Procedure
A square grid of 121 equally spaced points (11 x 11, distance between adjacent points: 20 cm) was drawn on the floor of the laboratory (see Fig 1). A low friction rotating stool with a plastic box was positioned over the grid with five reflective markers on its top, and three electromagnetic sensors were fixed with adhesive tape on one of the sides of the box along a vertical line, with 15 cm spacing in between (see Fig. 1). The antenna of the electromagnetic system was positioned on a wooden stick in the center of the grid, at a height of 120 cm from the floor. The base of the stool was moved in each of the points of the grid. The minimum distance of the stool from the antenna was set to 40 cm to allow the rotation of the stool, thus the points in the central square of the grid (3 x 3) were not used. For each position of the grid (11 x 11 points minus 3 x 3 points: 112 total points) the stool was manually turned around its rotation axis from the neutral position clockwise of approximately 270° and backwards until the neutral position two times. The angular velocity was approximately 120°/s in order to avoid vibrations or artifacts due to the inertia of the box. For each of the 112 positions, a recording was performed with both electromagnetic and optical motion capture systems.
Optical system
The optoelectronic position data were recorded with the BTS Elite (BTS, Italy) motion capture system, which included 6 infrared cameras positioned in standard points of the measurement room (four in the upper corners and two in the top center of the longest walls). The system was previously calibrated using a standard stick with four markers. The room had rectangular shape of 12 × 8 m and had no metal object or electromagnetic sources nearby. Four reflecting markers were positioned on the top of the plastic box, three in the corners of the top surface of the box (a rectangle of 25 × 30 cm) and the fourth in its center, at the top of a plastic stick of 20 cm, in order to have a minimal configuration of non-coplanar markers. The location of the optical markers was chosen in order to have the 4 markers always visible by all cameras, and their location on the object was similar to the position of markers on the head during cervical kinematics usually performed in clinical studies. The axis of rotation was along the z direction, perpendicular to the floor (see Fig. 1). The optical data from the infrared cameras were transformed by the Elite system which provided the positions in space (x, y, z) of the four markers positioned on the box at a sampling rate of 100 Hz.
Electromagnetic system
The electromagnetic data were recorded with the Polhemus-G4 acquisition system (Polhemus, USA), a device that tracks position and orientation of sensors relative to a source in three dimensions. The system has been used and shown to be accurate to within ± 0.2° [11, 12]. In our test, three sensors were fixed to the rigid plastic box at three different heights from the floor (105, 120, and 135 cm) at a distance of 15 cm from the rotation axis (see Fig. 1). The location of the sensors with respect to the antenna was selected in order to be similar to what is usually performed in clinical practice during cervical kinematics, where the sensors are positioned on the subject’s forehead. The wires were secured with adhesive tape to prevent traction on the sensors. The electromagnetic source was positioned over a wooden stick positioned in the middle of the room at a height of 120 cm from the floor (coordinates 0, 0,+120). The sensors were attached to a transmitter (hub) which had a wireless connection to a laptop PC, and continually recorded the position and orientation (x, y, z, pitch, roll, yaw) for each of the three sensors at a sampling rate of 120 Hz. Each marker was considered individually.
Signal processing
The position data obtained from the Elite system were analyzed in order to obtain the position and direction cosine matrices for each time instant using the singular value decomposition (SVD) technique. The Euler angles from the Polhemus-G4 system were converted into direction cosine matrices. The box was assumed to be a rigid body and its center was assumed to be in the center of the box at a height of 120 cm.
For both systems the position and orientation of the box were used to compute the Finite Helical Axis (FHA) for each time instant. The algorithm used for the extraction of FHA was previously described [7, 13]. For each acquisition one FHA was extracted for each pair of time instants selected in order to have always the same angular distance in between. The angle between the two frames was set to 10° according to the results of a previous study [7].
Since the electromagnetic data were affected by static field distortions, position data were compensated with a bi-dimensional function of the second order, whose parameter were empirically identified in order to reduce the deviation of the z positions from the theoretical horizontal plane (Fig. 2).
Since the recordings were lasting approximately 10 s, the number of FHA detected for each acquisition was about 1200 for the electromagnetic system and 1000 for the optical system. The intersections of each of the FHA with the horizontal plane at the height of the antenna were identified, and the distances between each FHA from the average intersection point was defined as position error. In addition the angle between each FHA with respect to the vertical was defined as angle error.
Statistical analysis
The mean value and standard deviation of the distribution of position and angle errors were computed for each position of the box and stool on the grid. The distribution of angle and position errors extracted with the two detection systems were compared using the 2-way Analysis of Variance (ANOVA). The fixed factors were: type of sensors (Elite, Polhemus sensor 1, Polhemus sensor 2, Polhemus sensor 3), and stool location on the grid as fixed factors. Post hoc differences were investigated using the Wilcoxon rank sum test for equal medians. Shapiro-Wilk test was applied to signals to evaluate the data normality. Significance level was set to α = 0.05.