Which functional movements for sensor-to-segment calibration for lower-limb movement analysis with inertial sensors?

If human motion analysis in laboratory can be considered as matured regarding the extensive research that has been performed in terms of technology and methodology, it is not the case for human motion analysis based on inertial sensors. Basically, for 3D movement analysis, angular velocities and linear accelerations measured by respectively the 3 gyroscopes and the 3 accelerometers present in one 3D-Inertial Measurement Unit (IMU) are sent to a data fusion algorithm in order to obtain orientation and, sometimes, also position (see Picerno 2017 for a review). Several challenges remain to be solved for this technology to be really effective and spread and this includes the sensor-to-segment calibration. Indeed, to estimate joint kinematics, the rotational matrix that enables to obtain the body segment referential frame orientation from that of the sensor is required for each sensor. Different procedures have been proposed in the literature (Picerno 2017). Some of them use static postures whereas others use devices to locate anatomical landmarks required to define segment axes relatively to the sensor referential frame. Unfortunately, these approaches are limited in terms of accuracy or require additional equipment. With the “functional approach”, specific movement performed at a joint is used to define a segment axis assuming that the angular velocity vector is aligned with the segment axis around which the movement is performed. Even if not yet demonstrated, this functional approach seems to provide the best ratio between time, ease, and accuracy. However, none of the functional approaches is currently recognized as a ‘‘gold standard’’. These procedures should then be more thoroughly investigated in order to define their advantages and drawbacks. We propose in the present study to investigate the calibration movements for lower-limbs sensor-to segment calibration. Indeed, the accuracy of the functional approach is limited by the precision with which the subjects can perform the motions, which is of particular importance to define axes in segment such as the thigh segment. In the present study, the segment axes will be defined with angular velocity vectors, not measured by inertial sensors but deduced from markers tracked by an optoelectronical system. The segment axes will then be confronted with those obtained by validated functional approach and model that have been proposed in traditional 3D motion analysis based on optoelectronical systems. To consider kinematics measures, models and methods based on optoelectronical systems as the gold standard enables to limit uncertainties due to lack of studies on human movement analysis based on inertial sensors (such as sensor locations for instance).


Introduction
If human motion analysis in laboratory can be considered as matured regarding the extensive research that has been performed in terms of technology and methodology, it is not the case for human motion analysis based on inertial sensors.
Basically, for 3D movement analysis, angular velocities and linear accelerations measured by respectively the 3 gyroscopes and the 3 accelerometers present in one 3D-Inertial Measurement Unit (IMU) are sent to a data fusion algorithm in order to obtain orientation and, sometimes, also position (see Picerno 2017 for a review). Several challenges remain to be solved for this technology to be really effective and spread and this includes the sensor-to-segment calibration.
Indeed, to estimate joint kinematics, the rotational matrix that enables to obtain the body segment referential frame orientation from that of the sensor is required for each sensor. Different procedures have been proposed in the literature (Picerno 2017). Some of them use static postures whereas others use devices to locate anatomical landmarks required to define segment axes relatively to the sensor referential frame. Unfortunately, these approaches are limited in terms of accuracy or require additional equipment.
With the "functional approach", specific movement performed at a joint is used to define a segment axis assuming that the angular velocity vector is aligned with the segment axis around which the movement is performed. Even if not yet demonstrated, this functional approach seems to provide the best ratio between time, ease, and accuracy. However, none of the functional approaches is currently recognized as a ''gold standard'' . These procedures should then be more thoroughly investigated in order to define their advantages and drawbacks.
We propose in the present study to investigate the calibration movements for lower-limbs sensor-to segment calibration. Indeed, the accuracy of the functional approach is limited by the precision with which the subjects can perform the motions, which is of particular importance to define axes in segment such as the thigh segment.
In the present study, the segment axes will be defined with angular velocity vectors, not measured by inertial sensors but deduced from markers tracked by an optoelectronical system. The segment axes will then be confronted with those obtained by validated functional approach and model that have been proposed in traditional 3D motion analysis based on optoelectronical systems. To consider kinematics measures, models and methods based on optoelectronical systems as the gold standard enables to limit uncertainties due to lack of studies on human movement analysis based on inertial sensors (such as sensor locations for instance).

Participants
12 subjects recruited in the institute took part in this study. They were aged between 22 to 60 years, their weight was 78.5 ± 22.2 kg, their height 175 ± 10.1 cm. They all provided their informed consent.

Protocol
32 reflective markers were placed on the subject at location limiting soft tissue artefact on segment coordinate frame definition. The marker positions were recorded by 20 cameras cadenced at 200 Hz. Table 1 presents the calibration movements tested and the segment axis that they define. Each movement was repeated 6 times. Technical coordinate frames were determined for each segment based on markers located on the segment. Quaternions corresponding to orientation of the technical coordinate frames in the global coordinate system were then computed. From these quaternions, angular velocity vectors were obtained following the formula: = 2̇qq *

Conclusions
This preliminary study proposed to investigate the functional calibration movements that could be used to perform sensor-to-segment calibration. According to the results, calibration movements don't significantly affect the functional axes obtained at least in subjects that haven't any lower-extremity dysfunction. However, it seems that for the thigh, segment coordinate system should be defined based on the flexion/extension and on the segment longitudinal axis. Moreover, squat movement -even if not statistically significant-seems to provide the best results to calibrate flexion/extension axes at the hip, knee and ankle joint.
where ω refers to the angular velocity, ̇q designed the first derivative of the quaternion and q * its conjugate.
Segment axis was then defined as the mean unit vector for which angular velocity was greater than 10% of the peak angular velocity.
The "gold standard" flexion/extension axis for the knee joint and planta/dorsiflexion axis of the ankle joint were obtained thanks to the functional method SARA (Ehrig et al. 2007). The hip joint centre was defined using the method described in (Halvorsen et al. 2005). Finally, the longitudinal segment axes were defined according to ISB recommendations.
To compare the different calibration movements, the angle existing between the segment axis obtained through the functional approach mimicking the one that could be applied with inertial sensors and the "gold standard" axes obtained with traditional methods based on optoelectronical systems.
An ANOVA for repeated measures was then used to compare these error angles obtained with the different calibration movements.

Results and discussion
Except for the planta/dorsiflexion flexion axis for which the axis obtained with the squat calibrating movement was significantly more aligned with the "gold-standard" axis (p<0.05), no difference was found between the calibrating movements.
One could notice that the hip abduction/adduction axes obtained by the two functional calibration movements