Robustness of a pacemaker to control chaotic oscillations in a two-mass model of the vocal folds under turbulence and muscle twitch fluctuations and vocal tremor

Abstract

A pacemaker for phonation could be feasible in the near future thanks to advances in smart materials technology. However, before attempting it, much theoretical work needs to be done to figure out how it could work. Human phonation is a complex and highly non-linear fluid–structure interaction process for the onset of regular self-oscillations of the vocal folds to produce voice. Such oscillations can become chaotic for even moderate changes in the physical parameters of the folds or the subglottal pressure. Traditionally, low-dimensional biomechanical mass models have been used to understand the intricacies of both normal and abnormal phonation. In this framework, the possibility of devising a mass–spring–damper pacemaker capable of regulating chaotic oscillations of the vocal folds, which uses an altering energy feedback control strategy acting on the pacemaker damping, was recently analyzed. However, phonation can undergo several perturbations and it is necessary to test the robustness of the pacemaker against them. This is the objective of this work. Two types of disturbances are considered: random and periodic. The former are associated with glottal flow turbulence and also with muscle twitches, which are partially responsible for voice jitter. The second are related to vocal tremor and are often found in patients with paresis, Parkinson’s disease or adductor spasmodic dysphonia, among others. Using tools for the analysis of nonlinear dynamical systems, it will be demonstrated that the pacemaker can respond quite well to random and periodic perturbations, supporting its potential for partial remedy of voice pathologies.