article: Male Rocky Mountain elk (Cervus elaphus nelsoni) produce loud and high fundamental frequency bugles during the mating season, in contrast to the male European Red Deer (Cervus elaphus scoticus) who produces loud and low fundamental frequency roaring calls. A critical step in understanding vocal communication is to relate sound complexity to anatomy and physiology in a causal manner. Experimentation at the sound source, often difficult in vivo in mammals, is simulated here by a finite element model of the larynx and a wave propagation model of the vocal tract, both based on the morphology and biomechanics of the elk. The model can produce a wide range of fundamental frequencies. Low fundamental frequencies require low vocal fold strain, but large lung pressure and large glottal flow if sound intensity level is to exceed 70 dB at 10 m distance. A high-frequency bugle requires both large muscular effort (to strain the vocal ligament) and high lung pressure (to overcome phonation threshold pressure), but at least 10 dB more intensity level can be achieved. Glottal efficiency, the ration of radiated sound power to aerodynamic power at the glottis, is higher in elk, suggesting an advantage of high-pitched signaling. This advantage is based on two aspects; first, the lower airflow required for aerodynamic power and, second, an acoustic radiation advantage at higher frequencies. Both signal types are used by the respective males during the mating season and probably serve as honest signals. The two signal types relate differently to physical qualities of the sender. The low-frequency sound (Red Deer call) relates to overall body size via a strong relationship between acoustic parameters and the size of vocal organs and body size. The high-frequency bugle may signal muscular strength and endurance, via a ‘vocalizing at the edge’ mechanism, for which efficiency is critical.
  Contrary to expectation based on body size, some large male mammals use high-pitched vocalization for display. The dichotomy between low frequency and high frequency calls for vocal signaling of male characteristics is rarely so dramatic as in two closely related cervid species: European red deer (Cervus elaphus scoticus) and Rocky Mountain elk (Cervus elaphus nelsoni). During the mating season, one species is recognizable by a low frequency roar, while the other is well-known for its high frequency bugle [1], [2]. Acoustic signals in the vocal communication of mammals are generally very complex because various selective pressures shape them [3]. The complexity can be related to natural and sexual selection. For example, a signal is considered honest if reliable information about the sender can be extracted, such as body size or physical strength. An animal' s body size or physical strength has important implications for its physiology, ecology, fecundity, or its aggressive interactions and mating success [4]. The male red deer mating call was selected for low vocal tract resonance characteristics that provide reliable information about body size due to interconnected size-dependent factors involved in sound production [5]. In contrast, it is difficult to make the case that body size is signaled by the high fundamental frequency whistle-like bugle (around 1000 Hz) of the elk. Elk calls sometimes contain low frequency components, but not consistently. The signature is the bugle. What provoked the evolution of such calls that would generally be associated with much smaller animals? Here we investigate the physiological tradeoffs related with the production of high and low frequency sounds. We have simulated red deer and elk calls with a finite-element model of oscillating vocal folds positioned within a laryngeal cartilaginous framework, applying intrinsic laryngeal muscle activations [6] and a wave propagation model of the vocal tract [7] with the goal to better understand the physiology of this intriguing system. The larynx finite element model was based on the anatomy and biomechanics of Rocky Mountain elk and red deer larynges [8], [9, and data presented here].
  The working range of the model is summarized using key physiological features in a muscle activation plot (MAP) in which CT activity is plotted against TA activity. Furthermore, the plot indicates the relationship between muscle activity, vocal fold strain, subglottic pressure and F0. The principal goal here was the identification of ranges of identical F0 ranges in so-called iso- F0 lines. These lines indicate points at which stable phonation near phonation threshold pressure (PTP) can be maintained. PTP is the minimum subglottal pressure required to initiate vocal fold oscillation [45]. In order to identify such points, repeated simulations were necessary. The protocol was as follows: For a given TA activity, CT activity and subglottic pressure were increased stepwise until a stable phonation at the goal fundamental frequency was achieved. Each simulation resulted in a wav-file which was visually inspected. Every sample of phonation was examined to determine periodicity and to calculate F0 by zero crossing or peak picking methods. If the oscillation was neither growing not damped, but survived for at least 10 cycles near threshold because glottal flow was nearly sinusoidal, it was considered stable and counted toward one of the 175 simulations (Figure S2). Each simulation was about 200 ms in duration. Based on these 175 simulations, iso-fundamental frequency lines were created that indicate a range of CT and TA activity combinations for which an identical F0 can be achieved with roughly the same phonation threshold pressured. Glottal efficiency (Eg) was computed as described in the literature (e. g. [28]): (3) Finally, the sound intensity level (SIL) at a 10 m distance was computed from the radiated output power as: (4) where R = 10m and I0 is the ISO standard reference intensity, 10−12 W/m2. Simulated elk and red deer calls were sampled at 44. 1 kHz, typically of 2 s duration. Some signals were simulated with a 1 s ramp-up in muscle activity and muscle activity was held constant during the second half of the call (“elk calls”), signals were simulated with constant muscle activities throughout the 2 s duration (“red deer calls”). All spectrographic measurements were made in the second half of a call. Natural vocalization for comparative purposes were collected from elk and red deer. Male elk were recorded between September and November of 2006 and 2007 in the Rocky Mountain National Park, Colorado, USA, with a Marantz PMD 222 tape recorder and Sennheiser microphone (ME80 head with K3U power module; on ChromeSuper tapes 60 min). Red deer calls were recorded in the Müritz National Park in northern Germany in September 1999 (same recording equipment as in Colorado). Vocalizations were sampled at 44. 1 kHz. All signals were analysed based on narrowband spectrograms and measurements therein using PRAAT [46].
  A large fundamental frequency (F0) range (60 Hz–1400 Hz) for self-sustained vocal fold oscillation was obtained when cricothyroid (CT) activity and thyroarytenoid (TA) activity were varied. In Figure 5 iso-fundamental frequency lines (solid lines) are plotted along with iso-strain lines (dashed lines). Each PTP value shown along the right margin of the MAP corresponds to an iso-F0 line. Note that PTP are approximations and vary slightly over each curve (not more than 5%). Elk vocalizations are near the top of the muscle activation plot and red deer vocalizations are near the bottom. Vocal fold oscillation could be self-sustained at a minimum F0 of 65 Hz (subglottic pressure = 0. 4 kPa; aTA ranging from about 0. 3–1. 0 and aCT activity ranging from 0–0. 3), and at a highest F0 of 1400 Hz (subglottic pressure = 12 kPa; aTA less than 0. 05, aCT activity approx. 1. 6). Because the simulation produced iso-F0 lines rather than single coordinate F0 points, any F0 could be produced over a range of muscle activity combinations. A value of aCT activity above 1. 0 poses no physiological non-reality. It simply means that the values are larger than what would be considered about maximum for average domestic dog muscle contraction, which was used as a normalization factor. Muscle activation greater than 1. 0 could also mean that the muscle is assisted by laryngeal strap muscles to increase vocal fold length, a well-known phenomenon in human high-note singing. Note that for F0 as high as 1200 Hz, the vocal fold strain requirement is about 0. 8, or 80% elongation of the vocal folds. F0 can be predicted by the formula for a vibrating string, assuming that the ligament is the string, (5) where L0 is the resting length (2. 6 cm from Table 1), ε is the strain from Figure 5 (dashed lines) or Equation 1, σL is the ligament stress from Figure 3, and ρ is the tissue density (1. 04 g/cm3). As an example, for ε = 0. 3 the stress σL = 400 kPa (4×106 dyn/cm2), producing an F0 of 296 Hz. Note that the 300 Hz iso-F0 line in Figure 5 is close to the ε = 0. 3 line, but the iso-F0 line is not straight, for reasons explained in a section below (Source-vocal tract interaction and irregular vocal fold oscillation). A natural red deer call, shown in Figure 6A, is characterized by a F0 of around 100 Hz. A rich harmonic spectrum allows formants to be seen. The elk call of approximately the same duration shows a F0 that starts at 550 Hz and successively increases to a maximum of 2100 Hz (Figure 6B). The increase occurs partly in a smooth upward glide and partly in frequency jumps. An interesting characteristic is the occurrence of noise between the harmonics. This noise sometimes highlights the formant characteristics, which would normally not be visible with only the harmonics present. This noise presumably arises from air turbulence at glottal exit and complex vibrational modes [11] of the vocal folds. The model is able to simulate most of the above features. A sound with low F0 (65 Hz) and rich harmonic spectrum and clearly visible formant structures is shown in Figure 6C. At different points in the MAP, call components like an elk bugle can be produced, also showing smooth upward gliding F0 (Figure 6D, E) and nonlinear phenomena such as sudden frequency jumps (Figure 6E) or chaotic call segments with harmonic windows (Figure 6D). Furthermore, the noisy components between the harmonics are also clearly visible and perceivable in the model sound (Figure 6D, E). Berry et al. [47] have shown that chaotic vibration can be produced with only two or three of the lowest modes of vibration (the empirical eigenmodes related to the cranio-caudal and latero-lateral modes described earlier) if these modes are desynchronized. The noise in our model does not stem from random number generators, but rather from this mode desynchronization when driving forces are large. For steady phonation, physiological input variables to the simulation model were lung pressure, muscle activations aCT, aLC, and aTA, and simulation time. All other parameters were held constant. Male elk bugles as well as red deer roars are powerful displays. For example, sound amplitudes in elk calls can reach 90 dB at a 5 m distance (measured in a farmed elk, our own unpublished data), which would correspond to 84 dB at 10 m according to the inverse square law. Calculations from the model are for a 10 m distance from the mouth. The following results show six components relevant to laryngeal sound production and their dependence on lung pressure. These are peak glottal area (Figure 7A), peak glottal airflow (Figure 7B), aerodynamic glottal power (Figure 7C), radiated power in mW (Figure 7D), glottal efficiency (Figure 7E), and radiated sound intensity level (at a 10 m distance from the end of the vocal tract tube) (Figure 7F). The peak glottal area remains small for high F0, suggesting that the elk cannot bend the ligament much to allow the glottis to open widely. The glottal area never exceeds 0. 2 cm2 in the high F0 vocalization (Figure 7A). Basically the ligament is a rather inflexible “beam” surrounded by soft, watery tissue. The soft tissue helps to create self-sustained oscillation in the form of a mucosal surface wave [34], but the deeper part of the vocal fold (ligament and muscle) never gain much vibrational amplitude. For low F0 and high pressure, however the peak glottal area reaches 0. 8 cm2. For high F0 and large lung pressure (4 to 10 kPa), large flows are forced through a small glottal opening (up to 1500 cm3/s peak flows) (Figure 7B). In general, even larger airflows are maintained at low F0 (for example a factor of 2 difference between 100 Hz and 950 Hz at 8 kPa; in Figure 7B). One important implication is that in low F0 calls, vital capacity may limit the call duration, given that on the order of 1 liter of air is forced through the glottis in a second. Aerodynamic power (Figure 7C), which is the product of lung pressure and mean glottal flow, rises to 5 W, which is an order of magnitude higher than in humans for high effort phonation [48]. As F0 increases, the reduction in aerodynamic power is linked directly to the lower mean glottal airflow, which in turn is linked to a smaller mean glottal area. Thus, at 950 Hz, there is only 3 W of aerodynamic power at 10 kPa of lung pressure. Radiated power from the mouth is shown in Figure 7D. An important factor in this is that acoustic radiation from a localized oscillating source quadruples with every doubling of frequency [49]. Thus, going from 100 Hz to 800 Hz should increase radiated power by a factor of 64, all else remaining the same. Figure 7E shows a factor of about 6 from 100 Hz to the higher frequency curves, but smaller airflows and smaller airflow derivatives account for the more moderate increase in F0. Glottal efficiency, as defined in Equation 3, is shown in Figure 7E. Note that high F0 calls are much more efficient than the 100 Hz call, which is again a function of radiation from the mouth. At 100 Hz and 10 kPa of lung pressure, glottal efficiency is 0. 4%, whereas at 605 Hz and 950 Hz it rises above 2%. In either case, most of the aerodynamic power is not radiated from the mouth, but is dissipated as kinetic energy loss at the glottis and in the vocal tract. Finally, sound intensity level at 605 Hz rises to about 80 dB at an assumed mouth-to-microphone distance of 10 m (Figure 7F). At the lowest F0 shown (100 Hz), the radiated sound intensity level is 10 dB lower. This illustrates that the elk may actually have an advantage at high frequency sound productions. High intensity sounds can more easily be produced with large lung pressures at high frequencies. But the cost is great since this requires a large and stiff ligament as will be explained in the next section. Vibrational amplitude grows with lung pressure, which was raised from phonation threshold pressure to as high as 10 kPa. The amplitude at large lung pressures (>5 kPa) was on the order of 5 mm at F0 = 100 Hz, but only on the order of 1 mm at 600 Hz. At F0 = 100 Hz, vocal fold oscillation was characterized by large oscillation on the cranial end and caudal edges (Figure 2), but not so large in the center. This characteristic vibration pattern refers to the caudo-cranial mode mentioned earlier [15]. This means also that there was not a lot of contact in the middle of the vocal fold during each cycle, but significant contact between the upper and lower edges. For the high-pitched sounds, the amplitudes were very small, on the order of 0. 2 mm at 1200 Hz. The sound source can be independent or interactive with the vocal tract filter [27]. In a linearly coupled source-filter system the source frequencies are produced independently of the acoustic pressures in the airways. The resonance frequencies of the vocal tract shape the source spectrum, giving rise to formants. The second mechanism is nonlinear coupling, where the acoustic airway pressures contribute to the production of frequencies at the source [27]. Nonlinear coupling has been demonstrated in in vivo studies and in modeling approaches [e. g. 42], [50]. In nonlinear coupling, the transglottal pressure includes a strong acoustic component. Weak coupling is obtained when the glottal impedance is high and the vocal tract tube input impedance is low, whereas strong coupling (nonlinear interaction) is obtained when the impedances are comparable. The curvatures in the iso-F0 lines of Figure 5 deserve some attention from the point of view source-vocal tract interaction [27]. When the acoustic vocal tract reactance is inertive, F0 is lowered slightly. Conversely, when the acoustic vocal tract inertance is compliant, F0 is raised slightly. But harmonics of F0 also play a role in this. Suffice it to say, for the purpose of this paper, that F0 can fluctuate above and below the natural frequency of the tissue fibers because self-sustained oscillation is (in part) governed by acoustic interaction with the vocal tract. We tested whether vocal tract interaction could have direct effects on the phonation threshold pressure. We found that phonation could be sustained better if F0 is near a resonance frequency. Figure 8 shows results of taking a detailed path through the MAP of Figure 5. The path was a vertical line at aTA = 0. 4, incrementing aCT in steps of 0. 05 from bottom to top. Figure 8A shows F0 versus aCT. The curve is relatively smooth. Figure 8B is a plot of phonation threshold pressure as a function of aCT. Note that phonation threshold pressure generally rises with aCT, but there are some peaks and valleys. To identify where these peaks and valleys occur, phonation threshold pressure is plotted against F0 in Figure 8C, with vertical lines showing the formant frequencies F1, F2, F3, and F4. The formant frequencies were determined to be 260,620,960, and 1370 Hz from an impulse response. Note that phonation threshold pressure is always lower in the vicinity of a formant, which is a clear indication of source-vocal tract interaction. On average, however, phonation threshold pressure is proportional to F0. It takes on the order of 9. 0 kPa of pressure to initiate phonation at 1200 Hz. The ligament stress required at such an F0 is very large by vocal fold standards. This is shown in Figure 8D. The solid line represents actual finite-element model computations and the dashed line is the simple string model (Equation 5) predicted from the strain ε and the ligament stress σL. For 1000 Hz, the ligament stress is about 10 MPa. This is in order of magnitude equivalent to stress developed in the anterior cruciate ligament (ACL) of the knee in humans [51]. Riede et al. [9] have shown that a stress of this magnitude can rupture the ligament in isolation, indicating that the in vivo ligament is probably operated at its mechanical limits. Maintaining a ligament stress of up to 10 MPa for several seconds requires not only large muscular effort, but also a stable laryngeal framework and exceptional material properties to prevent injury. At low F0 the mechanical stress due to tensile strain is much smaller, but shear strain due to an increased oscillation amplitude and vocal fold collision may be larger.
  The energetic processes involved in producing a sound are complex [e. g. 57], [58], [59]. They include 1) the metabolic costs for generating respiratory driving pressures, 2) the metabolic costs for activating and contracting laryngeal muscles and 3) the metabolic costs for adjusting the upper vocal tract geometry. Requirements for respiratory metabolic energy are presumably similar between elk and red deer call production because very high lung pressures are necessary in both cases (Figure 7) and mating calls are uttered at high rates during the rut in both species [1], [2]. The efficiency of the conversion of aerodynamic to acoustic energy in the laryngeal sound source demonstrated differences. We found that the production of calls with high F0 seems to provide an efficiency advantage. Vocal efficiency in laryngeal sound production has been defined as the power radiated from the mouth divided by the aerodynamic power developed in the lungs [28], [60]. To produce a high amplitude call, the glottal area (air space between vocal folds) is much smaller in the high frequency call (Figure 7A) than in the low frequency call leading to less airflow through the glottis (Figure 7B). Consequently the aerodynamic power required is about two times smaller in the high frequency call (Figure 7C). Calculations for power radiated from the mouth suggest a 7 dB difference for a lung pressure of about 8 kPa (Figure 7D). The power radiated from the mouth is shown in Figure 1E. Taking the ratio of radiated power (Figure 7E) to aerodynamic power (Figure 7D) shows a five-fold efficiency advantage for the high frequency call (Figure 7F). This increased efficiency is based on two phenomena, a) the well-known more efficient radiation of higher frequencies from orifices (+6 dB/octave increase) [49], and b) a two-fold reduction in aerodynamic power required to drive Cervid vocal fold oscillation at high amplitudes. Part of the vocal fold tissue, the vocal ligament, is very stiff and prevents large glottal areas and glottal airflows at high fundamental frequencies. The difference in glottal efficiency must be related to the metabolic energy to operate the sound source. The simulation indicates that the two species vocalize at two very distinct locations within a muscle activation plot. We might ask whether the different muscle activation result in different amounts of energy required to contract larynx muscles between the two species? Estimates (which remain speculative) suggest that there could be a difference in energy uptake for high versus low frequency sound production. A regular skeletal muscle demonstrates an ATP turnover rate of about 1 µmol ATP/g/sec during exercise [e. g. 61], [62], [63], [64]. 1 mol ATP provides about 29 kJ, which translates to about 0. 03W/g. The TA muscle weighs about 4. 9 g on each side (measured on the left and right side in a 5 year old male, left: 4. 5 and right: 5. 2 g) and the CT muscle is about 4. 6 g on each side (measured on the left and right side in the same 5 year old male, left: 4. 9 and right: 4. 3 g). Both pairs of muscles are roughly 10 g each. If both muscles are functioning as regular skeletal muscles they would use about 0. 3 W. The model suggests that for an elk call, the CT muscle must be activated to its maximum (at almost zero TA activity) while the red deer call requires approx. 50% TA activity (at zero CT activity) (Figure 5). Given that TA and CT muscles are comparable in size, and assuming that ATP turnover rate is proportional to muscle contraction intensity, this suggests a 2-fold difference in muscle energy uptake (“muscle metabolic rate”) giving the low F0 call a metabolic advantage (metabolic cost advantage of low F0 call 0. 15W versus 0. 3W). Even with an efficiency of muscles around 30% (muscle efficiency is the ratio of work and heat-plus-work, [65]), the metabolic advantage of producing low frequency calls is unlikely to be of a similar or greater magnitude as the aerodynamic power disadvantage (which for low F0 calls is 4W versus 2W, see Figure 7C at about 8kPa lung pressure). Furthermore, muscle efficiency is not indifferent to muscle fiber type. Fiber composition of TA, CT and other intrinsic laryngeal muscles are different [66] contributing to a more complex pattern of metabolic costs of force generation in the larynx. Body size and muscular strength are important determinants of fitness in animals [67]. The utility of performance related measures (such as sound amplitude, fundamental frequency or formant frequency) lies in their link to fitness via selection. How does the low and high fundamental frequency dichotomy transfer to honest signaling? On the one hand, larger surfaces and longer tubes can resonate low-frequency sound effectively [68]. This principle seems to be exploited by the red deer to communicate size, and thereby fitness [5] and by many other species [e. g. 69], [70], [71], [72], [73]. On the other hand, radiation from surfaces and orifices is more efficient at high frequencies. Furthermore, the aerodynamic power required to achieve similar radiated sound amplitudes is lower in high frequency calls. An animal can obtain higher intensity by raising fundamental frequency. Some females respond to high intensity sounds as a signal of fitness [56], [74]. But to obtain a high F0 phonation with a large larynx, an enormous stress has to be applied to stiffen otherwise flaccid vibrating tissue. This requires extreme muscular strength, which listeners may interpret as the alternative fitness signal under the assumption that strength in the larynx relates to strength in the rest of the body. In humans, it is currently not clear which acoustic parameters in a persons' voice account for physical strength. Nevertheless perceptual experiments suggest that a human listener is able to assess a males' physical strength from just hearing the voice [75]. Thus, at least in humans, physical strength is predictable from the voice signal. The vocal displays of other large mammals show also extreme vocal performances within and between species. For example, Chimpanzee (Pan troglodytes) panthoots are multi-call vocalizations, contrasting quieter and lower-pitched components with loud and high-pitched climax calls in the same bouts. As in our presented model for elk and red deer, a large F0 range can be produced with one and the same larynx design. Interestingly, highest ranking chimpanzee males are those who can drive the F0 of their voices to a maximum [76]. The vocal repertoire of the closely related Bonobo (Pan paniscus) demonstrates an even higher maximum F0 (e. g. [77]) paralleling the species dichotomy between elk and red deer. Another example is our own species. Many utterances of human males cover a wide range of fundamental frequencies. Low human male voices are considered masculine and powerful, but voices in combat and romantic heroism (e. g. opera or heavy metal) are often high-pitched. Thus, for extreme vocal display (size or strength), it appears that F0 is driven to both extremes. However, when competition is not an issue (or is dealt with by means other than vocal combat), as in normal human conversation at close range, the middle of the voice range is accessed [78] probably because tissue deformation and respiratory effort is less costly. The origin of the difference between elk and red deer male calling remains a fascinating, yet unresolved, phenomenon. A complex behavior such as vocal communication, is likely to have multiple constraints shaping it. The tradeoff between the advantage of high pitch sound production and the enormous laryngeal stress necessary seemingly works for the elk. Glottal efficiency increases with fundamental frequency in the Cervid larynx, thereby providing an advantage for high frequency vocalizations. Future studies also have to determine whether the auditory system of elk is better suited for high pitch than low pitch sounds. Other mechanisms, such as habitat acoustics or population density, along with the need to communicate over larger distances, must also be considered as driving forces.
summary: More than 5,000 species of mammals share a basic larynx design. Many of them use the larynx to produce an enormous variability of sounds, but only in a handful of species has the physiology of sound production been studied. It is impracticable in most species because observation requires invasive techniques. Furthermore, many mammals do not spontaneously vocalize if they are manipulated or handled. We have constructed a finite element model of vocal fold tissue vibration on the basis of morphological and biomechanical features of the Rocky Mountain elk vocal organs. Operating within reasonable physiological parameter ranges, it allows the investigation of sound production efficiency as well as selective forces. The model can produce sounds with fundamental frequencies ranging between 60 and 1,200 Hz, covering not only some of the natural vocal repertoire of the elk' s high-pitched bugle calls but also those of its close relative, the European Red Deer, who produces low-pitched roaring sounds with a similar anatomy. The approach is of broader interest, first because techniques can be adapted to other mammal species using only landmark anatomical and biomechanical features, and second, because simulations can serve as playbacks for perception studies investigating the role of vocalizations in communication.
keywords: physiology/motor systems
  physiology/respiratory physiology
  computational biology
title: A Cervid Vocal Fold Model Suggests Greater Glottal Efficiency in Calling at High Frequencies