Advertisement

Quasi-static ultrasound elastography of ex-vivo porcine vocal folds during passive elongation and adduction

Open AccessPublished:December 16, 2022DOI:https://doi.org/10.1016/j.jvoice.2022.11.033

      Abstract

      Objectives. The elastic properties of the vocal folds have great influence on the primary sound and thus on the entire subsequent phonation process. Muscle contractions in the larynx can alter the elastic properties of the vocal fold tissue. Quasi-static ultrasound elastography is a non-destructive examination method that can be applied to ex-vivo vocal folds. In this work, porcine vocal folds were passively elongated and adducted and the changes of the elastic properties due to that manipulations were measured. Methods. Manipulations were performed by applying force to sewn-in sutures. Elongation was achieved by a suture attached to the thyroid cartilage, which was pulled forward by defined weights. Adduction was effected by two sutures exerting torque on the arytenoid cartilage. A series of ten specimens was examined and evaluated using a quasi-static elastography algorithm. In addition, the surface stretch was measured optically using tattooed reference points. Results. This study showed that the expected stiffening of the tissue during the manipulations can be measured using quasi-static ultrasound elastography. The measured effect of elongation and adduction, both of which result in stretching of the tissue, is stiffening. However, the relative change of specific manipulations is not the same for the same load on different larynges, but is rather related to stretch caused and other uninvestigated factors. Conclusion. The passive elongation and adduction of vocal folds stiffen the tissue of the vocal folds and can be measured using ultrasound elastography.

      Keywords

      Introduction

      Our voice is one of the primary ways of interpersonal communication, many everyday routines rely on a functioning voice and sound production. The majority of voice production takes place in the upper airway, which begins at the larynx. The primary sound is created by the vocal folds located in the larynx. They oscillate self-sustained as a result of the airflow passing by.
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      The vocal tract finally forms the audible human voice. The process of voice formation is not yet fully understood, but it is clear that the biomechanical properties of the vocal folds play a crucial role in the overall phonation process.
      • Behrman A.
      • Finan D.
      Speech and voice science.
      In this oscillating system, the eigenfrequencies are not only set by the spatial dimensions and muscle contraction, but also by the mechanical properties.
      The objective of this work is to measure the change in elastic modulus due to elongation and adduction using ultrasound elastography. Elastography is a technique that measures the elastic properties of tissue in a cross-section using medi`cal imaging such as ultrasound. The main advantage of this approach is that the tissue remains intact and can potentially be used on the patient. The tissue of the vocal folds is manipulated, elongated and adducted with the help of sewn-in threads attached to predefined weights. This approach provides information about the change in elasticity due to the manipulations and can lead to a better understanding of the voice formation process. Moreover, changes in elasticity are a good marker for benign and malignant changes. Therefore, the diagnosis of voice disorders benefits from new methods that can investigate the biomechanical properties of the vocal folds.
      • Gómez-Vilda P.
      • Fernández-Baillo R.
      • Nieto A.
      • Díaz F.
      • Fernández-Camacho F.J.
      • Rodellar V.
      • et al.
      Evaluation of voice pathology based on the estimation of vocal fold biomechanical parameters.
      • Zhang Z.
      Characteristics of phonation onset in a two-layer vocal fold model.
      In summary, information about the biomechanics of vocal folds is useful not only for research but also for clinical evaluations.
      In this introduction, an overview of the physiology and anatomy of the larynx is given, followed by an illustration of voice production. Existing measurement techniques for identifying the biomechanical properties of the vocal folds will also be discussed.

      Physiology of the vocal folds and the voice production

      Physiology of the larynx The vocal folds are located in the larynx, which is formed by the cricoid and thyroid cartilage, the cricoid cartilage being annular and connected inferior to the trachea. The posterior part of the cricoid cartilage is much broader than the anterior part. The thyroid is superior of the cricoid and is connected to it by the cricothyroid joint. This joint enables the larynx to rock back and forth. Another important cartilage pair for the voice production are the arytenoid cartilages, which are located on the posterior superior surface of the cricoid cartilage and are connected to it by the cricoarytenoid joints.
      • Behrman A.
      • Finan D.
      Speech and voice science.
      The cartilages are connected by ligaments which form a fiber elastic membrane.
      Physiology of the vocal folds The human vocal folds are 3 mm to 10 mm thick and measure 10 mm to 20 mm in anterior-posterior and 8 mm to 12 mm in the medial-lateral direction.
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      The vocal folds can be separated into three main layers: epithelium, lamina propria and musculus vocalis, whereas the lamina is formed by sublayers (superficial, intermediate and deep lamina propria). The epithelium and the lamina propria are 0.05 mm and 1 mm thick, respectively.
      • Garrett C.G.
      • Coleman J.R.
      • Reinisch L.
      Comparative histology and vibration of the vocal folds: implications for experimental studies in microlaryngeal surgery.
      The shape of the vocal folds is maintained by the epithelium, which also provides protection for the underlying tissue. The musculus vocalis acts actively as a muscle and passively as a stiff rubber band.
      • Hirano M.
      • Kakita Y.
      • Ohmaru K.
      • Kurita S.
      Structure and mechanical properties of the vocal fold1 1a portion of this article was presented at the vocal fold physiology conference, kurume, japan, in january 1980.
      Primarily the superior layers consist of extracellular matrix, whereas the inner layers consist of cells.
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      The elastic properties of the vocal folds are mainly influenced by the lamina propria.
      • Hirano M.
      • Kakita Y.
      • Ohmaru K.
      • Kurita S.
      Structure and mechanical properties of the vocal fold1 1a portion of this article was presented at the vocal fold physiology conference, kurume, japan, in january 1980.
      To simplify the anatomical structures of the vocal folds, numerous models of the vocal fold are found in the literature.
      • Calvache C.
      • Solaque L.
      • Velasco A.
      • Peñuela L.
      Biomechanical models to represent vocal physiology: A systematic review.
      Usually, the basic structure is based on Hirano’s body-cover model, which describes the vocal folds by a two-layer continuum model. The body layer represents the vocalis muscle and the deep lamina, and superficial layers through the cover.
      • Hirano M.
      Morphological structure of the vocal cord as a vibrator and its variations.
      Excised animal larynges are a widely used model for ex-vivo experiments.
      • Luo R.
      • Kong W.
      • Wei X.
      • Lamb J.
      • Jiang J.J.
      Development of excised larynx.
      In this study, we used porcine vocal folds, which are a suitable model for human vocal folds.
      • Kazuto N.
      A comparative study of the layer structure of the vocal fold: A morphological investigation of 11 mammalian species.
      • Alipour F.
      • Jaiswal S.
      Phonatory characteristics of excised pig, sheep, and cow larynges.
      However, the porcine vocal folds lack one layer of lamina propria and it is more difficult to distinguish the individual layers. The thicknesses of the individual layers are comparable to those of human vocal folds.
      • Garrett C.G.
      • Coleman J.R.
      • Reinisch L.
      Comparative histology and vibration of the vocal folds: implications for experimental studies in microlaryngeal surgery.
      The nonlinear response of the vocal folds of pigs and humans is similar.
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      • Alipour-Haghighi F.
      • Titze I.R.
      Elastic models of vocal fold tissues.
      Voice production The vocal folds produce the primary sound in the phonation process, whereby they oscillate self-sustained at high frequency with a small amplitude.
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      Relevant for this study are two movements of the vocal folds respectively the larynx. The opening, the so-called abduction, of the vocal folds is characterized by an outward movement of the posterior part, controlled by the posterior cricoarytenoid muscle. The adduction or closing of the vocal folds is controlled by the lateral cricoarytenoid, the transverse arytenoid, and the oblique arytenoid muscles.
      • Behrman A.
      • Finan D.
      Speech and voice science.
      The elongation of the vocal folds is done by the cricothyroid muscle, which connects these two cartilages. It is a combined movement consisting of an anterior rotation and gliding of the thyroid cartilage on the cricoid cartilage.
      • Behrman A.
      • Finan D.
      Speech and voice science.
      Furthermore, the tension of the vocal fold body can also be controlled by the contraction of the vocalis muscle, while the covering layer itself has no contractile properties.
      • Zhang Z.
      Characteristics of phonation onset in a two-layer vocal fold model.
      The elongation regulates the fundamental frequency f0 of the primary sound.
      • Behrman A.
      • Finan D.
      Speech and voice science.
      An increase in body stiffness by vocal tension leads to a decrease in vibration amplitude and concentrates the vibration on the top layer. Depending on the ratios between body and overhead stiffness, the initial frequency of phonation is effectively controlled either by body stiffness at small ratios or by overhead stiffness at large ratios.
      • Zhang Z.
      Characteristics of phonation onset in a two-layer vocal fold model.
      Contraction of the vocalis muscle can lead to an increase or decrease in phonation frequency, whereas contraction of the cricothyroid muscle always leads to an increase in phonation frequency.
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      The mentioned muscular functions are not as straight forward as it may seem, different speakers used different strategies to achieve the same result.
      • Behrman A.
      • Finan D.
      Speech and voice science.

      Measurement of biomechanical properties

      Various methods have been developed for the characterization of the vocal fold tissue. The first thing to mention are mechanical methods, which are tensile testing, indentation testing and rheometry.
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      • Dion G.R.
      • Jeswani S.
      • Roof S.
      • Fritz M.
      • Coelho P.G.
      • Sobieraj M.
      • et al.
      Functional assessment of the ex vivo vocal folds through biomechanical testing: A review.
      Other approaches include pipette aspiration
      • Scheible F.
      • Lamprecht R.
      • Semmler M.
      • Sutor A.
      Dynamic biomechanical analysis of vocal folds using pipette aspiration technique.
      , optical methods (e.g., videostroboscopy, videoendoscopy)
      • Goodyer E.
      • J. Jiang J.
      • Devine E.
      • Sutor A.
      • Rupitsch S.
      • Zorner S.
      • et al.
      Devices and methods on analysis of biomechanical properties of laryngeal tissue and substitute materials.
      and medical imaging methods (e.g. optical coherence tomography, ultrasound, synchrotron X-ray microtomography).
      • Bailly L.
      • Cochereau T.
      • Orgéas L.
      • Henrich Bernardoni N.
      • Du Rolland Roscoat S.
      • McLeer-Florin A.
      • et al.
      3d multiscale imaging of human vocal folds using synchrotron x-ray microtomography in phase retrieval mode.
      • Hawkshaw M.J.
      • Sataloff J.B.
      • Sataloff R.T.
      New concepts in vocal fold imaging: a review.
      The vocal fold tissue shows nonlinear viscoelastic, anisotropic behavior and a layered structure.
      • Cochereau T.
      • Bailly L.
      • Orgéas L.
      • Henrich Bernardoni N.
      • Robert Y.
      • Terrien M.
      Mechanics of human vocal folds layers during finite strains in tension, compression and shear.
      Tissue anisotropy is caused by fibers oriented mainly in the anterior-posterior direction. Further, the tissue exhibits strain hardening under tension, which origins in the recruitment and reorientation of the fibers. Additionally, stretched tissue showed stress hysteresis after unloading, which may origins in viscoelastic effects.
      • Cochereau T.
      • Bailly L.
      • Orgéas L.
      • Henrich Bernardoni N.
      • Robert Y.
      • Terrien M.
      Mechanics of human vocal folds layers during finite strains in tension, compression and shear.
      The tissue response behaves nonlinearly, but for strain rates up to 15% the response can be modeled linearly.
      • Alipour-Haghighi F.
      • Titze I.R.
      Elastic models of vocal fold tissues.
      • Cochereau T.
      • Bailly L.
      • Orgéas L.
      • Henrich Bernardoni N.
      • Robert Y.
      • Terrien M.
      Mechanics of human vocal folds layers during finite strains in tension, compression and shear.
      Using a Hookean material, the material is fully described by the Young’s modulus E and the Poisson’s ratio ν, whereby the value of the modulus varies between the layers of the vocal folds, see Table 1.
      Table 1Reported values of the Young’s modulus of the porcine vocal fold tissue.
      LayerYoung’s modulus EAuthors
      Body5 kPa to 13 kPa
      • Dion G.R.
      • Coelho P.G.
      • Teng S.
      • Janal M.N.
      • Amin M.R.
      • Branski R.C.
      Dynamic nanomechanical analysis of the vocal fold structure in excised larynges.
      6 kPa to 10 kPa
      • van Loocke M.
      • Lyons C.G.
      • Simms C.K.
      A validated model of passive muscle in compression.
      Cover10 kPa to 16 kPa
      • Alipour F.
      • Jaiswal S.
      • Vigmostad S.
      Vocal fold elasticity in the pig, sheep, and cow larynges.
      25 kPa to 50 kPa
      • Miri A.K.
      Mechanical characterization of vocal fold tissue: a review study.
      3.1 kPa to 4.9 kPa
      • Heris H.K.
      • Miri A.K.
      • Tripathy U.
      • Barthelat F.
      • Mongeau L.
      Indentation of poroviscoelastic vocal fold tissue using an atomic force microscope.
      1.6 kPa to 5.7 kPa
      • Miri A.K.
      • Heris H.K.
      • Mongeau L.
      • Javid F.
      Nanoscale viscoelasticity of extracellular matrix proteins in soft tissues: A multiscale approach.
      The Poisson’s ratio can be assumed to be 0.495.
      • Zhang Z.
      Effect of vocal fold stiffness on voice production in a three-dimensional body-cover phonation model.
      In literature the values chosen for the Poisson’s ratio vary for isotropic material models from 0.45 to 0.495, using anisotropic material models the range is 0.3 to 0.9.
      • Shurtz T.E.
      • Thomson S.L.
      Influence of numerical model decisions on the flow-induced vibration of a computational vocal fold model.
      Effects of manipulations Stretching of the upper layers of the human vocal folds leads to stiffening of the tissue, the extent of the effect depending on the particular sample.
      • Zhang Z.
      • Samajder H.
      • Long J.L.
      Biaxial mechanical properties of human vocal fold cover under vocal fold elongation.
      Yin et al.
      • Yin J.
      • Zhang Z.
      The influence of thyroarytenoid and cricothyroid muscle activation on vocal fold stiffness and eigenfrequencies.
      developed a five parameter Mooney-Rivlin material model for human vocal folds that quantifies the stiffing of the tissue as function of the applied stretch. The same effect can be expected with adduction, as this movement can also lead to stretching of the tissue, but to a lesser extent.

      Ultrasound Elastography

      Ultrasound is already being used to examine the vocal folds, like B-mode-
      • Hu Q.
      • Zhu S.-Y.
      • Luo F.
      • Gao Y.
      • Yang X.-Y.
      High-frequency sonographic measurements of true and false vocal cords.
      • Tsai C.-G.
      • Chen J.-H.
      • Shau Y.-W.
      • Hsiao T.-Y.
      Dynamic b-mode ultrasound imaging of vocal fold vibration during phonation.
      , Doppler-
      • Hsiao T.-Y.
      • Wang C.-L.
      • Chen C.-N.
      • Hsieh F.-J.
      • Shau Y.-W.
      Elasticity of human vocal folds measured in vivo using color doppler imaging.
      , Nakagami-imaging
      • Tsui P.-H.
      • Wan Y.-L.
      • Chen C.-K.
      Ultrasound imaging of the larynx and vocal folds: recent applications and developments.
      , and elastography
      • Gao J.
      • Zhu Q.
      • Xia C.-X.
      • Shin J.
      • Shih G.
      • Min R.
      Shear wave elastography to assess false vocal folds in healthy adults: A feasibility study.
      • Gao J.
      • Xia C.-X.
      • Zhu Q.
      • Hamilton J.
      • Min R.
      Ultrasound strain imaging in assessment of false vocal folds in adults: A feasibility study.
      • Chen H.
      • Tridandapani S.
      • Yoshida E.
      • Moore C.
      • Beitler J.
      • Jani A.
      • et al.
      Tu-e-201c-01: Ultrasound elasticity evaluation of vocal cord function.
      . Except for B-mode imaging, these imaging methods reveal the elastic properties of the vocal folds directly or indirectly.
      • Sigrist R.M.S.
      • Liau J.
      • Kaffas A.E.
      • Chammas M.C.
      • Willmann J.K.
      Ultrasound elastography: Review of techniques and clinical applications.
      Elastography is an examination method where the biomechanical properties are displayed on medical images. Ultrasound elastography is widely used to assess changes in different organ systems, like the liver, breast, or prostate.
      • DeWall R.J.
      Ultrasound elastography: principles, techniques, and clinical applications.
      Quasi-static Elastography The basic idea behind strain imaging or quasi-static elastography is to use an ultrasound transducer to apply a slight deformation to a sample or tissue and then record the compression. The measured displacement can be calculated to a strain field. This step leads to strain images, which are often used as a synonym for elastography.
      • Chintada B.R.
      • Subramani A.V.
      • Raghavan B.
      • Thittai A.K.
      A novel elastographic frame quality indicator and its use in automatic representative-frame selection from a cine loop.
      Furthermore, the elastic characteristics of the assessed tissue or sample may be estimated using plausible stress assumptions. The calculation to quantitative results, e.g. the Young’s modulus, of the tissue needs further assumptions like a simplified or a continuum mechanical model.
      • Doyley M.M.
      Model-based elastography: a survey of approaches to the inverse elasticity problem.
      Quantitative solutions for the quasi-static elastography can be computed analytically
      • Sumi C.
      • Suzuki A.
      • Nakayama K.
      Estimation of shear modulus distribution in soft tissue from strain distribution.
      • Barbone P.E.
      • Gokhale N.H.
      Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in two dimensions.
      • Fehrenbach J.
      Influence of poisson’s ratio on elastographic direct and inverse problems.
      or model-based
      • Doyley M.M.
      • Meaney P.M.
      • Bamber J.C.
      Evaluation of an iterative reconstruction method for quantitative elastography.
      • Oberai A.A.
      • Gokhale N.H.
      • Feij o G.R.
      Solution of inverse problems in elasticity imaging using the adjoint method.
      • Smyl D.
      • Bossuyt S.
      • Liu D.
      OpenQSEI: A matlab package for quasi static elasticity imaging.
      • Mohammadi N.
      • Doyley M.M.
      • Cetin M.
      A statistical framework for model-based inverse problems in ultrasound elastography.
      .

      Material and methods

      We use an ex-vivo setup to measure the elastic properties of the vocal folds, which is a suitable model for physiological voice production.
      • Garica M.
      • Herbst C.
      Excised larynx experimentation: history, current developments, and prospects for bioacoustic research.
      The following section provides an overview of specimen preparation, measurement setup, and data evaluation.

      Experimental setup and measurement procedure

      Preparation of the specimens In this study we use ten porcine larynges (L110) from a local slaughterhouse near Erlangen, Germany. The larynges were frozen with 2-methylbutane at a temperature of -150 °C and stored at -80 °C to preserve tissue properties.
      • Chan R.W.
      • Titze I.R.
      Effect of postmortem changes and freezing on the viscoelastic properties of vocal fold tissues.
      The night before the experiments, the larynges were thawed in a refrigerator and immersed in a NaCl solution.
      • Birk V.
      • Kniesburges S.
      • Semmler M.
      • Berry D.A.
      • Bohr C.
      • Döllinger M.
      • et al.
      Influence of glottal closure on the phonatory process in ex vivo porcine larynges.
      Then, the thyroid cartilage is cut down to the level of the vocal folds, with the entire vestibular folds removed. The arytenoid cartilage is trimmed to obtain a clear view for suture insertion. After placement of the threads, the larynges are stored in NaCl solution until the start of the measurement.
      Manipulation by sewn-in threads The vocal fold are manipulated by sewn-in threads, see Fig. 1. Three threads are fixed in the arytenoid cartilage, one for the transduction and two for the adduction by rotation.
      Fig. 1
      Fig. 1The sewn-in threads in a photograph (left) and a schematic drawing (right) in top view of the prepared larynx. The threads for the elongation is displayed in green and the adduction in yellow. The transduction sutures are not marked, but can be seen in the left panel on the cut arytheroid cartilage. They each pass to the opposite side as which they are fixed and therefore close the glottis. The small plastic plates are visible in both illustrations.
      The transduction threads close the posterior gap between the vocal folds with a constant weight of 50 g, which acts as a constant adduction of the vocal folds. Bilateral variable adduction is achieved by two threads (yellow arrows in Fig. 1) applying torque to the arytenoid cartilage, resulting in rotation of the circoarytenoid joint. A suture (green arrow in Fig. 1) is attached to the most anterior part of the thyroid cartilage to mimic the elongation of the vocal folds.
      • Alipour F.
      • Jaiswal S.
      Phonatory characteristics of excised pig, sheep, and cow larynges.
      • Birk V.
      • Kniesburges S.
      • Semmler M.
      • Berry D.A.
      • Bohr C.
      • Döllinger M.
      • et al.
      Influence of glottal closure on the phonatory process in ex vivo porcine larynges.
      Additionally, small plastic plates are positioned to compensate for the structural integrity provided by the vestibular folds. These plates are loaded with 10 g. The threads of the weights are redirected by pulleys to achieve a physiological direction of force.
      Measurement setup The larynx is mounted on a 20 mm diameter stainless steel artificial tracheal tube and fixed using screws, see Fig. 2. The vocal folds are examined with the E-Cube 15 EX (Alpinion, Anyang-si, Gyeonggi-do, South Korea) using the IO8-17 transducer with a frequency range of 8 MHz to 17 MHz. The transducer is placed centrally in lateral orientation on the vocal folds, with a tailored gel pad (Aquaflex, Parker Laboratories, Fairfield, NJ, USA) coupling the ultrasound waves into the tissue.
      • Woo J.-W.
      • Kim S.K.
      • Park I.
      • Choe J.H.
      • Kim J.-H.
      • Kim J.S.
      A novel gel pad laryngeal ultrasound for vocal cord evaluation.
      • Knyazeva P.
      • Walz M.K.
      • Alesina P.F.
      A simple tool to improve visualization of the vocal cords on translaryngeal ultrasound in male patients.
      The movement of the transducer is operated by a computer-controlled linear drive. In addition, a load cell (KD23s, ME-Messsysteme, Hennigsdorf, Germany) with a measurement range of ±2 N is used to measure the compressive force.
      Fig. 2
      Fig. 2The measurement setup: The larynx is fixed on the artificial trachea and the transducer is connected to the tissue by a gel pad. In addition, manipulation threads and weights are visible.
      Stretch measurement The vocal folds are tattooed with ink to measure the surface stretch optically; the tattooed dot pattern is shown in Fig. 1 in the left panel. The stretch of the vocal folds is recorded with a high-speed camera (Phantom V2511, Vision Research, Wayne, NJ, USA) with a resolution of 768 pixel x 768 pixel immediately after the application of the weights.
      To extract definitive sub-pixel accurate 2D labels of the tattooed points, we first coarsely pre-label the points manually. However, due to the dilating nature of ink in soft tissue, further optimization of the 2D labels is necessary. Thus, we want to translate the pre-labeled points such that they lie in the centroid of the darkest region of the tattooed marker points. To achieve this, we first extract an 11 pixel x 11 pixel rectangular window around the pre-labeled points. Inside this window, we remove specular highlights by thresholding the region using an empirically estimated value and inpaint it using the method by Telea et al.
      • Telea A.
      An image inpainting technique based on the fast marching method.
      . Next, we normalize the histogram of the windowed region to [0, 255] and apply a s-shaped tone mapping to enhance contrast as well as increase the difference between dark and bright regions. We then apply kMeans clustering with k=2 to segment the window into the tattooed point and dilate the former by one pixel.
      • Lloyd S.
      Least squares quantization in pcm.
      Lastly, we calculate a weighted centroid of the tattooed point, based on the inverted intensities of its segmented region. This outputs an optimized label that is drawn towards the darkest area of the tattooed region.
      Based on the centers of the marker points calculated in that way, the elongation is measured by the change in length between the rearmost and the anteriormost marker point, separately for the left and right vocal folds.
      Measurement protocol The threads for the elongation and adduction are loaded according to the measurement protocol depicted in Table 2, followed by an iteration of measurements.
      Table 2The applied measurement protocol, with the two manipulation methods: Adduction is symmetrical on the left and right, so two weights are used and elongation is achieved with a central weight. The appended number indicates the time course of the measurement.
      Adduction
      Elongation10 g 10 g30 g – 30 g50 g – 50 g
      10 gM1, M4, M7M2M3
      30 gM5
      70 gM6

      Elastography

      The elastography algorithm is performed using the quasi-static approach presented in Lamprecht et al.
      • Lamprecht R.
      • Scheible F.
      • Semmler M.
      • Sutor A.
      A quasi-static quantitative ultrasound elastography algorithm using optical flow.
      , which will be described briefly here.
      Material Model At first approximation, we assume that the tissue is an isotropic, nearly incompressible, linear-elastic and locally homogeneous material.
      • Sigrist R.M.S.
      • Liau J.
      • Kaffas A.E.
      • Chammas M.C.
      • Willmann J.K.
      Ultrasound elastography: Review of techniques and clinical applications.
      Tissue can be described as linearly elastic if only small deformations are considered.
      • Doyley M.M.
      Model-based elastography: a survey of approaches to the inverse elasticity problem.
      Therefore, the linear formulation of Hooke’s law with strains ε and stresses σ is as follows
      σ=Cε,
      (1)


      with the 4th-order stiffness tensor C.
      • Argatov I.
      • Mishuris G.
      Indentation testing of biological materials.
      • Freutel M.
      • Schmidt H.
      • Dürselen L.
      • Ignatius A.
      • Galbusera F.
      Finite element modeling of soft tissues: material models, tissue interaction and challenges.
      Furthermore, we assume that the stress has no perpendicular components to the axial compressive stress σ0. The underlying idea is that the tissue expands in perpendicular directions while maintaining the volume of the tissue.
      • Barbone P.E.
      • Oberai A.A.
      • Hall T.J.
      Introduction to quasi-static elastography.
      Conclusively, we can compute the elastic modulus E using Hooke’s Law in Eq.  (1) with
      E=σ0ε0.
      (2)


      For nonlinear materials, the measured strain depends on the applied stress. Using this, a strain-dependent elastic modulus can be described by a Veronda-Westmann material.
      • Barbone P.E.
      • Oberai A.A.
      • Hall T.J.
      Introduction to quasi-static elastography.
      In the special case of small deformation and uniaxial stress, the response of the material can be described by
      σ0Eε0e3γε02forε01.
      (3)


      The non-linearity parameter was set γ=10, which has yielded to good results.
      • Barbone P.E.
      • Oberai A.A.
      • Hall T.J.
      Introduction to quasi-static elastography.
      • Goenezen S.
      • Dord J.-F.
      • Sink Z.
      • Barbone P.E.
      • Jiang J.
      • Hall T.J.
      • et al.
      Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis.
      • Czerner M.
      • Fellay L.S.
      • Suárez M.P.
      • Frontini P.M.
      • Fasce L.A.
      Determination of elastic modulus of gelatin gels by indentation experiments.
      Displacement We are using an image registration algorithm to measure the movement of the tissue.
      • Chuang B.-I.
      • Hsu J.-H.
      • Kuo L.-C.
      • Jou I.-M.
      • Su F.-C.
      • Sun Y.-N.
      Tendon-motion tracking in an ultrasound image sequence using optical-flow-based block matching.
      For that, it is necessary that the acoustic properties of the probe are constant over the entire measurement process.
      • Barbone P.E.
      • Oberai A.A.
      • Hall T.J.
      Introduction to quasi-static elastography.
      • Insana M.F.
      • Hall T.J.
      • Chaturvedi P.
      • Kargel C.
      Ultrasonic properties of random media under uniaxial loading.
      The optical flow algorithm DeepFlow was used to measure the displacement u between two consecutive images.

      Weinzaepfel P., Revaud J., Harchaoui Z., Schmid C.. Deepflow: Large displacement optical flow with deep matching. 2013. https://hal.inria.fr/hal-00873592/document.

      To get the total displacement field between unloaded and loaded condition the previous displacement fields are added to the newly estimated ones. The precision of the displacement estimation is measured by a performance estimator.
      • Jiang J.
      • Hall T.J.
      • Sommer A.M.
      A novel performance descriptor for ultrasonic strain imaging: a preliminary study.
      If the performance falls below the predefined value, the current frame is used as the new reference frame and all previous displacements are added to the newly measured ones.
      • Bayer M.
      • Hall T.J.
      Variance and covariance of accumulated displacement estimates.
      The minimum correlation coefficient is chosen ρmin=0.99.
      Strain The strain in the tissue can be calculated by deriving the displacement field
      u(x,t)=(δuxδxδuxδzδuzδxδuzδz)
      (4)


      where ux and uz are the x- and z-components of the displacement field u.
      • Barbone P.E.
      • Oberai A.A.
      • Hall T.J.
      Introduction to quasi-static elastography.
      The displacement field is noisy due to imaging noise, while the derivative in the strain calculation increases the primary error. Therefore the displacement field must be smoothed or filtered.
      • Sutton M.A.
      • Turner J.L.
      • Bruck H.A.
      • Chae T.A.
      Full-field representation of discretely sampled surface deformation for displacement and strain analysis.
      • Pan B.
      • Asundi A.
      • Xie H.
      • Gao J.
      Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements.
      • Meng L.B.
      • Jin G.C.
      • Yao X.F.
      Application of iteration and finite element smoothing technique for displacement and strain measurement of digital speckle correlation.
      The strain can be derived directly, with the shortcomings mentioned, or convolution filters can be used.
      • Kallel F.
      • Ophir J.
      A least-squares strain estimator for elastography.
      We use a Savitzky-Golay differentiator to compute the strain, with the applied filter width (45 pixel x 45 pixel) determining the degree of smoothing.
      • Pan B.
      Full-field strain measurement using a two-dimensional savitzky-golay digital differentiator in digital image correlation.
      Stress There is no known measurement method that can quantify the stress σ0. Usually, the stress distribution is therefore assumed to be constant.
      • Doyley M.M.
      Model-based elastography: a survey of approaches to the inverse elasticity problem.
      Love
      • Love A.E.H.
      Ix. the stress produced in a semi-infinite solid by pressure on part of the boundary.
      proposed an analytical solution for calculating σ0 in a semi-infinite, isotropic, and homogeneous sample loaded with a normal pressure over rectangular area.
      • Jin X.
      • Niu F.
      • Zhang X.
      • Zhou Q.
      • Lyu D.
      • Keer L.M.
      • et al.
      Love’s rectangular contact problem revisited: A complete solution.
      • Yuan L.
      • Pedersen P.C.
      Stress field calculation for quantitative ultrasound elastography via integration of force sensors.
      We can assume that the gel pad distributes the stress evenly over the surface.
      Taking the assumed stress and the measured strain, the Young’s modulus of the tissue can be calculated with Eq.  (2) and Eq.  (3). Again, the performance estimator was used that excluded all frames with a correlation coefficient less than ρmin=0.9.
      Measurement The vocal folds are compressed using the ultrasound transducer moved by a linear actuator for 1 mm in 1 s, then held in this position for another second and unloaded at the same rate. The procedure is recorded as an ultrasound video sequence.
      The measurement is repeated three times, immediately followed by a pause of 120 s, for a total of two iterations. With the seven manipulations and six measurements per manipulation, a total of 42 measurements per larynx are obtained.

      Results

      Fig. 3 shows photos of a larynx taken by the high-speed camera under the different manipulations, with the color indicating the difference between the reference condition and the applied manipulation. Configuration M1 will be used as the reference configuration for adduction and M4 for elongation, in addition M7 represents the reference configuration after the measurement run. It can be seen, that the applied elongation (Fig. 3(b)) has greater influence on the larynx than the adduction (Fig. 3(a)). The photographs show that the larynx does not return to its initial state, which can be seen during adduction in M4 and elongation in M7.
      Fig. 3
      Fig. 3The effect of adduction on the vocal folds: The reference configuration is shown in the leftmost panel and increasing weight in the following panels, with the last panel representing the return to the initial configuration. The photo of the manipulation is overlaid with the reference configuration in different colorbands, more specifically the gray areas indicate where the photos are identical and the magenta and green areas indicate where they differ.
      In the following, first the results of the optical stretch measurement and then those of the elastography are presented.

      Stretch measurement

      General trends The effect of adduction obtained by the optical stretch measurement is shown in Fig. 4(a), with little effect on vocal fold length. In contrast, the weights on the thyroid cartilage cause a larger elongation of the tissue, as can be seen in Fig. 4(b). However, the effect does not always seem to be reversible, since the stretch does not return to zero for M4 or M7, the reference configurations. This is consistent with the impression seen in Fig. 3, where the manipulation did not return to the initial state evident in the rightmost panel.
      Fig. 4
      Fig. 4The surface stretch of the vocal folds in the anterior-posterior direction caused by the adducting weights. The unloaded condition was taken as reference and the stretch in percent was calculated. The results for the left vocal fold are displayed in the left panel and for the right vis–vis. The line in the box marks the median of all measurement results, the edges indicate the 25th and 75th percentiles. The outliers are not considered in the data analysis, but are still displayed in the plot.
      Variability It was also found that the effect varies between the individual larynges and between the left and right sides. Fig. 5 shows the stretch in longitudinal direction during maximum elongation. It can be seen that the elongation is not equilateral and that the same weight does not result in the same elongation for different larynges.

      Elastography

      Fig. 6 shows a selected ultrasound image of a vocal fold on the right side and the measured elastic modulus superimposed on the image on the left side. The stiffer areas are the edge of the cartilage, while no measurement data are obtained in the cartilage itself due to the lack of compression and subsequent absence of strain.
      Fig. 5
      Fig. 5The longitudinal stretching of the left and right vocal folds for all larynges in the M6 configuration (70 g elongation). Whereby, the mean value is shown as solid line.
      Fig. 6
      Fig. 6The measured Young’s modulus in the left vocal fold of larynx L1 in manipulation M1 superimposed on the ultrasound image.
      Larynges L5, L6 and L9 are excluded from further analysis because the performance of the elastography algorithm in one of the vocal folds is too low. The reason for this is insufficient contact with one of the vocal folds or the impossibility of placing the transducer due to strongly curved surfaces of the vocal folds, thus making uniform contact with the surface impossible. This leads to instabilities in the determination of displacement and subsequently in the calculation of strain and elastic modulus.
      The mean value of the Young’s modulus in a manually chosen quadratic region of interest (1.5 mm x 1.5 mm) placed in the vocalis muscle bilaterally is used for further evaluation. In addition, the mean value of the six measurements per manipulation is analyzed. Due to the nonlinear elastic modulus of the vocal fold tissue, the Young’s moduli of the different larynges are compared at a defined compressive force of 0.15 N ± 0.0075 N. Because of that, one out of a total of 56 measurements is excluded, where no data are found in the defined force range.
      In addition, the measurements in which negative stretch is measured using the camera are excluded, since in this case it can be assumed that there was no sufficient manipulation of the tissue; this affects a total of seven measurements for adduction and two for elongation.
      Manipulation M1 will be used as reference value for the static Young’s modulus, whereby the results for the left and the right vocal fold are shown in Fig. 7. It is noticeable that the measured modulus is similar for the left and right vocal fold.
      Fig. 7
      Fig. 7The measured static Young’s modulus obtained in the M1 configuration in the regions of interest. The six iterations per manipulation are shown as small dots and the mean as large symbols, with the whiskers indicating the standard deviation.
      Effects of manipulation Hereinafter, the measured values of the Young’s modulus were normalized to M1 and M4, which represent the reference configuration for adduction and elongation, respectively. Fig. 8(a) shows a small change in Young’s modulus during adduction, with a general tendency to stiffen the tissue. The effect of elongation, see Fig. 8(b), is larger. While manipulation M5 has very little effect on tissue stiffness, manipulation M6 results in significant tissue stiffening in almost all larynges. As already noted in the measurement of stretch, the stiffening does not appear to be symmetrical in most cases.
      Fig. 8
      Fig. 8The relative change of the Young’s modulus in the defined region of interest during the applied manipulations. The mean of the six iterations per manipulation is shown here. The results for the left vocal fold are displayed in the left panel and for the right vis–vis.

      Statistical analysis

      The observed physical variables were stretch at the tissue surface and the change in Young’s modulus in the musculus vocalis, the hypothesis being that the higher manipulations weights lead to an increase in stretch and Young’s modulus. This hypothesis is tested using the Kendall correlation coefficient and a significance level of p<.001, which are displayed in Fig. 9. Kendall correlation was chosen because of the presence of both ordinal and metric variables and the small sample size.
      Fig. 9
      Fig. 9The correlation between the applied weight and the measured values, i.e. the optically measured stretch and the change of the Young’s modulus (cYm). The Kendall correlation coefficient τ is shown in the graph if the correlation is statistically significant (p<.001). In addition, the linear fit of the data points is displayed.
      Figs. 9 (a) and 9(b) show the correlations between the applied weight to achieve adduction and the measured values. It can be seen that the surface stretch has a strong correlation, which is statistically significant, with the applied weight. Furthermore, the change in Young’s modulus is correlated with the applied weight, although the effect is not as strong. Finally, the correlation between surface stretch and change in elastic modulus is also statistically significant. However, for unexplained reasons, the correlation is much stronger for the left vocal fold in all three cases.
      The effects of elongation are highlighted in Figs. 9(c) and 9(d), where again a strong correlation between surface stretch and applied weight can be seen. The correlation for the change in elastic modulus with applied weight is weaker, being at the same level for both vocal folds. Surface stretch and change in Young’s modulus correlate at lower level, but is statistically significant.

      Discussion

      In this study, quasi-static ultrasound elastography was applied to ten ex-vivo porcine larynges during five different manipulations.
      Manipulation The passive manipulations simulate the movement of the larynx during phonation, which controls among others the stiffness of the vocal folds. As the effects on the tissue do not return to the initial state after unloading, see M4 in Fig. 4(a) and M7 in Fig. 4(b), either the tissue has been altered or it shows strong hysteresis. Since the pauses between the individual measurements were about ten minutes, a persistent change in the tissue seems more likely. Physiological elongation of the vocal folds up to 25% can occur without permanent changes to the tissue.
      • Behrman A.
      • Finan D.
      Speech and voice science.
      Nevertheless, this effect needs to be carefully examined in future studies.
      Stretch This study can show that the applied manipulations lead to a surface stretch of the vocal folds, which is statistically significant. The stretch of the tissue under the same manipulation varies between the larynges, see Fig. 5. The most obvious reason could be the varying Young’s modulus of the tissue, but no clear correlation between the measured Young’s modulus and the maximum elongation can be seen. Another reason could be that the axis of rotation of the cricothyroid joint varies between (human) individuals, therefore, the variability of the stretch at the same load may be explained by that.
      • Storck C.
      • Gehrer R.
      • Fischer C.
      • Wolfensberger M.
      • Honegger F.
      • Friedrich G.
      • et al.
      The role of the cricothyroid joint anatomy in cricothyroid approximation surgery.
      The larynges were not examined after the measurement, therefore the influence of that effect cannot be evaluated in this work.
      The error in surface stretch measurement has two main components, first, the camera parameters, and second, the error in image registration. The camera parameters influence the image and thus the stretch measurement by distortion, which can be neglected in this study due to the large focal length and the high quality of the lens used.
      The greatest source of error in the image registration are certainly the changing illumination conditions and the blowout of the ink in the tissue, both artifacts can be seen in Fig. 10. The changing illumination is countered with the presented algorithm, which eliminates this influence. This can be seen in Fig. 10(a), where ink dot detection is reliable even with strong illumination changes. Regarding the blowout of the ink, the influence is minimized by detecting the weighted centroid of the ink spot, which remains the reference point under the assumption that diffusion of the ink in the tissue is isotropic. Fig. 10(b) indicates that the detection algorithm reliably detects the center of the ink dot.
      Fig. 10
      Fig. 10Detection of ink dots for stretch measurement, with the displacement vector of an ink dot shown for two larynges and three manipulations. ’×’ represents the detected point and additionally the magnitude of the displacement is indicated.
      Elastography The discussion of the elastography results is divided into two parts, first discussing the shortcomings of the algorithm itself and then the results.
      In the elastography algorithm, plane stress was assumed, which is not necessarily true due to the geometric dimensions of the vocal folds enclosed in the larynx. Therefore, the absolute values may not be exact, but lie within the expected range. With regard to the effects of the manipulations, a normalized comparison is possible. The stress is distributed uniformly at the boundary by the gel pad, which fits the assumptions of the elastography algorithm better than a forced displacement by a stiff indenter.
      • Saada A.S.
      • Irvine T.F.
      • Hartnett J.P.
      • Hughes W.F.
      Elasticity: Theory and Applications.

      Ophir J., Kallel F., Varghese T., Bertrand M., Cspedes I., Ponnekanti H. Elastography: A systems approach. International Journal of Imaging Systems and Technology. 1997;8(1):89–103. doi:10.1002/(SICI)1098-1098(1997)8:1<89::AID-IMA11>3.0.CO;2-G

      The nonlinearity parameter γ was chosen according to the literature for soft tissue, which gave a good agreement with the measured data. Nevertheless, this one shortcoming of the presented work could be addressed in future studies by detailed mechanical measurements. Alternatively, Goenezen et al.
      • Goenezen S.
      • Dord J.-F.
      • Sink Z.
      • Barbone P.E.
      • Jiang J.
      • Hall T.J.
      • et al.
      Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis.
      used an optimization procedure to estimate γ.
      The resolution of the presented approach is limited due to the frequency of the ultrasound device of about 15 MHz, higher frequencies would allow higher resolution. Vocal folds have already been examined with ultrasound frequencies of up to 50 MHz and a penetration depth of 5 mm to obtain high-resolution images.
      • Huang C.-C.
      • Sun L.
      • Dailey S.H.
      • Wang S.-H.
      • Shung K.K.
      High frequency ultrasonic characterization of human vocal fold tissue.
      The measured modulus of elasticity is within the expected range, see Table 1. Although, the tissue was not subsequently examined mechanically and thus no comparison with another measurement technique is possible. In addition, it would be advantageous to be able to distinguish the layers of the vocal folds in the elastography measurements. This was not possible due to the limited resolution of the ultrasound images. The use of an ultrasound research device where the raw data is accessible would overcome this limitation.
      The measurements showed that both passive adduction and stretching resulted in statistically significant stiffening of the tissue in most cases, but the magnitude of the response is highly individual. Therefore, a simple explanation using surface strain as a reference fails and other factors – not investigated in this study – must be considered. First, there may be unobserved anatomical differences, like the mentioned rotational axis of the cricothyroid joint. Second, the stress under tension is not evenly distributed between the layers.
      • Cochereau T.
      • Bailly L.
      • Orgéas L.
      • Henrich Bernardoni N.
      • Robert Y.
      • Terrien M.
      Mechanics of human vocal folds layers during finite strains in tension, compression and shear.
      This could lead to uncorrelated results between the measured surface stretch and the stiffening of the deeper layers, namely the vocalis muscle.

      Outlook & Conclusion

      This work presents a quasi-static elastography approach applied on porcine vocal folds to measure the influence of passive elongation and adduction. It could be shown that both manipulations influence the Young’s modulus of the tissue and lead to stiffening, which is not only depended on the superficially detected stretch, but also on other – uninvestigated – factors.
      The assessment of the elastic characteristics of the vocal folds may be useful for diagnosing voice abnormalities.
      • Gómez-Vilda P.
      • Fernández-Baillo R.
      • Nieto A.
      • Díaz F.
      • Fernández-Camacho F.J.
      • Rodellar V.
      • et al.
      Evaluation of voice pathology based on the estimation of vocal fold biomechanical parameters.
      The developed ultrasound method would be minimally invasive and would not expose the patient to radiation. Nevertheless, some improvements would be necessary, first a customized transducer that can be placed directly on the vocal folds of an anesthetized patient. Second, this transducer should have a high frequency to enhance the resolution of the images. Additionally, the used gel pads provide a convenient method to couple the ultrasound into the tissue, but cannot be used in-vivo in this form. With these improvements, we see this method as promising for future use in diagnostic and in the exploration of the material parameters of the vocal folds.

      Acknowledgments

      This work was supported by the Austrian Science Fund Grant No. I 3806-B28 and by the German research foundation (DFG) No. DO1247/9-1. All authors declare that they have no conflicts of interest.

      References

        • Miri A.K.
        Mechanical characterization of vocal fold tissue: a review study.
        Journal of Voice. 2014; 28: 657-667https://doi.org/10.1016/j.jvoice.2014.03.001
        • Behrman A.
        • Finan D.
        Speech and voice science.
        third edition. Plural, San Diego CA2018
        • Gómez-Vilda P.
        • Fernández-Baillo R.
        • Nieto A.
        • Díaz F.
        • Fernández-Camacho F.J.
        • Rodellar V.
        • et al.
        Evaluation of voice pathology based on the estimation of vocal fold biomechanical parameters.
        Journal of Voice. 2007; 21: 450-476https://doi.org/10.1016/j.jvoice.2006.01.008
        • Zhang Z.
        Characteristics of phonation onset in a two-layer vocal fold model.
        The Journal of the Acoustical Society of America. 2009; 125: 1091-1102https://doi.org/10.1121/1.3050285
        • Garrett C.G.
        • Coleman J.R.
        • Reinisch L.
        Comparative histology and vibration of the vocal folds: implications for experimental studies in microlaryngeal surgery.
        The Laryngoscope. 2000; 110: 814-824https://doi.org/10.1097/00005537-200005000-00011
        • Hirano M.
        • Kakita Y.
        • Ohmaru K.
        • Kurita S.
        Structure and mechanical properties of the vocal fold1 1a portion of this article was presented at the vocal fold physiology conference, kurume, japan, in january 1980.
        Speech and Language. 1982; 7: 271-297https://doi.org/10.1016/B978-0-12-608607-2.50015-7
        • Calvache C.
        • Solaque L.
        • Velasco A.
        • Peñuela L.
        Biomechanical models to represent vocal physiology: A systematic review.
        Journal of Voice. 2021; https://doi.org/10.1016/j.jvoice.2021.02.014
        • Hirano M.
        Morphological structure of the vocal cord as a vibrator and its variations.
        Folia phoniatrica. 1974; 26: 89-94https://doi.org/10.1159/000263771
        • Luo R.
        • Kong W.
        • Wei X.
        • Lamb J.
        • Jiang J.J.
        Development of excised larynx.
        Journal of Voice. 2020; 34: 38-43https://doi.org/10.1016/j.jvoice.2018.07.023
        • Kazuto N.
        A comparative study of the layer structure of the vocal fold: A morphological investigation of 11 mammalian species.
        Otologia Fukuoka. 1982; 28: 699-738
        • Alipour F.
        • Jaiswal S.
        Phonatory characteristics of excised pig, sheep, and cow larynges.
        The Journal of the Acoustical Society of America. 2008; 123: 4572-4581https://doi.org/10.1121/1.2908289
        • Alipour-Haghighi F.
        • Titze I.R.
        Elastic models of vocal fold tissues.
        The Journal of the Acoustical Society of America. 1991; 90: 1326-1331https://doi.org/10.1121/1.401924
        • Dion G.R.
        • Jeswani S.
        • Roof S.
        • Fritz M.
        • Coelho P.G.
        • Sobieraj M.
        • et al.
        Functional assessment of the ex vivo vocal folds through biomechanical testing: A review.
        Materials science & engineering C, Materials for biological applications. 2016; 64: 444-453https://doi.org/10.1016/j.msec.2016.04.018
        • Scheible F.
        • Lamprecht R.
        • Semmler M.
        • Sutor A.
        Dynamic biomechanical analysis of vocal folds using pipette aspiration technique.
        Sensors. 2021; 21: 2923https://doi.org/10.3390/s21092923
        • Goodyer E.
        • J. Jiang J.
        • Devine E.
        • Sutor A.
        • Rupitsch S.
        • Zorner S.
        • et al.
        Devices and methods on analysis of biomechanical properties of laryngeal tissue and substitute materials.
        Current Bioinformatics. 2011; 6: 344-361https://doi.org/10.2174/157489311796904718
        • Bailly L.
        • Cochereau T.
        • Orgéas L.
        • Henrich Bernardoni N.
        • Du Rolland Roscoat S.
        • McLeer-Florin A.
        • et al.
        3d multiscale imaging of human vocal folds using synchrotron x-ray microtomography in phase retrieval mode.
        Scientific Reports. 2018; 8: 14003https://doi.org/10.1038/s41598-018-31849-w
        • Hawkshaw M.J.
        • Sataloff J.B.
        • Sataloff R.T.
        New concepts in vocal fold imaging: a review.
        Journal of Voice. 2013; 27: 738-743https://doi.org/10.1016/j.jvoice.2013.05.011
        • Cochereau T.
        • Bailly L.
        • Orgéas L.
        • Henrich Bernardoni N.
        • Robert Y.
        • Terrien M.
        Mechanics of human vocal folds layers during finite strains in tension, compression and shear.
        Journal of biomechanics. 2020; 110: 109956https://doi.org/10.1016/j.jbiomech.2020.109956
        • Dion G.R.
        • Coelho P.G.
        • Teng S.
        • Janal M.N.
        • Amin M.R.
        • Branski R.C.
        Dynamic nanomechanical analysis of the vocal fold structure in excised larynges.
        The Laryngoscope. 2017; 127: E225-E230https://doi.org/10.1002/lary.26410
        • van Loocke M.
        • Lyons C.G.
        • Simms C.K.
        A validated model of passive muscle in compression.
        Journal of biomechanics. 2006; 39: 2999-3009https://doi.org/10.1016/j.jbiomech.2005.10.016
        • Alipour F.
        • Jaiswal S.
        • Vigmostad S.
        Vocal fold elasticity in the pig, sheep, and cow larynges.
        Journal of Voice. 2011; 25: 130-136https://doi.org/10.1016/j.jvoice.2009.09.002
        • Heris H.K.
        • Miri A.K.
        • Tripathy U.
        • Barthelat F.
        • Mongeau L.
        Indentation of poroviscoelastic vocal fold tissue using an atomic force microscope.
        Journal of the mechanical behavior of biomedical materials. 2013; 28: 383-392https://doi.org/10.1016/j.jmbbm.2013.05.026
        • Miri A.K.
        • Heris H.K.
        • Mongeau L.
        • Javid F.
        Nanoscale viscoelasticity of extracellular matrix proteins in soft tissues: A multiscale approach.
        Journal of the mechanical behavior of biomedical materials. 2014; 30: 196-204https://doi.org/10.1016/j.jmbbm.2013.10.022
        • Zhang Z.
        Effect of vocal fold stiffness on voice production in a three-dimensional body-cover phonation model.
        The Journal of the Acoustical Society of America. 2017; 142: 2311https://doi.org/10.1121/1.5008497
        • Shurtz T.E.
        • Thomson S.L.
        Influence of numerical model decisions on the flow-induced vibration of a computational vocal fold model.
        Computers & structures. 2013; 122: 44-54https://doi.org/10.1016/j.compstruc.2012.10.015
        • Zhang Z.
        • Samajder H.
        • Long J.L.
        Biaxial mechanical properties of human vocal fold cover under vocal fold elongation.
        The Journal of the Acoustical Society of America. 2017; 142: EL356https://doi.org/10.1121/1.5006205
        • Yin J.
        • Zhang Z.
        The influence of thyroarytenoid and cricothyroid muscle activation on vocal fold stiffness and eigenfrequencies.
        The Journal of the Acoustical Society of America. 2013; 133: 2972-2983https://doi.org/10.1121/1.4799809
        • Hu Q.
        • Zhu S.-Y.
        • Luo F.
        • Gao Y.
        • Yang X.-Y.
        High-frequency sonographic measurements of true and false vocal cords.
        Journal of Ultrasound in Medicine. 2010; 29: 1023-1030https://doi.org/10.7863/jum.2010.29.7.1023
        • Tsai C.-G.
        • Chen J.-H.
        • Shau Y.-W.
        • Hsiao T.-Y.
        Dynamic b-mode ultrasound imaging of vocal fold vibration during phonation.
        Ultrasound in medicine & biology. 2009; 35: 1812-1818https://doi.org/10.1016/j.ultrasmedbio.2009.06.002
        • Hsiao T.-Y.
        • Wang C.-L.
        • Chen C.-N.
        • Hsieh F.-J.
        • Shau Y.-W.
        Elasticity of human vocal folds measured in vivo using color doppler imaging.
        Ultrasound in medicine & biology. 2002; 28: 1145-1152https://doi.org/10.1016/s0301-5629(02)00559-8
        • Tsui P.-H.
        • Wan Y.-L.
        • Chen C.-K.
        Ultrasound imaging of the larynx and vocal folds: recent applications and developments.
        Current opinion in otolaryngology & head and neck surgery. 2012; 20: 437-442https://doi.org/10.1097/moo.0b013e32835896b4
        • Gao J.
        • Zhu Q.
        • Xia C.-X.
        • Shin J.
        • Shih G.
        • Min R.
        Shear wave elastography to assess false vocal folds in healthy adults: A feasibility study.
        Journal of Ultrasound in Medicine. 2018; 37: 2537-2544https://doi.org/10.1002/jum.14611
        • Gao J.
        • Xia C.-X.
        • Zhu Q.
        • Hamilton J.
        • Min R.
        Ultrasound strain imaging in assessment of false vocal folds in adults: A feasibility study.
        Clinical imaging. 2018; 51: 292-299https://doi.org/10.1016/j.clinimag.2018.05.013
        • Chen H.
        • Tridandapani S.
        • Yoshida E.
        • Moore C.
        • Beitler J.
        • Jani A.
        • et al.
        Tu-e-201c-01: Ultrasound elasticity evaluation of vocal cord function.
        Medical Physics. 2010; 37: 3404https://doi.org/10.1118/1.3469303
        • Sigrist R.M.S.
        • Liau J.
        • Kaffas A.E.
        • Chammas M.C.
        • Willmann J.K.
        Ultrasound elastography: Review of techniques and clinical applications.
        Theranostics. 2017; 7: 1303-1329https://doi.org/10.7150/thno.18650
        • DeWall R.J.
        Ultrasound elastography: principles, techniques, and clinical applications.
        Critical Reviews in Biomedical Engineering. 2013; 41: 1-19https://doi.org/10.1615/CritRevBiomedEng.2013006991
        • Chintada B.R.
        • Subramani A.V.
        • Raghavan B.
        • Thittai A.K.
        A novel elastographic frame quality indicator and its use in automatic representative-frame selection from a cine loop.
        Ultrasound in Medicine and Biology. 2017; 43: 258-272https://doi.org/10.1016/j.ultrasmedbio.2016.08.030
        • Doyley M.M.
        Model-based elastography: a survey of approaches to the inverse elasticity problem.
        Physics in Medicine & Biology. 2012; 57: R35-73https://doi.org/10.1088/0031-9155/57/3/R35
        • Sumi C.
        • Suzuki A.
        • Nakayama K.
        Estimation of shear modulus distribution in soft tissue from strain distribution.
        IEEE transactions on bio-medical engineering. 1995; 42: 193-202https://doi.org/10.1109/10.341832
        • Barbone P.E.
        • Gokhale N.H.
        Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in two dimensions.
        Inverse Problems. 2004; 20: 283-296https://doi.org/10.1088/0266-5611/20/1/017
        • Fehrenbach J.
        Influence of poisson’s ratio on elastographic direct and inverse problems.
        Physics in Medicine & Biology. 2007; 52: 707-716https://doi.org/10.1088/0031-9155/52/3/012
        • Doyley M.M.
        • Meaney P.M.
        • Bamber J.C.
        Evaluation of an iterative reconstruction method for quantitative elastography.
        Physics in Medicine & Biology. 2000; 45: 1521-1540https://doi.org/10.1088/0031-9155/45/6/309
        • Oberai A.A.
        • Gokhale N.H.
        • Feij o G.R.
        Solution of inverse problems in elasticity imaging using the adjoint method.
        Inverse Problems. 2003; 19: 297-313https://doi.org/10.1088/0266-5611/19/2/304
        • Smyl D.
        • Bossuyt S.
        • Liu D.
        OpenQSEI: A matlab package for quasi static elasticity imaging.
        SoftwareX. 2019; 9: 73-76https://doi.org/10.1016/j.softx.2019.01.004
        • Mohammadi N.
        • Doyley M.M.
        • Cetin M.
        A statistical framework for model-based inverse problems in ultrasound elastography.
        2020 54th Asilomar Conference on Signals, Systems, and Computers. 978-0-7381-3126-9 IEEE, 2020: 1395-1399https://doi.org/10.1109/IEEECONF51394.2020.9443450
        • Garica M.
        • Herbst C.
        Excised larynx experimentation: history, current developments, and prospects for bioacoustic research.
        Anthropological Science. 2018; 126: 9-17https://doi.org/10.1537/ase.171216
        • Chan R.W.
        • Titze I.R.
        Effect of postmortem changes and freezing on the viscoelastic properties of vocal fold tissues.
        Annals of biomedical engineering. 2003; 31: 482-491https://doi.org/10.1114/1.1561287
        • Birk V.
        • Kniesburges S.
        • Semmler M.
        • Berry D.A.
        • Bohr C.
        • Döllinger M.
        • et al.
        Influence of glottal closure on the phonatory process in ex vivo porcine larynges.
        The Journal of the Acoustical Society of America. 2017; 142: 2197https://doi.org/10.1121/1.5007952
        • Woo J.-W.
        • Kim S.K.
        • Park I.
        • Choe J.H.
        • Kim J.-H.
        • Kim J.S.
        A novel gel pad laryngeal ultrasound for vocal cord evaluation.
        Thyroid : official journal of the American Thyroid Association. 2017; 27: 553-557https://doi.org/10.1089/thy.2016.0402
        • Knyazeva P.
        • Walz M.K.
        • Alesina P.F.
        A simple tool to improve visualization of the vocal cords on translaryngeal ultrasound in male patients.
        World Journal of Surgery. 2021; 45: 1442-1445https://doi.org/10.1007/s00268-020-05946-9
        • Telea A.
        An image inpainting technique based on the fast marching method.
        Journal of Graphics Tools. 2004; 9: 23-34https://doi.org/10.1080/10867651.2004.10487596
        • Lloyd S.
        Least squares quantization in pcm.
        IEEE Transactions on Information Theory. 1982; 28: 129-137https://doi.org/10.1109/TIT.1982.1056489
        • Lamprecht R.
        • Scheible F.
        • Semmler M.
        • Sutor A.
        A quasi-static quantitative ultrasound elastography algorithm using optical flow.
        Sensors. 2021; 21: 3010https://doi.org/10.3390/s21093010
        • Argatov I.
        • Mishuris G.
        Indentation testing of biological materials.
        Advanced structured materials. vol. 91. 9783319785332 Springer, Cham, Switzerland2018
        • Freutel M.
        • Schmidt H.
        • Dürselen L.
        • Ignatius A.
        • Galbusera F.
        Finite element modeling of soft tissues: material models, tissue interaction and challenges.
        Clinical biomechanics (Bristol, Avon). 2014; 29: 363-372https://doi.org/10.1016/j.clinbiomech.2014.01.006
        • Barbone P.E.
        • Oberai A.A.
        • Hall T.J.
        Introduction to quasi-static elastography.
        in: Alam S.K. Garra B.S. Tissue Elasticity Imaging. 978-0-12-809661-1 Elsevier, Amsterdam2019: 61-83https://doi.org/10.1016/B978-0-12-809661-1.00004-2
        • Goenezen S.
        • Dord J.-F.
        • Sink Z.
        • Barbone P.E.
        • Jiang J.
        • Hall T.J.
        • et al.
        Linear and nonlinear elastic modulus imaging: an application to breast cancer diagnosis.
        IEEE transactions on medical imaging. 2012; 31: 1628-1637https://doi.org/10.1109/TMI.2012.2201497
        • Czerner M.
        • Fellay L.S.
        • Suárez M.P.
        • Frontini P.M.
        • Fasce L.A.
        Determination of elastic modulus of gelatin gels by indentation experiments.
        Procedia Materials Science. 2015; 8: 287-296https://doi.org/10.1016/j.mspro.2015.04.075
        • Chuang B.-I.
        • Hsu J.-H.
        • Kuo L.-C.
        • Jou I.-M.
        • Su F.-C.
        • Sun Y.-N.
        Tendon-motion tracking in an ultrasound image sequence using optical-flow-based block matching.
        BioMedical Engineering OnLine. 2017; 16: 47https://doi.org/10.1186/s12938-017-0335-x
        • Insana M.F.
        • Hall T.J.
        • Chaturvedi P.
        • Kargel C.
        Ultrasonic properties of random media under uniaxial loading.
        The Journal of the Acoustical Society of America. 2001; 110: 3243-3251https://doi.org/10.1121/1.1414703
      1. Weinzaepfel P., Revaud J., Harchaoui Z., Schmid C.. Deepflow: Large displacement optical flow with deep matching. 2013. https://hal.inria.fr/hal-00873592/document.

        • Jiang J.
        • Hall T.J.
        • Sommer A.M.
        A novel performance descriptor for ultrasonic strain imaging: a preliminary study.
        IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control. 2006; 53: 1088-1102https://doi.org/10.1109/tuffc.2006.1642508
        • Bayer M.
        • Hall T.J.
        Variance and covariance of accumulated displacement estimates.
        Ultrasonic imaging. 2013; 35: 90-108https://doi.org/10.1177/0161734613479246
        • Sutton M.A.
        • Turner J.L.
        • Bruck H.A.
        • Chae T.A.
        Full-field representation of discretely sampled surface deformation for displacement and strain analysis.
        Experimental Mechanics. 1991; 31: 168-177https://doi.org/10.1007/BF02327571
        • Pan B.
        • Asundi A.
        • Xie H.
        • Gao J.
        Digital image correlation using iterative least squares and pointwise least squares for displacement field and strain field measurements.
        Optics and Lasers in Engineering. 2009; 47: 865-874https://doi.org/10.1016/j.optlaseng.2008.10.014
        • Meng L.B.
        • Jin G.C.
        • Yao X.F.
        Application of iteration and finite element smoothing technique for displacement and strain measurement of digital speckle correlation.
        Optics and Lasers in Engineering. 2007; 45: 57-63https://doi.org/10.1016/j.optlaseng.2006.04.012
        • Kallel F.
        • Ophir J.
        A least-squares strain estimator for elastography.
        Ultrasonic imaging. 1997; 19: 195-208https://doi.org/10.1177/016173469701900303
        • Pan B.
        Full-field strain measurement using a two-dimensional savitzky-golay digital differentiator in digital image correlation.
        Optical Engineering. 2007; 46: 033601https://doi.org/10.1117/1.2714926
        • Love A.E.H.
        Ix. the stress produced in a semi-infinite solid by pressure on part of the boundary.
        Philosophical Transactions of the Royal Society of London Series A, Containing Papers of a Mathematical or Physical Character. 1929; 228: 377-420https://doi.org/10.1098/rsta.1929.0009
        • Jin X.
        • Niu F.
        • Zhang X.
        • Zhou Q.
        • Lyu D.
        • Keer L.M.
        • et al.
        Love’s rectangular contact problem revisited: A complete solution.
        Tribology International. 2016; 103: 331-342https://doi.org/10.1016/j.triboint.2016.07.011
        • Yuan L.
        • Pedersen P.C.
        Stress field calculation for quantitative ultrasound elastography via integration of force sensors.
        Proceedings of the 2010 IEEE 36th Annual Northeast Bioengineering Conference [NEBEC 2010]. 9781424468799 IEEE, Piscataway, NJ2010: 1-2https://doi.org/10.1109/nebc.2010.5458125
        • Storck C.
        • Gehrer R.
        • Fischer C.
        • Wolfensberger M.
        • Honegger F.
        • Friedrich G.
        • et al.
        The role of the cricothyroid joint anatomy in cricothyroid approximation surgery.
        Journal of Voice. 2011; 25: 632-637https://doi.org/10.1016/j.jvoice.2010.06.001
        • Saada A.S.
        • Irvine T.F.
        • Hartnett J.P.
        • Hughes W.F.
        Elasticity: Theory and Applications.
        Elsevier Science & Technology and ProQuest, Saint Louis and Ann Arbor, Michigan1974
      2. Ophir J., Kallel F., Varghese T., Bertrand M., Cspedes I., Ponnekanti H. Elastography: A systems approach. International Journal of Imaging Systems and Technology. 1997;8(1):89–103. doi:10.1002/(SICI)1098-1098(1997)8:1<89::AID-IMA11>3.0.CO;2-G

        • Huang C.-C.
        • Sun L.
        • Dailey S.H.
        • Wang S.-H.
        • Shung K.K.
        High frequency ultrasonic characterization of human vocal fold tissue.
        The Journal of the Acoustical Society of America. 2007; 122: 1827https://doi.org/10.1121/1.2756759