An anatomically based, time-domain acoustic model of the subglottal system for speech production

Continuous-Time Model Identification of the Subglottal System

Mathematical models that accurately simulate the physiological systems of the human body serve as cornerstone instruments for advancing medical science and facilitating innovative clinical interventions. One application is the modeling of the subglottal tract and neck skin properties for its use in the ambulatory assessment of vocal function, by enabling non-invasive monitoring of glottal airflow via a neck surface accelerometer. For the technique to be effective, the development of an accurate building block model for the subglottal tract is required. Such a model is expected to utilize glottal volume velocity as the input parameter and yield neck skin acceleration as the corresponding output. In contrast to preceding efforts that employed frequency-domain methods, the present paper leverages system identification techniques to derive a parsimonious continuous-time model of the subglottal tract using time-domain data samples. Additionally, an examination of the model order is conducted through the application of various information criteria. Once a low-order model is successfully fitted, an inverse filter based on a Kalman smoother is utilized for the estimation of glottal volume velocity and related aerodynamic metrics, thereby constituting the most efficient execution of these estimates thus far. Anticipated reductions in computational time and complexity due to the lower order of the subglottal model hold particular relevance for real-time monitoring. Simultaneously, the methodology proves efficient in generating a spectrum of aerodynamic features essential for ambulatory vocal function assessment.

Kalman Filter Implementation of Subglottal Impedance-Based Inverse Filtering to Estimate Glottal Airflow during Phonation

Subglottal Impedance-Based Inverse Filtering (IBIF) allows for the continuous, non-invasive estimation of glottal airflow from a surface accelerometer placed over the anterior neck skin below the larynx. It has been shown to be advantageous for the ambulatory monitoring of vocal function, specifically in the use of high-order statistics to understand long-term vocal behavior. However, during long-term ambulatory recordings over several days, conditions may drift from the laboratory environment where the IBIF parameters were initially estimated due to sensor positioning, skin attachment, or temperature, among other factors. Observation uncertainties and model mismatch may result in significant deviations in the glottal airflow estimates; unfortunately, they are very difficult to quantify in ambulatory conditions due to a lack of a reference signal. To address this issue, we propose a Kalman filter implementation of the IBIF filter, which allows for both estimating the model uncertainty and adapting the airflow estimates to correct for signal deviations. One-way analysis of variance (ANOVA) results from laboratory experiments using the Rainbow Passage indicate an improvement using the modified Kalman filter on amplitude-based measures for phonotraumatic vocal hyperfunction (PVH) subjects compared to the standard IBIF; the latter showing a statistically difference (p-value = 0.02, F = 4.1) with respect to a reference glottal volume velocity signal estimated from a single notch filter used here as ground-truth in this work. In contrast, maximum flow declination rates from subjects with vocal phonotrauma exhibit a small but statistically difference between the ground-truth signal and the modified Kalman filter when using one-way ANOVA (p-value = 0.04, F = 3.3). Other measures did not have significant differences with either the modified Kalman filter or IBIF compared to ground-truth, with the exception of H1–H2, whose performance deteriorates for both methods. Overall, both methods (modified Kalman filter and IBIF) show similar glottal airflow measures, with the advantage of the modified Kalman filter to improve amplitude estimation. Moreover, Kalman filter deviations from the IBIF output airflow might suggest a better representation of some fine details in the ground-truth glottal airflow signal. Other applications may take more advantage from the adaptation offered by the modified Kalman filter implementation.

Vocal fold dynamics in a synthetic self-oscillating model: Intraglottal aerodynamic pressure and energy

Self-sustained oscillations of the vocal folds (VFs) during phonation are the result of the energy exchange between the airflow and VF tissue. Understanding this mechanism requires accurate investigation of the aerodynamic pressures acting on the VF surface during oscillation. A self-oscillating silicone VF model was used in a hemilaryngeal flow facility to measure the time-varying pressure distribution along the inferior-superior thickness of the VF and at four discrete locations in the anterior-posterior direction. It was found that the intraglottal pressures during the opening and closing phases of the glottis are highly dependent on three-dimensional and unsteady flow behaviors. The measured aerodynamic pressures and estimates of the medial surface velocity were used to compute the intraglottal energy transfer from the airflow to the VFs. The energy was greatest at the anterior-posterior midline and decreased significantly toward the anterior/posterior endpoints. The findings provide insight into the dynamics of the VF oscillation and potential causes of some VF disorders.

Integrative Insights into the Myoelastic-Aerodynamic Theory and Acoustics of Phonation. Scientific Tribute to Donald G. Miller

In this tribute article to D.G. Miller, we review some historical and recent contributions to understanding the myoelastic-aerodynamic (MEAD) theory of phonation and the related acoustic phenomena in subglottal and vocal tract. At the time of the formulation of MEAD by van den Berg in late 1950s, it was assumed that vocal fold oscillations are self-sustained thanks to increased subglottal pressure pushing the glottis to open and decreased subglottal pressure allowing the glottis to close. In vivo measurements of subglottal pressures during phonation invalidated these assumptions, however, and showed that at low fundamental frequencies subglottal pressure rather tends to reach a maximum value at the beginning of glottal closure and then exhibits damped oscillations. These events can be interpreted as transient acoustic resonance phenomena in the subglottal tract that are triggered by glottal closure. They are analogous to the transient acoustic phenomena seen in the vocal tract. Rather than subglottal pressure oscillations, a more efficient mechanism of transfer of aerodynamic energy to the vocal fold vibrations has been identified in the vertical phase differences (mucosal waves) making the glottal shape more convergent during glottis opening than during glottis closing. Along with other discoveries, these findings form the basis of our current understanding of MEAD.

Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds

The influence of non-smooth trachea walls on phonation onset and offset pressures and the fundamental frequency of oscillation were experimentally investigated for three different synthetic vocal fold models. Three models of the trachea were compared: a cylindrical tube (smooth walls) and wavy-walled tubes with ripple depths of 1 and 2 mm. Threshold pressures for the onset and offset of phonation were measured at the lower and upper ends of each trachea tube. All measurements were performed both with and without a supraglottal resonator. While the fundamental frequency was not affected by non-smooth trachea walls, the phonation onset and offset pressures measured right below the glottis decreased with an increasing ripple depth of the trachea walls (up to 20% for 2 mm ripples). This effect was independent from the type of glottis model and the presence of a supraglottal resonator. The pressures at the lower end of the trachea and the average volume velocities showed a tendency to decrease with an increasing ripple depth of the trachea walls but to a much smaller extent. These results indicate that the subglottal geometry and the flow conditions in the trachea can substantially affect the oscillation of synthetic vocal folds.

Ambulatory assessment of phonotraumatic vocal hyperfunction using glottal airflow measures estimated from neck-surface acceleration

Phonotraumatic vocal hyperfunction (PVH) is associated with chronic misuse and/or abuse of voice that can result in lesions such as vocal fold nodules. The clinical aerodynamic assessment of vocal function has been recently shown to differentiate between patients with PVH and healthy controls to provide meaningful insight into pathophysiological mechanisms associated with these disorders. However, all current clinical assessment of PVH is incomplete because of its inability to objectively identify the type and extent of detrimental phonatory function that is associated with PVH during daily voice use. The current study sought to address this issue by incorporating, for the first time in a comprehensive ambulatory assessment, glottal airflow parameters estimated from a neck-mounted accelerometer and recorded to a smartphone-based voice monitor. We tested this approach on 48 patients with vocal fold nodules and 48 matched healthy-control subjects who each wore the voice monitor for a week. Seven glottal airflow features were estimated every 50 ms using an impedance-based inverse filtering scheme, and seven high-order summary statistics of each feature were computed every 5 minutes over voiced segments. Based on a univariate hypothesis testing, eight glottal airflow summary statistics were found to be statistically different between patient and healthy-control groups. L1-regularized logistic regression for a supervised classification task yielded a mean (standard deviation) area under the ROC curve of 0.82 (0.25) and an accuracy of 0.83 (0.14). These results outperform the state-of-the-art classification for the same classification task and provide a new avenue to improve the assessment and treatment of hyperfunctional voice disorders.

Acoustic impact of the gradual glottal abduction degree on the production of fricatives: A numerical study

The paper presents a numerical study about the acoustic impact of the gradual glottal opening on the production of fricatives. Sustained fricatives are simulated by using classic lumped circuit element methods to compute the propagation of the acoustic wave along the vocal tract. A recent glottis model is connected to the wave solver to simulate a partial abduction of the vocal folds during their self-oscillating cycles. Area functions of fricatives at the three places of articulation of French have been extracted from static MRI acquisitions. Simulations highlight the existence of three distinct regimes, named A, B, and C, depending on the degree of abduction of the glottis. They are characterized by the frication noise level: A exhibits a low frication noise level, B, which is a transitional unstable regime, is a mixed noise/voice signal, and C contains only frication noise. They have significant impacts on the first spectral moments. Simulations show that their boundaries depend on articulatory and glottal configurations. The transition regime B is shown to be unstable: it requires very specific configurations in comparison with other regimes, and acoustic features are very sensitive to small perturbations of the glottal configuration abduction in this regime.

An extended Kalman filter approach to non-stationary Bayesian estimation of reduced-order vocal fold model parameters

The Bayesian framework for parameter inference provides a basis from which subject-specific reduced-order vocal fold models can be generated. Previously, it has been shown that a particle filter technique is capable of producing estimates and associated credibility intervals of time-varying reduced-order vocal fold model parameters. However, the particle filter approach is difficult to implement and has a high computational cost, which can be barriers to clinical adoption. This work presents an alternative estimation strategy based upon Kalman filtering aimed at reducing the computational cost of subject-specific model development. The robustness of this approach to Gaussian and non-Gaussian noise is discussed. The extended Kalman filter (EKF) approach is found to perform very well in comparison with the particle filter technique at dramatically lower computational cost. Based upon the test cases explored, the EKF is comparable in terms of accuracy to the particle filter technique when greater than 6000 particles are employed; if less particles are employed, the EKF actually performs better. For comparable levels of accuracy, the solution time is reduced by 2 orders of magnitude when employing the EKF. By virtue of the approximations used in the EKF, however, the credibility intervals tend to be slightly underpredicted.

Non-stationary Bayesian estimation of parameters from a body cover model of the vocal folds

The evolution of reduced-order vocal fold models into clinically useful tools for subject-specific diagnosis and treatment hinges upon successfully and accurately representing an individual patient in the modeling framework. This, in turn, requires inference of model parameters from clinical measurements in order to tune a model to the given individual. Bayesian analysis is a powerful tool for estimating model parameter probabilities based upon a set of observed data. In this work, a Bayesian particle filter sampling technique capable of estimating time-varying model parameters, as occur in complex vocal gestures, is introduced. The technique is compared with time-invariant Bayesian estimation and least squares methods for determining both stationary and non-stationary parameters. The current technique accurately estimates the time-varying unknown model parameter and maintains tight credibility bounds. The credibility bounds are particularly relevant from a clinical perspective, as they provide insight into the confidence a clinician should have in the model predictions.

Formant measurement in children's speech based on spectral filtering

Children's speech presents a challenging problem for formant frequency measurement. In part, this is because high fundamental frequencies, typical of a children's speech production, generate widely spaced harmonic components that may undersample the spectral shape of the vocal tract transfer function. In addition, there is often a weakening of upper harmonic energy and a noise component due to glottal turbulence. The purpose of this study was to develop a formant measurement technique based on cepstral analysis that does not require modification of the cepstrum itself or transformation back to the spectral domain. Instead, a narrow-band spectrum is low-pass filtered with a cutoff point (i.e., cutoff "quefrency" in the terminology of cepstral analysis) to preserve only the spectral envelope. To test the method, speech representative of a 2-3 year-old child was simulated with an airway modulation model of speech production. The model, which includes physiologically-scaled vocal folds and vocal tract, generates sound output analogous to a microphone signal. The vocal tract resonance frequencies can be calculated independently of the output signal and thus provide test cases that allow for assessing the accuracy of the formant tracking algorithm. When applied to the simulated child-like speech, the spectral filtering approach was shown to provide a clear spectrographic representation of formant change over the time course of the signal, and facilitates tracking formant frequencies for further analysis.

Tracheo-bronchial soft tissue and cartilage resonances in the subglottal acoustic input impedance

This paper offers a re-evaluation of the mechanical properties of the tracheo-bronchial soft tissues and cartilage and uses a model to examine their effects on the subglottal acoustic input impedance. It is shown that the values for soft tissue elastance and cartilage viscosity typically used in models of subglottal acoustics during phonation are not accurate, and corrected values are proposed. The calculated subglottal acoustic input impedance using these corrected values reveals clusters of weak resonances due to soft tissues (SgT) and cartilage (SgC) lining the walls of the trachea and large bronchi, which can be observed empirically in subglottal acoustic spectra. The model predicts that individuals may exhibit SgT and SgC resonances to variable degrees, depending on a number of factors including tissue mechanical properties and the dimensions of the trachea and large bronchi. Potential implications for voice production and large pulmonary airway tissue diseases are also discussed.

Subglottal pressure oscillations accompanying phonation

Acoustic and aerodynamic properties of the voice source and vocal tract have been extensively analyzed during the last half century. Corresponding investigations of the subglottal system are rare but can be assumed to be relevant to voice production. In the present exploratory study, subglottal pressure was recorded in a male adult subject by means of tracheal puncture. Also recorded were the oral airflow and audio signals. Effects of vowel, phonation type, and vocal register shifts on the subglottal pressure waveform were examined. The moment of maximum flow declination rate was synchronous with the main positive peak of the subglottal pressure waveform. The three lowest subglottal resonance frequencies, determined by inverse filtering and long-term average spectra of the subglottal pressure during speech, were found to be about 500, 1220, and 2000Hz, irrespective of supraglottal variations and phonation type. However, the subglottal pressure waveform was affected by the supraglottal formants, whereas the radiated vowel spectra did not show clear influence by the subglottal resonances. The fundamental frequency immediately preceding and immediately following a register break in pitch glides did not show systematic relationships with formants or with the lowest subglottal resonance.

Subglottal Impedance-Based Inverse Filtering of Voiced Sounds Using Neck Surface Acceleration

A model-based inverse filtering scheme is proposed for an accurate, non-invasive estimation of the aerodynamic source of voiced sounds at the glottis. The approach, referred to as subglottal impedance-based inverse filtering (IBIF), takes as input the signal from a lightweight accelerometer placed on the skin over the extrathoracic trachea and yields estimates of glottal airflow and its time derivative, offering important advantages over traditional methods that deal with the supraglottal vocal tract. The proposed scheme is based on mechano-acoustic impedance representations from a physiologically-based transmission line model and a lumped skin surface representation. A subject-specific calibration protocol is used to account for individual adjustments of subglottal impedance parameters and mechanical properties of the skin. Preliminary results for sustained vowels with various voice qualities show that the subglottal IBIF scheme yields comparable estimates with respect to current aerodynamics-based methods of clinical vocal assessment. A mean absolute error of less than 10% was observed for two glottal airflow measures -maximum flow declination rate and amplitude of the modulation component- that have been associated with the pathophysiology of some common voice disorders caused by faulty and/or abusive patterns of vocal behavior (i.e., vocal hyperfunction). The proposed method further advances the ambulatory assessment of vocal function based on the neck acceleration signal, that previously have been limited to the estimation of phonation duration, loudness, and pitch. Subglottal IBIF is also suitable for other ambulatory applications in speech communication, in which further evaluation is underway.

Mobile voice health monitoring using a wearable accelerometer sensor and a smartphone platform

Many common voice disorders are chronic or recurring conditions that are likely to result from faulty and/or abusive patterns of vocal behavior, referred to generically as vocal hyperfunction. An ongoing goal in clinical voice assessment is the development and use of noninvasively derived measures to quantify and track the daily status of vocal hyperfunction so that the diagnosis and treatment of such behaviorally based voice disorders can be improved. This paper reports on the development of a new, versatile, and cost-effective clinical tool for mobile voice monitoring that acquires the high-bandwidth signal from an accelerometer sensor placed on the neck skin above the collarbone. Using a smartphone as the data acquisition platform, the prototype device provides a user-friendly interface for voice use monitoring, daily sensor calibration, and periodic alert capabilities. Pilot data are reported from three vocally normal speakers and three subjects with voice disorders to demonstrate the potential of the device to yield standard measures of fundamental frequency and sound pressure level and model-based glottal airflow properties. The smartphone-based platform enables future clinical studies for the identification of the best set of measures for differentiating between normal and hyperfunctional patterns of voice use.

Resonances and wave propagation velocity in the subglottal airways

Previous studies of subglottal resonances have reported findings based on relatively few subjects, and the relations between these resonances, subglottal anatomy, and models of subglottal acoustics are not well understood. In this study, accelerometer signals of subglottal acoustics recorded during sustained [a:] vowels of 50 adult native speakers (25 males, 25 females) of American English were analyzed. The study confirms that a simple uniform tube model of subglottal airways, closed at the glottis and open at the inferior end, is appropriate for describing subglottal resonances. The main findings of the study are (1) whereas the walls may be considered rigid in the frequency range of Sg2 and Sg3, they are yielding and resonant in the frequency range of Sg1, with a resulting ~4/3 increase in wave propagation velocity and, consequently, in the frequency of Sg1; (2) the "acoustic length" of the equivalent uniform tube varies between 18 and 23.5 cm, and is approximately equal to the height of the speaker divided by an empirically determined scaling factor; (3) trachea length can also be predicted by dividing height by another empirically determined scaling factor; and (4) differences between the subglottal resonances of males and females can be accounted for by height-related differences.