2.3.2. DYSKIMOT

The DYSKIMOT sensor is a MARG sensor based on the Micro-Electro-Mechanical Systems (MEMS) IMU LSM9DS1 (SparkFun, 14 €), with a mass of 10.44 gr and size of 3 × 3 cm (Figure 3A,C). It is composed of 3-axis accelerometer, gyrometer and magnetometer, plus a temperature sensor (Figure 3B). These internal components respectively measure acceleration (in [g], ±16 [g]), angular velocity (in [◦/s], ±2000 [◦/s]) and magnetic field (in [gauss], ±16 [gauss]).The apparatus can operate between −40 ◦C and +85 ◦C. The sensitivity depends on the sensor and on the selected range; detailed information is given in the datasheet (https://www.st.com/en/mems-and-sensors/lsm9ds1.html). For example, the gyrometer sensitivity is 8.75 10−<sup>3</sup> ◦/s /LSB at the range ± 245 ◦/s, i.e., the range we use in the present study. Communication with other electronic components is made via serial peripheral interface bus (SPI) or inter-integrated circuit (I2C) protocol. The data recorded at a sampling frequency *f* = 100 Hz are transmitted to a PC via an Arduino Uno Rev 3 (23 €) and a USB cable (RS232 serial link). That sampling frequency was actually the maximal reachable with the devices used. The Arduino contains the data recovery program, using the SparkFun library provided for this sensor, and transfers them to a home-made acquisition software.

**Figure 3.** (**A**) Micro Electro-Mechanical Systems (MEMS). (**B**) 3-axis accelerometer, a 3-axis gyrometer, a 3-axis magnetometer and a temperature sensor. (**C**) Dimension of the DYSKIMOT.

The DYSKIMOT sensor was placed in front of the helmet (Figure 1C) with the X-axis in the vertical direction (inferior-superior axis). The Y-axis was aligned with participant's mediolateral axis at the beginning of the test and the Z-axis was aligned with the antero-posterior axis. This choice has two advantages. From a clinical point of view it is the most reliable position to record cervical axial rotation as shown in [33]. From an algorithmic point a view, the sensor orientation is such that the relevant information about the DidRen Test is fully contained in the X-component of angular velocity measured by the gyroscope. The latter time series was denoted ω*i*. A trapezoidal integration gave the head's rotation angles θ*i*, where the constant of integration was chosen such that the angle was zero at the beginning of the test. The derivative α*i* = <sup>ω</sup>*i*+*n*<sup>−</sup>ω*i*−*<sup>n</sup>* 2.*n*.Δ*t* with *n* = 5 and Δ*t* = 1/*f* provided the head's angular acceleration. Angles computed from the gyroscope showed a linear drift. Since the DidRen Laser Test consists of quasi-periodic rotations of 30◦ around a neutral position, a straightforward way of removing the drift is to subtract the least square regression line from the time series θ*i*. Notice that Elite (DYSKIMOT) time series are written with (without) a bar.

Before using the DYSKIMOT in this study, a test was performed using a sensor attached to a servo motor (see Figure 4) to mimic the sequence of the cervical axial rotation during the DidRen test, i.e., angles from 30◦ to the left and right by going back through the 0 angle (Figure 4). The servo motor with an Arduino Uno Rev 3, was programmed to perform the sequence repeatedly. The result can be seen in Figure 5. The sensor was kept static during the first 20 s of the test. The linear drift is clearly observable on the raw angular data and the parameters of this line are computed by a least squares regression. Then comes the activation of the actuator and the beginning of the sequence (around 25 s) started. The fitted linear drift was eventually subtracted from the raw angular data. Such a procedure is satisfactory for time series displaying the typical behavior of the DidRen Laser Test (Figure 5). Such a procedure may actually work in all cases, including non-periodic tests. The regression line parameters may even be stored provided they do not change over time or with temperature. We checked that the drift stays linear at larger time scales (30 min).

#### *2.4. Data Analysis*

Signals from DYSKIMOT and Elite were synchronized by an external digital trigger (National Instrument, Austin TX, United States). Since the frequencies of both sensors were different (100 Hz vs 200 Hz), the accuracy of the synchronisation of the time series θ, ω, α (Elite) and θ, ω, α (DYSKIMOT) is in the order of 5 ms.

**Figure 4.** (**A**) Servo motor + housing adapted to its axis to fix the MARG. (**B**) Angle = 0◦, (**C**) Angle = <sup>+</sup>30◦, (**D**) Angle = <sup>−</sup>30◦.

**Figure 5.** Example of linear drift due to integration of DYSKIMOT's raw angular velocity (red line) and correction of the drift of the test angle Z with the servo motor (blue line). The corrected angle (blue line) is obtained by subtraction of the regression line to the raw angle. This plot has been obtained by fixing the DYSKIMOT sensor on a servo motor (MG995, Tower Pro) performing successive and opposite rotations of amplitude 30◦.

Then the following parameters were calculated during each cycle and averaged on the 5 cycles achieved by each participant, see Figures 6 and 7 for a graphical illustration of our computational procedure: (1) angle (range of motion, in ◦); (2) peak angular velocity (maximum angular velocity reached, in ◦s<sup>−</sup>1); average angular velocity (in ◦s<sup>−</sup>1); (3) peak angular acceleration (maximum angular acceleration reached, in ◦s<sup>−</sup>2); (4) peak angular deceleration (minimum angular acceleration reached, in ◦s<sup>−</sup>2). The beginning of all cycles has been manually marked by one of the authors (RH) within a homemade software that performed the averages over the 5 cycles for each trial. The peak value of a given time series Xi has been computed to be max(Xi) unless the maximal value was judged to be an artefact by visual inspection of the curves. Then, the value below this maximum was retained.

Although our goal was to measure the agreemen<sup>t</sup> between Elite and DYSKIMOT sensors for ND and NDP participants, the computed parameters were of clinical interest, as neck velocity during fast rotation can discriminate between nonspecific neck pain and healthy control [13,14].

A Passing–Bablok regression [34], which allows to compare the DYSKIMOT vs Elite data, was performed on the individual values of the parameters for DP and NDP simultaneously so that the agreemen<sup>t</sup> between both sensors could be appraised and summarized by a "calibration line".

**Figure 6.** Typical plots of variables analyzed during one right rotation in a DP (34 years, Male, NDI = 22, NRPS = 5) and an NDP (25 years, Male, NDI = 0, NPRS = 0): (**A**) Angle; (**B**) Angular velocity; (**C**) Angular acceleration. Elite curves (dotted lines) can be compared to DYSKIMOT ones (solid lines). Computed parameters are illustrated by blue (Elite) or red (DYSKIMOT) arrows. (1) angle; (2) peak angular velocity; (3) peak angular acceleration; (4) peak angular deceleration.

**Figure 7.** Typical traces of the head motion during the 5 cycles of the DidRen Laser Test showing comparison of Elite (red line) and DYSKIMOT (Blue line) angle discrepancies. In (**A**), the best angle agreemen<sup>t</sup> between Elite and DYSKIMOT (difference = 0.6◦, mean angle during 5 cycles = 25.7◦) in an DP (34 years, male, NDI=22, NPRS = 5), and in (**B**) the worst agreemen<sup>t</sup> (difference = 4.0◦, mean angle during 5 cycles = 27.5◦) in a NDP (22 years, male, NDI = 0, NPRS = 0). Cursors indicating the beginning (grey) and end (green) of one axial rotation movement are shown.

A two-way ANOVA was then used to assess potential differences between the two systems (System factor: Elite or DYSKIMOT) and between the groups (Status factor: NDP or DP) for the parameters mentioned above. When the ANOVA indicated significant interaction, a post hoc Holm-Sidak analysis with pairwise multiple comparisons was carried out. Significance was fixed at *p* < 0.05 and all statistical procedures were performed with SigmaPlot 13 (Systat Software, Inc).

Finally, a dynamic time warping (DTW) analysis (without windowing) was carried out on the z-normalized data and the Euclidian DTW distances between the time series angle θ, θ, angular velocity (<sup>ω</sup>, <sup>ω</sup>), angular acceleration (<sup>α</sup>, α) for DYSKIMOT and Elite were calculated for all the participants and then averaged. The z-normalization consisted in replacing a time series *X* by *<sup>X</sup>*−*<sup>E</sup>*(*X*) *SD*(*X*) , *E* and *SD* denoting the average and standard deviation respectively.

The Passing–Bablok regressions and the DTW were performed by using R v3.4.2 and the packages mcr and dtw.

It is worth saying that the accuracy of synchronization is not a matter of concern: the parameters have been independently computed from Elite and DYSKIMOT time series, and no locality constraint has been added in the DTW procedure through a window parameter. Synchronization was mainly a facilitating tool for graphical exploration of the data.
