Source-tract coupling in birdsong production

Dynamic System Coupling in Voice Production

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

Toward a Computational Neuroethology of Vocal Communication: From Bioacoustics to Neurophysiology, Emerging Tools and Future Directions

Recently developed methods in computational neuroethology have enabled increasingly detailed and comprehensive quantification of animal movements and behavioral kinematics. Vocal communication behavior is well poised for application of similar large-scale quantification methods in the service of physiological and ethological studies. This review describes emerging techniques that can be applied to acoustic and vocal communication signals with the goal of enabling study beyond a small number of model species. We review a range of modern computational methods for bioacoustics, signal processing, and brain-behavior mapping. Along with a discussion of recent advances and techniques, we include challenges and broader goals in establishing a framework for the computational neuroethology of vocal communication.

The evolution of the syrinx: An acoustic theory

The unique avian vocal organ, the syrinx, is located at the caudal end of the trachea. Although a larynx is also present at the opposite end, birds phonate only with the syrinx. Why only birds evolved a novel sound source at this location remains unknown, and hypotheses about its origin are largely untested. Here, we test the hypothesis that the syrinx constitutes a biomechanical advantage for sound production over the larynx with combined theoretical and experimental approaches. We investigated whether the position of a sound source within the respiratory tract affects acoustic features of the vocal output, including fundamental frequency and efficiency of conversion from aerodynamic energy to sound. Theoretical data and measurements in three bird species suggest that sound frequency is influenced by the interaction between sound source and vocal tract. A physical model and a computational simulation also indicate that a sound source in a syringeal position produces sound with greater efficiency. Interestingly, the interactions between sound source and vocal tract differed between species, suggesting that the syringeal sound source is optimized for its position in the respiratory tract. These results provide compelling evidence that strong selective pressures for high vocal efficiency may have been a major driving force in the evolution of the syrinx. The longer trachea of birds compared to other tetrapods made them likely predisposed for the evolution of a syrinx. A long vocal tract downstream from the sound source improves efficiency by facilitating the tuning between fundamental frequency and the first vocal tract resonance.

Self-entrainment of the right and left vocal fold oscillators

This article presents an analysis of entrained oscillations of the right and left vocal folds in the presence of asymmetries. A simple one-mass model is proposed for each vocal fold. A stiffness asymmetry and open glottis oscillations are considered first, and regions of oscillation are determined by a stability analysis and an averaging technique. The results show that the subglottal threshold pressure for 1:1 entrainment increases with the asymmetry. Within that region, both folds oscillate with the same amplitude and with the lax fold delayed in time with regard to the tense fold. At large asymmetries, a region involving several different phase entrainments or toroidal regimes at constant threshold pressure appears. The effect of vocal fold collisions and asymmetry in the damping coefficients of the oscillators are explored next by means of numerical analyses. It is shown that the damping asymmetry expands the 1:1 entrainment region at low subglottal pressures across the whole asymmetry range. In the expanded region, the oscillator with the lowest natural frequency is dominant and the other oscillator has a large phase advance and small amplitude. The theoretical results are finally compared with data collected from a mechanical replica of the vocal folds.

Integrative physiology of fundamental frequency control in birds

One major feature of the remarkable vocal repertoires of birds is the range of fundamental frequencies across species, but also within individual species. This review discusses four variables that determine the oscillation frequency of the vibrating structures within a bird's syrinx. These are (1) viscoelastic properties of the oscillating tissue, (2) air sac pressure, (3) neuromuscular control of movements and (4) source-filter interactions. Our current understanding of morphology, biomechanics and neural control suggests that a complex interplay of these parameters can lead to multiple combinations for generating a particular fundamental frequency. An increase in the complexity of syringeal morphology from non-passeriform birds to oscines also led to a different interplay for regulating oscillation frequency by enabling control of tension that is partially independent of regulation of airflow. In addition to reviewing the available data for all different contributing variables, we point out open questions and possible approaches.

Effect of source-tract acoustical coupling on the oscillation onset of the vocal folds

This paper analyzes the interaction between the vocal folds and vocal tract at phonation onset due to the acoustical coupling between both systems. Data collected from a mechanical replica of the vocal folds show that changes in vocal tract length induce fluctuations in the oscillation threshold values of both subglottal pressure and frequency. Frequency jumps and maxima of the threshold pressure occur when the oscillation frequency is slightly above a vocal tract resonance. Both the downstream and upstream vocal tracts may produce those same effects. A simple mathematical model is next proposed, based on a lumped description of tissue mechanics, quasi-steady flow and one-dimensional acoustics. The model shows that the frequency jumps are produced by saddle-node bifurcations between limit cycles forming a classical pattern of a cusp catastrophe. The transition from a low frequency oscillation to a high frequency one may be achieved through two different paths: in case of a large acoustical coupling (narrow vocal tract) or high subglottal pressure, the bifurcations are crossed, which causes a frequency jump with a hysteresis loop. By reducing the acoustical coupling (wide vocal tract) or the subglottal pressure, a path around the bifurcations may be followed with a smooth frequency variation.

Prosthetic avian vocal organ controlled by a freely behaving bird based on a low dimensional model of the biomechanical periphery

Because of the parallels found with human language production and acquisition, birdsong is an ideal animal model to study general mechanisms underlying complex, learned motor behavior. The rich and diverse vocalizations of songbirds emerge as a result of the interaction between a pattern generator in the brain and a highly nontrivial nonlinear periphery. Much of the complexity of this vocal behavior has been understood by studying the physics of the avian vocal organ, particularly the syrinx. A mathematical model describing the complex periphery as a nonlinear dynamical system leads to the conclusion that nontrivial behavior emerges even when the organ is commanded by simple motor instructions: smooth paths in a low dimensional parameter space. An analysis of the model provides insight into which parameters are responsible for generating a rich variety of diverse vocalizations, and what the physiological meaning of these parameters is. By recording the physiological motor instructions elicited by a spontaneously singing muted bird and computing the model on a Digital Signal Processor in real-time, we produce realistic synthetic vocalizations that replace the bird's own auditory feedback. In this way, we build a bio-prosthetic avian vocal organ driven by a freely behaving bird via its physiologically coded motor commands. Since it is based on a low-dimensional nonlinear mathematical model of the peripheral effector, the emulation of the motor behavior requires light computation, in such a way that our bio-prosthetic device can be implemented on a portable platform.

Brain Machine Interfaces (BMIs) decode motor instructions from neuro-physiological recordings and feed them to bio-mimetic effectors. Many applications achieve high accuracy on a limited number of tasks by applying statistical methods to these data to extract features corresponding to certain motor instructions. We built a bio-prosthetic avian vocal organ. The device is based on a low-dimensional mathematical model that accounts for the dynamics of the bird's vocal organ and robustly relates smooth paths in a physiologically meaningful parameter space to complex sequences of vocalizations. The two physiological motor gestures (sub-syringeal pressure and ventral syringeal muscular activity), are reconstructed from the bird's song, and the model is implemented on a portable Digital Signal Processor to produce synthetic birdsong when driven by a freely behaving bird via the sub-syringeal pressure gesture. This exemplifies the plausibility of a type of synthetic interfacing between the brain and a complex behavior. In this type of devices, the understanding of the bio-mechanics of the periphery is key to identifying a low dimensional physiological signal coding the motor instructions, therefore enabling real-time implementation at a low computational cost.

The anatomy of onomatopoeia

Virtually every human faculty engage with imitation. One of the most natural and unexplored objects for the study of the mimetic elements in language is the onomatopoeia, as it implies an imitative-driven transformation of a sound of nature into a word. Notably, simple sounds are transformed into complex strings of vowels and consonants, making difficult to identify what is acoustically preserved in this operation. In this work we propose a definition for vocal imitation by which sounds are transformed into the speech elements that minimize their spectral difference within the constraints of the vocal system. In order to test this definition, we use a computational model that allows recovering anatomical features of the vocal system from experimental sound data. We explore the vocal configurations that best reproduce non-speech sounds, like striking blows on a door or the sharp sounds generated by pressing on light switches or computer mouse buttons. From the anatomical point of view, the configurations obtained are readily associated with co-articulated consonants, and we show perceptual evidence that these consonants are positively associated with the original sounds. Moreover, the pairs vowel-consonant that compose these co-articulations correspond to the most stable syllables found in the knock and click onomatopoeias across languages, suggesting a mechanism by which vocal imitation naturally embeds single sounds into more complex speech structures. Other mimetic forces received extensive attention by the scientific community, such as cross-modal associations between speech and visual categories. The present approach helps building a global view of the mimetic forces acting on language and opens a new venue for a quantitative study of word formation in terms of vocal imitation.

Reconstruction of physiological instructions from Zebra finch song

We reconstruct the physiological parameters that control an avian vocal organ during birdsong production using recorded song. The procedure involves fitting the time dependent parameters of an avian vocal organ model. Computationally, the model is implemented as a dynamical system ruling the behavior of the oscillating labia that modulate the air flow during sound production, together with the equations describing the dynamics of pressure fluctuations in the vocal tract. We tested our procedure for Zebra finch song with, simultaneously recorded physiological parameters: air sac pressure and the electromyographic activity of the left and right ventral syringeal muscles. A comparison of the reconstructed instructions with measured physiological parameters during song shows a high degree of correlation. Integrating the model with reconstructed parameters leads to the synthesis of highly realistic songs.

Acoustic signatures of sound source-tract coupling

Birdsong is a complex behavior, which results from the interaction between a nervous system and a biomechanical peripheral device. While much has been learned about how complex sounds are generated in the vocal organ, little has been learned about the signature on the vocalizations of the nonlinear effects introduced by the acoustic interactions between a sound source and the vocal tract. The variety of morphologies among bird species makes birdsong a most suitable model to study phenomena associated to the production of complex vocalizations. Inspired by the sound production mechanisms of songbirds, in this work we study a mathematical model of a vocal organ, in which a simple sound source interacts with a tract, leading to a delay differential equation. We explore the system numerically, and by taking it to the weakly nonlinear limit, we are able to examine its periodic solutions analytically. By these means we are able to explore the dynamics of oscillatory solutions of a sound source-tract coupled system, which are qualitatively different from those of a sound source-filter model of a vocal organ. Nonlinear features of the solutions are proposed as the underlying mechanisms of observed phenomena in birdsong, such as unilaterally produced "frequency jumps," enhancement of resonances, and the shift of the fundamental frequency observed in heliox experiments.

A lumped mucosal wave model of the vocal folds revisited: recent extensions and oscillation hysteresis

This paper examines an updated version of a lumped mucosal wave model of the vocal fold oscillation during phonation. Threshold values of the subglottal pressure and the mean (DC) glottal airflow for the oscillation onset are determined. Depending on the nonlinear characteristics of the model, an oscillation hysteresis phenomenon may occur, with different values for the oscillation onset and offset threshold. The threshold values depend on the oscillation frequency, but the occurrence of the hysteresis is independent of it. The results are tested against pressure data collected from a mechanical replica of the vocal folds, and oral airflow data collected from speakers producing intervocalic /h/. In the human speech data, observed differences between voice onset and offset may be attributed to variations in voice pitch, with a very small or inexistent hysteresis phenomenon.

Computational model for vocal tract dynamics in a suboscine bird

In a recent work, active use of the vocal tract has been reported for singing oscines. The reconfiguration of the vocal tract during song serves to match its resonances to the syringeal fundamental frequency, demonstrating a precise coordination of the two main pieces of the avian vocal system for songbirds characterized by tonal songs. In this work we investigated the Great Kiskadee (Pitangus sulfuratus), a suboscine bird whose calls display a rich harmonic content. Using a recently developed mathematical model for the syrinx and a mobile vocal tract, we set up a computational model that provides a plausible reconstruction of the vocal tract movement using a few spectral features taken from the utterances. Moreover, synthetic calls were generated using the articulated vocal tract that accounts for all the acoustical features observed experimentally.

Physiologically driven avian vocal synthesizer

In this work, we build an electronic syrinx, i.e., a programmable electronic device capable of integrating biomechanical model equations for the avian vocal organ in order to synthesize song. This vocal prosthesis is controlled by the bird's neural instructions to respiratory and the syringeal motor systems, thus opening great potential for studying motor control and its modification by sensory feedback mechanisms. Furthermore, a well-functioning subject-controlled vocal prosthesis can lay the foundation for similar devices in humans and thus provide directly health-related data and procedures.