Table 2 Indices computed based on the 3D endpoint trajectory used for assessing UL movement accuracy, velocity and smoothness

Indices of accuracy

 HPR, %

Global Hand Path Ratio, defined as the ratio between the length of the endpoint trajectory during the reaching movement and the minimum distance between the starting point and target, expressed as a percentage. HPR equals 100 % for straight movements and increases with the trajectory curvature and presence of abnormal movements.

 locHPR, %

Local Hand Path Ratio, defined as the ratio between the length of the endpoint trajectory and the shortest trajectory within a circle with a 2.5 cm radius centered in the target, expressed as a percentage. The locHPR equals 100 % for straight movements towards the target and increases if the individual reaches the target with multiple adjustments.

 vertOS and horOS, cm

Vertical and horizontal overshoot, defined as the excess, if any, in both a vertical and horizontal direction beyond the region delineated by the starting point and target.

Indices of velocity

 maxVel, cm/s

Maximum velocity of the velocity profile of the 3D endpoint trajectory during each single reaching movement.

 meanVel, cm/s

Mean velocity of the velocity profile of the 3D endpoint trajectory during each single reaching movement.

 meanVel/maxVel, %

Ratio between mean and maximum velocity, expressed as a percentage. This ratio outlines the presence of a movement characterized by brisk movements with stops and starts.

Indices of smoothness

 NVelPeaks, adim

Number of local peaks in the velocity profile. This index counts the number of partial movements used to complete a single reaching movement. Also referred to as number of movement units.

 NormJerk, adim

The normalized jerk is a measurement of the trajectory smoothness. NormJerk was computed through numerical differentiation of the 3D endpoint trajectory and a zero phase lag low-pass Butterworth filtering with a cut-off frequency of 10 Hertz. NormJerk tends to be 1 for purely sinusoidal traces and greatly increases in the presence of acceleration variations.