Global and local dimensions of vocal dynamics.

The global embedding dimension (dE) and the local dynamical dimension (dL) are calculated from the microphone and electroglottographic (EGG) signals elicited from five healthy subjects and seven dysphonic subjects with laryngeal pathology during phonation of sustained/a/. The data from each pathologic subject contain at least one bifurcation and are divided into periodic and irregular segments for analysis. The dE values from both the microphone and EGG signals elicited from the healthy subjects indicate that a relatively small coordinate space can be used to reconstruct the attractor, with little residual noise. Consistent across all healthy subjects, three dominant degrees of freedom (dL) are found to govern local dynamics of the trajectories on the attractor. From the pathologic subjects, many of the dE values suggest the presence of a high-dimensional component in the signals. However, the noise does not completely obscure the deterministic dynamics of the source signal or prevent extraction of an optimal global embedding dimension. The data do not reveal consistent differences in degrees of freedom between healthy and pathologic phonation, or between different modes of pathologic phonation. However, the dL values suggest that the pathologic vocal fold vibration of these subjects, even highly irregular vibration, is governed locally by a low number of dominant degrees of freedom, sometimes no greater than those calculated from the signals of healthy subjects. Only in the cases of severe breathiness are the microphone and EGG signals sufficiently contaminated by noise to obscure any deterministic component.