Nonlinear behavior of vocal fold vibration: The role of coupling between the vocal folds

doi:10.1016/S0892-1997(99)80002-2

Journal of Voice

Volume 13, Issue 4, December 1999, Pages 465-476

https://doi.org/10.1016/S0892-1997(99)80002-2 Get rights and content

Summary

Coupling between the vocal folds is one of the nonlinear mechanisms allowing regulation and synchronization of mucosal vibration. The purpose of this study was to establish that modulations such as diplophonia and abnormalities observed in vocal signals that may be observed in some cases of laryngeal pathology can be considered as nonlinear behavior due to the persistence of some physical interaction (coupling). An experimental model using excised porcine larynx was designed to create tension asymmetry between the vocal folds and to obtain vocal signals with modulations. Signals were analyzed by spectral analysis and the phase portrait method. Results were compared with computer-generated synthetic signals corresponding to nonlinear combinations of sinusoid signals. Under these conditions, evidence of nonlinear behavior was detected in 85% of experimental signals. These findings were interpreted as a demonstration of vocal fold interaction. Based on these findings, the authors conclude that (1) coupling must be taken into account in physical models of laryngeal physiology, and that (2) methods of nonlinear dynamics may be used for objective voice analysis.

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Current voice assessments focus on perceptive evaluation and acoustic analysis. The interaction of vocal tract pressure (P_VT) and vocal fold (VF) vibrations are important for volume and pitch control. However, there are currently little non-invasive ways to measure P_VT. Limited information has been provided by previous human trials, and interactions between P_VT and VF vibrations and the potential clinical application remain unclear. Here, we propose a non-invasive method for monitoring the nonlinear characteristics of P_VT and VF vibrations, analyze voices from pathological and healthy individuals, and evaluate treatment efficacy.
Healthy volunteers and patients with benign laryngeal lesions were recruited for this study. P_VT was estimated using an airflow interruption method, VF vibrational frequency was calculated from accelerometer signals, and nonlinear relationships between P_VT and VF vibrations were analyzed. Results from healthy volunteers and patients, as well as pre- and post-operation for the patients, were compared.
For healthy volunteers, nonlinearity was exhibited as an initial increase and then prompt decrease in vibrational frequency at the end of phonation, coinciding with P_VT equilibrating with the subglottal pressure upon airflow interruption. For patients, nonlinearity was present throughout the phonation period pre-operatively, but showed a similar trend to healthy volunteers post-operatively.
This novel method simultaneously monitors P_VT and VF vibration and helps clarify the role of P_VT. The results demonstrate differences in nonlinear characteristics between healthy volunteers and patients, and pre-/post-operation in patients. The method may serve as an analysis tool for clinicians to assess pathological phonation and treatment efficacy.
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2021, Journal of Voice
This study investigates the effect of the ventricular folds on fundamental frequency (f_o) 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 f_o 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 f_o measured ex vivo for PS1 and PS2. The differing f_o 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.
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2020, Speech Communication
Hypernasality in the speech of children with cleft palate is a consequence of velopharyngeal insufficiency. The spectral analysis of hypernasal speech shows the presence of nasal formants and anti-formants in the spectrum which affects the harmonic-intensity. The nasal formants increase whereas the anti-formants decrease the magnitude of harmonics around its location of addition. Hence, the spectrum of hypernasal and normal speech is different from each other. To capture the spectral difference, three features namely, normalized harmonic amplitude (NHA), harmonic amplitude ratio (HAR), and prominent harmonics frequency (PHF) are proposed in this work. NHA feature is the magnitude of harmonics after their normalization with respect to the maximum magnitude, HAR feature is the relative magnitude of harmonics with respect to their previous harmonics, and the PHF feature is the frequencies of prominent harmonics in the spectrum. The combination of three features gives an accuracy of 82.46%, 87.89%, 84.25% for /a/, /i/ and /u/ vowels respectively for the detection of hypernasality using support vector machine classifier.
New Evidence That Nonlinear Source-Filter Coupling Affects Harmonic Intensity and fo Stability During Instances of Harmonics Crossing Formants
2017, Journal of Voice
Citation Excerpt :
Coupling has also been theorized and observed in the Iberian red deer, both excised and in vivo.10,11 Additionally, interaction has been observed in the form of fo jumps and the presence of subharmonics with acoustic coupling to the subglottal system12 as well as in excised canine and porcine larynges with an added supraglottal vocal tract.13,14 In human phonation, the interactions are often not severe, but nevertheless clearly observable.4,15–18
The traditional source-filter theory of voice production describes a linear relationship between the source (glottal flow pulse) and the filter (vocal tract). Such a linear relationship does not allow for nor explain how changes in the filter may impact the stability and regularity of the source. The objective of this experiment was to examine what effect unpredictable changes to vocal tract dimensions could have on fo stability and individual harmonic intensities in situations in which low frequency harmonics cross formants in a fundamental frequency glide. To determine these effects, eight human subjects (five male, three female) were recorded producing fo glides while their vocal tracts were artificially lengthened by a section of vinyl tubing inserted into the mouth. It was hypothesized that if the source and filter operated as a purely linear system, harmonic intensities would increase and decrease at nearly the same rates as they passed through a formant bandwidth, resulting in a relatively symmetric peak on an intensity-time contour. Additionally, fo stability should not be predictably perturbed by formant/harmonic crossings in a linear system. Acoustic analysis of these recordings, however, revealed that harmonic intensity peaks were asymmetric in 76% of cases, and that 85% of fo instabilities aligned with a crossing of one of the first four harmonics with the first three formants. These results provide further evidence that nonlinear dynamics in the source-filter relationship can impact fo stability as well as harmonic intensities as harmonics cross through formant bandwidths.
Nonlinear analyses of elicited modal, raised, and pressed rabbit phonation
2014, Journal of Voice
The purpose of this study was to use nonlinear dynamic analysis methods such as phase space portraits and correlation dimension (D₂) as well as descriptive spectrographic analyses to characterize acoustic signals produced during evoked rabbit phonation.
Seventeen New Zealand white breeder rabbits were used to perform the study. A Grass S-88 stimulator (SA Instrumentation, Encinitas, CA) and constant current isolation unit (Grass Telefactor, model PSIU6; West Warwick, RI) were used to provide electrical stimulation to laryngeal musculature, and transglottal airflow rate and stimulation current (mA) were manipulated to elicit modal, raised intensity, and pressed phonations. Central 1 second portions of the most stable portion of the acoustic waveform for modal, raised intensity, and pressed phonations were edited and then analyzed via phase space portraits, Poincaré sections, and the estimation of the D₂. In an attempt to limit the effects of the highly variable and nonstationary characteristics of some of the signals being analyzed, D₂ analysis was also performed on the most stable central 200-millisecond portion of the acoustic waveform. Descriptive analysis of each phonation was also conducted using sound spectrograms.
Results showed that the complexity of phonation and the subsequent acoustic waveform is increased as transglottal airflow rate and degree of glottal adduction are manipulated in the evoked rabbit phonation model. In particular, phonatory complexity, as quantified via D₂ analyses and demonstrated via spectrographic characteristics, increases from “modal” (ie, phonation elicited at just above the phonation threshold pressure) to raised intensity (phonation elicited by increasing transglottal airflow rate) to pressed (phonation elicited by increasing the stimulation current delivered to the larynx). Variations in a single dynamic dimension (airflow rate or adductory force) resulted in significantly increased productions of nonlinear phenomenon, including bifurcations from periodicity to regions of subharmonic content, fundamental frequency, and harmonic jumps, and evidence of periodicity within aperiodic regions (“chaos”).
The evoked rabbit phonation model described in this study allows for the elicitation of various types of phonations under controlled conditions and, therefore, has the potential to provide insight regarding important variables that may elicit examples of nonlinear phenomena such as subharmonics and deterministic chaos.
Vibrational dynamics of vocal folds using nonlinear normal modes
2013, Medical Engineering and Physics
Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues.
The results show very interesting and complex nonlinear phenomena including frequency–energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations.

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Nonlinear behavior of vocal fold vibration: The role of coupling between the vocal folds

Summary

J Voice

J Voice

J Voice

J Voice

Principles of Voice Production

Nonlinearity, complexity and control in vocal systems

Vocal fry as a phonational register

J Speech Hear Res

Amplitude modulations in patients with laryngeal diseases

J Acoust Soc Am

Characteristics of nodules through the high-resolution frequency analyser

Folia Phoniatr