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Relation Between Estimated Cardiorespiratory Fitness and Running
Performance in Free-Living: an Analysis of HRV4Training Data
Marco Altini1, Chris Van Hoof2and Oliver Amft1
Abstract— In this work, we propose to use anthropometrics
and physiological data to estimate cardiorespiratory fitness
(CRF) in free-living and analyze the relation between estimated
CRF and running performance. In particular, we use the ratio
between running speed and heart rate (HR) as predictor for
CRF estimation in free-living. The ratio is representative of
fitness as lower HR at a given speed is expected for more fit
individuals. Then, we analyze the relation between estimated
CRF and running performance for 10 km, half marathon and
full marathon runs. CRF estimation models were developed
using lab-based V O2max measurements. CRF estimates were
obtained from data collected in unsupervised free-living in
a sample of 532 runners for a period ranging between 1
and 8 months using the HRV4Training app. During the same
period, running performance was determined for all runners.
We show that the speed to HR ratio provides higher accuracy
in CRF estimation compared to resting HR or no-physiological
data (15% to 18% reduction in RMSE for person-independent
models). Secondly, we found moderate to strong correlations
between CRF estimated from free-living data and running
performance (Pearson’s r= 0.56 −0.61). We conclude that
estimating CRF in free-living using mobile technology and data
integration can be a valuable tool to support individualized
training plans and to track fitness and performance outside
laboratory settings.
I. INTRODUCTION AND RELATED WORK
In the past few years, ubiquitous sensing technologies
showed unprecedented insights into the relation between
physical activity, health and performance [1]. A multitude
of wearable devices and mobile applications have been
developed to support recreational and professional athletes in
tracking their workouts. Physiological data, including heart
rate (HR) and heart rate variability (HRV) have been used
to monitor athletes fitness levels as well as recovery from
previous workouts [2].
Due to fast paced technological developments and integra-
tions between different platforms and services (e.g. public
APIs), increased availability of multivariate data streams
acquired from mobile applications and wearable sensors (e.g.
GPS, accelerometer, physiological data), new applications
and techniques have been developed. Smartphone-based
measurements have become popular [3], as smartphone-
integrated sensors could be used, e.g. GPS to track distance
and photoplethysmography to track physiological data using
the phone’s camera and flash light as light source [4], [5].
While several mobile applications and wearable sensors
have been released on the market in the recent past, typically
providing users with estimates of calories burnt, steps taken
1M. Altini and O. Amft are with ACTLab, University of Passau, DE
altini.marco@gmail.com
2C. Van Hoof is with imec, Leuven, BE
(e.g. Fitbit) and workouts data such as distance, time, speed,
heart rate, etc. (e.g. Garmin), all important metrics reflecting
individual behavior, limited work has been carried out to
provide insights on the individual’s actual health and per-
formance status outside of laboratory settings. In particular,
cardiorespiratory fitness (CRF) can potentially provide more
information for both health and sports applications, as it is a
key health parameter [6], [7], [8] and performance indicator
in endurance sports [9], [10].
Current gold standard and practice for CRF measurement
is direct measurement of oxygen volume (V O2in ml/min)
during maximal exercise (i.e.V O2max). However, V O2max
tests are affected by multiple limitations. Medical supervision
is required and the test can be risky for individuals in non-
optimal health conditions. Sub-maximal tests have also been
developed [11], typically requiring to measure HR while
running at a certain speed or biking at a certain intensity.
HR while performing a specific activity in laboratory set-
tings, is discriminative of CRF levels due to the inverse
relation between HR and CRF [12], with more fit individuals
typically showing lower HR at a given workout intensity.
Commercial devices, for example some sport watches paired
to HR monitors [13] (e.g. Polar devices), provide CRF
estimation using a regression model including HR at a
predefined running speed as predictor. A few methods have
been recently proposed to estimate CRF using wearable
sensor data acquired in free-living [7], [8], [14], [15], without
the need for laboratory tests. Using wearable sensors in free-
living to estimate V O2max is a novel approach that could
be applied to a larger population compared to maximal or
sub-maximal laboratory tests.
The relation between V O2max and running performance
has been investigated several times in laboratory settings,
sometimes with conflicting results [9], [10]. V O2max es-
timation in free-living to track performance over a broad
population with different fitness levels has never been investi-
gated before. Technological advances make it finally possible
to monitor longitudinally physiological data in free-living
with minimal burden on the user, enabling new opportunities
beyond laboratory settings. Monitoring training progress
using free-living estimates, without the need for additional
protocols, could provide individuals with an effective tool
for individualized training and motivation.
In this work, we first analyzed different CRF estimation
models relying on anthropometrics data only, anthropomet-
rics and physiological data at rest as well as anthropometrics
and physiological data during exercise, proposing the speed
to HR ratio as predictor able to minimize estimation error.
Then, we used the HRV4Training app [5] to collect resting
HR and HRV data, training summaries (HR during exercise,
distance, duration, elevation gain for each workout) and a
user anthropometrics (age, weight, height and gender) for
a total of 532 runners. We used HRV4Training data to
derive running performance over 1to 8months as well as
to estimate V O2max according to the lab-validated CRF
estimation models. Finally, we compared estimated V O2max
and running performance by integrating data from additional
services. Our contribution is therefore twofold:
•We show that CRF estimation error can be reduced by
15% and 18% when using the speed to HR ratio as
predictor, with respect to anthropometrics data only and
resting physiological data respectively.
•We show moderate to strong correlations between free-
living CRF estimates and running time (Pearson’s r=
0.56 −0.61), consistently for distances between the 10
km and the full marathon, highlighting how estimated
V O2max can potentially be used to track individual
performance outside laboratory settings.
II. METHODS AND DATA COLLECTION
We used lab data and acquired data in free-living settings.
Lab data included measurements of HR at sub-maximal
intensities (rest and running at different speeds), used as
predictors for V O2max estimation, as well as a V O2max
test. Free-living data included training summaries (HR,
speed, distance, time), resting physiological measurements
(HR and HRV) and runner anthropometrics (age, gender,
height and weight). V O2max estimation models developed
in the lab were used to estimate V O2max from free-living
data and investigate the relation with running performance,
also derived from training summaries in free-living.
A. Laboratory data: V O2max modeling
Participants for laboratory studies were 48 (22 male, 26
female), age 25.0±6.2years, weight 67.8±10.4kg, height
173.3±9.1cm, BMI 22.5±2.3kg/m2and V O2max
44.8±7.2ml/min. Written informed consent was obtained,
and the study was approved by the ethics committee of
Maastricht University. HR data were acquired using the
ECG Necklace, a platform configured to acquire one lead
ECG data at 256 Hz, and three-axial accelerometer data
at 32 Hz. Reference CRF was determined as V O2max, by
means of an incremental test on a cycle ergometer [16] using
a indirect calorimeter that analyzed O2consumption and
CO2production. Two laboratory protocols were performed.
The first protocol included simulated activities performed
while wearing a portable indirect calorimeter and the ECG
Necklace. Activities included in this study were: lying down
and running (treadmill flat at 7,8,9,10 km/h). Activities
were carried out for a period of at least 4 minutes. The
second protocol was a V O2max test providing reference data
for CRF.
B. Free-living data: V O2max estimations
Runners were not recruited but downloaded the
HRV4Training application from the Apple Store and
agreed to provide collected measurements for research
purposes via a consent form embedded in the application.
Instructions were provided to reproduce conditions similar
to measurements at rest in laboratory settings. HR and
HRV duration was configurable between 1and 5minutes.
The HRV4Training app is used for morning measurements
at rest, and integrates with other commonly used services
to retrieve actual workouts data and training summaries.
Thus, training summaries including HR, speed, time,
distance and elevation gain were acquired using Strava’s
public APIs. Each user voluntarily linked HRV4Training to
Strava to retrieve training summaries in the HRV4Training
application.
We included in this analysis all runners that recorded train-
ings for at least 1 month. We included only runner trainings
when a HR rate monitor was used, as HR data during exercise
is required for our V O2max estimation. Finally, we included
in this analysis only users that ran one of the following
events: 10 km, half marathon (21.1 km) or full marathon
(42.2 km). The inclusion criteria yielded 532 runners (493
male, 34 female), 88581 physiological measurements at rest,
and 24712 trainings including HR and GPS data, i.e 46
trainings and 70 physiological measurements per user on
average. Mean age was 39.9±8.0years, mean weight was
72.5±9.1kg, mean height was 178.0±7.3cm and mean
BMI was 22.8±2.1kg/m2.
III. DATA ANALYS IS
A. Laboratory data: V O2max modeling
CRF was estimated using multiple linear regression mod-
els and different sets of predictors collected in laboratory set-
tings (see Sec. II-A). We compared the following three cases:
anth, including anthropometrics data only (BMI, age and
gender), resting including anthropometrics and physiological
data acquired at rest, i.e. morning HR and HRV, training
including anthropometrics, resting physiological data and
the speed to HR ratio. The speed to HR ratio was used
as it could be derived from free-living training summaries
regardless of a runner HR and preferred running speed and
is representative of fitness as lower HR at a given speed is
expected for more fit individuals.
B. Free-living data: V O2max estimations
Resting physiological data were acquired in free-living
using HRV4Training’s photoplethysmographic (PPG) mea-
surement. PPG is an unobtrusive technique for detecting
blood volume changes during a cardiac cycle and is often
measured using reflection by illuminating the skin using
a LED (e.g. the phone’s flash) and detecting the amount
of light that is reflected by a photodetector or a camera
located next to the light source. Details on this method can
be found in [5]. HR was computed as the mean HR over
the measurement window. As HRV feature we used rMSSD
as it was shown to be a clear marker of parasympathetic
activity and often used to determine physiological stress due
to training load [17]. rMSSD was computed as the square
root of the mean squared difference between PPG peak to
peak intervals.
Running performance was determined for each runner as
the fastest time over distances between the 10 km and full
marathon for the measurement period. Runners were also
split into performance categories based on their best times. In
particular, we created three categories: slow runners (10 km
above 47.5 minutes, half marathon time above 1 hour and 45
minutes, full marathon time above 4 hours and 15 minutes),
fast runners (10 km below 40 minutes, half marathon time
below 1 hour and 30 minutes, full marathon time below
3 hours and 15 minutes) and average runners, including
all remaining ones. Training summaries data were used to
determine running performance as well as running HR and
speed, used as predictors for V O2max estimates. The speed
to HR ratio was computed from training summaries and used
as predictor for V O2max estimation models.
IV. RESULTS AND DISCUSSION
A. Laboratory data: V O2max modeling
Results for leave one participant out cross-validation of
V O2max estimation models are shown in Fig. 1. Root mean
square error (RMSE) for anth was 4.2±3.0ml/kg/min, while
for resting was 4.1±3.1ml/kg/min and for training was
3.5±2.8ml/kg/min. Results are consistent with previous
research on V O2max estimation using sub-maximal HR,
confirming that physiological responses to more intense
exercise (e.g. the speed to HR ratio during running) consis-
tently improve V O2max estimation accuracy. In particular,
participant-independent RMSE is reduced by 15% and 18%
on our dataset when using training compared to resting and
anth respectively.
B. Free-living data: Running performance and V O2max
estimations
Running performance derived from training summaries
acquired in free-living was 48.8±6.0minutes for 10 km
runs, 108.0±15.9minutes for half marathon runs and 225.0±
36.6minutes for full marathons. Fig. 2 shows the relation
between V O2max estimated using the training model, i.e.
the best performing V O2max estimation model described in
Sec. IV-A, and running performance. A moderate to strong
inverse relation is visible for all running distances (Pearson’s
rranging between −0.56 and −0.61). Finally, Fig. 2.d
shows boxplots of the relation between estimated V O2max
and running category as defined in Sec. III-B, highlighting
consistent differences between groups.
Reported results are consistent with previous small-scale
studies showing moderate to strong correlations between
V O2max and running performance [9], [10]. While it is clear
that there is more to running performance than V O2max, and
other variables might serve as more accurate predictors in
laboratory settings (for example lactate threshold and running
efficiency [18], [9]), measuring these parameters requires
laboratory infrastructure, expensive equipment and dedicate
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Fig. 1. Relation between estimated and measured V O2max for the different
models implemented based on the lab data. Anth refers to anthropometrics
characteristics only, Resting includes anthropometrics, resting HR and
rMSSD, training includes anthropometrics and the speed to HR ratio during
running activities as predictors. Correlation between actual and estimated
V O2max is also reported for each analysis.
personnel. On the other hand, we showed that V O2max can
be estimated with good accuracy using the speed to HR
ratio as predictor, which can be easily acquired using today’s
smartwatches and mobile phone applications. Additionally,
we found the inverse relation between running performance
and estimated V O2max to be consistent across different
running distances. We believe that the availability of metrics
representative of running performance such as the proposed
V O2max estimate could help individuals keep track of their
fitness level, effectively closing the loop between training
and objective estimates of physical fitness and performance.
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<− Faster −−− Time (hours) −−− Slower −>
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a) Best 10km time in relation to VO2max
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b) Best half marathon time in relation to VO2max
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c) Best marathon time in relation to VO2max
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Estimated VO2max
d) Runner category and VO2max (all users)
Fig. 2. Relation between running performance (racing duration for
distances between the 10 km and the full marathon) and estimated V O2max
for data collected using the HRV4Training application in unsupervised
free-living settings. A moderate to strong inverse relationship is shown
independently of running distance. Distributions of V O2max values and
running performance are also shown.
V. CONCLUSIONS
In this paper we investigated the relation between es-
timated V O2max and running performance in free-living.
First, we used data acquired under laboratory settings to build
and validate V O2max estimation models and proposed the
speed to HR ratio as predictor that can be easily computed
from running workouts. We showed that V O2max estimation
error can be reduced by 15% and 18% with respect to anthro-
pometrics data only and resting physiological data (HR and
HRV) respectively. Then, we acquired free-living workouts
data from 532 individuals over a period of up to 8months
using the HRV4Training application. Trainings were used
to estimate V O2max and running performance. We found a
moderate to strong negative correlation between estimated
V O2max and running performance (r= 0.56 −0.61), for
all distances between the 10 km and the full marathon.
Given the greater sample size compared to typical studies,
we could provide confirmative insights on the feasibility of
using sub-maximal HR to estimate fitness level in free-living,
and use such estimated fitness level as a metric representative
of running performance. Estimated V O2max can potentially
be used to track individual performance outside laboratory
settings, driving motivation and helping athletes of all lev-
els keep track of progress as well as adopt individualized
training plans based on a person’s physiological response
to training. Our approach confirms the potential of mobile
technology and data integration to provide relevant insights
in free-living performance on the population level. Further
work is needed to investigate individual variance.
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