# Utilization of a Mobile Application for Motor Skill Evaluation in Children +
## 2 Materials and Methods
### Mobile App  
The mobile app has been developed for the Android operating system. Our objective is to provide a tool for the development of exercises for the evaluation of fine motor skills in children. The exercises are based on tracking the movement of an object (target) along different paths. The app implements a user-friendly interface for designing arbitrary paths and configuring several exercise parameters, such as the speed of the object or whether the path and /or the object will be visible during the exercise, which allow different degrees of difficulty. exercises that share similar properties can be grouped in levels, which allows the physiotherapists to follow the children's progression more easily. For the study presented in this work, we designed three levels, denoted as Level 1, Level 2 and Level 3, each one corresponding to a different path: a straight diagonal line, a parabola-like curve and a zigzag open polygonal line, respectively (Figure 1). Motor coordination is more in demand when the movements include changing patterns. Sudden direction changes pose a greater difficulty for children who are still developing it [23]. For each of these levels, three configurations of increasing difficulty were chosen: slow speed (3 cm/s for grades 1 st to 3 rd and 4 cm/s for grades 4 th to 6 th), fast speed (6 cm/s for grades 1 st to 3 rd and 8 cm/s for grades 4 th to 6 th) and fast speed with hiding of the trajectory of the moving object (with the same speeds as in the previous case). We will refer to them as Mode 1, Mode 2 and Mode 3 in the following (Table 1). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Nodes** & **Grades 1 st to 3 rd** & **Grades 4 th to 6 th** \\ \hline Mode 1 & Target speed of 3 cm/s & Target speed of 4 cm/s \\ Mode 2 & Target speed of 6 cm/s & Target speed of 8 cm/s \\  & Target speed of 6 cm/s & Target speed of 8 cm/s \\ Mode 3 & The path hides when the target & The path hides when the target \\  & starts moving & starts moving \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of each mode of a level or path type. Figure 1: The three levels designed for the study: (**a**) Level 1, corresponding to a straight diagonal line; (**b**) Level 2, corresponding to a parabola-like curve; (**c**) Level 3, for a zigzag polygonal line. The slow basal speeds were taken from reference speeds established by previous studies on the performance of children's writing and drawing tasks on a tablet [24,25]. Figure 2a shows the app configured with the three levels; Figure 2b shows the three modes that are contained in Level 1 for grades 1 st to 3 rd; and Figure 2c shows the configuration of Mode 1 in Level 2. During the assessment, the child must follow the path shown as closely as possible by dragging the finger at the same speed as the object. Depending on the options selected in the exercise configuration, the path, the object or both may disappear during the game, so that the child must remember the path shown at the start of the exercise. The results are displayed when the object reaches the end of the path. Figure 3 shows the screen before, Figure 3a, during, Figure 3b, and after, Figure 3c, the exercise. The green line in Figure 3c is the path that the user followed with his/her finger. In order to determine the difference between the target path and the user path, the app polls the position of display touch events periodically. For most Android devices, the polling interval is \(\mathrm{T_{p}}\)\(=\)\(1/60\) Hz \(\cong\)\(16\) ms. Thus, for each time instant \(\mathrm{t}\)\(=\)\(\mathrm{kT_{p}}\), if a touch is detected, the app calculates the instantaneous error made by the user as the squared Euclidean distance between the touch event and the target:  
\[\mathrm{E(t)}=(\mathrm{x_{u}(t)-x_{t}(t)})^{2}+(\mathrm{y_{u}(t)-y_{t}(t)})^{2}, \tag{1}\]  
where \((\mathrm{x_{t}(t),y_{t}(t)})\) is the position of the target and \((\mathrm{x_{u}(t),y_{u}(t)})\) is the detected touch position, both measured in centimeters from the top left corner of the display.