Vocal wow in an adapted reflex resonance model

Vocal wow and tremor are slow modulations of the voice presumed to result from integration of auditory and somatosensory feedback, respectively. This distinction has important implications for diagnosis and treatment of neurological disorders that may differentially impact these systems, but the underlying mechanisms remain poorly understood. An important contribution on this matter is the reflex resonance model [Titze et al. (2002). J. Acoust. Soc. Am. 111(5), 2272–2282], which demonstrates that a 4–7 Hz vibrato (or tremor) can indeed be elicited by adjusting feedback parameters in a simple model of laryngeal muscle activation, mediated by time-delayed somatosensory feedback. This paper expands on this model by incorporating an auditory feedback loop and shows that wow emerges as feedback parameters exceed critical values described by a Hopf bifurcation. The wow period increases with delay and is almost invariant with respect to gain for delays above 200 ms. Parametric formulas for recovering feedback parameters from the acoustic signal are presented. With both feedback loops in place, auditory and somatosensory parameters interact and alter vocal modulations. Model predictions are illustrated in two subjects, one with a diagnosis of multiple sclerosis and intermittent tremor. Findings suggest that phonatory instabilities provide considerable insight into normal and pathogenic changes to the sensorimotor control of voice.Vocal wow and tremor are slow modulations of the voice presumed to result from integration of auditory and somatosensory feedback, respectively. This distinction has important implications for diagnosis and treatment of neurological disorders that may differentially impact these systems, but the underlying mechanisms remain poorly understood. An important contribution on this matter is the reflex resonance model [Titze et al. (2002). J. Acoust. Soc. Am. 111(5), 2272–2282], which demonstrates that a 4–7 Hz vibrato (or tremor) can indeed be elicited by adjusting feedback parameters in a simple model of laryngeal muscle activation, mediated by time-delayed somatosensory feedback. This paper expands on this model by incorporating an auditory feedback loop and shows that wow emerges as feedback parameters exceed critical values described by a Hopf bifurcation. The wow period increases with delay and is almost invariant with respect to gain for delays above 200 ms. Parametric formulas for recovering feedback pa...