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¹ University Laboratory of Physiology, University of Oxford, Parks Road, Oxford OX1 3PT, UK

	Abstract

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Both exercise and hypoxia increase pulmonary ventilation. However, the combined effects of the two stimuli are more than additive, such that exercise may be considered to potentiate the acute ventilatory response to hypoxia (AHVR), and vice versa. Exposure to sustained hypoxia of 8 h duration or more has been shown to increase the acute chemoreflex responses to hypoxia and hypercapnia. The purpose of this study was to determine whether sustained exposure to hypoxia also changed the stimulus interaction between the effects of exercise and hypoxia on ventilation. Ten subjects undertook two main protocols on two separate days. On one day, subjects were exposed to isocapnic hypoxia (IH) at an end-tidal partial pressure of O₂ of 55 mmHg and on the other day, subjects were exposed to air as a control (C). Before and after each exposure, the sensitivity of AHVR was assessed during both resting conditions and exercise at 35% of the subjects' maximal oxygen uptake capacity. Average values (means ± S.D.) obtained for the sensitivity of AHVR from protocol IH were 0.85 ± 0.35 (rest, prehypoxic exposure), 1.60 ± 0.66 (exercise, prehypoxic exposure), 1.69 ± 0.63 (rest, posthypoxic exposure) and 1.81 ± 0.86 l min^–1 %^–1 (exercise, posthypoxic exposure). A non-dimensional variable, , was used to quantify the interaction present between exercise and hypoxia. The variable fell significantly following the sustained exposure to hypoxia (P < 0.02, ANOVA), indicating that the degree of stimulus interaction between acute hypoxia and exercise had declined. We suggest that the mechanisms by which sustained hypoxia modifies peripheral chemoreflex function may also modify the effects of exercise on the peripheral chemoreflex.

(Received 4 January 2006; accepted after revision 5 September 2006; first published online 11 September 2006)
Corresponding author P. A. Robbins: University Laboratory of Physiology, University of Oxford, Parks Road, Oxford OX1 3PT, UK. Email: peter.robbins{at}physiol.ox.ac.uk

	Introduction

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Numerous investigators have noted that the stimuli of acute hypoxia and muscular exercise have a more than additive effect on pulmonary ventilation (; Christensen, 1937; Asmussen & Neilsen, 1957; Hornbein & Roos, 1962; Cunningham et al. 1968; Weil et al. 1972; Masson & Lahiri, 1974). This interaction has been considered either as an increase in the slope of the ventilatory response to hypoxia under conditions of exercise, compared with rest, or alternatively, as an increase in the slope of the ventilatory response to exercise under conditions of acute hypoxia, compared with breathing air. The precise mechanism(s) and site(s) of action by which this interaction occurs remain unknown.

In humans, prior exposure to sustained hypoxia of several hours duration augments the ventilatory sensitivity to acute hypoxia when this sensitivity is measured against a background of unchanged end-tidal partial pressure of CO₂ (P_ET,CO2; Howard & Robbins, 1995). In the goat, it has been possible to confine the sustained hypoxia locally to the carotid body. Such hypoxia of a few hours duration induces a marked increase in the sensitivity of the peripheral chemoreflex to hypoxia even when the rest of the animal is maintained both euoxic and eucapnic (Bisgard et al. 1986b). These findings and others (Busch et al. 1985; Bisgard et al. 1986a; Weizhen et al. 1992) strongly suggest that the increase in chemoreflex sensitivity to hypoxia arises as a local effect of hypoxia at the carotid body.

It is unknown whether such a period of sustained hypoxia also affects the interaction that occurs between the two stimuli of acute hypoxia and muscular exercise. Two possible scenarios are illustrated in Fig. 1. If the effects of sustained hypoxia occur entirely upstream (or entirely downstream) of any interactive process (shaded

View larger version (17K): [in this window] [in a new window]   Figure 1.  Schematic illustration of the possible sites of action of sustained hypoxia on the pathways by which acute hypoxia and exercise stimulate ventilation Shaded areas A represent sites that do not affect exercise–hypoxia interaction; shaded area B represents sites at which sustained hypoxia in general will alter exercise–hypoxia interaction.

	Glossary of physiological symbols

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Symbol and unit Definition Gex (l min–1 W–1) Ventilatory sensitivity to exercise Gp (l min–1 %–1) Peripheral chemoreflex sensitivity to hypoxia Gpe (l min–1 %–1) Gp during exercise Gpr (l min–1 %–1) Gp at rest Hyp Hypoxic stimulus Pac,CO2 (mmHg) Arterialized capillary PCO2 Pac,O2 (mmHg) Arterialized capillary PO2 PET,CO2 (mmHg) End-tidal PCO2 PET,O2 (mmHg) End-tidal PO2 SO2 (%) Oxygen saturation of blood, estimated from PO2 (l min–1) Pulmonary ventilation, measured (l min–1) Component of ventilation not attributable to hypoxia (l min–1) during exercise (l min–1) at rest (l min–1) Component of ventilation attributable to hypoxia (l min–1) Air-breathing ventilation at rest (l min–1) Maximum oxygen uptake capacity WR (W) Work rate Strength of interaction between exercise and acute hypoxia

areas A of Fig. 1), then there should be no effect on the degree of interaction observed. In contrast, if sustained hypoxia acts on any aspect of the interactive process itself (shaded area B of Fig. 1), then in general, changes in the degree of interaction are likely to occur. Furthermore, since there is reasonable evidence to support the notion that sustained hypoxia of a few hours duration affects peripheral chemoreflex function through its actions on the carotid body, alterations in the degree of interaction between the two stimuli of acute hypoxia and exercise would suggest that at least some of this interaction arises through mechanisms within the carotid body itself. The purpose of this study is to determine whether or not the degree of interaction between the two respiratory stimuli of acute hypoxia and muscular exercise is altered by prior exposure to a sustained period of 8 h of hypoxia.

One complication with this study is that the level of euoxic is raised following an exposure to 8 h of hypoxia. In order to obtain an index of interaction that is unaffected by this complication, we first develop a general equation to describe the effects of stimulus interaction between hypoxia and exercise on . From this, we develop a single dimensionless constant, , that can be used to measure the strength of the stimulus interaction between acute hypoxia and exercise under conditions of constant P_ET,CO2. In essence, measures the degree to which the effect of two equipotent stimuli (exercise and hypoxia) when presented together exceeds the summed effects of the two stimuli when they are each presented on their own. The magnitudes of these two stimuli are set in relation to the basal level of . This procedure automatically compensates the value of for any effects that might arise through changes in the basal level of . We show that values for this parameter can be determined from a set of measurements of the acute ventilatory sensitivity to hypoxia under conditions of rest and exercise. This theory is then used as the basis for an experimental study to quantify the strength of the interaction before and after an 8 h exposure to hypoxia (protocol IH) and to compare it with the strength of interaction before and after an 8 h control exposure breathing room air (protocol C).

	Methods

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Theory

Development of general equation for the effect on of stimulus interaction between hypoxia and exercise.  We begin by defining a hypoxia stimulus function, x, of end-tidal partial pressure of O₂ (P_ET,O2), such that is linearly related to x. During acute isocapnic hypoxia, rises linearly in proportion to the fall of arterial oxygen saturation, as calculated at a standard partial pressure of CO₂ (Rebuck & Campbell, 1974). We therefore used a relationship that supplies arterial desaturation as a function of P_ET,O2 as x. Other studies have used hyperbolic (Lloyd & Cunningham, 1963) or exponential (Kronenberg et al. 1972) functions of P_ET,O2 as x. By analogy, we also define a work rate stimulus function, y, of the work rate (WR), such that is linearly related to y. In practice, for mild to moderate levels of exercise, is linearly related to work rate itself and so y may be treated simply as the work rate itself. Now, suppose that the sensitivity of to hypoxia is related in some general way to WR; then we may write:

(1)

In a similar manner, suppose that the sensitivity of to WR is related in some general way to hypoxia; then we may write:

(2)

From these two relations, it follows that the most general equation for the effect on of stimulus interaction between hypoxia and exercise is:

(3)

where A, B, C and are constants. Note that in the absence of stimulation by both hypoxia and exercise, = . The proof of this result is given in Appendix 1.

Expression of general equation in non-dimensional form.  Expression of the general equation for the effects of stimulus interaction in non-dimensional form is accomplished simply by dividing eqn (3) by the basal ventilation, , to yield:

(4)

This enables us to define non-dimensional stimulus functions for hypoxia, v, and WR, w, such that a doubling in the value of v or w (in the absence of the other stimulus) doubles the basal ventilation:

(5)

and

(6)

Substitution into eqn (4) of these non-dimensional stimulus functions yields:

(7)

where is a non-dimensional constant defining the strength of the stimulus interaction.

Technique for estimating .  The experimental approach to estimating adopted in this study (see subsection immediately below and Discussion) was to measure the ventilatory response to a fixed hypoxic stimulus (i.e. a fixed level of arterial desaturation) under conditions of both rest and exercise. Fitting a respiratory model to these data yielded parameter estimates for in the absence of hypoxia ( and for the data at rest and during exercise, respectively) together with parameter estimates of the ventilatory sensitivity to the hypoxic stimulus (G_p^r and G_p^e for the data at rest and during exercise, respectively). The value for may be determined directly from these parameters as follows:

(8)

The derivation of this expression is given in Appendix 2.

Experiment

Subjects.  Ten subjects (7 males and 3 females) aged between 19 and 25 years volunteered to take part in the study. All were healthy non-smokers with no history of respiratory or cardiovascular disease. The requirements of the study were explained in writing, and verbally, in such a way that the subjects remained naive to the exact purpose of the study, and to the particular protocol employed on the day. All subjects gave their written consent before taking part. The study conformed to the standards set by the Declaration of Helsinki, and ethical approval was obtained from the Central Oxford Research Ethics Committee.

Protocol: preliminary studies.  Each subject attended the laboratory on two or more separate occasions prior to undertaking the main experiments. During these short visits, the subjects were familiarized with the apparatus and some preliminary measurements were obtained. These preliminary measurements consisted of: (1) control measurements of P_ET,CO2 at rest; (2) measurement of maximal oxygen uptake capacity obtained from an incremental exercise test; (3) control measurements of P_ET,CO2 at a work rate associated with 35% of ; and (4) measurements of the partial pressures of CO₂ (P_CO2) and O₂ (P_O2) of arterialized capillary blood (P_ac,CO2 and P_ac,O2, respectively) associated with the end-tidal values to be used for the assessment of the acute ventilatory response to hypoxia (AHVR) under conditions of both rest, and exercise at 35% of .

Protocol: main studies.  The main experiments were carried out in a random order on 2 days separated by at least 1 week to ensure complete recovery from the exposure to hypoxia (Tansley et al. 1998). Female subjects were always studied during the same phase of their menstrual cycle, judged from their menstrual history. Subjects were asked to refrain from consuming any caffeinated beverages on the day of the experiment and to have eaten their breakfast at least 1 h before coming to the laboratory. Each experiment was approximately 12 h long and involved measurements of AHVR at rest and during exercise, before and after an 8 h chamber exposure.

The two chamber exposures used for each subject were: (1) isocapnic hypoxia (IH); and (2) control (C). For protocol IH, P_ET,O2 was held at 55 mmHg and P_ET,CO2 was held at the subject's normal air-breathing value at rest. For protocol C, the subject breathed room air throughout the exposure. The subjects were given a light lunch halfway through each exposure and were allowed to drink caffeine-free beverages throughout. Subjects were allowed to leave the chamber briefly when they needed to use the toilet.

The determinations of AHVR at rest and during exercise were undertaken before and after each exposure, with the measurements after the exposure starting 30 min after the end of the 8 h period. The determination of AHVR at rest lasted 17 min and the determination during exercise lasted 20 min. There was a rest period of 10 min between the two measurements. During these measurements, P_ET,CO2 was held constant at 1–2 mmHg above the subject's normal air-breathing value at rest or during exercise, as appropriate. This approach was adopted in order to maintain the same arterial P_CO2 throughout the measurements, since arterial P_CO2 remains very constant between rest and mild to moderate exercise in humans (Wasserman et al. 1967; Robbins et al. 1990). After a lead-in period of either 5 min (rest) or 8 min (exercise) with P_ET,O2 held at 100 mmHg, P_ET,O2 was cycled between a euoxic value of 100 mmHg and a hypoxic value of either 50 mmHg (rest) or 58 mmHg (exercise) in a series of six square waves, each with a period of 120 s. (The 8 mmHg difference in P_ET,O2 between rest and exercise was the difference that was predicted to provide matching values for arterial P_O2.) This protocol for assessing AHVR has been previously validated against other procedures (Zhang & Robbins, 2000). A check on the accuracy of this prediction is provided by the arterialized capillary samples taken during the preliminary measurements.

Experimental technique: preliminary measurements.  Preliminary measurements were made outside the chamber used for the 8 h exposures. Resting P_ET,CO2 was determined using a single nasal catheter connected to a mass spectrometer. Breath-by-breath values for P_ET,CO2 were averaged over a 10 min period.

For the incremental exercise test, the subject was seated on a cycle ergometer and breathed room air through the apparatus described below. After a 4 min period of unloaded pedalling, the work rate was increased by 20–25 W every 60 s until exhaustion. Maximum was calculated, and the work rate at 35% of maximum was taken as a subject-specific value for a mild to moderate level of work that was to be used for the remainder of the study.

End-tidal P_CO2 during steady-state exercise was measured by sampling gas from the dead space of the apparatus, close to the mouth, via a catheter connected to a mass spectrometer. A 10 min period of exercise was undertaken, and breath-by-breath values for P_ET,CO2 were averaged over the final 4 min of this period.

Arterialized capillary blood was obtained from the earlobe to check that blood gas values and pH were closely matched between the two conditions of rest and exercise at the chosen hypoxic values of P_ET,O2. Arterialization was achieved by application of capsaicin cream (0.075% w/w) to the earlobe for at least 25 min prior to taking the sample, and if necessary, by additional warming of the earlobe. The earlobe was punctured using a spring-loaded lancet, and blood was collected into a 70 µl heparinized glass capillary tube for blood gas analysis. Samples were analysed for P_O2 (mmHg), P_CO2 (mmHg) and saturation (S_O2, %) using a blood gas analyser. Samples were repeated if the duration of blood collection exceeded 20 s. This technique for sampling arterialized capillary blood has been shown to yield estimates for the end-tidal to arterial gradients for both P_CO2 and P_O2 that are in good agreement with those obtained from arterial blood (Crosby & Robbins, 2003).

Experimental technique: 8 h exposures.  The 8 h exposures were carried out using a purpose-built chamber in which an individual subject could be seated comfortably and move around if they wished to do so. The composition of gas within the chamber could be altered, and this removed the need for the subject to breathe through either a mouthpiece or facemask. Respired gas was sampled (80 ml min^–1) via a fine catheter held in place at the opening of the nostril with a nasal O₂-therapy mask, and analysed for P_O2 and P_CO2 by a mass spectrometer. The subject wore a pulse oximeter on a finger to monitor arterial S_O2. The values for P_O2, P_CO2 and S_O2 were sampled by a computer every 20 ms. Inspired and end-tidal values for P_O2 and P_CO2 were identified by the computer from the P_CO2 profile and, together with arterial S_O2, were recorded for each breath.

For protocol IH, the composition of inspired gas required to produce the desired end-tidal values was estimated and set manually before the subject entered the chamber. During the experiment, inspired gas composition was altered by the computer every 5 min, or at manually overridden intervals, to minimize the error between the actual and desired end-tidal values. This system has previously been described in more detail (Howard et al. 1995).

Measurements of AHVR.  Measurements of AHVR were made using a dynamic end-tidal forcing system. The subject was seated in an upright position, in a chair for the resting protocol and on a cycle ergometer for the exercise protocol, and breathed through a mouthpiece with the nose occluded by a clip. Respiratory volumes were measured using a turbine volume-measuring device fixed in series with the mouthpiece, and flows and timing information were recorded using a pneumotachograph. This apparatus had a total dead space of 180 ml. Gas was sampled (80 ml min^–1) continuously from this dead space, close to the mouth, and analysed for P_O2 and P_CO2 by a mass spectrometer. Arterial S_O2 was monitored continuously by a finger pulse oximeter (as a safety device). All the data were sampled every 20 ms by a data-acquisition computer, and P_ET,O2, P_ET,CO2, inspiratory and expiratory volumes and durations were recorded for each breath.

Before the experiment, a ‘forcing function’ containing the predicted inspired gas values needed to achieve the desired P_ET,O2 and P_ET,CO2 was entered into a second (controlling) computer. During the experiment, measured P_ET,O2 and P_ET,CO2 values were passed breath by breath from the data-acquisition computer to the controlling computer. These measured end-tidal values were compared with the desired values, and a new inspired gas mixture was calculated using an integral-proportional feedback scheme. The controlling computer adjusted the inspired gas mixture via a fast gas-mixing system. This system has previously been described in more detail (Robbins et al. 1982; Howson et al. 1987).

Data analysis

To obtain numerical values for the parameters required to estimate , a single-compartment model of the peripheral chemoreflex was fitted to the data from the six square waves of each AHVR measurement under conditions of both rest and exercise. The particular model chosen was model 3 of Clement & Robbins (1993), and is given by:

(9)

(10)

where is the component of that is not attributable to hypoxia, is the component of ventilation that is attributable to hypoxia, G_p is the peripheral chemoreflex sensitivity to hypoxia, S_O2 is the saturation (estimated using an equation relating saturation to P_O2; Severinghaus, 1979), is the time constant and Td is a pure delay. The values obtained for parameter G_p of this model were corrected by using the mean values for arterialized capillary P_O2 associated with the hypoxic values for P_ET,O2 to allow for the different relationship between P_ET,O2 and arterial P_O2 during exercise, compared with rest. The model containing these parameters was fitted to the data together with a stochastic model of the correlation between breaths (Liang et al. 1996). Different starting points were employed to check the reliability of convergence. Values for the ventilatory sensitivity to exercise (G_ex; under both non-hypoxic and hypoxic conditions) could be calculated directly from the differences in between exercise and rest given by the model divided by the measured work rate undertaken.

Differences between the parameters from the model were assessed statistically using ANOVA, with subject as a random factor and protocol (IH, C), activity (rest, exercise) and time (before, after) as fixed factors. The particular null hypothesis to be tested was that the degree of interaction between hypoxia and exercise in terms of their effects on would not be altered following a sustained exposure to hypoxia. This was assessed statistically using ANOVA on the values obtained for , with subject as a random factor, and protocol (IH, C) and time (before, after) as fixed factors. In this analysis, the interactive term has one degree of freedom and the error term has nine degrees of freedom. The test hypothesis would be rejected if the interactive term between protocol and time were significant. All statistical analysis was performed using the SPSS statistical software package. Statistical significance was taken as P < 0.05.

	Results

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Subjects

All 10 subjects completed the study. During the chamber exposures, subjects normally spent their time reading or watching television. The subjects were generally comfortable, although some complained of a mild headache during the exposure involving hypoxia.

Preliminary measurements

Average values for , P_ET,CO2 at rest, P_ET,CO2 at 35% of , and the change in P_ET,CO2 from rest to exercise are given in Table 1. Also shown are the arterialized capillary blood gas data associated with the values for P_ET,CO2 and P_ET,O2 employed for the euoxic and hypoxic conditions of the measurement of AHVR during both rest and exercise. Under both euoxic and hypoxic conditions, the differences in arterialized capillary values between rest and exercise were small. This suggests both that the hypoxic stimulus used to assess AHVR should have been well matched between rest and exercise and that the arterial P_CO2 at which AHVR was assessed should have been very similar for both rest and exercise.

Figure 2 illustrates the end-tidal gases recorded during both chamber exposures, averaged every 5 min, for each of the 10 subjects. The upper plots illustrate the deviation of P_ET,CO2 from the pre-exposure control values. For protocol IH, these deviations represent the error in the control of P_ET,CO2. Apart from one subject, whose P_ET,CO2 rose several millimetres of mercury above the pre-exposure control value in the afternoon, these deviations are small, indicating good control over P_ET,CO2. The lower plots illustrate P_ET,O2 during the course of the chamber exposures. Again, during protocol IH, the control was good.

View larger version (28K): [in this window] [in a new window]   Figure 2.  End-tidal values during chamber exposures Top, deviation of end-tidal PCO2 (PET,CO2) from pre-exposure control value (PET,CO2); middle, PET,CO2; and bottom, end-tidal PO2 (PET,O2) averaged every 5 min from data collected breath by breath for all 10 subjects. Left, isocapnic hypoxia protocol; right, control protocol.

Figure 3 illustrates the measurement of AHVR in one subject (subject 1183). Control over both P_ET,CO2 and P_ET,O2 was good. In the case of P_ET,CO2, there was little variation from the target value, despite large variations in . In the case of P_ET,O2, the stimulus can be seen to fall and rise sharply at the onset and offset, respectively, of each hypoxic step. Pulmonary ventilation (lower plot) closely follows the hypoxic stimulus, rising rapidly at the onset of hypoxia and returning rapidly to near baseline levels at the relief of hypoxia. These findings were typical of an AHVR measurement at rest. For measurements of AHVR during exercise, control of P_ET,CO2 tended to be slightly less tight.

View larger version (17K): [in this window] [in a new window]   Figure 3.  Breath-by-breath end-tidal gas control and ventilatory responsesduring a single measurement of the acute hypoxic ventilatory response for one subject (subject 1183; rest; post exposure to isocapnic hypoxia) Top, PET,CO2; middle, PET,O2; and bottom, ventilation.

Figure 4 illustrates a complete set of ventilatory responses from measurements of AHVR for one subject (subject 1183). Responses were determined at rest and during exercise before and after each 8 h exposure. In each case, the fit of the respiratory model to the data is also illustrated. The following points may be observed: (1) baseline and the ventilatory sensitivity to hypoxia are higher during exercise (lower panels) than at rest (upper panels); (2) the responses before the 8 h exposures are broadly similar between protocol IH and protocol C for both rest and exercise; (3) for protocol C, the responses following the 8 h exposure (closed symbols) are similar to those before the exposure (open symbols); and (4) for protocol IH, the responses appear to be augmented following the 8 h exposure compared with those before the exposure. The statistical significance of these general observations was explored through the associated changes in parameter estimates for the respiratory model, as described below.

View larger version (28K): [in this window] [in a new window]   Figure 4.  Breath-by-breath ventilatory responses to square-wave hypoxia for each protocol for one subject (subject 1183) Left, isocapnic hypoxia protocol; right, control protocol. Upper panels, ventilatory responses at rest; lower panels, ventilatory responses during exercise at 35% of maximal oxygen uptake capacity. Open symbols, measurements before 8 h exposures; closed symbols, measurements after 8-h exposures. Continuous lines indicate the fit of the deterministic component of the model to the data (the stochastic component is excluded).

Ventilatory sensitivity to hypoxia.  Numerical values for the sensitivity to hypoxia were provided by the values for G_p obtained from fitting the respiratory model to the ventilatory data from each set of responses. Table 2 gives values for G_p at rest and during exercise for each subject, before and after both 8 h exposures. The following points may be observed: (1) for the pre-exposure values for G_p, there were no significant differences between the two protocols, either for the values for G_p at rest or for the values for G_p during exercise; (2) values for G_p were significantly greater for exercise than for rest (P < 0.001, ANOVA, pre-exposure values); (3) the 8 h control exposure had no significant effect on G_p, either at rest or during exercise; and (4) the 8 h exposure to hypoxia significantly increased G_p at rest (P < 0.001), but any increase during exercise did not reach significance.

View this table: [in this window] [in a new window]   Table 3.  Values for calculated residual ventilation in the absence of hypoxia, , at rest and during exercise, before and after each protocol, for each subject

Ventilatory sensitivity to exercise.  The ventilatory sensitivity to exercise, G_ex, under both euoxic and hypoxic conditions may be calculated directly from the parameter estimates obtained from the respiratory model together with the level of exercise undertaken by each individual. The results are shown in Table 4. The following points may be observed: (1) for the pre-exposure values for G_ex, there were no significant differences between the two protocols; (2) pre-exposure values for G_ex were significantly greater in hypoxia than in the absence of hypoxia (P < 0.005); (3) the 8 h control exposure had no significant effect on G_ex, either in the presence or the absence of hypoxia; and (4) the 8 h exposure to hypoxia significantly increased G_ex (P < 0.05) in the absence of hypoxia, but not in the presence of hypoxia.

View this table: [in this window] [in a new window]   Table 5.  Values of the non-dimensional parameter, , for the interaction present between acute hypoxia and exercise, before and after each protocol

View larger version (29K): [in this window] [in a new window]   Figure 5.  Ventilatory responses to acute hypoxia Left, isocapnic hypoxia protocol; right, control protocol. Upper panels, responses before 8 h exposures; lower panels responses after 8 h exposures. Open circles and dashed lines represent responses at rest; filled circles and continuous lines represent responses during exercise. The dotted lines in the lower panels represent the responses before the 8 h exposures (i.e. the same as in upper panels) and are shown again to highlight the effect of sustained hypoxia on the ventilatory responses to acute hypoxia. Data points are average values for 10 subjects; the numbers on the plots indicate the slopes of the lines; error bars show 2S.E.M.

	Discussion

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Quantification of interaction through

The development of a non-dimensional measure of interaction is potentially useful in quantifying stimulus interaction in other areas. Intuitively, if you choose the magnitudes of the two stimuli so that when each is presented on its own it has the same effect on the response variable, then may be viewed as the degree to which the effect on the response variable exceeds that of the individual summed effects when the stimuli are presented together, this quantity being expressed as a fraction of the effect of either stimulus on its own. The basal value of the response variable (i.e. the value in the absence of stimulation) supplies the actual magnitude of the two stimuli for which is specified.

An advantage of using to assess interaction is that the two stimuli are treated in equal, or symmetric, manner. This is in contrast to a more commonly used asymmetric approach, where an investigator would typically choose to study either the effect of exercise on the hypoxia response or, alternatively, the effect of hypoxia on the exercise response. A particular disadvantage of the asymmetric approach is that the results are essentially incomplete, in the sense that it is not possible to determine, for example, the effect of exercise on the sensitivity of the hypoxia response from a study of the effect of hypoxia on the sensitivity of the exercise response, and vice versa. In contrast, provides a complete description of the interaction present within a single constant. A further advantage of is its dimensionless nature. This makes it possible to compare interactions across many different scenarios.

The theory developed in this study depends upon eqn (3) being a fair model of the interaction that exists between the two stimuli. Clearly, it is possible to write equations that have a more complex interaction term, for example involving non-linear functions of the stimuli in the interactive term. However, we have shown that any such equation would not be consistent with the starting conditions of eqns (1) and (2). These starting conditions essentially state that it is possible to linearize one stimulus with the same function at different levels of the other stimulus. So, for example, if plotting against desaturation gives a linear relationship at one work rate, then it will also give a linear relationship at a different work rate. Alternatively, if the relationship between and work rate is linear at one level of P_ET,O2, then it will be linear at another level of P_ET,O2. Although it is inevitable that there will be ranges beyond which this will not hold, it nevertheless would seem a fair approximation in the case of mild to moderate exercise with mild to moderate hypoxia. The important point is that, when eqns (1) and (2) hold, eqn (3) is the most general representation possible for any interaction that might be present.

In the protocol used to determine , we chose to have separate periods of rest and exercise, and to impose on each of these variations in P_O2. The data could then be described by using a respiratory model of the response to hypoxia against the backgrounds of both rest and exercise. In theory, there is no reason why a protocol could not have been adopted where there were separate periods of euoxia and hypoxia, and variations between rest and exercise were imposed upon each of these backgrounds. The data could then be described by a model of the ventilatory response to exercise against backgrounds of euoxia and hypoxia. In practice, we chose the former approach over the latter because the hypoxia stimulation protocol of this approach avoids the development of any significant degree of hypoxic ventilatory depression (Zhang & Robbins, 2000).

Comparisons with other studies quantifying the interactive effects between hypoxia and exercise on

We are unaware of any studies that have attempted to examine the interaction between exercise and hypoxia through the type of theoretical framework developed in the present study. Most studies have concentrated on the change in ventilatory sensitivity to hypoxia that is induced by light exercise. In itself, this is an incomplete characterization of the strength of interaction because it is not possible to calculate values for from these data alone. Furthermore, values obtained for the increment in G_p with exercise have differed between studies, with percentage increases of 59% (Pandit & Robbins, 1997), 68% (Pandit & Robbins, 1991), 146% (Regensteiner et al. 1988) and 245% (Martin et al. 1978) reported for work rates broadly similar to those used here. The increase of 88% reported in the present study is well within this range.

Comparisons with other studies examining the effects of sustained hypoxia on ventilatory sensitivities to hypoxia

Both the observed starting values for G_p at rest and the increment in this parameter after an 8 h exposure to isocapnic hypoxia were consistent with values reported from previous studies undertaken in our laboratory (Howard & Robbins, 1995; Ren et al. 2001). However, other studies involving acclimatization to altitude have reported much slower increases in the acute ventilatory sensitivity to hypoxia, with significant changes not occurring until after 3–4 days at altitude (Sato et al. 1992, 1994). The principal difference between these studies and ours was not the nature of the hypoxic exposure, but rather the background P_ET,CO2 against which the assessments of the acute ventilatory response to hypoxia were made. In our studies (Howard & Robbins, 1995; Ren et al. 2001), the level of P_ET,CO2 for these measurements was the same before and after the sustained hypoxic exposure. In the studies of Sato et al. (1992, 1994),P_ET,CO2 was adjusted downwards at altitude so that the euoxic level of was always the same before each assessment of the acute ventilatory response to hypoxia. The problem with their approach is illustrated in Table 1 of Sato et al. (1992). All their measurements of the acute ventilatory response to hypoxia conducted at altitude were undertaken against a much more alkaline arterial pH than the control measurements at sea level. Since it is well recognized that there is marked stimulus interaction between CO₂ (acting through pH; Hornbein & Roos, 1963; Donnelly et al. 1982) and hypoxia at the carotid body (Hornbein et al. 1961; Lahiri & DeLaney, 1975), their observation of an unchanged acute hypoxic ventilatory response during the first few days at altitude cannot be used to conclude that peripheral chemoreceptor function is similarly unchanged. Any related concerns about the need to match central chemoreflex drive between different measurements of the acute ventilatory sensitivity to hypoxia are far less important, because most evidence suggests that very little interaction occurs between the central and peripheral chemoreflexes (van Beek et al. 1983; Clement et al. 1995; St Croix et al. 1996).

Data pertaining to the effects of prior sustained hypoxia on the ventilatory sensitivity to hypoxia under exercising conditions appear to be limited to studies of acclimatization to high altitude. Where these studies have reported values for ventilation during exercise under both hypoxic (ambient air-breathing) and hyperoxic (air with added O₂) conditions, it is possible to calculate values for the ventilatory sensitivity to hypoxia under conditions of exercise. The data of Pugh et al. (1964) yield values for the ventilatory sensitivity to hypoxia of 0.68 l min^–1 %^–1 at 50 W and 1.00 l min^–1 %^–1 at 100 W, both at 5800 m. The data of Cerretelli (1976) yield a value for the ventilatory sensitivity to hypoxia of 1.94 l min^–1 %^–1 during 80 W exercise at 5350 m. The value of 1.81 l min^–1 %^–1 from the present study appears remarkably similar to that of Cerretelli (1976), but it should be realized that the experimental setting is very different. Not only does the overall duration of sustained exposure hypoxia differ enormously, but also the ventilatory sensitivity to hypoxia was determined under poikilocapnic conditions in the case of Cerretelli's study, whereas in the present study it was determined under isocapnic conditions.

Comparison with other studies on the mechanisms of interaction between exercise and acute hypoxia

The results from the present study demonstrate a functional interaction between the processes that mediate exercise–hypoxia stimulus interaction and the processes by which sustained hypoxia increases ventilatory sensitivity to acute hypoxia. However, our study does not provide any other information in relation to the particular physiological processes that might be involved within the ‘black box’ of interaction. Thus the interaction between exercise and hypoxia could be an entirely neural process, or a process involving alterations in humoral stimuli during exercise affecting oxygen sensing, or indeed, any combination of such processes.

There are relatively few studies of the mechanism(s) underlying the effects of exercise on the acute ventilatory sensitivity to hypoxia. However, Pandit & Robbins (1994) demonstrated that electrically induced leg exercise in humans increased the acute ventilatory sensitivity to hypoxia, and therefore that ‘central command’ was not necessary for this effect to occur. This observation was extended to electrically induced leg exercise in paraplegic subjects, indicating that afferents from the exercising muscle were also not necessary for this response (Pandit et al. 1994). These observations suggest that the increase in the acute ventilatory sensitivity to hypoxia may be mediated by humoral factor(s) released from the exercising muscles, which could then act via an effect on the carotid body.

A possible candidate for such a humoral mediator is K⁺. In anaesthetized cats, K⁺ has been shown to stimulate , an effect which is enhanced by hypoxia (Band & Linton, 1988; Burger et al. 1988). In humans, K⁺ is released from the muscles during exercise (Paterson et al. 1989), but the resulting increase in arterial K⁺ concentration does not appear to be quantitatively sufficient to explain the increase in the ventilatory sensitivity to hypoxia in its entirety (Qayyum et al. 1994). Overall, therefore, an adequate physiological mechanism has yet to be proposed that can explain the very marked effect of exercise on the ventilatory sensitivity to hypoxia.

	Appendix 1

Top Abstract Introduction Glossary of physiological... Methods Results Discussion Appendix 1 Appendix 2 References

 
Theorem

If

(11)

and

(12)

then

(13)

where A, B, C and are constants.

Proof

Integrating eqn (A1) with respect to x yields:

(14)

where m(y) is an arbitrary function of y. Differentiating eqn (A4) with respect to y yields:

(15)

Combining eqns (A2) and (A5), and eliminating /y yields the identity:

(16)

which implies f'(y) and m'(y) must be constants (K₁ and K₂, respectively), since g(x) is only a function of x. Integrating f'(y) and m'(y) yields the following two equations:

(17)

and

(18)

where K₃ and K₄ are constants of integration.

Substituting for f(y) from eqn (A7) and for m(y) from eqn (A8) into eqn (A4) yields the following:

(19)

This completes the proof because, by inspection, the form of eqns (A9) and (A3) is the same.

	Appendix 2

Top Abstract Introduction Glossary of physiological... Methods Results Discussion Appendix 1 Appendix 2 References

 
This appendix derives an expression for a non-dimensional measure of interaction, , in terms of parameters that can be experimentally determined. In non-dimensional terms, ventilation is given by the following equation:

(20)

The experimentally determined parameters are ^r, ventilation at rest in the absence of hypoxia; , ventilation during exercise in the absence of hypoxia; G_p^r, ventilatory sensitivity to hypoxia under conditions of rest; and G_p^e, ventilatory sensitivity to hypoxia under conditions of exercise.

The non-dimensional magnitude for the hypoxic stimulus is given by:

(21)

where Hyp is the magnitude of the dimensionless hypoxic stimulus.

The non-dimensional magnitude for the exercise stimulus may be written:

(22)

The non-dimensional ventilation when stimulated by both hypoxia and exercise may be written:

(23)

Substituting these expressions into eqn (A10) gives:

(24)

which, after rearranging and tidying, yields:

(25)

	References

Top Abstract Introduction Glossary of physiological... Methods Results Discussion Appendix 1 Appendix 2 References

 
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