Parameters Extraction

Indexes of movement of clinical interest

From the velocity measurements obtained from the optical flow and the coordinates of the centroid, all other parameters were obtained for the study of the movement of each region. Firstly the vectors of the trajectories were obtained through integration of the time average of velocity vectors for each region and the acceleration vectors were derived by the velocity vectors. From this information (trajectory, velocity and acceleration) the indices of motion described below were calculated, for both markerless [209] (see Chapter 2) and marker- based analysis [153, 224, 197].

Motion sequence

A motion sequence is defined as a time interval in which at least one of the body segments is considered in motion, that is, it moves at speed greater than 0.5 pixels / frame [197]. This sequence is completed when all the limbs are still (or moving with velocity <0.5pixel / frame) for a duration of at least 0.32sec (8 consecutive frames). The calculation of this index was made according to the perceptual evaluation with which clinicians identify different sequences of GMs in a recording of several minutes. The threshold values for the speed and for the duration of the pause between two sequences were obtained empirically, based on the assessments made by myself, certified observer of the General Movements. The procedure returns the number sequences of motion detected, the instants of beginning and ending for each sequence (in frames and in seconds), their duration and the time break between two consecutive sequences. This allowed the evaluation of all other indices of motion for both the individual sequences (knowing the instants of beginning and end of the sequence), and for the whole movie.

In this study, as in [197], the number of units of motion / minute is considered as an index of motion. The units of motion were calculated for all body segments of interest (head and limbs).

Average speed

For each region was calculated the average value of the speed for the duration of the recording and for each sequence of motion. average acceleration For each region was calculated the time average of the acceleration.

Skewness

The skewness (defined in Chapter 4.3) measures the velocity distribution in the limbs. Spontaneous movements in healthy infants are fluid movements of moderate speed that should be reflected in negative skewness values but not too large in magnitude, while in infants with neurological disorders such movements are spastic and cramping [153, 224]. The skewness of the speed was evaluated not only for the legs as in [153, 224], but also for the arms. Fig. 5.6 shows the distribution of the speed of the right arm for a LR

87 subject analysed. The long tail to the left reflects the negative skewness of the speed, and therefore fluid movements of moderate speed.

Figure 5.6. Speed distribution for the right arm of a LR newborn at 6 weeks of age. Kurtosis

As reported by Kanemaru [197, 198], the kurtosis quantifies the shape of the distribution of the acceleration. A high value of kurtosis indicates a distinct peak in the distribution and therefore the presence of intermittent jerky motion [197]. Conversely, data with low values of kurtosis indicate a flatter distribution around the average and a slower decline to the sides. Figure 5.7 shows the distribution of the acceleration of the right arm for the same case study. The sharp peak in correspondence of the average value reflects the high value of kurtosis of the acceleration, which corresponds to a jerky motion.

88 Cross-correlation of speed and acceleration

To investigate the coordination of movements of the limbs and their symmetry, the cross-correlation of speeds and accelerations is calculated for all possible combinations of the limbs (right arm-left arm, right leg-left leg, right arm-right leg, left arm-left leg, right arm-left leg, left arm-right leg) as in [197] and the cross-correlation of speed, as in [197, 224]. The cross-correlation coefficient was calculated as the mean value of the correlation function between the two vectors.

Area outside the standard deviation of the moving average of trajectories [153, 224] and [209]. For the trajectories of the regions of interest, the area outside the standard deviation of the moving average of 25 points of the trajectory was computed as the difference of integrals, in the intervals in which: m.a -σ <T <m.a + σ, where T is the trajectory, m.a is its moving average and σ the standard deviation of the mean. In fig. 5.8 the selection of these areas is represented graphically (green) on a sequence of the trajectory of the right arm of a subject analysed

Figure 5.8 Area outside the standard deviation of the moving average of the trajectory of the right arm (colored areas in green) for a LR newborn at 6 weeks of age

Periodicity

To compute the periodicity of trajectories and velocities, a method already applied in other studies both marker-based (Meinecke et al [224]) and markerless (Rahmati et al [209]) is used. The vector of the trajectory (and of speed) was divided into three parts of equal length and each part was averaged. For each part the intersections of the vector with its average were computed and the average distance between two consecutive intersections was measured along with the standard deviation of this distance. Finally the following index of periodicity of the signal was computed:

89 Where dmean is the average of the time intervals (in seconds) between two consecutive intersections and  is the their standard deviation. In Fig. 5.8 is graphically shown the comparison between the trajectory and the local averages computed for each of the three parts for the right arm of a LR newborn at 6 weeks of age. As shown in Fig. 5.9 the movement is greater in the second segment than in the other two.

Figure 5.9. Plot of the trajectory and of the local average for the computation of the periodicity. T2 is the trajectory along the x direction of the right arm of a LR newborn at 6 weeks of age. Lp2 depicts the three

local averages.

Jerk index

The jerk index, defined in [197] is an index that describes how is jerky the movement. It is defined as the change of the acceleration in time (thus through the derivative of the acceleration). It is computed by the following equation:

90 Where x and y are the (time-varying) coordinates of each limb and V is the average speed for the motion sequence considered. A high value of C corresponds to very jerky movements, while for low values of C the movements are more fluid. The jerk index was calculated only during active periods of motion, that is, for the time intervals during which the speed of at least one of the limbs was above the threshold of 0.5 pixels / frame.

Lateral mobility index

The lateral mobility index E is defined by Kanemaru et al [197] as the ratio between the overall mobility along the horizontal direction and that along the vertical direction. It is computed as the ratio of the root mean square of the speed of the arms and legs along the x direction compared to that along the y direction, according to the following equation:

Where 𝑥̇ is the speed (derivative of the position) for each limb along x and y respectively. RA=right arm, RL=right leg, LL=left leg and LA =left arm . A low value of E indicates reduced lateral mobility.

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