Abstract
Lai, Jie, and Eugene N. Bruce. Ventilatory stability to transient CO_{2} disturbances in hyperoxia and normoxia in awake humans. J. Appl. Physiol. 83(2): 466–476, 1997.—Modarreszadeh and Bruce (J. Appl. Physiol. 76: 2765–2775, 1994) proposed that continuous random disturbances in arterial
 periodic breathing
 central chemoreflex
 peripheral chemoreflex
 closedloop response
 openloop response
 impulse response
 transfer function
 pseudorandom binary sequence
it is commonly recognized that ventilatory instability in the form of oscillation or periodic breathing can be caused by unstable properties of respiratory chemical control loops, in which the loop gain has increased to unity or higher (6, 7). However, the loop gain concept may not give a complete explanation of ventilatory instability and oscillation. Modarreszadeh and Bruce (20), using an adaptive endtidal CO_{2} buffering technique to reduce spontaneous variability in arterial
Previous studies focusing on the ventilatory responses to
In this study we tested the hypothesis that transient ventilatory oscillations due to a brief CO_{2}disturbance are more likely in normoxia than in hyperoxia, and we examined the relationship between the closedloop and the openloop ventilatory responses in a frequency range representative of periodic breathing frequencies. Using a pseudorandom binary sequence (PRBS) to control inspired CO_{2} fraction (
METHODS
Experimental methods.
Nine healthy, young men (mean age 24 yr, range 19–30) participated in a pair of experiments consisting of a study in hyperoxia and a study in normoxia performed at the same time on separate days. The experimental setup was similar to that used in a previous study (19). In the awake state, subjects breathed through a face mask while in the supine position. During the experiments, subjects listened to soft music and were asked to keep their eyes open to show they were awake. The inspiratory inlet of the nonrebreathing valve (total dead space 45 ml) was switched between two Douglas bags containing the inhaled mixtures [100% O_{2} or 96% O_{2}4% CO_{2} (hyperoxia); 21% O_{2}79% N_{2} or 21% O_{2}4% CO_{2}75% N_{2} (normoxia)] by computercontrolled balloon valves, which were quieter than the solenoid valves used in the previous study (19). Airflow was obtained by measuring the pressure drop across a pneumotachograph (Hans Rudolph). CO_{2} fraction was measured by an infrared CO_{2}analyzer (Nellcor), and O_{2}fraction was measured by a zirconium O_{2} analyzer (Ametek). All the signals were recorded on chart and digital tape recorders and also simultaneously sampled by an analogtodigital board at a rate of 90 Hz and sent to a computer (Gateway 2000–486), which performed online breath detection and analysis. By analyzing the airflow signal, the online program controlled the valves so that only one valve was open during each inhalation.
The experimental protocol consisted of three sections. The first section was a baseline section in which, after ventilation became stable [assessed by monitoring endtidal
Sham experiments for a similar experimental setup in the previous study (19) confirmed that the responses were not due to the experimental procedure. In our study we repeated one sham experiment, in which the inspired gas was pseudorandomly switched between two identical bags containing 97.5% O_{2}2.5% CO_{2}. The results confirmed that the measured responses were not due to factors other than the gas switching, such as the faint clicking sound when valves were activated.
Data analysis.
From the digitized airflow and CO_{2}signals, we calculated the following breathbybreath values: inspiratory tidal volume (Vi), inspiratory and expiratory durations (Ti and Te), total breath duration (Tt = Ti + Te), inspiratory minute ventilation (V˙i = Vi/Tt),
To obtain the dynamic response ofV˙i to a CO_{2} disturbance, we used a general system identification technique known as PEM. A full explanation of PEM has been presented in a previous publication (22). Basically, if it is assumed that the input [u(n)] and output [y(n)] signals are related by a linear system, the relationship of the signals can be written as
For the openloop or controller estimation, forcing the absolute delay (nk in Eq.1 ) to be ≥1 acts to open the feedback loop to obtain the openloop ventilatory responses. Such assumption of delay is reasonable for the real physiological system. Actually, the delay for the closedloop system also was ≥1.
By use of PEM, the estimation of model parameters can be performed for given values of nn = [nb nc nd nf nk]. However, for a real system, these nn values are also unknown. To obtain the optimal nnvalues in each session of data for each subject, for the openloop and the closedloop system we started from initial values ofnn = [1 0 0 1 1] and increased one of these five values by 1 each time untilnn = [4 3 3 3 4], the maximum searching range of nn. For each set of nn values the estimation of model parameters was performed. The selection of the maximumnn values is based on the fact that the real physiological system consists of three major time constants: one for the peripheral chemoreceptor, one for the central chemoreceptor, and one dominant time constant for the respiratory plant. Actually, in the simulation and first several experimental data analyses, we tried nn values up to [5 5 5 5 5]; however, the results did not improve beyondnn = [4 3 3 3 4]. We therefore assumed that the optimal nnvalues for the real system were betweennn = [1 0 0 1 1] andnn = [4 3 3 3 4]. The final selection of the optimal nnvalues and corresponding model parameters was based on combining considerations of two criteria. The first was Akaike’s final prediction error (FPE) criterion. The FPE is determined as
Figure 1 shows the model and equations for the closedloop and the openloop transfer function estimation using the PEM method described above. For the closed loop we used the inspired CO_{2} volume (
All the data analyses were performed using MATLAB and the MATLAB Systems Identification Toolbox (Math Works, S. Natick, MA). Statistical significance was tested using pairedttest with Bonferroni’s correction or onefactor analysis of variance with repeated measures, as described below, using the software SYSTAT (SYSTAT, Evanston, IL).
Simulation studies.
To verify the theoretical validity of our experimental protocol and estimation method, especially under the condition of breathtobreath variability in ventilation, we performed simulation studies on a mathematical model of the respiratory chemical feedback control system of the normal adult human. This model, which has been described previously (20), was implemented and solved using the Advanced Continuous Simulation Language (ACSL; Mitchell and Gauthier, Concord, MA). A Gaussian white noise sequence with zero mean was added to ventilation to cause breathtobreath variation with a standard deviation of 1.0 l/min. Breath duration was assumed to be 4 s. At the end of each 4s interval, the values of model variables, such as
In each simulation the first 20 min of data were discarded to exclude any transient effects of the initial conditions. Each simulation run in hyperoxia or normoxia consisted of three segments: a 200breath baseline, a 630breath PRBSpaced inspired CO_{2} switching between 0 and 4%, and a 200breath segment after switching. Impulse responses and transfer functions for the closed loop and the open loop were obtained using the PEM method. To verify the simulation results obtained using the PRBS and PEM methods, we compared the transfer function results with the values of gain and phase delay from another set of simulations using sinusoidal variations in inspired CO_{2} level. This method has been used in previous experimental studies (9, 25, 27). The frequencies of sinusoidal inspired CO_{2} ranged from 0.001 to 0.1 Hz. After the model responses achieved a steady state, the gain of the transfer function at each frequency point was defined by the ratio of the magnitude of the sinusoidal ventilation response (fundamental frequency component) to the magnitude of sinusoidal inputs (inspired CO_{2}volume for the closedloop system and
In normoxia,
RESULTS
Simulation results.
Figure 2
Ashows the closedloopV˙i impulse response to a single breath of 0.01 liter of CO_{2} inhaled during hyperoxia and normoxia derived from the simulation model using PRBSpaced inspired CO_{2} input and PEM estimation. TheV˙i response has a higher peak value and faster decay from the peak during normoxia than during hyperoxia. The openloopV˙i impulse response to 1Torr increase in
The transfer functions from the same simulation data are displayed in Fig. 3 for the closedloop system and in Fig. 4 for the openloop system. For the closedloop system the gain of the transfer function is higher in normoxia than in hyperoxia from 0.005 to 0.125 Hz (Nyquist frequency); the phase delay is smaller in normoxia than in hyperoxia in the same frequency range. Here the phase delay is equivalent to the negative phase of the transfer function. Similar changes are found for the openloop system.
To verify the results using PRBSpaced inspired CO_{2} input and PEM estimation, in another set of simulations we used sinusoidally varying inspired CO_{2}, in which the sinewave frequency ranged from 0.001 to 0.1 Hz, and obtained the transfer functions for the closedloop and the openloop system. In this simulation the Gaussian white noise was removed from ventilation to make the ventilation noise free. Comparison of the two methods is shown in Figs. 3 and 4. The two methods have a good match in the transfer function results. We concluded that, using PRBSpaced inspired CO_{2} input and PEM estimation, we can accurately estimate the transfer functions for the closedloop and the openloop system.
In the simulation of the normoxic condition,
Experimental results.
Loworder models that minimized FPE and met the criteria for acceptability discussed above were found for all subjects in all conditions. Typical values for nn were [1 2 2 2 2] (hyperoxia, closed loop), [2 3 2 2 1] (normoxia, closed loop), [1 2 1 1 2] (hyperoxia, open loop), and [1 2 2 1 1] (normoxia, open loop).
Figure 6 shows an example of the respiratory responses to PRBSpaced inspired CO_{2} input in one typical subject (SA) during normoxia. All variables were resampled at the average breath duration for that session of data. The PEMpredicted ventilation output is also shown. When the variability in ventilation before the start of the PRBSpaced inspired CO_{2} input is considered, the predicted ventilation output matches the real ventilation output acceptably.
Figure 7 Ashows typical closedloopV˙i impulse responses to a single breath of 0.01 liter of inhaled CO_{2} during hyperoxia and normoxia from subject SA. Similar to the simulation, the closedloopV˙i impulse response has a higher peak value and faster decay from the peak in normoxia than in hyperoxia. In most subjects the responses are similar to those of subject SA. Only one subject (ER, whose response in hyperoxia was similar to other subjects) exhibited a damped, transient ventilatory oscillation in normoxia (Fig.7 B). Figure8 shows the statistical comparisons of the peak values and 50% response times (evaluated as the earliest time at which the integral of theV˙i impulse response reaches 50% of its final value) during hyperoxia and normoxia. On the basis of nine subjects, the closedloopV˙i impulse response has significantly higher peak value [0.143 ± 0.071 and 0.079 ± 0.034 (SD) l ⋅ min^{−1} ⋅ 0.01 l CO_{2} ^{−1}in normoxia and hyperoxia, respectively,P = 0.014] and significantly shorter 50% response duration (42.7 ± 13.3 and 72.3 ± 27.6 s in normoxia and hyperoxia, respectively,P = 0.020) in normoxia than in hyperoxia (Fig. 8). By use of a pairedttest with Bonferroni’s correction, individual P values <0.025 are considered to be significant.
The closedloop transfer functions for subjects SA and ER are shown in Fig. 9. Because we assume that the respiratory control system is linear, the oscillatory behaviors in ventilation that mimic periodic breathing (with a typical period of 20–100 s) correspond to a frequency range of 0.01–0.05 Hz. Because these oscillations will be affected only by the same frequency range in the transfer functions, our calculation of transfer function values focuses on this frequency range of periodic breathing. For both subjects, in the 0.01 to 0.05Hz range, the transfer function has larger gain and smaller phase delay in normoxia than in hyperoxia. In the transfer function of subject ER, a peak in the gain of the transfer function was found at ∼0.008 Hz, which corresponds roughly to the damped oscillation in theV˙i impulse response. For nine subjects, the gain of the closedloop transfer function in normoxia increased significantly (P < 0.0005), while phase delay decreased significantly [P < 0.0005 using 1factor (frequency) analysis of variance with repeated measures on the 2 situations (hyperoxia and normoxia); Fig.10]. In normoxia the gain increased by 108.5, 186.0, and 240.6%, while phase delay decreased by 26.0, 18.1, and 17.3%, at 0.01, 0.03, and 0.05 Hz, respectively.
Similar calculations were made for the openloop controller to determine theV˙i impulse response to a singlebreath increase of 1 Torr in
In experimental data the mean level of
DISCUSSION
The method of varying inspired CO_{2}according to a PRBS has been used previously to evaluate the respiratory chemical control system (17, 19, 22, 26, 29). The PRBS method provides better time resolution than traditional step and ramp methods. Unlike the singlebreath CO_{2} inhalation or the sinusoidal inspired CO_{2} method, when used with PEM the PRBS method does not need extensive ensemble averaging or many runs at different frequencies. Thus the test time will be reduced. Similar to white noise, the PRBS input contains relatively flat power over a wide frequency range, which is suitable for the dynamic response evaluation. In practical uses, however, some limitations may apply. As concluded by Sohrab and Yamashiro (26), use of a PRBS stimulus without the initial baseline data will underestimate the slow central component because of insufficient lowfrequency power. Also, because a PRBS input contains only two different levels, linearity of responses is assumed.
We used a smaller CO_{2}concentration than in our previous studies (19) (4 vs. 5%). This caused smaller disturbances and helped keep the system in the linear range. It also helped reduce the contribution of changes in
In this study we derived and compared the closedloop and the openloop ventilatory responses to a brief CO_{2} disturbance in terms of impulse responses and transfer functions in hyperoxia and normoxia in awake human subjects. Compared with hyperoxia the closedloop transfer function in normoxia had increased gain and decreased phase delay in the 0.01 to 0.05Hz range, which corresponds to typical periodic breathing cycles of 20–100 s. Also, the percentages of gain change are high (108.5, 186.0, and 240.6% at 0.01, 0.03, and 0.05 Hz, respectively), while the percentages of phase delay change are relatively low (26.0, 18.1, and 17.3%, respectively; Figs. 10 and 13). Whereas the increased gain theoretically increases the tendency of ventilatory oscillation in normoxia, the relatively small decrease in phase delay will move the potential ventilatory oscillation to a somewhat higher frequency range. Even though the transfer function gain was higher in normoxia than in hyperoxia, we observed that the initiation of oscillatory ventilation due to a small transient CO_{2} disturbance in normoxia is generally unlikely for normal subjects during wakefulness. However, similar to the simulation, the closedloop ventilatory impulse response showed a higher peak value and faster decay from the peak in normoxia than in hyperoxia. Such differences indicate that the ventilatory response to a brief CO_{2}disturbance is less damped in normoxia than in hyperoxia.
The loop gain is closer to unity during normoxia than during hyperoxia because of the increased closedloop transfer function gain in normoxia. Therefore, in contrast to a disturbance to
In contrast to a previous study (20), we found that closedloop and openloop responses changed in the same direction when our two experimental conditions were compared. Thus our conclusion from the direct calculation of the respiratory responses for the closedloop system is consistent with what has previously been inferred indirectly from measurement of only the controller responses; that is, the closedloop or whole system is closer to instability in normoxia than in hyperoxia (5, 9, 15, 16, 25, 27, 28).
Ventilation in hyperoxia is mediated by the central chemoreceptor, whereas ventilation in normoxia is mediated by the central and peripheral chemoreceptors. Our study in both conditions also allows us to draw conclusions about the contributions from these different pathways. From the data of subject SAwe can see that, for the open loop or controller, only one slow time constant is noted during hyperoxia. This slow time constant should correspond to the central chemoreceptor. Two time constants can be seen for the openloop response during normoxia. The fast time constant contributes to the fast rise and fast decay peak in the first 40 s. It was absent during hyperoxia and so likely is associated with the peripheral chemoreceptor. The slow constant dominates the subsequent slow decay of ventilation. It is close to the time constant observed in hyperoxia and, therefore, likely is due to the central chemoreceptor. For some subjects, such lowamplitude, slow decay may be difficult to observe, especially with a condition of noisy background and baseline drift. Also the fast peak during normoxia is higher than the largest response during hyperoxia. Because this peak in the first 40 s during normoxia has a fast time constant, it is generally believed that such a peak is mainly due to the peripheral chemoreceptors. However, comparing the openloop responses during hyperoxia and normoxia, we found that the response due to only the central chemoreceptor during hyperoxia has already risen to ∼40% of the peak value of normoxia in the first 40 s. This observation means that the contribution of the central chemoreceptor to the fast peak in normoxia is not negligible.
For the closedloop system the ventilatory impulse response should be equivalent to the response to a singlebreath stimulus (19). This equivalence has been shown for hypoxic responses in rats by Dhawale and Bruce (10). During normoxia the closedloop ventilatory response has a peak with a fast rise and fast decay in the first 40 s. Thereafter, the response is much lower than the peak value and slowly decays to zero (baseline). For the fast rise and fast decay, the time constant is comparable to the fast time constant of the openloop response. However, the slow time constant is not quantitatively comparable to the slow one in the open loop. The ventilatory response after the peak is much lower than the peak value and would be barely observable in a noisy background. This observation of the ventilatory impulse response in normoxia is consistent with the general assumption that ventilatory responses of humans to a transient (1–3 breaths) CO_{2} disturbance are mediated virtually exclusively by the peripheral chemoreceptor (26). Such behaviors of the closedloop ventilatory impulse response probably can be explained by the strong negativefeedback effect of the peak ventilation, which attenuates the
To verify the theoretical validity of our experimental protocol and estimation method, we evaluated the responses of a respiratory control model using both PRBS input with PEM estimation and the sinusoidal inspired CO_{2} method. The sinusoidal method, which has been used with promising results (9, 25,27), is a fundamental method to analyze a linear system by testing the system at several separate frequencies. On the other hand, PEM estimation deals with the system as a model (described inEq. 1 ). If the different principles of these two methods are considered, they have a good match in the transfer function results for the closedloop and the openloop system (Figs. 3 and 4). We concluded that we can accurately estimate the transfer functions for the closedloop and the openloop system using our PRBS input and PEM estimation.
In hyperoxia the high
Our estimated dynamic chemosensitivities, represented as gains of the openloop system, are consistent with the results in the previous studies using the PRBS method in hyperoxia by Modarreszadeh et al. (22) and in normoxia by Khoo et al. (17) but are slightly lower than those using the sinusoidal method (9, 25, 27). One possible source of these latter differences is that the “tail” of the ventilatory impulse response may remain at a nonzero level longer than one PRBS sequence (126 breaths). Estimation of this tail is significantly affected by the noisy background and baseline drift or trend. Longperiod increasing trends in ventilation (>30 min) during hyperoxia have been reported by Becker et al. (1) and were observed in our experiment. However, the estimation of the nonzero level of the tail generally only affects the steadystate or verylowfrequency component of the transfer function (lower than ∼0.002 Hz, corresponding to 1 PRBS sequence). It will not cause much error to the transfer function estimation in the periodic breathing frequency range (0.01–0.05 Hz). On the basis of these considerations, our estimations of impulse responses and transfer functions should well represent the “true” differences in ventilatory responses to a brief CO_{2} disturbance between hyperoxia and normoxia.
In the present study we considered the amount of inspired CO_{2} per breath to be the stimulus to the closedloop response rather than the level of inspired CO_{2}. In our opinion, the level of inspired CO_{2} by itself is inadequate, because the actual CO_{2}load delivered to the closedloop system can vary a great deal for the same
Our calculation of closedloop gain is not a direct measurement of chemoreflex loop gain. The relationship between the closedloop gain measurements in this study and the actual chemoreflex loop gain has been discussed (see Ref. 22,appendix). In concept, it would be possible to obtain estimates of the actual loop gain from our experiments by solving the first equation in theappendix of Ref. 22 forLG(ω) and using the assumption stated there that the ratio of the two lung transfer functions [i.e., P_{F}(ω) and P_{V}(ω)] is approximately constant and independent of frequency. However, one must know the constant value of that ratio. This value could be estimated from the mass balance equation for CO_{2} in the lung, but such an estimate will depend on the subject’s alveolar ventilation (which we did not measure). Nonetheless, one could design an experimental protocol using PRBSpaced inspired CO_{2}, combined with estimating the lung transfer functions, from which the true loop gain could be estimated. To obtain an estimate of the true loop gain in hyperoxia and normoxia in the present study, we have calculated the magnitude of the lung transfer function P_{v}(ω) at 0.01 Hz from the simulation model by forcing ventilation to vary at this frequency, then multiplying this magnitude by the openloop gain of the model at 0.01 Hz. The estimated chemoreflex loop gain was 0.21 in hyperoxia and 0.55 in normoxia. However, the estimates of the lung transfer function have not been validated against experimental data.
In summary, ventilatory oscillations due to a small transient CO_{2} disturbance in normoxia are generally unlikely for the majority of normal subjects during wakefulness, although respiratory chemical closedloop responses to continuous and random CO_{2}disturbances are theoretically more likely to elicit ventilatory oscillation patterns that mimic periodic breathing in normoxia than in hyperoxia. It is likely, however, that further increase in loop gain (e.g., due to an increase in peripheral chemosensitivity accompanying moderate hypoxia) is necessary before this latter mechanism contributes significantly to the genesis of ventilatory oscillations in normal awake subjects. This finding contrasts with the previous demonstration that continuous, random CO_{2}disturbances increase the level of spontaneous nonperiodic variability in ventilation of normal subjects even in hyperoxia (20).
Acknowledgments
The authors thank Pamela K. Houtz for technical assistance and Abhijit R. Patwardhan, Jian Zhong, and Amit Aggarwal for helpful discussions.
Footnotes

Address for reprint requests: E. N. Bruce, Center for Biomedical Engineering, Wenner Gren Laboratory, University of Kentucky, Lexington, KY 405060070.

This work was supported by National Heart, Lung, and Blood Institute Grant HL44889.
 Copyright © 1997 the American Physiological Society