An experimental study of the vibratory deformation of the human vocal folds was conducted. Experiments were performed using model vocal folds [1, 2], Fig. 1, made of silicone rubber implemented into an air supply system, Fig. 2. The material used to cast the model is an isotropic homogeneous material, [3] with a tangent modulus E=5 kPa at ε = 0, i.e. elastic properties similar to those of the human vocal fold cover [4]. The advantages of the use of model larynx systems over the use of excised larynges include easy accessibility to fundamental studies of the vocal fold vibration without invasive testing. Acoustic analysis of voice or electroglottography provide certain insight into voice production processes but optical techniques for the study of vocal fold vibrations have drawn considerable attention. Videoendoscopy, stroboscopy, high-speed photography, and kymography have shown to provide a visual impression of vocal fold dynamics but are limited in providing insight into the fundamental deformation processes of the vocal folds. Quantitative measures of deformation have been conducted through micro-suture techniques but are invasive and allows for measurements of only view image points. Laser triangulation is non-invasive but is limited to only one local measurement point. Here, digital image correlation technique with the software VIC 3D [5] is applied. For the experimental set-up see Fig. 2. The analysis consists of (1) stereo correlation to obtain in-plane displacements and (2) stereo triangulation step to obtain out-of-plane deformation. For the stereo correlation images of the object at two different stages of deformation are compared. A point in the image of the undeformed object is matched with the corresponding point in the deformed stage. “Subsets” of digital images are traced via their gray value distribution from the undeformed reference image to the deformed image. The uniqueness of the matching is enabled by the creation of a speckle pattern on the object’s surface. Here, a white pigment is mixed into the silicone rubber and subsequently black enamel paint is sprayed onto the superior surface of the vocal folds. The stereo triangulation requires two images of the object at each stage of deformation. These are obtained in a single CCD frame by placing a beam splitter in the optical axis between camera and object. These images provide a “left” and “right” view of the model larynx. Thus, the deformed shape of the vocal folds can be obtained. The method allows for noninvasive measurement of the full-field displacement fields. Images of the superior surface of the model larynx are obtained by the use of a high speed digital camera with a frame rate of 3000 frames per second allowing for more than 30 image frames for each vibration cycle. For the 3D digital image correlation analysis two images of the object are obtained for each time instance as a beam splitter is placed in the optical axis between the camera and the model larynx. Phonation frequencies and onset pressure are given in Fig. 3, showing that the model larynx behavior is close to actual physiological data. Figs 4(a) and (b) provide superior views of the model larynx at maximum glottal opening and at glottal closure, respectively. As one example of measured strain fields, Figs 5(a) and (b) depict the distributions of the transverse strain component, on the glottal surface in a contour plot on the deformed superior surface. The knowledge of the distribution of this strain component is relevant to the assessment of the impact of vocal fold collision on potential tissue damage. In the position of maximum opening the vocal folds are deformed by a combination of a bulging-type deformation and the opening movement. At this time instance, the transverse strains at the medial surface are found to be negative, an indication of Poisson’s deformation. During the closing stage, vocal folds collide and simultaneously a mode 3 vibration pattern emerges. Closure of the glottal opening is not complete and two incomplete closure areas are formed during the closure stage. These open areas are located at the anterior and posterior ends of the model larynx, see Fig. 4(b). The finding of this type of incomplete closure is agreement with both actual glottal measurements [6] and 3D finite element simulations of [7]. Transverse strains during that stage are now positive and considerably larger that during the opening stage. Finally, Fig. 6 depicts the time evolution of the out of plane displacements along the medial surface for the closing phase and Fig. 7 depicts the maximum values of the longitudinal strain (at the coronal section of the medial surface) in dependence of the flow rate. These examples of measurements indicate that the DIC method is promising for studies of vocal fold dynamics.
Determination of the stresses and strain on the superior surface of excised porcine larynges during phonation using digital image correlation
