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First published online June 13, 2008
Journal of Experimental Biology 211, 2144-2154 (2008)
Published by The Company of Biologists 2008
doi: 10.1242/jeb.017004
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Vocal fold elasticity of the Rocky Mountain elk (Cervus elaphus nelsoni) – producing high fundamental frequency vocalization with a very long vocal fold

Tobias Riede1,2,* and Ingo R. Titze1

1 National Center for Voice and Speech, 1101 13th Street, Denver, CO 80204, USA
2 Department of Biology, University of Colorado at Denver and Health Sciences, Denver, CO, USA


Figure 1
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  		Fig. 1. (A) Relationship between body mass and average fundamental frequency (F0) for non-human primate species [solid line (from Tembrock, 1996Go); 122 species considered; y=1443x–0.623] and several mammals, except primates [dotted line (from Fletcher (Fletcher, 2004Go); unknown number of species considered; y=1403x–0.409]. (B) Relationship between vocal fold length and average fundamental frequency (y=3537x–1.214). The regression is based on human vocal fold data and average F0 in the speaking voice [fig. 7.7 in Titze (Titze, 2000Go)]. In A and B, the North American elk, European red deer and an average male human are indicated by filled circles.

 

Figure 2
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  		Fig. 2. Schematic of a midsagittally opened elk larynx indicating the anatomical markers to measure vocal fold length. A, arytenoid cartilage; acj, crico-arytenoid joint; c, cricoid cartilage; ctm, cricothyroid muscle; e, epiglottis; t, trachea; th, thyroid cartilage; tr, tracheal ring; VFL, vocal fold length. The dotted line indicates the contour of the arytenoid cartilage. The dorsal end of the vocal fold is determined by palpating the processus vocalis of this cartilage. Scale bar, 5 cm.

 

Figure 3
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  		Fig. 3. Schematic of a sample mounting and the chamber.

 

Figure 4
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  		Fig. 4. (A–C) Stress–strain response in time from a 1 Hz sinusoidal elongation of vocal ligament. Note that the amplitude of strain remains constant (A) while stress (B) decreases over time. The decrease in stress is a result of tissue hysteresis, a phenomenon resulting from viscous properties of the tissue. (C) Stress–strain relationship for the same data set. The upper part of the `banana-shaped' curve is the loading phase (stretching). The lower part is the unloading phase (relaxation). The difference between both curves is due to hysteresis of the tissue, i.e. lower stress in the tissue during the unloading phase. The low strain region of the loading phase was fitted with a linear regression line, while the high-strain region was modeled with an exponential function. (D) The limit of the linear region (`Linear strain limit') determined by maximizing the sum of the two regression coefficients (`sum of r2'). The maximum linear strain limit ({epsilon}1) in this example is approx. 0.09.

 

Figure 5
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  		Fig. 5. Relationship between vocal fold length (cm) and estimated age (years). Females (open diamonds) and males (closed diamonds) are indicated separately. Regression function and coefficient (r2) are shown.

 

Figure 6
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  		Fig. 6. Three successive histological sections of the mid-membraneous part of the vocal fold of a 4-year-old elk. (A) Haemalaun-Eosin stain, (B) Elastica-van Gieson stain indicating elastic fibers in black stain, (C) trichrome stain indicating collagen fibers in blue stain. Scale bars, 5 mm. Thickness measurements of the epithelium, the vocal ligament and the thyro-arytenoid muscle were taken along the dotted line in A. (D) Schematic of the histological sections: CA, lateral cricoarytenoideus muscle; TA, thyroarytenoid muscle; CT, cricothyroid muscle; VL, vocal ligament; F, fat layer that sits on the thyroid cartilage.

 

Figure 7
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  		Fig. 7. Histological sections of a mid-membraneous part (A) and a dorsal-membraneous part (B) of the vocal fold of a 4-year-old elk (Masson's Trichrome stain). Scale bars, 5 mm. Note the bundle of muscle fibers leading deeply into the ligamentum vocale in dorsal section but not in the mid-membraneous one. (C) Schematic of a top view of the elk larynx. The position of a depression in the vocal ligament (VL), where a portion of the thyroarytenoid muscle (TA) inserts and could cause an effective shortening of the vocal folds, is shown. Arrows indicate likely directions of out-forces. Note that a line at the insertion point of the TA muscle at the base of the depression was drawn to indicate likely directions of forces; however, whether the tissue has different elastic properties at this point is unknown. A, arytenoid cartilage; T, thyroid cartilage.

 

Figure 8
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  		Fig. 8. Stress–strain relationship for vocal ligaments from a female (top) and male (bottom) elk vocal fold derived in a stepwise procedure. The symbols with a strike-through indicate the rupture point of the respective vocal fold. The lines represent the regression lines calculated for stress–strain data between 0 and 0.8 strain, in both cases only for the left vocal fold. Note that data points `slip off' from the regression model above strain 1.0 in the female and strain 0.8 in the male. This holds true for all ligaments investigated.

 

Figure 9
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  		Fig. 9. Comparative stress–strain relationship according to Eqn 8 for different species and tissue types. Top, stress–strain response as predicted for the elk (hypothesis), as measured in male and female elk, and data from one study in humans. Bottom, different studies in human vocal folds.

 

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© The Company of Biologists Ltd 2008