INTRODUCTION

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BECAUSE OF A HIGHER CHEST wall-to-lung compliance ratio in newborn infants, rats, and mice, the functional residual capacity (FRC), i.e., the relaxation volume, is a smaller fraction of total lung capacity than that in adult cats, dogs, and humans, and some closure of small airways may occur at the lower volume. Breathing from this low lung volume could result in decreased O₂ stores. Some evidence, however, suggests that the end-expiratory lung volume (EEV) in these mammals is actively maintained above relaxation lung volume (17, 18, 23, 24, 31). Several mechanisms could account for this breathing strategy: the relative rapid breathing rate, tonic activity of inspiratory muscles, expiratory airflow braking by changes in upper airway (UAW) resistance or by postinspiratory diaphragm or intercostal muscle activity. EEV is usually found to fluctuate from breath to breath in a complex, irregular manner, and this complex behavior might be a consequence of the concurrent operation of these mechanisms.

It is unclear whether the fluctuations in EEV are random variations or reflective of control processes. However, several studies on EEV indicated that these breath-to-breath variations are probably not uncorrelated white noise. In 1973, Hlastala et al. (16) studied cyclical oscillation of FRC in resting humans and found that FRC showed an oscillating pattern with from two to seven predominant frequencies. Data from anesthetized rats breathing with a continuous negative airway pressure (CNAP) that is presumed to forcibly reduce mean EEV have shown a highly variable and asymmetric respiratory pattern, which is consistent with onset of low-dimensional chaos. The irregular dynamics seen with CNAP are probably due, in part, to the activation of pulmonary feedback mechanisms responsive to reduction in EEV (24, 25). These observations suggest that alteration in mean EEV modifies the respiratory pattern. But how various mechanisms involved in EEV control discussed above are integrated into the process of respiratory rhythm generation is not fully understood and cannot be understood by studying them separately. A plausible approach to an integrated analysis is to determine whether the fluctuations arising from the dynamics of the complex system show long-term correlation that might be indicative of coupled control processes acting over a range of time scales.

Fractal correlation models such as fractional Brownian motion (FBM) and discrete fractional Gaussian noise (20) have been applied as models of the correlation in many natural processes. Fractal time series demonstrate the property of statistical self-similarity, in which the fluctuation possesses no characteristic time scale. Several methods have been proposed for estimating the Hurst exponent (H), a single parameter that characterizes the scaling property of a fractal process. In a previous study (33), the modified dispersional analysis was used to examine EEV in anesthetized, tracheotomized, vagi-intact rats. It was found that there is a long-term correlation in EEV, and also H increased when the rat was subjected to continuous negative transrespiratory pressure (NTRP), which is expected to lower mean lung volume. The difference in H for EEV between positive transrespiratory pressure (PTRP) and NTRP was absent after bilateral vagotomy. These findings supported the hypotheses that fluctuations of EEV were not random and that the interactions of vagal pulmonary afferent activity with central pattern generation might be responsible for the observed long-term correlation in EEV. It also suggested that EEV control might be a fractal process that reflects the involvement of multiple processes with different time scales.

In the above study, the UAW was bypassed. It is well known (3, 10) that UAW has considerable influence on the rate of respiratory flow, particularly during expiration. Also the laryngeal motor control of the expiratory flow is hypothesized to be an important mechanism for the control of lung volume in several species including rats. Lambs (15) and dog pups (10) have high levels of thyroarytenoid muscle (TA, a laryngeal adductor) activity during expiration, and it is suggested that increased airflow resistance by TA activity results in an elevated EEV. Moreover, activity of UAW muscles is modulated by vagally mediated feedback to a larger extent than that of diaphragm (25, 28, 30). Thus natural control of EEV in rats with intact UAWs involves additional levels of complexity not present in the tracheotomized rats studied previously.

In this study, we assessed the variability and the correlation structure of EEV in anesthetized rats with intact UAWs subjected to PTRP and NTRP. We expected that fractal correlation would still be present in EEV but would exhibit different H values than we had found in tracheotomized rats.

	METHODS

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Studies were performed on 10 adult male rats, weighing between 250 and 350 g. They were anesthetized with urethan (1,200 mg/kg). Atropine (0.4 mg/kg) was injected intramuscularly to reduce airway secretions. Rectal temperature was monitored continuously and maintained at ~37°C via a heat lamp and a heating pad. The rat was placed in the prone position in a head-out plethysmograph. The animal breathed 100% humidified O₂ through a face mask sealed over the nose and mouth with petroleum jelly and cotton. Airflow was measured with a pneumotachograph and Validyne transducer (±2 cm H₂O) in a bias flow circuit. An apparatus dead space <0.4 ml was achieved. Bias flow circuit has been described in detail before (24). Pressure in the plethysmograph (Pbox) was varied using a pump.

Recording protocol. Spontaneous tracheal airflow signal was recorded and sampled at 150 Hz using LabTech Notebook Software. After an initial control recording with Pbox = 0 cmH₂O, data were acquired while the animal was exposed to PTRP (Pbox = 3 cmH₂O) or NTRP (Pbox = +3 cmH₂O) for ~10-20 min. The sequence of PTRP and NTRP was randomized. After each trial, at least 3 min with Pbox = 0 cmH₂O was allowed for the breathing pattern to return to control values before changing to a different value of Pbox.

Data analysis. A band-pass filter (0.075~15 Hz) was used to remove the mean level of the bias flow signal and noise from the flow signal. Breath-by-breath tidal volume (V_T), inspiratory duration (TI), and expiratory duration (TE) and ventilation (E) were computed from the filtered flow signal. The change of end-expiratory lung volume (EEV) on each breath was calculated by subtracting the expiratory volume from the inspiratory volume. The accumulated change in EEV from the first breath of the data record was determined by calculating a cumulative sum of these EEV changes. Approximately 1,000 consecutive breaths (500~1,500) for each trial were used for analysis. All the data processing and the following analyses were performed using MATLAB (Mathworks).

	RESULTS

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The mean values of TI, TE, V_T, and E during control, PTRP and NTRP are summarized in Table 1. The values were similar among three pressure levels. Statistical analysis did not show any significant differences.

View this table: [in this window] [in a new window]   Table 1.   Mean values for TI, TE, VT, and E during control, PTRP, and NTRP in 10 upper airway intact rats

NTRP caused a change in the profile of flow within a breath. Typical responses of flow to NTRP and PTRP are shown in Fig. 1, top. With NTRP, interruption or braking of expiratory flow frequently occurred. The flow pattern shown by this rat was clearly evident in almost all the rats to some degree.

View larger version (19K): [in this window] [in a new window]   Fig. 1.   Typical example of flow signal with positive (PTRP) and negative transrespiratory pressure (NTRP) and corresponding flow-volume plots from rat 14. Loops are clockwise in direction, with expiration encompassing bottom half. Calibration bars: volume, 0.5 ml; flow, 5 ml/s.

The flow-volume curves from the same rat with PTRP and NTRP are shown in Fig. 1 (bottom), each with 20 consecutive breaths. A difference in the expiratory part of the flow-volume curve is apparent between PTRP and NTRP. With PTRP, expiration usually proceeded along an approximately linear slope to, or nearly to, the minimal volume at the zero-flow line. This linear portion suggests that relaxation of respiratory muscles occurred. In contrast, with NTRP, the pattern of the expiratory limb indicated that the transition from expiration to inspiration involved an interruption of expiratory flow at substantial flow rate. Furthermore, at the beginning of expiration, the flow at a given volume was much lower with NTRP than that with PTRP, which suggests the braking of expiratory airflow. In other words, expiration during NTRP had a long time constant because it is much flatter compared with that during PTRP.

Representative examples of the effect of PTRP and NTRP on the EEV fluctuation are shown in Fig. 2. Mean V_T in this rat was 0.57 and 0.58 ml with PTRP and NTRP, respectively. It can be seen that breath-by-breath EEV fluctuation reveals a complex type of variability, as demonstrated in a previous study in tracheotomized rats (33).

View larger version (41K): [in this window] [in a new window]   Fig. 2.   Representative end-expiratory volume (EEV) time series (ml) with PTRP (A) and with NTRP (B). Mean tidal volume in this rat was 0.57 and 0.58 ml with PTRP and NTRP, respectively.

The SD of EEV was 0.0088 ± 0.0031, 0.0091 ± 0.0029, and 0.0099 ± 0.0061 with PTRP, control, and NTRP, respectively. There was no significant difference in this measure of variability of EEV among the three conditions.

Histograms of EEV are presented in Fig. 3. The histograms were constructed from the breaths analyzed from one rat and represent the cumulative data of 1,301 breaths with PTRP and 1,402 breaths with NTRP. The histograms of EEV were tested for normality. The P values from the Kolmogorov-Smirnov test for normality are given. The two histograms in Fig. 3 appear to be normal. For most EEV time series (24 of 30) examined in UAW intact rats, we could not reject the hypothesis of normality and thus felt justified in assuming a normal distribution for EEV. In contrast, most EEV time series (26 of 27) from tracheotomized rats appear to be nonnormal at the 5% level. Figure 4 displays typical histograms from one tracheotomized rat. Notice that normal curves would fit the distribution poorly. Most of the histograms of EEV in tracheotomized rats of a previous study (33) are positively skewed.

View larger version (33K): [in this window] [in a new window]   Fig. 3.   Distribution histograms of EEV from 1 rat with intact upper airway. Total number of breaths was 1,301 with PTRP (A) and 1,402 with NTRP (B). Two histograms appear to be normal.

View larger version (34K): [in this window] [in a new window]   Fig. 4.   Distribution histograms of EEV from 1 tracheotomized rat. Total number of breaths was 1,237 with PTRP (A) and 1,151 with NTRP (B). Both histograms appear to be nonnormal at 5% level.

Figure 5 compares the fractal analysis of representative EEV time series with PTRP and NTRP. In this example, H for EEV is 0.53 with PTRP and 0.69 with NTRP. This implies that EEV fluctuations exhibit a long-term correlation with NTRP and possibly with PTRP too. To see whether the correlation structure in EEV is a result of the sequential ordering, the same analysis was performed on shuffled EEV. H for shuffled EEV is 0.48 and 0.47 with PTRP and NTRP, respectively. The result suggests that the shuffled data behave as uncorrelated white noise.

View larger version (12K): [in this window] [in a new window]   Fig. 5.   Example of dispersional analysis of EEV time series with PTRP (A) and with NTRP (B). *, Original EEV; , shuffled EEV.

For the group of 10 rats, as summarized in Fig. 6, H for original unshuffled EEV was 0.5362 ± 0.0763, 0.5576 ± 0.0680 and 0.6403 ± 0.0561 (means ± SD) with PTRP, control, and NTRP, respectively. H for shuffled EEV was 0.4661 ± 0.0146, 0.4702 ± 0.0089, and 0.4695 ± 0.0133, respectively, for the three conditions. Statistical analysis showed that all H for original EEV were significantly different from those obtained after random shuffling of the original time series (P < 0.005), indicating a positive long-term correlation in EEV. Also, H with NTRP was significantly greater than that with PTRP (P = 0.029).

View larger version (24K): [in this window] [in a new window]   Fig. 6.   Mean H for original and shuffled EEV in 10 rats with PTRP, control, and NTRP. x H for original EEV were significantly different from those obtained after random shuffling of original time series (P < 0.005). * H with NTRP was significantly greater than that with PTRP (P = 0.029).

To see the influence of other respiratory parameters on EEV, H for TI, TE, V_T, and E were also calculated. As shown in Table 2, H for TI, TE, and E with NTRP were significantly greater than the corresponding parameters during PTRP (P < 0.05).

	DISCUSSION

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This study has shown that rats breathing through an intact UAW exhibit long-term correlation in EEV, which is significantly different from that of an uncorrelated random process. It is also shown that although the SD of EEV is not statistically different between PTRP and NTRP, H for EEV is greater with NTRP than that with PTRP. The present observation implies that the correlation structure in EEV depends on the mean EEV. We infer that long-term correlation helps stabilize EEV and that this stabilization is more important during NTRP when different mechanisms act to maintain a dynamic equilibrium above relaxation lung volume.

The mean values of respiratory variables (TI, TE, V_T, and E) with NTRP were not significantly different from control values or those with PTRP. This result differs from several previous studies. Marlot and Mortola (21) found in newborn rats that with distending pressures, E decreased mainly due to a prolongation of TE, whereas with collapsing pressures, only small changes in breathing patterns occurred. D'Angelo and Agostoni (8), in anesthetized cats, rabbits, and dogs, reported that decrease of FRC shortened TE, and they also found reciprocal changes in TI. Green and Kanfman (14) studied anesthetized and open-chest dogs. They observed that as EEV was decreased below FRC (one-half lung collapse), there were significant increases in both V_T and breathing frequency. The differences between these results and our results may be explained partly by different animal preparations, different levels of anesthesia, or different anesthetic agents used in the studies. Also, most of these studies evaluated the breathing pattern of several breaths during PTRP or NTRP. Our measurements were made during long-term steady states.

There may be little contribution of changes in chemical drive of ventilation to the responses because no change in ventilation was observed during our study. It is most possible that reflexes initiated by the stimulation of lung mechanoreceptors in the rats are different from other species. A large portion of vagal fibers have been characterized as low-threshold slowly adapting receptors responsive to NTRP in rats (6, 29). The vagus nerves in cats and dogs exhibit a much lower percentage of afferents from these receptors.

The long-term correlation in EEV observed in the present study is consistent with our previous finding in tracheotomized rats with PTRP and NTRP (33). It means that EEV fluctuations are not random like white noise, nor do they exhibit only short-term correlations such that the instantaneous EEV value is influenced by only the most recent EEV. Instead, the present EEV is influenced by EEV many breaths earlier, and this dependence decays in a scale-invariant (fractal) manner. Although the mechanisms responsible for this fractal property of EEV remain unclear, it is generally considered that fluctuations arising from a complex, multiple-component system usually show long-term correlation. There are usually two types of long-term correlation, i.e., exponential and fractal correlation. The falloff in fractal correlation with separation is slower than the exponential one. The correlation in EEV is the fractal type. Our data may therefore be interpreted to indicate that the mechanisms governing EEV are complex and involve many subprocesses. In other words, EEV control may be mediated by a fractal neuromechanical system. It is obviously true, from a physiological viewpoint, that EEV control is complex. EEV depends on a number of factors. Under static relaxed condition, EEV is passively determined by the balance between the elastic recoil of the lungs and that of the chest wall. The dynamic equilibrium during breathing reflects the additional influences of respiratory muscle activity and other factors that influence transrespiratory pressure. Both types of factors may be significant at the end of expiration under certain circumstances. For example, inspiratory or expiratory muscles may have a tonic or phasic activity, and a balance of alveolar and mouth pressures at end expiration may not be achieved. These mechanisms usually operate concurrently, and the individual role of these factors is difficult to quantitate. The current information for EEV in rats highlights that the combined effects of all these mechanisms result in power-law, scale-invariant fluctuations in EEV.

There has been considerable interest over the years in the role of vagal afferents in the control of respiration. Most of these studies have indicated that reduction of EEV stimulates rapidly adapting receptors and the deflation slowly adapting receptors (1, 9, 27, 6, 29), reduces activity in pulmonary stretch receptors (1), and has little or no effect on pulmonary or bronchial C fibers (2). However, it has been impossible to correlate activity changes with specific dynamic control of EEV. The present study examined the vagally mediated influence on EEV control from a different aspect. We found that H for EEV increased with NTRP. Because the change in H for EEV disappeared after bilateral vagotomy in the previous study, we infer that this change in fractal characteristics in EEV with changed lung volume in the present study depends on vagal afferents. Although we measured the breath-by-breath change in EEV instead of the absolute values of EEV in the present study, it is likely that during NTRP, EEV is actively maintained above the relaxation volume of the lung, as suggested by the examination of expiratory flow-volume curves. Goldberger and West (13) have proposed that pathological perturbation of a fractal system may narrow the frequency response of the system, such as the loss of heart rate variability. The present data are consistent with this proposal. The increase in H with NTRP suggests that there is a progressive narrowing of the frequency response of EEV control system as the animal is subjected to a deflating pressure. Therefore, the price for a system actively maintaining EEV above relaxation lung volume is diminished stability.

Although the correlation structure in EEV in rats breathing through an intact UAW is similar to what we found in the previous study in tracheotomized rats, there are differences in the SD and distribution of EEV between intact UAW rats and tracheotomized rats. SD of EEV in UAW intact rats is smaller compared with that of tracheotomized rats, in which SD was 0.019 ± 0.008, 0.022 ± 0.007, and 0.043 ± 0.032, respectively with PTRP, control, and NTRP. Also the differences in histograms of EEV between UAW intact rats and tracheotomized rats are apparent. Whereas the distribution of EEV in UAW intact rats is mostly normal, the EEV in tracheotomized rats has a nonnormal distribution. Some histograms are positively skewed (with a long right tail), whereas others look bimodal. The broader histograms are consistent with greater SD of EEV in tracheotomized rats. For EEV from short series with high variance, this result of nonnormal distribution is not surprising. The reason for the difference in EEV distribution is not understood. It seems that UAW receptors sensitive to pressure, flow, temperature, etc., may be involved in the response, because they have been shown to influence the breathing pattern (7, 32). Loss of the mechanisms responsible for braking of expiratory airflow by laryngeal muscles could also account for the greater variability in EEV in tracheotomized rats.

EEV is dependent on the relationship between respiratory system time constant for lung emptying and TE. Thus lung volume can be elevated either by increasing the time constant, i.e., expiratory airflow braking, or by decreasing TE. The expiratory braking could result from postinspiratory activity of inspiratory muscles (PIIA), late-expiratory activation of the diaphragm, or activation of laryngeal adductor TA. The latter two mechanisms were observed in rats during NTRP in a previous study (24) and possibly occurred in the present study. PIIA could also be operating in the rats. Interruption of expiration has been reported in infants and attributed to laryngeal narrowing (12, 22). A similar laryngeal control of the expiratory flow has been observed in the young opossum (11) and newborn lambs (15). The use of laryngeal adductors would tend to increase the effective expiratory time constant of the respiratory system. Because it is the balance between the time constant of a breath and TE that determines EEV, shortening of TE also can contribute to the elevation of EEV. England and Stogryn (10), in unanesthetized dog pups, found a greater time constant (0.41 vs. 0.19 s) during nasal breathing and a 40% reduction in TE during tracheal breathing and predicted that dog pups during tracheal breathing maintained an elevated EEV, although complete compensation for loss of UAW was not achieved. If their prediction is correct, it is obvious that rats studied by us previously, unlike the dog pups, only decreased TE slightly (7%) during NTRP when breathing through a tracheotomy. Although absolute lung volume was not measured in our present or previous study, it seems reasonable to suggest that in tracheostomized rats, the effect of the compensatory mechanisms for maintenance of EEV seems smaller, i.e., EEV is elevated less than in rats breathing through an intact UAW. On the other hand, tracheostomized rats seem likely to use PIIA more. Therefore, functional loss of the UAW results in a greater variability in breath-by-breath EEV in tracheostomized rats. As discussed previously, the individual contribution of the factors involved in EEV maintenance is hard to separate. It is, however, interesting that the compensatory mechanisms are substantially more effective in rats breathing through an intact UAW, as reflected by the smaller SD of EEV.

Perspectives