The mechanisms leading to hypoxemia during sleep in patients with respiratory failure remain poorly understood, with few studies providing a measure of minute ventilation (V˙ i) during sleep. The aim of this study was to measure ventilation during sleep in patients with nocturnal desaturation secondary to different respiratory diseases. The 26 patients studied had diagnoses of chronic obstructive pulmonary disease (COPD) (n = 9), cystic fibrosis (CF) (n = 2), neuromusculoskeletal disease (n = 4), and obesity hypoventilation syndrome (OHS) (n = 11). Also reported are the results for seven normal subjects and seven patients with effectively treated obstructive sleep apnea (OSA) without desaturation during sleep. Ventilation was measured with a pneumotachograph attached to a nasal mask. In the treated patients with OSA and in the normal subjects, only minor alterations in V˙ i were observed during sleep. In contrast, mean V˙ i for the group with nocturnal desaturation decreased by 21% during non–rapid-eye-movement (NREM) sleep and by 39% during rapid-eye-movement (REM) sleep as compared with wakefulness. This reduction was due mainly to a decrease in tidal volume (V˙ t). Hypoventilation was most pronounced during REM sleep, irrespective of the underlying disease. These data indicate that hypoventilation may be the major factor leading to hypoxia during sleep, and that reversal of hypoventilation during sleep should be a major therapeutic strategy for these patients.
Ventilation has been shown to decrease by 10 to 15% during non–rapid-eye-movement (NREM) sleep as compared with wakefulness in healthy subjects (1-5). However, the changes reported during rapid-eye-movement (REM) sleep are somewhat conflicting. Some investigators have shown a similar decrease in minute ventilation (V˙i) during NREM and REM sleep (5, 6), whereas others have found a more pronounced reduction of 15% in V˙i during REM sleep, as compared with a reduction of only 6% during NREM sleep (2).
Oxyhemoglobin saturation decreases in sleep in a wide variety of lung, neuromuscular, and skeletal disorders. Desaturation is usually worse in REM sleep. The exact mechanism leading to desaturation in sleep is unclear. Hypoventilation (7-9) and ventilation/perfusion mismatching (8, 10) are both possible mechanisms. Increased upper airway load, decreased reflex drive, and muscle fatigue are all potential causes of hypoventilation, whereas a reduced FRC (7) is a likely cause of further ventilation/perfusion mismatching. Clinical experience suggests that one of these various mechanisms may dominate in one patient whereas a different mechanism may dominate in another.
A limited number of studies of V˙i during sleep have been done exclusively in patients with chronic obstructive pulmonary disease (COPD) (7-9, 11). These studies have suggested that during NREM sleep, V˙i decreases by about the same amount as in normal subjects, but that there is a more pronounced reduction during REM sleep. Inductive plethysmography was used to measure ventilation in all except one (11) of these studies. This method has limitations in accuracy if used over several hours and with the subject in different body positions (12). In diseases other than COPD in which nocturnal desaturation occurs, there are no quantitative data on ventilation.
Upper-airway resistance is known to increase by more than 200% in NREM sleep in normal subjects (13, 14). Even in healthy subjects with normal muscle function, an increase in respiratory muscle activity does not completely compensate for this additional load (15). Thus, an increase in upper-airway resistance might decrease V˙i in patients with respiratory disease.
A decade ago it was merely of scientific interest to distinguish the most relevant mechanisms leading to nocturnal hypoxemia from other mechanisms, since supplemental oxygen was the only available treatment for this condition. Although correction of hypoxemia may be achieved with the use of appropriate oxygen therapy, worsening hypercapnia may occur in some patients, particularly those in whom hypoventilation is the major reason for desaturation (16-18). With the introduction of new forms of treatment, especially nasal continuous positive airway pressure (nCPAP) (19) and nasal ventilation (20), it is now clinically important to determine the main cause(s) of hypoxemia so that the most appropriate of the many different treatment options can be used.
We hypothezized that hypoventilation is a major cause of hypoxemia during sleep not only in COPD but in all forms of respiratory failure. In order to quantitate the amount of hypoventilation occurring, in such conditions, we sought to directly measure ventilation during sleep in patients with a variety of diseases causing nocturnal desaturation, after eliminating upper-airway obstruction as one possible cause of desaturation.
We studied 41 consecutive patients with nocturnal oxyhemoglobin desaturation who were investigated and treated at the Centre for Respiratory Failure and Sleep Disorders at the Royal Prince Alfred Hospital in Sydney. All subjects underwent a baseline diagnostic polysomnographic study and were asked to participate in the present study if: (1) their initial sleep study showed episodes of intermittent desaturation during sleep, but no significant obstructive sleep apnea (OSA) (apnea–hypopnea index [AHI] < 5/h); or (2) if episodes of intermittent desaturation persisted, despite nCPAP treatment in which all obstructive events were effectively controlled. Desaturation was defined as a decrease in SaO2 to less than 85% for more than 5 min in patients with an SaO2 of at least 90% during wakefulness according to the definition used by Fletcher and colleagues (21). In patients with an SaO2 of less than 90% during wakefulness, desaturation was defined as an additional decrease in SaO2 of more than 5% for at least 5 min.
Following the diagnostic sleep study, patients were allowed to adapt to the nasal mask for one treatment night. Another polysomnographic study was then performed, during which ventilation was measured with a pneumotachograph placed between the nasal mask and the exhalation port of the breathing circuit. All patients received nCPAP of at least 4 cm H2O (IPAP mode of the VPAP II; ResMed, Sydney, Australia, or BiPAP ST; Respironics, Murreysville, PA) throughout the entire study, during both wakefulness and sleep, in order to control known upper-airway collapse or to provide a fresh gas flow into the mask and thus minimize discomfort from the breathing circuit. In patients who showed upper-airway obstruction during diagnostic polysomnography, nCPAP was titrated to a pressure that effectively prevented apneas, hypopneas, and upper-airway obstruction, as measured by the prevention of airflow limitation. The effective treatment pressure was determined prior to the ventilation study night. Ventilation was recorded for 10-min periods, on multiple occasions when possible, during wakefulness, stable NREM sleep and REM sleep. During the study, O2 was given to five patients who were on long-term oxygen therapy, at the flow rate prescribed for home use (1 to 2 L/min).
Measurements could not be completed on 15 patients, either because the patient did not reach stable sleep, did not have sufficient amounts of stable NREM and REM sleep, or had persistent significant mouth or mask leaks despite the use of a chin strap. Complete measurements were available for 26 patients, and the data for these patients are reported here. Anthropometric data and the diagnoses in these 26 cases are shown in Table 1.
|Patient||Diagnosis||Sex||Age (yr)||BMI (kg/m2 )||pH||PaCO2 (mm Hg)||PaO2 (mm Hg)||FVC (% pred )||FEV1(% pred )||Pi max(cm H2O)|
|Mean ± SD||55.3||37.1||7.363||52.3||61.0||56.6||46.7||64.9|
|± 15.9||± 15.9||± 0.04||± 6.4||± 10.3||± 18.8||± 24.9||± 21.6|
In order to verify that our methodology produced results similar to those previously reported in the literature, we also studied seven normal subjects receiving nCPAP at 4 cm H2O during both sleep and wakefulness, and seven patients with OSA who were being effectively treated with nCPAP. Furthermore, to determine whether there was any significant effect of nasally applied CPAP on breathing at rest, we measured V˙i, Vt, and frequency of breathing in eight healthy subjects with and without nCPAP at 4 cm H2O.
During polysomnography, continuous recordings were made on a chart recorder (GModel 78; Grass Instruments, Quincy, MA) or a computerized system (Sleepwatch; Compumedics, Melbourne, Australia), from two electroencephalogram (EEG) leads (C3/A2, C4/A1), two electroocculogram (EOG) leads, and one electromyogram (EMG) lead (submental), as well as of SaO2 with an ear oximeter (Model 3700e; Ohmeda, Boulder, CO), diaphragmatic EMG activity with surface electrodes, and oronasal airflow via a pressure transducer (Model DP-45; Validyne Corp., Northridge, CA). During the ventilation study night, both nasal airflow and mask pressure were measured with a pressure transducer (Model DP-45; Validyne). Transcutaneous carbon dioxide (PtcCO2 ) (TCM3; Radiometer, Copenhagen, Denmark) was also measured continuously overnight.
Ventilation was measured directly with a pneumotachograph (ResMed) coupled to a pressure transducer (DP-45; Validyne) placed between the nasal mask and the exhalation port of the mask system. The dead space of the mask and the pneumotachograph was approximately 100 ml, and the resistance of the system was 0.244 kPa · s · L−1. Vt (mean value of inspiratory and expiratory Vt), respiratory rate (RR), and breath-by-breath V˙i were calculated from the flow signal produced by the pneumotachograph. The accuracy of the pneumotachograph was checked with a calibrated syringe at Vt values of 200, 250, 350, 500, and 650 ml. For each calibration volume, an average of 77 ± 17 measurements were recorded at frequencies of 10 to 25/min. The measured Vt value was 99.2 ± 1.7% of the syringe volume. Prior to each patient study, the pneumotachograph was calibrated against a syringe of known volume. On the following morning the calibration of the pneumotachograph was checked. The measured value was 99.8 ± 2.3% of the syringe volume.
During all recordings the flow signal was continuously displayed on a monitor so that significant mask or mouth leaks could be immediately detected as either a deviation from the zero-flow value at end-expiration or a difference in the inspiratory and expiratory Vt values. Only periods free of leaks were selected for analysis. Mean values for SaO2 were calculated for each breath. These data were acquired on-line with a 12-bit AC/DC converter, with sampling at 125 Hz.
Arterial blood gases were measured and spirometry was conducted with the patient at rest. Maximal inspiratory mouth pressure (Pi max) was measured from residual volume (RV) with a calibrated manometer. The results of blood gas analysis, spirometry, and measurement of Pi max are presented in Table 1.
Mean values of Vt, RR, and V˙i were calculated during wakefulness and during NREM and REM sleep for each subject.
The baseline diagnostic sleep study was analyzed according to standard criteria (22). Apnea was defined as the cessation of airflow for at least 10 s. Hypopnea was defined as a reduction of airflow by at least 50% for 10 s or more, accompanied by a decrease in SaO2 of at least 4% of the preceding stable SaO2 . The number of apneas and hypopneas per hour of sleep time was calculated and reported as the AHI. Sleep stages were scored in 30-s epochs according to the criteria of Rechtschaffen and Kales (22). Statistical analysis was done with the Statgraphics plus (Manugraphics, Rockville, MD) and SPSS (SPSS Inc., Chicago, IL) statistical packages. Differences in ventilatory parameters in different sleep stages were analyzed through analysis of variance (ANOVA) for repeated measures. Differences between sleep stages were then analyzed by calculating a priori contrasts (wakefulness versus NREM sleep, wakefulness versus REM sleep, and NREM sleep versus REM sleep). In the patients with nocturnal oxyhemoglobin desaturation, V˙i and Vt values were not normally distributed. Therefore, for these values, a nonparametric statistical test (Friedman's test) was used. Differences between groups were then tested with Wilcoxon's signed rank test.
Data are reported as mean ± SD. Statistical significance was assumed at p < 0.05.
The results of diagnostic polysomnography in the 26 patients with nocturnal desaturation are presented in Table 2. There was a significant reduction in V˙i, from 8.9 ± 2.0 L/min during wakefulness to 7.0 ± 1.8 L/min (−20.7 ± 14.3%) during NREM sleep (p < 0.005). A further reduction in V˙i, to 5.4 ± 1.6 L/min, occurred during REM sleep (p < 0.005), constituting a decrease of 38.9 ± 15.5% from V˙i during wakefulness. V˙i was significantly lower in REM sleep than in NREM sleep (p < 0.005). The individual changes in V˙i from wakefulness to NREM and REM sleep are shown in Figure 1. Individuals were grouped according to their primary disease: obesity hypoventilation syndrome (OHS), COPD, or other disorder. The average decrease in V˙i from wakefulness to NREM sleep was 25.0 ± 14%, 15.9 ± 15.5%, and 20.0 ± 12.8% in the OHS, COPD and other-disorder groups, respectively. V˙i decreased from wakefulness to REM sleep by 40.9 ± 12.8%, 31.8 ± 13.3%, and 46.0 ± 20.9% in the OHS, COPD, and other-disorder groups, respectively. The decrease in V˙i among the three groups was not significantly different.
|TST, min||322.0 ± 70.9|
|NREM, %TST||80.8 ± 7.9|
|REM, %TST||19.3 ± 7.9|
|SaO2 , min, %||53.4 ± 18.8|
|SaO2 < 90%, %TST||66.3 ± 18.7|
|SaO2 < 80%, %TST||26.2 ± 23.6|
|AHI, h−1||8.9 ± 5.4|
Figure 2 shows an example of the marked decrease in V˙i accompanying the transition from NREM to REM sleep.
V˙i decreased by more than 10% in 21 of the 26 patients during the transition from wakefulness to stable NREM sleep, and by at least 20% (range: 20.4 to 74.1%) in all patients during REM sleep as compared with wakefulness.
The reduction in V˙i was due mainly to a decrease in Vt from 0.51 ± 0.14 L during wakefulness to 0.38 ± 0.1 L during NREM and 0.33 ± 0.09 L during REM sleep (p < 0.005). The small changes in breathing frequency during NREM (19.3 ± 4.4 breaths/min) and REM sleep (17.6 ± 3.6 breaths/min) were not significantly different from the frequency during wakefulness (18.5 ± 3.9 breaths/min). In 15 patients, PtcCO2 measurements from baseline wakefulness to NREM and then to REM sleep appeared reliable. In these patients, PtcCO2 rose from a baseline value of 59 ± 11.6 mm Hg during wakefulness to 69 ± 13.7 mm Hg in NREM sleep, with a further rise to 74 ± 17.6 mm Hg during REM sleep. In the 21 patients who were not receiving supplemental oxygen therapy, SaO2 decreased from 91.3 ± 1.3% during wakefulness to 88.6 ± 1.1% during NREM sleep (p < 0.05) and to 79.8 ± 5.1% during REM sleep (p < 0.01, wakefulness versus REM sleep; p < 0.01 NREM versus REM sleep). Mean values for V˙i, Vt, and frequency of breathing are shown in Figure 3, which illustrates differences between patients with nocturnal desaturation, patients with OSA effectively treated with nCPAP, and the healthy control group. The change in accessory respiratory muscle activity that can occur from NREM to REM sleep is shown in Figure 4.
In the seven normal subjects, V˙i remained virtually unchanged from wakefulness (6.8 ± 1.2 L/min) to NREM (6.1 ± 0.8 L/min) and REM sleep (6.6 ± 1.1 L/min) (p = NS). A statistically significant decrease in Vt from wakefulness (0.55 ± 0.1 L) to NREM (0.43 ± 0.02 L) and REM sleep (0.43 ± 0.05 L) was seen (p < 0.05). However, the significant increase in breathing frequency from wakefulness to NREM and REM sleep (p < 0.05) meant that V˙i was maintained. In the seven patients with OSA who were receiving effective nCPAP therapy (and therefore not desaturating during sleep), V˙i during NREM and REM sleep showed small but significant (p < 0.05) reductions of 9.2 ± 9.3% and 7.4 ± 10.5%, respectively, from its value during wakefulness. However, there were no significant differences in V˙i during NREM and REM sleep in this group. The reduction in V˙i resulted from a decrease in Vt (p < 0.05). Breathing frequency increased from wakefulness to NREM and REM sleep, but only the increase during REM sleep reached statistical significance (p < 0.05). These results are summarized in Figure 3.
In order to identify any significant effect of nasally applied CPAP on breathing at rest during wakefulness, V˙i was measured in eight healthy subjects with and without nCPAP at 4 cm H2O. V˙i without CPAP was 8.7 ± 2.6 L/min, and with nCPAP at 4 cm H2O it was 8.2 ± 2.0 L/min (p = NS). Vt (0.76 ± 0.2 L versus 0.74 ± 0.2 L) and frequency of breathing (11.4 ± 2.8 breaths/min versus 11.8 ± 2.4 breaths/min) were almost identical with and without nCPAP (p = NS).
We measured ventilation directly in a group of patients with oxyhemoglobin desaturation during sleep. Our results clearly show that in this group of patients, V˙i decreases from wakefulness to NREM sleep, with further decreases in REM sleep irrespective of the disease process responsible for sleep-related desaturation. On average, the decrease in V˙i seen during REM sleep was 39% of the value during wakefulness. This decrease was mainly due to a reduction in Vt, with only minor changes in respiratory rate (RR). These results contrast with those for our normal subjects and for the effectively treated OSA patients, in whom nocturnal desaturation did not occur. In these groups, V˙i during NREM and REM sleep fell only marginally from its values during wakefulness, and there was no relevant difference between NREM and REM sleep. Although Vt did decrease in both groups, the increase in breathing frequency offset any major decrease in V˙i.
Except in healthy subjects, quantitative data on changes in V˙i during sleep are scarce. To our knowledge, V˙i has been quantitatively measured only in patients with COPD (7-9, 11) and those with cystic fibrosis (CF) (23). Three of the studies in which this was done used an inductance vest (7-9). A decrease in V˙i of approximately 15 to 25% has been reported to occur during NREM sleep as compared with wakefulness in patients with COPD (7, 9). During REM sleep, V˙i decreased by approximately 42% as compared with its value during wakefulness (7) and by 25% as compared with that during NREM sleep (8). The accuracy of inductance plethysmography in patients with lung disease and over longer recording periods with changes in posture has been questioned (12). In a recent study, ventilation was measured with a body plethysmograph in five COPD patients. V˙i decreased by 18.5% during stages 3 and 4 NREM sleep, and by 35.5% during REM sleep as compared with wakefulness (11). The investigators went on to study ventilation during sleep in a small group of patients with CF (23). Decreases in V˙i of 16 to 17% of baseline values during wakefulness were observed during NREM sleep, but no REM sleep data were obtained in this study. Nine of the patients in our study had a diagnosis of COPD, and our direct measurements of V˙i in these patients showed a decrease of 15.9% during NREM and of 31.8% during REM sleep, which are in agreement with the previously reported data.
Our data show that marked hypoventilation, most pronounced during REM sleep, is uniformly present in patients with nocturnal desaturation regardless of these patients' primary diagnosis. Because the decrease in V˙i was mainly due to a reduction in Vt, the patients' alveolar ventilation had decreased by even more than the 38.9% decrease seen in V˙i.
The measurement of V˙i with a pneumotachograph is the standard way of measuring ventilation, is accurate and reproducible, and does not depend on body position. Our results indicate that this technique is reliable over long periods of recording. However, it does require the placement of a mask. The accuracy of inductive plethysmography has been called into question by some investigators, particularly in patients with lung disease, and during sleep (12). Our methods have produced results similar to those of other investigators using the inductive plethysmography vest, with the exception of a recently published study (24) in which the absolute values for ventilation during wakefulness and sleep in COPD patients were substantially lower (less than 50%) than all our directly measured values for wakefulness and for NREM and REM sleep. The most likely explanation for this discrepancy is that the calibration procedure for pneumotachography in COPD may not adequately represent the real V˙i values in this condition, especially during sleep with body movement. The accuracy of the pneumotachograph used in our experiments, as determined with a calibration syringe, was approximately 99%. The greatest source of measurement error in our experimental setting might have been mouth and mask leak. However, because there was a continuous display of the airflow signal on a computer monitor, we were able to detect periods in which relevant leaks were occurring through the differences between inspiratory and expiratory Vt and through deviation of the airflow signal from the zero baseline. Recording periods in which relevant leaks occurred were not used in our analysis.
Our patients had to wear a nasal mask during sleep when ventilation was measured, and a pneumotachograph was attached to the mask. The dead space of the mask and pneumotachograph was approximately 100 ml. The dead space stimulated breathing to a slight extent, but since it remained constant throughout the test it should not have influenced the relative changes we were interested in measuring.
In order to determine whether the low level of nCPAP used in our study altered ventilation, we studied eight normal subjects with and without nCPAP at 4 cm H2O during wakefulness. V˙i, frequency of breathing, and Vt values did not change. Other investigators have previously shown that the use of nCPAP in stable COPD did not influence ventilation (25). In our study, patients with upper-airway obstruction were treated with nCPAP at a therapeutic level during ventilation measurements. This was done to prevent obstructive disturbances in breathing, which in themselves and through the effects of arousal would have markedly influenced the study results.
REM sleep is of most interest to the clinician, since it is the sleep stage in which sleep-disordered breathing typically first becomes apparent, and in which the most severe derangements in gas exchange subsequently occur. However, REM sleep is not a homogenous state, and consists of both tonic and phasic periods, the latter being characterized by rapid eye movements. It has been reported that hypoventilation is most pronounced during phasic REM sleep (9, 26). We also noticed that tidal volumes were lowest during rapid-eye-movement epochs in REM sleep, but we were unable to quantify these differences, since V˙i during tonic and phasic REM sleep was averaged in our study. Even in young, healthy adults ventilation during REM sleep is quite variable and related to the intensity of phasic activity (26). This may explain why published measured values of ventilation in normal subjects during REM sleep have varied so greatly (2, 6), since values obtained in any epoch will depend on how much phasic activity occurs in that epoch.
Hypoxemia during sleep may be potentially caused by disturbances of gas exchange or hypoventilation. Clearly, our results do not exclude worsening ventilation/perfusion inequality, as a cause of hypoxemia, but they do indicate that hypoventilation was a very important source of desaturation during sleep in the patients in our study. The rise in PtcCO2 from 59 mm Hg at baseline to 74 mm Hg during REM sleep provides additional evidence for the occurrence of hypoventilation in these patients. Hypoventilation, most pronounced during REM sleep, was found in all our patients, and therefore seems to be a universal finding in patients with sleep related hypoxemia irrespective of their underlying disease. Although it is not possible from the present study to distinguish mechanisms responsible for the hypoventilation seen in patients with sleep-related hypoxemia, some general observations can be made. The addition of an inspiratory resistive load to breathing during sleep has been shown to reduce ventilation (27). In patients with COPD, Ballard and coworkers (11) demonstrated that there was an increase in upper-airway resistance with the onset of sleep, which increased to maximum levels during periods of REM sleep. However, in our study, all patients had some level of CPAP, either to control known upper-airway collapse or at a low pressure level to provide fresh gas flow into the mask. In either circumstance, the pressure used would have been sufficient to minimize the effects of upper-airway resistance (28). Therefore, it is unlikely that sleep-related increases in upper-airway resistance played a major role in the reduction in V˙i that we observed in NREM and REM sleep.
Another likely cause of hypoventilation may be a reduction in neural drive. Support for this mechanism comes from work by Ballard and collegues in patients with emphysema (11). Their data suggest that respiratory drive, as measured through P0.1, decreases during sleep in this group of patients without changes in lower-airway resistance or pulmonary mechanics. The same investigators found similar results in patients with CF during NREM sleep (23).
Marked alterations in respiratory muscle activity and chest wall motion occur with changes in sleep stage. Normally, there is an increase in intercostal muscle activity during NREM sleep, producing an increase in the rib cage contribution to spontaneous ventilation over that during wakefulness (29). One of the hallmarks of REM sleep is the suppression of postural and accessory respiratory muscle activity, with a relative sparing of diaphragmatic activity (29). These changes in the electrical activity of the respiratory muscles are associated with a marked reduction in the rib cage contribution to Vt and, consequently, a greater reliance on the diaphragm to maintain ventilation. In patients with a mechanically inefficient diaphragm or diaphragmatic weakness, the REM-induced loss of intercostal and accessory muscle activity causes a significant reduction in inspiratory pressure generation, and impairs ventilation, contributing to the hypoventilation seen in such patients. In both patients with severe COPD and in those with generalized neuromuscular disorders, it has been shown that accessory inspiratory muscles such as the sternomastoid and scalene muscles (30), as well as the abdominal muscles (31), play an important role in augmenting ventilation during wakefulness and NREM sleep. With loss of this activity during REM sleep, a significant degree of hypoventilation is expected to occur, which in turn is associated with a deterioration in gas exchange.
Our study shows that hypoventilation, most pronounced during REM sleep, is found in patients with sleep related oxyhemoglobin desaturation, irrespective of the disease underlying this condition. Hypoventilation, due mainly to a reduction in Vt, is the major factor leading to sustained decreases in SaO2 during sleep. Although untreated upper-airway obstruction almost certainly contributes to a decrease in V˙i, a reduction in neural drive during sleep, or more accurately a reduction in postural drive, seems the most likely cause of such hypoventilation, since the reduction in V˙i observed in our study persisted despite the prevention of upper-airway obstruction through the nCPAP. The clinical implication of this study is that reversal of hypoventilation by nasal assisted ventilation should be a major therapeutic strategy in patients with sleep-related oxyhemoglobin desaturation.
The authors thank Mark Norman, Peter Bateman, Dimitri Nikulin, and Frank Schüttler for technical assistance with recordings. Werner Cassel and Dirk Dugnus provided valuable assistance with the statistical analysis.
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