American Journal of Respiratory and Critical Care Medicine Vol 165. pp. 1245-1250, (2002)
© 2002 American Thoracic Society
ApneaHypopnea Threshold for CO2 in Patients with Congestive Heart Failure
Ailiang Xie,
James B. Skatrud,
Dominic S. Puleo,
Peter S. Rahko and
Jerome A. Dempsey
Departments of Medicine and Preventive Medicine, University of Wisconsin, and the Middleton Memorial Veterans Hospital, Madison, Wisconsin
Correspondence and requests for reprints should be addressed to Ailiang Xie, M.D., Ph.D., Pulmonary Physiology Laboratory, William S. Middleton Veterans Hospital, 2500 Overlook Terrace, Madison, WI 53705. E-mail: axie{at}facstaff.wisc.edu
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ABSTRACT
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To understand the pathogenesis of central sleep apnea (CSA) in patients with congestive heart failure (CHF), we measured the end-tidal carbon dioxide pressure (PETCO2) during spontaneous breathing, the apneahypopnea threshold for CO2, and then calculated the difference between these two measurements in 19 stable patients with CHF with (12 patients) or without (7 patients) CSA during nonrapid eye movement sleep. Pressure support ventilation was used to reduce the PETCO2 and thereby determine the thresholds. In patients with CSA, 1.53% CO2 was supplied temporarily to stabilize breathing before determining the thresholds. Unlike patients without CSA whose eupneic PETCO2 increased during sleep (37.7 ± 1.4 mm Hg versus 40.2 ± 1.5 mm Hg, p < 0.01), patients with CSA showed no rise in PETCO2 from wakefulness to sleep (37.5 ± 0.9 mm Hg versus 38.2 ± 1.0 mm Hg, p = 0.2). Patients with CHF and CSA had their eupneic PETCO2 closer to the threshold PETCO2 than patients without CSA ( PETCO2 [eupneic PETCO2 threshold PETCO2] was 2.8 ± 0.3 mm Hg versus 5.1 ± 0.7 mm Hg for apnea, p < 0.01; 1.7 ± 0.7 versus 4.1 ± 0.5 mm Hg for hypopnea, p < 0.05). In summary, patients with CHF and CSA neither increase their eupneic PETCO2 during sleep nor proportionally decrease their apneahypopnea threshold. The resultant narrowed PETCO2 predisposes the patient to the development of apnea and subsequent breathing instability.
Key Words: congestive heart failure apnea threshold
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INTRODUCTION
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Nearly half the patients with congestive heart failure (CHF) have periodic breathing and central sleep apnea (CSA) (1, 2). Previous studies have emphasized the critical importance of hypocapnia in the pathogenesis of the CSA (3, 4). The chronic hyperventilation observed in these patients (5, 6) has been proposed to drive the arterial carbon dioxide pressure (PaCO2) toward the hypocapnic apnea threshold, thereby predisposing the patients to periodic breathing (4, 6). An increased chemosensitivity (79) has also been reported in these patients and considered to be a major contributor to the periodic breathing (10). However, hyperventilation and hypocapnia alone are insufficient to account for breathing instability in humans (1114) or animals (15). More important than the degree of hyperventilation is the difference between the eupneic PaCO2 and the apnea threshold carbon dioxide pressure (PCO2). For example, in sleeping dogs, metabolic acidosis decreases the apnea threshold more than it decreases the eupneic PCO2. As a result of the consequent greater difference between the eupneic PCO2 and the apnea threshold, the dog is less susceptible to periodic breathing during metabolic acidosis (15). In contrast, hypoxia reduces the eupneic PaCO2 more than the apnea threshold PCO2, thereby narrowing the difference between the two and predisposing to apnea both humans (16) and dogs (15). These findings indicate that the difference between the eupneic and threshold PCO2 may be a crucial determinant of the susceptibility to apnea.
We hypothesized that the eupneic PaCO2 is closer to the apneahypopnea threshold in CHF patients with CSA compared with those patients without CSA. Accordingly, we measured the apneahypopnea threshold and eupneic PCO2 and then calculated the proximity between the two in patients with stable CHF with or without CSA. In an attempt to identify the factors affecting the relationship between the eupneic PCO2 and the apneahypopnea threshold, we also examined the influence of sleep state on PCO2 and the ventilatory response to PCO2 below eupnea in the two groups.
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METHODS
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Subjects
We studied 19 patients with stable CHF: 12 with CSA (CSA group) and 7 without CSA (control group) (see Table 1). The CSA group had an apnea/hypopnea index (AHI) of 10 or more per hour of sleep with at least 80% of the respiratory events central in nature. The control group had an AHI of 5 or less per hour of sleep. The patients in the two groups were matched with respect to age, sex, body mass index (BMI), and left ventricular ejection fraction (LVEF). The study was approved by the University of Wisconsin Health Sciences Human Subjects Committee, and all patients provided informed written consent before the study.
Protocol
Before the sleep study, all patients had routine pulmonary function tests, performed at least two hours after a meal. LVEF was measured using two-dimensional echocardiography. Nocturnal polysomnography (17) was performed to classify subjects with and without CSA. On the second night, patients breathed through a full-face mask attached to a mechanical ventilator as previously described (16). After a 15-minute period of stable wakefulness, zolpidem (10 mg) was administrated to all subjects. The ventilator was set in the pressure support mode. During stable nonrapid eye movement (NREM) sleep, each threshold determination was initiated with a 35-minute period of spontaneous breathing at a low value of continuous positive airway pressure (CPAP; 26 cm H2O) that was sufficient to eliminate any evidence of flow limitation on the inspiratory flow signal. The inspiratory pressure was increased to 6 cm while the expiratory pressure was maintained at CPAP value. If no apnea or hypopnea occurred after two minutes, the inspiratory pressure was increased in 2-cm H2O increments at two-minute intervals, with the end-expiratory pressure unchanged. When apneas and/or hypopneas occurred, the patient was returned to baseline CPAP and spontaneous breathing.
If patients had spontaneous periodic breathing during sleep that lasted longer than 30 minutes, 1.53% CO2 was administrated to eliminate apneas and hypopneas and thereby stabilize their breathing. If the stable breathing pattern persisted, the patients were switched to room air for another five minutes followed by pressure support trials as described previously. If the periodic breathing returned within a five-minute room air period, CO2 was again administered until the breathing pattern was stabilized. CO2 inhalation was then stopped, and the apneahypopnea threshold was determined by the following method.
Sleep eupneic PETCO2 and other ventilatory parameters were measured during stable status, which means stable NREM sleep with rhythmic breathing. Apnea was defined as the absence of inspiratory effort on the mask pressure and absence of flow and chest/abdomen movement for at least 10 seconds (Figures 1 and 2)
. Hypopnea was defined as two or more untriggered efforts detected on the mask pressure tracing associated with a 50% or greater reduction in tidal volume. The apneahypopnea thresholds were determined by averaging PETCO2 of the 3 successive breaths that had the lowest PETCO2 of the last 10 breaths before either the first hypopnea or the first apnea. The eupneic PETCO2 was measured during the three to five minutes of spontaneous stable breathing before each trial and averaged for all trials. Trials that resulted in awakening or arousal were excluded from analysis.

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Figure 1. Polygraph record of a pressure support trial in a sleeping patient. The baseline period shows spontaneous, stable breathing with CPAP of 2 cm H2O. When the pressure support value was increased to 10 cm H2O (12/2 cm H2O), the reduction of PETCO2 was sufficient to cause an apnea as manifested by absence of flow for longer than 10 seconds. The initial apnea was followed by a hypopnea characterized by several untriggered breaths, indicating an inspiratory effort below 2 cm H2O. The apnea threshold was determined as the mean PETCO2 of the lowest three consecutive breaths preceding the first apnea (indicated by the thick horizontal line). On the VT channel, inspiration is up, and expiration is down.
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Figure 2. Polygraph record of a spontaneous apnea in a sleeping subject. Exogenous CO2 had previously stabilized the breathing pattern and had been stopped for five minutes. The patient was breathing spontaneously on room air with CPAP of 2 cm H2O. Before the apnea, oscillation of ventilation was noted, but rhythmic breathing persisted. An apnea occurred, as manifested by absence of flow for longer than 10 seconds. The apnea threshold was determined as the mean PETCO2 of the lowest three consecutive breaths preceding the first apnea (indicated by the thick horizontal line).
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Data Analysis
Comparisons of the eupneic PETCO2 (control versus CSA and awake versus sleep within the same group), threshold PETCO2, and the difference between eupneic and threshold PETCO2 (control versus CSA and apnea versus hypopnea within the same group) were made using two-way repeated measures analysis of variance. Post hoc analysis was performed with a StudentNewmanKeuls test. The ventilatory response was calculated by dividing VE (eupneic VE apneic or hypopneic VE) by PETCO2 (eupneic PETCO2 apnea or hypopnea threshold PETCO2). The slopes of the ventilatory responses of the two groups were compared using Student's unpaired t test. Data are reported as mean ± standard error in the text, table, and figures. p Values less than 0.05 were considered statistically significant.
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RESULTS
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Characteristics of Patients with and without CSA
The characteristics of patients with and without CSA are shown in Table 1. By design, the AHI was significantly and pathologically higher in the CSA group, compared with the control group (50 ± 7 events per hour versus 3 ± 0 events per hour, p < 0.01), which associated with a greater arousal index (29 ± 5 events per hour versus 9 ± 2 events per hour, p < 0.01). Both groups consisted of elderly men (61 ± 4 yr versus 62 ± 4 yr, p > 0.05) with moderate increase in weight (BMI 29 ± 3 versus 30 ± 1, p = 0.56). In five subjects of the control group and eight subjects of the CSA group, CHF was secondary to ischemic cardiomyopathy, with the remainder of patients having nonischemic dilated cardiomyopathy. Patients in the two groups had a similar degree of severe left ventricular dysfunction as indicated by a low LVEF (31 ± 4% versus 26 ± 2%, p = 0.21). The two groups were also similar with respect to their pulmonary function and medications. In the control group, six subjects were on angiotensin-converting enzyme inhibitors, four were on diuretics, four were on digoxin, and five were on a beta-blocker. In the CSA group, 10 patients were on angiotensin-converting enzyme inhibitors, 10 were on diuretics, 6 were on digoxin, and 4 were on a beta-blocker. In the control group, two patients had mitral regurgitation, and none had atrial fibrillation or pulmonary hypertension. In the CSA group, four patients had atrial fibrillation, five had mitral regurgitation, and three had pulmonary hypertension on the basis of echocardiographic criteria.
Effect of Sleep on Breathing Pattern and Eupneic PCO2
During periods of stable breathing, we examined the effect of sleep on eupneic PCO2, breathing frequency, tidal volume, and minute ventilation. There was no difference in PETCO2 during wakefulness (37.7 ± 1.4 mm Hg versus 37.5 ± 0.9 mm Hg, p > 0.05) or during sleep (40.2 ± 1.5 mm Hg versus 38.2 ± 1.0 mm Hg, p > 0.05) between the two groups. However, the increase in PETCO2 from wakefulness to sleep was smaller in the CSA group compared with the control group. Patients in the control group showed a consistent and significant rise in eupneic PETCO2 at the onset of sleep (from 37.7 ± 1.4 mm Hg to 40.2 ± 1.5 mm Hg, p < 0.01) compared with patients with CSA (37.5 ± 0.9 mm Hg versus 38.2 ± 1.0 mm Hg, p = 0.2; see Figure 3)
. Sleep did not significantly affect breathing patterns in either the control or CSA group in terms of frequency (15.0 ± 0.6 breaths per minute versus 14.9 ± 1.7 breaths per minute in the control group; 13.5 ± 1.1 breaths per minute versus 15.5 ± 0.9 in the CSA group), tidal volume (570 ± 65 ml versus 504 ± 61 ml in the control group; 599 ± 71 ml versus 562 ± 35 ml in the CSA group), or minute ventilation (8.5 ± 1.0 L/min versus 7.0 ± 0.5 L/min in the control group; 8.9 ± 0.7 L/min versus 8.6 ± 0.6 L/min in the CSA group). Sleep arterial oxygen saturation (SaO2) during stable breathing was 96 ± 1% in the control group and 95 ± 1% in the CSA group, and the difference was not statistically significant.
Proximity of Eupneic PETco2 to Threshold during Sleep
In the control group, four patients developed both apneas and hypopneas, one patient had only apneas, and two patients had only hypopneas. As a result, we analyzed the apnea threshold in five patients and the hypopnea threshold in six patients. In the CSA group, all 12 patients had apneas, but only 10 patients had hypopneas. As shown in Figures 3 and 4
, the apneahypopnea threshold was not statistically different between the control group versus the CSA group (apnea threshold 34.7 ± 2.1 mm Hg versus 35.5 ± 0.9 mm Hg, p > 0.05; hypopnea threshold 37.5 ± 1.2 mm Hg versus 37.2 ± 1.3 mm Hg, p > 0.05). However, PETCO2 (eupneic PETCO2 threshold PETCO2) was significantly smaller in the CSA group than in the control group (apnea: 2.8 ± 0.3 mm Hg versus 5.1 ± 0.7 mm Hg, p < 0.01; hypopnea: 1.7 ± 0.7 mm Hg versus 4.1 ± 0.5 mm Hg, p < 0.05). Although PETCO2 (eupneicapnea threshold) tended to be greater than PETCO2 (eupnoeichypopnea threshold) in both groups, the difference was not significant.
Another way of examining the relationship between the reduction of PETCO2 and the development of periodic breathing was to calculate the ventilatory response to CO2 below eupnea. As shown in Figure 5 , the ventilatory response was significantly greater in the CSA group than in the control group (3.86 ± 0.79 L/minute per mm Hg versus 1.47 ± 0.18 L/minute per mm Hg, p < 0.05).
Effect of Pressure Support on ApneaHypopnea Threshold
Because not all subjects had their apneahypopnea threshold determined with pressure support, we examined whether the threshold was different if it was determined with pressure support versus a spontaneously falling PETCO2. In the seven patients from the CSA group who had both spontaneous and ventilator-induced apneas or hypopneas, the apneahypopnea threshold was almost identical with the two methods (spontaneously falling PETCO2 versus ventilator-induced: 35.7 ± 1.3 mm Hg versus 35.7 ± 1.6 mm Hg, p > 0.05, for apnea threshold and 37.3 ± 2.0 mm Hg versus 36.7 ± 1.6 mm Hg, p > 0.05, for hypopnea threshold). In addition, the nadir of SaO2 immediately before the onset of apnea was 95.0 ± 0.1% for spontaneous apneas and 95.5 ± 0.3% for the ventilator-induced apneas. The difference was not statistically significant.
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DISCUSSION
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Patients with CHF and CSA showed a decreased proximity of eupneic PETCO2 to the threshold PETCO2 and a greater hypocapnic ventilatory response below eupnea compared with patients with CHF but without CSA. These findings shed light on the pathophysiologic interaction between cardiac dysfunction and ventilatory control instability, because the narrow proximity of eupneic and threshold PETCO2 makes a transient reduction of PCO2 much more likely to fall below the apnea threshold, and the increased ventilatory sensitivity below eupneic PCO2 makes the respiratory system more sensitive to any reduction of CO2. Thus, both abnormalities predispose patients to periodic breathing. Although a low eupneic PCO2 has been reported, and a eupneic PCO2 close to the apneic threshold has been suggested as the main mechanism of CSA (3, 4, 6), previous studies have not precisely measured the threshold during steady-state conditions in CSA or compared it with age-, BMI-, and heart functionmatched control subjects. Our study also extends the previous body of work regarding the ventilatory response to added chemical stimuli above the eupneic value (7, 8) by looking at the respiratory sensitivity to a withdrawal of chemical stimulus below eupneic value, which directly addresses the vulnerability of the respiratory system to a transient reduction of CO2. It is not clear what causes the eupneic PCO2 to be closer to the threshold in patients with CSA. On the basis of our data, the small difference between the two results from a combination of a relatively lower eupneic PCO2 and a disproportionately high apneahypopnea threshold.
Effect of Sleep on Eupneic PCO2
Unlike the control patients, patients with CSA demonstrated an unusual response to the sleeping state, in that their PETCO2 did not increase in going from wakefulness to sleep. This disparity has been previously reported (4). In normal subjects, the hypercapnic effect of sleep persists even in the presence of ventilatory stimulation or inhibition with progesterone or hypoxia or with metabolic alkalosis (18). These findings suggest that the sleeping state in our patients is associated with an added ventilatory drive that offsets the removal of the ventilatory drive associated with wakefulness.
Nonchemical ventilatory stimulation resulting from pulmonary congestion might be a source of the additional ventilatory drive during sleep (4, 19). Although our control and CSA patients had similar pulmonary function and LVEF, we cannot exclude the possibility of a higher pulmonary capillary wedge pressure or mean pulmonary arterial pressure in the patients with CSA (20). Our patients with CSA had a higher incidence of atrial fibrillation and mitral regurgitation. Both disorders are associated with increased left ventricular end-diastolic volume and filling pressure, which in turn have been reciprocally related to the increase in PaCO2 from wakefulness to sleep (4). The elevation of interstitial pressure may stimulate pulmonary irritant and juxtacapillary receptors, resulting in rapid shallow ventilation and consequent hypocapnia (21). The manifestation of the ventilatory stimulation associated with pulmonary vascular congestion is more prominent in unconscious, compared with conscious, dogs (22). Thus, the failure of the PCO2 of our patients with CSA to increase normally during sleep may be related to increasing pulmonary vascular congestion during sleep and an unmasking of the enhanced ventilatory response by the sleeping state. However, evidence against a vagal mechanism for the hyperventilation and CSA is provided by the observation that a patient with CHF after bilateral lung transplantation showed a lower eupneic PCO2 and CSA despite vagal denervation (23).
Relatively High Apnea-Hypopnea Threshold
If the ventilatory drive during sleep was enhanced in patients with CSA, we would expect a proportional lowering of the apnea threshold. On the contrary, the apneahypopnea thresholds were not different compared with the control patients. As a result, the patients with CSA demonstrated a closer proximity of the eupneic PCO2 to the apneahypopnea threshold. This finding contrasts with the effect of other ventilatory stimulants that were studied in sleeping dogs, including metabolic acidosis and almitrine (15). With these ventilatory stimulants, the apnea threshold was decreased out of proportion to the reduction of the eupneic PCO2, and thus, the proximity of the eupneic PCO2 to the apnea threshold was widened.
A ventilatory stimulant that is somewhat analogous to our observations in the patients with CSA is hypoxia (16). Hypoxia narrows the difference between eupneic PCO2 and threshold PCO2 by failing to proportionally reduce the threshold in the face of a reduction of eupneic PCO2. In the present study, however, the CSA group had an SaO2 that was similar to that of the control group and was within the normal range. Therefore, we do not believe that hypoxia contributed to the narrow proximity in our patients with CSA. Because both CHF and hypoxia facilitate periodic breathing in association with a narrowed difference between eupneic PCO2 and threshold PCO2, we cannot eliminate the possibility that the high threshold in these two conditions may have a common mechanism.
Implications for Periodic Breathing
The narrowed proximity of the eupneic PCO2 to the apnea threshold has two important implications for the development of periodic breathing in patients with CHF. First, this narrowed proximity is consistent with an increased sensitivity of ventilation to reductions in PCO2 below the eupneic PCO2 in a manner similar to what has been reported regarding the ventilatory response to PCO2 above eupnea (79). We detected a higher ventilatory response to CO2 below the eupneic value in patients with CSA compared with the control group. In the control group, the ventilatory response below eupnea was 1.5 L/minute per mm Hg, which is similar to the 1.61.9 L/minute per mm Hg in normal subjects without heart dysfunction or sleep-disordered breathing (16, 24, 25). In the CSA group, the ventilatory response to CO2 below eupnea was 3.9 L/minute per mm Hg, which is similar to the 36 L/minute per mm Hg in normal subjects during hypoxia (16, 26). This increased ventilatory control system gain both above and below eupnea will exaggerate the ventilatory overshoot and undershoot associated with oscillations in respiratory drive and thereby predispose patients to ventilatory instability.
The second important consequence of the close proximity of the apnea threshold to the eupneic PCO2 is the enhanced susceptibility to apnea and the destabilizing effect of apnea itself on the breathing pattern. The occurrence of apnea introduces a profound delay between the rising chemical stimuli that accumulate during the apnea and the eventual ventilatory response (27). In the study of Leevers and associates, reinitiation of breathing was not observed after an apnea until the chemical stimuli accumulated to hypercapnic and hypoxic levels compared with eupnea. When ventilation is resumed at the termination of the apnea, the high level of chemical stimuli results in a ventilatory overshoot that serves to perpetuate the periodic breathing pattern. Thus, apnea itself, by introducing phase delays between the accumulating chemical stimuli and the ventilatory response, can contribute to ventilatory instability.
Methodologic Considerations
As an indication of the threshold, we chose the PETCO2 from the 3 consecutive breaths that had the lowest PETCO2 of the last 10 breaths before each apnea or hypopnea, rather than the breath immediately preceding the apnea/hypopnea. Our rationale for this approach was based on the observation that the time from lowest PETCO2 in each hyperpneaapnea cycle to the onset of apnea has been shown to be the same as lung to ear circulatory delay, suggesting that the lowest PETCO2 sensed at the peripheral chemoreceptors might be best correlated with the subsequent apnea (3).
In patients with CSA, we chose to stabilize the breathing pattern with exogenous CO2 rather than to determine the threshold during the nonsteady state periodic breathing. The strength of this approach is related to the following consideration. Determination of the apnea threshold during periodic breathing would be influenced by the previous apnea-induced asphyxia and associated arousal. To avoid this problem, we first stabilized the breathing pattern with 1.53% CO2, then stopped the CO2 administration for at least five minutes, and finally recorded the threshold at the first appearance of apnea and hypopnea. Previous studies have shown that five minutes is sufficient time to return the ventilation and PCO2 back to baseline following even higher levels of CO2 (46%) (28). In the eight patients who required CO2 to stabilize their breathing pattern, PETCO2 (eupneic PCO2- - threshold PCO2) was actually larger than in the four patients who did not receive CO2 and had their threshold determined with pressure support (3.3 ± 0.3 mm Hg versus 1.4 ± 0.4 mm Hg). Thus, we do not believe that CO2 inhalation had an independent effect in producing the systematic narrowing of the eupneic PCO2threshold relationship that we observed in our patients with CSA compared with the control patients.
The apneahypopnea threshold determination could have been affected by the method used to lower the PCO2, pressure support ventilation versus spontaneous breathing. It has been demonstrated that positive pressure ventilation produces neuromechanical inhibition to the respiratory drive (29), which might introduce hypopnea despite the isocapnic conditions (30). In our study, pressure support ventilation was used in all of the control patients but in only part of the patients with CSA. To assess the apneahypopnea threshold determined by pressure support versus spontaneous reduction in PCO2, we compared the threshold values in seven patients with CSA who had their apnea threshold determined by both the pressure support and spontaneous breathing techniques. The relationship between eupneic PETCO2 and threshold was similar with both techniques, indicating that the difference we observed between the CSA and control groups was not related to the use of different measuring techniques. The lack of influence of pressure support on the apneahypopnea threshold may be due to the lower pressure support level used in the CSA group. Because the pressure support level required to produce apnea or hypopnea was higher in the control than in the CSA group, the mechanical inhibition of ventilatory drive would have been higher in the control group. If neuromechanical inhibition increased the susceptibility to apnea or hypopnea in the control group, we may have actually underestimated the difference in the threshold between the control and CSA groups.
We investigated the possibility that variation in medication usage could account for the differences in eupneic PCO2 and apneahypopnea threshold that were observed in patients with and without CSA. Most patients in both groups were on angiotensin-converting enzyme inhibitors, diuretics, beta-blockers, and digoxin. Zolpidem was used in all patients to facilitate sleep and minimize arousal from sleep. This medicine at a dosage of 10 mg has been shown to have no effect on respiration in terms of occlusion pressure, ventilation, PaCO2, SaO2, ventilatory response to CO2, or respiratory disturbance index (3135). Therefore, it is unlikely that zoplidem affected the apneahypopnea threshold in our study; even if an anticipated effect was present, it would be present in both groups and thus not alter our conclusions.
In summary, patients with CHF and CSA demonstrate a pattern of ventilatory stimulation that is unique compared with other nonhypoxic ventilatory stimulants. First, they do not hypoventilate during sleep to the degree observed in control patients. Secondly, the apneahypopnea threshold is not proportionally reduced, and the sensitivity of the ventilatory response to CO2 below eupnea is enhanced. These two abnormalities result in a narrowed difference between the eupneic PCO2 and the ventilatory threshold, which in turn is associated with an unusual susceptibility to apnea and breathing pattern instability.
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Acknowledgments
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The authors would like to thank General Clinical Research Centre of University Wisconsin for assistance.
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FOOTNOTES
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Supported by the VA Research Service, NIH R01 HL62561-02, and UW General Clinical Research Center.
Received in original form October 9, 2001;
accepted in final form December 21, 2001
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