ORIGINAL RESEARCH
published: 01 November 2017
doi: 10.3389/fphys.2017.00850
An Inertial Sensor-Based Method for
Estimating the Athlete’s Relative
Joint Center Positions and Center of
Mass Kinematics in Alpine Ski Racing
Benedikt Fasel 1 , Jörg Spörri 2, 3 , Pascal Schütz 4 , Silvio Lorenzetti 4 and Kamiar Aminian 1*
1
Laboratory of Movement Analysis and Measurement, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland,
Department of Sport Science and Kinesiology, University of Salzburg, Hallein-Rif, Austria, 3 Department of Orthopedics,
Balgrist University Hospital, University of Zurich, Zurich, Switzerland, 4 Department of Health Sciences and Technology, ETH
Zürich, Zürich, Switzerland
2
Edited by:
Luca Paolo Ardigò,
University of Verona, Italy
Reviewed by:
Thomas Leonhard Stöggl,
University of Salzburg, Austria
Giovanni Messina,
University of Foggia, Italy
*Correspondence:
Kamiar Aminian
kamiar.aminian@epfl.ch
Specialty section:
This article was submitted to
Exercise Physiology,
a section of the journal
Frontiers in Physiology
Received: 20 July 2017
Accepted: 12 October 2017
Published: 01 November 2017
Citation:
Fasel B, Spörri J, Schütz P,
Lorenzetti S and Aminian K (2017) An
Inertial Sensor-Based Method for
Estimating the Athlete’s Relative Joint
Center Positions and Center of Mass
Kinematics in Alpine Ski Racing.
Front. Physiol. 8:850.
doi: 10.3389/fphys.2017.00850
Frontiers in Physiology | www.frontiersin.org
For the purpose of gaining a deeper understanding of the relationship between external
training load and health in competitive alpine skiing, an accurate and precise estimation of
the athlete’s kinematics is an essential methodological prerequisite. This study proposes
an inertial sensor-based method to estimate the athlete’s relative joint center positions
and center of mass (CoM) kinematics in alpine skiing. Eleven inertial sensors were fixed
to the lower and upper limbs, trunk, and head. The relative positions of the ankle, knee,
hip, shoulder, elbow, and wrist joint centers, as well as the athlete’s CoM kinematics
were validated against a marker-based optoelectronic motion capture system during
indoor carpet skiing. For all joints centers analyzed, position accuracy (mean error) was
below 110 mm and precision (error standard deviation) was below 30 mm. CoM position
accuracy and precision were 25.7 and 6.7 mm, respectively. Both the accuracy and
precision of the system to estimate the distance between the ankle of the outside leg
and CoM (measure quantifying the skier’s overall vertical motion) were found to be below
11 mm. Some poorer accuracy and precision values (below 77 mm) were observed for
the athlete’s fore-aft position (i.e., the projection of the outer ankle-CoM vector onto the
line corresponding to the projection of ski’s longitudinal axis on the snow surface). In
addition, the system was found to be sensitive enough to distinguish between different
types of turns (wide/narrow). Thus, the method proposed in this paper may also provide a
useful, pervasive way to monitor and control adverse external loading patterns that occur
during regular on-snow training. Moreover, as demonstrated earlier, such an approach
might have a certain potential to quantify competition time, movement repetitions and/or
the accelerations acting on the different segments of the human body. However, prior
to getting feasible for applications in daily training, future studies should primarily focus
on a simplification of the sensor setup, as well as a fusion with global navigation satellite
systems (i.e., the estimation of the absolute joint and CoM positions).
Keywords: inertial sensors, center of mass, alpine skiing, movement analysis, body model, posture estimation,
validation
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INTRODUCTION
of the relationship between specific loading patterns and health
in competitive sports. Another option might be the fusion or
combination of GNSS with body worn inertial sensor systems
(Brodie et al., 2008; Fasel et al., 2016a). In recent years, several
experimental field studies considered these systems to estimate
athlete’s relative joint center positions and CoM kinematics
(Brodie et al., 2008; Supej, 2010; Fasel et al., 2016a). Currently,
there exists no validated commercial product estimating the CoM
kinematics based on inertial sensors. However, in the context of
alpine skiing only the study Fasel et al. (2016a) critically validated
such a fusion under in-field conditions, implying a certain need
for additional scientific evidence and further improvements of
the underlying body model. Specifically, they were using segment
lengths obtained from the optical reference system, the upper
trunk was divided in two segments not following literature
recommendations (e.g., Dumas et al., 2007), and arm movement
was not considered.
Thus, based on the aforementioned current stage of
knowledge, the first objective of this study was to expand the
body model suggested by Fasel et al. (2016a) for the estimation
of the CoM to a more comprehensive and scalable model and
including the upper limbs. The second objective was to validate
the relative positions for the upper and lower limb joint centers
and the athlete’s CoM obtained from the inertial sensors against a
video-based stereophotogrammetric reference system. The third
objective was to evaluate the benefits of adding the upper limbs
to the CoM estimation. The fourth objective was to assess
the sensitivity of the wearable system to detect changes in the
equipment used and turn types performed.
For the purpose of gaining a deeper understanding of the
relationship between training load and health in competitive
sports, an accurate and precise estimation of the athlete’s
kinematics is an essential methodological prerequisite (Soligard
et al., 2016). External load such as competition time, movement
repetition counts, speed, acceleration, etc. (Soligard et al.,
2016) could thus be quantified based on the estimated athlete’s
kinematics. In the context of alpine skiing, a major aim of
coaching is to optimize the skier’s posture and, thus, the
relationship between his center of mass (CoM) and his left
and right feet (Tjørhom et al., 2007; Kipp et al., 2008; Spörri
et al., 2012b). In order to formalize this concept, a previous
study focused on the parameter “vertical distance,” the distance
between the left or right foot and the skier’s CoM, and the
parameter “fore-aft position,” the projection of the vector relying
the CoM with the left or right foot onto the snow surface
(Spörri et al., 2012b). Earlier studies in alpine skiing primarily
used video-based stereophotogrammetric systems to determine
an athlete’s kinematics on a ski track (Supej et al., 2003;
Federolf, 2012; Spörri et al., 2012a,b, 2016b; Hébert-Losier
et al., 2014). Under such in-field conditions, photogrammetric
errors of <1.5 cm were reported (Klous et al., 2010; Spörri
et al., 2016c). However, despite major advantages regarding
accuracy, corresponding measurement setups are complex,
capture volumes are limited to a few turns only, and postprocessing is time consuming.
Accelerated by these limitations and recent advances in
wearable measurement technology, in the last few years,
differential global navigation satellite systems (GNSS) have
gained substantial attention as being a valuable alternative for
estimating absolute CoM kinematics in-field (Brodie et al., 2008;
Lachapelle et al., 2009; Waegli and Skaloud, 2009; Supej, 2010;
Gilgien et al., 2013, 2014a,b, 2015a,b, 2016; Supej et al., 2013;
Fasel et al., 2016a; Kröll et al., 2016). A major challenge of
this alternative approach is that the GNSS antenna cannot be
placed on the CoM directly and, therefore, the relative position
of the GNSS antenna with respect to the CoM needs to be
estimated. Parallel to these developments, CoM kinematics were
also approximated based on a single inertial sensor for both
human (e.g., Esser et al., 2009; Peyrot et al., 2009; Myklebust
et al., 2015) and animal (e.g., Pfau et al., 2005; Warner et al.,
2010) motion analysis. The hypothesis of these studies was that
the chosen sensor location would match the CoM location. While
this hypothesis may be true for gait, it may be violated in certain
sports where upper and lower limb movement may alter the CoM
position relative to the chosen sensor location. For example, for
cross-country skiing, Myklebust et al. (2015) reported average
RMS differences between the true CoM position and a sensor
located at the sacrum on S1 of up to 32 ± 4 mm.
In alpine ski racing, one approach to resolve the issue of the
CoM moving relative to the sensor location is the use of a simple
pendulum model as suggested by Gilgien et al. (2015b) and Supej
et al. (2013). However, while providing reasonable estimates of
the athlete’s overall CoM kinematics, such a model could not
estimate the athlete’s posture, which is key for the understanding
Frontiers in Physiology | www.frontiersin.org
METHODS
Measurement Protocol
The measurements were conducted on an indoor skiing carpet
(Maxxtracks Indoor Skislopes, The Netherlands) with belt
dimensions 6 × 11 m and 12◦ inclination (Figure 1). Eleven
male competitive alpine skiers (20.9 ± 5.2 years, 176.1 ± 6.7 cm,
74.0 ± 10.9 kg) participated in the study. Written informed
consent was obtained from all athletes prior to the measurements
and the study was approved by the ethics committee of École
Polytechnique Fédérale de Lausanne (Study Number: HREC 0062016). Each athlete skied two trials with 140 cm long skis and two
trials with 110 cm long skis at maximum belt speed of 21 km/h.
Two types of skis were used to cover a broad range of different
turn dynamics. Each trial lasted approximately 120 s and during
the first half the athlete skied wide turns taking up the entire
carpet width, while for the second half the athlete skied narrow
turns taking up half the carpet width. Cones placed in the front of
the treadmill were used to indicate the turn width. To ensure that
the athletes stayed in the measurement volume, a spring system
attached to a custom made belt pulled the athlete backwards
(Figure 1).
Reference System
Ten infrared cameras (T160, Vicon Peak, UK) sampling at 100 Hz
surrounded the carpet and covered the entire volume spanned
by the carpet. The IfB marker set with 71 markers (List et al.,
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Center of Mass in Skiing
2013) (Figure 2) was used to obtain functionally determined
ankle, knee, and hip joint centers and the 3D orientation of the
shanks, thighs, pelvis, and lumbar, thoracic, and cervical trunk
segments. Basic motion tasks as described in List et al. (2013)
were performed to define the functional joint centers barefoot.
The foot markers were then moved from the feet to the ski boots
and a static posture was used to register the ski boot markers
with the previously determined foot anatomical frame. Trunk
markers were used to determine the trunk segments, as described
in List et al. (2013). Since the IfB marker set could not directly
measure upper limb joint centers, additional markers have been
placed on the lateral humeral epicondyle, ulnar styloid, and radial
styloid of both the left and right upper limbs. The shoulder joint
center was defined to lie 3 cm below the acromion marker in
the direction of the marker placed on the scapula inferior angle.
The wrist joint center was defined to lie in the middle between
the markers placed on the ulnar and radial styloids. The elbow
joint center was defined to lie 3 cm to the medial direction with
respect to the marker placed on the lateral humeral epicondyle.
The medial direction has been defined to be normal to the plane
FIGURE 1 | Illustration of the treadmill skiing setup. (A) Left turn, (B) right turn. To ensure that the athlete stayed in the capture volume, a rope connected a spring
system with the athlete. The small white boxes are the inertial sensors and the gray dots the reflective markers.
FIGURE 2 | Sensor and marker setup from the front (A), back (B) and side view (C). The four markers fixed to the helmet are not shown here. The inertial sensors
placed in the middle and upper back were not used for this study.
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movement in the sagittal plane where the hands hold a pole
horizontally with both thumbs pointing medially. The hands
were spaced approximately equal to the shoulder width and
elbows were kept straight during the entire movement. Three
movement cycles of up/down arm movement in the sagittal
plane were performed. (2) Upright posture where the arms
and wrists were kept vertically with straight elbows. The hands
were oriented such that the palms were barely touching the
thighs on their lateral side. For the functional calibration the
following constraints were assumed: (i) the main rotation during
the arm swing was supposed to occur along the medio-lateral
axis of the arm and along the anterior-posterior axis of the wrist
(e.g., forearm); (ii) the longitudinal axes of the arms and wrists
were presumed to pass parallel to gravity during the upright
posture.
spanned by the shoulder, wrist and lateral humeral epicondyle. In
order to allow a comparison with the wearable model, the cervical
joint center (CJC) and lumbar joint center (LJC) were estimated
based on the anatomical tables from Dumas et al. (2007) scaled to
the athlete height. CJC was estimated with respect to the marker
placed on C7. LJC was estimated based on the average estimated
LJC position with respect to the left and right hip joint centers.
Four markers were placed on the athlete’s helmet. Their mean
position was used to approximate the position of the head vertex.
Two markers were placed on each ski’s tip and tail and allowed
defining the skis’ longitudinal axis. For the entire measurement in
total 81 markers were attached to the participants. The segments’
CoM were computed according to Dumas et al. (2007). The
upper limb CoM was assumed to lie on the respective segment’s
longitudinal axes where the hand’s longitudinal axis was the same
as the forearm’s longitudinal axis. The head’s CoM was assumed
to lie in the mid-point between the marker placed on C7 and
the average position of the two markers fixed at the front of the
helmet.
In order to allow a comparison to the inertial system, the
joint and CoM positions were expressed relative to the LJC. The
reference (global) coordinate system was defined as follows: the
Y-axis was vertical, pointing upwards (e.g., vertical direction); Zaxis was horizontal and parallel to the treadmill-plane pointing to
the right (e.g., lateral direction); the X-axis was the cross-product
of the Z- and Y-axis and was pointing forwards (e.g., forwards
slope direction in the horizontal plane).
The coaching-relevant parameters vertical distance and foreaft position were computed according to Spörri et al. (2012b).
For each leg (left and right) the vector vCoM, ankle (t) connecting
the CoM with the ankle joint center was computed. The
vertical distance was the norm of vCoM, ankle (t). The fore-aft
position was obtained by the projection of vCoM, ankle (t) onto
the line corresponding to the projection of ski’s longitudinal
axis on the snow surface. The snow surface was mathematically
defined as the X-Z plane inclined by 12◦ around the
Z-axis.
Estimating Segment Orientation
Segment orientation was obtained based on the strap-down
and joint drift correction as described in Fasel et al. (2017a,b).
For initializing segment orientation, the athletes were standing
straight, looking into the slope direction for 5 s before the
treadmill was switched on. The wearable system’s global frame
was identical to the reference system’s global frame and defined
as follows: the Y-axis (e.g., vertical axis) was aligned with gravity,
pointing upwards. X-axis (e.g., forwards axis) was perpendicular
to gravity (i.e., horizontal) and pointing in the direction of the
slope, facing downwards. The Z-axis (e.g., lateral axis) was the
cross-product between the X- and Y-axis, pointing to the right.
It was observed that, despite a standardized posture, the upper
limbs’ azimuths (i.e., direction of the segments’ anterior-posterior
axes) were not aligned. In order to find the segment’s azimuths
the same principle as for the joint drift correction presented in
Fasel et al. (2017a,b) was used: after initial strap-down integration
the segments’ azimuths were assumed to be equal to the average
joint acceleration orientation difference over the entire trial.
Based on this principle, first the initial orientations of the arms
were found with respect to the sternum. Second, the initial
orientations of the wrists were found with respect to the arms.
After this procedure orientation drift was corrected normally as
in Fasel et al. (2017a,b). Example data and the matlab source
code for the functional calibration, initial segment orientation
estimation, and joint drift correction is available on Code Ocean
(doi: 10.24433/CO.23792aee-07c5-4cdc-bfe9-9e85fa1bf5d5).
As no inertial sensors were placed on the skis, for computing
the fore-aft position the ski orientations were estimated based
on the shank orientations. To this end, it was assumed that
the ankle was held in a constant position by the ski boot with
a flexion of 17◦ without ankle abduction or internal rotation.
In other words, the rotation between the ski’s longitudinal axis
and the shank’s anterior-posterior axis was 17◦ around the
shank’s medio-lateral axis. The fore-aft parameters were then
computed identically as for the reference system and described
above.
Wearable System
Eleven inertial sensors (Physilog 4, GaitUp, Switzerland) were
attached with adhesive tape to the shanks, thighs, sacrum,
sternum, head, arms and wrists (Figure 2). Acceleration and
angular velocity were measured at 500 Hz. Offset and sensitivity
of the accelerometers were corrected according to Ferraris et al.
(1995). To this end, each accelerometer was held static for a few
seconds in the six positions where each sensing axis was either
parallel, anti-parallel or orthogonal to the Earth’s gravity field.
Then a least-square fit was used to determine the sensors’ offset
and sensitivity such that the measured values would be 1, −1,
0, respectively. Offset of the gyroscopes was estimated during
the standing still posture before each trial. The wearable system
was synchronized with the reference system by an electronic
trigger. The sensors’ local frames were aligned with the segments’
anatomical frames based on the functional calibration (squats,
trunk rotation, hip abduction, and upright standing) described
in Fasel et al. (2017b). In addition, the functional calibration of
the arm sensors consisted of two movements, as illustrated on
protocols.io (doi: 10.17504/protocols.io.jzncp5e): (1) slow arm
Frontiers in Physiology | www.frontiersin.org
Body Model
The body model was estimated based on a kinematic chain
similarly to Fasel et al. (2016a). However, since the main aim
of the body model was estimating the athlete’s CoM, the origin
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Center of Mass in Skiing
anatomical frame, and vleft knee the vector connecting the left hip
to the left knee in the left thigh’s anatomical frame.
of the kinematic chain was chosen as the LJC (Figure 3A). All
segment dimensions were then defined according to Dumas et al.
(2007), scaled for athlete height. It was assumed that the segment
orientations obtained by the inertial sensors were identical to
the anatomical frames of the corresponding segments. The trunk
was modeled as two independent segments: pelvis and trunk. It
was assumed that the pelvis orientation was equal to the sacrum
orientation, and that the trunk orientation was equal to the
sternum orientation. Thus, for example, the left hip joint position
pleft hip (t) was determined based on Equation (1) and the left
knee position pleft knee (t) based on Equation (2). All other joint
positions were obtained with the same iterative way. Once the
joint positions were known, the segment CoMs were estimated
according to Dumas et al. (2007). In order to estimate the CoM
of the hand, the hand was assumed to have the same orientation
as the wrist. To estimate the foot CoM, it was assumed that the
foot had the same orientation as the ski (i.e., 17◦ ankle flexion).
A weight of 2 kg was added to each foot to take into account the
weight of the ski boot. The skis were ignored for computing the
CoM. The athlete’s CoM was the weighted average of all segment
CoMs. In a simplified model, without the arm and wrist sensors,
the upper limbs’ combined CoM was approximated at the relative
position of (0.15, 0.10, 0.00 m) with respect to LJC expressed
in the trunk’s (i.e., sternum) anatomical frame (Figure 3B). The
upper limb’s relative CoM position was determined from average
values of the full model and was scaled for athlete height with the
same scaling factor as for the other segments.
pleft hip (t) =
pleft knee (t) = pleft hip (t) +
sacrum
left thigh
R(t) ∗ vleft hip
(1)
R(t) ∗ vleft knee
(2)
Validation
A total of 44 trials (11 athletes, 4 trials per athlete) were analyzed.
Error curves were computed by subtracting for each time sample
the 3D position of the joint centers and CoM expressed relative
to the LJC obtained with the reference system from the wearable
system. For each trial, each individual axis and the total distance
(i.e., the error norm), mean and standard deviation of the error
were computed. Accuracy was defined as the group average of all
trial mean errors and precision was defined as the group average
of all trial standard deviations of the error.
The same error analysis was performed for the fore-aft
parameters, whereas in addition Pearson’s correlation coefficient
was computed. For each trial 14 wide and 14 narrow turns were
automatically segmented based on the crossing points of left
and right vertical distance (i.e., norm of vCoM, ankle (t)) (Fasel
et al., 2016b). For each turn the range of motion (RoM) of
the vertical distance and the fore-aft position was computed
and compared to the reference system with a Bland-Altman
plot (Bland and Altman, 2007). Since the data points for the
same trial were correlated, the limits of agreements (LoA) were
computed as described in Fasel et al. (2017b). To assess whether
the wearable system was sensitive to changes, Cohen’s d was
computed separately for the RoM obtained with the reference and
the wearable system between trials (140 vs. 110 cm skis) and turn
types (wide vs. narrow).
RESULTS
Where t is the time, sacrum R(t) the orientation matrix of the
sacrum, left thigh R(t) the orientation matrix of the left thigh, vleft hip
the vector connecting the LJC to the left hip in the sacrum’s
Errors for the left and right side were similar, thus, for the sake
of clarity, in the following only the results for the left side are
FIGURE 3 | (A) Body model including the upper limbs. Each red circle represents a segment’s CoM. The athlete’s CoM is highlighted by the blue star. The LJC is
indicated by an arrow and lies on the dotted line. (B) Simplified body model without the upper limbs. The approximated location of the upper limb’s combined CoM is
illustrated by the purple circle.
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added a bias in the forwards and vertical direction, in which the
CoM was estimated 8.5 mm too low and 13.5 mm too posterior
(Table 2).
For both the full and simplified models, correlation was
>0.98 for the vertical distance and approximately 0.90 for foreaft position (Table 3). For the full model, fore-aft position was
underestimated by 74 mm on average and its average precision
was 34 mm. For the full model, vertical distance was on average
overestimated by 3 mm with a precision of 11 mm (Table 3).
Errors were only slightly different for the simplified model.
Figure 5 shows the average ± standard deviation curves for 14
wide double turns of two representative athletes. The full model
was used to obtain the wearable curves.
LoA for the RoM of the vertical distance and fore-aft position
were considerately lower for the outside leg than the inside
leg (Table 4, Figure 6). The reference average value (standard
deviation) of the vertical distance RoM was 53.8 mm (23.5 mm)
for the outside leg and 168.9 mm (45.0 mm) for the inside leg.
The reference average value (standard deviation) of the foreaft position RoM was 92.7 mm (40.1 mm) for the outside leg
presented. Please refer to the appendix for the results of the right
side.
Both accuracy and precision worsen for the more distal joint
centers, and were worst for the ankles (total distance accuracy
and precision of 109 and 30 mm) and wrists (total distance
accuracy and precision of 97 and 16 mm) (Table 1). Standard
deviation of the joint center accuracy was found to be between 6.3
and 57.6 mm. CoM accuracy and precision for the total distance
were 25.7 and 6.7 mm, respectively.
Especially the knee and ankle joint position errors were
dependent on the turn phase, i.e., were different for the inside
than the outside leg. Figure 4 shows time-normalized errors
for the knee and ankle joints for a typical athlete and nine
wide left/right turns of the trial with 140 cm skis. While the
hip’s vertical position error (Y-axis) remained below 10 mm
throughout the turn cycle, the knee joint position had large errors
during left turns (i.e., for inside leg).
Accuracy and precision for the CoM computed with the full
model was found to be <8.6 mm and <11.2 mm for each axis.
Simplifying the model did not impact the CoM precision, but
TABLE 1 | Average (standard deviation) accuracy and precision of the relative joint center positions along the X-axis (forwards slope direction), Y-axis (vertical direction),
Z-axis (lateral direction), and total distance (norm of 3D difference).
Joint center position
X-axis
Y-axis
Z-axis
Total distance
Accuracy
Precision
Accuracy
Precision
Accuracy
Precision
Accuracy
Ankle
56.7 (57.6)
35.5 (14.5)
−16.3 (24.5)
20.8 (11.7)
23.1 (46.7)
48.4 (14.6)
109.1 (43.2)
29.7 (12.9)
Knee
26.2 (32.9)
25.3 (6.4)
20.8 (7.8)
40.0 (33.3)
34.6 (10.4)
79.7 (33.0)
18.9 (6.4)
21.8 (21.2)
Precision
Hip
−10.0 (10.1)
5.9 (1.6)
−3.8 (6.5)
4.7 (2.4)
21.4 (6.7)
5.1 (2.0)
28.1 (6.3)
4.7 (1.9)
CJC
−22.9 (28.1)
11.9 (3.4)
−5.9 (28.0)
9.1 (3.0)
−1.7 (35.9)
18.5 (5.1)
56.5 (24.7)
12.7 (4.7)
Head Vertex
−58.7 (39.2)
17.2 (6.1)
92.8 (56.6)
10.3 (3.4)
−3.3 (44.8)
25.5 (8.0)
127.3 (57.8)
16.9 (7.3)
−7.7 (31.9)
17.9 (4.8)
−69.0 (26.5)
14.0 (3.3)
−49.5 (28.8)
18.4 (5.7)
99.4 (24.3)
14.3 (4.6)
Shoulder
Elbow
Wrist
14.0 (28.4)
17.3 (4.9)
−6.1 (30.5)
15.3 (4.6)
−9.4 (27.4)
17.5 (5.3)
55.1 (20.3)
14.7 (3.4)
−50.8 (39.3)
20.4 (6.9)
−49.7 (35.7)
21.4 (7.2)
−14.4 (32.37)
21.4 (7.2)
97.0 (29.4)
16.3 (4.8)
All units are mm.
FIGURE 4 | Average (solid lines) ± 1 standard deviation (dashed lines) of time-normalized hip (blue) and knee (orange) joint position errors along the vertical Y-axis for
9 left and right turns of a representative trial. The first 100% of the turn cycle is a left turn where the left leg is the inside leg and the second 100% is a right turn where
the left leg is the outside leg.
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TABLE 2 | Average (standard deviation) accuracy and precision of the relative CoM positions for the full model with arms and the simplified model without arms.
CoM position
X-axis
Accuracy
Body model with arms
Body model without arms
Y-axis
Precision
Accuracy
Z-axis
Precision
Accuracy
Total distance
Precision
Accuracy
Precision
−8.6 (13.8)
6.4 (1.7)
0.6 (14.2)
4.5 (1.7)
−0.5 (13.1)
11.2 (3.3)
25.7 (10.9)
6.7 (2.2)
−13.5 (12.2)
6.6 (1.6)
−8.5 (14.4)
4.5 (1.7)
−0.1 (12.5)
11.5 (3.5)
28.6 (9.6)
7.2 (2.6)
All units are mm.
Dumas et al. (2007) and were scaled for athlete height only.
Therefore, athlete-individual deviations from the model were not
considered and led to a potential bias in the estimation of the
segment length. As an example, our athletes had on average a
40 mm wider pelvis and 69 mm shorter trunk. Subject-specific
anthropometric measurements could reduce this error; however,
at the costs of a more complicated measurement procedure.
Furthermore, segment orientation estimation errors might have
directly affected joint estimation errors. For example, knee joint
position errors were by a factor of 3–4 higher than for the hip
joint. The large precision decrease observed could be attributed to
soft tissue artifacts of the thigh. Actually, high muscle activation
levels during the turns could have temporarily changed the
sensor’s alignment with respect to the underlying bone. In this
context, it is known that during a turn the inside leg has higher
hip and knee flexion angles but has to support less force (Klous
et al., 2012; Kröll et al., 2015). Thus, it is reasonable that the
muscle activation at the inside leg is different compared to the
outside leg (Kröll et al., 2011), what, while turning, might have
led to a different amount of soft tissue artifact and, therefore,
different errors in the estimation of the thigh segment orientation
(Figure 4). To overcome these limitations, soft tissue artifacts
could be modeled for example with a double static calibration
as proposed by Cappello et al. (1997), as well as by measuring
different static postures with and without muscle pre-activation
(e.g., upright standing or sitting on a chair).
TABLE 3 | Average (standard deviation) accuracy and precision of the fore-aft
parameters and their correlation to the reference system for the full model with
arms and the simplified model without arms.
Parameter
Vertical distance
Body Model
With arms
Precision
Correlation
3.3 (19.8)
10.6 (5.4)
0.990 (0.010)
−5.5 (19.7)
10.9 (5.7)
0.989 (0.010)
With arms
−73.9 (47.0)
34.0 (11.0)
0.896 (0.087)
Without arms
−76.7 (49.1)
33.8 (10.9)
0.897 (0.087)
Without arms
Fore-aft position
Accuracy
Units for accuracy and precision are mm.
and 136.7 mm (47.2 mm) for the inside leg. Cohen’s d for the
RoM computed with the reference system and the full model
were similar: between wide and narrow turns >1 for the foreaft position and >2 for the vertical distance. Simplifying the
model by removing the arms did only slightly change the foreaft parameters’ accuracy and precision. As for the full model,
Cohen’s d were similar to the reference system.
DISCUSSION
In the current paper, an inertial sensor-based method to estimate
the athlete’s relative joint center positions and center of mass
(CoM) kinematics during alpine skiing has been proposed.
In addition to these estimates, the joint center- and CoMrelated measures “vertical distance” and “fore-aft position” were
computed. The new method’s validity was assessed by comparing
it to an optoelectronic stereophotogrammetric reference system
(gold standard). Accuracy (precision) for the CoM, vertical
distance and fore-aft position were 25.7 mm (6.7 mm), 3.3 mm
(10.6 mm), and −73.9 mm (34.0 mm), respectively. Excluding the
upper limbs from the body model decreased the accuracy and
precision of all curves by less than 3 mm, except for the vertical
distance where the accuracy changed from 3.3 to −5.5 mm.
The proposed procedure for estimating relative segment azimuth
during posture initialization seemed sufficiently accurate and
precise. Interestingly, the elbow joint position was estimated
with better accuracy than the shoulder and wrist joint positions.
However, prior to analyzing specific movements for which arm
motion is key, the proposed orientation initialization should be
validated more specifically.
CoM Position
Despite the limited performance of joint position estimation,
CoM position was estimated with very good accuracy and
precision. One explanation could be that errors from individual
joint positions were averaged out when computing the athlete’s
CoM. Surprisingly, and in contrast to the findings from Eames
et al. (1999) and Whittle (1997) for walking, removing the
upper limbs from the model did not decrease CoM accuracy
and precision significantly. One potential explanation for this
observation might be the fact that during alpine skiing arm
movements are mostly symmetrical and that (at least for the
current indoor carpet skiing setup) the arms were almost held in a
constant position. Another explanation might be the fact that the
upper limbs contribute on average only 10% to total body mass
(Dumas et al., 2007). Thus, even if arm movements may not have
been estimated correctly, corresponding effects on CoM position
are rather marginal.
Joint Center Positions
As expected, errors of the relative joint positions increased along
the kinematic chain. Two factors might have contributed to these
errors: incorrect segment dimensions and inaccurate segment
orientation estimations. Segment dimensions were taken from
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Vertical Distance and Fore-Aft Position
Both vertical distance and fore-aft position were estimated
with higher precision than reported previously in
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Center of Mass in Skiing
FIGURE 5 | Average (solid lines) ± 1 standard deviation (dotted lines) of vertical distance (top) and fore-aft position (bottom) of the left leg for the same condition for
two athletes A and B (left vs. right) and 14 wide double turns. The wearable system is shown in blue and the reference system in black. The first 100% of the turn were
a left turn, thus the left leg was the inside leg. The second 100% of the turn were a right turn, thus the left leg was the outside leg.
TABLE 4 | Limits of agreements (LoA) for the range of motion (RoM) of the vertical distance and fore-aft positions.
Parameter
RoM Vertical distance
RoM Fore-aft position
Body model
Errors outside leg
Errors inside leg
Lower LOA
Mean
Upper LoA
Lower LoA
Mean
Upper LoA
With arms
−18.6
8.4
32.4
−49.1
−5.2
40.1
Without arms
−17.8
8.4
30.9
−50.0
−5.8
37.8
With arms
−26.8
48.9
117.6
−30.5
29.0
91.9
Without arms
−29.4
47.9
117.3
−25.5
37.0
92.5
All units are in mm.
study, the snow surface was defined mathematically for both the
reference and wearable system. For on-snow measurements this
surface has to be estimated first, for example by constructing
a 3D terrain model with drones (e.g., Pix4Dmapper, Pix4D,
Switzerland).
Fasel et al. (2015), underlining the better suitability of the
revised body model used in the current study. Particularly, for
the measure “vertical distance,” accuracy was slightly improved,
while for the fore-aft position accuracy was slightly reduced.
Moreover, compared to vertical distance fore-aft position was
found to be more sensitive to ankle position errors (Figure 7).
Under the hypothesis that the largest error source could
be attributed to incorrectly estimated thigh orientation due
to soft tissue artifacts, a change in thigh orientation would
essentially affect the direction of the vector relying the ankle to
the CoM, but not its length. Accordingly, soft tissue artifacts
may only marginally alter the vertical distance, however, may
substantially influence fore-aft position (Figure 7), why in
the context of inertial-based measurements this parameter
should be used with caution. However, future improvements
regarding a reduction of the soft tissue artifacts might help to
overcome these fore-aft position-related limitations. In this
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Methodological Limitations
Despite the carefully chosen reference system and setup, the
study has some limitations that are worth to be discussed:
first, the model was specifically designed for lower limb and
trunk motion capture. Accordingly, upper limb joints (shoulders,
elbows, wrists) and head vertex were only approximately tracked.
Especially for the shoulder joint and head vertex reference
positions might have been estimated with errors of up to a
few centimeters. This inaccuracy was judged to be acceptable,
since a validation of the upper limb position and orientation
was not the main aim of this study. Second, for the estimation
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Center of Mass in Skiing
FIGURE 6 | Bland-Altman plots for the range of motion of the vertical distance (left) and fore-aft position (right). The model without arms was used to generate the
figures and compute the LoA (dashed lines). Mean error is shown with the solid lines. Blue marks the outside leg and yellow the inside leg. LoA for both models and
outside and inside legs are reported in Table 4.
either. Therefore, it is expected that errors for on-snow skiing
might be slightly larger than presented here.
Perspective
Overall, based on the system’s accuracy and precision and,
specifically, based on Cohen’s d, the proposed method was found
to be sensitive enough to distinguish between different types
of turns (wide/narrow). Thus, the current method may also
provide a useful information for monitoring and controlling
adverse external loading patterns that occur during regular onsnow training. Moreover, as demonstrated earlier and in other
settings (Chardonnens et al., 2012, 2014; Rawashdeh et al., 2016;
Yu et al., 2016; Whiteside et al., 2017), such an approach is also
suitable for quantifying competition time, movement repetitions
and/or the accelerations acting on the different segments of the
human body. However, prior to getting feasible for applications
in settings of daily training, future studies should primarily focus
on a simplification of the sensor setup, as well as a fusion with
global navigation satellite systems (i.e., the estimation of the
absolute joint and CoM positions). It has to be pointed out that,
in order to fully quantify the total load, not only the external but
also the internal load should be quantified (Soligard et al., 2016).
FIGURE 7 | Influence of thigh orientation estimation error on ankle position.
Black shows the original leg position and gray the leg position with a thigh and
shank orientation error. The blue lines show the ankle – CoM vectors. The
fore-aft position (projection of ankle – CoM vector onto the fore-aft axis) is
more affected by this orientation error (difference shown in red) than the
vertical distance (length of ankle – CoM vector).
of CoM, segment inertial parameters were taken from Dumas
et al. (2007) and were only scaled to athlete height. However,
the body model could be further individualized by taking into
account the athlete’s segment lengths and an estimation of their
muscle masses. Third, as inertial sensors cannot provide absolute
position measurements, only the relative joint and CoM positions
were validated. For reasons of convenience, the lumbar joint
center (LJC) has been defined as the origin for both systems,
even though it could not be measured directly by the reference
system. However, by averaging the LJC estimated from the left
and right hip joint center, measurement errors were aimed to
be minimized. Fourth, the ecological validity of the study might
be limited. Despite the fact that the movement patterns on the
treadmill are known to correspond well to the real on-snow
skiing situation (Spörri et al., 2016a), the reduced speed might
have led to less dynamic movements and less arm motion.
Moreover, vibration from skidding on the snow did not exist
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CONCLUSION
The system allowed computing the athlete’s relative joint center
and CoM position with sufficient accuracy and precision for
detecting meaningful difference in alpine skiing. Only the
accuracy and precision of the most distal joints (e.g., ankle) are
on the limit of an acceptable range. The accuracy and precision of
the ankle positions can be considered acceptable for computing
the vertical distance, but not for calculating the fore-aft position.
Future developments should aim at reducing soft tissue artifacts
such that knee and ankle positions could be estimated with better
precision. To compute the absolute CoM position with respect to
a fixed global reference frame, the obtained relative CoM position
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Center of Mass in Skiing
and body model could be combined with an absolute position of
a body part (e.g., head), for example measured with differential
GNSS. A future study should also address how to simplify
the system so that it could be used for everyday external load
monitoring, with fully automated calibration and data analysis.
approved the final version and agreed to be accountable for all
aspects of this work.
FUNDING
The study was funded by the Swiss Federal Office of Sport
(FOSPO), grant 15-01; VM10052.
AUTHOR CONTRIBUTIONS
BF, JS, PS, SL, and KA conceptualized the study design. BF, JS,
PS, SL conducted the data collection. BF, JS, PS contributed
to the analysis and interpretation of the data. BF drafted the
manuscript, all other authors revised it critically. All authors
ACKNOWLEDGMENTS
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Conflict of Interest Statement: The authors declare that the research was
conducted in the absence of any commercial or financial relationships that could
be construed as a potential conflict of interest.
The reviewer TS declared a shared affiliation, with no collaboration, with
one of the authors JS to the handling Editor.
Copyright © 2017 Fasel, Spörri, Schütz, Lorenzetti and Aminian. This is an openaccess article distributed under the terms of the Creative Commons Attribution
License (CC BY). The use, distribution or reproduction in other forums is permitted,
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