[Acoustic characterization of an averaged vocal tract model based on the MRI
data of professional tenors]
Judith PROBST(1) , Alexander LODERMEYER(1) , Sahar FATTOUM(2) , Matthias ECHTERNACH(3) , Stefan BECKER(1) ,Stefan KNIESBURGES(2)(1) Department of Process Machinery and Systems Engineering, Friedrich-Alexander-University Erlangen-Nürnberg, Cauerstrasse

4, 91058 Erlangen, Germany; pro@ipat.uni-erlangen.de (J.P); lo@ipat.uni-erlangen.de (A.L.); sb@ipat.uni-erlangen.de (S.B)(2) Division of Phoniatrics and Pediatric Audiology at the Department of Otorhinolaryngology, Head and Neck Surgery,

University Hospital Erlangen, Medical School at Friedrich-Alexander-University Erlangen-Nürnberg, Waldstraße 1, 91054
Erlangen, Germany; sahar.fattoum@uk-erlangen.de (S.F.); stefan.kniesburges@uk-erlangen.de (S.K.)(3) Division of Phoniatrics and Pediatric Audiology at the Department of Otorhinolaryngology, Head and Neck Surgery,

University of Munich, Campus Grosshadern, Marchioninistrasse 15, 81377 München, Germany;
matthias.echternach@med.uni-muenchen.de

Abstract
Human speech is created in the larynx and the vocal tract. For vowels, the basic sound is generated by theoscillating vocal folds and ﬁltered by the vocal tract to produce the typical formants. In the present study, weinvestigate the inﬂuence of the vocal tract on phonation. Based on Magnet Resonance Imaging (MRI) data, theacoustic behavior of the vocal tract can be characterized using numerical and experimental models. However,previous studies only analyzed single vocal tracts that were directly obtained from individuals. To investigate
the basic inﬂuence of the vocal tract on phonation, a vocal tract model is necessary that shows preferably
little individual but the typical acoustic characteristics of the speciﬁc vowel. Hence, we computed an averagevocal tract geometry based on six simpliﬁed individual vocal tracts that were extracted from MRI images ofprofessional tenors. The resulting vocal tract model was evaluated in an experimental setup including artiﬁcial
vocal folds. The comparison with the tenors’ vocal recordings shows that the model reproduces the acoustic
properties well. Hence, the average vocal tract model presented here is suitable for future investigations of theinﬂuence of the vocal tract on phonation.
Keywords: voice production modeling; vocal tract acoustics; artiﬁcial vocal fold models

1INTRODUCTION

The human voice is generated by the ﬂow induced oscillation of the vocal folds. This acoustic primary signal,
which is composed of the fundamental frequency of the vocal fold oscillation, the higher harmonics and thebroadband sound, is ﬁltered through the vocal tract and thus formed into the different sounds of a language [1].
The human vocal tract can in an idealized way be considered as resonator. The resonance frequencies, which
form in the vocal tract and depend on its geometry, are called formants. The ﬁrst two formants are used todistinguish the different vowels. Higher formants, on the other hand, determine the timbre of a voice [2].
Since the acoustic properties of the vocal tract are determined by its geometry, geometric data based on MRI
images are used for the characterization of the vocal tract [3, 4, 5]. For simpliﬁcation, the vocal tract is often
expressed by an area function that describes the cross-sections along the centerline of the vocal tract [3]. This
simpliﬁcation is valid from an acoustic point of view, since the sound propagation up to a frequency 5 kHz canbe regarded as one-dimensional [6].
As the geometry is obtained by imaging methods, previous studies are based on the data of individual subjects.
In order to investigate the inﬂuence of the vocal tract on the ﬂuid-structure-acoustic interaction of phonation andthe radiation of sound, however, a more general model, which does not show strong individual inﬂuences, is1788

necessary. Hence, the aim of the study is to create a simpliﬁed model of the vocal tract that shows preferably
little individual but the typical acoustic characteristics of the speciﬁc vowel. This is achieved by averaging over
six simpliﬁed individual vocal tract geometries based on MRI images of professional tenors.
In order to consider the inﬂuence of the ﬂow that is present in human phonation, the vocal tract models areinvestigated in an experimental setup with artiﬁcial vocal folds.

2METHODS

2.1 Vocal tract models
The vocal tract geometries used are based on MRI images of professional tenors taken at the Institute Musicians’
Medicine of the University Hospital Freiburg by Echternach et al. [4, 7]. Based on these data, a vocal tract
model with realistic geometry and one with simpliﬁed form was created for each of the six tenors. The realistic
geometries are generated by a manual segmentation of the MRT data in the open source software 3D Slicer.
The simpliﬁed models are based on the area functions of the tenors by Echternach et al. [7] and are represented
by straight models with circular cross-sections.
In order to investigate the inﬂuence of the vocal tract on phonation and the underlying physical processes, amore general, simpliﬁed model of the vocal tract was created in addition to the individual vocal tract models.
This averaged vocal tract geometry was calculated by averaging the area functions of the six tenor vocal tracts.
As shown in ﬁgure 1, the vocal tracts were normalized to mean length and the cross-sectional areas wereaveraged.
The vocal tract models were produced using additive manufacturing methods.

Figure 1. Method for averaging the vocal tract geometry

2.2 Experimental Setup
The investigation of the acoustic properties of the vocal tract is done in an experimental setup based on thesetup by Kniesburges et al. [8, 9] and Lodermeyer et al. [10, 11], as depicted in ﬁgure 2.
It consists of a unit for providing and conditioning the airﬂow, an artiﬁcial larynx, a subglottal channel, and thevocal tract replica. The artiﬁcial larynx consists of an artiﬁcial pair of silicone vocal folds that are based on
the M5 model by Scherer et al. [12] and Thomson et al. [13], from the silicone Ecoﬂex 30 (Smooth-On, USA)and have a Young’s modulus of E = 4,4 kPa.

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2.3 Measurement setup and evaluation methods
The sound pressure measurements were done in an anechoic chamber with a 1/2” free ﬁeld microphone Type4189 (Brüel & Kjaer, Denmark) placed at a distance of 90 cm and an angle of 45◦ from the exit of the vocal
tract. The recorded signal was ampliﬁed with the Nexus Conditioning Ampliﬁer (Brüel & Kjaer, Denmark) andsampled by the multifunctional module PXIe-6356 (National Instruments, USA) with a sample rate of 44.1 kHz.
The evaluation of the measurement data and the calculation of the sound pressure level of the acoustic pressure
is done in Matlab. (Mathworks, USA). Based on the resulting spectra, the formant frequencies of the individual
vocal tracts were detected using inverse ﬁltering.

Figure 2. Experimental setup with subglottal channel, artiﬁcial vocal folds, and MRI-based vocal tract

3Results and Discussion

3.1 Analysis of formant frequencies
Figure 3 shows the obtained spectra of the sound pressure level for the MRI-based and simpliﬁed models ofthe six subjects. Each spectrum shows the fundamental frequency, the harmonics and the broadband noise. Thecomparison between the spectra of the MRT-based and simpliﬁed models shows, however, that the broadband
sound differs between the MRI-based and the simpliﬁed geometry. These differences indicate that the ﬂow ﬁeld
and the resulting ﬂow sound in the vocal tract are changed by the simpliﬁcation.
In addition, the formant frequencies, as detected by inverse ﬁltering are marked with dashed lines in ﬁgure
3. For comparison the physiological formants that where determined from audio recordings of the subjects byEchternach et al. [7] are marked as well. The formant frequencies are depicted in ﬁgure 4, which shows thedetermined formant frequencies of the MRI-based and the simpliﬁed vocal tract model for each subject and of
the mean vocal tract model compared to the physiological formants determined by Echternach et al. [7]. For
all models four formant frequencies can be determined in the range between 50 Hz and 5 kHz. The mean
deviations of the formant frequencies from the reference values for the MRI-based models are less than 18 %and less than 16 % for the simpliﬁed models.
However, as a vowel is not characterized by a discrete formant frequency, but varies for each individual [14],the vowel-speciﬁc ﬁlter properties of the vocal tract are reproduced with sufﬁcient accuracy.
3.2 Analysis of the averaged vocal tract
To analyze the vocal intelligibility of the mean vocal tract, the ﬁrst two formant frequencies of the averaged
vocal tract are plotted in a formant chart, as presented by Peterson and Barney [14], together with the physiological values by Echternach et al. [7], see ﬁgure 5. The comparison shows that the formants of the averaged
vocal tract differ by 10 % from the mean value of the ﬁrst formants and by 3 % from the mean value ofthe second formants. Despite the deviation of 10 % for the ﬁrst formant frequency it can be seen, that the1790

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Figure 3. Sound pressure level of the MRI-based (blue) and simpliﬁed (red) models for all subjects. The
formant frequencies, as detected by inverse ﬁltering are marked with vertical lines

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formants produced by the mean vocal tract are in the same frequency range as the subjects’ formants. Due tothe fact that a vowel is characterized by a frequency band, this shows that the vowel characteristics can be preserved. Hence, the averaging over area functions of the vocal tracts is a suitable procedure to reduce individualinﬂuences while preserving the essential acoustic properties of the vocal tract.

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Figure 5. The formant chart, according to Peterson and Barney [14] shows the formant frequencies of the mean
vocal tract compared to the physiological formants of the tenors.

4CONCLUSIONSIn this study, the acoustic properties of the vocal tract were investigated in an experimental setup with anartiﬁcial larynx and MRI-based and simpliﬁed vocal tract models, respectively. In addition a simpliﬁed mean

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vocal tract was generated to reduce the individual inﬂuences. The comparison with the tenors’ vocal recordings
show that the vowel characteristics can be reproduced with all vocal tract models. However, contrary to thecurrent literature, a change in the broadband sound level due to the simpliﬁcation of the geometry is detected
if the oscillation of the vocal folds and the resulting ﬂow are taken into account. This indicates that thesimpliﬁcation of the geometry leads to a change of the ﬂow ﬁeld in the vocal tract and the resulting ﬂowinduced sound.
The validation of the mean vocal tract model based on the physiological reference values shows that the acoustic
properties and the given vowel sound are reproduced. Hence, the average vocal tract model presented here issuitable for future investigations of the inﬂuence of the vocal tract on phonation.

ACKNOWLEDGEMENTS
This research was funded by Else Kröner-Fresenius Stiftung under grant agreement number 2016 A78. The authors also gratefully acknowledge the support of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German Research Foundation (DFG) in the framework of the German excellence initiative.

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