Elementary Movement: Lateral Bending

The subject was first asked to position himself with his back to the bars, in the acquisition volume of the cameras. Then, after starting the acquisition with both systems and impacting the right heel to the ground, the subject made a series of five elementary movements. The elementary movements chosen was the one in the frontal plane. The recruited subject was asked to perform the movement purely in the selected plane, starting to the right side, without reaching the maximum possible lateral flexion. This is to avoid the displacement of the sensors and markers, but also to avoid the oscillation of the column in other anatomical planes outside the frontal plane.

In the post-processing phase, the markers information from the two bars were combined in such way that there was no gap in the acquisition of markers coordinates. After this, the data was resampled because Optitrack adopted an acquisition frequency of 120 Hz, while for Xsens the sampling frequency was set to 50 Hz.

Before the dynamic movement begun, the subject was asked to remain upright for a few seconds. The data obtained in that acquisition section were used to define the calibration matrices of the three triad markers and the three inertial sensors.

The processing carried out on the matrices on the inertial sensors, described in the Chapter 3 Section 2, is the same as that used in the case of the matrices of the triad markers. The angles obtained with Tilt-Twist Method from inertial sensors were compared with Roll, Pitch ang Yaw angels defined for Optitrack in the following way, according to the defined axis system:

𝑃𝑖𝑡𝑐ℎ = 𝑎𝑡𝑎𝑛2 (𝑍^′_𝑥 𝑍^′_𝑧)

𝑅𝑜𝑙𝑙 = 𝑎𝑡𝑎𝑛2 (−𝑋^′_𝑦 𝑋^′_𝑥 )

𝑌𝑎𝑤 = −𝑎𝑡𝑎𝑛2 (−𝑍^′_𝑦 𝑍^′_𝑧 )

The convention (Tab. 4.5.1-1) adopted to obtain the angles with Optitrack system is the same used in Xsens system.

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PITCH ROLL YAW

POSITIVE + Flexion Right Right NEGATIVE - Extension Left Left

Tab. 4.5.1-1 Angles convention for Optitrack system.

The Roll, Pitch and Yaw angles were filtered using the Matlab routine Curve Fitting Tool and in particular, a Smoothing Spline was used for interpolation. In the Figs. 4.5.1-1,4.5.1-2,4.5.1-3 are shown examples of the result of the interpolation have been reported.

Fig. 4.5.1-1 Smoothing of S1 pitch angle.

Fig. 4.5.1-2 Smoothing of S1 roll angle.

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Fig. 4.5.1-4 shows the movement patterns of C7 vertebra compared to the T12 vertebra detected by the two different measuring systems in the three planes. Visually from these graphs it is possible to notice that the patterns relative to the two measurement systems are very similar in the frontal and transversal planes, while in the sagittal plane there are some discrepancies.

Moreover, in the frontal plane the Optitrack system pattern seems to be wider Focusing on the pattern in the frontal plane, it is possible to recognize five complete movements: from the upright posture to positive lateral flexion (to the right side), from positive lateral flexion to upright posture, from upright posture to negative lateral flexion (left side) to return at upright posture. From these patterns it is possible to notice how a movement, even if executed in a specific plane, is accompanied by, more or less, wide movements in the other planes.

Fig. 4.5.1-5 shows the trends of the T12 vertebra compared to the Pelvis. Here again, in the sagittal plane, the two measurement systems return information that is not strictly consistent.

In the frontal plane and in the transversal plane, on the other hand, the trends can be superimposed. In the transversal plane Optitrack pattern is slightly wider.

Finally, Fig. 4.5.1-6 shows the trend of the Pelvis with respect to its starting position, during lateral flexion movement. Unlike what happens in the other segments considered, the patterns are superimposed in all three anatomical planes.

Fig. 4.5.1-3 Smoothing of S1 yaw angle.

129 Fig. 4.5.1-4 Angles patterns of C7 vertebra compared to T12 vertebra during lateral bending.

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Fig. 4.5.1-5 Angles patterns of t12 vertebra with respect to Pelvis segment during lateral bending movement.

131 Fig. 4.5.1-6 Pelvis angles patterns during lateral bending.

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Examining the results obtained in the sagittal plane, it can be deducted that the discrepancy in the patterns between C7-T12 are due to the more consistent oscillation of the cervical zone that causes a possible misalignment between the two reference systems attached to the C7 vertebra.

The same reasoning can be associated with T12-S1 patterns, with the difference that the oscillation at T12 level is certainly less consistent than at C7 level. In fact, the patterns related to T12-S1 are less divergent than the patterns related to C7-T12. The consideration just made could explain the minor inconsistencies in the other two planes.

Tab. 4.5.1-2 shows the Range of Motions (ROMs) of the three segments considered in the three anatomical planes.

C7-T12 ROM (°) T12-S1 ROM (°) S1 ROM (°)

Sagittal Plane

Frontal Plane

Transv Plane

Sagittal Plane

Frontal Plane

Transv Plane

Sagittal Plane

Frontal Plane

Transv Plane Xsens 12.98 24.08 49.22 7.50 49.34 23.06 3.06 7.02 13.82 Optitrack 14.19 26.64 54.55 6.53 46.53 25.34 4.29 6.95 14.15

Difference 1.21 2.56 5.33 0.97 2.81 2.28 1.23 0.07 0.33

Tab. 4.5.1-2 Segments ROM obtained with the two measuring systems. The yellow row shows the difference between values corresponding to the spinal segment and the anatomical plane.

Analysing the ROMs in the frontal plane, the T12-S1 segment with respect to the Pelvis is the one that contributes most to the movement followed by the C7-T12 segment with respected to the T12-S1 segment. As already mentioned, it appears that C7 vertebra compared to T12 has a not negligible movement in the transversal plane, which is even greater than that in the main plane of movement. The same behaviour is found in the pelvic segment.

By looking at the differences between the two measurement systems, it is possible to confirm that the Xsens system is more reliable on the Pelvis than the other vertebral levels. It should be noted once again that the problem may be hidden in the structure used for the markers positioning.

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