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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.

I. INTRODUCTION

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

dynamics.

II. POPULATION

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,

Switzerland

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.

III. DETRENDING

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

follow:

(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

1

, C. Chabert

2

, M. Gomez Extremera

3

, O. Hue

2

, D. S. Courvoisier

1

, P. Carpena

3

,

P. A. Bernaola Galvan3

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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.

IV. CONCLUSION

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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