# Spatial Information on Voice Generation from a Multi-Channel Electroglottograph
## 3 Methodologies  
In order to describe the laryngeal _manoeuvres_, it was very important to focus on acquiring, visualizing, and saving data on a computer from the MC-EGG. Moreover, an algorithm for the evaluation of the larynx position inside the neck has been developed. For the acquisition, we used a DAQ 6035E, 38.5 kHz, and we developed a Labview (National Instrument) tool to interface the device with a laptop. This tool included a user interface (Front Panel) and a code interface (Block Diagram), following the numerical description of the phenomenon [12]. The Front Panel tool consisted of a macro-box with three folders (Figure 4): the first was used for the electrodes' positioning; the second, called the EGG, was developed to acquire data and to evaluate the larynx position inside the neck. The same box also includes a graph that shows the real-time dynamic of one channel (user defined), which represents the TEC variation in time (the typical EGG signal that evaluates the glottal dynamic). The second folder included another box that allowed the user to set the simulation time or to manually stop it. The third (last) folder, called \"Setting\", enclosed all the settable parameters. The acquired-data matrix is also visualized in that folder. This might be saved as a text file, which is useful for a Matlab post-processing, in a spreadsheet (.xls) file, or both [13]. The output matrix contained 36 columns, with each one representing a possible current path inside the neck between a sender and a receiver electrode: the number of rows depends on the simulation time. The algorithm for the evaluation of the larynx position has been developed in a \"light\" version, in terms of computational cost, in order to work online with Labview. In Matlab, the algorithm is more complex and more precise because it might work offline. The EGG signal consists of an AM (Amplitude Modulated) signal; its value is bigger when the current flows through the vocal folds' plane. On the other hand, it becomes smaller if that plane is partially crossed or not crossed at all. We approximated the field between two electrodes as a cylindrical shape. Therefore, we used the  
Figure 4: Labview Main Panel for acquiring data: EGG page. information given by the EGG signal to obtain information about the distance between the axis of each cylinder and the vocal folds' plane. When the distance between electrodes is known, we can calculate all the 36 possible cylinders representing the 36 current paths (Figure 5). The mathematical equation that should be solved for each cylinder is:  
\[(X-X_{i0})^{2}+(Y-Y_{i0})^{2}+(Z-Z_{i0})^{2}-\left[(X-X_{i0})v_{ijy}+(Y-Y_{i0}) v_{ijy}+(Z-Z_{i0})v_{ijy}\right]^{2}-{R_{ij}}^{2}=C_{ij} \tag{1}\]  
where i = 1,...,6 is the index for the sending electrodes; j = 1,...,6 is for the receiver ones; and X, Y, Z represents the larynx position coordinates, which start from position (\(X_{i0}\), \(Y_{i0}\), \(Z_{i0}\)). They should potentially assume any value inside the volume mapped by the two electrodes' arrays. In Formula (1), C represents the \"cost function\". Therefore, for each set of X, Y, Z, we could obtain 36 possible cost functions. The sum of the cost function for all 36 paths will give the global cost function. The most probable point where the larynx is located is obtained by minimizing the global cost function, by varying the X, Y, Z sets. Since in a volume we could localize infinite values for X, Y, and Z, it was necessary to divide them into finite elements in each direction, otherwise the problem could not be solved in a continuous medium. In order to obtain a finite number of values for X, Y, and Z in a specific volume, we have divided the global volume through three grids on the main axis, evaluating only the intersection points. Nevertheless, even in this case, we would have had an excessive number of points, aiming to reach a good spatial resolution (i.e., millimeters). Figure 6 reports the position of MC-EGG for humans. Figure 5: Cylindrical field between two electrodes.