## Abstract

Persistence of respiratory sinus arrhythmia (RSA) has been described in humans during intense exercise and attributed to an increase in ventilation. However, the direct influence of ventilation on RSA has never been assessed. The dynamic evolution of RSA and its links to ventilation were investigated during exercise in 14 healthy men using an original modeling approach. An evolutive model was estimated from the detrended and high-pass-filtered heart period series. The instantaneous RSA frequency (*F*_{RSA}, in Hz) and amplitude (*A*_{RSA}, in ms) were then extracted from all recordings. *A*_{RSA} was calculated with short-time Fourier transform. First, measurements of *F*_{RSA} and *A*_{RSA} were performed from data obtained during a graded and maximal exercise test. Influences of different ventilation regimens [changes in tidal volume (V_{T}) and respiratory frequency (*F*_{R})] on *A*_{RSA} were then tested during submaximal [70% peak O_{2} consumption (V̇o_{2peak})] rectangular exercise bouts. Under graded and maximal exercise conditions, *A*_{RSA} decreased from the beginning of exercise to 61.9 ± 3.8% V̇o_{2peak} and then increased up to peak exercise. During the paced breathing protocol, normoventilation (69.4 ± 8.8 l/min), hyperventilation (81.8 ± 8.3 l/min), and hypoventilation (56.4 ± 6.2 l/min) led to significantly (*P* < 0.01) different *A*_{RSA} values (3.8 ± 0.5, 4.6 ± 0.8, and 2.9 ± 0.5 ms, respectively). In addition, no statistical difference was found in *A*_{RSA} when ventilation was kept constant, whatever the *F*_{R}-V_{T} combinations. Those results indicate that RSA persists for all exercise intensities and increases during the highest intensities. Its persistence and increase are strongly linked to both the frequency and degree of lung inflation, suggesting a mechanical influence of breathing on RSA.

- cardiorespiratory coupling
- heart period variability
- paced breathing
- time-varying model

respiratory sinus arrhythmia (RSA) is a well-known cardiorespiratory coupling that results in the modulation of sinus rhythm by breathing. At rest, RSA improves the efficiency of pulmonary gas exchange in matching pulmonary blood flow to lung inflation (14, 16) and buffers blood pressure and cardiac output variations mechanically induced by respiration (37).

At rest, because the RSA power spectrum is nearly abolished by cholinergic blockade or functional vagotomy, RSA is believed to be mainly mediated by vagal activity (1, 22, 30). Nevertheless, the use of the RSA power spectrum as an index of cardiac vagal tone is not widely accepted. Indeed, an increase in tidal volume (V_{T}) or in respiratory frequency (*F*_{R}) can enhance or reduce RSA power, respectively (17), and this phenomenon has no bearing on cardiac vagal control (19). Moreover, a small degree of RSA has been observed in heart transplant subjects, pointing out that the denervated human heart retains the intrinsic ability to regulate heart rate in response to respiration (4). During exercise, from low to mild intensity, the RSA power quickly decreases in accordance with vagal withdrawal but does not reach a zero value (39). Subsequently, RSA power has been observed to increase with the highest exercise intensities only when expressed in normalized (percentage of the total power spectrum) units (4, 28). This increase, which could not be explained by vagal activity, was attributed to a mechanical stretch of the sinus node in response to a ventilation increase (4, 9). Increase in ventilation enhances fluctuations in blood return to the right heart that modulates atrial transmural pressure and pacemaker activity (6, 29).

To study RSA, spectral power analysis of the R-R interval variability, i.e., heart period (HP) variability (HPV), has been frequently used. This analysis decomposes a signal into its frequency components and evaluates the relative power of each component as a function of frequency. Therefore, RSA corresponds to the high-frequency band (usually ranging from 0.15 to 0.4 Hz), centered at a frequency that corresponds to *F*_{R} (5, 36). The spectral power analysis requires stationarity of the signal studied; consequently, the study of RSA during exercise has been limited to constant load or very slow trend ramp load protocols (4, 9, 26–28).

In regard to methods of analysis, no study has accurately examined the dynamic pattern of RSA and its link to ventilation during graded or intense exercise. In recent years, to overcome these methodological limitations, time-varying models have been successfully developed to depict HPV power spectrum in nonstationary conditions such as rest-tilt maneuvers, vasovagal syncope, or acute ischemic periods (10, 18). Those methods evaluate the spectrum over moving windows, estimating power as a function of time and frequency, and produce instantaneous or evolutionary spectra. Time-varying methods adapted to HPV analysis over a graded and maximal exercise test could describe the dynamic pattern of RSA and provide information about the respective contribution of autonomic (vagal tone) and nonautonomic (mechanical stretch) mechanisms.

Thus the first objective of this study was to use our original signal processing method to describe RSA dynamic patterns during graded and maximal exercise tests. After this descriptive step, controlled breathing conditions were used during rectangular exercise bouts to evaluate the respective contributions of *F*_{R}, V_{T}, and respiratory flow to RSA during exercise.

## METHODS

### Subjects

Fourteen healthy sedentary men (with characteristics shown in Table 1) participated in the present study. All subjects were nonsmokers, and none was taking any medication. Physical activity and alcohol and caffeinated beverages consumption were prohibited 24 h before any exercise testing session. Initially, 16 subjects were included in the study. However, in two subjects, ECG recordings were unsuccessful during exercise. Written informed consent was obtained before study participation, and ethical approval was granted by the Local Ethics Committee.

### Experimental Design

#### Experiment n°1: graded exercise test.

After a 5-min baseline resting data collection, subjects performed a graded and maximal exercise test on a cycle ergometer (Ergomedic 824 E, Monark Exercise AB; Vansbro, Sweden) in a quiet room at a controlled temperature of 21°C, at least 3 h after the morning meal. The initial load was fixed at 75 W and implemented by 37.5 W every 2 min until exhaustion. The pedaling rate was kept constant at 75 revolutions/min.

#### Experiment n°2: rectangular exercises bouts.

To test the hypothesis that RSA persistence during exercise is linked to ventilation (V̇_{I}), 8 of 14 men performed 5 exercise bouts (6 min each) on a cycle ergometer. The workload was fixed at 70% of peak O_{2} consumption (V̇o_{2peak}) achieved during the previously described graded and maximal exercise test. Breathing was paced, and the inspiration-to-expiration ratio was 1:1. The first exercise bout consisted of a normoventilation session where *F*_{R} was set at 0.42 Hz and V_{T} was uncontrolled. The measured V̇_{I} was considered as the reference V̇_{I}. Subjects then performed, at random, hypo- and hyperventilation sessions (*F*_{R}=0.42 Hz and assigned high and low V_{T}) and two steady V̇_{I} sessions where *F*_{R} was set at 0.31 or 0.63 Hz (steady V̇_{I1} or steady V̇_{I2} sessions, respectively), and V_{T} was controlled to reach reference V̇_{I}. In all exercise bouts, subjects controlled their *F*_{R} and V_{T} via a personal computer displaying auditive and visual feedback informations. Recovery time between each exercise bout was 12 min.

In both experiments, ventilatory indices and gas exchanges were measured by an automatic ergospirometer on a breath-by-breath basis (Metasys TR-M, Brainware; Toulon, France). Subjects breathed through a silicon facemask connected to a two-way nonrebreathing valve (Hans Rudolph; Kansas City, MO). *F*_{R} and V_{T} were calculated by integration of the data obtained from a pneumotachograph. Inspired and expired O_{2} and CO_{2} concentrations were measured by paramagnetic and infrared sensors, respectively, and end tidal Po_{2} and Pco_{2} (Pet_{O2} and Pet_{CO2}, respectively) were determined. Before each test, the gas analyzers were calibrated with gases of known composition, and an accurate controlled volume syringe adjusted the pneumotachograph. During the exercise tests and the preceding 5 min (rest), a one-lead ECG (Cardiocap II, Datex Engstrom; Helsinki, Finland) was recorded and digitized on-line by a 12-bit analog-to-digital converter (DAS 1600, Keithley Instruments; Taunton, MA) at a sampling rate of 1,000 Hz on a personal computer.

#### ECG preprocessing

The R wave peak occurrence was estimated using a threshold technique applied to the filtered and demodulated ECG signal. Successive R-R intervals then defined the HP series [HP(*k*)]. Resampling of the ECG was not used in this study to avoid interpolation artifacts such as low-pass effects. Moreover, the analysis of HP was preferred to the analysis of heart rate, because the heart rate is a nonlinear transformation of the basic R-R interval measure (5). Furthermore, when HP(*k*) is defined as a sum of the instantaneous mean HP [*T*(*k*)] and the variability [*V*(*k*)], considered small compared with *T*(*k*), the heart rate series [HR(*k*)] can be developed as follows: (1) where it is clear that the amplitude of the variability is biased by *T*(*k*).

HP series were visually inspected to ensure the absence of artifacts. In the case of artifacts arising from a spurious R-wave detection, the HP was restored by summing the two or more spuriously short periods. In cases of undetected R-waves, the erroneous HP was replaced by the mean of the two surrounding HP values. Those artifacts did not exceed 0.1% of the total HP series. The first 30 s of exercise were removed to overpass the limitation of the tracking algorithm induced by the abrupt decrease in HP. It was then assumed that the HP signal [hp(*k*)=*t*_{k} − *t*_{k − 1} (where *t*_{k} is the occurrence time of the *k*th beat)] was able to reveal the modulation signal [*r*(*t*)] containing the RSA information (23). The first processing applied to hp(*k*) was to remove *T*(*k*) using a polynomial approximation [po(*k*)] (order equal to 20). The second preprocessing was a 100th order high-pass finite-impulse response filter (designed with a Hamming window and a cutoff frequency equal to 0.03, with 0.5 corresponding to the half of the normalized sample rate) applied to hp(*k*) after the trend po(*k*) was removed. The resulting signal was referenced as *m*(*k*) (example in Fig. 1*B*).

Because the stationarity conditions are not fulfilled under dynamic exercise, because of the variations in both mean HP and *F*_{R}, classical spectral analysis methods such as fast Fourier transform were replaced by a more acute time-frequency analysis tool. The proposed method can be decomposed into two parts: time-varying frequency and time-varying amplitude estimates.

#### Time-varying frequency estimate.

As we mentioned in a previous study (25), when the signal demonstrates spectral lines, it can be approximately modeled as an autoregressive (AR) process. When the signal is nonstationary, the classical AR model no longer applies and must be replaced by: (2) giving a time-varying parametric model, where *v*(*k*) is the white Gaussin input, *p* is the AR order, *N* is the length of the record, and *i* is an index. Furthermore, to update the AR coefficients *a*_{i}(*k*) using algorithms such as Recursive Least Square (21), the evolutive approach requires the *a*_{i}(*k*) to be a linear combination of some known basic functions (25).

In our application, we used the Fourier basis with an order chosen using the Akaike criterion, and we selected the order of the AR model equal to 12, i.e., *p* = 12 (25).

This modeling allowed us to estimate time-varying spectral lines by solving the following equation: (3) where * stands for the complex conjugate. Because root computing is a difficult task to ensure a correct tracking of the frequencies *f*_{i}(*k*), we used the solution provided by Meste et al. (25).

#### Time-varying amplitude estimate.

Several procedures were available depending on the accuracy of the previous estimation of frequency. We used a method that consisted of using time-varying filters defined by the frequency tracks to obtain the phase of the signal rather than working directly on the signal power. By defining the short-time Fourier transform (STFT) of *m*(*k*) as HP(*k*,*f*), using time-varying filter *G*_{i}(*k*,*f*) designed with *f*_{i}(*k*), we obtained the filtered signal *m*_{i}(*k*) as *m*_{i}(*k*) = STFT^{−1}[*G*_{i}(*k*,*f*) × HP(*k*,*f*)], where STFT^{−1} stands for the inverse STFT (25). A filtered signal was calculated for each *f*_{i}(*k*) (*i* = 1...6). With the filtered signal *m*_{i}(*k*) being a narrow band signal, we used the Hilbert transform to extract the envelope *A*_{i}(*k*) of the signal as the modulus of the analytical signal. The signal *m*_{i}(*k*) corresponding to the *A*_{i}(*k*) with the highest energy was assumed to be the observed modulation caused by breathing, and the corresponding *f*_{i}(*k*) was referred to as the normalized *f*_{RSA}(*k*). This *m*_{i}(*k*) and *A*_{i}(*k*) were named *m*_{RSA}(*k*) and *A*_{RSA}(*k*) respectively. The quantity *F*_{RSA}(*t*_{k}) was deduced from the corresponding *f*_{RSA}(*k*) by *F*_{RSA}(*t*_{k}) = *f*_{RSA}(*k*)/*T*(*k*).

The next step of our analysis was to relate the quantities extracted from *m*_{RSA}(*k*) to the respiratory pattern. To do so, a model linking the HP and the respiratory function was introduced. In a previous study (24), we demonstrated that the pulse frequency modulation (PFM) model was a candidate for this aim. In the following, the PFM results are given under stationary conditions. In this case, the mean HP and the pattern of the respiration function are assumed to be constant. Moreover, it has been demonstrated (25) that the following expressions, where the index *k* has been omitted, are valid in nonstationary conditions.

Considering the PFM model (24), the time of occurrence *t*_{k} was the solution of the equation: (4) where *r*(*t*_{k}) was, in this case, the modulation function related to breathing, whose amplitude was *c*_{RSA} when assumed to be a pure sinusoid, and *c*_{5} is a phase constant.

The RSA amplitude *A*_{RSA} of the observed modulation *m*_{RSA}(*k*) related to breathing was linked to *c*_{RSA} by the following expressions: (5) Under our specific exercise test, the *F*_{RSA} and *T* values allowed us to use the approximation sin(*x*) = *x* to simplify *Eq. 5*, as follows: (6) If breathing is the modulator, and the frequency *F*_{RSA} and the amplitude *c*_{RSA} of the oscillating modulation are *F*_{R} and αV_{T}/2, respectively, (where α is a coefficient), then *Eq. 6* can be simplified to the following: (7) *A*_{RSA} was examined in absolute (ms) and relative (percentage of the total spectrum) units.

ECG preprocessing was performed using Matlab software 6.0 R12 (MathWorks; Natick, MA).

### Statistical Analysis

In *experiment n°1*, individual relationships between the dynamic evolutions of *F*_{RSA} and *F*_{R} were tested by calculating Pearson correlation coefficients (*r*) on raw data. The means and 95% confidence intervals of individual *F*_{R}, V_{T}, V̇_{I}, *F*_{RSA}, and *A*_{RSA} profiles were constructed as a function of percent V̇o_{2peak}. Differences between notable points in the *A*_{RSA} profile were tested using a paired Student’s *t*-test. A polynomial fitting of the 10th order was applied to the time-varying evolution of *A*_{RSA}, *F*_{R}, V_{T}, and V̇_{I}. From these obtained data, individual relationships between *A*_{RSA} on the one hand and *F*_{R}, V_{T}, and V̇_{I} on the other hand were tested by calculating *r* values. Results are expressed as means ± SD.

In *experiment n°2*, the effects of hypo-, normo-, and hyperventilation on V̇_{I}, V_{T}, HP, *A*_{RSA,} *c*_{RSA}, Pet_{CO2}, and Pet_{O2} were tested using one-way repeated-measures ANOVA, and protected least-significant difference (PLSD) post hoc comparisons were performed when appropriate. Similarly, the effects of *F*_{R} and V_{T} combinations (normoventilation, steady V̇_{I1} and steady V̇_{I2} sessions) on V̇_{I}, V_{T}, HP, *A*_{RSA,} *c*_{RSA}, Pet_{CO2}, and Pet_{O2} were tested using one-way repeated-measures ANOVA, and PLSD post hoc comparisons were performed when appropriate. Comparisons of the α-coefficient obtained from the five rectangular exercise bouts were performed using one-way repeated-measures ANOVA. To test the relationship between *A*_{RSA} and V̇_{I}, V_{T}, Pet_{CO2}, and Pet_{O2}, all hypo-, normo-, and hyperventilation data were pooled, and linear regression analysis was performed. To test the relationship between *c*_{RSA} and V_{T}, results obtained during all five ventilation conditions were pooled, and linear regression analysis was performed. In these two analyses, ventilatory and RSA components units were normalized (100% corresponding to the value obtained during the normoventilation session). Statistical analysis was performed using Statistica software 5.5 (Statsoft; Tulsa, OK). Statistical significance was set at *P* < 0.05. Results are means ± SD.

## RESULTS

### Values at Rest

Baseline O_{2} consumption, V_{T}, V̇_{I}, and HP were 0.42 ± 0.05 l/min, 0.74 ± 0.11 liters, 8.5 ± 1.9 l/min, and 789.2 ± 81.0 ms, respectively. *F*_{RSA} and *F*_{R} were similar and centered at 0.20 ± 0.05 Hz, and *A*_{RSA} was 51.6 ± 19.2 ms.

### Graded Exercise Test

All subjects completed the exercise test without any clinical abnormalities or discomfort. O_{2} consumption at the start of exercise represented 29.5 ± 5.8% of V̇o_{2peak}. Mean HP and its global variability decreased from low to mild exercise, whereas the variability increased during the highest intensities (see example in Fig. 1). Consistent with the variability decrease, the overall amplitude of HPV decreased with exercise in an exponential-like shape, whereas it increased during the highest intensities (see example in Fig. 1*C*).

A conspicuous high-frequency oscillation synchronous with the *F*_{R} was found in all recordings, clearly indicating the persistence of RSA over the entire graded and maximal exercise protocol (see example in Fig. 2). The dynamic evolutions of *F*_{RSA} and *A*_{RSA} were accurately extracted from the HP series, and *F*_{RSA} positively correlated (*r* = 0.97 ± 0.03, *P* < 0.01) with *F*_{R}. Means and 95% confidence intervals of individual V̇_{I}, V_{T}, *F*_{R}, *F*_{RSA}, and *A*_{RSA} profiles are shown in Fig. 3.

In regard to the amplitude, the lowest *A*_{RSA} value was measured at 61.9 ± 3.8% V̇o_{2peak} (hereafter called the “minimal point”). At this minimal point, the mean HP was 384 ± 38.4 ms. From rest to the start of exercise, *A*_{RSA} quickly decreased (51.6 ± 19.2 vs. 21.3 ± 9.7 ms, *P* < 0.01). *A*_{RSA} then dynamically varied in relation to the exercise load, and two different patterns emerged (Fig. 3*A*). From the start of exercise to the minimal point, *A*_{RSA} dramatically decreased (21.3 ± 9.7 vs. 0.7 ± 0.3 ms, *P* < 0.01). *A*_{RSA} then demonstrated a significant increase (0.7 ± 0.3 vs. 6.4 ± 3.2 ms, *P* < 0.01) up to the maximal workload in 11 subjects. In the three remaining subjects, *A*_{RSA} increased, but its maximum value was reached between 77.6% and 85.8% of V̇o_{2peak}. *A*_{RSA} then remained constant in two subjects and decreased in one subject up to peak exercise. In all cases, *A*_{RSA} represented the main oscillation of HPV at peak exercise and accounted for 61.3 ± 10.4% to the total spectrum.

Moreover, from the minimal point to peak exercise, *A*_{RSA} positively correlated with V̇_{I} (*r* = 0.76, *P* < 0.01), V_{T} (*r* = 0.79, *P* < 0.01), and *F*_{R} (*r* = 0.74, *P* < 0.01).

### Rectangular Exercise Test

No statistical difference was observed between HP measured in every condition. Mean HP was 344.3 ± 2.1 ms. In all recordings, a conspicuous RSA was identified, and *F*_{RSA} and *A*_{RSA} were accurately extracted (see example in Fig. 4). Mean *A*_{RSA}, *c*_{RSA}, V̇_{I}, V_{T}, Pet_{O2}, and Pet_{CO2} are shown in Fig. 5. Compared with normoventilation, hypo- and hyperventilation regimens led to an *A*_{RSA} decrease and increase, respectively. On the other hand, when V̇_{I} was kept constant, *A*_{RSA} was constant, whatever the imposed values of *F*_{R} and V_{T} (Fig. 5*A*). When the results from hypo-, normo-, and hyperventilation exercise bouts were pooled, *A*_{RSA} significantly correlated to V̇_{I} and V_{T} (*r* = 0.99, *P* < 0.01; Fig. 6). Indeed, when V̇_{I} and V_{T} are expressed in normalized units, V̇_{I} = V_{T} because *F*_{R} is constant. Moreover, significant positive and negative correlations were found between *A*_{RSA} and Pet_{O2} (*r* = 0.93, *P* < 0.01) and *A*_{RSA} and Pet_{CO2} (*r* = −0.91, *P* < 0.01), respectively. When the results from all five rectangular exercise bouts were pooled, significant correlations were found between *c*_{RSA} and V_{T} (r = 0.94, *P* < 0.01; Fig. 7). The comparison of the α-coefficients obtained from all five rectangular exercise bouts showed no statistical difference.

## DISCUSSION

During exercise, spectral analysis of HPV has highlighted that RSA represents the main mechanism regulating short-term HP fluctuations. This is particularly true when the highest exercise intensities are considered (4, 27, 28). Nevertheless, accurate data about RSA under exercise conditions are scarce. This may be explained by the fact that spectral approaches typically require HP stationarity (rarely encountered during exercise) and by the difficulty of controlling respiratory patterns in humans during exercise. This is the reason why we have developed and validated an original method of HPV and RSA assessment during nonstationary exercise conditions (25). In the present study, this method was tested to process cardiac signals during a maximal and graded exercise test and during a series of rectangular exercise bouts.

Our results showed that the dynamic pattern of the frequency and the amplitude of RSA can be accurately extracted from R-R interval series obtained during a graded and maximal exercise test. To the best of our knowledge, this is the first study to show accurate and time-varying quantification of RSA amplitude in nonstationary exercise conditions.

### F_{RSA} Is Linked to F_{R}

During a graded and maximal exercise test, RSA and breathing dynamically developed at the same frequency. This result confirms previous findings (2, 4, 9) that showed that during exercise, the sinus node activity is modulated by breathing at a frequency that corresponds to *F*_{R}. It has been suggested that breathing-related changes in the cardiac axis (mean direction of the wave of ventricular depolarization in the vertical plane) may induce changes in the shape of the QRS complex and thus in the measure of the R-R interval (34). This could be responsible for the small degree of RSA seen in patients after heart transplant (34). After having tested our raw data with the methods previously described (4, 9), we confirm that the persistence of RSA during exercise is not attributable to a modulation of the cardiac axis direction and the QRS complex. Thus the time-frequency method of signal processing used in this study may help in providing reliable information on respiratory patterns, without respiratory measurement devices, when very accurate measures are not required. For instance, extraction of respiratory frequencies from HP series may be helpful to the noninvasive determination of the anaerobic threshold (2) in field tests, where nonstationary exercise conditions are frequent.

### A_{RSA} Decreases at Low and Medium Workloads

The reduction in *A*_{RSA} observed in the present study could be explained by a progressive vagal tone withdrawal. Indeed, this finding concurs with previous works (12, 13, 32, 33) that reported that an exercise-induced reduction of the vagal control of the heart helped to adapt to the cell metabolic demand. Warren et al. (39) stated that the measurement of RSA provided a reliable index of cardiac vagal activity during exercise. When the relation of “RSA amplitude/exercise intensity” was constructed, these authors reported that glycopyrrolate, a muscarinic antagonist, significantly reduced RSA amplitude up to exercise intensities corresponding to 62.1% of V̇o_{2peak}. Above this intensity, muscarinic blockade did not affect the RSA amplitude. It is interesting to note that this threshold value is very close to our 61.9 ± 3.8% of V̇o_{2peak}. However, using RSA amplitude as an index of the vagal withdrawal during exercise remains questionable, because it has been shown, using ganglion blockade (9), that the contribution of nonneural mechanisms to the RSA power was ∼33% when exercising at 25% of V̇o_{2peak}. Considering those results, one may state that the decrease observed in *A*_{RSA} reported in our study is linked to the progressive vagal tone withdrawal, even though this index probably overestimates the cardiac vagal control.

### A_{RSA} Persists and Increases at High Workload

When compared with the value measured at the minimal point, *A*_{RSA} showed, in most of the subjects, an 814% increase at V̇o_{2peak}. In three subjects, *A*_{RSA} increased from the minimal point, but its maximum was observed before V̇o_{2peak}. In these cases, this phenomenon cannot be linked to a ventilation decrease because V̇_{I} tended to increase up to peak exercise. Such a phenomenon may be explained by a poorly structured ventilatory pattern, with very short-term changes in V_{T} and *F*_{R}. However, the overall HPV increase observed during intense exercise (see Fig. 1) was consistent with an *A*_{RSA} increase. Thus, at peak exercise, RSA accounted for ∼61.3% of the total spectrum and became the main oscillation contributing to HPV. To the best of our knowledge, our study is the first to report an increase of RSA in absolute units (ms) during exercise. Previous studies (4, 9, 27, 28) have pointed out the persistence of RSA in relative units (relative prevalence of the RSA spectral component over the low-frequency spectral component, expressed as a percent). However, an increase of the relative amplitude of RSA does not necessarily mean an increase in the modulating effect of respiration on the sinus node activity, but only a higher RSA contribution to the total spectrum. When expressed in absolute units, those studies failed to detect a consistent RSA increase. This may be explained by the lack of sensitivity and specificity of the classical spectral methods. In those studies, the high-frequency band upper limit has frequently been extended to 0.8 or 1 Hz to capture RSA at the high *F*_{R} observed during intense exercise. Such rigid and wide frequency ranges that are not physiologically relevant do not take into account interindividual differences in the respiratory pattern (8) and may add noise in the spectral power evaluation as well. The presently reported signal processing method may overcome some of the common limitations of spectral analysis during exercise.

We have shown that over 61.9 ± 3.8% of V̇o_{2peak}, modulation of *A*_{RSA} by breathing was a continuous phenomenon and an increase in ventilation proportionally increased RSA. Breathing affects the cardiovascular system, either directly (mechanical effects) or indirectly (neurally mediated effects). The RSA persistence and increase during intense exercise observed in this study cannot be linked to vagal activity, because it is common knowledge that vagal influence on HP is abolished during intense exercise (12, 13, 32, 33, 38). Moreover, it has been demonstrated that muscarinic blockade did not attenuate RSA power spectrum at intensities corresponding to 62.1% of V̇o_{2peak} (39). The alternative hypothesis of a sympathetic contribution to our observed *A*_{RSA} increase is unlikely because the sympathetic nervous system responds too slowly to mediate HP fluctuations in the respiratory frequency range (1). Thus the most likely hypothesis that can be drawn from our results obtained during intense exercise is the enhancement of a nonneural mechanism in response to the V̇_{I} increase. Indeed, those results support the existence of a periodic stretching of the sinus node secondary to changes in atrial transmural pressure with breathing. This phenomenon has been previously pointed out from data obtained from animals after vagotomy (6, 29) and suggested in humans from data obtained during exercise in heart transplant subjects (4). Briefly, the breathing-induced changes in thoracic pressure will influence the right ventricle preload via an increase or decrease of the systemic venous return to the right heart (11). The observed increase of the right ventricle filling, in the case of inspiration, increases atrial transmural pressure and stretches myocardial tissue and sinus node, thus activating positive chronotropic response via mechanosensitive Cl^{−} channels (3, 15). Therefore, exercising at high intensity could enhance this mechanical stretch (4) via an increased ventilation.

The aim of the second experiment was to determine the respective contributions of V̇_{I}, V_{T}, and *F*_{R} to *A*_{RSA} during exercise, in connection to the sinus node stretching hypothesis. The use of muscarinic blockade, such as by atropine or glycopyrrolate, would be of interest. This pharmacological intervention was not used in our study because administration of muscarinic blockade during intense exercise may place the subject at risk during the exercise or the recovery period and is ethically questionable. To overcome such limitations, the exercise intensity was fixed at 70% V̇o_{2peak} to make sure that vagal influence on both the heart activity and the RSA amplitude was abolished, as previously suggested by numerous studies using muscarinic blockade (12, 13, 32, 33, 39). We have then shown that *A*_{RSA} was proportionally increased or reduced by a respective increase or decrease in V_{T} when *F*_{R} was kept constant, suggesting a direct influence of the degree of lung inflation on *A*_{RSA}. Our results confirm that, during exercise, there is the same direct link between RSA and breathing in humans as the one observed in the vagotomized animal at rest (6, 29). Moreover, our findings are consistent with the results obtained during exercise in heart transplant patients or individuals under ganglion blockade (4, 9). One should expect that the high V_{T} in the hyperventilation session increases blood flow return to the right heart and the degree of stretch of the sinus node and so RSA. In the present study, the voluntary hypo- and hyperventilation altered Pet_{O2} and Pet_{CO2}. Pet_{CO2} was increased during the hypoventilation session and associated with a lower *A*_{RSA}. This finding is different from results obtained in conscious and resting humans, where an increase in *A*_{RSA} was reported during hypercapnia (31, 35). Sasano et al. (35) stated that the hypercapnic-induced RSA increase improves the pulmonary gas exchange to facilitate CO_{2} elimination. This phenomenon is probably mediated by an increased respiratory modulation of vagal outflow (31, 35). The exercise-induced vagal withdrawal can explain the difference between results obtained at rest and during intense exercise. Moreover, our data are consistent with previous findings in vagotomized animals where *A*_{RSA} did not depend on CO_{2} (29). Although further studies on the topic are needed, our results suggest that influences (if any) of Pco_{2} on *A*_{RSA} during exercise are different from those observed at rest.

In the constant V̇_{I} tests, we have shown that *A*_{RSA} remained unchanged whatever the values of *F*_{R} and V_{T} (Fig. 5). These results suggest that both the frequency and degree of lung inflation are important determinant of the RSA persistence and increase during exercise. At rest, V_{T} and *F*_{R} alter RSA amplitude in opposite directions: RSA amplitude is higher at high V_{T} and lower at high *F*_{R} (17). However, the results obtained during exercise conditions were different, because we have shown that *A*_{RSA} was constant when the combinations of “high V_{T}-low *F*_{R}” and “low V_{T}-high *F*_{R}” produced similar V̇_{I}. If we consider that ventilation exerts mechanical stretch of the sinus node, as previously suggested (29), *A*_{RSA} depends on the combination of the frequency and degree of stretch rather than the absolute degree of stretch. Similar results have been observed in the vagotomized rabbit, using dextran infusion (29), and concur with previous findings (7, 20) where rapid stretch was observed to cause greater chronotropic response than slow stretch, even though the force or displacement induced by stretch was identical. An intrinsic effect of the rate of development of lung pressure changes (i.e., the time spent with high or low lung pressures) on *A*_{RSA} cannot be discarded and may represent a methodological limitation of our study design. However, such sophisticated control of lung pressure regimen is impossible in conscious humans during exercise and may require artificial ventilation in anesthetized subjects under pharmacological influences.

It is interesting to note that our second experiment results matched the mathematical model we developed to study RSA in nonstationary conditions. Indeed, if breathing is the modulator, *Eq. 6* (see methods) reads *A*_{RSA} ≈ *T*^{2}(αV_{T}/2)*F*_{R} ≈ *T*^{2}(αV̇_{I}/2). Considering a constant mean HP (which is true in our second experiment), when V̇_{I} = V_{T} × *F*_{R} = constant, *A*_{RSA} is nearly constant, which concurs with results from the second experiment. Moreover, because α-coefficients were similar over the five different experimental conditions tested, *c*_{RSA} could provide reliable information on the V_{T} pattern. This last hypothesis is partly confirmed by the positive correlation found between *c*_{RSA} and V_{T} values after all conditions were pooled from the second experiment. These findings confirm that the approach we developed is a good candidate for RSA modeling at exercise.

Mechanical stretch of the sinus node, in response to ventilation increase, was suggested to explain RSA persistence during exercise intensity, where the vagal activity is known to be abolished. Our original approach of RSA dynamic tracking during graded and maximal exercise test confirmed RSA persistence over all exercise intensities. By measuring the influences of different respiratory regimens on RSA during submaximal rectangular exercise bouts, we then showed that *A*_{RSA} was closely linked to respiratory flow, because *A*_{RSA} was constant when respiratory flow was constant whatever *F*_{R} or V_{T}. Thus the respiratory contribution to RSA is likely to vary according to both the frequency and degree of lung inflation.

## Acknowledgments

We thank Nicolas Scronias and Benjamin Biguer from the Brainware Company (Toulon, France) for the technical support.

## Footnotes

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- Copyright © 2005 by the American Physiological Society