Bifurcations and chaos in register transitions of excised larynx experiments

Nonlinear dynamics and chaos in a vocal-ventricular fold system

In humans, ventricular folds are located superiorly to the vocal folds. Under special circumstances such as voice pathology or singing, they vibrate together with the vocal folds to contribute to the production of voice. In the present study, experimental data measured from physical models of the vocal and ventricular folds were analyzed in the light of nonlinear dynamics. The physical models provide a useful experimental framework to study the biomechanics of human vocalizations. Of particular interest in this experiment are co-oscillations of the vocal and ventricular folds, occasionally accompanied by irregular dynamics. We show that such a system can be regarded as two coupled oscillators, which give rise to various cooperative behaviors such as synchronized oscillations with a 1:1 or 1:2 frequency ratio and desynchronized oscillations with torus or chaos. The insight gained from the view of nonlinear dynamics should be of significant use for the diagnosis of voice pathologies, such as ventricular fold dysphonia.

Multi-synchronization and other patterns of multi-rhythmicity in oscillatory biological systems

While experimental and theoretical studies have established the prevalence of rhythmic behaviour at all levels of biological organization, less common is the coexistence between multiple oscillatory regimes (multi-rhythmicity), which has been predicted by a variety of models for biological oscillators. The phenomenon of multi-rhythmicity involves, most commonly, the coexistence between two (birhythmicity) or three (trirhythmicity) distinct regimes of self-sustained oscillations. Birhythmicity has been observed experimentally in a few chemical reactions and in biological examples pertaining to cardiac cell physiology, neurobiology, human voice patterns and ecology. The present study consists of two parts. We first review the mechanisms underlying multi-rhythmicity in models for biochemical and cellular oscillations in which the phenomenon was investigated over the years. In the second part, we focus on the coupling of the cell cycle and the circadian clock and show how an additional source of multi-rhythmicity arises from the bidirectional coupling of these two cellular oscillators. Upon bidirectional coupling, the two oscillatory networks generally synchronize in a unique manner characterized by a single, common period. In some conditions, however, the two oscillators may synchronize in two or three different ways characterized by distinct waveforms and periods. We refer to this type of multi-rhythmicity as ‘multi-synchronization’.

Influence of vocal fold cover layer thickness on its vibratory dynamics during voice production

The influence of vocal fold cover layer thickness on the flow-induced vibration and voice production was studied by using a continuum-mechanics based computational model. The cover-body thickness ratio of a three-layer vocal fold was systematically varied. The effect on the vocal fold stiffness, eigenfrequencies and eigenmodes, fundamental frequencies, glottal flow rate, vocal fold vibratory dynamics, and synchronization of the eigenmodes were analyzed by using the structure eigen analysis and flow-structure interaction simulations. It was found that the cover-body layer thickness ratio significantly affected the strength and synchronization of the eigenmodes during flow-structure interactions, and ultimately affected the fundamental frequency and vibration pattern. With the increasing cover-body thickness ratio, the strength of the wave-type higher-eigenfrequency modes increased, and that resulted in a nonlinear bifurcation of the system in which the system evolved from a regular periodic vibration to a periodic doubling vibration and then back to a regular periodic vibration with increased fundamental frequencies. During the transition, the system vibrated chaotically. Because of the increased strength of the wave-type modes, the maximum divergent angle of the glottis was also increased with the increasing cover-body thickness ratio.

Expression of Emotional Arousal in Two Different Piglet Call Types

Humans as well as many animal species reveal their emotional state in their voice. Vocal features show strikingly similar correlation patterns with emotional states across mammalian species, suggesting that the vocal expression of emotion follows highly conserved signalling rules. To fully understand the principles of emotional signalling in mammals it is, however, necessary to also account for any inconsistencies in the way that they are acoustically encoded. Here we investigate whether the expression of emotions differs between call types produced by the same species. We compare the acoustic structure of two common piglet calls—the scream (a distress call) and the grunt (a contact call)—across three levels of arousal in a negative situation. We find that while the central frequency of calls increases with arousal in both call types, the amplitude and tonal quality (harmonic-to-noise ratio) show contrasting patterns: as arousal increased, the intensity also increased in screams, but not in grunts, while the harmonicity increased in screams but decreased in grunts. Our results suggest that the expression of arousal depends on the function and acoustic specificity of the call type. The fact that more vocal features varied with arousal in scream calls than in grunts is consistent with the idea that distress calls have evolved to convey information about emotional arousal.

Complex vibratory patterns in an elephant larynx

Elephants' low-frequency vocalizations are produced by flow-induced self-sustaining oscillations of laryngeal tissue. To date, little is known in detail about the vibratory phenomena in the elephant larynx. Here, we provide a first descriptive report of the complex oscillatory features found in the excised larynx of a 25 year old female African elephant (Loxodonta africana), the largest animal sound generator ever studied experimentally. Sound production was documented with high-speed video, acoustic measurements, air flow and sound pressure level recordings. The anatomy of the larynx was studied with computed tomography (CT) and dissections. Elephant CT vocal anatomy data were further compared with the anatomy of an adult human male. We observed numerous unusual phenomena, not typically reported in human vocal fold vibrations. Phase delays along both the inferior-superior and anterior-posterior (A-P) dimension were commonly observed, as well as transverse travelling wave patterns along the A-P dimension, previously not documented in the literature. Acoustic energy was mainly created during the instant of glottal opening. The vestibular folds, when adducted, participated in tissue vibration, effectively increasing the generated sound pressure level by 12 dB. The complexity of the observed phenomena is partly attributed to the distinct laryngeal anatomy of the elephant larynx, which is not simply a large-scale version of its human counterpart. Travelling waves may be facilitated by low fundamental frequencies and increased vocal fold tension. A travelling wave model is proposed, to account for three types of phenomena: A-P travelling waves, 'conventional' standing wave patterns, and irregular vocal fold vibration.

Visualization of system dynamics using phasegrams

A new tool for visualization and analysis of system dynamics is introduced: the phasegram. Its application is illustrated with both classical nonlinear systems (logistic map and Lorenz system) and with biological voice signals. Phasegrams combine the advantages of sliding-window analysis (such as the spectrogram) with well-established visualization techniques from the domain of nonlinear dynamics. In a phasegram, time is mapped onto the x-axis, and various vibratory regimes, such as periodic oscillation, subharmonics or chaos, are identified within the generated graph by the number and stability of horizontal lines. A phasegram can be interpreted as a bifurcation diagram in time. In contrast to other analysis techniques, it can be automatically constructed from time-series data alone: no additional system parameter needs to be known. Phasegrams show great potential for signal classification and can act as the quantitative basis for further analysis of oscillating systems in many scientific fields, such as physics (particularly acoustics), biology or medicine.

Behavioural and neurobiological implications of linear and non-linear features in larynx phonations of horseshoe bats

Mammalian vocalizations exhibit large variations in their spectrotemporal features, although it is still largely unknown which result from intrinsic biomechanical properties of the larynx and which are under direct neuromuscular control. Here we show that mere changes in laryngeal air flow yield several non-linear effects on sound production, in an isolated larynx preparation from horseshoe bats. Most notably, there are sudden jumps between two frequency bands used for either echolocation or communication in natural vocalizations. These jumps resemble changes in “registers” as in yodelling. In contrast, simulated contractions of the main larynx muscle produce linear frequency changes, but are limited to echolocation or communication frequencies. Only by combining non-linear and linear properties can this larynx therefore produce sounds covering the entire frequency range of natural calls. This may give behavioural meaning to yodelling-like vocal behaviour and reshape our thinking about how the brain controls the multitude of spectral vocal features in mammals.

Experiments on Analysing Voice Production: Excised (Human, Animal) and In Vivo (Animal) Approaches

Experiments on human and on animal excised specimens as well as in vivo animal preparations are so far the most realistic approaches to simulate the in vivo process of human phonation. These experiments do not have the disadvantage of limited space within the neck and enable studies of the actual organ necessary for phonation, i.e., the larynx. The studies additionally allow the analysis of flow, vocal fold dynamics, and resulting acoustics in relation to well-defined laryngeal alterations.

PURPOSE OF REVIEW

This paper provides an overview of the applications and usefulness of excised (human/animal) specimen and in vivo animal experiments in voice research. These experiments have enabled visualization and analysis of dehydration effects, vocal fold scarring, bifurcation and chaotic vibrations, three-dimensional vibrations, aerodynamic effects, and mucosal wave propagation along the medial surface. Quantitative data will be shown to give an overview of measured laryngeal parameter values. As yet, a full understanding of all existing interactions in voice production has not been achieved, and thus, where possible, we try to indicate areas needing further study.

RECENT FINDINGS

A further motivation behind this review is to highlight recent findings and technologies related to the study of vocal fold dynamics and its applications. For example, studies of interactions between vocal tract airflow and generation of acoustics have recently shown that airflow superior to the glottis is governed by not only vocal fold dynamics but also by subglottal and supraglottal structures. In addition, promising new methods to investigate kinematics and dynamics have been reported recently, including dynamic optical coherence tomography, X-ray stroboscopy and three-dimensional reconstruction with laser projection systems. Finally, we touch on the relevance of vocal fold dynamics to clinical laryngology and to clinically-oriented research.

Nonlinear vocal fold dynamics resulting from asymmetric fluid loading on a two-mass model of speech

Nonlinear vocal fold dynamics arising from asymmetric flow formations within the glottis are investigated using a two-mass model of speech with asymmetric vocal fold tensioning, representative of unilateral vocal fold paralysis. A refined theoretical boundary-layer flow solver is implemented to compute the intraglottal pressures, providing a more realistic description of the flow than the standard one-dimensional, inviscid Bernoulli flow solution. Vocal fold dynamics are investigated for subglottal pressures of 0.6 < p(s) < 1.5 kPa and tension asymmetries of 0.5 < Q < 0.8. As tension asymmetries become pronounced the asymmetric flow incites nonlinear behavior in the vocal fold dynamics at subglottal pressures that are associated with normal speech, behavior that is not captured with standard Bernoulli flow solvers. Regions of bifurcation, coexistence of solutions, and chaos are identified.

Observation and analysis of in vivo vocal fold tissue instabilities produced by nonlinear source-filter coupling: a case study

Different source-related factors can lead to vocal fold instabilities and bifurcations referred to as voice breaks. Nonlinear coupling in phonation suggests that changes in acoustic loading can also be responsible for this unstable behavior. However, no in vivo visualization of tissue motion during these acoustically induced instabilities has been reported. Simultaneous recordings of laryngeal high-speed videoendoscopy, acoustics, aerodynamics, electroglottography, and neck skin acceleration are obtained from a participant consistently exhibiting voice breaks during pitch glide maneuvers. Results suggest that acoustically induced and source-induced instabilities can be distinguished at the tissue level. Differences in vibratory patterns are described through kymography and phonovibrography; measures of glottal area, open/speed quotient, and amplitude/phase asymmetry; and empirical orthogonal function decomposition. Acoustically induced tissue instabilities appear abruptly and exhibit irregular vocal fold motion after the bifurcation point, whereas source-induced ones show a smoother transition. These observations are also reflected in the acoustic and acceleration signals. Added aperiodicity is observed after the acoustically induced break, and harmonic changes appear prior to the bifurcation for the source-induced break. Both types of breaks appear to be subcritical bifurcations due to the presence of hysteresis and amplitude changes after the frequency jumps. These results are consistent with previous studies and the nonlinear source-filter coupling theory.

Smooth operator: avoidance of subharmonic bifurcations through mechanical mechanisms simplifies song motor control in adult zebra finches

Like human infants, songbirds acquire their song by imitation and eventually generate sounds that result from complicated neural networks and intrinsically nonlinear physical processes. Signatures of low-dimensional chaos such as subharmonic bifurcations have been reported in adult and developing zebra finch song. Here, we use methods from nonlinear dynamics to test whether adult male zebra finches (Taenopygia guttata) use the intrinsic nonlinear properties of their vocal organ, the syrinx, to insert subharmonic transitions in their song. In contrast to previous data on the basis of spectrographic evidence, we show that subharmonic transitions do not occur in adult song. Subharmonic transitions also do not arise in artificially induced sound in the intact syrinx, but are commonly generated in the excised syrinx. These findings suggest that subharmonic transitions are not used to increase song complexity, and that the brain controls song in a surprisingly smooth control regimen. Fast, smooth changes in acoustic elements can be produced by direct motor control in a stereotyped fashion, which is a more reliable indicator of male fitness than abrupt acoustic changes that do not require similarly precise control. Consistent with this view is the presence of high fidelity at every level of motor control, from telencephalic premotor areas to superfast syringeal muscles.

Effects of mucosal loading on vocal fold vibration

A chain model was proposed in this study to examine the effects of mucosal loading on vocal fold vibration. Mucosal loading was defined as the loading caused by the interaction between the vocal folds and the surrounding tissue. In the proposed model, the vocal folds and the surrounding tissue were represented by a series of oscillators connected by a coupling spring. The lumped masses, springs, and dampers of the oscillators modeled the tissue properties of mass, stiffness, and viscosity, respectively. The coupling spring exemplified the tissue interactions. By numerically solving this chain model, the effects of mucosal loading on the phonation threshold pressure, phonation instability pressure, and energy distribution in a voice production system were studied. It was found that when mucosal loading is small, phonation threshold pressure increases with the damping constant R(r), the mass constant R(m), and the coupling constant R(mu) of mucosal loading but decreases with the stiffness constant R(k). Phonation instability pressure is also related to mucosal loading. It was found that phonation instability pressure increases with the coupling constant R(mu) but decreases with the stiffness constant R(k) of mucosal loading. Therefore, it was concluded that mucosal loading directly affects voice production.

Asymmetric spatiotemporal chaos induced by a polypoid mass in the excised larynx

In this paper, asymmetric spatiotemporal chaos induced by a polypoid mass simulating the laryngeal pathology of a vocal polyp is experimentally observed using high-speed imaging in an excised larynx. Spatiotemporal analysis reveals that the normal vocal folds show spatiotemporal correlation and symmetry. Normal vocal fold vibrations are dominated mainly by the first vibratory eigenmode. However, pathological vocal folds with a polypoid mass show broken symmetry and spatiotemporal irregularity. The spatial correlation is decreased. The pathological vocal folds spread vibratory energy across a large number of eigenmodes and induce asymmetric spatiotemporal chaos. High-order eigenmodes show complicated dynamics. Spatiotemporal analysis provides a valuable biomedical application for investigating the spatiotemporal chaotic dynamics of pathological vocal fold systems with a polypoid mass and may represent a valuable clinical tool for the detection of laryngeal mass lesion using high-speed imaging.