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J Appl Physiol 98: 437-446, 2005. First published October 8, 2004; doi:10.1152/japplphysiol.00532.2004
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Impact of changes in inspired oxygen and carbon dioxide on respiratory instability in the lamb

Malcolm H. Wilkinson, Kah-Ling Sia, Elizabeth M. Skuza, Vojta Brodecky, and Philip J. Berger

Ritchie Centre for Baby Health Research, Institute of Reproduction and Development, Monash University, Clayton, Victoria, Australia

Submitted 20 May 2004 ; accepted in final form 6 October 2004


   ABSTRACT
TOP
 ABSTRACT
METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
We examined the effect of hypoxia and hypercapnia administered during deliberately induced periodic breathing (PB) in seven lambs following posthyperventilation apnea. Based on our theoretical analysis, the sensitivity or loop gain (LG) of the respiratory control system of the lamb is directly proportional to the difference between alveolar PO2 and inspired PO2. This analysis indicates that during PB, when by necessity LG is >1, replacement of the inspired gas with one of reduced PO2 lowers LG; if we made inspired PO2 approximate alveolar PO2, we predict that LG would be approximately zero and breathing would promptly stabilize. In six lambs, we switched the inspired gas from an inspiratory oxygen fraction of 0.4 to one of 0.12 during an epoch of PB; PB was immediately suppressed, supporting the view that the peripheral chemoreceptors play a pivotal role in the genesis and control of unstable breathing in the lamb. In the six lambs in which we administered hypercapnic gas during PB, breathing instability was also suppressed, but only after a considerable time lag, indicating the CO2 effect is likely to have been mediated through the central chemoreceptors. When we simulated both interventions in a published model of the adult respiratory controller, PB was immediately suppressed by CO2 inhalation and exacerbated by inhalation of hypoxic gas. These fundamentally different responses in lambs and adult humans demonstrate that PB has differing underlying mechanisms in the two species.

Cheyne-Stokes respiration; hypoxia; hypercapnia; sleep apnea syndromes; control of breathing; periodic breathing

PERIODIC BREATHING (PB), or Cheyne-Stokes respiration, appears under a wide range of physiological and clinical conditions. It is particularly prevalent during sleep, occurring at sea level in apparently normal-term and preterm infants (22, 43), at high altitude in normal adults (27), and after hypoxic exposure in experimental animals (11, 21). It also occurs in patients with congestive heart failure (36), with idiopathic central sleep apnea (52), with bilateral brain stem lesions (40), and in periodic obstructive sleep apnea (41). A form of PB can also be found in hibernating animals (7, 34).

Although it is often assumed that the underlying mechanisms causing PB in infants and adults are similar, in each case involving instability of the chemical control system that regulates breathing, there are some marked differences in the pattern of PB and its responses to changes in inspired gas that remain largely unexplained. For example, in preterm infants, the waxing and waning pattern of PB that is characteristic of the adult is replaced by a more or less abrupt on-off pattern that shows little change in tidal volume during the breathing phase (42); this pattern resembles that seen in hibernating animals (34). Furthermore, although the response to hyperoxic inspired gas applied during PB is generally similar in adults and infants (17, 27, 51) in that the instability is transiently enhanced as evidenced by the immediate increase in the duration of the apneic pause, incidental observations show that the response to hypoxia applied during PB in preterm infants (44) is apparently opposite to that of adults (48). In the preterm infant, PB is suppressed by hypoxic inspired gas, whereas it is enhanced in adults. When a comparison is made between experimental animal models of PB and infants, further major discrepancies are revealed. Unlike in human infants (and adults), spontaneous PB has not been reported in intact experimental animals and cannot be induced during exposure to hypoxic inspired gas (11, 21), even though hypoxic stimulus of the carotid bodies, consistently implicated in PB (11, 25, 50, 51), is at a maximum during hypoxia; curiously, in animals, PB appears only after the return to room air after hypoxic exposure.

Although theoretical models of the respiratory control system have been proposed that support the view that PB involves the activity of central and peripheral chemoreceptors either individually or in concert (25, 31), it is not clear whether all of the conditions/discrepancies cited above can be accounted for by one theoretical model. Nor are there experimental tests currently available to determine which chemosensitive receptor systems are responsible for a particular type of instability. As a result, the treatment of these breathing disorders lacks a firm scientific foundation. This problem is particularly evident in the treatment of breathing irregularities in the infant where commonly used drug therapies are aimed at stimulating both central and peripheral chemoreceptor activity (8) with little recognition of the potential impact these interventions may have on the stability of the developing respiratory control system.

A profound effect of increasing the inspired gas concentration of O2 during PB is evident in our earlier work in the lamb and human infant. In both models, we demonstrated that the unstable breathing pattern of PB was transiently exacerbated by administration of hyperoxic inspired air in a setting in which the initial conditions included hypoxemia at the peripheral chemoreceptors. We interpreted this observation in terms of hyperoxic inspired gas increasing the loop gain (LG), or more specifically the plant gain (for oxygen), of the respiratory control system (4, 50, 51), such that increments in ventilation cause larger changes in arterial PO2 (PaO2) than if air were the inspired gas. This observation suggests that if we were to adopt the opposite strategy and apply hypoxic inspired air during PB in the lamb, we would transiently reduce or even suppress the ventilatory instability of PB as a result of a reduction of the LG of the respiratory control system to <1. This prediction is supported by a theoretical analysis presented in the present work.

In this study, we test the predicted effect of hypoxia applied during PB in a newborn lamb model of PB our laboratory has established in earlier studies (50, 51). In addition, because there is theoretical evidence that CO2 administration should suppress PB in adult humans (31, 33) and because CO2 administration has recently been used clinically in an attempt to control breathing instability in both adults (2, 32, 47) and infants (1), we also examined the effect of CO2 administration on PB. Our immediate aim was to compare and contrast the effects of inspired hypoxic and hypercapnic gas on the unstable newborn respiratory control system. The results of the experimental study and our theoretical analysis clearly show that manipulations of inspired CO2 and O2 can be used to establish the dominant receptor system driving a particular breathing instability.


   METHODS
TOP
 ABSTRACT
 METHODS
RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
Theoretical Model

Background.   In the past, a number of mathematical models have been used to describe quantitatively the oscillations in breathing that appear as part of PB (25, 31, 33). Because these models incorporate nonlinear differential system equations, a solution is usually sought using either an analog or digital computer simulation. The effect of changing the system parameters must then be investigated by using repeated simulations.

An alternative approach to determining factors that are likely to destabilize (or stabilize) control systems is perturbation analysis (39), which is widely used by engineers as the means for evaluating the performance of nonlinear control systems (20, 39). Importantly, this technique has been successfully applied in studies of the human respiratory control system (25). In this method, the system equations are linearized around a particular equilibrium point, and the stability of the system under study is examined locally by assuming small perturbations from this point. The advantage of this method is that the impact of changes in multiple system parameters can often be expressed within a single equation so that the interaction between these parameters is easily deduced. Although the method is not strictly applicable to making precisely quantitative predictions in nonlinear systems undergoing limit-cycle oscillations, such as those that occur in PB, the local stability of the system can still be assessed by performing an analysis at a number of different equilibrium points. Typically, these points are chosen so as to be not too close to known nonlinearities such as an apneic threshold. The method is particularly useful in determining whether an instability is likely to develop (or be suppressed) for the particular equilibrium conditions under consideration. For the respiratory system, these equilibrium conditions may include the current values of PaO2 and arterial PCO2 (PaCO2) at a receptor site. Ultimately, a full numerical simulation, supported by the insights gained from a perturbation analysis, can provide a detailed picture of the performance of the respiratory control system after a disturbance, as we demonstrate later.

The particular issue we seek to address is what effect changes in the inspired concentration of oxygen have on breathing stability. In particular, since the parameter that determines stability is the system LG, we seek to determine an analytical expression for LG in the lamb.

Lamb model.   In the 10-day-old lamb, the magnitude of the rapid response to inspired hypercapnic gas, which is mediated by the peripheral chemoreceptors, is small (9, 14, 50). Calculations based on the data of Carroll et al. (14), and our own unpublished data, suggest that within the brief three- to four-breath time span of the ventilatory period of PB in the lamb, only an 8% increase in ventilation is predicted when a CO2 stimulus similar to that expected during PB is applied (~7 Torr; Ref. 16). By contrast, during a –10% step change in arterial oxygen saturation, approximating in magnitude that seen during PB in the lamb, we typically observe a 60% increase in ventilation over this same time period. It appears, therefore, that the 10-day-old lamb has a powerful response to hypoxia but lacks the multiplicative effect of hypoxia on the slope of the CO2 response that is present in humans and is assumed to originate within the carotid bodies.

The central CO2 controller contribution to LG, and hence the instability of PB, is also likely to be small (25). It is clear from Fig. 6 of Carroll et al. (14) that the response to hypercapnia in the peripheral chemoreceptor-denervated lambs is still not fully developed 60 s after exposure to hypercapnia. Therefore, if we assume a conservative time constant of 1 min for the central CO2 response, the filtering effect of this time constant on the 10-s oscillation in PaCO2 during PB is likely to be severe. Our calculations suggest that a 7-Torr oscillation in PaCO2 would be reduced to 0.18 Torr in the brain tissue if we assume, as is usually the case, that the central receptors monitor cerebral tissue levels of CO2. Thus the contribution of these receptors to the oscillatory drive of PB will be small. Furthermore, a more detailed calculation of LG for the central CO2 control loop, using the equations given by Khoo et al. (25) and using published values of brain weights and cerebral blood flow for the lamb (3), gives a central contribution to LG of only 0.03 during hypoxic challenge, confirming our view that the central receptors make a negligible contribution to oscillatory ventilatory drive during PB in the lamb and can reasonably be neglected in the formulation of the analytical expression for LG.



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  		Fig. 6. Predicted response to hypoxia and hypercapnia applied during PB in adult humans. Three theoretical model results, obtained by simulating the experiments carried out in the lamb, using a published mathematical model of the adult human respiratory controller (25). After a period of hyperventilation resulting in apnea at the start of each run, breathing began with air as the inspired gas. A: LG for O2 (LG; 0.16), LG for CO2 (LG; 1.42), and overall LG (1.57) during the second cycle of PB; these values apply to all 3 experiments. Inspired gas remained air throughout (A); it was switched to an FIO2 of 0.12 for the period between the 2 arrows (B); and 5% CO2 was added to the inspired air for the period between the 2 arrows (C). In B, notice that after 1 subsequent cycle of PB, where no change occurred, the amplitude of breathing during PB was enhanced. This continued until the return to an FIO2 of 0.21. During this run, LGwas decreased after hypoxia from 0.16 to 0.04, but notice that LGwas increased from 1.42 to 1.72 so that overall LG was also increased from 1.57 to 1.72 as a result of the hypoxic challenge. Such a change is consistent with the increased amplitude of PB observed. In C, the hypercapnic challenge suppressed PB immediately rather than after several cycles as in the lamb. In this case LG was increased from 0.16 to 0.42, whereas LG was decreased from 1.42 to 0.07, and the overall LG was decreased from 1.57 to 0.48, immediately suppressing PB. {triangleup}, Time at which LG values were calculated in each experiment. Note that LGand LGare calculated at a phase shift of 180°. The magnitude of the mean arterial PO2 and PCO2 at the lung and carotid bodies, which are required in the calculation of LG, are computed at each instant in time using a center-weighted moving average technique, with a window size of 30 s.

 
Accordingly, for the purpose of analysis, the major factor directly controlling breathing stability in the lamb is assumed to be the peripheral chemoreceptor sensitivity to hypoxia. By contrast, as we have outlined above, the peripheral CO2 response has a negligible direct role in the genesis of respiratory instability in the 10-day-old lamb because the peripheral receptors are apparently unable to adequately follow the relatively "fast" changes of arterial CO2 that occur during PB. Nonetheless, as discussed later, increased (nonoscillatory) CO2 stimulus of the central and peripheral chemoreceptors can have a marked indirect effect on LG by increasing ventilation and consequently increasing the mean PaO2 at the peripheral chemoreceptors. In addition, nonlinearities associated with the apneic threshold can also affect LG, as we discuss below.

To establish the required LG equation for the lamb, we have used the results of Khoo et al. (25), modified to include the appropriate peripheral controller response for the lamb. To implement the analysis, we assume a small perturbation (~) in alveolar ventilation (A) and proceed around the peripheral chemoreceptor control loop (see Fig. 1) calculating the resultant perturbations in PaO2 at the heart and carotid bodies until we finally calculate the response of the controller (P). The ratio of the original disturbance, A to the controller response P gives the LG of the peripheral control loop (see APPENDIX), which is given by

(1)
where F({omega},{tau}x) is the magnitude of the frequency-dependent portion of the LG expression in Eq. A5; {omega} is radian frequency; {tau}x is the collective effect of all the lung and tissue washout time constants and circulatory delays in Eq. A5; aand aare the mean PaO2 at the lung and carotid bodies, respectively; VO2 is the lung gas volume of oxygen; and Gpe–ka is the exponential ventilatory response to hypoxia of the carotid bodies.



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  		Fig. 1. Schematic diagram of the peripheral oxygen control loop in the lamb. Flow diagram showing the essential elements of the peripheral control loop used to calculate loop gain (LG), comprising the controlled system or plant (lung and tissues) and the peripheral controller. This proceeds by assuming a small perturbation in alveolar ventilation [A(s)] and calculating subsequent disturbances in arterial PO2 (aO2) at the lung and peripheral chemoreceptors using transfer function analysis. Finally, the peripheral controller response to this disturbance [P(s)] is calculated, followed by LG defined as the ratio of P(s) to A(s). Dead-space ventilation is assumed constant. s, Complex frequency (rad/s); A, mean PaO2 at the carotid bodies.

 
This expression represents, in concise format, the major factors that influence the stability of the lamb respiratory control system, including the lung gas volume of oxygen, the washout time constants of the lung and tissue for oxygen, the circulatory delays between lung and chemoreceptors, the hypoxic sensitivity of the carotid bodies, and the inspired gas concentration of oxygen. It is the last variable that is the focus of our attention in this paper, because changing the inspired gas concentration is a convenient means of manipulating the LG of the peripheral chemoreceptor control loop. Specifically, Eq. 1 indicates that if aremains constant, LG will fall if the difference between the inspired PO2 (PIO2) and the mean PaO2 is reduced; based on control theory, breathing will be stabilized once LG falls to <1.

Impact of the apneic threshold on LG.   The presence of an apneic threshold in the respiratory controller may have a significant effect on the magnitude of LG computed from linear theory. However, on the assumption that the oscillation in PaO2 or PaCO2 that drives ventilation is approximately sinusoidal, a method known as describing function analysis (20, 24) can be used to calculate an equivalent linear gain for any nonlinearity. Importantly, this linearization allows the powerful array of linear techniques, including the application of the Nyquist stability theorem that states that LG ≥ 1 and {phi} = 180° for instability to occur. Unlike in linear systems, the equivalent linear gain may vary with the amplitude and the mean value of the driving oscillation, so this equivalent gain must be specified at a particular value of the driving function. Applying this method to the analysis of the well- known linear respiratory controller plus threshold, it can be shown that the equivalent gain of the controller is always less than or equal to the linear gain (24). On the other hand, if the respiratory controller gain is increased below eupnea compared with that above, as proposed in the lamb (4, 50, 51), the controller gain will be increased from its linear value as the apneic threshold is approached (26). In summary, if the oscillation in PaCO2 or PaO2 occurs in the vicinity of the threshold, the LG magnitude expressed in Eq. 1 may be augmented or reduced depending on the type of respiratory controller present.

Thus consideration of the LG expressed in Eq. 1 combined with a knowledge of the equivalent linear gain associated with the particular form of controller under consideration can be used to predict the LG and the likelihood and magnitude of an instability using the Nyquist stability theorem, even though nonlinearity is present. Finally, we note that it is often the case that oscillations build up, starting first at low amplitude (i.e., during exposure to hypocapnic hypoxia or during sleep onset) before threshold crossings develop. In this case, linear theory, as exemplified by Eq. 1, is adequate to predict LG and the onset of instability.

Animal preparation.   Surgical preparation of animals in this study was identical to that already described in detail (50, 51). We anesthetized seven lambs of 11–20 days of age with a mean weight of 8.6 ± 0.8 kg using intravenous {alpha}-chloralose (80 mg/kg as a starting bolus followed by 20 mg·kg–1·h–1 as a continuous infusion). The lambs were intubated and ventilated with a Bournes BP-200 infant ventilator. All animals were maintained under an effective but light level of anesthesia by continuously monitoring blood pressure and heart rate and by making regular tests for a response to stimulation of the inner canthus of the eye. The tracheal tube was attached to a ventilator circuit, through which gas passed at 30 l/min, a very high flow that enabled us to change between hypoxic, normoxic, hyperoxic, or hypercapnic gas mixtures within 1 s. The circuit permitted us to ventilate the animal or to allow the animal to ventilate itself.

We inserted a catheter nonocclusively into the carotid artery for blood gas sampling and for measurement of blood pressure (HP 1280 blood pressure transducer connected to a Hewlett-Packard 8805B Carrier Amplifier). Heart rate was derived from the blood pressure signal (Neotrace NT 122). A second nonocclusive catheter in the jugular vein was used for blood gas sampling and infusion of glucose saline (5% glucose in 0.9% saline at a rate of 4.0 ml·kg–1·h–1). We maintained rectal temperature within the range of 39.8 ± 1.0°C using an overhead radiant heater.

A Fleisch no. 0 pneumotachograph, in conjunction with a Gaeltec MP-15 differential pressure transducer, was used to measure respiratory airflow, and this signal was electronically integrated to provide tidal volume (HP-8815A electronic integrator). End-expired PCO2 and PO2 were measured using a Morgan 901 MK2 CO2 analyzer and an Amatek S-3A oxygen analyzer, respectively. The probe of a Nellcor pulse oximeter (model N-200) was placed across the lower jaw, but with the tongue reflected out of the way so that the light beam passed through the soft tissues of the jaw.

Pulse oximeter calibration.   We calibrated the Nellcor N-200 pulse oximeter over the arterial oxygen saturation (SaO2) range from 40 to 100% using the SaO2 (Radiometer OSM-2 hemoximeter) of samples of carotid artery blood taken while the animal breathed progressively more hypoxic gas mixtures. All saturation values reported in this paper were corrected by using a curve relating the real (Radiometer) saturation to the indicated (Nellcor) saturation. At the end of the protocols, the lambs were killed with an overdose of anesthetic (Lethabarb, 150 mg/kg; Virbac, Sydney, Australia). All surgical and experimental procedures conformed with the guidelines established by the National Health and Medical Research Council of Australia and had the approval of the Standing Committee in Ethics in Animal Experimentation of Monash University.

Experimental Protocols

Control.   Lambs were hyperventilated with air for a period of 5 min, after which the ventilator was turned off. By adjusting the tidal volume and respiratory frequency during the hyperventilation period, it was possible to produce a posthyperventilation apnea (PHA) that was terminated at an SaO2 of 40–50%. During PHA (i.e., before the commencement of breathing), the inspired gas was switched from an inspired oxygen fraction (FIO2) of 0.21 to an FIO2 of 0.4. Previous experiments have shown that this procedure produces PB in 95% of lambs (51). The epoch of PB produced was allowed to terminate spontaneously.

Hypoxic test.   The procedure outlined in control was repeated except that, after two cycles of PB had occurred and before the ventilatory period of the third cycle was initiated, the inspired gas was switched abruptly to an FIO2 of 0.12. This level of hypoxia was sufficient to maintain SaO2 close to 50% for the 1-min duration of the challenge. At the end of this period, the inspired gas was returned to an FIO2 of 0.4 until after the resumption of stable breathing. At the end of the hypoxic test, the protocol described in control was repeated, with PB again allowed to terminate spontaneously. As a result, each hypoxic challenge was bracketed by a control procedure. The study sequence comprised control 1, hypoxia, and control 2.

Hypercapnic test.   This protocol was similar to that described in the hypoxic test, except that the inspired gas during PB was switched after one cycle to an inspired CO2 fraction of 0.05 in a gas mixture containing an FIO2 of 0.4. To quantify the central CO2 stimulus and the peripheral O2 stimulus at the resolution of PB, we took a jugular venous blood sample to determine the jugular venous PCO2 (PJV), and we also noted the corrected value of SaO2 at the onset of regular breathing. Each hypercapnic challenge was bracketed by an identical control challenge, during which the inspired gas remained at an FIO2 of 0.4 throughout. The study sequence was made up of control 1, hypercapnia, and control 2.

Data Analysis

In both the hypoxic and hypercapnic protocols, we measured the epoch duration of PB from the point at which the challenge was given until regular breathing was restored; this method of analysis was carried out for the control and the hypoxic and hypercapnic gas challenges alike. To test whether PB was induced under uniform initial conditions for each procedure, we measured the duration of PHA, the nadir value of SaO2 reached during PHA, and the end-tidal CO2 of the last ventilated breath before PHA. To assess whether the mean hypoxic stimulus at the carotid chemoreceptors immediately before and after the hypoxic challenge had changed, we estimated the mean SaO2 for one complete cycle of PB (including both the ventilatory and apneic periods) before the challenge and for an equal time period starting at the beginning of the hypoxic challenge; this was done by averaging the corrected SaO2 values taken every 2 s from the oximeter recording after allowing for the processing delay of the oximeter. If the oximeter failed to track the rapid changes in oxygen saturation for short periods as evidenced by a flat section on the SaO2 from pulse oximetry trace (see Fig. 2), either the data for that section were discarded or the data were interpolated over that period to obtain an estimate of the likely saturation (see Fig. 2). Both estimates are recorded in RESULTS.



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  		Fig. 2. Hypoxia during periodic breathing (PB) (data recording). Typical data recording showing the time course of respiratory flow rate (), tracheal gas concentrations of oxygen and CO2 (ETO2 and ETCO2, respectively), pulse oximeter saturation (Sp), and carotid artery pressure (Pca) during a typical hypoxic challenge during PB. The record commences during hyperventilation with a mechanical ventilator, and this is maintained until the ventilator is turned off at t1, after which the inspired gas is immediately switched to an inspired oxygen fraction (FIO2) of 0.4. After a period of posthyperventilation apnea, during which Spfalls progressively, spontaneous PB is generated at t2, and after 2 cycles of PB the inspired gas was switched to an FIO2 of 0.12 at t3 for 1 min. Breathing was immediately stabilized and remained so until the inspired gas was switched back to an FIO2 of 0.4 at t4, after which PB reappeared. Notice that Spjust before the hypoxic challenge approximates that immediately after the challenge. The dotted sections of the Sptrace marked with an x are estimates of the time course of oxygen saturation during periods where pulse oximeter tracking was lost (see METHODS for further details).

 
Statistics.   All data are means ± SE. Differences between means were tested using a one-way repeated-measures analysis of variance, with P < 0.05 being taken as the critical level and using Tukey's post hoc test for multiple comparisons.


   RESULTS
TOP
 ABSTRACT
 METHODS
 RESULTS
DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 
Hypoxia During PB

There was no significant difference in the duration of PHA between control 1, hypoxia, and control 2 (22.5 ± 2.9 vs. 25.0 ± 2.1 vs. 23.2 ± 2.6 s, respectively), in nadir SaO2 during PHA (42.3 ± 3.3 vs. 40.7 ± 3.2 vs. 42.6 ± 3.6%, respectively), or in the end-tidal CO2 before PHA (3.1 ± 0.2 vs. 3.2 ± 0.3 vs. 3.2 ± 0.3%, respectively). Thus conditions before the induction of PB were similar in the three tests. In all six lambs challenged with hypoxia during PB, the instability was immediately terminated after the switch of FIO2 from 0.4 (hyperoxia) to 0.12 (hypoxia) as illustrated in Figs. 2 and 3. Significantly, the mean SaO2 immediately before the challenge (56.5 ± 4.1%) was not different to that immediately after the challenge (53.7 ± 4.4%), suggesting that , the mean PaO2 at the peripheral chemoreceptors, was similar during PB and during the regular breathing that resulted from switching inspired gas to a hypoxic mixture. A second estimate of the prechallenge SaO2 deduced using interpolation of the saturation data to account for poor oximeter tracking (see Fig. 2) was similarly not significantly different from that immediately after the challenge. In this case, the prechallenge SaO2 was 57.3 ± 4.1 vs. 53.7 ± 4.4% immediately after the challenge.



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  		Fig. 3. Effect of hypoxia during PB. Ventilation data from Fig. 2 (middle) bracketed with 2 sets of control data shown in the top and bottom (control 1 and 2, respectively) in which PB is induced by applying an FIO2 of 0.4 during posthyperventilation apnea (PHA). Notice the abrupt braking effect of hypoxia applied during PB in the middle and the contrasting destabilizing effect of hyperoxia on return to an FIO2 of 0.4.

 
All lambs once again exhibited PB (mean epoch duration of 44.5 ± 6.8 s) when the inspired gas was returned to an FIO2 of 0.4 after 1 min of hypoxia (Figs. 2 and 3). The mean epoch duration of PB for control 1 was 41.1 ± 7.8 s and for control 2 was 45.3 ± 12.0 s (P = not significant).

Hypercapnia During PB

As in protocol 1, there was no significant difference in the duration of PHA between control 1, hypercapnia, or control 2 (20.8 ± 3.4 vs. 21.7 ± 2.1 vs. 23.5 ± 2.6 s, respectively) in nadir SaO2 during PHA (41.3 ± 3.8 vs. 43.8 ± 3.9 vs. 41.4 ± 2.0%, respectively) or in the end-tidal CO2 before PHA (2.8 ± 0.2 vs. 3.0 ± 0.3 vs. 3.0 ± 0.3%, respectively). In the six lambs challenged with hypercapnic gas during PB, there was a significant reduction in the poststimulus epoch duration of PB with respect to control (Figs. 4 and 5A). Epoch durations in the three experimental periods were 46.1 ± 8.2 s during control 1; 23.3 ± 8.0 s during hypercapnia (inspired CO2 fraction = 0.05), and 51.2 ± 9.9 s during control 2. There was no significant difference in epoch duration between control 1 and 2.



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  		Fig. 4. Effect of hypercapnia during PB. Typical tracings showing the response to hypercapnia (middle) applied during induced PB in a lamb. At top and bottom (control 1 and 2, respectively), PB is induced and allowed to terminate spontaneously. Note that with an inspired CO2 fraction (FI) of 0.05 there is no evidence of an immediate respiratory response after the challenge, in marked contrast to the response to hypoxia (Fig. 3).

 


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  		Fig. 5. Influence of hypercapnia on PB. A: epoch duration of PB after administration of hypercapnic gas was significantly reduced compared with control; P < 0.05, n = 6. B: at the point where regular breathing resumed after PB, the jugular venous PCO2 (PJV) was not significantly different between the control and hypercapnic challenge, suggesting that stimulation of the central CO2-sensitive chemoreceptors mediates the conversion to regular breathing after PB. C: hypercapnic gas applied during PB significantly increased minute ventilation. D: there was no significant difference in the arterial oxygen saturation (SaO2) at the start of regular breathing between the control period and the hypercapnic challenge with 5% CO2. The dotted lines show the mean nadir of SaO2 reached at the start of PB.

 
The PJVthat coincided with the commencement of regular breathing after PB was 46.0 ± 1.9 Torr in control 1, 45.8 ± 2.4 Torr during hypercapnia, and 45.5 ± 2.0 Torr during control 2 (Fig. 5B). There were no significant differences in these PJVvalues. The corrected value of SaO2 at the commencement of regular breathing was 90.3 ± 3.9 in control 1, 83.0 ± 5.9 during hypercapnia, and 90.1 ± 2.9 during control 2 (Fig. 5D). There was no significant differences in these SaO2 values.

To assess the impact of hypercapnia on PB, the minute ventilation during PB was compared between control 1, hypercapnia, and control 2. As shown in Fig. 4C, there was a significant increase in minute ventilation during hypercapnia (140.8 ± 15.0 ml·min–1·kg–1) compared with control 1 (116.5 ± 11.0 ml·min–1·kg–1) and control 2 (116.4 ± 9.8 ml·min–1·kg–1). There was no significant difference in minute ventilation between control 1 and control 2.


   DISCUSSION
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
APPENDIX
 GRANTS
 REFERENCES
 
We report two principal findings in this study. First, inspiration of hypoxic gas during PB at a level chosen not to lead to further hypoxemia at the peripheral chemoreceptors immediately stabilizes breathing in the lamb. We interpret this effect of hypoxic gas in terms of a reduction in LG (plant gain for oxygen), making ventilation less effective at changing blood gases, reducing the overshoot in PaO2, and effectively braking the oscillation that causes PB. Second, hypercapnia also stabilizes breathing, but it does so only after a considerable delay; our findings also show that when continuous breathing resumes after an epoch of PB there is a similar level of jugular venous PCO2 in the control and in the hypercapnia phases of the protocol, suggesting that breathing stabilizes when central PCO2 reaches a threshold level. These findings strongly suggest that the stabilization of breathing brought about by hypoxic inspired gas during PB in the lamb is mediated via the rapidly responding, O2-sensitive carotid bodies, whereas the stabilizing effect of inspired CO2 is mediated via the CO2-sensitive, slowly responding medullary chemoreceptors.

Although our laboratory (4, 51) and others (17, 44) have already shown that hyperoxia applied during PB can transiently destabilize breathing further, this present work represents the first systematic demonstration that hypoxia applied in similar circumstances stabilizes breathing, at least in the lamb. LG is an effective unifying concept to explain the effects of increased or decreased oxygen level on PB. By reference to Eq. 1, it is clear that oxygen enters the LG equation that defines the respiratory controller of the lamb in two places. The first is via the difference between PIO2 and a. The second is via Gpe–ka, the peripheral chemoreceptor contribution to LG, which increases exponentially as afalls.

The first bracketed term in the numerator of Eq. 1 predicts that the introduction of hypoxic inspired gas during PB will decrease LG and therefore will tend to suppress breathing instability. Conversely, hyperoxia will increase the difference between PIO2 and a, augment LG, and promote breathing instability. This effect can also be understood qualitatively without reference to the LG equation in that the breathing and apneic phases of PB result from cyclic increases and decreases in carotid body discharge (50, 51). During the apneic phase, arterial O2 level falls, with the result that there is an increase of carotid body discharge that eventually exceeds the threshold needed to trigger breathing. Once breathing begins, PaO2 rises, carotid body discharge falls below the apneic threshold, and an apnea ensues. The inhalation of hypoxic gas during PB decreases the tendency of PaO2 to rise and to overshoot when breathing returns after the apneic pause. Without an overshoot in PaO2, the carotid bodies continue to discharge, and hence breathing continues. Hyperoxia has the reverse effect, exacerbating the ventilatory overshoot and thereby enhancing the respiratory instability (51).

The second bracketed term in the numerator of the LG equation represents the contribution of the carotid bodies through their sensitivity to hypoxia. When PIO2 is suddenly reduced during the hypoxic challenge, any fall in LG through the effect of a decline in PIO2-acould be counteracted by a rise in the contribution of the carotid bodies via their sensitivity to the imposed hypoxia. For such a carotid body effect to occur in our study, there would have to be a fall in aduring the hypoxic challenge compared with the control period of PB. That no immediate change in carotid body contribution occurs in our hypoxic challenge experiments is illustrated in Fig. 2 and is clear from our analysis showing that the mean SaO2 just before the challenge (56.5 ± 4.1%) is not significantly different from that occurring just after the challenge (53.5 ± 4.4%) (see also Fig. 2). Thus the switch to hypoxic inspired gas leads to a fall in LG as a result of the fall in PIO2-aand plant gain, thereby providing an explanation for the stabilization of breathing we observed.

Are there other possible explanations for our observations? Recently, a good deal of attention has been focused on the role of proximity of the eupneic point to the CO2 apneic threshold (10, 35, 45). The concept of a CO2 reserve, defined as the difference between the end-tidal CO2 at eupnea and the end-tidal CO2 at the apneic threshold, has developed (46), and its magnitude has been used as an explanation for the occurrence of apnea and PB. The CO2 reserve is reduced in such conditions as acute hypoxia (53) in patients with congestive heart failure (54) or when ventilatory drive is very low; importantly, these are conditions in which ventilatory instability occurs. In contrast, the CO2 reserve is increased when ventilatory drive is increased by nonhypoxic means, such as during treatment with theophyline and acetazolamide, and these drugs suppress PB (10, 23). Although we did not measure CO2 reserve, increased hypoxemia in the lamb could conceivably cause an increased CO2 reserve by shifting the CO2 response curve to the left without change in slope. However, this did not occur in our experiments because the mean level of hypoxemia did not change during the prehypoxic cycle of PB and the immediate post-PB period (see Fig. 2). Accordingly, an increase in CO2 reserve by this mechanism does not explain our findings. We conclude, therefore, that a decrease in LG, specifically plant gain (for oxygen), is the key mechanism stabilizing breathing in the lamb after hypoxic exposure during PB. The important role of plant and controller gain in controlling ventilatory instability has been stressed recently (18).

Our experimental results for challenge with inspired CO2 during PB are in marked contrast to our results with hypoxia, because although the epoch duration of PB was reduced after an increase in inspired CO2, this occurred only after a considerable delay and not instantaneously as in the hypoxic challenge. In addition, even though the epoch duration was shortened during the CO2 challenge, the PB reverted to a regular pattern at the same value of PJVas in the control run when no CO2 was applied. Accepting that this measure accurately portrays central tissue CO2 levels, as we have argued previously (51), this finding strongly suggests that PB is resolved when the central respiratory drive reaches a threshold value.

After PHA in the lamb, transient PB develops as a direct result of the increased LG provided principally by the hypoxic stimulation of the peripheral chemoreceptors (50, 51). The fact that respiratory instability is present implies that LG exceeds 1 during the epoch of PB and falls below 1 on return to regular breathing. During this period, both aand cerebral CO2 rise as they return to their prehyperventilation values. Accordingly, central CO2 chemoreceptor drive is being progressively augmented and peripheral oxygen drive decremented. Thus LG, which we have argued is determined principally by peripheral oxygen drive in the lamb, falls progressively with time throughout the PB epoch. Eventually, at some specific value of a, which we refer to as aO2, LG falls to 1, and soon after regular breathing returns.

The result of adding CO2 to the inspired gas during PB is relatively easy to visualize since the resulting extra CO2-sensitive central drive increases ventilation during PB (see Fig. 5C) so that both aand cerebral CO2 rise more rapidly and aO2 is reached earlier, shortening the PB epoch. Because the sum of the central neural drive and the peripheral hypoxic drive determined by aO2 will be the same as previously (unless the apneic threshold changes), it follows that PJVmust be the same also. Clearly, the experimental finding that PJVsampled at the commencement of regular breathing after an epoch of PB is the same during both the control protocol and the hypercapnia protocol indicates an important role for central CO2 chemosensitivity in terminating respiratory instability in the lamb.

The issue of how the properties of the respiratory controller of the lamb relate to the adult human case is an interesting one. What is immediately evident from perturbation analysis is that the adult human controller has, in addition to the peripheral O2 component present in the lamb, a peripheral CO2 component (25). These two components, each with separate LG, which we will refer to as LG, analogous to our Eq. 1, and LG, respectively (this component of LG is not present in the lamb), arise because of the multiplicative effect of hypoxia on CO2 sensitivity in the adult human. The system LG is then equal to the vector summation of LGand LG, with the contribution to LG of the central CO2 controller during PB being neglected (25). A further important difference is that the human controller apparently has a relatively fixed apneic threshold for CO2 (19, 30), whereas the lamb and several other species do not (12, 28). It seems likely that these fundamental differences are the reason hypoxia normally precipitates PB in sleeping humans (6, 27), whereas it has never been reported to do so in the lamb.

A full discussion of the impact these controller differences would have on the genesis of PB is beyond the scope of this paper, but several differences might be expected. First, the traditional view of PB being an oscillation about a fixed apneic threshold for CO2 (38) is not applicable to the lamb since the oscillation in PaO2 apparently dominates the generation of PB in this species. Second, the effect of inspired CO2 on the resolution of PB might be accelerated in the adult human because of the brisk carotid body response to CO2, a feature not present in the lamb. In effect, the inspiration of CO2 in humans reduces LGin much the same way that hypoxia reduces LGin the lamb. We note in passing that the absence of a brisk response to inspired CO2 during PB in the lamb and the failure to suppress PB immediately on exposure to CO2 suggests that LGis small and supports our view that PB is driven primarily by oscillations in PaO2. Third, although the effect of hypoxia on the peripheral oxygen controller in the adult human would be expected to be similar with LGfalling after hypoxia, as in the lamb, hypoxia could augment the human LGso that PB may be unchanged or even enhanced on switching to a hypoxic inspired gas during PB.

We can take the first steps toward testing these important predictions by performing a numerical simulation using an established model of the adult human respiratory control system (25, 49). The results of this simulation, illustrated in Fig. 6, show that challenge with hypoxia during the transient PB that follows hyperventilation has a radically different effect than in the lamb: it clearly enhances PB. Furthermore, it is clear from the LG calculations included in Fig. 6 that, although LGfalls after hypoxic challenge as in the lamb, the LGrises and the overall system LG is increased, leading to an enhancement of the instability. Challenge with CO2 suppresses PB as in the lamb, but, as expected, it does so more rapidly because of the brisk carotid body response to hypercapnia in the human. This result is supported by the experimental results of Cherniack et al. (15) that clearly demonstrate the rapid suppression of servorespirator-induced PB that follows the addition of CO2 to the inspired gas in adult cats, a model that has been shown to exhibit a brisk response to changes in end-tidal CO2 (5).

Further support for our predictions comes from the experimental observation (48) that hypoxia applied during PB in snorers does not suppress PB. This observation and our modeling results raise the interesting possibility that a hypoxic challenge during PB could differentiate between the form of respiratory controller present in the lamb, in which the carotid bodies are rapidly responsive only to oxygen vs. the multiplicative respiratory controller of the adult human in which the peripheral chemoreceptors are rapidly responsive to both oxygen and CO2.

An obvious inference from our results in the lamb and our simulation for the adult human is that the presence of a brisk CO2 response at the carotid bodies has a major impact on the effect of hypoxia on PB. Interestingly, there is evidence that the respiratory controller of the newborn human infant, and indeed the infants of some other species, resembles the lamb rather than the adult human. In a series of experiments aimed at characterizing the respiratory response to hypoxia in preterm infants, Rigatto et al. (44) observed that when hypoxia was applied during PB in one infant it immediately restored regular breathing, a response that is clearly consistent with the human newborn having a controller similar to the lamb. Other evidence that the peripheral chemoreceptors of the newborn predominantly have an oxygen sensitivity comes from studies in both in vivo and in vitro preparations of the immature cat (13) and rat (37). In these preparations, over a period of weeks, there is a shift toward a controller that manifests a multiplicative type CO2-oxygen interaction characteristic of the human adult. We suggest that the application of hypoxia or CO2 during PB may provide a simple means for determining whether the respiratory controller has a simple oxygen-sensitive character in early development before converting to a multiplicative controller with postnatal development.

We are currently exploring this possibility using a numerical model of the lamb respiratory control system that incorporates a central CO2 control loop and an additive peripheral oxygen feedback loop representing an early life model that then matures progressively toward a multiplicative interaction, where both peripheral O2 and CO2 responses are present as in the adult controller. This more accurate model should also allow us to determine whether the peripheral O2 feedback loop is in fact dominant in the lamb as we contend in this present work. The model should also allow us to examine the impact of the apneic threshold on breathing instability and LG in the lamb.

In conclusion, there is considerable evidence from our work and that of others that during PB the newborn respiratory controller may be dominated by O2 sensitivity before converting to a controller in which O2 modulates the response to CO2. The methods developed in this paper, which essentially manipulate LG during PB by changing the inspired gas, represent a powerful tool for discriminating the stage of development of the infantile respiratory control system. This information may in turn allow more appropriate use of drugs to control LG of specific receptor systems and to suppress breathing instabilities.


   APPENDIX
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
GRANTS
 REFERENCES
 
Using a perturbation analysis following that used by Khoo et al. (25) and applying it to the peripheral chemoreceptor control loop of the lamb (see Fig. 1), a disturbance in A (A)will cause a disturbance in a given by

(A1)
where TT2 is tissue washout time for oxygen; TE2 is overall washout time for oxygen, including the effect of tissue washout by perfusion and lung washout by perfusion and ventilation; and s is complex frequency (rad/s).

This disturbance (a) is filtered as it passes through the heart and associated vasculature and is further delayed by {tau}p seconds in transit to the carotid bodies. Denoting the filtered and delayed stimulus that arrives at the carotid bodies as a, we can write (29)

(A2)
where {tau}1 and {tau}2 are filtering time constants and {tau}p is circulation delay (lung to carotid body).

This disturbance in partial pressure stimulates the carotid bodies to produce a change in ventilation P. In previous work, our laboratory has shown that the lamb, unlike the human, has a negligible brisk response to hypercapnia (50), suggesting that the usual multiplicative effect of hypoxia on the carotid body response to PaCO2 is absent under the conditions of our experiments, and as a result the exponential response to hypoxia (the peripheral controller response) can be adequately modeled as

(A3)
where k is a constant, ais mean PaO2 at the peripheral chemoreceptor. Differentiating Eq. A3 with respect to Paand expressing the differential as a small perturbation yields

(A4)
And finally, if we assume as did Khoo et al. (25) that the dead-space ventilation is constant in Fig. 1, then substituting Eqs. A1 and A2 into Eq. A4, we can write an expression for the LG of the lamb peripheral controller as

(A5)
This expression can be used to derive the magnitude and phase of LG. However, for our purposes, it is sufficient to recognize that the magnitude of LG can be written as

(A6)
where F({omega},{tau}x) is the magnitude of the frequency-dependent portion of the LG expression in Eq. A5, {omega} is radian frequency, and {tau} is the collective effect of all the time constants in Eq. A5.

This expression represents, in concise format, the factors that influence the stability of the lamb respiratory control system, including the hypoxic sensitivity of the carotid bodies, the lung gas volume, the washout time constants of the lung and tissue for oxygen, and the inspired gas concentration of oxygen. It is the latter that is the focus of our attention in this paper because it shows that changes in the inspired gas concentration can be viewed as a manipulation of LG of the peripheral chemoreceptor control loop.


   GRANTS
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
REFERENCES
 
This study was supported by the National Health and Medical Research Council of Australia Grant Nos. 34836 and 194403 and the National SIDS Council of Australia Grant G94-13/161.


   FOOTNOTES
 

Address for reprint requests and other correspondence: M. H. Wilkinson, Ritchie Centre for Baby Health Research, Institute for Reproduction and Development, Monash Medical Centre, 246 Clayton Rd., Clayton, 3168 Australia (E-mail: mal.wilkinson{at}med.monash.edu.au)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 METHODS
 RESULTS
 DISCUSSION
 APPENDIX
 GRANTS
 REFERENCES
 

  1. Al-Saif S, Alvaro R, Manfreda J, Kwiatkowski K, Cates D, and Rigatto H. Inhalation of low (0.5–15%) CO2 as a potential treatment for apnea of prematurity. Semin Perinatol 25: 100–106, 2001.
  2. Andreas S, Weidel K, Hagenah G, and Heindl S. Treatment of Cheyne-Stokes respiration with nasal oxygen and carbon dioxide. Eur Respir J 12: 414–419, 1998.
  3. Barfield CP, Yu VYH, Noma O, Kukita J, Cussen LJ, Oates A, and Walker AM. Cerebral blood volume measured using near-infrared spectroscopy and radiolabels in the immature lamb brain. Pediatr Res 46: 50–56, 1999.
  4. Berger PJ, Skuza EM, Brodecky V, Cranage SM, Adamson TM, and Wilkinson MH. Unusual respiratory response to oxygen in an infant with repetitive cyanotic episodes. Am J Respir Crit Care Med 161: 2107–2111, 2001.
  5. Berkenbosch A, DeGoede J, Ward DS, Olievier CN, and VanHartevelt J. Dynamic response of peripheral chemoreflex loop to changes in end-tidal CO2. J Appl Physiol 64: 1779–1785, 1988.
  6. Berssenbrugge A, Dempsey J, Iber C, Skatrud J, and Wilson P. Mechanisms of hypoxia-induced periodic breathing during sleep in humans. J Physiol 343: 507–524, 1983.
  7. Biorck G, Johansson B, and Schmid H. Reactions of hedgehogs, hibernating and non-hibernating, to the inhalation of oxygen, carbon dioxide and nitrogen. Acta Physiol Scand 37: 71–83, 1956.
  8. Blanchard PW and Aranda JV. Pharmacotherapy of respiratory control disorders. In: Respiratory Control Disorders in Infants and Children, edited by Beckerman RC, Brouillette RT, and Hunt CE. Baltimore, MD: Williams & Wilkins, 1992, p. 352–370.
  9. Blanco CE, Dawes MA, Hanson GS, and McCooke HB. The response to hypoxia of arterial chemoreceptors in fetal sheep and new-born lambs. J Physiol 351: 25–37, 1984.
  10. Bradley TD. Crossing the threshold: implications for central sleep apnea. Am J Respir Crit Care Med 165: 1203–1204, 2002.
  11. Canet E, Praud JP, and Bureau MA. Periodic breathing induced on demand in awake newborn lamb. J Appl Physiol 82: 607–612, 1997.
  12. Canet E, Praud JP, Laberge JM, Blanchard PW, and Bureau MA. Apnea threshold and breathing rhythmicity in newborn lambs. J Appl Physiol 74: 3013–3019, 1993.
  13. Carroll JL, Bamford OS, and Fitzgerald RS. Postnatal maturation of carotid chemoreceptor responses to O2 and CO2 in the cat. J Appl Physiol 75: 2383–2391, 1993.
  14. Carroll JL, Canet E, and Bureau MA. Dynamic ventilatory responses to CO2 in the awake lamb: role of the carotid chemoreceptors. J Appl Physiol 71: 2198–2205, 1991.
  15. Cherniack NS, von Euler C, Homma I, and Kao FF. Experimentally induced Cheyne-Stokes breathing. Respir Physiol 37: 185–200, 1979.
  16. Chernick V, Heldrich F, and Avery ME. Periodic breathing of premature infants. J Pediatr 64: 330–340, 1964.
  17. Cross KW and Oppe TE. The effect of inhalation of high and low concentrations of oxygen on the respiration of the premature infant. J Physiol 117: 38–55, 1952.
  18. Dempsey JA, Smith CA, Przybylowski T, Chenuel B, Xie A, Nakayama H, and Skatrud JB. The ventilatory responsiveness to CO2 below eupnoea as a determinant of ventilatory stability in sleep. J Physiol 560: 1–11, 2004.
  19. Duffin J and McAvoy GV. The peripheral-chemoreceptor threshold to carbon dioxide in man. J Physiol 406: 15–26, 1988.
  20. Elgerd OI. Control Systems Theory. Tokyo: McGraw-Hill, 1967, p. 309–331.
  21. Han F, Subramanian S, Price ER, Nadeau J, and Strohl KP. Periodic breathing in the mouse. J Appl Physiol 92: 1133–1140, 2002.
  22. Henderson-Smart DJ. Apnea of prematurity. In: Respiratory Control Disorders in Infants and Children, edited by Beckerman RC, Brouillette RT, and Hunt CE. Baltimore, MD: Williams & Wilkins, 1992, p. 161–177.
  23. Javaheri S, Parker TJ, Wexler L, Liming JD, Lindower P, and Roselle GA. Effect of theophylline on sleep disordered breathing in heart failure. N Engl J Med 335: 562–567, 1996.
  24. Khoo MCK. Nonlinear analysis of physiological control systems. In: Physiological Control Systems, Analysis, Simulation and Estimation. Hoboken, NJ: Wiley, 2000, p. 229–270.
  25. Khoo MCK, Kronauer RE, Strohl KP, and Slutsky AS. Factors inducing periodic breathing in humans: a general model. J Appl Physiol 53: 644–659, 1982.
  26. Korta LB, Horgan JD, and Lange RL. Stability analysis of the human respiratory system. Proc National Elect Conf 201–206, 1965.
  27. Lahiri S, Maret K, and Sherpa MG. Dependence of high altitude sleep apnoea on ventilatory sensitivity to hypoxia. Respir Physiol 52: 281–301, 1983.
  28. Lahiri S, Mokashi A, DeLaney RG, and Fishman AP. Arterial PO2 and PCO2 stimulus threshold for carotid chemoreceptors and breathing. Respir Physiol 34: 359–375, 1978.
  29. Lange RL, Horgan JD, Botticelli JT, Tsagaris T, Carlisle RP, and Kuida H. Pulmonary to arterial circulatory transfer function: importance in respiratory control. J Appl Physiol 21: 1281–1291, 1966.
  30. Lloyd BB, Jukes MGM, and Cunningham DJC. The relation between alveolar oxygen pressure and the respiratory response to carbon dioxide in man. Q J Exp Physiol 43: 214–227, 1958.
  31. Longobardo GS, Cherniack NS, and Fishman AP. Cheyne-Stokes breathing produced by a model of the human respiratory control system. J Appl Physiol 21: 1839–1846, 1966.
  32. Lorenzi-Filho G, Rankin F, Bies I, and Bradley TD. Effects of inhaled carbon dioxide and oxygen on Cheyne-Stokes respiration in patients with heart failure. Am J Respir Crit Care Med 159: 1490–1498, 1999.
  33. Milhorn HT and Guyton AC. An analog computer analysis of Cheyne-Stokes breathing. J Appl Physiol 20: 328–333, 1965.
  34. Milsom WK. Intermittent breathing in vertebrates. Annu Rev Physiol 53: 87–105, 1991.
  35. Nakayama H, Smith CA, Rodman JR, Skatrud JB, and Dempsey JA. Effect of ventilatory drive on carbon dioxide sensitivity below eupnea during sleep. Am J Respir Crit Care Med 165: 1251–1259, 2002.
  36. Naughton MT, Benard D, Tam A, Rutherford R, and Bradley TD. Role of hyperventilation in the pathogenesis of central sleep apneas in patients with congestive heart failure. Am Rev Respir Dis 148: 330–338, 1993.
  37. Pepper DR, Landauer RC, and Kumar P. Postnatal development of CO2-O2 interaction in the rat carotid body in vitro. J Physiol 485: 531–541, 1995.
  38. Phillipson EA. Control of breathing during sleep. Am Rev Respir Dis 118: 909–937, 1978.
  39. Pipes LA and Harvill LR. Transfer functions and impulse responses. In: Applied Mathematics for Engineers and Physicists, edited by Martin WT and Spanier EH. Tokyo: McGraw-Hill, 1970, p. 313–318.
  40. Plum F and Brown HW. The effect on respiration of central nervous system disease. Ann NY Acad Sci 109: 915–931, 1963.
  41. Remmers JE, deGroot WJ, Sauerland EK, and Anch AM. Pathogenesis of upper airway occlusion during sleep. J Appl Physiol 44: 931–938, 1978.
  42. Rigatto H. Periodic breathing. In: Respiratory Control and Disorders in the Newborn, edited by Mathews OP. New York: Dekker, 2003, p. 237–272.
  43. Rigatto H and Brady JP. Periodic breathing and apnoea in preterm infants. II. Hypoxia as a primary event. Pediatrics 50: 219–228, 1972.
  44. Rigatto H, Brady JP, and de la Torre Verduzco R. Chemoreceptor reflexes in preterm infants: 1. The effect of gestational and postnatal age on the ventilatory response to inhalation of 100% and 15% oxygen. Pediatrics 55: 604–613, 1975.
  45. Skatrud JB and Dempsey JA. Interaction of sleep state and chemical stimuli in sustaining rhythmic ventilation. J Appl Physiol 55: 813–822, 1983.
  46. Smith CA, Nakayama H, and Dempsey JA. The essential role of carotid body chemoreceptors in sleep apnea. Can J Physiol Pharmacol 81: 774–779, 2003.
  47. Steens RD, Millar TW, Xiaoling S, Boberdorf D, Buckle P, Ahmed M, and Kryger MH. Effect of inhaled 3% CO2 on Cheyne-Stokes respiration in congestive heart failure. Sleep 17: 61–68, 1994.
  48. Warner G, Skatrud JB, and Dempsey JA. Effect of hypoxia-induced periodic breathing on upper airway obstruction during sleep. J Appl Physiol 62: 2201–2211, 1987.
  49. Wilkinson MH and Berger PJ. Identifying potential pathways leading to sudden infant death using mathematical modelling of respiratory control. In: Second SIDS International Conference and First SIDS Global Strategy Meeting, edited by Walker AM and McMillen C. Ithaca, NY: Perinatology Press, 1993, p. 229–237.
  50. Wilkinson MH, Berger PJ, Blanch N, Brodecky V, and Jones C. Source of respiratory drive during periodic breathing in lambs. Respir Physiol 104: 115–126, 1996.
  51. Wilkinson MH, Berger PJ, Blanch N, Brodecky V, and Jones CA. Paradoxical effect of oxygen administration on breathing stability following post-hyperventilation apnoea in lambs. J Physiol 504: 199–209, 1997.
  52. Xie A, Rutherford R, Rankin F, Wong B, and Bradley TD. Hypocapnia and increased ventilatory responsiveness in patients with idiopathic central sleep apnea. Am J Respir Crit Care Med 152: 1950–1955, 1995.
  53. Xie A, Skatrud JB, and Dempsey JA. Effect of hypoxia on the hypopnoeic and apnoeic threshold for CO2 in sleeping humans. J Physiol 535: 269–278, 2001.
  54. Xie A, Skatrud J, Puleo DS, Rahko PS, and Dempsey JA. Apnea-hypopnea threshold for CO2 in patients with congestive heart failure. Am J Respir Crit Care Med 165: 1245–1250, 2002.




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