both cardiac preload and afterload (24). The former tends to decrease CO whereas the latter tends to increase it (24). What happens to CO accordingly depends on which effect dominates. A decrease in CO increases Gp (11, 12) and increases circulatory delay; both of which effects are destabilizing. An increase in CO would have the opposite effect. Thoracic compliance is an important determinant of ventilatory response to changes in respiratory muscle activation (Figure 4), and hence of Gc. What happens to compliance with CPAP depends on the location of FRC relative to the sigmoid pressure–volume (P–V) curve of the respiratory system (35). In obese patients, FRC is reduced and the respiratory system may be operating on the stiff lower range of the P–V curve. CPAP would then raise lung volume into a volume range in which compliance, and hence Gc, is higher. Conversely, if FRC is located, as it normally is (35), in the midrange of VC (where compliance is highest), an increase in lung volume with CPAP may move the respiratory system into a stiffer range in terms of compliance, with a consequently lower Gc.

It is evident from the foregoing summary that in a patient in whom the effect of CPAP on CO is nil to positive and the effect on thoracic compliance is nil to negative (e.g., a lean patient), the net effect of CPAP (independent of its direct effect on UA resistance) will definitely be to reduce LG and stabilize breathing. Thus, in such patients, LG without CPAP should be higher, and those with a relatively high LG during CPAP may thus develop spontaneous oscillation (i.e., LG > 1.0) without CPAP, even with a stable UA. In patients in whom the effect of CPAP on CO is negative and/or its effects on thoracic compliance are positive (e.g., a very obese patient with a very low FRC), the net effect of CPAP would depend on the relative weight of the stabilizing and destabilizing influences. This is complicated by the fact that the response of a given variable to CPAP may display a wide quantitative range. For example, in the 21 patients in whom we measured ΔFRC with CPAP, the range was 0 to 0.85 L. The correlation between FRC and CPAP was only weakly positive (r = 0.44, p < 0.03), indicating that factors other than the level of CPAP play the dominant role in determining the extent of increase in FRC. Notwithstanding those complexities, it may reasonably be expected that even in patients in whom the effects of CPAP are mixed, a subset would have a higher LG without CPAP than with it. In these subjects, those with a higher LG during CPAP will be more likely to develop spontaneous oscillations.

Figure 5 provides a framework for explaining the complex way by which changes in UA resistance with sleep and with CPAP may influence LG. For simplicity, only the ventilatory response to CO2 will be discussed. Hypoxic drive will clearly supplement hypercapnic drive under ordinary circumstances, but its inclusion here would not alter the basic analysis.

The isopleths in Figure 5 describe, schematically, the ventilatory response to CR CO2 at different levels of UA ( and hence respiratory) resistance (R). The uppermost isopleth is the ventilatory response during wakefulness. The isopleth marked “normal” represents the response with a normal, widely open UA such as may obtain during sleep under optimal CPAP. The lowermost isopleth (occ) represents the situation with a completely closed UA (a minimal slope is shown to distinguish this isopleth from the abscissa). Resistance is infinite and the ventilatory response, and hence Gc, is zero. There is considerable evidence that arousals occur when inspiratory efforts reach a critical level (36). Let us assume that in the subject under discussion, the threshold for arousal is reached at a CR Pco 2 of 48 mm Hg. This is given by the vertical heavy dashed line at Pco 2 = 48 mm Hg. The line identified as the metabolic hyperbola defines the relation between V˙e and Pcr CO2 that is consistent with a steady state at the prevailing metabolic rate (V˙co 2) and Vd/Vt: (PaCO2 = [0.863 · V˙co 2]/ [V˙e(1 − Vd/Vt)])*. The line shown pertains to a patient with a V˙co 2 = 200 ml/min and Vd/Vt of 0.4. When V˙ is below the line, PaCO2 must rise until the hyperbola is reached, and vice versa.

UA resistance increases with sleep onset in all humans (37), but the magnitude of the increase varies widely from fairly small to infinite (complete occlusion). With sleep onset, therefore, V˙e should immediately decrease by an amount that is related to the increase in UA resistance (Figure 5, solid vertical down-pointing arrows). As a result, Pcr CO2 and inspiratory efforts begin increasing. What happens to UA resistance subsequently depends on the balance between the collapsing effect of increasing diaphragmatic efforts and the dilating effects of recruitment of UA dilators (38).

In the event that the net effect is such that UA resistance remains constant as chemical drive increases, ventilation will increase along the isopleth corresponding to the prevailing UA resistance during sleep (Figure 5, arrows a to d). If the relevant isopleth reaches the metabolic hyperbola before reaching the right vertical (arousal) boundary (e.g., a relatively small increase in resistance, a low metabolic hyperbola, or a high arousal threshold), a new steady state of ventilation can be reached at a Pcr CO2 level that is below the arousal threshold. There is no sleep apnea (Figure 5, arrows a and b).

In the event the sleep-induced increase in UA resistance results in ventilation following an isopleth that would intercept the metabolic hyperbola at a Pcr CO2 that is higher than the arousal threshold, a steady state is not possible (Figure 5, arrows c and d). Arousal occurs before a steady state can be reached, the UA opens up, and V˙e increases to a point corresponding to the prevailing Pcr CO2 but at a much higher isopleth (Figure 5). V˙e is above the metabolic hyperbola, Pcr CO2 declines below the arousal threshold, sleep resumes, V˙e declines again to the appropriate sleep isopleth, and the cycle recurs. It follows that when resistance during sleep is independent of chemical drive, the occurrence of cycling depends strictly on the relationship between the arousal threshold, the position of the metabolic hyperbola, and the ventilatory response to CO2. These three variables may change from time to time during sleep. For example, the arousal threshold may change with sleep stage, the metabolic rate may rise in the presence of leg movements, Vd/Vt may be position-dependent, and the ventilatory response may change because of sleep stage or position-related changes in UA resistance or because of sleep stage-related differences in the central response to CR input. As a result, a patient may show periodic obstructive events at certain times while snoring steadily at other times.

In the type of patient represented in Figure 5 (i.e., in whom resistance is independent of chemical drive during sleep), instability of chemical control cannot be responsible for cycling. In fact, to the extent that Gc is lower than it would be with a wide open airway (compare the slope of any isopleth with that of the “normal” isopleth), the sleep-induced increase in resistance would tend to stabilize chemical control, and the greater the increase in resistance, the more stable chemical control becomes. By placing Gc on the “normal” isopleth, CPAP would tend to destabilize chemical control, and this effect on Gc may far outweigh any stabilizing effect of CPAP on plant factors (Table 2). Even though instability of chemical control per se may not be responsible for the cycling, it may increase the frequency of cycling (AHI). Thus, a high LG with a wide-open airway (e.g., during CPAP), as was found in this study, indicates that Gp and/or Gm and/or Gc up to the level of Pmus (Figure 4) is/are high. Accordingly, even though the overall LG for chemical control of respiration may be depressed during sleep because of the greatly reduced gain of the last step (Pmus → V˙e), the response of the RC and Pmus, to a given hypopnea in patients with a high LG on CPAP should be more brisk than in patients with a lower LG on CPAP. To the extent that arousal is related to CR output or to Pmus level (36), and not to absolute V˙e, a high LG on CPAP should translate into an earlier occurrence of arousal and a faster decline in respiratory output once arousal occurs. A greater AHI may therefore result.

The situation, however, is quite different if the sleep-induced increase in resistance is partly reversible with increasing chemical drive, and there is accumulating evidence that this is the case in many patients (39-44). A progressive decrease in UA resistance as CO2 rises would result in the ventilatory response line crossing increasingly higher isopleths in the interval after a sleep induced-obstructive hypopnea (Figure 6). In this case the ventilatory response to the ensuing hypercapnia is amplified because of the double effect of increasing effort and simultaneously decreasing resistance. This at once offers opportunities for decreased stability or increased stability. Figure 6A illustrates how a progressive decrease in resistance may destabilize breathing. With sleep onset, ventilation decreases to an isopleth that intersects the metabolic hyperbola before the arousal threshold (Figure 6A, line b). If resistance remains constant, ventilation and Pcr CO2 will follow this line until the metabolic hyperbola is reached. Because the slope of this isopleth is decreased relative to the “normal” line, LG is low and the transition to a new steady state is orderly (as in Figure 5, arrow b). Instability does not occur. Arrow b1 in Figure 5, however, describes the situation in which resistance decreases as chemical drive increases. The ventilatory response (Gc) is now higher than it would be otherwise (compare arrow b1 with arrow b in Figure 5), and it may be even higher than Gc with a widely open (but fixed) UA, such as is the case with CPAP (compare the slope of arrow b1 with the slope of isopleth N in Figure 6A). Whether or not this increase in Gc is tolerated, resulting in a steady state (Figure 6A, open circle), depends on the LG for chemical control in the presence of stable, normal UA resistance. If the latter is close to 1.0, the additional increase in Gc may raise the overall LG above 1.0, resulting in a ventilatory overshoot above the metabolic hyperbola (Figure 6A, dashed diagonal arrow continuing from b1), which would be followed by an undershoot (not shown), with repetition of the cycle. Ventilatory instability is produced when it would not otherwise have developed.

Figure 6B shows the opposite scenario. With sleep onset, ventilation decreases to an isopleth that intersects the arousal threshold before the metabolic hyperbola (Figure 6B, c). If resistance remains constant, repetitive arousal-induced cycling will develop (as in Figure 5, c). An increase in ventilatory response produced by the orderly decrease in UA resistance as chemical drive increases may make it possible for a steady state to be reached (note that arrow c1 in Figure 6 intersects the metabolic hyperbola first). Breathing is made stable when it would otherwise not be. If the response is excessive, however, and LG with normal resistance is close to 1.0, cycling would still occur (Figure 6B, arrow c2). Arousal-mediated instability would simply be replaced by instability of chemical control.

In summary, we have shown that when the UA is stabilized with CPAP, patients with severe OSA have a higher LG for chemical control, and are therefore more susceptible to repetitive ventilatory cycling than are patients with less severe OSA. There are theoretical reasons to believe that this may contribute to the severity of OSA in the absence of CPAP, at least in some patients. A cause-and-effect relation, however, remains to be established experimentally.

The authors would like to thank Robyn Melnichuk for secretarial assistance.

Supported by the Medical Research Council of Canada.

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Correspondence and requests for reprints should be addressed to Dr. M. Younes, Respiratory Hospital, RS 315, 810 Sherbrook Street, Winnipeg, MB, R3A 1R8 Canada. E-mail:

* Even at high levels of support in these patients, peak Paw during inspiration is higher than CPAP, usually by no more than 10 cm H2O (for example, see Figure 3). Given a triangular inspiratory Paw waveform and a Ti/Ttot ratio of 0.4 (as in Figure 3), the increase in mean Paw (over CPAP) produced by high levels of PAV support is 2 cm H2O.

In this account it is assumed that, in the steady state, PaCO2 and Pcr CO2 are in stable equilibrium.


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