3.1. Handwriting Feature Extraction
In this paper, we extracted a set of 82 features. From this set, we performed a Wilcoxon statistical test between different phases in order to detect significant differences.
We found significant differences in six features in phase 1/Post-FA, 11 features in phase 2/Pre-FA, 17 features in phase 2/Post-FA, and 29 features in phase 3/FA. Thus, the higher the physical effort, the higher the number of features where significant differences were detected. However, we selected only a subset of these relevant features, which are depicted in Table 2
. In this way, we improved the interpretability of results by nontechnical experts (medical doctors, physiotherapists, etc.). The meaning of these features is the following:
Entropy: It is a complexity measure related to the information content. The more unpredictable and complex is a signal, the higher the entropy. The entropy was applied to different signals such as X and Y coordinates, pressure, etc. Entropy is a classic measure used in information theory [34
Entropy refers to disorder or uncertainty. It is a measure of unpredictability of information content. For instance, the entropy of the pressure signal p, which ranges [0, 2047], can be defined as:
where prob is the probability of pressure value p.
In handwriting tasks, entropy is related to the complexity of the writing. The more complex it is, the higher the entropy. This measurement can be applied to trajectories, pressure patterns, etc.
First derivative: The first derivative of a given signal (X, Y coordinate, pressure, etc.) over time is the speed of this signal. Thus, average speed detects if a signal changes fast or slowly. In MATLAB it can be easily calculated. For instance, for the X coordinate:
In handwriting tasks, it is related to the execution speed of the writing. It can be applied to spatial coordinates X and Y and pressure signal, too.
Second derivative: The second derivative of a given signal (X or Y coordinate, pressure, etc.) over time is the acceleration of this signal. Thus, the average acceleration detects the changes of speed of this signal. For instance, for the X coordinate:
In handwriting tasks, it is related to speed changes of the writing. It can be applied to spatial coordinates X and Y and pressure signal, too.
Time in air: Time in air or time up is the time spent with the pen exerting no pressure. This time is considered at short distance (smaller than 1 cm from the tip of the pen to the surface [35
]). This time is zero for those tasks where the whole drawing can be produced in a single stroke, and is large when the drawing requires a large amount of strokes.
Given a pressure signal p, it can be obtained with the following MATLAB code:
While some movements in air are necessary to change from one stroke to another one, it is also related to pauses and hesitations during the handwriting task. Long times spent in air can be indicative of problems. For example, they are typical in Alzheimer disease.
Normalized time up: The previous feature, time in air, is normalized by the number of strokes in the air. Thus, the previous feature is divided by the number of strokes performed in the air, where a stroke has a specific direction, length, and curvature relative to the other strokes and has been performed between two consecutive instants where the pen touches the surface. Its computation is based on zero-crossing rate (ZCR) value. Zero-crossing rate (ZCR) is the number of times that a given signal crosses from positive to negative (or zero) values or vice versa. It can be defined using the following equations:
%zero crossing rate for pressure signal
v = diff(p > 0);
strokes_d = (p(1) > 0) + sum(v == 1); %strokes down
strokes_u = (p(1) == 0) + sum(v == −1); %strokes up
nt_up = t_up/strokes_u; %normalized time up.
Time down: Time spent with the pen exerting some pressure. Thus, the tip of the pen is touching the surface of the tablet. The slower the speed of movements, the higher the time down to finish the task.
p > N: is defined as the number of samples of a specific handwritten task with pressure higher than this N value. Several N values were tested.
P[N1-N2]: is defined as the number of samples on a specific handwritten task with pressure between N1 and N2 value, where N1 > 0 and N2 < 1024. Large values imply long time to raise the pressure while small values imply a fast increase in pressure.
shows an example of pressure profile as well as pressure equal to level 100 and 600. The p100 and p600 are defined as the number of samples with pressure value higher than 100 and 600 value, respectively.
Max speed: given the instantaneous speed of a signal, its maximum value is selected.
dx = diff(x); %first derivative of x coordinate
dy = diff(y); %first derivative of y coordinate
speed = sqrt(dx.^2 + dy.^2); %instantaneous speed
max_speed = max(speed)
3.4. Mechanical Results
In vertical flight height (CMJ test), a significant CMJ x time interaction effect was observed (p
= 0.03, ηp2 = 0.17, SP = 0.65). A significant CMJ and time effect were detected (p
< 0.001, ηp2 = 0.46, SP = 0.99; p
= 0.01, ηp2 = 0.31, SP = 0.77, respectively) (Table 3
). Bonferroni assessment confirmed that significant flight height losses were only observed between Ph2-Pre and Ph2-Post (p
= 0.03; anaerobic lactic metabolism). Also, significant flight height losses were detected only between Ph1-Post (anaerobic alactic metabolism) and Ph2-Post (anaerobic lactic metabolism) (p
In power output (CMJ test), a significant CMJ x time interaction effect was verified (p
= 0.003, ηp2 = 0.31, SP = 0.91). A significant CMJ effect was found (p
< 0.001, ηp2 = 0.42, SP = 0.99) (Table 3
). No time effect was found (p
> 0.05). Bonferroni post hoc confirmed that significant power output losses were detected between Ph2-Pre and Ph2-Post (p
= 0.01; anaerobic lactic metabolism) and between Ph2-Post and Ph3. Significant power output losses were found between Ph1-Post and Ph2-Post (p
= 0.041); however, a greater power output was observed in Ph2-Post than in Ph3 (p
Rating of Perceived Exertion (RPE)
A significant RPE x time interaction effect was corroborated (p
< 0.001, ηp2 = 0.93, SP = 1.00). A significant metabolic (p
< 0.001, ηp2 = 0.97, SP = 1.00) and time effect were evidenced (p
< 0.001, ηp2 = 0.92, SP = 1.00) (Table 3
). Bonferroni adjustment confirmed lower RPE in Ph1-Pre than in Ph1-Post (p
< 0.001). A higher RPE was proven in Ph2-Post than in Ph2-Pre (p
< 0.001) and in Ph2-Post than in Ph3 (p
< 0.001). Moreover, significant changes were found among Ph1-Post, Ph2-Post, and Ph3 (p