# Reliability of a Global Gait Symmetry Index Based on Linear Joint Displacements
## 2 Materials and Methods
### Data Processing  
The marker trajectories were low pass filtered using a 4 th order Butterworth filter with a cut off frequency of 10 Hz. A model with 8 segments (thorax, pelvis, thighs, shanks and feet) was built from a standing trial, allowing 6 degrees of freedom per segment. The segments local coordinate systems were defined based on the method described in [28], using the following anatomical landmarks: the medial and lateral femoral condyles and the hip joint centre (estimated by regression from the anterior superior iliac spines [29]) for the thigh; the medial and lateral malleoli and the mid-point between the femoral condyles for the shank; the first and fifth metatarsal heads and the mid-point between the malleoli (all projected onto the floor) for the foot; the right and left acromia and the mid-point between the anterior and posterior superior iliac spines for the thorax. The pelvis was defined as a CODA segment, using the four iliac spines previously mentioned [28]. The position and orientation of the segments during the walking trials was computed using a segment optimization technique [30] using the following tracking markers: the spinous process of C7, suprasternal notch and xiphoid process for the thorax; the highest point of each iliac crest, and the anterior and posterior superior iliac spines for the pelvis; the rigid clusters of markers for the thighs and shanks; and the lateral malleoli, first and fifth metatarsal heads, and posterior aspect of the calcaneus for the virtual feet. To calculate the symmetry index, firstly the Euclidean distances (Figure 2) from the \"joint centres\" to the pelvis origin (midpoint between the anterior and posterior superior iliac spines) were calculated and normalized to the gait cycle duration (101 points), for both sides. The \"joint centres\" positions were given by the coordinates of the distal extremities of the feet (midpoint between the first and fifth metatarsal heads), shanks (midpoint between the malleoli), thighs (midpoint between the femoral condyles) and thorax (midpoint between the acromia) in relation to the global coordinate system. More specifically, for the thorax, the same point is used for both sides, but normalised to the  
Figure 1: Anterior (**left**) and posterior (**right**) views of the marker placement. The rigid clusters (squares with 4 markers) were placed on the lateral aspect of the thighs and shanks. Anatomical markers are in black, tracking markers are in white with a black outline, and anatomical markers also used for tracking are in black with a white outline. The white marker with dotted black outline is a virtual marker created at the origin of the pelvis (midpoint between the anterior and posterior superior iliac spines), which was used to define the trunk. respective gait cycle. For the pelvis, the Euclidean distance from the left hip joint centre to the pelvis origin was calculated for the left gait cycle, and the Euclidean distance from the right hip joint centre to the pelvis origin was calculated for the right gait cycle. Secondly, for each component of the time normalized Euclidean distances and for each joint, the squared differences between the left and right curves were computed for each of the 101 time points. For the frontal plane, the sign of the distance between the pelvis origin and the left \"joint centres\" was inverted prior to calculating the bilateral differences. For each joint and each component, these bilateral differences were summed throughout the gait cycle and the square root was taken. This yields the 15 components of the LGGA, which are the absolute bilateral differences obtained for each segment component (3 axes of five segments). Finally, these components were added to give the symmetry index as explained in Equation (2).