Ingo R. Titze

The physics of small-amplitude oscillation of the vocal folds

A theory of vocal fold oscillation is developed on the basis of the body-cover hypothesis. The cover is represented by a distributed surface layer that can propagate a mucosal surface wave. Linearization of the surface-wave displacement and velocity, and further small-amplitude approximations, yields closed-form expressions for conditions of oscillation. The theory predicts that the lung pressure required to sustain oscillation, i.e., the oscillation threshold pressure, is reduced by reducing the mucosal wave velocity, by bringing the vocal folds closer together and by reducing the convergence angle in the glottis. The effect of vocal tract acoustic loading is included. It is shown that vocal tract inertance reduces the oscillation threshold pressure, whereas vocal tract resistance increases it. The treatment, which is applicable to falsetto and breathy voice, as well as onset or release of phonation in the absence of vocal fold collision, is harmonized with former treatments based on two-mass models and collapsible tubes.

Physiologic and acoustic differences between male and female voices

Comparison is drawn between male and female larynges on the basis of overall size, vocal fold membranous length, elastic properties of tissue, and prephonatory glottal shape. Two scale factors are proposed that are useful for explaining differences in fundamental frequency, sound power, mean airflow, and glottal efficiency. Fundamental frequency is scaled primarily according to the membranous length of the vocal folds (scale factor of 1.6), whereas mean airflow, sound power, glottal efficiency, and amplitude of vibration include another scale factor (1.2) that relates to overall larynx size. Some explanations are given for observed sex differences in glottographic waveforms. In particular, the simulated (computer-modeled) vocal fold contact area is used to infer male-female differences in the shape of the glottis. The female glottis appears to converge more linearly (from bottom to top) than the male glottis, primarily because of medial surface bulging of the male vocal folds.

Populations in the U.S. workforce who rely on voice as a primary tool of trade: A preliminary report

The United States Bureau of Labor Statistics and other sources were consulted about the percentages of the working population that we identified as professional voice users. The largest percentage may be in sales and sales-related occupations (13%), but the exact breakdown of those who approach their clients vocally rather than by mail is still uncertain. The second largest population is teachers, who comprise 4.2% percent of the U.S. workforce (1994 statistic). Teachers have been identified as having the greatest incidence of voice disorders. Population data are also given for professional voice users who could present a significant hazard to public safety if their vocal communication skills were severely impaired.

On the relation between subglottal pressure and fundamental frequency in phonation

The change in fundamental frequency with subglottal pressure in phonation is quantified on the basis of the ratio between vibrational amplitude and vocal fold length. This ratio is typically very small in stringed instruments, but becomes quite appreciable in vocal fold vibration. Tension in vocal fold tissues is, therefore, not constant over the vibratory cycle, and a dynamic tension gives rise to amplitude-frequency dependence. It is shown that the typical 2-6 Hz/cm H2O rise in fundamental frequency with subglottal pressure observed in human and canine larynges is a direct and predictable consequence of this amplitude-frequency dependence. Results are presently limited to phonation in the chest register.

Nonlinear source–filter coupling in phonation: Theory

A theory of interaction between the source of sound in phonation and the vocal tract filter is developed. The degree of interaction is controlled by the cross-sectional area of the laryngeal vestibule (epilarynx tube), which raises the inertive reactance of the supraglottal vocal tract. Both subglottal and supraglottal reactances can enhance the driving pressures of the vocal folds and the glottal flow, thereby increasing the energy level at the source. The theory predicts that instabilities in vibration modes may occur when harmonics pass through formants during pitch or vowel changes. Unlike in most musical instruments (e.g., woodwinds and brasses), a stable harmonic source spectrum is not obtained by tuning harmonics to vocal tract resonances, but rather by placing harmonics into favorable reactance regions. This allows for positive reinforcement of the harmonics by supraglottal inertive reactance (and to a lesser degree by subglottal compliant reactance) without the risk of instability. The traditional linear source-filter theory is encumbered with possible inconsistencies in the glottal flow spectrum, which is shown to be influenced by interaction. In addition, the linear theory does not predict bifurcations in the dynamical behavior of vocal fold vibration due to acoustic loading by the vocal tract.

Phonation threshold pressure: A missing link in glottal aerodynamics

Phonation threshold pressure has previously been defined as the minimum lung pressure required to initiate phonation. By modeling the dependence of this pressure on fundamental frequency, it is shown that relatively simple aerodynamic relations for time-varying flow in the glottis are obtained. Lung pressure and peak glottal flow are nearly linearly related, but not proportional. For this reason, traditional power law relations between vocal power and lung pressure may not hold. Glottal impendance for time-varying flow should be defined differentially rather than as a simple ratio between lung pressure and peak flow. It is shown that the peak flow, the peak flow derivative, the open quotient, and the speed quotient of inverse-filtered glottal flow waveforms all depend explicitly on phonation threshold pressure. Data from singers are compared with those from nonsingers. The primary difference is that singers obtain two to three times greater peak flow for a given lung pressure, suggesting that they adjust their glottal or vocal tract impedance for optimal flow transfer between the source and the resonantor.

Acoustic interactions of the voice source with the lower vocal tract

The linear source-filter theory of speech production assumes that vocal fold vibration is independent of the vocal tract. The justification is that the glottis often behaves as a high-impedance (constant flow) source. Recent imaging of the vocal tract has demonstrated, however, that the epilarynx tube is quite narrow, making the input impedance to the vocal tract comparable to the glottal impedance. Strong interactions can exist, therefore. In particular, the inertance of the vocal tract facilitates vocal fold vibration by lowering the oscillation threshold pressure. This has a significant impact on singing. Not only does the epilarynx tube produce the desirable singers formant (vocal ring), but it acts like the mouthpiece of a trumpet to shape the flow and influence the mode of vibration. Effects of the piriform sinuses, pharynx expansion, and nasal coupling are also discussed.

Viscoelastic shear properties of human vocal fold mucosa: Measurement methodology and empirical results

A standard method for the empirical rheological characterization of viscoelastic materials was adopted to measure the viscoelastic shear properties of human vocal-fold mucosal tissues (the superficial layer of lamina propria). A parallel-plate rotational rheometer was employed to measure shear deformation of viscoelastic tissue samples, which were deformed between two rigid circular plates rotating in small-amplitude sinusoidal oscillations. Elastic and viscous shear moduli of the samples were then quantified as a function of oscillation frequency (0.01 to 15 Hz) based on shear stresses and strains recorded by the rheometer. Data were obtained from 15 excised human larynges (10 male and 5 female). Results showed that the elastic shear modulus mu and the damping ratio zeta of human vocal-fold mucosa were relatively constant across the range of frequencies observed, while the dynamic viscosity eta decreased monotonically with frequency (i.e., shear thinning). Intersubject differences in mu and eta as large as an order of magnitude were observed, part of which may reflect age-related and gender-related differences. Some molecular interpretations of the findings are discussed.

Changes in phonation threshold pressure with induced conditions of hydration

Summary The purpose of this pilot study was to investigate the relationship between phonation threshold pressure and level of hydration in human subjects. Six adult subjects produced consonant-vowel-consonant strings as quietly as possible at low, medium, and high pitches in no-treatment, hydrated, and slightly dehydrated conditions. Average oral pressures for these trials were used to estimate minimal subglottal pressures required for phonation (phonation threshold pressure). Main effects for hydration and for pitch were significant, as was the interaction of hydration times pitch. Overall, the lowest pressures were seen for the hydrated (or “wet”) condition, and reduction in baseline pressures was greatest for high pitches in this condition. The highest pressures were found for the dry condition, and the greatest increase in pressure relative to the baseline was found at low pitches for this condition. Threshold pressures for intermediate (speaking) pitches were not affected by hydration condition. The findings are consistent with previously reported theoretical predictions regarding the relationship between oscillation threshold pressures and tissue viscosity. They are also consistent with previous empirical reports on the effect of direct hydration of vocal fold tissue in nonhuman subjects.

A finite-element model of vocal-fold vibration

A finite-element model of the vocal fold is developed from basic laws of continuum mechanics to obtain the oscillatory characteristics of the vocal folds. The model is capable of accommodating inhomogeneous, anisotropic material properties and irregular geometry of the boundaries. It has provisions for asymmetry across the midplane, both from the geometric and tension point of view, which enables one to simulate certain kinds of voice disorders due to vocal-fold paralysis. It employs the measured viscoelastic properties of the vocal-fold tissues. The detailed construction of the matrix differential equations of motion is presented followed by the solution scheme. Finally, typical results are presented and validated using an eigenvalue method and a commercial finite-element package (ABAQUS).