![on the left, pure joint rotation about the flexion-extension axis (functional approach). On the right, the FE axis is highlighted in red and it is assumed to be coincident with the mean relative angular velocity vector. Taken from [5].](https://www.researchgate.net/profile/Marco-Caruso-2/publication/326033519/figure/fig1/AS:642445238870019@1530182289433/on-the-left-pure-joint-rotation-about-the-flexion-extension-axis-functional-approach_Q320.jpg)
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GNB2018, June 25th-27nd 2018, Milan, Italy
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Abstract—This work deals with the implementation of a
procedure to estimate the knee flexion-extension angle using
MIMU data. The influence of two algorithms for orientation
estimate on the knee angle was also analyzed. The good accuracy
of the two methods was assessed indoor by comparing their mean
flexion-extension waveforms with those of an electrogoniometer
(=-3.1° vs 1.1°, RMSDm=3.1° vs 5°). The within-gait
cycle variability was computed as the average STD computed
across waveforms. A general decrease of the STD values of about
1° was observed in outdoor conditions due to lower intensity of
the ferromagnetic disturbances.
Keywords—MIMU, sensor fusion, knee angle, gait analysis.
I. INTRODUCTION
HE estimate of knee joint kinematics is useful for
evaluating gait alterations. Optical stereophotogrammetry
gait analysis represents the gold-standard in clinical practice.
Alternatively, when a description of the knee motion in the
sagittal plane is sufficient, electrogoniometers can be used.
However, the latter techniques do not allow to analyze the
subject during free living conditions since the observation is
limited in restricted measurement volumes.
Magnetic and inertial measurement units (MIMU) is an
emerging technology for gait analysis because of its low-cost,
low-power consumption and miniaturization. These units
generally include a triaxial accelerometer, gyroscope and
magnetometer whose complementary information are
exploited in a sensor fusion framework to estimate the
orientation of the MIMU Coordinate System (MCS) with
respect to a Global Coordinate System (GCS) which is defined
by the directions of the Earth’s gravity and magnetic North.
However, accelerometer and gyroscope noise and
ferromagnetic disturbances hamper the estimation of the
MIMU orientation which, in turn, negatively affects the knee
joint kinematic estimates. Errors in knee joint kinematics due
to measurement noise can be minimized by exploiting
biomechanical constraints.
Five steps are adopted in this work to estimate the knee
flexion-extension (FE) angle:
1) Computation of the orientation of the MIMUs placed on
thigh and shank with respect to their GCSs (which may not be
coincident because of a different definition of the local
magnetic North due to ferromagnetic disturbances);
2) Estimation of the direction of the knee FE axis by means of
a functional movement;
3) Realignment of the GCSs by exploiting the knee joint
constraint (the FE axis must have the same direction in a
common GCS when the knee acts as a pure hinge joint);
4) Computation of the relative orientation between thigh and
shank;
5) Estimation of the knee FE angle by decomposition of the
joint kinematics around the mean FE axis through an
optimization approach.
In the above-mentioned sequence, the first step is the most
critical one since it directly affects both the estimate of the
relative thigh-shank orientation and of the FE axis direction.
Aim of this work was two-fold: (i) to implement and validate
a robust method for knee FE angle estimation out of the
laboratory, and (ii) to investigate the influence of two different
sensor fusion algorithms for MIMU orientation on the final
knee FE angle estimate (.
The first method (KJE) is based on a revisited version of the
algorithm proposed in [1], the second method (KJX) is based
on the orientation provided by a commercial available
algorithm (Xsens, MT manager version 4.6). Both KJE and
KJX represent the orientation in the quaternion form.
The performances of KJE and KJX were evaluated in terms
of accuracy and variability in an indoor environment by taking
an electrogoniometer as gold standard. Experiments were
replicated in outdoor conditions to investigate the influence of
various magnetic environments to the knee FE angle
estimation. In outdoor environment, the performances were
only evaluated in terms of variability of the two MIMU
systems because the gold standard was not available due to its
technological setup.
II. METHODS
A. Theoretical background
The estimate of the knee joint FE angle requires at first the
definition of a model for the knee joint and its subject-specific
calibration. The knee is modelled by a hinge joint which only
allows the description of the relative movement between the
thigh and the shank on the sagittal plane defined by the flexion-
extension axis.
The majority of sensor fusion algorithms proposed in the
literature [1]–[3] addresses the problem of the orientation
estimate in the quaternion form instead of Euler angles or
orientation matrix because of it allows to avoid singularity
such as Gimbal Lock and because of it is low computationally
demanding [4]. The quaternion is a four-terms representation,
given an angle of rotation θ and the rotation axis
(angle-axis representation) the orientation of the
MCS with respect to the GCS can be expressed as in Eq. (1):
Sensor fusion algorithms only provide the orientation of the
GCS relative to the MCS, which is in general not aligned with
An innovative MIMU-based procedure for the
estimate of the knee flexion-extension angle
M. Caruso1,2, M. Knaftliz1, and A. Cereatti1,2
1 Department of Electronics and Telecommunications, Politecnico di Torino, Torino, Italy
2 Department of Biomedical Sciences, University of Sassari, Sassari, Italy
T
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the coordinate system of the body-segment where the MIMU
is attached (BCS). Therefore, a “sensor-to-segment-
alignment” procedure must be implemented to determine the
relative orientation between BCS and MCS. However, when
3D joint kinematic description is not required, the knee joint
kinematics can be more conveniently described as the
composition of a single rotation around the FE axis [5]. The
problem is therefore reduced to the identification of the
direction of the FE axis by means of a functional approach
which consists in asking the subject to perform a rotation of
the shank with respect to the thigh in the sagittal plane. The
direction of FE axis is assumed to be coincident with the one
of the mean relative angular velocity vector (Figure 1).
Figure 1: on the left, pure joint rotation about the flexion-extension axis
(functional approach). On the right, the FE axis is highlighted in red and it is
assumed to be coincident with the mean relative angular velocity vector.
Taken from [5].
As previously mentioned, a poor estimate of the orientation
of the two MIMUs would be reflected to the estimate of the FE
axis direction. In addition, because of the ferromagnetic
disturbances, the two MIMUs may sense two different GCSs.
In the best-case scenario, the orientation difference between
the two GCSs does not change with the movement and the
knee joint angle is affected by an offset. However, it is more
likely that this erroneous relative orientation is time-variant,
(this can happen especially if the subject is moving near iron
manufacturers and electrical appliances). This would result in
time-variant errors in the estimated knee joint angle (Figure 2).
In this work, a recent approach [6] was implemented to realign
the two GCSs at each time step by exploiting the constraint
that the FE axis must have the same orientation in the two
GCSs when the knee acts predominantly as a pure hinge joint.
Once the quaternions that describe the orientation of tight
and shank
are realigned then the relative orientation
between the two segments can be computed for each time step
as in Eq. (2):
The joint angular configuration
is defined as in Eq. (3):
where the * symbol represents the quaternion complex
conjugate operator and
is the “zero” joint configuration.
This configuration for the knee is in general defined when the
axes associated to the tibial and the femur are aligned. When
the direction of the knee FE axis is known the “zero” joint
configuration is assigned by imposing a selected posture,
typically the neutral standing posture [7].
Mathematically, the “zero” joint configuration is defined as
in Eq. (4):
where
and
are the thigh and shank starting
orientation, respectively.
Finally, the joint FE angle can be estimated by forcing the
decomposition of
at each time step into a single rotation
around the mean FE axis. For this purpose, an optimization
approach adapted from [8] was used.
Figure 2: comparison between the time series of computed with and
without the alignment procedure. In the latter case is affected by an
unpredictable error.
B. Experimental setup
The experiments were conducted in one healthy subject
from the academic staff of the University of Sassari. The study
was exempt from IRB approval given that there were no safety
issues. We ensured that the study was performed by following
the principles outlined in the Helsinki Declaration of 1975,
later revised in 2000. Before starting the acquisitions, the spot
check described in [9] was executed to select the two MIMUs
which exhibited the smallest deviations from what the
ensemble of MIMUs were observing on average.
a) Indoor walking
The subject worn the two MIMUs (MTw, Xsens) on the
lateral thigh and on the tibial plateau of the right leg to
minimize the soft tissue artefacts, as suggested by the MTw
User Manual. The knee electrogoniometer (Step 32, Medical
Technology s.r.l.) was also equipped with three foot-switches
sensors mounted on the sole of the foot to detect gait events
(Figure 3). The functional approach was executed by performing
five repetitions of a rotation movement of the shank around the
FE axis which had to be estimated while the thigh was kept
almost stationary. During the knee rotations the direction of
the instantaneous FE axis exhibited small changes (STD less
than 8°). The “zero” joint configuration was assigned by
imposing the neutral standing posture. The trial began with the
subject standing still in the neutral standing posture for ten
seconds. Since Step 32 (sample frequency, fs=2 KHz) and
MIMU (fs=100 Hz) systems were recording independently, the
subject was asked to execute three free squats, after the resting
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period, to allow instruments synchronization using cross-
correlation in the subsequent data processing. Then, the
subject was asked to walk at a self-selected normal speed back
and forth in one direction in a university classroom for three
times. At the end of the trial the subject performed other three
free squats. This protocol was repeated three times. To
consider for positioning variability, before each repetition, the
MIMUs were removed and then mounted again in similar
position and the calibration process was repeated.
Figure 3: the subject was equipped with MIMUs and Step 32
(electrogoniometer and foot switches).
b) Outdoor walking
The trials were conducted in a in a wide corridor. The
subject walked along the middle of the sidewalk to try to limit
the ferromagnetic disturbances. The trial began with the
subject still in the neutral standing posture for ten seconds,
then he was asked to walk at a self-selected normal speed in
one direction for about forty seconds and then to return at the
starting point along the same direction. This trial was repeated
at a fast speed.
The time series of the FE angle were automatically
segmented into gait cycles following an approach similar to
the one proposed in [10] for both indoor and outdoor walking
conditions. Knee FE waveforms were normalized to the gait
cycle percentage and the mean curve was obtained (Figure 4).
The general concept is to estimate the initial contact events of
the physiological gait cycle from the morphology of the shank
angular velocity along the medio-lateral direction (knee FE
axis) through an analysis based on wavelet transformation.
Since in the experiments we conducted, the MIMU was
mounted on the tibial plateau and its z-axis was not necessarily
aligned with the FE axis, we mathematically reoriented the
MIMU by means of the Rodrigues’ rotation formula in order
to align one of the MIMU axis with the FE axis. This was
accomplished by maximizing the angular velocity component
about the searched axis. The time instants corresponding to
initial contact events identified with this approach were
consistent with the ones provided by the foot-switches sensors
of Step 32 assumed as a standard because they allow a direct
measure of the gait events.
III. RESULTS
A. Indoor walking
Data from Step 32 were downsampled by a factor 20 to allow
a quantitative comparison with the data of MIMU systems.
The accuracy of MIMU-based estimates was assessed in
terms of (1): mean value difference between the mean
waveform measured by the gold standard and the MIMU-
based methods (); (2) root mean square difference
between the two mean waveforms after their mean values were
removed (RMSDm). Results obtained for KJE and KJX are
reported in Table I.
KJE vs Step 32
KJX vs Step 32
-3.1° ± 1.5°
1.1° ± 1.2°
RMSDm
3.1° ± 0.9°
5° ± 2.5°
Table I: values averaged over the three repetitions. Total number of gait cycles
considered: 92.
Figure 4: Indoor walking, first repetition. Normalized gait cycle of the mean knee flexion-extension waveforms obatined from JKE, JKX, and Step 32 systems.
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Within-gait cycle variability of the Knee FE angles as
estimated by the KJE and KJX methods was assessed by
computing the average standard deviation (STD) of their mean
waveforms. The STD values were then compared with that
obtained from the Step 32. The standard deviation (STD) of
each waveform is reported in Table II.
KJE
KJX
Step 32
STD
3.3° ± 0.3°
2.5° ± 0.4°
2.3° ± 0.4°
Table II: values averaged over the three repetitions. Total number of gait
cycles considered: 92.
B. Outdoor walking
In this case, the methods comparison was limited to within-
gait cycle variability of the Knee FE angles. The standard
deviation (STD) of each waveform is reported in Table III.
KJE
KJX
STD (normal speed)
2.5°
2°
STD (fast speed)
4.4°
3.3°
Table III: The number of gait cycles considered amounted to 57 and 45 for
the normal and fast speed walking conditions, respectively.
IV. DISCUSSION
With reference to the indoor walking it is possible to
observe that KJE underestimated the mean value of while
KJX provided an overestimate of it, as suggested by the
negative and positive values of , respectively. In
addition, the values of highlighted in general a better
accuracy of KJX than KJE (1.1° vs 3.1°).
The smaller values RMSDm of the KJE compared to the
KJX (3.1° vs 5°) indicated a better waveform reconstruction
for the KJE. The within-gait cycle variability estimated by KJE
was slightly higher than the one estimated by KJX (3.3° vs
2.5°). This could be related to the limited ability of KJE to
properly deal with the ferromagnetic disturbances that affect
the indoor environments [11]. The within-gait cycle variability
estimated by KJX was very close to the physiological
variability measured in the subject under analysis by the gold
standard (2.5° vs 2.3°).
Within-gait cycle variability was closer to the physiological
variability when walking in an outdoor environment for both
methods at normal speed. This may be due to the lower
intensity of the ferromagnetic disturbances in the outdoor
environments.
When walking at fast speed, a general increase of the
within-gait cycle variability was observed for both methods.
Lower variability was found for the KJX method. This could
be partially explained by the lower values of the effective
sample frequencies: despite the data for both KJE and KJX
were provided in output at 100 Hz, the Xsens Kalman filter
worked on board at an internal sample frequency of 1800 Hz.
All the sensor fusion algorithms rely on the fundamental
hypothesis of a constant angular velocity inside the sampling
intervals. When the speed walking increases a higher value of
the sample frequency helps this hypothesis to hold.
V. CONCLUSION
The experiments conducted in this work aimed to test the
effectiveness of the proposed procedure for the knee flexion-
extension angle estimation based on magneto-inertial data.
The second aim was to investigate the differences in the
estimate of the FE angle as computed using two different
MIMU-based sensor fusion algorithms. In general, both KJX
and KJE applied to the proposed procedure provide accurate
estimates when compared with the gold standard. It is worth
noting that because MIMU sensors and the electrogoniometer
were attached on the skin of the subject in different locations,
the relevant measurements will be necessarily affected by
different soft tissue artefacts which will cause some
differences in the final knee kinematics estimation. The
variability of the knee angle estimated with both KJE and KJX
differed at most of about 1° from the gold standard and it was
consistent with the physiological variability observed in
normal knee kinematics.
Both KJE and KJX exhibited a smaller within-gait cycle
variability of the knee FE angles during outdoor walking
conditions. This improvement can be due to a lower intensity
of the ferromagnetic disturbances. In general, slightly lower
STD values were observed in KJX for both indoor and outdoor
walking conditions. This may be related to the solutions
implemented in the sensor fusion algorithm by Xsens to
compensate for the ferromagnetic issues [10].
Future studies will be devoted to compare more MIMU-
based sensor fusion algorithms for the knee FE angle
estimation and to enroll a larger number of subjects.
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