Abstract Ventilatory thresholds (VT1 and VT2

A Benítez

F Rodríguez

J M Padullés

M A García-González

M Marina

R Angulo

R Bescós

X Iglesias

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Ventilatory Threshold Prediction by Spectral Analysis of Heart Rate Variability 
in Incremental Maximal Tests 
A Benítez1,2, M A García-González1, R Angulo2, F Rodríguez2, X Iglesias2, R Bescós2, M Marina2, J 
M Padullés2 
1Group of Biomedical and Electronic Instrumentation. Department of Electronic Engineering, 
Technical University of Catalonia (UPC), Barcelona, Spain 
2National Physical Education Institute of Catalonia, University of Barcelona (UB), Barcelona, 
Spain 
Abstract 
Ventilatory thresholds (VT1 and VT2) are useful in 
many fields of medicine and sports. Nevertheless, their 
measurement is cumbersome and needs trained 
personnel. This work proposes an alternative method to 
predict VT1, VT2 and maximum loads in incremental 
maximal tests based on heart rate variability (HRV) 
analysis. Twelve competitive male cyclists executed an 
incremental exhaustive test. During the test, RR time 
series and gas concentrations were recorded. After 
artifact correction the power spectrum was estimated in a 
sliding window, and central frequency (CF) and 
bandwidth that contains half the total power (BW) were 
computed. An automatic algorithm recognized the loads 
where CF and BW undergo a significant change. These 
loads were used as inputs in linear regression models to 
predict VT1, VT2 and maximum loads. The errors of the 
predictions are similar to the load resolution. 
 
1. Introduction 
The estimation of the First and Second Ventilatory 
Thresholds (VT1 and VT2) is useful in many fields in 
medicine and sport, like cardiac or pulmonary therapy or 
enables to program an endurance sport season [1]. 
VT1 and VT2 are assessed during a maximal 
incremental test with a gas analyzer [2]. VT1 is the 
ventilatory threshold and VT2 is the threshold of 
decompensated metabolic acidosis. VT1 is determined 
visually by an expert as the point where VE’/VO2’ 
increases nonlinearly while VE’/VCO2’ remains constant; 
and VT2 is the point where VCO2’ increases nonlinearly 
with respect to VO2’ (being VE’ the respiratory flow, VO2’ 
oxygen consumption and VCO2’ the carbon dioxide 
production). 
VT1 and VT2 assessment is cumbersome because a 
gas analyzer and trained personnel are needed. During an 
incremental test it is very common to measure, 
simultaneously with gas concentrations, the heart rate or 
the electrocardiogram. These measurements enable us to 
obtain the RR time series for further analysis of heart rate 
variability (HRV).  
VT2 has been estimated through analysis of HRV 
[3],[4],[5]. Nevertheless, all these studies need the 
complete test and an expert observer in order to ascertain 
the threshold location. One drawback in the traditional 
spectral analysis of HRV [6] is the partition of the power 
spectrum in bands with constant limits. In incremental 
tests, the breathing frequency increases with the load so it 
is presumable to lie above the maximum limit of the high 
frequency band (typically 0.4 Hz) being the result of the 
power of the high frequency band completely 
meaningless.  
The aim of this work is to propose a HRV processing 
methodology that predicts the load at which VT1 and 
VT2 occur. The signal processing is based on spectral 
indices that don’t require a band definition as opposed to 
the classical spectral indices. 
 
2. Materials and methods 
Twelve competitive male cyclist (34.1±5.7 years old) 
participated in this study. Prior to the test, each subject 
was familiarized with the experimental procedure and 
was informed of the risks associated with the protocol. 
All subjects gave their written voluntary informed 
consent. The measurement protocol was an incremental 
exercise test in the upright position on an electronically 
braked cycle ergometer (Excalibur Sport, Lode, The 
Netherlands) modified with clip-in pedals. Each subject 
performed a 25W/min incremental test [2]. The pedaling 
frequency was chosen at will between 70 and 100 rpm. 
During the test, the RR time series was collected with 
a Polar RS800 (Polar Electro, Finland, OY) with a 1 kHz 
sampling frequency, and the gas measurement was 
performed with a Cosmed Quark PFT-Ergo gas analyzer 
(Cosmed, Italy). Before each test, ambient conditions 
were measured and the gas analyzers and inspiratory 
flowmeter were calibrated. Gas measurements were used 
by an expert doctor in order to estimate VT1 and VT2 
loads.  
ISSN 0276−6574 939 Computing in Cardiology 2010;37:939−942.
Prior to processing, the artifacts of the RR time series 
were corrected with the software Kubios HRV 2.0 
(University of Kuopio). Then, the analysis was done 
using a sliding window with a length of 300 beats and an 
incremental shift along the RR time series of one beat. 
Inside the window, the RR time series were first 
detrended with a smooth priors detrending method with 
そ= 100 [7] and then resampled at 10 Hz. The power 
spectrum was estimated using the FFT and a Hann 
window. 
To characterize the power spectrum without a band 
definition, we have computed the accumulated power 
spectrum as: 




N
1i
RR
n
1i
RR
RR
(i)P
(i)P
(n)AP    (1) 
 
where PRR(i) is the power spectrum estimation at 
frequency f(i) and f(N) is the Nyquist frequency (5 Hz in 
our case). The central frequency (CF) was defined as the 
frequency where APRR is equal to 0.5. The bandwidth at 
50% (BW) was defined as the difference between the 
frequency where APRR is equal to 0.75 and the frequency 
where APRR is equal to 0.25. Figure 1 shows an example 
of the computation of both indices. 
For each power spectrum, the CF and BW were 
computed. So, for each test, time series of CF and BW 
indices were obtained. The central frequency threshold 
(CFT) was defined as the first sample since the start of 
the exercise where  
 
CF(CFT)-CF(CFT-100)>0.15 Hz             (2) 
 
so it corresponds to a drastic change in CF. The 
bandwidth threshold (BWT) was defined as the sample 
where, starting at CFT and looking backwards, the 
bandwidth falls below BW(CFT)/2. Finally, the loads at 
which CFT and BWT occur were obtained (PCFT and 
PBWT, respectively). 
PCFT and PBWT were considered as the independent 
variables in linear regression models to estimate the 
values of the maximum load (PMax), VT2 load (PVT2) and 
VT1 load (PVT1) estimated from the gas analyzer 
measurements by trained personnel. Figure 2 shows an 
example of all this procedure. 
 
3. Results 
Table 1 shows the mean, maximum and minimum 
values of the loads where the different threshold occur. It 
is worth noting that PCFT and PBWT always occur for lower 
loads than the other thresholds. 
 
 
Results for the linear regressions are shown in table 2. 
Each threshold can be estimated as: 
 
CFTBWToi PPPP ·· 21     (3) 
 
0 1 2 3 4 5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
A
c
c
u
m
u
la
te
d
 P
o
w
e
r 
S
p
e
c
tr
a
l 
D
e
n
s
it
y
Central frequency: 0.32 Hz
Bandwidth 50%:
1.26 Hz 
Fmin 50%: 0.13 Hz
Fmax 50%: 1.39 Hz
 
Figure 1. Example of the computation of CF and BW 
corresponding to the accumulated power spectral density 
of a subject exercising with a mild load. 
 
Time (min)
18 20 22 24 26 28 30 32 34
(s
) 
o
r 
(H
z
)
0.0
0.2
0.4
0.6
0.8
1.0
L
o
a
d
 (
W
)
0
100
200
300
400
500
VT1 VT2BWT CFT
 
Figure 2. Example of one incremental maximal test. The 
thick solid line corresponds to the RR time series, the thin 
stepwise line corresponds to the incremental load used 
during the test, the dotted line shows the evolution of BW 
and the dashed line shows CF. VT1 and VT2 are the 
expert’s annotations while BWT and CFT are, as 
described in the text, the automatically located instants 
were sudden changes in CF and BW occur. 
 
Figure 3 show the Bland-Altman plots comparing the 
estimated loads from equation (3) and the measured loads 
using the gas analyzer and the expert annotations. The 
plots also show two horizontal lines indicating the size of 
the load increments (± 25 W which is the resolution of 
our measurements). As seen, in most of the cases the 
940
difference between the annotation and the predicted load 
is below the load resolution. 
 
Table 1. Mean, maximum and minimum loads measured 
in the twelve subjects 
 
 
 
 
 
 
 
 
 
 
Table 2. Linear regression models to estimate maximum, 
VT2 and VT1 loads. The Standard Error of Estimate is 
also shown. 
 
Load Po (W)   SEE (W) 
PMax 278.2 0.299 0.384 24.3 
PVT2 196.0 0.313 0.395 23.6 
PVT1 203.4 -0.150 0.523 22.6 
 
 
4. Discussion and conclusion 
Results show that BW and CF can be used to predict 
the load events on a maximal incremental test. For the 
whole twelve participants, the abrupt changes in BW and 
CF happened always in advance of VT1 so this 
methodology can be applied in real time and stop the test 
once CFT is detected. Nevertheless, all participants were 
competitive male cyclist and further studies must be done 
in order to ascertain if this methodology is also valid for 
other groups. 
Spectral indices without band definition could prove 
useful in the analysis of RR time series during exercise 
because the drastic physiological changes associated with 
physical effort cause a radical modification of the heart 
rate variability power spectrum. 
In conclusion, BW and CF can predict VT1, VT2 and 
maximum loads in competitive male cyclists while 
performing a maximal incremental test with an error 
comparable to the load resolution. 
 
Acknowledgments 
This work was supported by MEC project PSI2008-
06417-C03 
 
 
 
Figure 3. Bland-Altman plots for the agreement of expert 
annotated loads (reference measurement) and predicted 
loads from BW and CF measurements. Horizontal lines 
show the resolution of the load. Top panel: maximum 
load. Middle panel: VT2. Bottom panel: VT1. 
 
References 
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Load Max Mean Min 
PMax (W) 425 394.2 350 
PVT2 (W) 350 329.5 300 
PVT1 (W) 300 274.5 250 
PBWT (W) 200 168.0 125 
PCFT(W) 225 198.7 175 
941
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[6]  Malik M Heart Rate Variability. Standards of Measurement, 
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Address for correspondence. 
 
Miguel Ángel García González .  
C/ Jordi Girona 1-3, Edifici C-4, Campus Nord UPC, 08034, 
Barcelona, Spain. 
magarcia@eel.upc.edu 
942


Ventilatory Threshold Prediction by Spectral Analysis of Heart Rate Variability in Incremental Maximal Tests

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Ventilatory Threshold Prediction by Spectral Analysis of Heart Rate Variability in Incremental Maximal Tests

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