Gait Analysis

As explained in Section 1, handling arbitrary sensor-to-segment mounting is a major challenge in gait analysis with inertial sensors. Manual measurements, as well as calibration poses and movements, are commonly suggested solutions. Furthermore, we pointed out that the use of magnetometers is typically limited by the assumption of a homogeneous magnetic field. In this section, we describe a set of methods for IMU-based joint angle estimation that allow us to face these two challenges in a new way. We will combine elements of the methods reviewed above, but unlike most previous attempts, we will:

avoid sensor-to-segment mounting assumptions;

require no manual measurements of any distances, etc.;

not rely on the accuracy with which the subject performs predefined postures or movements;

and avoid the use of magnetometers.

Instead of employing any of these commonly used assumptions and restrictions, we make use of the fact that the knee joint behaves approximately like a mechanical hinge joint. The kinematic constraints that result from this fact are exploited to obtain the position vector and the direction vector of the knee flexion/extension axis in the local coordinates of both sensors. As outlined above, this information is crucial to precise joint angle calculation. We will use it to fill the gap between the sensor coordinate systems and the joint-related coordinate systems in which the angles are denned. Subsequently, this will allow us to calculate flexion/extension joint angles on joints with a major axis of motion, for example the knee and the ankle during walking. All of the methods that we will introduce use only angular rates and accelerations, while the use of magnetometer readings is completely avoided.
Before we describe the respective algorithms, let us define the available measurement signals. Assume that two inertial sensors, one attached to the upper leg and the other attached to the lower leg, measure the accelerations, a₁(t),a₂(t)ϵ ℝ³, and angular rates, g₁(t),g₂(t)ϵ ℝ³, at some sample period, Δt. Additionally, we calculate the time derivatives ġ₁(t),ġ₂(t)ϵ ℝ³ of the angular rates via the third order approximation:
${\dot{g}}_{1/2}(t)\approx \frac{g_{1/2}(t-2\mathrm{\Delta }t)-8g_{1/2}(t-\mathrm{\Delta }t)+8g_{1/2}(t+\mathrm{\Delta }t)-g_{1/2}(t+2\mathrm{\Delta }t)}{12\mathrm{\Delta }t}$

Two models, i.e., generic-scaled and personalized, were created for each participant and used to perform MSK simulations with OpenSim 4.2 to estimate muscle and joint contact forces acting on the femur (Delp et al., 2007 (link); Steele et al., 2012 (link)). For the generic-scaled models, the generic ‘gait2392’ OpenSim model (Delp et al., 2007 (link)) with locked metatarsophalangeal joints was linearly scaled to fit to the participants’ anthropometry based on the location of surface markers (Kainz et al., 2017 (link)). For the personalized model, the Torsion Tool (Veerkamp et al., 2021 (link)) was used to modify the femoral geometry in the ‘gait2392’ model to match each child’s NSA and AVA before scaling the model. The maximum isometric muscle forces of all models were scaled based on the ratio of the body mass between the participant’s model and unscaled reference model (Eq. (1)) (van der Krogt et al., 2016 (link); Kainz et al., 2018 (link)). In summary, we had two models for each participant which were exactly equivalent except for the femoral geometry and corresponding muscle paths and attachments of muscles. ${\mathit{F}}_{\mathit{s}\mathit{c}\mathit{a}\mathit{l}\mathit{e}\mathit{d}}={\mathit{F}}_{\mathit{g}\mathit{e}\mathit{n}\mathit{e}\mathit{r}\mathit{i}\mathit{c}}*{\left({\mathit{m}}_{\mathit{s}\mathit{c}\mathit{a}\mathit{l}\mathit{e}\mathit{d}}/{\mathit{m}}_{\mathit{g}\mathit{e}\mathit{n}\mathit{e}\mathit{r}\mathit{i}\mathit{c}}\right)}^{\left(\mathbf{2}/\mathbf{3}\right)}$
All models and the corresponding gait analysis data were used to calculate joint angles, joint moments, muscle forces and joint contact forces using inverse kinematics, inverse dynamics, static optimization by minimizing the sum of squared muscle activations and joint reaction load analyses, respectively. Knee and ankle joint markers were only used for scaling and excluded during inverse kinematics. The remaining markers were weighted equally. Maximum marker errors and root-mean-square errors were accepted if less than 4 cm and 2 cm, respectively, as recommended by OpenSim’s best practice recommendations (Hicks et al., 2015 (link)). Additional analyses were performed to identify muscle attachments on the femur and obtain the effective directions of muscle forces (van Arkel et al., 2013 (link)). The mean waveform of the resultant HCF from all trials was calculated and the trial with the lowest root mean square difference to the mean waveform was selected as a representative loading condition. Similar to previous studies (Yadav et al., 2016 (link); Kainz et al., 2020 (link)) nine load instances were selected based on the HCF peaks and the valley in-between during the stance phase. The HCF and muscle forces acting on the femur during the nine load instances were used as loading conditions for FE analysis.

Gait analysis was performed on a Catwalk XT according to manufacturer’s instructions. Briefly, mice were habituated to the Catwalk for 5 min, and then the glass was cleaned prior to acquisition. Each mouse (n > 4 per experimental group) was then allowed to perform at least 3 runs across the Catwalk, which records paw position and analyses gait patterns using the Catwalk XT 10.6 Acquisition and Analysis Software.