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.

Twin vocal folds as a novel evolutionary adaptation for vocal communications in lemurs.

Primates have varied vocal repertoires to communicate with conspecifics and sometimes other species. The larynx has a central role in vocal source generation, where a pair of vocal folds vibrates to modify the air flow. Here, we show that Madagascan lemurs have a unique additional pair of folds in the vestibular region, parallel to the vocal folds. The additional fold has a rigid body of a vocal muscle branch and it is covered by a stratified squamous epithelium, equal to those of the vocal fold. Such anatomical features support the hypothesis that it also vibrates in a manner like the vibrations that occur in the vocal folds. To examine the acoustic function of the two pairs of folds, we made a silicone compound model to demonstrate that they can simultaneously vibrate to lower the fundamental frequency and increase vocal efficiency. Similar acoustic effects are achieved using different features of the larynx for the other primates, e.g., by vibrating multiple sets of ventricular folds in several species and further by an evolutionary modification of enlarged larynx in howler monkeys. Our multidisciplinary approaches found that these functions were acquired through a unique evolutionary adaptation of the twin vocal folds in Madagascan lemurs.

Ventricular fold oscillations lower the vocal pitch in rhesus macaques.

We carried out ex vivo and in vivo experiments to explore the functional role of the ventricular folds in sound production in macaques. In the ex vivo experiments, 29 recordings out of 67 showed that the ventricular folds co-oscillated with the vocal folds. Transitions from normal vocal fold oscillations to vocal-ventricular fold co-oscillations as well as chaotic irregular oscillations were also observed. The in vivo experiments indicated that the vocal-ventricular fold co-oscillations were also observed in two macaque individuals. In both ex vivo and in vivo experiments, the vocal-ventricular fold co-oscillations significantly lowered the fundamental frequency. A mathematical model revealed that the lowering of the fundamental frequency was caused by a low oscillation frequency inherent in the ventricular folds, which entrained the vocal folds to their low-frequency oscillations. From a physiological standpoint, the macaques may utilize the ventricular fold oscillations more frequently than humans. The advantages as well as disadvantages of using the ventricular folds as an additional vocal repertory are discussed.

Detecting the dynamical instability of complex time series via partitioned entropy.

A method is proposed to detect the dynamical instability of complex time series. We focus on how the partitioned entropy of an initially localized region of the attractor evolves in time and show that its growth rate corresponds to the first Lyapunov exponent. To avoid spurious detection of the dynamical instability, a criterion is further introduced to distinguish chaos from limit cycles or tori. Numerical experiments using prototypical models of chaotic systems demonstrate that the growth rate of the partitioned entropy indeed provides a good estimate of the first Lyapunov exponent. The method is also shown to be robust against observational noise and dynamical noise. Analysis of experimental data measured from a physical model of the vocal folds highlights the practical applicability of the present method to real-world data. Advantages of the present method over conventional methods are also discussed.

Dynamic System Coupling in Voice Production.

Voice is a major means of communication for humans, non-human mammals and many other vertebrates like birds and anurans. The physical and physiological principles of voice production are described by two theories: the MyoElastic-AeroDynamic (MEAD) theory and the Source-Filter Theory (SFT). While MEAD employs a multiphysics approach to understand the motor control and dynamics of self-sustained vibration of vocal folds or analogous tissues, SFT predominantly uses acoustics to understand spectral changes of the source via linear propagation through the vocal tract. Because the two theories focus on different aspects of voice production, they are often applied distinctly in specific areas of science and engineering. Here, we argue that the MEAD and the SFT are linked integral aspects of a holistic theory of voice production, describing a dynamically coupled system. The aim of this manuscript is to provide a comprehensive review of both the MEAD and the source-filter theory with its nonlinear extension, the latter of which suggests a number of conceptual similarities to sound production in brass instruments. We discuss the application of both theories to voice production of humans as well as of animals. An appraisal of voice production in the light of non-linear dynamics supports the notion that voice production can best be described with a systems view, considering coupled systems rather than isolated contributions of individual sub-systems.

Anticipating the occurrence and type of critical transitions.

Critical transition can occur in many real-world systems. The ability to forecast the occurrence of transition is of major interest in a range of contexts. Various early warning signals (EWSs) have been developed to anticipate the coming critical transition or distinguish types of transition. However, no effective method allows to establish practical threshold indicating the condition when the critical transition is most likely to occur. Here, we introduce a powerful EWS, named dynamical eigenvalue (DEV), that is rooted in bifurcation theory of dynamical systems to estimate the dominant eigenvalue of the system. Theoretically, the absolute value of DEV approaches 1 when the system approaches bifurcation, while its position in the complex plane indicates the type of transition. We demonstrate the efficacy of the DEV approach in model systems with known bifurcation types and also test the DEV approach on various critical transitions in real-world systems.

Physical modeling of the vocal membranes and their influence on animal voice production.

The vocal membrane, i.e., an extended part of the vocal fold, is observed in a wide range of species including bats and primates. A theoretical study [Mergell, Fitch, and Herzel (1999). J. Acoust. Soc. Am. 105(3), 2020-2028] predicted that the vocal membranes can make the animal vocalizations more efficient by lowering the phonation threshold pressure. To examine this prediction, a synthetic model of the vocal membrane was developed, and its oscillation properties were examined. The experiments revealed that the phonation threshold pressure was lower in the vocal membrane model compared to that in a model with no vocal membrane. Chaotic oscillations were observed as well.

Evolutionary loss of complexity in human vocal anatomy as an adaptation for speech.

Human speech production obeys the same acoustic principles as vocal production in other animals but has distinctive features: A stable vocal source is filtered by rapidly changing formant frequencies. To understand speech evolution, we examined a wide range of primates, combining observations of phonation with mathematical modeling. We found that source stability relies upon simplifications in laryngeal anatomy, specifically the loss of air sacs and vocal membranes. We conclude that the evolutionary loss of vocal membranes allows human speech to mostly avoid the spontaneous nonlinear phenomena and acoustic chaos common in other primate vocalizations. This loss allows our larynx to produce stable, harmonic-rich phonation, ideally highlighting formant changes that convey most phonetic information. Paradoxically, the increased complexity of human spoken language thus followed simplification of our laryngeal anatomy.

Potential negative effect of total parenteral nutrition on the human circadian clock.

When patients cannot eat on their own, total parenteral nutrition (TPN) is a clinically beneficial method of maintaining nutrition. However, many animal studies have demonstrated that circadian rhythms are strongly affected by feeding time, raising the concern that continuous TPN around the clock may have an unexpected negative impact on the circadian clock of patients. To investigate this concern, we compared clock gene expression of aged subjects with or without TPN using hair follicle cells and found that while none of the non-TPN subjects showed any obvious defects in circadian rhythms of peripheral clock gene expression, a portion of aged subjects receiving continuous TPN showed abnormal circadian rhythms in peripheral clocks. Continuous TPN around the clock may therefore potentially perturb peripheral circadian rhythms, giving rise to the proposal that TPN needs to be administered with consideration to time factors.

Experimental study on the quasi-steady approximation of glottal flows.

To examine the quasi-steady approximation of the glottal flow, widely used in the modeling of vocal fold oscillations, intraglottal pressure distributions were measured in a scaled-up static vocal fold model under time-varying flow conditions. The left and right vocal folds were slightly open and set to a symmetric and oblique configuration with a divergence angle. To realize time-varying flow conditions, the flow rate was sinusoidally modulated with a frequency of 2 and 10 Hz, which correspond to 112.5 and 562.5 Hz, respectively, in real life. Measurements of the intraglottal pressures under both steady and time-varying flows revealed that the pressure profiles of the time-varying flow conditions are non-distinguishable from those of the steady flow conditions as far as they have the same subglottal pressure as an input pressure. The air-jet separation point was also non-distinguishable between the steady and the time-varying flow conditions. Our study therefore suggests that the time-varying glottal flow can be approximated as a series of steady flow states with a matching subglottal pressure in the range of normal vocalization frequencies. Since the glottal closure was not taken into account in the present experiment, our argument is valid except for such a critical situation.

A spatial model of the plant circadian clock reveals design principles for coordinated timing.

Individual plant cells possess a genetic network, the circadian clock, that times internal processes to the day-night cycle. Mathematical models of the clock are typically either "whole-plant" that ignore tissue or cell type-specific clock behavior, or "phase-only" that do not include molecular components. To address the complex spatial coordination observed in experiments, here we implemented a clock network model on a template of a seedling. In our model, the sensitivity to light varies across the plant, and cells communicate their timing via local or long-distance sharing of clock components, causing their rhythms to couple. We found that both varied light sensitivity and long-distance coupling could generate period differences between organs, while local coupling was required to generate the spatial waves of clock gene expression observed experimentally. We then examined our model under noisy light-dark cycles and found that local coupling minimized timing errors caused by the noise while allowing each plant region to maintain a different clock phase. Thus, local sensitivity to environmental inputs combined with local coupling enables flexible yet robust circadian timing.

Experimental Study on Inspiratory Phonation Using Physical Model of the Vocal Folds.

In inspiratory phonation, the air is inhaled from the mouth. The inhaled air passes through the glottis towards the lungs, thereby inducing the vocal fold vibrations. Such phonation takes place in various situations such as sighs, laughter, and crying. To characterize the inspiratory phonation, an experimental study was carried out using a physical model of the vocal folds. By reversing the direction of the airflow that passed through the vocal fold model, the inspiratory phonation was experimentally realized and compared with the normal expiratory phonation. Our experiments revealed that the phonation threshold pressures as well as the volume flow rates decreased under the inspiratory condition. Accordingly, the vocal efficiency was increased. The fundamental frequency was also increased under the inspiratory condition. The kymograms showed that phase of the upper edge of the vocal fold advanced that of the lower edge under the inspiratory phonation. A mathematical model of the vocal folds was further constructed to elucidate these experiments. Except for few aspects, our experimental findings are in good agreement with the preceding studies on inspiratory phonation (e.g., reversed propagation of the mucosal waves observed in a singer, increased pitches in human subjects, and use of inspiratory phonation in speech therapy).

Synchronized and Desynchronized Dynamics Observed from Physical Models of the Vocal and Ventricular Folds.

The ventricular folds, located superiorly to the vocal folds, do not usually vibrate during normal phonations. It has been shown, however, that they do vibrate together with the vocal folds under special circumstances such as voice pathology and singing voice. Towards understanding the effect of the ventricular fold oscillations on the vocal fold oscillations, the present study developed a synthetic model that takes into account anatomical features of the human ventricular folds. The synthetic model is made of flexible silicone compounds with material properties comparable to those of human ventricular fold tissues. In our experiment, an air-flow was injected into the vocal and ventricular fold models. As the distance between the left and right ventricular folds was reduced, the ventricular folds started to co-vibrate with the vocal folds. Depending upon the distance, various oscillation patterns of the vocal-ventricular folds were observed, e.g., synchronized dynamics with 1:1 or 1:2 frequency ratio and desynchronized chaotic dynamics. The observed chaotic dynamics might be related to voice pathology induced by the ventricular phonation. A computational model was further presented to elucidate the experimental findings.

Effect of gravity on synchronization of two coupled buoyancy-induced turbulent flames.

We study the effect of gravity on the synchronization of two coupled buoyancy-induced turbulent flames by recurrence-based analysis and machine learning. A significant change from nearly complete synchronization in the near field to partial synchronization appears in the far field under low gravity. The synchronized state is gradually lost with increasing gravity level. These results are clearly identified from cross recurrence plots and symbolic recurrence plots and by reservoir computing.

The singularity response reveals entrainment properties of the plant circadian clock.

Circadian clocks allow organisms to synchronize their physiological processes to diurnal variations. A phase response curve allows researchers to understand clock entrainment by revealing how signals adjust clock genes differently according to the phase in which they are applied. Comprehensively investigating these curves is difficult, however, because of the cost of measuring them experimentally. Here we demonstrate that fundamental properties of the curve are recoverable from the singularity response, which is easily measured by applying a single stimulus to a cellular network in a desynchronized state (i.e. singularity). We show that the singularity response of Arabidopsis to light/dark and temperature stimuli depends on the properties of the phase response curve for these stimuli. The measured singularity responses not only allow the curves to be precisely reconstructed but also reveal organ-specific properties of the plant circadian clock. The method is not only simple and accurate, but also general and applicable to other coupled oscillator systems as long as the oscillators can be desynchronized. This simplified method may allow the entrainment properties of the circadian clock of both plants and other species in nature.

Effect of Ventricular Folds on Vocalization Fundamental Frequency in Domestic Pigs (Sus scrofa domesticus).

This study investigates the effect of the ventricular folds on fundamental frequency (fo) in the voice production of domestic pigs (Sus scrofa domesticus). The excised larynges of six subadult pigs were phonated in two preparation stages, with the ventricular folds present (PS1) and removed (PS2). Vocal fold resonances were tested with a laser vibrometer, and a four-mass computational model was created. Highly significant fo differences were found between PS1 and PS2 (means at 93.7 and 409.3 Hz, respectively). Two tissue resonances were found at 115 Hz and 250-290 Hz. The computational model had unique solutions for abducted and adducted ventricular folds at about 150 and 400 Hz, roughly matching the fo measured ex vivo for PS1 and PS2. The differing fo encountered across preparation stages PS1 and PS2 is explained by distinct activation of either a high or a low eigenfrequency mode, depending on the engagement of the ventricular folds. The inability of the investigated larynges to vibrate at frequencies below 250 Hz in PS2 suggests that in vivo low-frequency calls of domestic pigs (pre-eminently grunts) are likely produced with engaged ventricular folds. Allometric comparison suggests that the special, mechanically coupled "double oscillator" has evolved to prevent signaling disadvantages. Given these traits, the porcine larynx might - apart from special applications relating to the involvement of ventricular folds - not be an ideal candidate for emulating human voice production in excised larynx experimentation.

Experimental study of vocal-ventricular fold oscillations in voice production.

Ventricular folds are located in the supraglottal region above the vocal folds. Although the ventricular folds do not vibrate under normal vocalizations, they vibrate under certain conditions, e.g., throat singing or ventricular fold dysphonia. In throat singing, the ventricular folds vibrate at the same frequency as (or at integer ratios of) the vocal fold vibration frequency. In ventricular fold dysphonia, on the other hand, the ventricular folds interfere with the vocal folds, giving rise to a hoarse voice. In the present study, the synthetic larynx model was utilized to examine the vocal-ventricular fold oscillations. Our experiments revealed that the vocal and ventricular folds can co-oscillate at the same frequency with an out-of-phase relation. Compared to the control condition, under which no ventricular folds exist, the phonation threshold pressure was increased in the presence of the ventricular folds. Acoustic analysis indicated that jitter was reduced and vocal efficiency was increased by the ventricular folds. Distance between the vocal and ventricular folds did not alter these oscillation properties. A computational model was further simulated to elucidate the mechanism underlying the observed vocal-ventricular fold oscillations. It has been suggested that out-of-phase oscillations of the vocal and ventricular folds are important for sustaining periodic laryngeal vibrations.

A detection method for latent circadian rhythm sleep-wake disorder.

BACKGROUND: Individuals with typical circadian rhythm sleep-wake disorders (CRSWDs) have a habitual sleep timing that is desynchronized from social time schedules. However, it is possible to willfully force synchronisation against circadian-driven sleepiness, which causes other sleep problems. This pathology is distinguishable from typical CRSWDs and is referred to here as latent CRSWD (LCRSWD). Conventional diagnostic methods for typical CRSWDs are insufficient for detecting LCRSWD because sufferers have an apparently normal habitual sleep timing. METHODS: We first evaluated the reliability of circadian phase estimation based on clock gene expression using hair follicles collected at three time points without sleep interruption. Next, to identify detection criteria for LCRSWD, we compared circadian and sleep parameters according to estimated circadian phases, at the group and individual level, between subjects with low and high Pittsburgh Sleep Quality Index (PSQI) scores. To validate the reliability of identified detection criteria, we investigated whether the same subjects could be reproducibly identified at a later date and whether circadian amelioration resulted in sleep improvement. FINDINGS: We successfully validated the reliability of circadian phase estimation at three time points and identified potential detection criteria for individuals with LCRSWD attributed to delayed circadian-driven sleepiness. In particular, a criterion based on the interval between the times of the estimated circadian phase of clock gene expression and getting out of bed on work or school days was promising. We also successfully confirmed the reproducibility of candidate screening and sleep improvement by circadian amelioration, supporting the reliability of the detection criteria. INTERPRETATION: Although several limitations remain, our present study demonstrates a promising prototype of a detection method for LCRSWD attributed to delayed circadian-driven sleepiness. More extensive trials are needed to further validate this method. FUNDING: This study was supported mainly by JSPS, Japan.