Journal of Applied Physiology
Vol. 83, No. 2, pp. 466-476, August 1997
CONTROL OF BREATHING, CIRCULATION, AND TEMPERATURE

Ventilatory stability to transient CO₂ disturbances in hyperoxia and normoxia in awake humans

Jie Lai and Eugene N. Bruce

Center for Biomedical Engineering, University of Kentucky, Lexington, Kentucky 40506-0070

ABSTRACT

INTRODUCTION

METHODS

RESULTS

DISCUSSION

ACKNOWLEDGEMENTS

FOOTNOTES

REFERENCES

ABSTRACT

Lai, Jie, and Eugene N. Bruce. Ventilatory stability to transient CO₂ 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 PCO₂ are more likely to elicit ventilatory oscillation patterns that mimic periodic breathing in normoxia than in hyperoxia. To test this hypothesis experimentally, in nine awake humans we applied pseudorandom binary inspired CO₂ fraction stimulation in normoxia and hyperoxia to derive the closed-loop and open-loop ventilatory responses to a brief CO₂ disturbance in terms of impulse responses and transfer functions. The closed-loop impulse response has a significantly higher peak value [0.143 ± 0.071 vs. 0.079 ± 0.034 (SD) l · min¹ · 0.01 l CO₂¹, P = 0.014] and a significantly shorter 50% response duration (42.7 ± 13.3 vs. 72.3 ± 27.6 s, P = 0.020) in normoxia than in hyperoxia. Therefore, the ventilatory responses to transient CO₂ disturbances are less damped (but generally not oscillatory) in normoxia than in hyperoxia. For the closed-loop transfer function, the gain in normoxia increased significantly (P < 0.0005), while phase delay decreased significantly (P < 0.0005). 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. Changes in the same direction were found for the open-loop system. Generally, an oscillatory ventilatory response to a small transient CO₂ disturbance is unlikely during wakefulness. However, changes in parameters that lead to additional increases in chemoreflex loop gain are more likely to initiate oscillations in normoxia than in hyperoxia.

periodic breathing; central chemoreflex; peripheral chemoreflex; closed-loop response; open-loop response; impulse response; transfer function; pseudorandom binary sequence

INTRODUCTION

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 end-tidal CO₂ buffering technique to reduce spontaneous variability in arterial PCO₂ (Pa_CO2), observed reduced variability in ventilation during hyperoxic hypercapnia, whereas without CO₂ buffering they observed oscillatory patterns in ventilation, despite the fact that the respiratory chemical control system showed stable behavior (i.e., loop gain < 1). They suggested that respiratory chemical closed-loop responses to continuous and random disturbances in Pa_CO2 should be considered a possible cause of oscillatory patterns in ventilation that mimic periodic breathing. In simulation studies they validated their experimental results during hyperoxia and predicted the closed-loop ventilatory response to a single-breath CO₂ disturbance during normoxia, which showed slight oscillatory behavior compared with the overdamped response in hyperoxia. They speculated that random disturbances in Pa_CO2 are more likely to elicit ventilatory oscillation patterns in normoxia than in hyperoxia.

Previous studies focusing on the ventilatory responses to Pa_CO2, which represent the open-loop or controller responses to a CO₂ disturbance (2, 9, 17, 25, 27, 29), have shown that dynamic controller gain and steady-state loop gain increase in normoxia compared with hyperoxia (5, 9, 15, 16, 25, 27, 28). Thus it was inferred that the closed-loop or whole system should be more unstable in normoxia. However, it has been demonstrated recently that the open-loop or controller responses may not necessarily reflect the properties of the closed-loop or whole system responses (22). Furthermore, steady-state measurements may not reflect closed-loop properties at the frequencies of periodic breathing. Specifically, it is unknown how dynamic closed-loop gain in normoxia differs from that in hyperoxia, especially at periodic breathing frequencies.

In this study we tested the hypothesis that transient ventilatory oscillations due to a brief CO₂ disturbance are more likely in normoxia than in hyperoxia, and we examined the relationship between the closed-loop and the open-loop ventilatory responses in a frequency range representative of periodic breathing frequencies. Using a pseudorandom binary sequence (PRBS) to control inspired CO₂ fraction (FI_CO2) and transfer function estimation based on the prediction error method (PEM), we derived and compared the closed-loop and the open-loop ventilatory responses to a brief CO₂ disturbance in a single group of subjects in hyperoxia and normoxia. To verify the theoretical validity of our experimental protocol and data analysis method, we evaluated the responses of a respiratory chemical control model under the same experimental conditions using the same analysis method and compared these simulation results with values from another set of simulation studies using sinusoidal variations in inspired CO₂ level. In simulation studies we also evaluated the effect of changes in arterial PO₂ (Pa_O2), caused by ventilatory responses to the CO₂ stimuli, on the transfer function in normoxia.

METHODS

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RESULTS

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DISCUSSION

The method of varying inspired CO₂ 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 single-breath CO₂ inhalation or the sinusoidal inspired CO₂ 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 low-frequency power. Also, because a PRBS input contains only two different levels, linearity of responses is assumed.

We used a smaller CO₂ 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 Pa_O2 due to the ventilatory responses from the hypercapnic stimulus (see below). Our use of every-other-breath switching and our inclusion of the baseline data have the effect of increasing the input low-frequency power and improving the low-frequency estimation. In our transfer function estimation we used the PEM. Compared with the cross-correlation method (19, 26), PEM gives a smooth estimate of the impulse response. The Box-Jenkins model (Eq. 1) used in our PEM estimation deals better with nonwhite or correlated noise than the cross-correlation method or methods using an autoregressive with exogenous input (ARX) model. With use of PEM estimation, it is very easy to obtain the ventilatory impulse response and the transfer function directly from the model. A full explanation of these advantages of PEM estimation can be found elsewhere (22).

In this study we derived and compared the closed-loop and the open-loop ventilatory responses to a brief CO₂ disturbance in terms of impulse responses and transfer functions in hyperoxia and normoxia in awake human subjects. Compared with hyperoxia the closed-loop transfer function in normoxia had increased gain and decreased phase delay in the 0.01- to 0.05-Hz 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 CO₂ disturbance in normoxia is generally unlikely for normal subjects during wakefulness. However, similar to the simulation, the closed-loop 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 CO₂ 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 closed-loop transfer function gain in normoxia. Therefore, in contrast to a disturbance to FI_CO2, it should be more likely that a disturbance to the system parameters would cause the loop gain to reach unity in normoxia than in hyperoxia. On the basis of their model study, Khoo et al. (16) suggested that a sufficiently strong disturbance to Pa_CO2 and Pa_O2 could push a high-gain system into instability by changing the chemosensitivity, even when the original loop gain is below unity. Also, ElHefnawy et al. (11, 12) emphasized that any change in effective tissue volume via redistribution of blood flow could increase the plant gain. It may be that such factors do not cause loop gain to be unity when they occur individually, but if more than one occurs simultaneously, the possibility of periodic breathing will increase substantially. Such a possibility should be greater in normoxia than in hyperoxia. We did find that one subject (ER) exhibited a damped transient ventilatory oscillation in normoxia; however, his response in hyperoxia was similar to other subjects. Thus we conclude that a transient ventilatory oscillation due to a brief CO₂ disturbance should be more easily elicited in normoxia than in hyperoxia in awake humans, although in the absence of additional alterations of system parameters, such an oscillatory response is unlikely in the majority of normal subjects.

In contrast to a previous study (20), we found that closed-loop and open-loop 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 closed-loop system is consistent with what has previously been inferred indirectly from measurement of only the controller responses; that is, the closed-loop 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 SA we 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 open-loop 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 low-amplitude, 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 open-loop 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 closed-loop system the ventilatory impulse response should be equivalent to the response to a single-breath stimulus (19). This equivalence has been shown for hypoxic responses in rats by Dhawale and Bruce (10). During normoxia the closed-loop 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 open-loop 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) CO₂ disturbance are mediated virtually exclusively by the peripheral chemoreceptor (26). Such behaviors of the closed-loop ventilatory impulse response probably can be explained by the strong negative-feedback effect of the peak ventilation, which attenuates the Pa_CO2 stimulus before the central response fully develops. During hyperoxia, without the initial high-amplitude but fast-decaying peak, the negative-feedback effect of ventilation is relatively weak and slow. Consequently, one observes the slow response due to the central chemoreceptors (19). However, as mentioned above in reference to the open-loop ventilatory responses, we suspect that the contribution of the central chemoreceptor to the initial peak of the closed-loop response during normoxia is not negligible.

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 CO₂ 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 in Eq. 1). If the different principles of these two methods are considered, they have a good match in the transfer function results for the closed-loop and the open-loop system (Figs. 3 and 4). We concluded that we can accurately estimate the transfer functions for the closed-loop and the open-loop system using our PRBS input and PEM estimation.

In hyperoxia the high Pa_O2 suppresses or "turns off" the response of the peripheral chemoreceptor to a CO₂ disturbance. Therefore, in hyperoxia we ignored the contribution of changes in Pa_O2, which were secondary to the changes in ventilation due to the hypercapnic stimulus during PRBS-paced CO₂ disturbance. In normoxia such changes in Pa_O2 may affect the dynamic gain of the peripheral chemoreceptor. In this study, first, we used a smaller CO₂ concentration (4 vs. 5%) to decrease the amplitude of Pa_O2 changes. Second, in simulation studies, we compared the open-loop transfer function results without control of Pa_O2 with the results when Pa_O2 was held to the mean level during PRBS switching using the PRBS-paced inspired CO₂ stimulus and the sinusoidal inspired CO₂ input method. The simulation results in Fig. 5 show that the open-loop transfer function without control of Pa_O2 closely matches that with Pa_O2 held at the mean level during PRBS switching for both methods. From this simulation result we concluded that using our experimental protocol and estimation method, even without controlling Pa_O2, we still could closely estimate the ventilatory responses exclusively due to the hypercapnic stimulus. Such responses correspond to the mean Pa_O2 during PRBS switching, which was 111.9 ± 3.7 Torr for our experimental data. If this level changes but is still in the normoxia range, the dynamic gain of the open-loop transfer function will change slightly.

Our estimated dynamic chemosensitivities, represented as gains of the open-loop 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. Long-period 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 steady-state or very-low-frequency 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 CO₂ disturbance between hyperoxia and normoxia.

In the present study we considered the amount of inspired CO₂ per breath to be the stimulus to the closed-loop response rather than the level of inspired CO₂. In our opinion, the level of inspired CO₂ by itself is inadequate, because the actual CO₂ load delivered to the closed-loop system can vary a great deal for the same FI_CO2. Because we wish to interpret our findings in terms of an equivalent transient response to a standard single-breath stimulus (or disturbance), it seems more appropriate to consider the amount of CO₂ delivered on each breath as the stimulus rather than the level of inspired CO₂. Furthermore, using FI_CO2 × VI as the input partially corrects for the effects of variations in tidal volume. When FI_CO2 = 0, the calculated input is not affected by variations in VI. This consequence is appropriate, because the only effect of an increase in VI is to lower alveolar PCO₂ (PA_CO2), assuming that expired tidal volume also increases. This effect is present whether we use FI_CO2 alone or FI_CO2 × VI as the stimulus, and (for either input signal) in the analysis this effect on PA_CO2 appears as a noise component. When FI_CO2 > 0, using FI_CO2 as the input would leave us with two noise components: the one just noted and another related to the fact that the CO₂ level in the lungs is indeed altered by alterations in VI in this situation. For example, although an increase in VI would lead to a net lowering of PA_CO2 even in the presence of nonzero FI_CO2, the increase in CO₂ in the lungs due to the increase in VI will partially buffer the fall in PA_CO2. In other words, even in this situation an increase in the amount of CO₂ delivered to the lungs has the same qualitative effect on PA_CO2: it acts to increase it. Although the increased expired tidal volume still acts to decrease PA_CO2, just as when FI_CO2 = 0, our method compensates for the additional effect on PA_CO2 due to the increased CO₂ load from VI. However, the principal quantitative difference between the two input signals (other than a scale factor) occurs at the onset of pseudorandom switching, when the mean tidal volume increases slowly for a few minutes because of the increased mean FI_CO2. The practical consequence is that our input stimulus might be expected to be transiently lacking in high-frequency components (compared with those present in the abrupt transition of FI_CO2), but the pseudorandom signal contains sufficient high-frequency components to permit identification of the response.

Our calculation of closed-loop gain is not a direct measurement of chemoreflex loop gain. The relationship between the closed-loop 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 the APPENDIX of Ref. 22 for LG() and using the assumption stated there that the ratio of the two lung transfer functions [i.e., P_F() and P_V()] 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 CO₂ 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 PRBS-paced inspired CO₂, 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() at 0.01 Hz from the simulation model by forcing ventilation to vary at this frequency, then multiplying this magnitude by the open-loop 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 CO₂ disturbance in normoxia are generally unlikely for the majority of normal subjects during wakefulness, although respiratory chemical closed-loop responses to continuous and random CO₂ 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 CO₂ disturbances increase the level of spontaneous nonperiodic variability in ventilation of normal subjects even in hyperoxia (20).

ACKNOWLEDGEMENTS

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 40506-0070.

Received 30 October 1995; accepted in final form 11 April 1997.

REFERENCES