A quantitative model of voice F0 control.

A mathematical model of the larynx, based on biomechanical principles, is described. Components represented include two cartilage elements (cricoid with locked arytenoids, and thyroid), three muscles (thyroarytenoid [TA], cricothyroid pars rectus [CTr], and cricothyroid pars oblique [CTo]), and two ligaments (cricothyroid and vocal ligaments), as well as subglottal pressure (PS). For any combination of muscle activities and PS level, equilibrium positions and tensions could be calculated for components in the system. The tensions and lengths of vocal fold elements were then used to calculate fundamental frequency (F0) of vocal fold vibration. Systematic variation of model muscle activation and PS patterns allowed study of the behavior of the model. TA activity tended to shorten the vocal folds; increased levels of CTr and CTo activity, and PS, had the opposite effect. Increased activity of any muscle tended to increase vocal fold tension, while PS increases were mainly ineffective. F0 was generally increased by increased CTr, CTo, and PS values. However, TA activity had a strongly nonmonotonic effect on F0. Best control of F0 could be achieved only by a process of co-contraction of all muscles at low frequencies, followed by sustained contraction of CTr and CTo with decreasing TA activity for F0's increasing above this low-frequency range. These results are discussed in terms of their possible implications for norma and abnormal voice production, and as a set of constraints for neural modeling efforts.