=Paper=
{{Paper
|id=Vol-1842/paper_13
|storemode=property
|title=Heart Rate Modelling as a Potential Physical Fitness Assessment for Runners and Cyclists
|pdfUrl=https://ceur-ws.org/Vol-1842/paper_13.pdf
|volume=Vol-1842
|authors=Dimitri de Smet,Marc Francaux,Julien M. Hendrickx,Michel Verleysen
|dblpUrl=https://dblp.org/rec/conf/pkdd/SmetFHV16
}}
==Heart Rate Modelling as a Potential Physical Fitness Assessment for Runners and Cyclists==
https://ceur-ws.org/Vol-1842/paper_13.pdf
Heart rate modelling as a potential physical
fitness assessment for runners and cyclists
Dimitri de Smet1 , Marc Francaux2 , Julien M. Hendrickx1 , and Michel
Verleysen1
1
ICTEAM
2
Institute of Neuroscience
Université catholique de Louvain, Louvain-la-Neuve, Belgium
{dimitri.desmet,marc.francaux,julien.hendrickx,michel.verleysen}@
uclouvain.be
Abstract. Assessment of physical fitness of endurance athletes is usu-
ally performed by means of standardized exercise protocols in specialized
laboratories. The recent development of devices measuring heart rate,
power output, speed, etc. raises the possibility to assess the fitness level
from data collected on the field. We propose a model based on cardiac pa-
rameters identification on training activities. Identified parameters prove
to allow for heart rate simulations that match measurements with an av-
erage root mean square error of 4 beats/min for cycling activities for
which power output and heart rate were provided and 6 beats/min for
running activities for which the heart rate was provided and power out-
put was estimated based on global positioning system (GPS) tracking.
Keywords: fitness assessment, system modeling, heart rate, power out-
put
1 Introduction
Improvement of sport performance is dependent on physiological adaptations
amongst others. These training adaptations are of particular importance for en-
durance athletes like cyclists and runners. Training optimization requires knowl-
edge about how humans adapt to workout sessions. This knowledge can be seen
as a model linking training workout characteristics to fitness level. Such system
modeling approaches have been refined for at least four decades [1]. Although
models are well described and increasingly used instead of relying solely on the
empirical experience of coaches [2], they are unable to provide physiologically
relevant parameters.
The athlete adaptation model takes as inputs quantifiable training work-
load w(t) to predict the fitness level f l(t) evolution over time as represented in
the upper part of Fig. 1. Building and evaluating such a model requires input-
output instances. Inputs are easy to gather thanks to the emerging tendency of
athletes to log all their activities on a server by using their smartphone, sport
watch or bike computer. On the other hand, endurance fitness is multifactorial
2 Dimitri de Smet, Marc Francaux, Julien M. Hendrickx, Michel Verleysen
Fig. 1. Conceptual model of the human adaptation to workout sessions. The bottom
part illustrates how objective measurements help to fit the athlete’s adaptation model.
(cardiovascular, metabolic, endocrine, ...) and quantitative metrics are not di-
rectly available. Currently, the evaluation of the endurance fitness is assessed by
incremental exercise protocols performed in specialized laboratories[4].
This work aims to provide a methodology that will help inferring the fitness
level from workout sessions data themselves. For this purpose, a parametric heart
rate model is proposed (see bottom part of Fig. 1).
The main principle is that a lower heart rate observed for a given intensity
of exercise indicates a better endurance fitness level [7] but the kinetics of heart
rate increase at the onset of exercise, or decrease after the discontinuation of
exercise are also modified by the training process. Our intuition is that the
assessment of physiological parameters explaining cardiac adaptations during the
training sessions might provide relevant information regarding the fitness level
of endurance athletes. As it could be able to give daily personal feedback, such
a model is potentially very helpful for monitoring the physiological adaptations
to training on a regular basis and without requiring a standardized laboratory
protocol.
The validity of the proposed heart rate model will be assessed by simula-
tion with cyclists’ data for which we have instant power output and heart rate
measurements. The model will then be re-used with runners’ activities. For the
latter, the power output needs to be estimated as it is not directly measured
during the run.
2 Methods
This paper proposes a parametric heart rate model that describes the relation-
ship between an athlete instant power output po(t) and his heart rate hr(t) as it
is illustrated in Fig. 2. The model parameters can be identified to best reproduce
heart rate measurements on a single activity.
2.1 Heart Rate Model
Steady state The steady state heart rate HRss refers to the heart rate that
is reached after stabilisation at constant power output P O. The relationship
Heart rate modelling 3
Fig. 2. Parametric heart rate model
between steady-state heart rate and power output is athlete-dependent and is
known to be very close to linear as long as the heart rate is below its maximum
value called maximum heart rate HRmax [5]. Higher power output is achievable
for short periods of time but the heart rate will remain at HRmax . The three
athlete-time specific parameters describing the steady state relationship are rest-
ing heart rate HRrest in beats/min [bpm], the maximum heart rate HRmax in
[bpm] and the slope coefficient m in [bpm/watt] following the equation
(
HRrest + m ∗ P O, if HRrest + m ∗ P O < HRmax
HRss (P O) =
HRmax , otherwise.
Fig. 3. Segment of ergometer measurement that shows the exponential-looking heart
rate response to power steps.
Transient Response It appears from exercise laboratory measurements on
ergometers (a segment of measurement is illustrate in Fig. 3) that a power step
upward leads to a new steady state heart rate that is reached after a few seconds.
The exponential-looking shape of the heart rate curve in response to power steps
suggests this phenomenon can be roughly described by a first order differential
equation :
dHR(t) 1
+ HR(t) = P O(t)
dt τr
with τr an athlete-specific time constant. It will be shown below that this as-
sumption allows for accurate simulations.
In a time frame [t0 , t] where power output is constant, the solution of this
equation is given by
4 Dimitri de Smet, Marc Francaux, Julien M. Hendrickx, Michel Verleysen
t
HR(t) = HR(t0 ) + (HRss (P O(t)) − HR(t0 ))e− τr .
In the discrete over-sampled time domain, an iterative form given by
1
HR(t + 1) = HR(t) + (HRss (P O(t)) − HR(t))
τr
can be used.
As there is no reason to assume equality between rise time τr and fall time
τf . The equation is allowed to differ for increasing and decreasing heart rate and
becomes
(
HR(t) + τ1r (HRss (po(t)) − HR(t)), if HRss (po(t)) ≥ HR(t)
HR(t+1) =
HR(t) + τ1f (HRss (po(t)) − HR(t)), if HRss (po(t)) < HR(t).
The heart rate transient response is thus captured by two athlete-time specific
parameters which are τr and τf .
2.2 Runners Power Output Estimation
Running activities are provided as timestamped geolocalized points with ele-
vation that was corrected using elevation maps. The elevation can be derived
with respect to the curvilinear horizontal distance to get the slope. The runner
velocity is also derived from locations and timestamp. Both are smoothed using
factors that were chosen to give best simulation accuracy. It is assumed that the
smoothing factors are not athlete- or activity- specific.
Minetti et al [6] show that the energy cost of running does not depend on the
speed but only on the distance. It also gives the energy cost of running EC as
a function of the slope relative to the runner’s weight in [J/m/kg]. As velocity
v(t) and slope were evaluated, the runner’s power output P O(t) is
P O(t) = EC(slope).v(t)
in [w/kg].
Cardiovascular Drift Intra-session workload results in fatigue that induces
increased heart rate for the same power output[5, 8]. The increase is assumed
to be proportional to the energy expenditure from the beginning of the activity.
The power output can then be replaced in the above equations by
Z t
P O(t) + kf P O(t)dt
t0
with kf being the athlete’s sensitivity to fatigue. This intuitive formulation might
not be accurate but proved to help the heart rate model to better fit activities
measurements.
Heart rate modelling 5
2.3 Fitting of the Athlete’s parameters
The model that was described contains three parameters that account for the
steady state relationship (HRrest [bpm],HRmax [bpm] and m [bpm/watt]); two
that account for heart rate transient response (τr and τf [s]); and one that ac-
counts for the athlete’s sensitivity to fatigue (kf coefficient). Those parameters
are identified on an activity from which heart rate HR(t) and power output
P O(t) are known or estimated. Given the power output P O(t), a set of cardiac
\ that can be compared to the heart
parameters can result in a simulation HR(t)
rate measurement HR(t). The six parameters are tuned to minimize the mean
square error between simulation and measurement using a non-linear optimiza-
tion algorithm known as Nelder-Mead method [9].
2.4 Data
In most modern activity tracking platforms (Nike+, Runkeeper, Strava, Garmin
Connect, Endomondo, TrainingPeaks, ...), activities are shared as tuples of ge-
olocalized points associated with timestamps recorded by athletes with their
device. They can potentially record more parameters like heart rate, cycling
power, cadence, accelerations, temperature or baro-metric pressure.
The cardiac model was first fitted to 72 cycling activities of three cyclists
containing instant power output and heart rate measures sampled every second.
The power was measured with a torque meter in the crankshaft of their bikes.
The same was done with 234 running activities of two runners containing
heart rate and geolocalized points. Instant power output was estimated based
on based on global positioning system (GPS) tracking coordinates.
3 Results and Discussion
Cardiac parameters that were identified on activities with the described method-
ology enable accurate heart rate simulation on the same activity taking solely
the instant power measure or estimation as input. Heart rate simulations differ
from heart rate measurements with an average root mean square error of 4 bpm
for the 72 cycling activities recorded with the use of a power meter. On average,
a root mean square error of 6 bpm was observed for the 234 running activities.
Fig. 4 and 5 show respectively cycling and running activities simulation ex-
amples with measurement curves that were used.
In most activities, identified heart rate rising time constant τr was found to be
smaller than heart rate falling time constant τf ; with respective average values of
24 and 30 seconds. Sensitivity to fatigue was modeled with an additional power
output in the range [1; 6].10−5 [w/J]. Steady state heart rate parameters were
more subject to intra- and inter-athlete variability. Resting heart rate HRrest
was found to be in the range [60; 100] [bpm] that does not necessarily correspond
to the conventional resting heart rate that is taken on a person laying down. The
slope coefficient m was found in the range [0.15; 0.45] [bpm/w].
6 Dimitri de Smet, Marc Francaux, Julien M. Hendrickx, Michel Verleysen
Fig. 4. Cycling activity. Top: Power measurement. Bottom: Simulated vs recorded
heart rate
Fig. 5. Running activity. Plot 1 and 2: Elevation and speed measurements. Plot 3:
Estimated power output computed on speed and slope (elevation’s derivative). Plot 4:
Simulated vs recorded heart rate
Although parameters identification proved to result in accurate simulations,
their variability seems higher than what is expected from real cardiac parameters.
The parameter variability over different activities taking place at different times
during the year can be imputed to the athlete state (which is of interest) but
other factors can be invoked:
1. The day-to-day heart rate variability that is believed to be around 2-4 bpm
according to [5].
2. Exogenous information such as temperature or altitude that are not included
in the model and are known to impact heart rate [5].
Heart rate modelling 7
3. The methodology itself:
– Given the model that was chosen, maximum heart rate is impossible to
identify if it was not reached by the athlete during the activity.
– Activities characteristics influence the expected accuracy of the param-
eters. For instance, steady state line coefficients are better estimated if
activities sweep over a large range of power output.
4. Data accuracy or sensor model that are device-dependant and that were not
discussed here.
How cardiac parameters are exactly linked to fitness levels or performances is
not considered in this work. We rely on the fact that part of them are measured
by coaches during standardized exercise in laboratory for the periodic follow-up
of their athletes.
4 Conclusion
We identified a pressing need for objective fitness assessments based on data
acquired on the field in training situations, in order to better understand hu-
man adaptation to physical training and to enable adaptive training plans. We
propose a framework that provides the basis of a potential solution through car-
diac parameters identification. Identified parameters prove to be sufficient for
athletes heart rate simulation based on athletes power output for running and
cycling activities.
In further research, parameters accuracy can be improved by including ex-
ogenous meteorological information in the heart rate model. Fixing parameters
that are easy to obtain, like resting heart rate, might also help accuracy of the
other parameters.
The natural continuation of this work would compare identified parameters
to exercise laboratory measurements, or even more interesting, to athletes target
performances such as race times.
References
1. Calvert, T. W., Banister, E. W., Savage, M. V., Bach, T.: A systems model of the
effects of training on physical performance. IEEE Transactions on Systems, Man,
and Cybernetics, (2), 94-102 (1976)
2. Borresen, J., Lambert, M. I.: The quantification of training load, the training
response and the effect on performance. Sports Medicine, 39(9), 779-795 (2009)
3. Halson, S. L.: Monitoring training load to understand fatigue in athletes. Sports
Medicine, 44(2), 139-147 (2014)
4. Faria, E. W., Parker, D. L., Faria, I. E.: The science of cycling. Sports medicine,
35(4), 285-312 (2005)
5. Achten, J., Jeukendrup, A. E.: Heart rate monitoring. Sports medicine, 33(7), 517-
538 (2003)
6. Minetti, A. E., Moia, C., Roi, G. S., Susta, D., Ferretti, G.: Energy cost of walking
and running at extreme uphill and downhill slopes. Journal of applied physiology,
93(3), 1039-1046 (2002)
8 Dimitri de Smet, Marc Francaux, Julien M. Hendrickx, Michel Verleysen
7. Francis, K. T., McClatchey, P. R., Sumsion, J. R., Hansen, D. E.: The relation-
ship between anaerobic threshold and heart rate linearity during cycle ergometry.
European journal of applied physiology and occupational physiology, 59(4), 273-277
(1989)
8. Brueckner, J. C., Atchou, G., Capelli, C., Duvallet, A., Barrault, D., Jousselin, E., ...
Di Prampero, P. E.: The energy cost of running increases with the distance covered.
European journal of applied physiology and occupational physiology, 62(6), 385-389
(1991)
9. Nelder, J. A., Mead, R.: A simplex method for function minimization. The computer
journal, 7(4), 308-313 (1965)