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Abstract We use recent developments in heart rate
dynamic estimation to detrend athlete’s heart rate measured
during effort tests and study how heart rate variability (HRV)
changes during exercise, in a sample of 18 young athletes. RR
interval standard deviation decays exponentially with the heart
rate, and the decay rate is linked with physical fitness.
Heart rate variability (HRV) has been employed mainly at
rest as a marker of potential cardiac diseases [1] or as a
measure of training and physical fitness [2]. Although HRV
dynamics during exercise has been the subject of theoretical
developments [3] and may be a marker of physical condition
as well [4], few studies have focused on the experimental
evolution of HRV during exercise and its potential link with
training or physical condition. Decrease of the standard
deviation of RR intervals (the time between successive R
waves of the electrocardiogram) during exercise has been
reported [5], but a clear analysis of this evolution is still
lacking [6]. Using a simple first order differential equation to
estimate the mean heart rate (HR) dynamics during
incremental exercise as a function of the exercise load, we
study how the obtained stationary fluctuations of HR evolve
during the effort test, and estimate how fitness influence such
variable Mean value (sd)
Number of subjects 18
age (year) 15.22 (1.96)
Weight (kg) 64.76 (15.55)
Height (cm) 173.28 (10.45)
VO2 max (mL/kg) 39. 06 (7.51)
Maximum power (W) 235.00 (60.2 2)
Table 1: characteristic of t he studied group
18 young athletes (10 males and 8 females; 15.2 2 year-
old, Table 1) of the Regional Physical and Sports Education
Centre (CREPS) of French West Indies (Guadeloupe,
France), performed an incremental testing on a SRM Indoor
Trainer electronic cycloergometer. It consisted in a 3 minutes
*Research supported by the SNSF scientific exchange grant
IZSEZ0_183540 and the ICARUS SNSF fund 100019_166010
1 Quality of Care Unit, University Hospitals of Geneva, Geneva,
2 ACTES laboratory, UPRES-EA 35 96 UFR -STAPS, University o f the
French West Indies, Guadeloupe, France.
3 Departamento de Fisica Aplicada II, E.T.S.I. de Telecomunicacíon,
Universidad de Málaga, Málaga, Spain
rest phase, followed by a 3 min cycling period at 50 watts
and an incremental power testing of +15 Watts by minute
until exhaustion.
Although the use of simple linear detrending is often used to
study HRV [7], we propose here to use recent developments
in dynamical analysis to model the non-stationary
component of HR. As already proposed for oxygen
consumption [8] and for heart rate [9], the main trend of
heart rate dynamic during an incremental effort test can be
modeled by a simple first order differential equation as
 (equation 1)
where 
is the time derivative of the heart rate HR, is
the characteristic exponential decay time of such first order
differential equation,  the resting heart rate, the work
load (in Watt) during the step of the incremental effort test,
the associated gain, i.e. the ratio between the HR steady
state increase and the power increase of step that caused it,
and the number of power steps during the effort test. The
mean HR trend that such model can produce has the
advantage of relying only on experimental data (HR and
workload) and not on any user parameter.
Figure 1. Measured RR interval during an incremental maximal effort
test, its estimation by a first or der differential equation, and the resulting
detrended RR serie
To estimate the coefficients of equation 1, we used a two-
step procedure similar to the one developed by Boker and
co-authors [10], consisting in first estimating the HR time-
derivative by the means of a spline regression, to then
estimate equation 1 as a linear mixed effect regression. Each
set of estimated individual parameter and workload is used
to generate an estimated HR and RR curve, which is used to
detrend the data. An example of the final estimate of our
procedure is shown in Figure 1, together with the resulting
Changes of heart rate variability during exercise
D. Mongin
, C. Chabert
, M. Gomez Extremera
, O. Hue
, D. S. Courvoisier
, P. Carpena
P. A. Bernaola Galvan3
Authorized licensed use limited to: Universite de Geneve. Downloaded on August 05,2020 at 08:15:08 UTC from IEEE Xplore. Restrictions apply.
detrended data. The dynamical model used produces an
individual estimation of RR with a median R2 of 0.93 over
the athletes [IQR: 0.87 – 0.95]. HRV
A. Mean trend
The analysis of HRV consisted in the computation of SDRR
for each power step of the effort test. It has been reported [6]
that the logarithm of SDRR (ln-SDRR) display a “somewhat
linear decrease” as a function of exercise intensity
(expressed as percentage of VO2 max, see figure 2).
Because HRV is a result of both parasympathetic and
sympathetic neuronal activity that both take part in the
regulation of the mean HR, we propose to display SDRR on
a logarithmic scale as a function of the corresponding mean
heart rate, normalized by its maximum value (see Figure 2).
A linear regression of ln-SDRR as a function of the
normalized HR leads to an R2 of 0.80 and an AIC of 294, to
be compared to AIC = 389 and R2= 0.71 obtained with the
regression between ln-SDRR and the exercise intensity.
Figure 2. mean SDRR (in log scale) for each power step, as a function of
Exercise intensity (left) and normalized HR (right).
The evolution of the SDRR is thus better explained by the
heart rate itself, following the model:
   !"
!"#$%&'& (equation 2)
B. Link with physical fitness
We are interested in studying how the parameter a
(Equation 2), i.e. the characteristic scale of HRV decreasing,
is linked with fitness. Performing a nonlinear regression of
equation 2 on the entire SDRR dataset yields a global value
of a =()*)+,  )*))-- (p < 10-6), meaning that an increase
of HR of 15% of its maximum value will decrease SDRR by
a bit more than one order of magnitude each effort test.
Doing the same for each individual effort test allow us to
determine the individual coefficients a of equation 2.
Strikingly, a is inversely correlated with VO2 max (.
()*//01  )*)23), maximum aerobic power reached during
the effort test (.  &()*+30 1  )*))42), and also with the
first and second ventilatory thresholds (.  &()*+)01 
)*))35 and . &()*/401  )*)43 respectively). These
results indicate that individuals with better physical
condition tend to have a faster decrease of their heart rate
variability with their heart rate increase during the effort test.
Among young athletes, the main factor predicting the change
of beat to beat variability before, during and after an
incremental exercise is the normalized HR. The standard
deviation of the RR time observed decreases exponentially
with the heart rate increase, and this exponential decrease
of HRV with HR increase is faster for trained subjects.
Similarly to the well-known faster parasympathetic
reactivation observed for trained subject after effort [2], this
result may find its origin in a greater parasympathetic
deactivation during effort implying a quicker
sympathetic/parasympathetic equilibrium for trained person.
The novel approach presented should be further applied to
diverse population (e.g., different age, untrained persons)
and other types of effort, to explore the universality of HRV
change observed and its link with physical fitness.
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Full-text available
Cardiac parasympathetic activity may be non-invasively investigated using heart rate variability (HRV), although HRV is not widely accepted to reflect sympathetic activity. Instead, cardiac sympathetic activity may be investigated using systolic time intervals (STI), such as the pre-ejection period. Although these autonomic indices are typically measured during rest, the “reactivity hypothesis” suggests that investigating responses to a stressor (e.g., exercise) may be a valuable monitoring approach in clinical and high-performance settings. However, when interpreting these indices it is important to consider how the exercise dose itself (i.e., intensity, duration, and modality) may influence the response. Therefore, the purpose of this investigation was to review the literature regarding how the exercise dosage influences these autonomic indices during exercise and acute post-exercise recovery. There are substantial methodological variations throughout the literature regarding HRV responses to exercise, in terms of exercise protocols and HRV analysis techniques. Exercise intensity is the primary factor influencing HRV, with a greater intensity eliciting a lower HRV during exercise up to moderate-high intensity, with minimal change observed as intensity is increased further. Post-exercise, a greater preceding intensity is associated with a slower HRV recovery, although the dose-response remains unclear. A longer exercise duration has been reported to elicit a lower HRV only during low-moderate intensity and when accompanied by cardiovascular drift, while a small number of studies have reported conflicting results regarding whether a longer duration delays HRV recovery. “Modality” has been defined multiple ways, with limited evidence suggesting exercise of a greater muscle mass and/or energy expenditure may delay HRV recovery. STI responses during exercise and recovery have seldom been reported, although limited data suggests that intensity is a key determining factor. Concurrent monitoring of HRV and STI may be a valuable non-invasive approach to investigate autonomic stress reactivity; however, this integrative approach has not yet been applied with regards to exercise stressors.
Full-text available
Background Autonomic regulation of heart rate (HR) as an indicator of the body’s ability to adapt to an exercise stimulus has been evaluated in many studies through HR variability (HRV) and post-exercise HR recovery (HRR). Recently, HR acceleration has also been investigated. Objective The aim of this systematic literature review and meta-analysis was to evaluate the effect of negative adaptations to endurance training (i.e., a period of overreaching leading to attenuated performance) and positive adaptations (i.e., training leading to improved performance) on autonomic HR regulation in endurance-trained athletes. Methods We searched Ovid MEDLINE, Embase, CINAHL, SPORTDiscus, PubMed, and Academic Search Premier databases from inception until April 2015. Included articles examined the effects of endurance training leading to increased or decreased exercise performance on four measures of autonomic HR regulation: resting and post-exercise HRV [vagal-related indices of the root-mean-square difference of successive normal R–R intervals (RMSSD), high frequency power (HFP) and the standard deviation of instantaneous beat-to-beat R–R interval variability (SD1) only], and post-exercise HRR and HR acceleration. Results Of the 5377 records retrieved, 27 studies were included in the systematic review and 24 studies were included in the meta-analysis. Studies inducing increases in performance showed small increases in resting RMSSD [standardised mean difference (SMD) = 0.58; P < 0.001], HFP (SMD = 0.55; P < 0.001) and SD1 (SMD = 0.23; P = 0.16), and moderate increases in post-exercise RMSSD (SMD = 0.60; P < 0.001), HFP (SMD = 0.90; P < 0.04), SD1 (SMD = 1.20; P = 0.04), and post-exercise HRR (SMD = 0.63; P = 0.002). A large increase in HR acceleration (SMD = 1.34) was found in the single study assessing this parameter. Studies inducing decreases in performance showed a small increase in resting RMSSD (SMD = 0.26; P = 0.01), but trivial changes in resting HFP (SMD = 0.04; P = 0.77) and SD1 (SMD = 0.04; P = 0.82). Post-exercise RMSSD (SMD = 0.64; P = 0.04) and HFP (SMD = 0.49; P = 0.18) were increased, as was HRR (SMD = 0.46; P < 0.001), while HR acceleration was decreased (SMD = −0.48; P < 0.001). Conclusions Increases in vagal-related indices of resting and post-exercise HRV, post-exercise HRR, and HR acceleration are evident when positive adaptation to training has occurred, allowing for increases in performance. However, increases in post-exercise HRV and HRR also occur in response to overreaching, demonstrating that additional measures of training tolerance may be required to determine whether training-induced changes in these parameters are related to positive or negative adaptations. Resting HRV is largely unaffected by overreaching, although this may be the result of methodological issues that warrant further investigation. HR acceleration appears to decrease in response to overreaching training, and thus may be a potential indicator of training-induced fatigue.
Full-text available
In this paper, an approach for heart rate variability analysis during exercise stress testing is proposed based on the integral pulse frequency modulation (IPFM) model, where a time-varying threshold is included to account for the nonstationary mean heart rate. The proposed technique allows the estimation of the autonomic nervous system (ANS) modulating signal using the methods derived for the IPFM model with constant threshold plus a correction, which is shown to be needed to take into account the time-varying mean heart rate. On simulations, this technique allows the estimation of the ANS modulation on the heart from the beat occurrence time series with lower errors than the IPFM model with constant threshold (1.1% ± 1.3% versus 15.0% ± 14.9%). On an exercise stress testing database, the ANS modulation estimated by the proposed technique is closer to physiology than that obtained from the IPFM model with constant threshold, which tends to overestimate the ANS modulation during the recovery and underestimate it during the initial rest.
Measurements of oxygen uptake are central to methods for the assessment of physical fitness and endurance capabilities in athletes. Two important parameters extracted from such data of incremental exercise tests are the maximal oxygen uptake and the critical power. A commonly accepted model of the dynamics of oxygen uptake during exercise at a constant work rate comprises a constant baseline oxygen uptake, an exponential fast component, and another exponential slow component for heavy and severe work rates. We have generalized this model to variable load protocols with differential equations that naturally correspond to the standard model for a constant work rate. This provides the means for predicting the oxygen uptake response to variable load profiles including phases of recovery. The model parameters have been fitted for individual subjects from a cycle ergometer test, including the maximal oxygen uptake and critical power. The model predictions have been validated by data collected in separate tests. Our findings indicate that the oxygen kinetics for a variable exercise load can be predicted using the generalized mathematical standard model. Such models can be applied in the field where the constant work rate assumption generally is not valid.
Models from dynamical systems theory were fit to the intraindividual variability In adolescent self-reported cigarette and alcohol use. A dampened linear oscillator model (potentially like a pendulum with friction) and a nonlinear oscillator model with two attractors were compared. The nonlinear oscillator model and two coupled oscillators for cigarette and alcohol use were rejected. Independent dampened linear oscillators for smoking and drinking provided high internal R2 but were unable to account for a substantial correlation between the acceleration in cigarette usage and alcohol usage; thus evidence was found for an intrinsic self-regulation mechanism in both smoking and drinking behavior, but the hypothesis was rejected that the intrinsic mechanism leading to increases in use in one substance directly predicted increased use in the other substance. Given the hypothesis of independent linear oscillators, the sign of the dampening parameter was found to be positive, indicating a system with dynamic instability; a self-regulation mechanism in which small changes in substance use lead to amplified changes after a short period of time.
Beat-to-beat heart rate (HR) dynamics were studied by plotting each R-R interval as a function of the previous R-R interval (Poincaré plot) during incremental doses of atropine followed by exercise for 10 subjects and during exercise without autonomic blockade for 31 subjects. A quantitative two-dimensional vector analysis of a Poincaré plot was used by measuring separately the standard deviation of instantaneous beat-to-beat R-R interval variability (SD1) and the standard deviation of continuous long-term R-R interval variability (SD2) as well as the SD1/SD2 ratio. Quantitative Poincaré measures were compared with linear measures of HR variability (HRV) and with approximate entropy (ApEn) at rest and during exercise. A linear progressive reduction was observed in SD1 during atropine administration, and it remained almost at the zero level during exercise after a parasympathetic blockade. Atropine resulted in more variable changes in SD2 and the SD1/SD2 ratio, but during exercise after parasympathetic blockade, a progressive increase was observed in the SD1/SD2 ratio until the end of exercise. The SD1/SD2 ratio had no significant correlations with the frequency domain measures of HRV. However, the SD1/SD2 ratio had a modest correlation with ApEn at rest (r = -0.69, P < 0.001), but not during exercise (r = 0.27, P = NS). All measures of vagal modulation of HR decreased progressively until the ventilatory threshold level was reached, when sympathetic activation was reflected as changes in the SD1/SD2 ratio. These results show that quantitative two-dimensional vector analysis of a Poincaré plot can provide useful information on vagal modulation of R-R interval dynamics during exercise that are not easily detected by linear summary measures of HRV or by ApEn.
Patients with chronic heart failure (CHF) have a continuing high mortality. Autonomic dysfunction may play an important role in the pathophysiology of cardiac death in CHF. UK-HEART examined the value of heart rate variability (HRV) measures as independent predictors of death in CHF. METHODS and In a prospective study powered for mortality, we recruited 433 outpatients 62+/-9.6 years old with CHF (NYHA functional class I to III; mean ejection fraction, 0.41+/-0.17). Time-domain HRV indices and conventional prognostic indicators were related to death by multivariate analysis. During 482+/-161 days of follow-up, cardiothoracic ratio, SDNN, left ventricular end-systolic diameter, and serum sodium were significant predictors of all-cause mortality. The risk ratio for a 41.2-ms decrease in SDNN was 1.62 (95% CI, 1.16 to 2.44). The annual mortality rate for the study population in SDNN subgroups was 5.5% for >100 ms, 12.7% for 50 to 100 ms, and 51.4% for <50 ms. SDNN, creatinine, and serum sodium were related to progressive heart failure death. Cardiothoracic ratio, left ventricular end-diastolic diameter, the presence of nonsustained ventricular tachycardia, and serum potassium were related to sudden cardiac death. A reduction in SDNN was the most powerful predictor of the risk of death due to progressive heart failure. CHF is associated with autonomic dysfunction, which can be quantified by measuring HRV. A reduction in SDNN identifies patients at high risk of death and is a better predictor of death due to progressive heart failure than other conventional clinical measurements. High-risk subgroups identified by this measurement are candidates for additional therapy after prescription of an ACE inhibitor.
Heart rate variability (HRV) is a non-invasive indicator of cardiac autonomic modulation at rest. During rhythmic exercise, global HRV decreases as a function of exercise intensity. Measures reflecting sympathovagal interactions at rest do not behave as expected during exercise. This makes interpretation of HRV measures difficult, especially at higher exercise intensities. This problem is further confounded by the occurrence of non-neural oscillations in the high-frequency band due to increased respiratory effort. Alternative data treatments, such as coarse graining spectral analysis (CGSA), have demonstrated expected changes in autonomic function during exercise with some success. The separation of harmonic from fractal and/or chaotic components of HRV and study of the latter during exercise have provided further insight into cardioregulatory control. However, more research is needed. Some cross-sectional differences between HRV in athletes and controls during exercise are evident and data suggest longitudinal changes may be possible. Standard spectral HRV analysis should not be applied to exercise conditions. The use of CGSA and non-linear analyses show much promise in this area. Until further validation of these measures is carried out and clarification of the physiological meaning of such measures occurs, HRV data regarding altered autonomic control during exercise should be treated with caution.
Dynamics of Return to Equilibrium During Multiple Inputs
  • D Mongin
  • A Uribe
  • D Courvoisier
D. Mongin, A. Uribe, and D. Courvoisier, 'doremi: Dynamics of Return to Equilibrium During Multiple Inputs', 2019. [Online].