Ziyad Samara

Mathieu Raux

Marie-Noëlle Fiamma

Alexandre Gharbi

Stewart B Gottfried

Chi-Sang Poon

Thomas Similowski

Dr Christian Straus
email: christian.straus@psl.aphp.fr.

Effects of inspiratory loading on the chaotic dynamics of ventilatory flow in humans

Keywords: chaos, respiratory control, inspiratory loading

Human ventilation at rest exhibits complexity and chaos. The aim of this study was to determine whether suprapontine interferences with the automatic breathing control could contribute to ventilatory chaos. We conducted a post-hoc analysis of a previous study performed in awake volunteers exhibiting cortical pre-motor potentials during inspiratory loading. In 8 subjects, flow was recorded at rest, while breathing against inspiratory threshold loads (median 21.5 cmH 2 O) and resistive loads (50 cmH 2 O/L/s) loads, and while inhaling 7%CO 2 -93%O 2 . Chaos was identified through noise titration (noise limit, NL) and the sensitivity to initial conditions was assessed through the largest Lyapunov exponent (LLE). Breath-by-breath variability was evaluated using the coefficient of variation of several ventilatory variables. Chaos was consistently present in ventilatory flow recordings, but mechanical loading did not alter NL, LLE, or variability. In contrast, CO 2 altered chaos and reduced variability. In conclusion, inspiratory loading -and any resultant respiratoryrelated cortical activity-were not associated with changes in ventilatory chaos in this study, arguing against suprapontine contributions to ventilatory complexity.

Introduction

Lung ventilation depends on the alternation between inspiratory and expiratory gas flow. In humans, this process seems periodic. In fact, it is not. Rather, the dynamics of ventilatory flow exhibit complexity and have the mathematical features of chaos [START_REF] Wysocki | Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration[END_REF]Fiamma et al., 2007a;Fiamma et al., 2007b). This behaviour is similar to the behaviour of other human physiological processes, such as the heart rhythm [START_REF] Poon | Decrease of cardiac chaos in congestive heart failure[END_REF] and the electroencephalographic activity of the brain [START_REF] Iasemidis | Long-term prospective on-line real-time seizure prediction[END_REF]. In mathematical terms, this indicates that the trajectory of ventilatory flow is bounded and depends on deterministic processes, but is unpredictable in the long term and sensitive to the initial conditions.

Chaos is altered in biological systems in response to physiological stimulation or disease. For example, cardiac chaos decreases during congestive heart failure [START_REF] Poon | Decrease of cardiac chaos in congestive heart failure[END_REF]. Changes in the chaotic behaviour of electroencephalographic activity occur prior to the onset of overt clinical seizures [START_REF] Iasemidis | Long-term prospective on-line real-time seizure prediction[END_REF]. Stimulating breathing with carbon dioxide increases the sensitivity of ventilatory flow to initial conditions as well as its unpredictability (Fiamma et al., 2007b). In patients with respiratory failure, ventilatory chaos increases when coordination between the patient's breathing efforts and the respiratory assist device improves [START_REF] Mangin | Source of human ventilatory chaos: Lessons from switching controlled mechanical ventilation to inspiratory pressure support in critically ill patients[END_REF]. Characterising ventilatory chaos is thus of physiological interest as well as clinical importance.

Nevertheless, the physiological basis of the chaotic dynamics of ventilatory flow is not well understood. In addition to the intrinsic properties of the central respiratory pattern generators within the brainstem, the presence and/or intensity of ventilatory chaos may depend on one or more additional factors. These would include: the mechanical properties of the respiratory system, afferent information from mechanoreceptors, chemoreceptor reflexes, and suprapontine or behavioural influences. Several reports point to the automatic ventilatory command -produced by the activity of brainstem rhythmogenetic neurones-, possibly modulated by vagal afferents, as the main source of ventilatory chaos in mammals [START_REF] Sammon | Vagal afferent activity increases dynamical dimension of respiration in rats[END_REF][START_REF] Negro | Periodicity, mixed-mode oscillations, and quasiperiodicity in a rhythm-generating neural network[END_REF]Fiamma et al., 2007b). By failing to detect ventilatory chaos in patients undergoing passive mechanical ventilation, Mangin et al. [START_REF] Mangin | Source of human ventilatory chaos: Lessons from switching controlled mechanical ventilation to inspiratory pressure support in critically ill patients[END_REF] provided a strong argument against the contribution of the mechanical properties of the respiratory system. The information available on the potential effects on ventilatory chaos of suprapontine volitional or behavioural factors (which are particularly abundant in humans) is somewhat contradictory and difficult to reconcile. Voluntary control of breathing abolished ventilatory chaos [START_REF] Fortrat | Respiratory influences on non-linear dynamics of heart rate variability in humans[END_REF]. Such a result suggests that cortical influences would tend to decrease chaos. The decrease in ventilatory chaos during slow wave sleep (as compared to wakefulness, [START_REF] Burioka | Non-linear dynamics applied to human respiratory movement during sleep[END_REF] and its increase in patients with panic-anxiety disorders [START_REF] Yeragani | Nonlinear measures of respiration: respiratory irregularity and increased chaos of respiration in patients with panic disorder[END_REF] suggest the opposite.

It has recently been shown that in awake normal humans the pre-motor cerebral cortex is activated by the application of inspiratory resistive or threshold loads [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF]. The presence of cortical pre-motor activity during loaded breathing, that is neither voluntary nor necessarily conscious, provides an opportunity to examine the influence of suprapontine behavioural factors on ventilation during wakefulness. The objective of this study was therefore to assess the effect of inspiratory resistive and threshold loading on the chaotic dynamics of breathing. We hypothesized that any changes that occurred compared to unloaded breathing would reflect the behavioural cortical pre-motor influence on ventilatory control. To test this hypothesis, we analyzed the ventilatory flow dynamics of the subjects who participated in the previously published study of [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF] mentioned earlier.

Methods

Subjects

This study was carried out on the ventilatory flow signals recorded previously by [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF] during their initial description of respiratory pre-motor potentials associated with inspiratory loading. The experimental protocol received appropriate legal and ethical clearance (Comité Consultatif de Protection des Personnes se prêtant à des Recherches Biomédicales, Pitié-Salpêtrière, Paris, France) and the participants gave written informed consent. The methods have been previously described in detail [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF]. Briefly, ten subjects participated in the study (age 19-34 years, three men, body mass index 21.5 ± 2.2 kgm 2 ). They received detailed information about the methods used but were naive concerning the purpose of the study and had not previously participated in respiratory physiology experiments. All were healthy with no prior history of respiratory or neurological disease, other significant medical illness, or medication use.

Equipment and procedures

Subjects sat in a comfortable chair with full support of the head, neck and back. For the purpose of recording pre-motor potentials as previously reported, subcutaneous needle electrodes were inserted into the scalp and surface electrodes were attached to the earlobes (see [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF]. Periodically, subjects were asked to perform stereotyped hand movements (finger snapping). They watched a movie -the same movie for all subjects, that they all had already seen-on a computer monitor during the whole experiment, while wearing headphones to exclude auditory cues and extraneous noise.

The experimental protocol included two sets of measurements. In the first one, the subjects wore a nose clip and breathed through a mouthpiece attached to a low dead space linear pneumotachometer (3700A series, Hans Rudolph, Kansas City, MO, USA, dead space 14 ml, flow resistance 0.02 to 0.04 cmH 2 O.l.s -1 ) connected to a differential pressure transducer (DP-45-18; ± 2 cm H 2 O, Validyne, Northridge, CA, USA). The flow signal was digitized at 2 kHz (Chart v5.2, ADInstruments, Sydney, Australia) and stored on a personal computer for off-line analysis. Inspiration was loaded by attaching either a 50 cm H 2 O.l -1 .s -1 linear resistor or a threshold loading device (Spring-to-Stretch ® ,Threshold Inspiratory Muscle Trainer, Model #730, Health Scan Products, Cedar Grove, NJ, USA) to the inspiratory port of a medium two-way non-rebreathing valve (2600 series, Hans Rudolph, Kansas City, MO, USA) placed in series with the pneumotachometer. The median value of the threshold load was 21.5 cmH 2 O (interquartile range, 19-25). End-tidal CO 2 was measured from a side port of the mouthpiece using an infrared CO 2 gas analyser (IR 1505, Servomex, Plaine Saint Denis, France).

In the second set of measurements, a low resistance pneumotachometer linear over the experimental range of flow (MLT 1000 l, ADInstruments, Sydney, Australia; dead space 350 ml, flow resistance 0.002 cmH 2 O.1 -1 .s -1 ) replaced the low dead space pneumotachometer. It was connected in series to a large two-way non-rebreathing valve (2700 series; Hans Rudolph, Kansas City, MO, USA). The inspiratory port was used for the breathing of a gas mixture of 7% CO 2 and 93% O 2 .

The two sets of measurements were performed in random order. One set consisted of: 1) a control period of quiet breathing, 2) inspiratory threshold loading, 3) a 15 min rest period following disconnection from the respiratory apparatus, and 4) inspiratory resistive loading. The other set of measurements consisted of: 1) an additional control period of quiet room air breathing, 2) breathing a gas mixture of 7% CO 2 and 93% O 2 , and 3) a 15 min rest period following disconnection from the respiratory apparatus. In each condition, 5-10 min were allowed for stabilization of the respiratory pattern before recording. Of note, the subjects did not receive any instruction regarding their ventilatory pattern.

Only unfragmented continuous recordings of the flow signal were retained for analysis. The duration was 6-10 minutes for the assessment of the effect of mechanical loading and 4-7 minutes for CO 2 stimulated breathing.

Data analysis

2.3.1 Breath-by-breath variability-A specific routine developed with Matlab ™ , V.7.0.1 R14 (MathWorks Inc, Natick, MA, USA) permitted the calculation for each ventilatory cycle of tidal volume (V T ), total respiratory cycle time (T T ), inspiratory time (T I ), expiratory time (T E ), mean inspiratory flow (V T /T I ), inspiratory duty cycle (T I /T T ), and minute ventilation (V ′ I ). The breath-by-breath variability was expressed in terms of the coefficient of variation (standard deviation/mean) for each of these parameters.

Non-linear analysis and assessment of chaos-

The non-linear analysis of ventilatory flow was performed as previously described in humans by our group [START_REF] Wysocki | Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration[END_REF]Fiamma et al., 2007a;Fiamma et al., 2007b;[START_REF] Mangin | Source of human ventilatory chaos: Lessons from switching controlled mechanical ventilation to inspiratory pressure support in critically ill patients[END_REF]. A detailed description of the methods is provided in [START_REF] Wysocki | Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration[END_REF].

Detection of chaos:

For each recording, the frequency content of the flow signal was described using a 1024 point fast Fourier transform function (Hamming window, no overlap, zero values removed). The digitized files were then subsampled at 5 Hz (Dataplore ™ , Datan, Teltow, Germany), a frequency always greater than the Nyquist frequency and previously shown to yield the best results for the detection of chaos in ventilatory flow using the noise titration technique [START_REF] Wysocki | Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration[END_REF]. We used the latter because of its robustness and specificity to detect chaos in short and noisy time series [START_REF] Poon | Titration of chaos with added noise[END_REF]. In brief, noise titration begins with the generation of several Volterra-Wiener-Korenberg series. They are generated with different degrees of non-linearity (d) and embedding dimensions, Kappa (K), to produce a family of linear and non-linear polynomial autoregressive models. The models are then compared and the null hypothesis (linearity) is tested against the alternate hypothesis (nonlinearity) using parametric (F-test) and non-parametric (Whitney-Mann) statistics [START_REF] Barahona | Detection of nonlinear dynamics in short, noisy time series[END_REF]. If the null hypothesis is rejected, white noise of incrementally increasing standard deviation is added to the time-series until the null hypothesis can no longer be rejected. This defines a "noise limit" (NL) which, when above 0, indicates chaos and provides an estimate of its intensity. When the noise limit is equal to 0 or when no non-linearity is detected, the presence of chaos cannot be ascertained. We performed the noise titration technique using a specific routine developed for Matlab ™ , V.6.5 R13 (MathWorks Inc, Natick, MA, USA) according to a trial-and-error process including the testing of K values of 4 to 6 and of nonlinear degrees of 3 to 5. We retained the highest value for each condition.

Sensitivity to the initial conditions:

In order to assess the sensitivity of the ventilatory flow to initial conditions (that also reflects its instability), we calculated the largest Lyapunov exponent (LLE). To this aim, we determined the Lyapunov spectrum (Dataplore ™ Software Package, Datan, Teltow, Germany) using the polynomial interpolation approach described by Briggs [START_REF] Briggs | An improved method for estimating Lyapunov exponents of chaotic time series[END_REF].

Statistical analysis

The distribution of the values obtained for each test condition was first tested for normality using the Kolmogorov-Smirnov test. Since all distributions were found to be normal, the results were expressed as the mean ± standard deviation (SD). The effects of inspiratory loading on ventilatory variability and chaos were assessed in comparison with the control situation using an analysis of variance for repeated measures, with a subject factor and the breathing condition as the between-subject factor (control, resistive loading, threshold loading). Since we did not use the same pneumotachometer (low resistance instead of low dead space) and nonrebreathing valve to assess the effects of CO 2 , we did not include this data in the same analysis of variance. Instead, ventilatory variability and chaos were assessed in comparison with the corresponding control condition using Student's paired t-test (Prism ™ 4.01, Graphpad Software, San Diego, CA, USA). Differences were considered significant when the risk P of a type I error was less than 0.05.

Results

Of the ten subjects studied by Raux et al. [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF], two were excluded from the present analysis. One was omitted because the ventilatory pattern changed dramatically for unknown reasons during threshold loading. The other was excluded because the recording of the control condition before mechanical loading was segmented into several epochs of short duration. Among the eight remaining subjects, one did not participate in the hypercapnic challenge.

Breath-by-breath variability

According to the analysis of variance, the coefficient of variation for the pattern of breathing variables measured were not altered by inspiratory threshold or resistive loading compared to the control condition (F values ranged from 1.320 to 1.936, P values varied between 0.0992 and 0.2984) (Fig. 1). Of note, end tidal PCO 2 did not change during mechanical loading [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF]. In contrast, CO 2 stimulated breathing reduced the coefficient of variation for V T (p=0.0155), T T (p=0.0480), T E (p=0.0157), T I /T T (p=0.0238), and V′ I (p=0.0444). The coefficient of variation of T I (p=0.8267) and of V T /T I (p=0.0883) did not change (Fig. 2).

Non-linear analysis of ventilatory flow

3.2.1 Noise titration (Fig. 3)-The noise limit was above zero for all test conditions in all subjects. The noise limit was 22.25 ± 7.52% during the control condition and was not altered by inspiratory threshold (23.63 ± 9.41%) or resistive loading (24.00 ± 8.09%) (F 2,7 = 0.1395, p=0.8710). During CO 2 breathing, however, the noise limit increased significantly from 26.71 ±12.66 to 47.57 ± 6.13% (p=0.0108).

3.2.2

Lyapunov exponents (Fig. 4)-In all test conditions for all subjects, at least one of the Lyapunov exponents was positive, at least one was negative, and their sum was always negative, a pattern compatible with the presence of chaos. LLE did not change with mechanical loading, amounting to 0.3026 ± 0.0694 bit/it during the control condition compared with 0.3190 ± 0.1138 bit/it and 0.3090 ± 0.1073 bit/it during threshold and resistive loading, respectively (F 2,7 = 0.05123, p=0.9502). In contrast, LLE increased during CO 2 breathing from 0.2025 ± 0.09981 bi/it to 0.3866 ± 0.11074 bit/it (p=0.0009).

Discussion

This study shows that sustained high-level inspiratory mechanical loading does not modify the chaotic dynamics of ventilatory flow in awake humans. Given the cortical activity elicited by inspiratory mechanical loading [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF], our observations suggest that modulation of the automatic drive to breathe through behavioural suprapontine pathways has little effect, if any, on ventilatory chaos.

Methodological considerations

Chaos detection-How to best identify chaos in short and noisy time series remains a matter of debate, a detailed discussion of which would be beyond the scope of this article. Rather than other methods, we used the noise titration technique since it has been previously validated in this type of experimental setting [START_REF] Poon | Titration of chaos with added noise[END_REF]. It is also in keeping with our previous work [START_REF] Wysocki | Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration[END_REF]Fiamma et al., 2007a;Fiamma et al., 2007b;[START_REF] Mangin | Source of human ventilatory chaos: Lessons from switching controlled mechanical ventilation to inspiratory pressure support in critically ill patients[END_REF], allowing for more meaningful comparison of findings amongst studies. In this view, the results observed with CO 2 in the present study are reassuring. They derive from the posthoc treatment of a ventilatory signal gathered from a purpose entirely unrelated with chaos analysis. Yet they are closely similar to those described in a completely separate set of experiments designed specifically to study chaos (Fiamma et al., 2007b). However, the values for LLE obtained during the control periods are higher than those we reported previously (see, in particular Fiamma et al., 2007b), possibly in line with differences in the experimental setting and protocol.

Worthy of emphasis, the noise titration approach has the major advantage to be robust to measurement noise because it uses the noise itself to detect (titrate) chaos. In contrast, LLE estimates obtained by traditional approaches such as the Briggs method [START_REF] Briggs | An improved method for estimating Lyapunov exponents of chaotic time series[END_REF] are highly sensitive to noise. It has been shown [START_REF] Poon | Titration of chaos with added noise[END_REF]) that the noise limit (NL) correlates with the LLE of the equivalent noise-free dynamics. In this regard, the similar behaviour of NL and LLE in our study (Fig. 3 and Fig. 4, respectively) is reassuring.

Finally, it should be noted that the noise titration is a sufficient proof of chaos when the studied system is "autonomous", namely not driven by dynamic noise [START_REF] Poon | Titration of chaos with added noise[END_REF]; see also [START_REF] Lei | The influence of noise on nonlinear time series detection based on Volterra-Wiener-Korenberg model[END_REF]. However, stochastic inputs (or "dynamic noise", as opposed to "additive noise") can lead to a positive noise limit even when the original non-linear system itself is non-chaotic. This situation is denominated "stochastic chaos" by some, in contrast to "deterministic chaos". There is currently no available technique to readily distinguish these two situations, including noise titration that will provide a NL value above zero in both cases. In the specific case of ventilation, the dynamics of the respiratory pattern depend critically on the intrinsic properties the respiratory rhythm generator [START_REF] Negro | Periodicity, mixed-mode oscillations, and quasiperiodicity in a rhythm-generating neural network[END_REF][START_REF] Rachmuth | Transistor analogs of emergent iono-neuronal dynamics[END_REF] as well as the time-dependent modulation of the pontomedullary respiratory neuronal networks by chemical and vagal afferent feedbacks [START_REF] Sammon | Vagal afferent activity increases dynamical dimension of respiration in rats[END_REF][START_REF] Young | Integration-differentiation and gating of carotid afferent traffic that shapes the respiratory pattern[END_REF]Fiamma et al., 2007a). Thus, it seems reasonable to assume that the underlying process is primarily deterministic, although it could be influenced secondarily by dynamic random noise through interaction with other physiologic (non-respiratory related) processes. However, from a physiological standpoint, it is immaterial whether the chaos present in a biological system is purely deterministic or whether it is generated by the interaction of a nonlinear system with dynamic noise. Therefore, when the noise limit does not change from a control state to a test state (as it is the case during mechanical inspiratory loading in this study), then it is reasonable to conclude that the non-linear process that contribute to the generation of the chaos has not changed, be this chaos entirely deterministic or partly stochastic. In other words, the lack of change in NL after inspiratory loading in our study indicates that inspiratory loading in itself does not interfere with the process (and dynamic noise, if any) that produces ventilatory chaos.

Breathing route-Mouth breathing, used in this study, influences the breathing pattern [START_REF] Perez | Separation of factors responsible for change in breathing pattern induced by instrumentation[END_REF]Fiamma et al., 2007a;[START_REF] Rameckers | The influence of a mouthpiece and noseclip on breathing pattern at rest is reduced at high altitude[END_REF], but it does not stamp out ventilatory chaos [START_REF] Wysocki | Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration[END_REF]Fiamma et al., 2007a). In addition, the breathing route was the same for all the experimental conditions in the present study. As a result, the influence of mouth breathing should not be an issue in the interpretation of the present results, where what matters is the comparison of sequential situations.

Study power-The lack of an effect of mechanical loading on respiratory variability and chaos could be attributed to insufficient power, because of the small size of the study population. We have no means to rule out this possibility. However, it should be emphasized that CO 2 stimulated breathing produced highly significant changes in respiratory variability (Fig. 2) and chaos (increased noise limit, increased LLE), in keeping with previous reports [START_REF] Suyama | Reduction of correlation dimension in human respiration by inhaling a mixture gas of 5% carbon dioxide and 95% oxygen[END_REF]Fiamma et al., 2007b). This indicates that if insufficient power due to the small sample size masked the true impact of inspiratory loading on chaos, this impact would have to be modest and of a far lesser magnitude than seen with CO 2 breathing.

Comparison with available data

4.2.1 Breath-by-breath variability-The effects of sustained loading on breath-by-breath variability have been evaluated using resistive (3 to 6 cmH2O/L/s) and elastic (~10 cmH2O/ L) loads [START_REF] Daubenspeck | Influence of small mechanical loads of variability of breathing pattern[END_REF][START_REF] Brack | Effect of resistive loading on variational activity of breathing[END_REF]. To the best of our knowledge, the effect of inspiratory threshold loading on respiratory pattern variability has not been previously reported. Resistive loading (~3 cmH2O/L/s) decreased the standard deviation of respiratory frequency, V′ I , V T , V T /T I and T E [START_REF] Daubenspeck | Influence of small mechanical loads of variability of breathing pattern[END_REF][START_REF] Brack | Effect of resistive loading on variational activity of breathing[END_REF] as well as the coefficient of variation of respiratory frequency, V T , T I and V′ I [START_REF] Brack | Effect of resistive loading on variational activity of breathing[END_REF]. In contrast, a larger resistive load (6 cmH2O/L/s) increased the standard deviation of V′ I , V T , T I and T E ., but did not affect the corresponding coefficients of variation [START_REF] Brack | Effect of resistive loading on variational activity of breathing[END_REF]. Elastic loading did not change ventilatory variability [START_REF] Daubenspeck | Influence of small mechanical loads of variability of breathing pattern[END_REF]. Taken together, these results suggest that small inspiratory loads can decrease ventilatory variability, whereas with larger loads it can be increased or remain unchanged. This was the case for the extremely high resistance used in our study. This was also true for threshold loading, the magnitude of which was also considerable.

Chaotic dynamics of ventilation-By virtue of the noise titration technique, our

study demonstrates that the dynamics of breathing remain chaotic during mechanical loading. This information is new. It contradicts the prediction made by Thibault et al. [START_REF] Thibault | Effects of resistive loading on breathing variability non linear analysis and modelling approaches[END_REF] from a model analysis that stated that very high resistive loads (80 cmH2O/L/s) would render breathing non-chaotic (negative LLE). Of note, [START_REF] Thibault | Effects of resistive loading on breathing variability non linear analysis and modelling approaches[END_REF] modelled and measured a decrease in LLE with increasing levels of resistive loadings (3.6, 5.8, and 8.8 cmH2O/L/s). Curiously, a secondary rise in LLE occurred at 13.1 cmH2O/L/s. Larger loads were not tested. Specific studies would be needed to determine whether the discrepancies between our approach and that of [START_REF] Thibault | Effects of resistive loading on breathing variability non linear analysis and modelling approaches[END_REF] are real, and the possible reasons for this.

Physiological significance of the results

How suprapontine factors affect ventilatory chaos has seemingly never been specifically examined, but indirect information does exist. In a study of the effects of breathing on the nonlinear dynamics of heart rate variability in humans, [START_REF] Fortrat | Respiratory influences on non-linear dynamics of heart rate variability in humans[END_REF] noted that the underlying ventilatory dynamics present during volitional breathing (which depends on activation of well-identified structures residing predominantly in the primary motor cortex, e.g. [START_REF] Colebatch | Regional cerebral blood flow during volitional breathing in man[END_REF] were not chaotic. These findings appear to indicate that volitional breathing abolishes ventilatory chaos. However, the approach used by [START_REF] Fortrat | Respiratory influences on non-linear dynamics of heart rate variability in humans[END_REF] to characterize ventilatory complexity in humans led these authors to doubt the chaotic nature of spontaneous resting breathing, which is contradictory with more extensive recent data [START_REF] Wysocki | Chaotic dynamics of resting ventilatory flow in humans assessed through noise titration[END_REF]Fiamma et al., 2007a;Fiamma et al., 2007b). Furthermore, other circumstances where suprapontine influence on ventilation may be altered have been shown to increase ventilatory complexity. For example, ventilatory complexity is less marked during slow-wave sleep [START_REF] Burioka | Relationship between correlation dimension and indices of linear analysis in both respiratory movement and electroencephalogram[END_REF][START_REF] Sako | Nonlinear behavior of human respiratory movement during different sleep stages[END_REF][START_REF] Burioka | Approximate entropy of human respiratory movement during eye-closed waking and different sleep stages[END_REF], where by definition the suprapontine influence on respiration is minimal. The corollary of this observation is that wakefulness increases complexity. Ventilatory complexity is also increased in panic-anxiety disorders [START_REF] Yeragani | Nonlinear measures of respiration: respiratory irregularity and increased chaos of respiration in patients with panic disorder[END_REF]. Pre-frontal cortical abnormalities [START_REF] Berkowitz | The human dimension: how the prefrontal cortex modulates the subcortical fear response[END_REF] have been noted in such individuals, which might be expected to alter the nature and/or extent of suprapontine control over breathing behaviour. Reliably interpreting the above results remains difficult, however, in the absence of objective documentation of suprapontine involvement, or lack thereof. The circumstances involved are themselves inherently complex, potentially impacting on the control of breathing at multiple sites and/or through varied mechanisms.

The recordings analyzed in the present study were obtained under conditions (i.e., inspiratory loading) during which respiratory-related cortical activity was unambiguously demonstrated by the presence of inspiratory pre-motor potentials [START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF]. This activity arises from a well-defined cortical structure, namely the pre-motor cortex (and likely the supplementary motor area as well, [START_REF] Ball | The role of higher-order motor areas in voluntary movement as revealed by high-resolution EEG and fMRI[END_REF][START_REF] Raux | Electroencephalographic evidence for pre-motor cortex activation during inspiratory loading in humans[END_REF]. Breathing against a sustained mechanical load induced a suprapontine response that was of a behavioural rather than volitional nature (the subjects were not asked to voluntarily modify their breathing pattern, as in the study by [START_REF] Fortrat | Respiratory influences on non-linear dynamics of heart rate variability in humans[END_REF]. The cortical activation was specific for the respiratory stimulus, rather than "global", as in the case of the influence of wakefulness or panic-anxiety disorders on ventilation. Our results demonstrate that inspiratory loading has no appreciable effect on the chaotic dynamics of ventilation. By extension, any respiratory-related activity of the cerebral cortex evoked by inspiratory loading can also be said to have no effect on the chaotic dynamics of ventilation. Of importance, inspiratory mechanical loading is often not associated with increased ventilatory drive, as assessed by the measurement of airway occlusion pressure, for instance [START_REF] Lopata | Respiratory muscle function during CO2 rebreathing with inspiratory flow-resistive loading[END_REF][START_REF] Ramonatxo | Effect of resistive loads on pattern of respiratory muscle recruitment during exercise[END_REF][START_REF] Clague | Effort sensation, chemoresponsiveness, and breathing pattern during inspiratory resistive loading[END_REF][START_REF] Locher | Inspiratory resistances facilitate the diaphragm response to transcranial stimulation in humans[END_REF].

In conclusion, the available data can be summarized as follows. Conditions that increase respiratory neural drive or responsiveness, such as hypercapnia, wakefulness (compared to sleep, [START_REF] Douglas | Hypercapnic ventilatory response in sleeping adults[END_REF], and panic-anxiety disorders -often associated with abnormal CO 2 sensitivity [START_REF] Klein | False suffocation alarms, spontaneous panics, and related conditions. An integrative hypothesis[END_REF] -also enhance the intensity of ventilatory chaos [START_REF] Sako | Nonlinear behavior of human respiratory movement during different sleep stages[END_REF][START_REF] Burioka | Non-linear dynamics applied to human respiratory movement during sleep[END_REF]Fiamma et al., 2007b). Conversely, circumstances in which respiratory neural drive is not markedly affected, such as mechanical loading [START_REF] Lopata | Respiratory muscle function during CO2 rebreathing with inspiratory flow-resistive loading[END_REF][START_REF] Ramonatxo | Effect of resistive loads on pattern of respiratory muscle recruitment during exercise[END_REF][START_REF] Clague | Effort sensation, chemoresponsiveness, and breathing pattern during inspiratory resistive loading[END_REF][START_REF] Locher | Inspiratory resistances facilitate the diaphragm response to transcranial stimulation in humans[END_REF], do not change the chaotic dynamics of ventilation even though the influence of suprapontine factors on breathing control can be demonstrated (this study). Conditions that decrease respiratory neural drive, such as sleep [START_REF] Douglas | Hypercapnic ventilatory response in sleeping adults[END_REF], also reduce the intensity of ventilatory chaos [START_REF] Sako | Nonlinear behavior of human respiratory movement during different sleep stages[END_REF][START_REF] Burioka | Non-linear dynamics applied to human respiratory movement during sleep[END_REF]. Finally, situations that totally disrupt the automatic command, like volitional breathing, abolish ventilatory chaos [START_REF] Fortrat | Respiratory influences on non-linear dynamics of heart rate variability in humans[END_REF]. Ventilatory chaos therefore seems to be a feature of the brainstem central respiratory pattern generators. Whether this is an intrinsic property or the result of afferent feedback, vagal or otherwise, remains to be determined. Mean value of coefficient of variation ± SD for tidal volume (V T ), total cycle time (T T ), inspiratory time (T I ), expiratory time (T E ), mean inspiratory flow (V T /T I ), duty cycle (T I /T T ) and minute ventilation during mechanical loading. There was no significant difference between the three conditions. Left panel: mean value ± SD of the noise limit during unloaded breathing (control), threshold loading and resistive loading. There was no significant difference between the three conditions (ANOVA, p=0.87). Right panel: mean value ± SD of the noise limit during room air breathing (control) and breathing a gas mixture of 7%CO 2 -93%O 2 (7%CO 2 ). * indicates a significant difference (t-test, p=0.0108). Left panel: mean value ± SD of the largest Lyapunov exponent (LLE) during unloaded breathing (control), threshold loading and resistive loading. There was no significant difference between the three conditions (ANOVA, p=0.9502). Right panel: mean value ± SD of the largest Lyapunov exponent during room air breathing (control) and breathing a gas mixture of 7% CO 2 -93%O 2 (7%CO 2 ). *indicates a significant difference (t-test, p=0.0009

  Figure 1.

Figure 2 .

 2 Figure 2. Mean value of coefficient of variation ± SD for tidal volume (V T ), total cycle time (T TOT ), inspiratory time (T I ), expiratory time (T E ), mean inspiratory flow (V T /T I ), duty cycle (T I /T T ) and minute ventilation during CO 2 breathing. * indicates a significant difference in comparison to the control condition.

  Figure 3.

  Figure 4.

Respir Physiol Neurobiol. Author manuscript; available in PMC 2010 January 1.

Acknowledgements

The authors are grateful to Brigitte Quenet, from the Ecole Supérieure de Physique et Chimie Industrielle, Paris, France, for her help.

This study was funded in part by a grant "Santé Environnement -Santé travail" of the French Agence Nationale pour la Recherche (ANR0003205, "Transport et transfert via le système pulmonaire humain"); it was also supported by the Association pour le Développement et l'Organisation de la Recherche en Pneumologie, Paris, France. Chi-Sang Poon was supported by U.S. National Institute of Health grants HL079503 and HL072849. Ziyad Samara was supported in part by a scholarship from the « Société de Pneumologie de Langue Française » and by a grant from the French "Ministère des Affaires Etrangères". Mathieu Raux was a Lavoisier scholar of the French "Ministère des Affaires Etrangères". Marie-Noëlle Fiamma was supported by a grant from the "Comité d'organisation de l'Assistance Respiratoire a Domicile d'Ile-de-France (C.A.R.D.I.F.)", Fontenay-aux-Roses, France.


Chrystèle Locher
email: chrystèlelocher-ch-locher@ch-meaux.fr

Mathieu Raux
email: mathieu.raux@psl.ap-hop-paris.fr

Marie-Noelle Fiamma
email: marie-noelle.fiamma@psl.aphp.fr

Capucine Morélot-Panzini

Marc Zelter
email: marc.zelter@psl.aphp.fr

Thomas Similowski
email: thomas.similowski@psl.aphp.fr

Christian Straus
email: christian.straus@psl.aphp.fr

Jean-Philippe Derenne
email: jean-philippe.derenne@psl.aphp.fr

Inspiratory resistances facilitate the diaphragm response to transcranial stimulation in humans

Background

Breathing in humans fulfils both metabolic and behavioral functions. The automatic activity of brainstem central pattern generators continuously adapts ventilation to the production of carbon dioxide by the tissues. Suprapontine descending pathways convey voluntary and emotional respiratory commands that are independent of bodily requirements. Spinal respiratory motoneurons integrate the corresponding bulbospinal and corticospinal inputs [START_REF] Aminoff | Spinal integration of segmental, cortical and breathing inputs to thoracic respiratory motoneurones[END_REF][START_REF] Sears | Spinal integration of cortical, brainstem, and segmental inputs to thoracic respiratory motoneurons[END_REF], hence a reciprocal modulation of the two types of command. In one direction, direct corticospinal projections [START_REF] Corfield | Does the motor cortical control of the diaphragm 'bypass' the brain stem respiratory centres in man?[END_REF] account for voluntary disruptions of the respiratory rhythm during voluntary respiratory maneuvers or non-respiratory uses of the respiratory system (e.g. speech). In the other direction, increases in the automatic drive to breathe facilitate the diaphragm response to transcranial magnetic stimulation (TMS). This is true during quiet tidal breathing [START_REF] Mehiri | Responses of the diaphragm to transcranial magnetic stimulation during wake and sleep in humans[END_REF], where such inspiration-related facilitation has been described during wake and sleep. This is also true during CO2-stimulated breathing [START_REF] Straus | Facilitation of the diaphragm response to transcranial magnetic stimulation by increases in human respiratory drive[END_REF], that accelerates the diaphragm response to TMS applied during both inspiration and expiration.

The ventilatory responses to chemical stimuli such as hypoxia or hypercapnia are automatic and brainstem-generated. In contrast, the ventilatory adaptations to inspiratory mechanical loading in humans are believed to involve suprapontine mechanisms (see reviews in [START_REF] Younes | Mechanisms of respiratory load compensation[END_REF][START_REF] Horn | Suprapontine control of respiration[END_REF]). This postulate is generally called on to explain why awake humans faced with mechanical loads tend not to hypoventilate, whereas hypoventilation does develop in animals and anesthetized humans under similar conditions. The precise neural origin and pathway of inspiratory load compensation are not known. It could involve reflex mechanisms increasing the automatic drive to breathe, but there are arguments against this hypothesis in the literature [START_REF] Clague | Effort sensation, chemoresponsiveness, and breathing pattern during inspiratory resistive loading[END_REF][START_REF] Lopata | Respiratory muscle function during CO2 rebreathing with inspiratory flow-resistive loading[END_REF][START_REF] Ramonatxo | Effect of resistive loads on pattern of respiratory muscle recruitment during exercise[END_REF]. It could also involve either or both of the known corticospinal pathways to the diaphragm (one from the primary motor cortex [START_REF] Gandevia | Activation of the human diaphragm from the motor cortex[END_REF][START_REF] Similowski | Facilitation-independent response of the diaphragm to cortical magnetic stimulation[END_REF], the other from premotor areas [START_REF] Macefield | The cortical drive to human respiratory muscles in the awake state assessed by premotor cerebral potentials[END_REF][START_REF] Sharshar | Demonstration of a second rapidly conducting cortico-diaphragmatic pathway in humans[END_REF]). In the latter case, resistive loading is not expected to increase the automatic drive to breathe but the response of the diaphragm to transcranial magnetic stimulation should be facilitated, because of spinal integration of the suprapontine command activated for load compensation. We designed the present study to test this hypothesis.

Results

Breathing through a 20 cmH 2 O/L/s inspiratory resistance (R20 condition) significantly reduced respiratory frequency as compared with unloaded breathing (R0 condition)(16.58 ± 1.37 cycles/min versus 12.23 ± 0.83 cycles/ min; p = 0.03). A 5 cmH 2 O/L/s inspiratory resistance (R5 condition) did not significantly affect respiratory frequency. There were slight increases in tidal volume that did not reach statistical significance; thus minute ventilation remained grossly unchanged. The end-tidal partial pressure in carbon dioxide in the expired gas ( ) was unaffected by inspiratory resistances. This was also the case for the tidal volume to inspiratory time ratio (VT/ TI), the inspiratory duty cycle or inspiratory to total time ratio (TI/TT), and one millisecond mouth occlusion pressure (Pm 0.1 )(Figure 1).

Inspiratory resistive loading did not influence the esophageal pressure (Pes), gastric pressure (Pga) and transdiaphragmatic pressure (Pdi) to phenic nerve stimulation (cervical magnetic stimulation, CMS) during expiration or inspiration (Table 1), nor did it influence the corresponding latencies and amplitudes (Figure 2).

The Pes, Pga and Pdi responses to transcranial magnetic stimulation (TMS)(Figure 3) were also unaffected by inspiratory resistive loading, both during inspiration and expiration (Table 2). There was no effect of inspiratory resistive loading on the amplitudes of the diaphragmatic motor evoked potentials (MEP) (Figure 4). Conversely, the latencies of the diaphragm MEPs obtained in response to inspiratory TMS were significantly shorter in the R20 condition than in the R0 condition (mean difference -

PET CO 2

Inspiratory resistive loading and breathing pattern The "*" stands for a significant difference at the 5% threshold.

PET CO 2 0.903 ms, 95%CI from -1.79 to -0.016, p = 0.03) (Figure 4). This shortening was not observed in response to expiratory TMS.

The EMG responses of the abductor pollicis brevis to cervical and transcranial magnetic stimulations were not altered by inspiratory resistive breathing, both in terms of latency and amplitude (Figure 5).

Discussion

In our subjects, and in line with previous observations [START_REF] Clague | Effort sensation, chemoresponsiveness, and breathing pattern during inspiratory resistive loading[END_REF][START_REF] Lopata | Respiratory muscle function during CO2 rebreathing with inspiratory flow-resistive loading[END_REF][START_REF] Ramonatxo | Effect of resistive loads on pattern of respiratory muscle recruitment during exercise[END_REF][START_REF] Lopata | Effects of flow-resistive loading on mouth occlusion pressure during CO2 rebreathing[END_REF], inspiratory resistive breathing did not increase the automatic ventilatory drive (and if anything tended to decrease it). In contrast, inspiratory loading facilitated the response of the diaphragm to transcranial magnetic stimulation. This indicates that sources other than the brainstem respiratory generators were activated by resistive breathing and increased the inputs received by the phrenic motoneurons. For reasons that will be discussed below, increased afferent traffic is unlikely and therefore our observations point to the involvement of suprapontine Diaphragm response to transcranial magnetic stimulation delivered during loaded inspiration Mean values (± SD) of esophageal (Pes), gastric (Pga) and transdiaphragmatic (Pdi) pressure (in cmH2O) in response to cervical magnetic stimulation while the subjects were breathing room air (R0) or against a resistance of either 5 (R5) or 20 (R20) cmH2O/l/s. Stimulations were applied either during early inspiration or late expiration.

Effects of inspiratory loading on the diaphragm EMG response to cervical magnetic stimulation structures. We believe that these results provide a neurophysiological substratum to the behavioral nature of inspiratory load compensation in awake humans, and could open new perspectives regarding the functional role of the premotor representation of the diaphragm [START_REF] Sharshar | Demonstration of a second rapidly conducting cortico-diaphragmatic pathway in humans[END_REF]. This is summarized in Figure 6. Mean values (± SD) of esophageal (Pes), gastric (Pga) and transdiaphragmatic (Pdi) pressure (in cmH2O) in response to transcranial magnetic stimulation while the subjects were breathing room air (R0) or against a resistance of either 5 (R5) or 20 (R20) cmH2O/l/s. Stimulations were applied either during early inspiration or late expiration.

Effects of inspiratory loading on the abductor pollicis brevis EMG response to transcranial magnetic stimulation

Effects of inspiratory loading on the diaphragm EMG response to transcranial magnetic stimulation

Mechanisms of inspiratory resistive induced facilitation of the diaphragm response to transcranial magnetic stimulation

The facilitation of the response of a muscle to single pulse TMS can occur at the cortical or at the spinal level. Cortical facilitation typically increases the size of the motor evoked potentials without latency changes [START_REF] Kasai | Evidence for facilitation of motor evoked potentials (MEPs) induced by motor imagery[END_REF][START_REF] Kiers | Facilitatory effect of thinking about movement on magnetic motor-evoked potentials[END_REF]. Spinal facilitation, in contrast, tends to shorten latency. This can occur through the recruitment of additional motoneurons ("spatial" facilitation) that, in line with the size principle of motoneuron recruitment, have increasingly fast conduction properties. In this case, there is a simultaneous decrease in latency and increase in amplitude (that can also be the expression of concurrent cortical facilitation). This is typically what happens when TMS is superimposed on a voluntary contraction [START_REF] Calancie | Motor-unit responses in human wrist flexor and extensor muscles to transcranial cortical stimuli[END_REF][START_REF] Thompson | Further observations on the facilitation of muscle responses to cortical stimulation by voluntary contraction[END_REF], and it has been repeatedly verified for the diaphragm [START_REF] Corfield | Does the motor cortical control of the diaphragm 'bypass' the brain stem respiratory centres in man?[END_REF][START_REF] Similowski | Facilitation-independent response of the diaphragm to cortical magnetic stimulation[END_REF][START_REF] Similowski | Cervical magnetic stimulation: a new painless method for bilateral phrenic nerve stimulation in conscious humans[END_REF][START_REF] Maskill | Motor cortical representation of the diaphragm in man[END_REF][START_REF] Davey | Site of facilitation of diaphragm EMG to corticospinal stimulation during inspiration[END_REF]. Spinal facilitation can also occur in the absence of motoneuron recruitment. Indeed, single pulse TMS produces successive descending volleys, early ones through the direct excitation of pyramidal tract neurons ("D-waves"), and later ones through the activation of cortical interneurons ("Iwaves"). Normally, spinal cells require the temporal summation of D-and I-waves to fire [START_REF] Thompson | Further observations on the facilitation of muscle responses to cortical stimulation by voluntary contraction[END_REF][START_REF] Hess | Responses in small hand muscles from magnetic stimulation of the human brain[END_REF][START_REF] Kaneko | Spinal cord potentials after transcranial magnetic stimulation during muscle contraction[END_REF]. If pre-conditioned they can respond to early I-waves or D-waves, as evidenced by studies of single motor unit potentials [START_REF] Calancie | Motor-unit responses in human wrist flexor and extensor muscles to transcranial cortical stimuli[END_REF] ("temporal" facilitation). For the diaphragm, spinal facilitation of the temporal type has been invoked to explain the effects of changes in the bulbospinal drive to breathe on the response to TMS [START_REF] Mehiri | Responses of the diaphragm to transcranial magnetic stimulation during wake and sleep in humans[END_REF][START_REF] Straus | Facilitation of the diaphragm response to transcranial magnetic stimulation by increases in human respiratory drive[END_REF]. Mehiri et al. [START_REF] Mehiri | Responses of the diaphragm to transcranial magnetic stimulation during wake and sleep in humans[END_REF] have indeed observed that superimposing TMS upon inspiration rather than expiration shortened the latency of the diaphragm response by about 1 ms without modifying the amplitude of the diaphragm MEPs. This effect was magnified when afferent and cortical traffics were minimized by sleep. Straus et al [START_REF] Straus | Facilitation of the diaphragm response to transcranial magnetic stimulation by increases in human respiratory drive[END_REF] showed that similar changes were provoked by breathing 7% CO 2 .

In the present study, an inspiratory resistance of 20 cmH 2 O/L/s significantly shortened the latency of the diaphragmatic response to inspiratory TMS. This shortening was 0.9 ms on average (Figure 4), which corresponds to similar changes observed with other experimental designs [START_REF] Mehiri | Responses of the diaphragm to transcranial magnetic stimulation during wake and sleep in humans[END_REF][START_REF] Straus | Facilitation of the diaphragm response to transcranial magnetic stimulation by increases in human respiratory drive[END_REF]. We did not observe a significant change in amplitude, but we acknowledge that this could be due to insufficient statistical power (Figure 4). However, even if this was the case, the effect of resistive breathing on MEPs amplitudes would still be much less marked than the effect on latencies. According to the above described mechanisms and observations, we postulate that the facilitation of the diaphragm response to transcranial magnetic stimulation that we observed occurred at the spinal level. Of note, the lack of influence of resistive breathing on the response of the abductor pollicis brevis to transcranial magnetic stimulation indicates that the observed phenomenon was specific to the diaphragm rather than concerning the corticospinal tract globally. Whatever the source of the facilitation of the diaphragm response to TMS that inspiratory resistive breathing provoked (see below), this interpretation of our findings is coherent with the integration of afferent, segmental and supraspinal inputs that is characteristic of phrenic motoneurons [START_REF] Aminoff | Spinal integration of segmental, cortical and breathing inputs to thoracic respiratory motoneurones[END_REF][START_REF] Sears | Spinal integration of cortical, brainstem, and segmental inputs to thoracic respiratory motoneurons[END_REF].

Interactions between bulbospinal and corticospinal com-mands at spinal phrenic motoneuron level

Interactions between bulbospinal and corticospinal commands at spinal phrenic motoneuron level. Schematic representation of the interactions between bulbospinal and corticospinal commands at the level of the spinal phrenic motoneuron. Arrow "1" represents the bulbospinal inputs to the spinal motoneurons, responsible for the production of ventilation and its automatic adaptation to bodily requirements. Arrow "2" represents the direct input from the primary motor cortex. This pathway carries voluntary respiratory commands, and is considered to be the main pathway activated by transcranial magnetic stimulation (TMS) as performed in this study. The diaphragm response to TMS depends on the polarization of the phrenic motoneurons when TMS is applied. It is therefore facilitated if TMS is superimposed on an increased bulbospinal drive (arrow 1) or on a voluntary contraction of the diaphragm (arrow 2). Arrow "3" represents the pathway from the premotor area of the cerebral cortex to the diaphragm [START_REF] Sharshar | Demonstration of a second rapidly conducting cortico-diaphragmatic pathway in humans[END_REF]. Resistive inspiratory loading does not increase the bulbospinal drive but facilitates the response to TMS, possibly in line with the activation of this latter pathway.

Putative source of facilitation during resistive breathing (Figure 6)

Conceivably, reflex mechanisms increasing the automatic drive to breathe could explain the compensation of inspiratory loading in humans, but data in the literature goes against this hypothesis [START_REF] Clague | Effort sensation, chemoresponsiveness, and breathing pattern during inspiratory resistive loading[END_REF][START_REF] Lopata | Respiratory muscle function during CO2 rebreathing with inspiratory flow-resistive loading[END_REF][START_REF] Ramonatxo | Effect of resistive loads on pattern of respiratory muscle recruitment during exercise[END_REF]. Our subjects did not exhibit signs of increased ventilatory drive when confronted with resistive loading (no change in VT/TI or Pm 0.1 ). On the contrary, they exhibited a decreased breathing frequency. The discrepancy between frequency and VT/TI or Pm 0.1 probably illustrates the differences in the control of the intensity of ventilatory drive and that of its timing. As a result, it seems safe to rule out facilitation through increased bulbospinal inputs as the explanation of our observations. We acknowledge that, because stimulations were triggered at a fixed Pes level and because resistive breathing slowed respiration down, TMS was delivered later in inspiration during resistive breathing than during unloaded breathing. The corresponding interval was however sufficiently narrow (150-300 ms) not to influence the diaphragm MEPs latencies (unpublished observations by our group).

TMS was delivered at a fixed level of inspiratory pressure, and sufficiently early during inspiration for the peak activity of inspiratory muscles to have not yet occurred [START_REF] Younes | Mechanisms of respiratory load compensation[END_REF]. Therefore, the afferent traffic from the diaphragm was probably not very different during free breathing and during loaded breathing. This makes facilitation from afferent stimulation all the more unlikely as the costal diaphragm is poor in spindles [START_REF] Duron | Intercostal and diaphragmatic muscle endings and afferents[END_REF]. In addition, afferent stimulation is associated with larger MEPs [START_REF] Komori | Influence of peripheral afferents on cortical and spinal motoneuron excitability[END_REF], which we did not observe.

The remaining explanation for the inspiratory resistive breathing related facilitation of the diaphragm response to TMS would be the activation of suprapontine regions. Indeed, fighting an inspiratory resistance can activate multiple such regions [START_REF] Horn | Suprapontine control of respiration[END_REF][START_REF] Fink | Human cerebral activity with increasing inspiratory force: a study using positron emission tomography[END_REF]. The primary motor representation of the diaphragm is not a good candidate because our subjects were not instructed to fight the load, and had to breathe against it in a sustained manner. Voluntary load compensation is thus not likely. It would have been expected to induce "spatial" facilitation with an increase in amplitude of diaphragm MEPs [START_REF] Similowski | Facilitation-independent response of the diaphragm to cortical magnetic stimulation[END_REF][START_REF] Sharshar | Effect of voluntary facilitation on the diaphragmatic response to transcranial magnetic stimulation[END_REF], which we failed to observe. Finally, inspiratory loading does not seem to activate the sensorimotor cortex [START_REF] Isaev | Areas of the brain concerned with ventilatory load compensation in awake man[END_REF]. Inspiratory muscles obey premotor commands [START_REF] Macefield | The cortical drive to human respiratory muscles in the awake state assessed by premotor cerebral potentials[END_REF] likely to originate in the medial premotor cortex [START_REF] Ball | The role of higher-order motor areas in voluntary movement as revealed by high-resolution EEG and fMRI[END_REF]. There is a cortico-diaphragmatic pathway originating in the supplementary motor area [START_REF] Sharshar | Demonstration of a second rapidly conducting cortico-diaphragmatic pathway in humans[END_REF]. However, the exact "respiratory role" of premotor regions is unknown. These regions are involved in the preparation of movement. Their activation could hypothetically be called upon to explain the progressive change in breathing pattern that follows the imposition of an inspiratory load, with a shift from an initially highly variable respiration to a much more steady one [START_REF] Younes | Mechanisms of respiratory load compensation[END_REF]. As there are direct projections of premotor areas to the phrenic spinal motoneurons, it is reasonable to postulate that the activation of the premotor control of the diaphragm would depolarize them and thus increase their "receptiveness" to a concurrent input (Figure 6), which would explain our findings. This hypothesis is supported by the demonstration that a premotor negativity has a facilitating effect on the response of the target muscle to TMS [START_REF] Zaaroor | Time course of motor excitability before and after a task-related movement[END_REF]. It must be emphasized that the facilitation of the diaphragm response that we observed is most certainly independent of any direct activation of the premotor diaphragm pathway that is best stimulated with a 110 mm double cone coil orientated antero-posteriorly and has a higher motor threshold than the primary motor diaphragm pathway [START_REF] Sharshar | Demonstration of a second rapidly conducting cortico-diaphragmatic pathway in humans[END_REF].

Conclusion

In summary, we submit that inspiratory load compensation in awake humans may involve the activation of a premotor cortical area. Confirmatory studies are necessary, but this information could be relevant to a better understanding of the respiratory sensations elicited by inspiratory loading, and possibly to the pathophysiology of diseases where inspiratory load compensation is mandatory to sustain ventilation. In this view, it has been shown that patients with chronic obstructive pulmonary disease (COPD) tend to exhibit facilitated diaphragm response to TMS [START_REF] Hopkinson | Corticospinal control of respiratory muscles in chronic obstructive pulmonary disease[END_REF]. Understanding whether, and in what proportion, this is due to an increased ventilatory drive, inspiratory loading, or both would probably be worthwhile.

Methods

Subjects

Six healthy subjects (2 women, 4 men, 22-25 years-old) participated in the study after ethical and legal clearance (Comité Consultatif de Protection des Personnes se prêtant à des Recherches Biomédicales Pitié-Salpêtière). They were naive to respiratory physiology experiments, were not sleep deprived, and had been instructed to refrain from consuming alcohol or psychotropic substances of any kind during the preceding 24 hours. They received detailed information and gave written consent.

Ventilation and respiratory pressures

The subjects were studied seated, with abdomen unbound and wearing a nose clip. They breathed through a mouth piece connected to a pneumotachometer and a nonrebreathing two-way valve (Hans Rudolph, Kansas City, MO, USA) for the measurement of respiratory rhythm, tidal volume, minute ventilation, mean inspiratory flow (VT/TI) and duty cycle (TI/TT)(Respiratory Pressure Module, MedGraphics, Medical Graphic Corporation, Saint Paul, Minnesota, USA). was monitored in the expiratory gas with an infra-red gas analyzer (Medical gas Analyzer LB-2 Beckman, California, USA). Pm 0.1 was measured at the mouth as follows. With the subjects breathing through a two-way valve separating the inspiratory and the expiratory limbs of the circuit, the inspiratory limb was occluded silently using an inflatable balloon during a randomly selected expiration. In this way, the next inspiration was performed against an occluded airway. The occlusion pressure was defined as the value reached 100 ms after the beginning of the ensuing drop in mouth pressure, namely at a time too early for the occlusion to have been perceived by the subject. The upper airway was freed by deflating the occlusion balloon within 3-400 ms of the beginning of effort. Pm 0.1 measurements were performed every four to seven breathing cycles. The values hereafter provided are the average of at least ten steady-state measurements in each condition for each subject. Pes and Pga were measured using two air-filled (1 ml) balloon catheters inserted through the nose (length 80 cm, 1.5 mm internal diameter, Marquat, Boissy Saint Léger, France) and connected to linear differential pressure transducers (Validyne MP45, ± 100 cmH 2 O, Northridge, CA, USA).

Electromyograms (EMG)

Surface recordings of the right diaphragmatic electromyogram were obtained using a pair of skin-taped silver cup electrodes filled with conductive paste and positioned on the chest according to a technique previously described as minimizing the risk of signal contamination by the activity of extradiaphragmatic muscles [START_REF] Demoule | Validation of surface recordings of the diaphragm response to transcranial magnetic stimulation in humans[END_REF][START_REF] Verin | Validation of improved recording site to measure phrenic conduction from surface electrodes in humans[END_REF]. In brief, the active electrode was placed in the lowest accessible intercostal space, between the midclavicular line and the lateral edge of the sternum. The reference electrode was on the rib above, at a 2 cm distance. The surface electromyogram of a hand muscle, the right abductor pollicis brevis, was simultaneously recorded to serve as control. EMG signals were amplified, band pass filtered (20 Hz -5 kHz) digitized (10 kHz) and stored as computer files for subsequent analysis (Neuropack Sigma, Nihon Kohden, Tokyo, Japan).

Stimulations

All magnetic stimulations were carried out with a Magstim 200 stimulator equipped with a 90 mm circular coil and set to its maximum output (2.5 Tesla)(Magstim, Sheffield, UK). Cervical magnetic stimulation (CMS) [START_REF] Similowski | Cervical magnetic stimulation: a new painless method for bilateral phrenic nerve stimulation in conscious humans[END_REF] was used to describe the diaphragmatic responses to peripheral phrenic stimulation. Transcranial magnetic stimulation (TMS) was achieved with the coil placed over the vertex, after optimization of the response and careful maintenance of the coil position. CMS and TMS were performed during either late expiration or early inspiration. The stimulator was triggered from the Pes signal, with a threshold value that was always identical and set slightly below endexpiratory Pes. With this approach, expiratory stimulations occurred at a late phase of expiration, namely at a time where a residual post-inspiratory activity was most unlikely. The timing of inspiratory stimulations was thus not fixed by definition, and depended on the rate of change of Pes. Nevertheless, all the inspiratory stimulations occurred between 150 and 300 ms after the beginning of the Pes drop.

Data analysis

Responses to stimulations were observed in terms of Pes and Pga (noted "cms" or "tms" depending on the site of stimulation) and of motor evoked potentials. MEP amplitudes were measured between the highest and the lowest peak of the evoked responses. MEP latencies were measured as the time elapsed between the stimulus and the first departure of the signal from baseline (Figure 3). Pes,cms, Pes,tms, Pga,cms and Pga,tms were calculated as the difference between the value at the time of stimulation and the peak of the ensuing pressure wave. The corresponding Pdi values were calculated off line by subtracting Pes from Pga. The values reported for each subject are the average of five CMS and ten TMS.

Effect on breathing through linear inspiratory resistances

The subjects first accustomed themselves to the experimental setting by calmly breathing room air without added resistance (R0) through the apparatus. Ventilatory variables were measured and CMS and TMS were performed. Then inspiratory linear resistances of 5 cmH 2 O/L/ s (R5) and 20 cmH 2 O/L/s (R20) (Hans Rudolph, 7100 R5 and R20, Kansas City, MO, USA) were added to the circuit in random order. Ten minutes were allowed for stabilization, after which ventilatory variables were again measured before the application of CMS and TMS. The subjects did not receive any instructions on how to behave when confronted with inspiratory loading.

Statistical analysis

It was conducted using Statistix ® software (v 8.0, Tallahassee, FL, USA). The normality of data distributions as tested with the Shapiro-Wilk test being consistently confirmed, the results were described in terms of means ± SD and linear models were used. The ventilatory variables and respiratory pressures taken as dependent variables were submitted to an analysis of variance for repeated measures (with the "subject" variable as a random factor, and the loading condition as the within-subjects factor). The responses to TMS were studied with a nested split-plot design, to separately analyze the effects of inspiratory PET CO 2 loading and stimulation timing. Dependent variables were the Pdi responses to TMS and the amplitudes and latencies of the diaphragm and the abductor pollicis brevis MEPs. The stimulation timing factors were randomly assigned to the subjects (main plot) and the loading condition factors were assigned to the split plot. Posthoc comparisons were conducted in reference to the R0 condition using Dunnett's procedure. The results were considered significant when the probability p of a type I error was less than 5%.

Figure 1

 1 Inspiratory resistive loading and breathing pattern. Effectof breathing against inspiratory linear resistive loads onrespiratory frequency (RF), tidal volume (VT), minute ventilation(V'E), end-tidal carbon dioxide in the expired gas ( ), mean inspiratory flow (VT/TI), duty cycle (TI/TT) and occlusion pressure (Pm 0.1 ). Each bar corresponds to the mean of the corresponding data, with indication of ± 1 SD.

Figure 3

 3 Diaphragm response to transcranial magnetic stimulation delivered during loaded inspiration. Example of the response of the diaphragm electromyogram (MEPdi, top), esophageal pressure (Pes, middle), and gastric pressure (Pga, bottom) to transcranial magnetic stimulation applied during inspiration in a subject breathing against a 5 cmH 2 0/L/s resistance. On the EMG trace, the triangle indicates the point at which the latency of the motor evoked potential (MEP) is measured.

Figure 2

 2 Effects of inspiratory loading on the diaphragm EMG response to cervical magnetic stimulation. Effect of breathing against inspiratory linear resistive loads on the latency (top) and the amplitude (bottom) of the electromyographic responses of the diaphragm to cervical magnetic stimulations (CMS) delivered during inspiration (left) or expiration (right). R0, R5 and R20 correspond to breathing against no resistance, against a resistance of 5 cmH 2 O/L/s, and against a resistance of 20 cmH 2 O/L/s, respectively. Vertical bars correspond to mean values with indication of ± 1 SD. Statistical analysis did not detect any significant difference at the 5% threshold.

Figure 5

 5 Effects of inspiratory loading on the abductor pollicis brevis EMG response to transcranial magnetic stimulation. Effect of breathing against inspiratory linear resistive loads on the latency (top) and the amplitude (bottom) of the electromyographic responses of the abductor pollicis brevis to magnetic transcranial stimulations (TMS) delivered during inspiration (left) or expiration (right). R0, R5 and R20 correspond to breathingagainst no resistance, against a resistance of 5 cmH 2 O/L/s, andagainst a resistance of 20 cmH 2 O/L/s, respectively. Vertical barscorrespond to mean values with indication of ± 1 SD. No significant differences were found between conditions.

Figure 4

 4 Effects of inspiratory loading on the diaphragm EMG response to transcranial magnetic stimulation. Effect of breathing against inspiratory linear resistive loads on the latency (top) and the amplitude (bottom) of the electromyographic responses of the diaphragm to transcranial magnetic stimulations (TMS) delivered during inspiration (left) or expiration (right). R0, R5 and R20 correspond to breathing against no resistance, against a resistance of 5 cmH 2 O/L/s, and against a resistance of 20 cmH 2 O/L/s, respectively. Vertical bars correspond to mean values with indication of ± 1 SD. The "*" stands for a significant difference at the 5% threshold.

Table 1 : Pressure responses to cervical magnetic stimulation Cervical Magnetic Stimulation R0 R5 R20

 1

		Inspiration	Expiration	Inspiration	Expiration	Inspiration	Expiration
	Pes	16.5 ± 11.9	12.1 ± 9.8	15.6 ± 8.6	11.8 ± 6.9	19.4 ± 17.2	9.2 ± 7.0
	Pga	3.4 ± 3.6	3.7 ± 4.9	2.6 ± 1.6	2.7 ± 1.6	2.4 ± 1.4	2.7 ± 1.2
	Pdi	19.9 ± 13.5	19.9 ± 10.9	18.2 ± 9.3	14.9 ± 7.0	21.8 ± 17.0	11.9 ± 7.5

Table 2 : Pressure responses to transcranial magnetic stimulation

 2

				Transcranial Magnetic Stimulation
		R0		R5		R20
		Inspiration	Expiration	Inspiration	Expiration	Inspiration	Expiration
	Pes	5.8 ± 5.6	3.9 ± 5.8	7.1 ± 4.8	4.1 ± 6.3	8.7 ± 7.5	4.4 ± 4.0
	Pga	1.6 ± 1.4	1.1 ± 2.0	1.6 ± 1.4	1.5 ± 2.6	1.3 ± 1.8	1.4 ± 1.7
	Pdi	7.1 ± 6.8	5.1 ± 7.8	8.7 ± 6.1	5.6 ± 8.8	10.1 ± 8.5	5.8 ± 5.4

(page number not for citation purposes)

Acknowledgements

The authors are indebted to Marilyn Amouyal-Jones for help with the English manuscript. This work was supported by a Contrat de Recherche "Legs Poix" de la Chancellerie des Universités de Paris, and by the Association pour le Développement et l'Organisation de la Recherche en Pneumologie (ADOREP), Paris, France. Chrystèle Locher was supported by a grant of the Académie Nationale de Médecine, France. Marie-Noëlle Fiamma was supported by a grant from the Société de Pneumologie de Langue Française. Mathieu Raux was the recipient of a "Médaille d'Or" grant from Assistance Publique-Hôpitaux de Paris, Paris, France.

Authors' contributions

CL participated in study design, carried out data acquisition, analyzed the results, and helped to draft the manuscript; MR participated study design, contributed significantly (or greatly) to data interpretation, and contributed to the writing of the manuscript; MNF contributed to data interpretation and to the writing of the manuscript; CMP contributed to data analysis and interpretation and to the writing of the final manuscript; MZ and JPD critically reviewed the design of the study and the manuscript, with important impact on intellectual content; TS and CS were responsible for study design and statistical processing of data; they contributed the largest part of data interpretation and produced the final manuscript that received approval from all authors.