Synthetic, self-oscillating vocal fold models for voice production research^a)

I. BACKGROUND AND OVERVIEW

Human voice production arises from a complex set of interactions between neurological, physiological, and mechanical processes (Gray, 2000; Titze, 2000; Zhang, 2016). During voicing, air flow from the lungs provides the energy for vocal fold (VF) self-oscillation, which in turn causes a temporal pressure fluctuation within the supraglottal airway that is the source of voiced sounds. In this process of phonation, aerodynamics, tissue dynamics, and acoustics are tightly coupled. To understand these mechanical processes, researchers have employed a range of theoretical analyses, computational simulations, and physical experiments.

Early experiment-based explorations of the larynx and voice production include Leonardo da Vinci's 17th century annotated anatomical sketches (da Vinci, c. 1510-11; Clayton and Philo, 2014). Excised larynx studies were conducted as early as the 18th century, including Ferrein (1741), who is credited as having been the first to use the term “vocal cords” (Berke et al., 1987; Markatos et al., 2019). Müller (1839) reported experiments using excised avian and primate larynges. As summarized by Flanagan (1972) and Fagyal (2001), this time period also saw the development of mechanical devices to synthesize voiced sounds via flow-induced vibration of reeds (e.g., von Kempelen, 1791). Development of vocal fold-like structures to provide sound for talking robots has continued in modern times (e.g., Fukui et al., 2005; Fukui et al., 2007; Fukui et al., 2008; Endo et al., 2014). For additional historical discussion, see Berke et al. (1987) and Markatos et al. (2019).

Synthetic VF models have also long been used to study the physics of phonation, including static models (e.g., Scherer et al., 2001), models with prescribed motion (e.g., Mongeau et al., 1997), and self-oscillating models. Self-oscillating VF models mimic the fundamental flow-induced vibration characteristic of human VFs to study coupled fluid, structure, and acoustic interactions and have been designed with varying degrees of fidelity. In addition to his excised larynx studies mentioned previously, Müller (1839) described synthetic larynx and vocal fold models (see Fig. 1). Other early descriptions of synthetic, self-oscillating VF models include Ewald (1913), Wethlo (1918), and Smith (1961, 1966). Since the 1990s, there has been a significant increase in the number of studies using self-oscillating VF models. Scientific advances that have facilitated these increased modeling efforts include the availability of commercial materials with stiffness characteristics suitable for VF modeling; the emergence of modern experimental tools, such as high-speed imaging, particle image velocimetry (PIV), and data acquisition devices; and continued research into laryngeal morphology and function that has driven the need for experimental validation as well as in-depth, systematic exploration.

A review of static, driven, and self-oscillating VF models was published by Kniesburges et al. (2011). Since that time, self-oscillating VF modeling has experienced accelerated growth in terms of design, functionality, and application. The purpose of this review is to provide an up-to-date, comprehensive review of synthetic, self-oscillating VF models. This paper is organized as follows. A brief overview of human VF morphology and function is provided, the use of VF models in voice research is introduced, and the two most common types of synthetic, self-oscillating VF models are described in detail. Applications in which these models have been used are surveyed, and experimentation techniques are summarized. Finally, areas for future development are recommended.

II. VOCAL FOLD MORPHOLOGY AND FUNCTION

The structure and function of the human VFs are well-documented (e.g., Hirano and Sato, 1993; Gray, 2000; Titze, 2000; Sato, 2018). A brief overview of aspects most pertinent to VF modeling is here provided; for a more complete review, see Zhang (2016). As illustrated in Fig. 2, two opposing VFs are located at the top of the trachea in the respiratory airway within the larynx. The glottis is the space between the VFs, and the spaces above and below are the supraglottic and subglottic regions, respectively. Each VF is comprised of multiple layers of tissue of differing composition and stiffness, including muscle, lamina propria, and epithelium, with the lamina propria consisting of three layers as shown in Fig. 2. The intermediate and deep layers of the lamina propria are commonly collectively termed the vocal ligament (Hirano et al., 1982).

During respiration, the VFs are abducted to allow air exchange between the lungs and mouth. During voicing, the VFs are adducted and air flowing from the lungs initiates and sustains VF flow-induced vibration. This causes periodic interruption of the glottal jet, with the associated pressure fluctuations being the source of sound for voice production. This process is termed phonation.

The relative composition of collagen and elastin fibers causes a variation in stiffness between VF layers (Gray, 2000; Madruga de Melo et al. (2003); Tateya et al., 2006; Chan et al., 2007). For modeling purposes, key characteristics of the spatial stiffness variation include the following. The muscle, which is also referred to as the VF body, is relatively stiff when active. The ligament consists of the intermediate and deep layers of the lamina propria and is transversely isotropic, with the plane of isotropy being aligned with the frontal anatomical plane and the anterior-posterior (out-of-plane) stiffness exceeding that of the in-plane stiffness. The superficial lamina propria is exceedingly flexible, and the epithelium is thin yet strong enough to withstand vibration. During voicing, the superficial lamina propria and epithelium layers experience the bulk of vibration, although the ligament and body also experience motion.

III. VOCAL FOLD MODELING

Phonation involves coupled, complex biological and mechanical phenomena including neurological feedback and control mechanisms, cellular mechanobiological responses, muscle activity, air flow, blood flow, vibrating tissue dynamics, acoustical source-filter interactions, and ultimately sound production. A variety of models have been employed to investigate the underlying mechanical components of phonation, i.e., primarily air flow, tissue dynamics, and acoustics. Such approaches have included in vivo and excised larynx models (Döllinger et al., 2011), theoretical and computational models (Alipour et al., 2011; Döllinger et al., 2023), and synthetic models (Kniesburges et al., 2011).

In vivo, excised, computational, and synthetic models constitute a set of approaches with complementary limitations and capabilities. The relative merits of these types of models include the following (portions of which have been adapted from Hilton and Thomson, 2022). In vivo and excised larynx models are morphologically authentic but limited in terms of repeatability, parameterizability, and longevity. Excised larynges are subject to tissue degradation. The material properties and geometries of computational models can be precisely defined and used to directly generate desired data (e.g., pressure, velocity, flow rate, and vibratory motion) with spatiotemporal resolution commensurate with model fidelity. However, computational models are based on mathematical approximations of highly nonlinear physical phenomena, and high-fidelity simulations require substantial resources of time and hardware to set up, validate, simulate, and post-process. In contrast, the physical phenomena that are only approximated in computational simulations are inherently present within in vivo, excised, and synthetic model experiments; physical experiments are thus necessary to validate computational simulations. Synthetic models typically exhibit greater longevity and are generally more materially and geometrically parameterizable than in vivo and excised larynges but less so than computational models.

Experiments using synthetic VF models possess several key advantages. First, experimental data are directly measured, as opposed to being modeled in simulations. This is critical owing to complex, nonlinear, and coupled phenomena such as turbulence, flow separation, large deformation and strain, collision, acoustic coupling, and radiated acoustics that are, in many cases, difficult to accurately model theoretically or simulate computationally. This first advantage is shared with in vivo/excised larynx-based experiments. Second, data can be gathered in a benchtop setup that would be more difficult to acquire (if not impossible) than in vivo. This is facilitated by synthetic model longevity as well as greater instrument access than in vivo and that is, in some cases, more convenient than in excised larynx experiments. Third, control over synthetic model stiffness and geometry enables parametric exploration of isolated variables. With in vivo and excised larynges, abduction and adduction can be controlled, but there is only limited control over other parameters such as viscoelasticity and underlying geometry. Further, duplicate synthetic models of the same nominal configuration can be fabricated and tested. Fourth, synthetic VF models can vibrate without interruption for a very long time. For example, the study of Drechsel and Thomson (2008) required approximately 4.5 h of continuous vibration of a synthetic, self-oscillating VF model, in addition to several additional hours of vibration during experiment preparation. Finally, while synthetic model experimentation requires model fabrication and setup, they can be conducted without excised larynx procurement and preparation, and they do not require heating and humidification of air or periodic specimen hydration.

The previously noted synthetic VF modeling advantages are common to rigid, driven, and self-oscillating models. The need for self-oscillating models stems from human phonation being, fundamentally, a flow-induced vibratory process in which flow, solid, and acoustic dynamics are tightly coupled. Thus, self-oscillating models offer the advantages of synthetic models with the benefit of providing a phonomimetic platform to facilitate the study of phonatory flow-structure-acoustic interactions.

Synthetic VF models, and particularly self-oscillating VF models, possess limitations and present unique challenges. First, physiological and neuromuscular processes are not represented. Second, owing to the complex tissue composition of the VFs, developing models that accurately mimic human VF form and function is difficult. For example, VF tissue is materially nonlinear (Alipour‐Haghighi and Titze, 1991; Alipour et al., 2013), anisotropic (Alipour et al., 2000; Cook and Mongeau, 2007; Cook et al., 2008; Cook et al., 2009), and exhibits variations between tissue types (Gray, 2000) with concomitant spatial variations in stiffness. On the other hand, synthetic models typically have distinct layer transitions and are comprised of linear, isotropic materials (with a few exceptions, as discussed in the following). Further, the geometries and material properties of the human VFs have yet to be fully defined and are highly variable between individuals, across the lifespan, and according to physiological state (e.g., health, hydration, and vocal conditioning). Fabrication challenges arise due to some human VF tissue layers being exceptionally soft and thin (e.g., Hirano et al., 1982, reported cover layer thicknesses of around 0.3 mm and combined intermediate and deep lamina propria layer thicknesses of around 1 mm). Third, achieving synthetic VF model self-oscillation with lifelike characteristics (e.g., mucosal wave and collision) is nontrivial. Finally, whereas the motion of driven synthetic models is known and highly repeatable, the motion of self-oscillating models is unknown and must be measured, is less repeatable, and is subject to temporal and vibration-induced material property changes, such as creep and stress relaxation. In many respects, therefore, self-oscillating models occupy a space between rigid/driven models and excised/in vivo larynges in terms of complexity.

IV. SYNTHETIC, SELF-OSCILLATING VOCAL FOLD MODELS

The advantages and limitations of synthetic, self-oscillating VF models have led to numerous development and application research pursuits. A key underlying premise is that if a model is defined with a spatial distribution of stiffness (i.e., a combination of geometry and material properties) that matches the human VFs, and if the airway configuration is similarly representative of the human airway, then the model will vibrate with frequency, onset pressure, and motion characteristics that are typical of human phonation. However, phenomenological modeling approaches have also proved to be beneficial. While efforts to develop truly phonomimetic models are still ongoing, models with favorable flow-induced responses have been developed and successfully used in a range of applications. In this section, the models are presented in detail, and in Sec. V, applications are surveyed.

While the different synthetic, self-oscillating VF models described in the literature share varying degrees of structural and functional commonality, most can be classified as being one of two types: those comprised of a thin membrane that encapsulates a liquid or viscoelastic substance (e.g., a water-filled latex tube), and those that are predominantly comprised of soft elastic solid(s) (e.g., ultrasoft silicone formed into a VF-like shape). For convenience, these are here referred to as “membranous” and “elastic solid” types, respectively. Other types of self-oscillating models have been studied, such as collapsible tubes for human phonation (Conrad, 1980, 1985; Berke et al., 1991), avian phonation (Elemans et al., 2009), and tracheoesophageal speech (Tourinho and da Silva, 2023); a spring-supported VF model (Sidlof et al., 2011); and a vibrating reed (Yoshinaga et al., 2021). The membranous and elastic solid models are the focus of this review owing to their prevalence in recent literature and are discussed in Secs. IV A and IV B, respectively.

V. APPLICATIONS

Synthetic VF models have been used for a wide variety of purposes, ranging from theoretical model validation to experimental exploration of complex fluid, solid, and acoustic phenomena. In this section, examples of such applications are discussed. Additionally, values for measures of primary relevance to phonation are summarized in Table III for membranous and elastic solid VF models along with corresponding human in vivo values.

Titze (1988) developed a theoretical expression for phonation onset pressure, $P_{th}$,

where $k_t$ is the transglottal pressure coefficient, $T$ is the vocal fold thickness, $B$ is a viscous damping coefficient, $c$ is the mucosal wave velocity, and ${\xi }_0$ is the pre-phonatory glottal half-width. Titze et al. (1995) used the membranous VF model shown in Fig. 3(a) to test the predicted linear relationships between $P_{th}$ and ${\xi }_0$ and between $P_{th}$ and $B$. Onset and offset pressures were measured for varying degrees of pre-phonatory glottal half-width and different fluids, with the lowest onset pressures being on the order of 0.4 kPa for water and from around 0.45 to 0.5 kPa for higher-viscosity fluids. The expected linear relationship between $P_{th}$ and $B$ was confirmed. However, while a portion of the $P_{th}$ vs ${\xi }_0$ data were linear, the data also suggested the presence of an optimal non-zero pre-phonatory glottal gap for minimum $P_{th}$ and showed consistent hysteresis between onset and offset threshold pressures (Fig. 10). These trends and other associated phenomena were subsequently explored by Lucero (1995, 1996, 1998, 1999, 2009), Fulcher et al. (2019), and Lucero et al. (2020). Additional studies using synthetic models based on that of Titze et al. (1995) were conducted by Chan et al. (1997) and Chan and Titze (2006) to explore relationships between threshold pressure and prephonatory angle, membrane thickness, vocal tract inertance, and other cover materials, including fat, hyaluronic acid, and fibronectin.

Physical models have also been used for the development, validation, and exploration of theoretical and low-order models of VF flow-induced vibration (e.g., Ruty et al., 2007; Van Hirtum et al., 2007; Van Hirtum and Pelorson, 2015; Tokuda and Shimamura, 2017; Lucero et al., 2020; Yokota et al., 2021) as well as for high-fidelity computational model development, validation, and comparison (Farahani and Zhang, 2016; Sadeghi et al., 2019; Schoder et al., 2020; Falk et al., 2021). Regarding the latter, however, synthetic VF models remain relatively underutilized as a tool for providing data for development and validation of high-fidelity computational models.

Because repeated collision of opposing vocal folds is thought to be an important contributor to the etiology of voice disorders (Titze, 1994; Gunter, 2003; Gunter et al., 2005; Motie-Shirazi et al., 2023), methods to predict and measure contact stress have been of considerable interest. Synthetic VF models have been used to develop such methods. Spencer et al. (2008) used digital image correlation to measure stress and strain on the superior surface of a VF model, and then used a Hertzian impact model to estimate the collision stress. Diaz-Cadiz et al. (2019) proposed a first-order approximation for estimating collision stress from high-speed videoendoscopy, and using a synthetic VF model, compared the approximation to the actual collision pressure measured using a pressure sensor. Direct measurements of synthetic VF model impact stress have been obtained using a probe microphone mounted in a hemilarynx wall (Chen and Mongeau, 2011), a contact sensor placed between opposing VF models (Horacek et al., 2016), a pressure sensor array using an electromechanical film transducer (Weiss et al., 2016), and a contact pressure transducer mounted in a hemilarynx wall with inferior-superior sliding capability (Diaz-Cadiz et al., 2019; Motie-Shirazi et al., 2019; Motie-Shirazi et al., 2021a,b; Motie-Shirazi et al., 2022, Motie-Shirazi et al., 2023).

Synthetic VF models have been used as initial test beds for development activities related to excised larynx or in vivo quantitative phonation instruments. For example, the synthetic model contact pressure study of Motie-Shirazi et al. (2019) was a precursor to the excised larynx intraglottal pressure study of Mehta et al. (2019). Other examples include the development of an endoscopic two-point laser projection device for measuring glottal width (Popolo and Titze, 2008), a laser grid projection system for acquiring 3D measurements of the vibrating superior surface of the VFs (Luegmair et al., 2010), and validation of stereo-endoscopic high-speed imaging (Stevens et al., 2016).

Fluid-structure-acoustic interactions are at the core of the mechanics of phonation. Consequently, characterization and study of the glottal jet and other flow-structure-acoustic effects and interactions have led to greater understanding of the fundamental physics of phonation. Owing to their longevity, ability to be parameterized, and similar dependence on flow-structure-acoustic interactions, self-oscillating synthetic VF models have been used for this purpose. Neubauer et al. (2007) used flow visualization of the glottal jet in a synthetic VF model to describe aspects of an unconfined supraglottal jet and identify flow structures that could be of relevance during phonation (see Fig. 11). Studies on the confined supraglottal jet using PIV have been conducted with (e.g., Drechsel and Thomson, 2008; Bailly et al., 2008; Kniesburges et al., 2017) and without (e.g., Becker et al., 2009; Sidlof et al., 2011; Sciamarella et al., 2012; Kniesburges et al., 2013; Lodermeyer et al., 2015; Näger et al., 2023) ventricular folds. In the case of Sciamarella et al. (2012), the phenomenon of axis switching was evident in the confined tube downstream of the VFs. However, the presence of axis switching and other flow structures and phenomena identified by these authors has yet to be experimentally verified using realistic vocal tract models. Other studies involving interactions between fluid flow, structural motion, and/or acoustics include the role of supraglottal flow structures on acoustic production (Zhang and Neubauer, 2010); source-tract interactions using straight (Migimatsu and Tokuda, 2019) and MRI-based vocal tract models (Probst et al., 2019), as well as using vocal tract models with varying degrees of constriction (May and Scherer, 2023) and of varying lengths (Kraxberger et al., 2023); the role of model closure on sound generation (Kniesburges et al., 2020); and the use of PIV to identify aeroacoustic sound sources during phonation (Lodermeyer et al., 2018; McPhail et al., 2019; Lodermeyer et al., 2021).

While a degree of asymmetry in VF motion is not uncommon in normal phonation (e.g., Shaw and Deliyski, 2008; Bonilha and Deliyski, 2008; Kendall, 2009; Chen et al., 2014), significant asymmetries concomitant with some voice disorders (e.g., paralysis, paresis, or asymmetric lesions) may result in impaired voicing. Since synthetic VF models can be fabricated and tested with pre-determined asymmetries in geometry, material properties, and/or tension, they may be used to understand the effects of asymmetry on phonation, the degree to which various asymmetric conditions cause asymmetric motion, and the potential effects of phonosurgical interventions to repair asymmetry. For example, left-right stiffness asymmetry has been studied in membranous models by varying internal liquid pressure (Ruty et al., 2006; Haas et al., 2016; Lucero et al., 2020) and in cast synthetic VF models by varying material stiffness (Pickup and Thomson, 2009; Zhang, 2010; Zhang and Hieu Luu, 2012; Zhang et al., 2013; Signorello et al., 2016). Geometric asymmetries that have been explored using synthetic VF models include (see Fig. 12) simulated unilateral cordectomy (Mendelsohn et al., 2014), left-right vertical asymmetry (Shimamura and Tokuda, 2017; Tokuda and Shimamura, 2017; Bouvet et al., 2020c; Bouvet et al., 2021), surface masses such as polyps and nodules (Luizard and Pelorson, 2017; Conte et al., 2021b; Motie-Shirazi et al., 2023), and augmentation injection to correct for vocal bowing (Murray et al., 2014).

Brief mention is here made of other applications. These include spatiotemporal analysis using empirical eigenfunctions to explore irregular vibration, including subharmonic phonation and biphonation (Berry et al., 2006); subharmonic tone generation (Kniesburges et al., 2016); the effects of surface liquid on vibration [Van Hirtum et al., 2019; Bouvet et al., 2020a,b; Yoshinaga et al., 2023; see Fig. 13(a)]; the response of an injectable biomaterial to vibration in a phonomimetic bioreactor system [Latifi et al., 2016; see Fig. 13(b)]; water resistance voice therapy (Horacek et al., 2019a,b); development of a surgical training model [Saliba and Barros, 2023; Fig. 13(c)]; and coupling synthetic VF model data with finite element data for estimating VF material properties (Hadwin et al., 2019). Finally, synthetic VF models have been used to explore non-human vocalization, including mammalian air sacs (Riede et al., 2008), the vocal membrane of non-human mammalian species (Kanaya et al., 2022) [Fig. 13(d)], and the avian syrinx (Elemans et al., 2009; Riede et al., 2019) [Fig. 13(e)].

VI. EXPERIMENTAL TECHNIQUES

With the development of synthetic VF models has been the development and application of numerous experimental techniques for their study. In this section, an overview of experimental methods specifically used for studying VF model flow, motion, and acoustics is given.

In all cases, self-oscillating VF model studies require a flow supply; see Fig. 14 for representative cases. This is typically provided by means of compressed air from a building supply or a standalone air tank. In contrast to excised larynx setups, neither heating nor humidification of the flow supply is required to maintain health of the VF model, although such would not be inherently problematic. As with excised larynx experiments, flow conditioning, such as a large square box plenum (e.g., Fig. 14), is often used to settle airflow prior to entering the subglottic tube and, in some cases if desired, to create an area difference between the subglottic tube and the plenum to create a well-defined, reflective acoustic boundary. Hemilarynx as well as full larynx configurations have been used in synthetic VF model experiments, with and without vocal tracts.

A characteristic of VF models is the potential for coupling with subglottal acoustics to drive or assist model vibration. Zhang et al. (2006b) first identified this issue with elastic solid models in a study involving subglottic tubes of varying lengths. It was shown that the one-layer model followed quarter-wavelength resonance theory, demonstrating the importance of appropriately taking into consideration subglottic tube length [see Fig. 15(a)]. Distinct vibratory shapes for aerodynamic vs acoustically driven vibration modes were observed by Zhang et al. (2006a) [see Fig. 15(b)]. Acoustically coupled modes exhibited a “swinging-door”-type motion characterized by large inferior-superior motion, whereas aerodynamic modes were characterized by limited inferior-superior motion and greater medial-lateral motion, the latter being more characteristic of the human VF mucosal wave. Further, in general, longer tubes and VF models that produce acoustically driven modes of vibration often yield significantly lower onset pressures, but at the cost of increased vertical motion and reduced wave-like motion. The roles of VF model stiffness and acoustic loading were studied by Zhang et al. (2009), and acoustic and aerodynamic coupling was further explored by Probst et al. (2019) with a synthetic VF model and an MRI-based vocal tract replica. Given these studies which have shown the potential for model vibration to couple with subglottic resonance, it is important that studies using self-oscillating, synthetic VF models—membranous as well as elastic solid—should describe in detail the subglottic setup and address whether the model vibration was acoustically or aerodynamically coupled.

A diverse array of experimental techniques has been incorporated to study acoustics, fluid dynamics, and structural motion of self-oscillating VF models. In addition to well-known methods of processing microphone signal data to analyze radiated acoustics, human listener evaluations of model-generated acoustic data have been used to assess perceptual effects caused by changing body stiffness (Zhang et al., 2013, Signorello et al., 2016). Flow measurement techniques that have been employed include hot-wire anemometry (Thomson et al., 2005; Becker et al., 2009), laser Doppler velocimetry (Becker et al., 2009), flow visualization (Neubauer et al., 2007; Drechsel and Thomson, 2008; Horacek et al., 2011; Misun et al., 2011; Kniesburges et al., 2013; Fulcher et al., 2019), and PIV (Neubauer et al., 2007; Drechsel and Thomson, 2008; Becker et al., 2009; Pickup and Thomson, 2009; Krebs et al., 2012; Sciamarella et al., 2012; Lodermeyer et al., 2015; Lodermeyer et al., 2018; Lodermeyer et al., 2021; Sadeghi et al., 2019). In a study comparing high-speed vs phase-averaged PIV, it was shown that phase-averaging can yield useful flow information, although aeroacoustic sound generation exploration via PIV requires high-speed interrogation (Lodermeyer et al., 2016). Principal component analysis (PCA) has been a means of identifying coherent flow structures (Neubauer et al., 2007; Kniesburges et al., 2016). Analysis techniques for measuring motion of synthetic VF models include videokymography (Popolo and Titze, 2008; Spencer et al., 2008; Pickup and Thomson, 2009, 2010; Luegmair et al., 2010; Murray and Thomson, 2011, 2012; Zhang and Hieu Luu, 2012; Tokuda and Shimamura, 2017; Migimatsu and Tokuda, 2019; Motie-Shirazi et al., 2019; Bouvet et al., 2021; Greenwood and Thomson, 2021; Matsumoto et al., 2021; Matsumoto et al., 2024; Stewart and Erath, 2021; Taylor and Thomson, 2022; Hasegawa et al., 2022), modal decomposition techniques (Berry et al., 2006; Zhang et al., 2006a,b; Van Hirtum and Pelorson, 2017), direct linear transformation (DLT) to track small numbers of points on model medial surfaces (Murray and Thomson, 2012; Murray et al., 2014; Stevens et al., 2016), laser dot projection to measure superior surface motion (Luegmair et al., 2010), digital image correlation (DIC, a solid domain counterpart to PIV) to track model motion via randomly-distributed dot patterns (Spencer et al., 2008; Chen and Mongeau, 2011), MRI for simultaneous internal and external motion (Taylor et al., 2019), internal motion using optically transparent VF model materials (Motie-Shirazi, 2022), and laser Doppler vibrometry for model velocity (Spencer et al., 2008; Becker et al., 2009; Elemans et al., 2009; Lodermeyer et al., 2021; Kraxberger et al., 2023) and model frequency response (Luizard and Pelorson, 2017; Riede et al., 2019).

Some pitfalls and considerations of particular relevance to synthetic VF model experimentation are here noted. As discussed previously, models mounted on long subglottal tubes that produce quarter wavelengths on the order of the model in vacuo modal frequencies are prone to acoustic coupling. In some cases, acoustic coupling may be acceptable, but in studies where mucosal wave-like characteristics are central to the research question, shorter subglottal tubes for aerodynamic coupling should be utilized. In all cases, the geometric characteristics of the subglottic system should be reported because of model susceptibility to acoustic coupling.

The use of a vocal tract is an important consideration. Häsner et al. (2021) studied the influence of smooth vs wavy subglottal tube profile on flow and vibratory characteristics, including subglottal pressure, onset pressure, pulmonary power, and vibratory frequency (see Fig. 16). VF models with different anterior-posterior cross-sectional shapes (round, quadrilateral, and triangular) were employed along with different degrees of tracheal wall waviness and the presence or absence of a vocal tract model. They reported that including a vocal tract model decreased onset pressure by around 400 to 500 Pa, which is a significant reduction. Slight decreases in pulmonary power with waviness depth were seen. Waviness minimally affected pressures measured at the low end of the trachea at vibration onset, but significantly reduced the corresponding onset pressures at the upper end of the trachea. Model vibration frequencies were significantly higher with a vocal tract model than without, but they did not vary with waviness depth. This study demonstrated the potential influence of a vocal tract model on synthetic VF model response. Pitfalls of extrapolating conclusions based on acoustical data obtained without a vocal tract to a configuration with a vocal tract were highlighted by Signorello et al. (2016). Given these findings, the presence or absence of a vocal tract model should always be documented when presenting results using synthetic VF models, and it is recommended that vocal tract models be included where possible.

For VF models themselves, environmental and temporal factors that affect properties, and hence vibratory characteristics, should be carefully observed and controlled where possible. These include model heating from intense illumination for high-speed imaging, material creep and relaxation, potential leeching of silicone thinner to adjacent regions of cured silicone in multi-layer elastic solid VF models, and changing of model geometry over time. For example, Thacker (2023) demonstrated silicone swelling/shrinking when immersed in water/mineral oil, respectively. Häsner and Birkholz (2023) systematically studied changes in elastic solid VF model vibration caused by aging over an eight-week period, finding significant variability in phonatory response measures over such an extended time. Finally, silicone is gas permeable, a potentially significant characteristic when using silicone VF models in conjunction with biological, bioengineered, or hydrogel components. Owing to considerations such as these, authors of studies using synthetic VF models should take great care to report relevant fabrication, experimental setup, and experimental procedure details.

VII. CONCLUSIONS AND FUTURE WORK

A comprehensive review of synthetic, self-oscillating VF models for voice production research has been provided. The designs, capabilities, and limitations of the two most common types of such models have been presented, the two types being membranous models (e.g., water-filled latex tubes), and elastic solid models (e.g., ultrasoft silicones formed into VF-like shapes). Materials and fabrication processes unique to the implementation of elastic solid models have been discussed. Applications and experimental configurations associated with both types of models have been provided. Recommendations for future studies have been given, including comparing the vibratory motion of liquid-filled elastic tube models to that of human VFs; pursuing membranous models with nonlinear and/or anisotropic material properties; further exploring the use of fibers in elastic solid VF models; using ASTM D412 for acquiring stress-strain data of synthetic model materials; acquiring Poisson's ratio data of synthetic model materials; including vocal tract models whenever possible; carefully reporting model fabrication and experimental setup and procedure details, particularly regarding subglottic configurations and resonance characteristics; measuring model geometric and material properties, ideally close to the time of model testing; and increasing utilization of synthetic VF model data for development and validation of high-fidelity computational models of phonation.

In addition to the previous recommendations, while significant progress has been made in recent decades to create and use models to study the biomechanical underpinnings of phonation, there remain significant opportunities to develop models with ever increasing lifelike motion that can produce even more clinically relevant results. To date, most synthetic VF models have been based on the adult human male. Female morphological characteristics, as well as those of children, remain underrepresented in VF modeling studies. Future VF modeling efforts should fill this important gap. Additionally, key success measures of modeling VF vibration include low onset pressure, mucosal wave-like motion, and glottal closure. Factors that affect these characteristics include geometric definitions, boundary conditions, and the spatial distribution of stiffness. The “M5” geometric profile of Scherer et al. (2001) has been widely used, in part because it provided the basis for early elastic solid synthetic model studies (Thomson et al., 2005) and in part because of its well-defined shape. However, more lifelike geometries can improve model response (Pickup and Thomson, 2009; Murray and Thomson, 2012). Notably, while shape variation along the anterior-posterior direction exists in the human VFs (e.g., Titze and Talkin, 1979), most synthetic VF models have been defined using uniform cross-sections. Some exceptions to this include studies by Pickup and Thomson (2009), Murray and Thomson (2012), Bouvet et al. (2021), Häsner et al. (2021), Matsumoto et al. (2021), Matsumoto et al. (2024), Van Hirtum et al. (2022), Hasegawa et al. (2022), and Tur et al. (2023). The fabrication of models with non-uniform cross-sections is slightly more complex, particularly with multi-layer models; however, this important aspect of human VF shape should be routinely incorporated in VF models. Research to quantify VF exterior profile and layer geometries with greater detail to enable more accurate modeling is needed. More lifelike boundary conditions, as opposed to rigid mounting plates, may also improve model response; see the computational study by Jones et al. (2015) and experimental incorporation by Motie-Shirazi et al. (2019), Motie-Shirazi et al. (2021a,b), Motie-Shirazi et al. (2022), Motie-Shirazi et al. (2023), and Stewart and Erath (2021). Furthermore, while elastic solid models that achieve complete closure and realistic open quotient values have been reported (e.g., Zhang, 2011; Motie-Shirazi et al., 2021a,b; Taylor and Thomson, 2022), fabrication of these models that consistently produce desired levels of glottal closure remains somewhat elusive. Owing to the significant role of collision in phonation and phonotrauma, a mature understanding of the mechanisms that govern glottal closure, followed by application in VF modeling efforts, is needed. The degree to which the epithelium layer affects VF vibration has been explored using excised human larynges and computational simulations (see Tse et al., 2015, and Deng and Peterson, 2023, respectively) but has yet to be studied using synthetic models. Methods for creating consistent and repeatable transverse isotropy and material nonlinearity are two advancements that would significantly improve VF models. Finally, neuromuscular control of the larynx plays a significant role in phonation due to the effects of intrinsic muscle activity on VF position, stiffness, and shape. VF models with artificial, soft muscle activation do not yet appear to have been reported in the literature. Consequently, this area presents a significant opportunity for VF model development, in particular by drawing upon the extensive existing studies on artificial soft actuators for robotics applications (e.g., Yang and Wang, 2024).

AUTHOR DECLARATIONS

DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.