Modeling of chaotic vibrations in symmetric vocal folds

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.

Identification and analysis of Nonlinear behaviors of vocal fold biomechanics during phonation to assess efficacy of surgery for benign laryngeal Diseases

BACKGROUND

Current voice assessments focus on perceptive evaluation and acoustic analysis. The interaction of vocal tract pressure (PVT) and vocal fold (VF) vibrations are important for volume and pitch control. However, there are currently little non-invasive ways to measure PVT. Limited information has been provided by previous human trials, and interactions between PVT and VF vibrations and the potential clinical application remain unclear. Here, we propose a non-invasive method for monitoring the nonlinear characteristics of PVT and VF vibrations, analyze voices from pathological and healthy individuals, and evaluate treatment efficacy.

METHOD

Healthy volunteers and patients with benign laryngeal lesions were recruited for this study. PVT was estimated using an airflow interruption method, VF vibrational frequency was calculated from accelerometer signals, and nonlinear relationships between PVT and VF vibrations were analyzed. Results from healthy volunteers and patients, as well as pre- and post-operation for the patients, were compared.

RESULTS

For healthy volunteers, nonlinearity was exhibited as an initial increase and then prompt decrease in vibrational frequency at the end of phonation, coinciding with PVT 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.

CONCLUSION

This novel method simultaneously monitors PVT and VF vibration and helps clarify the role of PVT. 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.

Differences and Reliability of Linear and Nonlinear Acoustic Measures as a Function of Vocal Intensity in Individuals With Voice Disorders

PURPOSE

Linear acoustic indices are significantly influenced by speaking voice intensity. The main aim of this work was to compare acoustic measures based on linear and nonlinear models in different speaking voice intensity levels and to analyze the reliability of those measures in different intensity levels in subjects with voice disorders.

METHODS

435 samples from subjects (314 women, 121 men with a mean age of 41.07 ± 13.73) diagnosed with various voice disorders were used. In total, 17 acoustic measures were derived from the vowel /ɛ/ sustained at three intensity levels (soft, comfortable, and loud). Five were linear (standard deviation of the fundamental frequency (f0), jitter, shimmer, harmonics-to-noise ratio (HNR) and smoothed cepstral peak prominence (CPPS)), and twelve were nonlinear measures, namely correlation dimension (D2), correlation entropy (H2), first minimum of the mutual information function (FMMI), relative entropy (ENTR-R), largest Lyapunov exponent (Lyap), determinism (DET), transitivity, mean diagonal line length (Lmed), Shannon entropy (ENTR-S), mean length of vertical structures, also known as trapping time (TT), laminarity (LAM) and recurrence period density entropy (RPDE). Differences between speaking voice intensity levels were assessed by Friedman's test and Nemenyi as posthoc test. Intraclass correlation coefficient was used to investigate if each acoustic measure remains in agreement (reliability) between different voice intensity levels.

RESULTS

There were significant differences in all acoustic measures about vocal intensity level (P < 0.001). Intraclass correlation coefficient was very good for HNR (>0.61) and good for Lyap, DET, ENTR-S, Lmed, RPDE, and TT (0.41-0.60).

CONCLUSIONS

All acoustic measures varied as a function of vocal intensity in voice disordered adults, while this relation was different for linear and nonlinear measures. Only the measures HNR, Lyap, DET, ENTR-S, Lmed, RPDE and TT had an acceptable reliability between different voice intensity levels. Therefore, patient`s voice SPL should be controlled or indicated during acoustic vocal assessment.

Deriving Vocal Fold Oscillation Information from Recorded Voice Signals Using Models of Phonation

During phonation, the vocal folds exhibit a self-sustained oscillatory motion, which is influenced by the physical properties of the speaker's vocal folds and driven by the balance of bio-mechanical and aerodynamic forces across the glottis. Subtle changes in the speaker's physical state can affect voice production and alter these oscillatory patterns. Measuring these can be valuable in developing computational tools that analyze voice to infer the speaker's state. Traditionally, vocal fold oscillations (VFOs) are measured directly using physical devices in clinical settings. In this paper, we propose a novel analysis-by-synthesis approach that allows us to infer the VFOs directly from recorded speech signals on an individualized, speaker-by-speaker basis. The approach, called the ADLES-VFT algorithm, is proposed in the context of a joint model that combines a phonation model (with a glottal flow waveform as the output) and a vocal tract acoustic wave propagation model such that the output of the joint model is an estimated waveform. The ADLES-VFT algorithm is a forward-backward algorithm which minimizes the error between the recorded waveform and the output of this joint model to estimate its parameters. Once estimated, these parameter values are used in conjunction with a phonation model to obtain its solutions. Since the parameters correlate with the physical properties of the vocal folds of the speaker, model solutions obtained using them represent the individualized VFOs for each speaker. The approach is flexible and can be applied to various phonation models. In addition to presenting the methodology, we show how the VFOs can be quantified from a dynamical systems perspective for classification purposes. Mathematical derivations are provided in an appendix for better readability.

Evaluating the Voice Type Component Distributions of Excised Larynx Phonations at Three Subglottal Pressures

Purpose The excised canine larynx provides an advantageous experimental framework in the study of voice physiology. In recent years, signal processing methods have been applied to analyze phonations in excised canine larynx experiments. However, phonations have a highly complex and nonstationary nature corresponding to different proportions of regular and chaotic signal elements. Current nonlinear dynamic methods that are used to assess the degree of irregularity in the voice fail to recognize the distribution of voice type components (VTCs). Method Based on measures of intrinsic dimension, this article presents a method to analyze the VTC distribution of phonations in excised canine larynx experiments. Thirty-nine phonation samples from 13 excised canine larynges at three different subglottal pressures were analyzed. Results Phonation produced with subglottal pressures above phonation instability pressure (PIP) and below phonation threshold pressure (PTP) resulted in high proportions of Voice Types 3 and 4, characterized by chaotic and noisy signals. Phonation produced with pressure between PTP and PIP contained mostly Type 1 voice, characterized by a regular and nearly periodic signal. Mean proportions of all VTCs varied significantly in comparisons of phonations produced with Sub-PTP and PTP as well as in comparisons of phonations produced with PTP and PIP. Conclusions Across all VTCs, the VTC profiles of normal and abnormal phonation differ significantly. Normal phonation is strongly associated with VTC₁ (Voice Type Component 1), whereas abnormal phonation exhibits increased VTC₄ (Voice Type Component 4). The study further demonstrates the ability of intrinsic dimension to successfully detect multiple voice types in an acoustic signal and highlights the need for expanded use of intrinsic dimension in human voice. Supplemental Material https://doi.org/10.23641/asha.14417585.

Performance of Different Acoustic Measures to Discriminate Individuals With and Without Voice Disorders

The goal of this study is to compare and combine different acoustic features in discriminating subjects with and without voice disorders. A database of 484 adult patients participated in the research. All subjects recorded a sustained vowel /Ɛ/ and underwent a laryngoscopic examination of the larynx. From the results of the laryngeal examination performed by a physician and the auditory-perceptual judgment performed by a Speech-Language Pathologist, the subjects were allocated to the group with (n = 52) and without (n = 432) voice disorder. Four types of acoustic features were used: traditional measures, cepstral measures, nonlinear measures, and recurrence quantification measures. Recordings comprised the emission of the vowel /ε/. Quadratic discriminant analysis was used as classifier. Individual features in the context of traditional, cepstral, and recurrence quantification measures achieved an acceptable performance of ≥70%. Combination of measures improved the classifier performance. The best classification result (86.43% accuracy) was obtained by combining traditional linear and recurrence quantification measures. Results shown that Traditional, Cepstral, and recurrence quantification measures are promising features that capture meaningful information about voice production, which provides good classification performances. The findings of this study can be used to develop a computational tool for voice disorders diagnosis and monitoring.

Human roars communicate upper-body strength more effectively than do screams or aggressive and distressed speech

Despite widespread evidence that nonverbal components of human speech (e.g., voice pitch) communicate information about physical attributes of vocalizers and that listeners can judge traits such as strength and body size from speech, few studies have examined the communicative functions of human nonverbal vocalizations (such as roars, screams, grunts and laughs). Critically, no previous study has yet to examine the acoustic correlates of strength in nonverbal vocalisations, including roars, nor identified reliable vocal cues to strength in human speech. In addition to being less acoustically constrained than articulated speech, agonistic nonverbal vocalizations function primarily to express motivation and emotion, such as threat, and may therefore communicate strength and body size more effectively than speech. Here, we investigated acoustic cues to strength and size in roars compared to screams and speech sentences produced in both aggressive and distress contexts. Using playback experiments, we then tested whether listeners can reliably infer a vocalizer's actual strength and height from roars, screams, and valenced speech equivalents, and which acoustic features predicted listeners' judgments. While there were no consistent acoustic cues to strength in any vocal stimuli, listeners accurately judged inter-individual differences in strength, and did so most effectively from aggressive voice stimuli (roars and aggressive speech). In addition, listeners more accurately judged strength from roars than from aggressive speech. In contrast, listeners' judgments of height were most accurate for speech stimuli. These results support the prediction that vocalizers maximize impressions of physical strength in aggressive compared to distress contexts, and that inter-individual variation in strength may only be honestly communicated in vocalizations that function to communicate threat, particularly roars. Thus, in continuity with nonhuman mammals, the acoustic structure of human aggressive roars may have been selected to communicate, and to some extent exaggerate, functional cues to physical formidability.

Descriptive Analysis of the Interactive Patterning of the Vocalization Subsystems in Healthy Participants: A Dynamic Systems Perspective

Purpose Normative data for many objective voice measures are routinely used in clinical voice assessment; however, normative data reflect vocal output, but not vocalization process. The underlying physiologic processes of healthy phonation have been shown to be nonlinear and thus are likely different across individuals. Dynamic systems theory postulates that performance behaviors emerge from the nonlinear interplay of multiple physiologic components and that certain patterns are preferred and loosely governed by the interactions of physiology, task, and environment. The purpose of this study was to descriptively characterize the interactive nature of the vocalization subsystem triad in subjects with healthy voices and to determine if differing subgroups could be delineated to better understand how healthy voicing is physiologically generated. Method Respiratory kinematic, aerodynamic, and acoustic formant data were obtained from 29 individuals with healthy voices (21 female and eight male). Multivariate analyses were used to descriptively characterize the interactions among the subsystems that contributed to healthy voicing. Results Group data revealed representative measures of the 3 subsystems to be generally within the boundaries of established normative data. Despite this, 3 distinct clusters were delineated that represented 3 subgroups of individuals with differing subsystem patterning. Seven of the 9 measured variables in this study were found to be significantly different across at least 1 of the 3 subgroups indicating differing physiologic processes across individuals. Conclusion Vocal output in healthy individuals appears to be generated by distinct and preferred physiologic processes that were represented by 3 subgroups indicating that the process of vocalization is different among individuals, but not entirely idiosyncratic. Possibilities for these differences are explored using the framework of dynamic systems theory and the dynamics of emergent behaviors. A revised physiologic model of phonation that accounts for differences within and among the vocalization subsystems is described. Supplemental Material https://doi.org/10.23641/asha.7616462.

Performance of Phonatory Deviation Diagrams in Synthesized Voice Analysis

OBJECTIVE

To analyze the performance of a phonatory deviation diagram (PDD) in discriminating the presence and severity of voice deviation and the predominant voice quality of synthesized voices.

METHOD

A speech-language pathologist performed the auditory-perceptual analysis of the synthesized voice (n = 871). The PDD distribution of voice signals was analyzed according to area, quadrant, shape, and density.

RESULTS

Differences in signal distribution regarding the PDD area and quadrant were detected when differentiating the signals with and without voice deviation and with different predominant voice quality. Differences in signal distribution were found in all PDD parameters as a function of the severity of voice disorder.

CONCLUSION

The PDD area and quadrant can differentiate normal voices from deviant synthesized voices. There are differences in signal distribution in PDD area and quadrant as a function of the severity of voice disorder and the predominant voice quality. However, the PDD area and quadrant do not differentiate the signals as a function of severity of voice disorder and differentiated only the breathy and rough voices from the normal and strained voices. PDD density is able to differentiate only signals with moderate and severe deviation. PDD shape shows differences between signals with different severities of voice deviation.

Fully-coupled aeroelastic simulation with fluid compressibility - For application to vocal fold vibration

In this study, a fully-coupled fluid-structure interaction model is developed for studying dynamic interactions between compressible fluid and aeroelastic structures. The technique is built based on the modified Immersed Finite Element Method (mIFEM), a robust numerical technique to simulate fluid-structure interactions that has capabilities to simulate high Reynolds number flows and handles large density disparities between the fluid and the solid. For accurate assessment of this intricate dynamic process between compressible fluid, such as air and aeroelastic structures, we included in the model the fluid compressibility in an isentropic process and a solid contact model. The accuracy of the compressible fluid solver is verified by examining acoustic wave propagations in a closed and an open duct, respectively. The fully-coupled fluid-structure interaction model is then used to simulate and analyze vocal folds vibrations using compressible air interacting with vocal folds that are represented as layered viscoelastic structures. Using physiological geometric and parametric setup, we are able to obtain a self-sustained vocal fold vibration with a constant inflow pressure. Parametric studies are also performed to study the effects of lung pressure and vocal fold tissue stiffness in vocal folds vibrations. All the case studies produce expected airflow behavior and a sustained vibration, which provide verification and confidence in our future studies of realistic acoustical studies of the phonation process.

Evaluation of aerodynamic characteristics of a coupled fluid-structure system using generalized Bernoulli's principle: An application to vocal folds vibration

In this work we explore the aerodynamics flow characteristics of a coupled fluid-structure interaction system using a generalized Bernoulli equation derived directly from the Cauchy momentum equations. Unlike the conventional Bernoulli equation where incompressible, inviscid, and steady flow conditions are assumed, this generalized Bernoulli equation includes the contributions from compressibility, viscous, and unsteadiness, which could be essential in defining aerodynamic characteristics. The application of the derived Bernoulli's principle is on a fully-coupled fluid-structure interaction simulation of the vocal folds vibration. The coupled system is simulated using the immersed finite element method where compressible Navier-Stokes equations are used to describe the air and an elastic pliable structure to describe the vocal fold. The vibration of the vocal fold works to open and close the glottal flow. The aerodynamics flow characteristics are evaluated using the derived Bernoulli's principles for a vibration cycle in a carefully partitioned control volume based on the moving structure. The results agree very well to experimental observations, which validate the strategy and its use in other types of flow characteristics that involve coupled fluid-structure interactions.

Quantifying the Subharmonic Mucosal Wave in Excised Larynges via Digital Kymography

OBJECTIVES

In this paper, a nonlinear least squares fitting method was proposed to quantify subharmonic mucosal waves.

STUDY DESIGN AND METHODS

Subharmonic mucosal waves from 10 excised canine larynges were recorded using digital kymography and analyzed using nonlinear least squares and linear least squares methods. Amplitudes of fundamental and subharmonic mucosal wave components of right-upper, right-lower, left-upper, and left-lower vocal fold lips were calculated. Lastly, phase differences of fundamental and subharmonic components of the left and right vocal folds were compared.

RESULTS

The results showed that the nonlinear least squares analysis method provides a more effective complement to the linear fitting method for subharmonic mucosal wave extraction. There was a significant difference in amplitudes between the subharmonic and the fundamental components of mucosal waves (P < 0.05). The phase differences of the fundamental and the subharmonic components of the right and left vocal folds were not significantly different.

CONCLUSIONS

The application of the nonlinear least squares analysis method in digital kymography is useful for the characterization of subharmonic mucosal waves.

Comprehensive, Population-Based Sensitivity Analysis of a Two-Mass Vocal Fold Model

Previous vocal fold modeling studies have generally focused on generating detailed data regarding a narrow subset of possible model configurations. These studies can be interpreted to be the investigation of a single subject under one or more vocal conditions. In this study, a broad population-based sensitivity analysis is employed to examine the behavior of a virtual population of subjects and to identify trends between virtual individuals as opposed to investigating a single subject or model instance. Four different sensitivity analysis techniques were used in accomplishing this task. Influential relationships between model input parameters and model outputs were identified, and an exploration of the model’s parameter space was conducted. Results indicate that the behavior of the selected two-mass model is largely dominated by complex interactions, and that few input-output pairs have a consistent effect on the model. Results from the analysis can be used to increase the efficiency of optimization routines of reduced-order models used to investigate voice abnormalities. Results also demonstrate the types of challenges and difficulties to be expected when applying sensitivity analyses to more complex vocal fold models. Such challenges are discussed and recommendations are made for future studies.

Inducing rostrum interfacial waves by fluid-solid coupling in a Chinese river dolphin (Lipotesvexillifer)

Through numerically solving the appropriate wave equations, propagation of biosonar signals in a Chinese river dolphin (baiji) was studied. The interfacial waves along the rostrum-tissue interfaces, including both compressional (longitudinal) and shear (transverse) waves in the solid rostrum through fluid-solid coupling were examined. The baiji's rostrum was found to effect acoustic beam formation not only as an interfacial wave generator but also as a sound reflector. The wave propagation patterns in the solid rostrum were found to significantly change the wave movement through the bone. Vibrations in the rostrum, expressed in solid displacement, initially increased but eventually decreased from posterior to anterior sides, indicating a complex physical process. Furthermore, the comparisons among seven cases, including the combination of (1) the rostrum, melon, and air sacs; (2) rostrum-air sacs; (3) rostrum-melon; (4) only rostrum; (5) air sacs-melon; (6) only air sacs; and (7) only melon revealed that the cases including the rostrum were better able to approach the complete system by inducing rostrum-tissue interfacial waves and reducing the differences in main beam angle and -3 dB beam width. The interfacial waves in the rostrum were considered complementary with reflection to determine the obbligato role of the rostrum in the baiji's biosonar emission. The far-field beams formed from complete fluid-solid models and non-fluid-solid models were compared to reveal the effects brought by the consideration of shear waves of the solid structures of the baiji. The results may provide useful information for further understanding the role of the rostrum in this odontocete species.

Scaling and universality in the human voice

Speech is a distinctive complex feature of human capabilities. In order to understand the physics underlying speech production, in this work, we empirically analyse the statistics of large human speech datasets ranging several languages. We first show that during speech, the energy is unevenly released and power-law distributed, reporting a universal robust Gutenberg-Richter-like law in speech. We further show that such 'earthquakes in speech' show temporal correlations, as the interevent statistics are again power-law distributed. As this feature takes place in the intraphoneme range, we conjecture that the process responsible for this complex phenomenon is not cognitive, but it resides in the physiological (mechanical) mechanisms of speech production. Moreover, we show that these waiting time distributions are scale invariant under a renormalization group transformation, suggesting that the process of speech generation is indeed operating close to a critical point. These results are put in contrast with current paradigms in speech processing, which point towards low dimensional deterministic chaos as the origin of nonlinear traits in speech fluctuations. As these latter fluctuations are indeed the aspects that humanize synthetic speech, these findings may have an impact in future speech synthesis technologies. Results are robust and independent of the communication language or the number of speakers, pointing towards a universal pattern and yet another hint of complexity in human speech.

Simulation of ultrasound beam formation of baiji (Lipotes vexillifer) with a finite element model

The baiji (Lipotes vexillifer) of the Yangtze River possesses a sophisticated biosonar system. In this study, a finite element approach was used to numerically investigate the propagation of acoustic waves through the head of the Yangtze River dolphin, which possesses an inhomogeneous and complex structure. The acoustic intensity distribution predicted from models with and without the melon and/or skull showed that the emitted sound beam was narrow and formed a highly directed acoustic beam, and the skull and melon significantly enhanced the directional characteristics of the emitted sound. Finally, for a short duration impulsive source, the emitted sound pressure distributions were also simulated at different propagation times. The results provide useful information for better understanding the operation of the biosonar system in this rare and perhaps extinct animal.

Acoustic assessment of the voices of children using nonlinear analysis: proposal for assessment and vocal monitoring

OBJECTIVE

To analyze the accuracy of recurrence measurements, both isolated and combined, to assess the intensity of vocal disorders in children.

METHOD

A total of 93 children of both sexes (48 girls and 45 boys), aged between 3 and 10 years, participated. The vocal-deviation intensity was evaluated by the consensus of three speech therapists from the pronunciation of vowel /ε/ using the visual analog scale. In the acoustic analysis, eight recurrence plot characteristics were evaluated and extracted with neighborhood radius values that maintained the recurrence rate at 1%, 2%, 3%, 4%, and 5%. The classification was performed using quadratic discriminant analysis applied for individual and combined measurements. The performance was evaluated by measuring the accuracy, which related the cases correctly classified to all the analyzed cases.

RESULTS

In the classification cases concerning individual measure performance, the trapping time and maximum length of the diagonal lines showed the best classification potential to discriminate between healthy and disturbed voices, with accuracy rates above 80%. In the healthy and mild deviation cases, the trend (TREND) measure was also relevant. For the mild versus moderate deviation classification, the best performance was obtained by the TREND measure (85.00% ± 7.64%). A gain was obtained in the classification rate when the measures of recurrence were combined, reaching an accuracy of 95.00% ± 5.00%, for discriminating between healthy voices and those with mild deviation.

CONCLUSIONS

The measures of recurrence, either alone or combined, may be useful in detecting healthy and disturbed voices and in differentiating the intensity of vocal disorders in children.

Computational study of effects of tension imbalance on phonation in a three-dimensional tubular larynx model

OBJECTIVES

The present study explores the use of a continuum-based computational model to investigate the effect of left-right tension imbalance on vocal fold (VF) vibrations and glottal aerodynamics, as well as its implication on phonation. The study allows us to gain new insights into the underlying physical mechanism of irregularities induced by VF tension imbalance associated with unilateral cricothyroid muscle paralysis.

METHODS

A three-dimensional simulation of glottal flow and VF dynamics in a tubular laryngeal model with tension imbalance was conducted by using a coupled flow-structure interaction computational model. Tension imbalance was modeled by reducing by 20% the Young's modulus of one of the VFs, while holding VF length constant. Effects of tension imbalance on vibratory characteristic of the VFs and on the time-varying properties of glottal airflow as well as the aerodynamic energy transfer are comprehensively analyzed.

RESULTS AND CONCLUSIONS

The analysis demonstrates that the continuum-based biomechanical model can provide a good description of phonatory dynamics in tension imbalance conditions. It is found that although 20% tension imbalance does not have noticeable effects on the fundamental frequency, it does lead to a larger glottal flow leakage and asymmetric vibrations of the two VFs. A detailed analysis of the energy transfer suggests that the majority of the energy is consumed by the lateral motion of the VFs and the net energy transferred to the softer fold is less than the one transferred to the normal fold.

Comparison of SVM and ANFIS for snore related sounds classification by using the largest Lyapunov exponent and entropy

Snoring, which may be decisive for many diseases, is an important indicator especially for sleep disorders. In recent years, many studies have been performed on the snore related sounds (SRSs) due to producing useful results for detection of sleep apnea/hypopnea syndrome (SAHS). The first important step of these studies is the detection of snore from SRSs by using different time and frequency domain features. The SRSs have a complex nature that is originated from several physiological and physical conditions. The nonlinear characteristics of SRSs can be examined with chaos theory methods which are widely used to evaluate the biomedical signals and systems, recently. The aim of this study is to classify the SRSs as snore/breathing/silence by using the largest Lyapunov exponent (LLE) and entropy with multiclass support vector machines (SVMs) and adaptive network fuzzy inference system (ANFIS). Two different experiments were performed for different training and test data sets. Experimental results show that the multiclass SVMs can produce the better classification results than ANFIS with used nonlinear quantities. Additionally, these nonlinear features are carrying meaningful information for classifying SRSs and are able to be used for diagnosis of sleep disorders such as SAHS.

Ray chaos in an architectural acoustic semi-stadium system

The semi-stadium system is composed of a semicircular cap and a rectilinear platform. In this study, a dynamic model of the side, position, and angle variables is applied to investigate the acoustic ray chaos of the architectural semi-stadium system. The Lyapunov exponent is calculated in order to quantitatively describe ray instability. The model can be reduced to the semi-circular and rectilinear platform systems when the rectilinear length is sufficiently small and large. The quasi-rectilinear platform and the semicircular systems both produce regular trajectories with the maximal Lyapunov exponent approaching zero. Ray localizations, such as flutter-echo and sound focusing, are found in these two systems. However, the semi-stadium system produces chaotic ray behaviors with positive Lyapunov exponents and reduces ray localizations. Furthermore, as the rectilinear length increases, the scaling laws of the Lyapunov exponent of the semi-stadium system are revealed and compared with those of the stadium system. The results suggest the potential application of the proposed model to simulate chaotic dynamics of acoustic ray in architectural enclosed systems.

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.

Computation of physiological human vocal fold parameters by mathematical optimization of a biomechanical model

With the use of an endoscopic, high-speed camera, vocal fold dynamics may be observed clinically during phonation. However, observation and subjective judgment alone may be insufficient for clinical diagnosis and documentation of improved vocal function, especially when the laryngeal disease lacks any clear morphological presentation. In this study, biomechanical parameters of the vocal folds are computed by adjusting the corresponding parameters of a three-dimensional model until the dynamics of both systems are similar. First, a mathematical optimization method is presented. Next, model parameters (such as pressure, tension and masses) are adjusted to reproduce vocal fold dynamics, and the deduced parameters are physiologically interpreted. Various combinations of global and local optimization techniques are attempted. Evaluation of the optimization procedure is performed using 50 synthetically generated data sets. The results show sufficient reliability, including 0.07 normalized error, 96% correlation, and 91% accuracy. The technique is also demonstrated on data from human hemilarynx experiments, in which a low normalized error (0.16) and high correlation (84%) values were achieved. In the future, this technique may be applied to clinical high-speed images, yielding objective measures with which to document improved vocal function of patients with voice disorders.

Experimental and Theoretical Investigations of Phonation Threshold Pressure as a Function of Vocal Fold Elongation

The relationship between the vocal fold elongation and the phonation threshold pressure (PTP) was experimentally and theoretically investigated. The PTP values of seventeen excised canine larynges with 0% to 15% bilateral vocal fold elongations in 5% elongation steps were measured using an excised larynx phonation system. It was found that twelve larynges exhibited a monotonic relationship between PTP and elongation; in these larynges, the 0% elongation condition had the lowest PTP. Five larynges exhibited a PTP minimum at 5% elongation. To provide a theoretical explanation of these phenomena, a two-mass model was modified to simulate vibration of the elongated vocal folds. Two pairs of longitudinal springs were used to represent the longitudinal elastin in the vocal folds. This model showed that when the vocal folds were elongated, the increased longitudinal tension would increase the PTP value and the increased vocal fold length would decrease the PTP value. The antagonistic effects contributed by these two factors were found to be able to cause either a monotonic or a non-monotonic relationship between PTP and elongation, which were consistent with experimental observations. Because PTP describes the ease of phonation, this study suggests that there may exist a nonzero optimal vocal fold elongation for the greatest ease for phonation in some larynges.

Toward a simulation-based tool for the treatment of vocal fold paralysis

Advances in high-performance computing are enabling a new generation of software tools that employ computational modeling for surgical planning. Surgical management of laryngeal paralysis is one area where such computational tools could have a significant impact. The current paper describes a comprehensive effort to develop a software tool for planning medialization laryngoplasty where a prosthetic implant is inserted into the larynx in order to medialize the paralyzed vocal fold (VF). While this is one of the most common procedures used to restore voice in patients with VF paralysis, it has a relatively high revision rate, and the tool being developed is expected to improve surgical outcomes. This software tool models the biomechanics of airflow-induced vibration in the human larynx and incorporates sophisticated approaches for modeling the turbulent laryngeal flow, the complex dynamics of the VFs, as well as the production of voiced sound. The current paper describes the key elements of the modeling approach, presents computational results that demonstrate the utility of the approach and also describes some of the limitations and challenges.

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.

Theoretical modeling and experimental high-speed imaging of elongated vocal folds

In this paper, the role of vocal fold elongation in governing glottal movement dynamics was theoretically and experimentally investigated. A theoretical model was first proposed to incorporate vocal fold elongation into the two-mass model. This model predicted the direct and nondirect components of the glottal time series as a function of vocal fold elongation. Furthermore, high-speed digital imaging was applied in excised larynx experiments to visualize vocal fold vibrations with variable vocal fold elongation from -10% to 50% and subglottal pressures of 18- and 24-cm H(2)O. Comparison between theoretical model simulations and experimental observations showed good agreement. A relative maximum was seen in the nondirect component of glottal area, suggesting that an optimal elongation could maximize the vocal fold vibratory power. However, sufficiently large vocal fold elongations caused the nondirect component to approach zero and the direct component to approach a constant. These results showed that vocal fold elongation plays an important role in governing the dynamics of glottal area movement and validated the applicability of the proposed theoretical model and high-speed imaging to investigate laryngeal activity.

Ex vivo canine vocal fold lamina propria rehydration after varying dehydration levels

OBJECTIVES

To examine the recoverability of canine vocal fold (VF) lamina propria (LP) on rehydration from varying dehydration levels.

STUDY DESIGN

Open, controlled experimental trial.

METHODS

The VF LP was excised en bloc using a scalpel from 10 canine larynges, providing 20 tissue samples. The initial volume of each sample was measured. Ten samples were dehydrated to 30% by mass and the other 10 samples to 70%. Each sample was rehydrated in 0.9% saline until the mass stabilized. The liquid mass and volume fractions, liquid:solid mass and volume ratios, and the fractions of the original tissue masses and volumes were calculated.

RESULTS

All calculated parameters were significantly different between 30% and 70% dehydration recovery, with all parameters lesser in the 70% dehydration treatment group. Half of the tissue samples subjected to 30% dehydration fully recovered to their original volumes, whereas only one of the 10 samples subjected to 70% dehydration fully recovered its volume.

CONCLUSIONS

The level of attainable rehydration recovery of VF LP tissue in an ex vivo setting depends on the level of dehydration. The results correspond to the biphasic theory and may be used to help model the biomechanical and physiological properties of VF LP tissue during rehydration.

Peripheral mechanisms for vocal production in birds - differences and similarities to human speech and singing

Song production in songbirds is a model system for studying learned vocal behavior. As in humans, bird phonation involves three main motor systems (respiration, vocal organ and vocal tract). The avian respiratory mechanism uses pressure regulation in air sacs to ventilate a rigid lung. In songbirds sound is generated with two independently controlled sound sources, which reside in a uniquely avian vocal organ, the syrinx. However, the physical sound generation mechanism in the syrinx shows strong analogies to that in the human larynx, such that both can be characterized as myoelastic-aerodynamic sound sources. Similarities include active adduction and abduction, oscillating tissue masses which modulate flow rate through the organ and a layered structure of the oscillating tissue masses giving rise to complex viscoelastic properties. Differences in the functional morphology of the sound producing system between birds and humans require specific motor control patterns. The songbird vocal apparatus is adapted for high speed, suggesting that temporal patterns and fast modulation of sound features are important in acoustic communication. Rapid respiratory patterns determine the coarse temporal structure of song and maintain gas exchange even during very long songs. The respiratory system also contributes to the fine control of airflow. Muscular control of the vocal organ regulates airflow and acoustic features. The upper vocal tract of birds filters the sounds generated in the syrinx, and filter properties are actively adjusted. Nonlinear source-filter interactions may also play a role. The unique morphology and biomechanical system for sound production in birds presents an interesting model for exploring parallels in control mechanisms that give rise to highly convergent physical patterns of sound generation. More comparative work should provide a rich source for our understanding of the evolution of complex sound producing systems.

Parameters quantifying dehydration in canine vocal fold lamina propria

OBJECTIVES/HYPOTHESIS

The goal of this study was to measure the solid and liquid volume and mass of canine vocal fold lamina propria tissue at varying dehydration levels, and to calculate parameters to test the biphasic theory of vocal fold physiology and biomechanics.

STUDY DESIGN

Open, controlled, experimental trial.

METHODS

The vocal fold lamina propria was dissected from 15 canine larynges, yielding 30 tissue samples. The initial volumes and masses of the tissue samples were measured. The masses of the tissue samples were then measured every 2 minutes during 30%, 50%, and 70% dehydration, with 10 samples subjected to each of the three treatments, followed by complete dehydration to yield the solid component of the tissue. The liquid mass and volume fractions and liquid:solid mass and volume ratios of the vocal fold lamina propria samples were calculated.

RESULTS

The liquid mass and volume fractions and liquid:solid mass and volume ratios were significantly different at each dehydration level, except for the liquid:solid volume ratios at 30% versus 50% dehydration. Linear regression analysis suggested that all of the solid and liquid parameters measured could be predicted by dehydration level based on inverse, linear relationships.

CONCLUSIONS

These results provide further experimental evidence supporting the biphasic theory and suggest that the extent of vocal fold lamina propria tissue dehydration may be quantified based on the biphasic model parameters.

A computational study of the effect of vocal-fold asymmetry on phonation

Unilateral laryngeal paralysis leads to tension imbalance and hence to asynchronous movements between the two vocal folds during phonation. In the current study, a computational model of phonation that couples a two-mass model of the vocal folds with a Navier-Stokes model of the glottal airflow, has been used to examine the dynamics of vocal fold configurations with tension imbalance and its implications for phonation. The simulations show that tension imbalance influences phonation onset, intensity as well as the fundamental phonation frequency. Distinct non-linear effects such as period-doubling bifurcation and preferential frequency selection are also observed.

Arytenoid Adduction for Correcting Vocal Fold Asymmetry: High-Speed Imaging

Objectives

We hypothesized that high-speed digital imaging provides a quantitative method to evaluate the effect of arytenoid adduction for the correction of asymmetric and irregular vocal fold vibration in unilateral vocal fold paralysis.

Methods

Six subjects with unilateral vocal fold paralysis participated in the study (4 male, 2 female; mean [±SD] age, 52.5 ± 21.3 years). Videokymographic and laryngotopographic methods for image analysis were performed for highspeed recordings of vocal fold vibration for visualizing the glottal vibratory patterns, and for quantifying the frequency of vibration of each vocal fold, respectively. Comparisons of the paralyzed and the normal vocal folds were made before and after arytenoid adduction.

Results

Analysis of the laryngotopographs revealed 2 distinct frequencies of vibration for the paralyzed and the contralateral vocal folds for all subjects before surgery. After arytenoid adduction, the vibration frequencies became identical or nearly identical in all subjects.

Conclusions

Asymmetric vibration in vocal fold paralysis was exemplified by differences in vibration frequency between the vocal folds. The present data showed that after arytenoid adduction the vibration frequencies and the vibratory patterns of the contralateral vocal folds approached symmetry. This surgical procedure could improve the functional symmetry of the larynx for phonation.

Perturbation and nonlinear dynamic analysis of adult male smokers

OBJECTIVE

Smoking results in a voice change, and the perception by smokers of an abnormal voice may encourage quitting behavior. Moreover, a disordered voice is often the first sign of vocal pathology. Efforts to evaluate voice have focused on classical acoustic analysis; however, nonlinear dynamic analysis has been shown to be a reliable objective method for the evaluation of voice. We compare the discriminatory ability of these two methods when applied to normal and smokers' voices.

STUDY DESIGN

Prospective study.

METHODS

The study included 73 subjects, 36 nonsmokers and 37 smokers. A segment of sustained vowel production was obtained from each subject. Acoustic dimension and correlation dimension (D2) analyses were applied to the data. Results were compared with a Mann-Whitney rank sum test, logistic regression, and receiver operating characteristics (ROC) analysis.

RESULTS

D2 values for smokers were significantly higher than D2 values for nonsmokers (P<0.001). Jitter and shimmer analysis showed higher values for these parameters among smokers. Logistic regression indicated a higher predictive power with D2, and ROC analysis found no significant difference between the analysis methods.

DISCUSSION

This study indicated that D2 is highly sensitive to changes associated with smoking and has the potential to be implemented clinically as an indicator of abnormal voice. Further research could focus on using nonlinear dynamic analysis to create a normative database, producing standards for monitoring voice changes caused by cigarette smoking.

Objective dysphonia quantification in vocal fold paralysis: comparing nonlinear with classical measures

Clinical acoustic voice-recording analysis is usually performed using classical perturbation measures, including jitter, shimmer, and noise-to-harmonic ratios (NHRs). However, restrictive mathematical limitations of these measures prevent analysis for severely dysphonic voices. Previous studies of alternative nonlinear random measures addressed wide varieties of vocal pathologies. Here, we analyze a single vocal pathology cohort, testing the performance of these alternative measures alongside classical measures. We present voice analysis pre- and postoperatively in 17 patients with unilateral vocal fold paralysis (UVFP). The patients underwent standard medialization thyroplasty surgery, and the voices were analyzed using jitter, shimmer, NHR, nonlinear recurrence period density entropy (RPDE), detrended fluctuation analysis (DFA), and correlation dimension. In addition, we similarly analyzed 11 healthy controls. Systematizing the preanalysis editing of the recordings, we found that the novel measures were more stable and, hence, reliable than the classical measures on healthy controls. RPDE and jitter are sensitive to improvements pre- to postoperation. Shimmer, NHR, and DFA showed no significant change (P>0.05). All measures detect statistically significant and clinically important differences between controls and patients, both treated and untreated (P<0.001, area under curve [AUC]>0.7). Pre- to postoperation grade, roughness, breathiness, asthenia, and strain (GRBAS) ratings show statistically significant and clinically important improvement in overall dysphonia grade (G) (AUC=0.946, P<0.001). Recalculating AUCs from other study data, we compare these results in terms of clinical importance. We conclude that, when preanalysis editing is systematized, nonlinear random measures may be useful for monitoring UVFP-treatment effectiveness, and there may be applications to other forms of dysphonia.

Typing vocal fold vibratory patterns in excised larynx experiments via digital kymography

OBJECTIVES

Signal typing is central to the understanding of vocal fold vibratory patterns. Digital kymography (DKG) allows the direct observation of vocal fold vibratory patterns, and therefore, using DKG for vibratory signal typing may provide a useful complement to traditional signal typing techniques.

METHODS

Video data collected from 20 larynges excised from mongrel dogs were observed with DKG in order to find examples of type 1 (nearly periodic), type 2 (subharmonic), and type 3 (aperiodic) vibratory patterns. The time series, frequency spectra, and correlation dimensions were calculated for each signal type.

RESULTS

The type 1 pattern showed a periodic time series of glottal edges and a discrete frequency spectrum. The type 2 vibratory pattern displayed a time series of alternating high- and low-amplitude waves and a frequency spectrum that included a subharmonic (F0/2) frequency component. Regular and symmetric vibratory patterns were observed in the type 1 and type 2 patterns. The type 3 vibratory pattern was characterized by an aperiodic time series of glottal edges, a broadband frequency spectrum, and irregular and asymmetric vibratory patterns. The correlation dimension estimates increased from type 1 to type 2 to type 3.

CONCLUSIONS

Imaging with DKG demonstrated an ability to assign a signal type to various laryngeal vibrations. Signal typing techniques utilizing direct observation of the vocal folds could be useful in determining valid methods for the analysis of vocal fold vibrations.

Liquid accumulation in vibrating vocal fold tissue: a simplified model based on a fluid-saturated porous solid theory

The human vocal fold is treated as a continuous, transversally isotropic, porous solid saturated with liquid. A set of mathematical equations, based on the theory of fluid-saturated porous solids, is developed to formulate the vibration of the vocal fold tissue. As the fluid-saturated porous tissue model degenerates to the continuous elastic tissue model when the relative movement of liquid in the porous tissue is ignored, it can be considered a more general description of vocal fold tissue than the continuous, elastic model. Using the fluid-saturated porous tissue model, the vibration of a bunch of one-dimensional fibers in the vocal fold is analytically solved based on the small-amplitude assumption. It is found that the vibration of the tissue will lead to the accumulation of excess liquid in the midmembranous vocal fold. The degree of liquid accumulation is positively proportional to the vibratory amplitude and frequency. The correspondence between the liquid distribution predicted by the porous tissue theory and the location of vocal nodules observed in clinical practice, provides theoretical evidence for the liquid accumulation hypothesis of vocal nodule formation (Jiang, Ph.D., dissertation, 1991, University of Iowa).

A rat excised larynx model of vocal fold scar

PURPOSE

To develop and evaluate a rat excised larynx model for the measurement of acoustic, aerodynamic, and vocal fold vibratory changes resulting from vocal fold scar.

METHOD

Twenty-four 4-month-old male Sprague-Dawley rats were assigned to 1 of 4 experimental groups: chronic vocal fold scar, chronic vocal fold scar treated with 100-ng basic fibroblast growth factor (bFGF), chronic vocal fold scar treated with saline (sham treatment), and unscarred untreated control. Following tissue harvest, histological and immunohistochemical data were collected to confirm extracellular matrix alteration in the chronic scar group; acoustic, aerodynamic, and high-speed digital imaging data were collected using an excised larynx setup in all groups. Phonation threshold pressure (P(th)), glottal resistance (R(g)), glottal efficiency (E(g)), vibratory amplitude, and vibratory area were used as dependent variables.

RESULTS

Chronically scarred vocal folds were characterized by elevated collagen Types I and III and reduced hyaluronic acid abundance. Phonation was achieved, and data were collected from all control and bFGF-treated larynges; however, phonation was not achieved with 3 of 6 chronically scarred and 1 of 6 saline-treated larynges. Compared with control, the chronic scar group was characterized by elevated P(th), reduced E(g), and intralarynx vibratory amplitude and area asymmetry. The bFGF group was characterized by P(th) below control-group levels, E(g) comparable with control, and vocal fold vibratory amplitude and area symmetry comparable with control. The sham group was characterized by P(th) comparable with control, E(g) superior to control, and vocal fold vibratory amplitude and area symmetry comparable with control.

CONCLUSIONS

The excised larynx model reported here demonstrated robust deterioration across phonatory indices under the scar condition and sensitivity to treatment-induced change under the bFGF condition. The improvement observed under the sham condition may reflect unanticipated therapeutic benefit or artifact. This model holds promise as a tool for the functional characterization of biomechanical tissue changes resulting from vocal fold scar and the evaluation of experimental therapies.

Analysis of flow-structure interaction in the larynx during phonation using an immersed-boundary method

A recently developed immersed-boundary method is used to model the flow-structure interaction associated with the human phonation. The glottal airflow is modeled as a two-dimensional incompressible flow driven by a constant subglottal pressure, and the vocal folds are modeled as a pair of three-layered, two-dimensional, viscoelastic structures. Both the fluid dynamics and viscoelasticity are solved on fixed Cartesian grids using a sharp-interface immersed boundary method. It is found that the vibration mode and frequency of the vocal fold model are associated with the eigenmodes of the structures, and that the transition of the vibration mode takes place during onset of the sustained vibration. The computed glottal waveforms of the volume flux, velocity, and pressure are reasonably realistic. The glottal flow features an unsteady jet whose direction is deflected by the large-scale vortices in the supraglottal region. A detailed analysis of the flow and vocal fold vibrations is conducted in order to gain insights into the biomechanics of phonation.

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.

Measurement of liquid and solid component parameters in canine vocal fold lamina propria

This study aimed to measure solid and liquid component parameters for canine vocal fold lamina propria tissue, as is consistent with the solid and liquid fraction parameters in the context of the biphasic theory. A liquid-displacement apparatus was developed and utilized to estimate volumes of small samples of tissue. Accuracy was determined by calibrations with an object of known mass and density (copper). The experimental apparatus was then used to determine the volume of eight tissue samples, followed by an apparently complete dehydration of the samples, yielding the dry or solid tissue. The mass and volume fractions of the liquid component were sufficiently higher than those of the solid component. These results represent preliminary experimental evidence for the biphasic composition (solid-liquid) of canine lamina propria tissue as predicted in the biphasic theory. This study presents an effective experimental method to estimate some of the biphasic model parameters, and may provide a valuable application in exploring the viscoelastic behaviors of vocal fold lamina propria tissue.

A computational study of the effect of false vocal folds on glottal flow and vocal fold vibration during phonation

The false vocal folds are believed to be components of the acoustic filter that is responsible for shaping the voice. However, the effects of false vocal folds on the vocal fold vibration and the glottal aerodynamic during phonation remain unclear. This effect has implications for computational modeling of phonation as well as for understanding laryngeal pathologies such as glottal incompetence resulting from unilateral vocal fold paralysis. In this study, a high fidelity, two-dimensional computational model, which combines an immersed boundary method for the airflow and a continuum, finite-element method for the vocal folds, is used to examine the effect of the false vocal folds on flow-induced vibration (FIV) of the true vocal folds and the dynamics of the glottal jet. The model is notionally based on a laryngeal CT scan and employs realistic flow conditions and tissue properties. Results show that the false vocal folds potentially have a significant impact on phonation. The false vocal folds reduce the glottal flow impedance and increase the amplitude as well as the mean glottal jet velocity. The false vocal folds also enhance the intensity of the monopole acoustic sources in the glottis. A mechanism for reduction in flow impedance due to the false vocal folds is proposed.

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.

An immersed-boundary method for flow-structure interaction in biological systems with application to phonation

A new numerical approach for modeling a class of flow-structure interaction problems typically encountered in biological systems is presented. In this approach, a previously developed, sharp-interface, immersed-boundary method for incompressible flows is used to model the fluid flow and a new, sharp-interface Cartesian grid, immersed boundary method is devised to solve the equations of linear viscoelasticity that governs the solid. The two solvers are coupled to model flow-structure interaction. This coupled solver has the advantage of simple grid generation and efficient computation on simple, single-block structured grids. The accuracy of the solid-mechanics solver is examined by applying it to a canonical problem. The solution methodology is then applied to the problem of laryngeal aerodynamics and vocal fold vibration during human phonation. This includes a three-dimensional eigen analysis for a multi-layered vocal fold prototype as well as two-dimensional, flow-induced vocal fold vibration in a modeled larynx. Several salient features of the aerodynamics as well as vocal-fold dynamics are presented.