5886 lines
473 KiB
HTML
5886 lines
473 KiB
HTML
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<style>
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@media screen and (min-width: 64em) {
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div.pmc-wm {
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background: repeat-y;
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padding-left: 3rem;
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<link rel="apple-touch-icon"
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<title>
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Synthetic, self-oscillating vocal fold models for voice production research - PMC
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<!-- Logging params: Pinger defaults -->
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<meta name="ncbi_app" content="cloudpmc-viewer" />
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<meta name="ncbi_db" content="pmc" />
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<link rel="preconnect" href="https://cdn.ncbi.nlm.nih.gov" />
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<!-- Include USWDS Init Script -->
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<script src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/assets/uswds-init.js"></script>
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<meta name="citation_journal_title" content="The Journal of the Acoustical Society of America">
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<meta name="citation_title" content="Synthetic, self-oscillating vocal fold models for voice production research">
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<meta name="citation_author" content="Scott L Thomson">
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<meta name="citation_author_institution" content="Department of Mechanical and Civil Engineering, Brigham Young University-Idaho, Rexburg, Idaho 83460, USA">
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<meta name="citation_publication_date" content="2024 Aug 22">
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<meta name="citation_volume" content="156">
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<meta name="citation_issue" content="2">
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<meta name="citation_firstpage" content="1283">
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<meta name="citation_doi" content="10.1121/10.0028267">
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<meta name="citation_pmid" content="39172710">
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<meta name="citation_abstract_html_url" content="https://pmc.ncbi.nlm.nih.gov/articles/PMC11348498/">
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<meta name="citation_fulltext_html_url" content="https://pmc.ncbi.nlm.nih.gov/articles/PMC11348498/">
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<meta name="description" content="Sound for the human voice is produced by vocal fold flow-induced vibration and involves a complex coupling between flow dynamics, tissue motion, and acoustics. Over the past three decades, synthetic, self-oscillating vocal fold models have played an ...">
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<meta name="og:title" content="Synthetic, self-oscillating vocal fold models for voice production research">
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<meta name="og:type" content="article">
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<meta name="og:site_name" content="PubMed Central (PMC)">
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<meta name="og:description" content="Sound for the human voice is produced by vocal fold flow-induced vibration and involves a complex coupling between flow dynamics, tissue motion, and acoustics. Over the past three decades, synthetic, self-oscillating vocal fold models have played an ...">
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<meta name="og:url" content="https://pmc.ncbi.nlm.nih.gov/articles/PMC11348498/">
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<meta name="twitter:site" content="@ncbi">
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</head>
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<body >
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<a class="usa-skipnav " href="#main-content">
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Skip to main content
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<section class="usa-banner " aria-label="Official website of the United States government" >
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<div class="usa-accordion">
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<header class="usa-banner__header">
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<div class="grid-col-auto">
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<img aria-hidden="true"
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An official website of the United States government
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<span class="usa-banner__header-action">Here's how you know</span>
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<button
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type="button"
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class="usa-accordion__button usa-banner__button
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"
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aria-expanded="false"
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aria-controls="gov-banner-default"
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data-testid="storybook-django-banner"
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<span class="usa-banner__button-text">Here's how you know</span>
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</div>
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</header>
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<div class="usa-banner__content usa-accordion__content"
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id="gov-banner-default"
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hidden>
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<img class="usa-banner__icon usa-media-block__img"
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alt=""
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aria-hidden="true" />
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<div class="usa-media-block__body">
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<p>
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<strong>Official websites use .gov</strong>
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<br />
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A
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<strong>.gov</strong> website belongs to an official
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government organization in the United States.
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<img class="usa-banner__icon usa-media-block__img"
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src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/icon-https.svg"
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alt=""
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aria-hidden="true" />
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<div class="usa-media-block__body">
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<p>
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<strong>Secure .gov websites use HTTPS</strong>
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<br />
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A <strong>lock</strong> (
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<span class="icon-lock">
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<svg xmlns="http://www.w3.org/2000/svg"
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height="64"
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viewBox="0 0 52 64"
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class="usa-banner__lock-image"
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role="graphics-symbol"
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aria-labelledby="banner-lock-description"
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focusable="false">
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<title id="banner-lock-title">Lock</title>
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Locked padlock icon
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fill-rule="evenodd"
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d="M26 0c10.493 0 19 8.507 19 19v9h3a4 4 0 0 1 4 4v28a4 4 0 0 1-4 4H4a4 4 0 0 1-4-4V32a4 4 0 0 1 4-4h3v-9C7 8.507 15.507 0 26 0zm0 8c-5.979 0-10.843 4.77-10.996 10.712L15 19v9h22v-9c0-6.075-4.925-11-11-11z" />
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</svg>
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</span>) or <strong>https://</strong> means you've safely
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connected to the .gov website. Share sensitive
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information only on official, secure websites.
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</p>
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</div>
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</div>
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</div>
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</div>
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</div>
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</section>
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<div class="usa-overlay">
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</div>
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<header class="usa-header usa-header--extended usa-header--wide" data-header data-testid="header" >
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<div class="ncbi-header">
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<div class="ncbi-header__container">
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<a class="ncbi-header__logo-container"
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href="https://www.ncbi.nlm.nih.gov/">
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<img alt="NCBI home page"
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class="ncbi-header__logo-image"
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src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/ncbi-logos/nih-nlm-ncbi--white.svg"
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width="410"
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height="100" />
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</a>
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<!-- Mobile menu hamburger button -->
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<button
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type="button"
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class="usa-menu-btn ncbi-header__hamburger-button
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"
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aria-label="Show menu"
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data-testid="navMenuButton"
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>
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<svg aria-hidden="true"
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class="ncbi-hamburger-icon"
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fill="none"
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focusable="false"
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viewBox="0 0 31 21"
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width="31"
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xmlns="http://www.w3.org/2000/svg">
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<path clip-rule="evenodd"
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d="M0.125 20.75H30.875V17.3333H0.125V20.75ZM0.125 12.2083H30.875V8.79167H0.125V12.2083ZM0.125 0.25V3.66667H30.875V0.25H0.125Z"
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fill="#F1F1F1"
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fill-rule="evenodd" />
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</button>
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<!-- Desktop buttons-->
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<div class="ncbi-header__desktop-buttons">
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<!-- Desktop search button -->
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<button
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type="button"
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class="usa-button
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usa-button--unstyled ncbi-header__desktop-button
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"
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aria-expanded="false"
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aria-controls="search-field-desktop-navigation"
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aria-label="Show search overlay"
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data-testid="toggleSearchPanelButton"
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data-toggle-search-panel-button
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>
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<img
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src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/search.svg"
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class="usa-icon "
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aria-hidden="true"
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/>
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Search
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</button>
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<!-- Desktop login dropdown -->
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<div class="ncbi-header__login-dropdown">
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<button
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type="button"
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class="usa-button
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usa-button--unstyled ncbi-header__desktop-button ncbi-header__login-dropdown-button
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"
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aria-expanded="false"
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aria-controls="login-dropdown-menu"
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aria-label="Show login menu"
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data-testid="toggleLoginMenuDropdown"
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data-desktop-login-button
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>
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<img
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src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/person.svg"
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class="usa-icon "
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aria-hidden="true"
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/>
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<span data-login-dropdown-text>Log in</span>
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<!-- Dropdown icon pointing up -->
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<img
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src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/expand_less.svg"
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class="usa-icon ncbi-header__login-dropdown-icon ncbi-header__login-dropdown-icon--expand-less ncbi-header__login-dropdown-icon--hidden"
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aria-hidden="true"
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data-login-dropdown-up-arrow
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/>
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<!-- Dropdown icon pointing down -->
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<img
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src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/expand_more.svg"
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class="usa-icon ncbi-header__login-dropdown-icon ncbi-header__login-dropdown-icon--expand-more ncbi-header__login-dropdown-icon--hidden"
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aria-hidden="true"
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data-login-dropdown-down-arrow
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/>
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</button>
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<!-- Login dropdown menu -->
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<ul class="usa-nav__submenu ncbi-header__login-dropdown-menu"
|
||
id="login-dropdown-menu"
|
||
data-desktop-login-menu-dropdown
|
||
hidden>
|
||
|
||
<li class="usa-nav__submenu-item">
|
||
<!-- Uses custom style overrides to render external and document links. -->
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://www.ncbi.nlm.nih.gov/myncbi/" class="usa-link " >
|
||
|
||
|
||
|
||
Dashboard
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
</li>
|
||
|
||
<li class="usa-nav__submenu-item">
|
||
<!-- Uses custom style overrides to render external and document links. -->
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://www.ncbi.nlm.nih.gov/myncbi/collections/bibliography/" class="usa-link " >
|
||
|
||
|
||
|
||
Publications
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
</li>
|
||
|
||
<li class="usa-nav__submenu-item">
|
||
<!-- Uses custom style overrides to render external and document links. -->
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://www.ncbi.nlm.nih.gov/account/settings/" class="usa-link " >
|
||
|
||
|
||
|
||
Account settings
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
</li>
|
||
|
||
<li class="usa-nav__submenu-item">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<button
|
||
type="button"
|
||
|
||
|
||
class="usa-button
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
usa-button--outline ncbi-header__login-dropdown-logout-button
|
||
"
|
||
|
||
|
||
|
||
data-testid="desktopLogoutButton"
|
||
data-desktop-logout-button
|
||
>
|
||
|
||
|
||
|
||
Log out
|
||
|
||
|
||
|
||
|
||
</button>
|
||
|
||
|
||
|
||
</li>
|
||
</ul>
|
||
</div>
|
||
|
||
</div>
|
||
|
||
</div>
|
||
</div>
|
||
|
||
<!-- Search panel -->
|
||
|
||
<div class="ncbi-search-panel ncbi--show-only-at-desktop"
|
||
data-header-search-panel
|
||
hidden>
|
||
<div class="ncbi-search-panel__container">
|
||
<form action="https://www.ncbi.nlm.nih.gov/search/all/"
|
||
|
||
autocomplete="off"
|
||
class="usa-search usa-search--big ncbi-search-panel__form"
|
||
data-testid="desktop-navigation-search-form"
|
||
method="GET"
|
||
role="search">
|
||
<label class="usa-sr-only" for="search-field-desktop-navigation">
|
||
Search…
|
||
</label>
|
||
<input class="usa-input"
|
||
id="search-field-desktop-navigation"
|
||
name="term"
|
||
|
||
placeholder="Search NCBI"
|
||
|
||
type="search"
|
||
value="" />
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<button
|
||
type="submit"
|
||
|
||
|
||
class="usa-button
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
"
|
||
|
||
|
||
|
||
|
||
|
||
>
|
||
|
||
|
||
|
||
|
||
<span class="usa-search__submit-text">
|
||
Search NCBI
|
||
</span>
|
||
|
||
|
||
|
||
|
||
|
||
</button>
|
||
|
||
|
||
|
||
</form>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
|
||
|
||
<nav aria-label="Primary navigation" class="usa-nav">
|
||
<p class="usa-sr-only" id="primary-navigation-sr-only-title">
|
||
Primary site navigation
|
||
</p>
|
||
|
||
<!-- Mobile menu close button -->
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<button
|
||
type="button"
|
||
|
||
|
||
class="usa-nav__close ncbi-nav__close-button
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
"
|
||
|
||
|
||
aria-label="Close navigation menu"
|
||
data-testid="navCloseButton"
|
||
|
||
>
|
||
|
||
|
||
|
||
|
||
<img src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/usa-icons/close.svg" alt="Close" />
|
||
|
||
|
||
|
||
|
||
|
||
</button>
|
||
|
||
|
||
|
||
|
||
|
||
<!-- Mobile search component -->
|
||
<form class="usa-search usa-search--small ncbi--hide-at-desktop"
|
||
action="https://www.ncbi.nlm.nih.gov/search/all/"
|
||
|
||
autocomplete="off"
|
||
data-testid="mobile-navigation-search-form"
|
||
method="GET"
|
||
role="search">
|
||
<label class="usa-sr-only" for="search-field-mobile-navigation">
|
||
Search
|
||
</label>
|
||
|
||
<input class="usa-input"
|
||
id="search-field-mobile-navigation"
|
||
type="search"
|
||
|
||
placeholder="Search NCBI"
|
||
|
||
name="term" />
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<button
|
||
type="submit"
|
||
|
||
|
||
class="usa-button
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
"
|
||
|
||
|
||
|
||
|
||
|
||
>
|
||
|
||
|
||
|
||
|
||
<!-- This SVG should be kept inline and not replaced with a link to the icon as otherwise it will render in the wrong color -->
|
||
<img src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIGhlaWdodD0iMjQiIHZpZXdCb3g9IjAgMCAyNCAyNCIgd2lkdGg9IjI0Ij48cGF0aCBkPSJNMCAwaDI0djI0SDB6IiBmaWxsPSJub25lIi8+PHBhdGggZmlsbD0iI2ZmZiIgZD0iTTE1LjUgMTRoLS43OWwtLjI4LS4yN0E2LjQ3MSA2LjQ3MSAwIDAgMCAxNiA5LjUgNi41IDYuNSAwIDEgMCA5LjUgMTZjMS42MSAwIDMuMDktLjU5IDQuMjMtMS41N2wuMjcuMjh2Ljc5bDUgNC45OUwyMC40OSAxOWwtNC45OS01em0tNiAwQzcuMDEgMTQgNSAxMS45OSA1IDkuNVM3LjAxIDUgOS41IDUgMTQgNy4wMSAxNCA5LjUgMTEuOTkgMTQgOS41IDE0eiIvPjwvc3ZnPg=="
|
||
class="usa-search__submit-icon"
|
||
alt="Search" />
|
||
|
||
|
||
|
||
|
||
|
||
</button>
|
||
|
||
|
||
|
||
</form>
|
||
|
||
|
||
|
||
|
||
<!-- Primary navigation menu items -->
|
||
<!-- This usa-nav__inner wrapper is required to correctly style the navigation items on Desktop -->
|
||
|
||
|
||
|
||
<div class="ncbi-nav__mobile-login-menu ncbi--hide-at-desktop"
|
||
data-mobile-login-menu
|
||
hidden>
|
||
<p class="ncbi-nav__mobile-login-menu-status">
|
||
Logged in as:
|
||
<strong class="ncbi-nav__mobile-login-menu-email"
|
||
data-mobile-login-email-text></strong>
|
||
</p>
|
||
<ul class="usa-nav__primary usa-accordion">
|
||
|
||
<li class="usa-nav__primary-item">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://www.ncbi.nlm.nih.gov/myncbi/" class="usa-link " >
|
||
|
||
|
||
|
||
Dashboard
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
</li>
|
||
|
||
<li class="usa-nav__primary-item">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://www.ncbi.nlm.nih.gov/myncbi/collections/bibliography/" class="usa-link " >
|
||
|
||
|
||
|
||
Publications
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
</li>
|
||
|
||
<li class="usa-nav__primary-item">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<a href="https://www.ncbi.nlm.nih.gov/account/settings/" class="usa-link " >
|
||
|
||
|
||
|
||
Account settings
|
||
|
||
|
||
|
||
</a>
|
||
|
||
|
||
</li>
|
||
|
||
</ul>
|
||
</div>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<button
|
||
type="button"
|
||
|
||
|
||
class="usa-button
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
ncbi-nav__mobile-login-button ncbi--hide-at-desktop
|
||
"
|
||
|
||
|
||
|
||
data-testid="mobileLoginButton"
|
||
data-mobile-login-button
|
||
>
|
||
|
||
|
||
|
||
Log in
|
||
|
||
|
||
|
||
|
||
</button>
|
||
|
||
|
||
|
||
</nav>
|
||
</header>
|
||
|
||
|
||
|
||
|
||
|
||
<section class="pmc-header pmc-header--basic" aria-label="PMC Header with search box">
|
||
<div class="pmc-nav-container">
|
||
<div class="pmc-header__bar">
|
||
<div class="pmc-header__logo">
|
||
<a href="/" title="Home" aria-label="PMC Home"></a>
|
||
</div>
|
||
<button
|
||
type="button"
|
||
class="usa-button usa-button--unstyled pmc-header__search__button"
|
||
aria-label="Open search"
|
||
data-ga-category="search"
|
||
data-ga-action="PMC"
|
||
data-ga-label="pmc_search_panel_mobile"
|
||
>
|
||
<img src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/search.svg" alt="PMC search open icon" aria-hidden="true" class="usa-icon usa-icon--size-4 pmc-icon__open" />
|
||
<img src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/close.svg" alt="PMC search close ison" aria-hidden="true" class="usa-icon usa-icon--size-4 pmc-icon__close" />
|
||
</button>
|
||
</div>
|
||
<div class="pmc-header__search">
|
||
|
||
|
||
|
||
<form class="usa-search usa-search--extra usa-search--article-right-column pmc-header__search__form" id="pmc-search-form" autocomplete="off" role="search">
|
||
<label class="usa-sr-only" for="pmc-search">Search PMC Full-Text Archive</label>
|
||
<span class="autoComplete_wrapper flex-1">
|
||
<input class="usa-input width-full maxw-none" required="required" placeholder="Search PMC Full-Text Archive" id="pmc-search" type="search" name="term" data-autocomplete-url="https://pmc.ncbi.nlm.nih.gov/autocomp/search/autocomp/"/>
|
||
</span>
|
||
<button
|
||
class="usa-button"
|
||
type="submit"
|
||
formaction="https://pmc.ncbi.nlm.nih.gov/search/"
|
||
data-ga-category="search"
|
||
data-ga-action="PMC"
|
||
data-ga-label="PMC_search_button"
|
||
>
|
||
<span class="usa-search__submit-text">Search in PMC</span>
|
||
<img
|
||
src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/usa-icons-bg/search--white.svg"
|
||
class="usa-search__submit-icon"
|
||
alt="Search"
|
||
/>
|
||
</button>
|
||
</form>
|
||
<div class="display-flex flex-column tablet:flex-row tablet:flex-justify flex-justify-center flex-align-center width-full desktop:maxw-44">
|
||
<ul class="pmc-header__search__menu">
|
||
<li>
|
||
|
||
<a class="usa-link" href="/journals/" data-ga-action="featured_link" data-ga-label="journal list">
|
||
Journal List
|
||
</a>
|
||
|
||
</li>
|
||
<li>
|
||
|
||
<a class="usa-link" href="/about/userguide/" data-ga-action="featured_link"
|
||
data-ga-label="user guide">
|
||
User Guide
|
||
</a>
|
||
|
||
</li>
|
||
</ul>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</section>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="usa-section padding-top-0 desktop:padding-top-6 pmc-article-section" data-article-db="pmc" data-article-id="11348498">
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<div class="grid-container pmc-actions-bar" aria-label="Actions bar" role="complementary">
|
||
<div class="grid-row">
|
||
<div class="grid-col-fill display-flex">
|
||
<div class="display-flex">
|
||
<ul class="usa-list usa-list--unstyled usa-list--horizontal">
|
||
<li class="margin-right-2 mobile-lg:margin-right-4 display-flex mob">
|
||
<button
|
||
type="button"
|
||
class="usa-button pmc-sidenav__container__open usa-button--unstyled width-auto display-flex"
|
||
aria-label="Open resources"
|
||
data-extra-class="is-visible-resources"
|
||
data-ga-category="resources_accordion"
|
||
data-ga-action="click"
|
||
data-ga-label="mobile_icon"
|
||
>
|
||
<img src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/more_vert.svg" alt="Open resources icon" class="usa-icon usa-icon--size-4 usa-icon--link" />
|
||
</button>
|
||
</li>
|
||
|
||
<li class="margin-right-2 mobile-lg:margin-right-4 display-flex mob">
|
||
<a
|
||
href="https://doi.org/10.1121/10.0028267"
|
||
class="usa-link display-flex usa-tooltip"
|
||
role="button"
|
||
target="_blank"
|
||
rel="noreferrer noopener"
|
||
title="View on publisher site"
|
||
data-position="bottom"
|
||
aria-label="View on publisher site"
|
||
data-ga-category="actions"
|
||
data-ga-action="click"
|
||
data-ga-label="publisher_link_mobile"
|
||
>
|
||
<img src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/launch.svg" alt="View on publisher site icon" class="usa-icon usa-icon--size-4 usa-icon--link" />
|
||
</a>
|
||
</li>
|
||
|
||
|
||
<li class="margin-right-2 mobile-lg:margin-right-4 display-flex">
|
||
<a
|
||
href="pdf/JASMAN-000156-001283_1.pdf"
|
||
class="usa-link display-flex usa-tooltip"
|
||
role="button"
|
||
title="Download PDF"
|
||
data-position="bottom"
|
||
aria-label="Download PDF"
|
||
data-ga-category="actions"
|
||
data-ga-action="click"
|
||
data-ga-label="pdf_download_mobile"
|
||
>
|
||
|
||
<img src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/file_download.svg" alt="Download PDF icon" aria-hidden="true" class="usa-icon usa-icon--size-4 usa-icon--link" />
|
||
</a>
|
||
</li>
|
||
|
||
<li class="margin-right-2 mobile-lg:margin-right-4 display-flex">
|
||
<button
|
||
class="usa-button usa-button--unstyled usa-tooltip collections-dialog-trigger collections-button display-flex collections-button-empty"
|
||
title="Add to Collections"
|
||
data-position="bottom"
|
||
aria-label="Save article in MyNCBI collections."
|
||
data-ga-category="actions"
|
||
data-ga-action="click"
|
||
data-ga-label="collections_button_mobile"
|
||
data-collections-open-dialog-enabled="false"
|
||
data-collections-open-dialog-url="https://account.ncbi.nlm.nih.gov/?back_url=https%3A%2F%2Fpmc.ncbi.nlm.nih.gov%2Farticles%2FPMC11348498%2F%23open-collections-dialog"
|
||
data-in-collections="false"
|
||
>
|
||
<img src="https://cdn.ncbi.nlm.nih.gov/pmc/pd-medc-pmc-cloudpmc-viewer/production/674d4f95/var/data/static/img/action-bookmark-full.svg" alt="Collections icon" aria-hidden="true" class="usa-icon usa-icon--size-4 usa-icon--link usa-icon--bookmark-full" />
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<hgroup><h1>Synthetic, self-oscillating vocal fold models for voice production research<sup><a href="#tr1" class="usa-link">a)</a></sup>
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</h1></hgroup><div class="cg p">
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<a href='https://pubmed.ncbi.nlm.nih.gov/?term="Thomson%20SL"[Author]' class="usa-link" aria-describedby="id1"><span class="name western">Scott L Thomson</span></a><div hidden="hidden" id="id1">
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<h3><span class="name western">Scott L Thomson</span></h3>
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<sup>1</sup>Department of Mechanical and Civil Engineering, Brigham Young University-Idaho, Rexburg, Idaho 83460, USA</div>
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<div class="p">Find articles by <a href='https://pubmed.ncbi.nlm.nih.gov/?term="Thomson%20SL"[Author]' class="usa-link"><span class="name western">Scott L Thomson</span></a>
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<sup>1,</sup><sup>b),</sup><sup>✉</sup>
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<sup>1</sup>Department of Mechanical and Civil Engineering, Brigham Young University-Idaho, Rexburg, Idaho 83460, USA</div>
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<sup>b)</sup><p class="display-inline">Email: <span>thomsons@byui.edu</span></p>
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<sup>✉</sup><p class="display-inline">Corresponding author.</p>
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<div id="anp_a" class="d-panel p" style="display: none"><div class="notes p"><section id="historyarticle-meta1" class="history"><p>Received 2023 Aug 31; Revised 2024 Jul 26; Accepted 2024 Jul 30; Issue date 2024 Aug.</p></section></div></div>
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<div>PMCID: PMC11348498 PMID: <a href="https://pubmed.ncbi.nlm.nih.gov/39172710/" class="usa-link">39172710</a>
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</div></section></section><section aria-label="Article content"><section class="body main-article-body"><section class="abstract" id="abstract1"><h2>Abstract</h2>
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<p>Sound for the human voice is produced by vocal fold flow-induced vibration and involves a complex coupling between flow dynamics, tissue motion, and acoustics. Over the past three decades, synthetic, self-oscillating vocal fold models have played an increasingly important role in the study of these complex physical interactions. In particular, two types of models have been established: “membranous” vocal fold models, such as a water-filled latex tube, and “elastic solid” models, such as ultrasoft silicone formed into a vocal fold-like shape and in some cases with multiple layers of differing stiffness to mimic the human vocal fold tissue structure. In this review, the designs, capabilities, and limitations of these two types of models are presented. Considerations unique to the implementation of elastic solid models, including fabrication processes and materials, are discussed. Applications in which these models have been used to study the underlying mechanical principles that govern phonation are surveyed, and experimental techniques and configurations are reviewed. Finally, recommendations for continued development of these models for even more lifelike response and clinical relevance are summarized.</p></section><section id="s1"><h2 class="pmc_sec_title">I. BACKGROUND AND OVERVIEW</h2>
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<p>Human voice production arises from a complex set of interactions between neurological, physiological, and mechanical processes (<a href="#c71" class="usa-link" aria-describedby="c71">Gray, 2000</a>; <a href="#c188" class="usa-link" aria-describedby="c188">Titze, 2000</a>; <a href="#c219" class="usa-link" aria-describedby="c219">Zhang, 2016</a>). During voicing, air flow from the lungs provides the energy for vocal fold (VF) self-oscillation, which in turn causes a temporal pressure fluctuation within the supraglottal airway that is the source of voiced sounds. In this process of phonation, aerodynamics, tissue dynamics, and acoustics are tightly coupled. To understand these mechanical processes, researchers have employed a range of theoretical analyses, computational simulations, and physical experiments.</p>
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<p>Early experiment-based explorations of the larynx and voice production include Leonardo da Vinci's 17th century annotated anatomical sketches (<a href="#c47" class="usa-link" aria-describedby="c47">da Vinci, c. 1510-11</a>; <a href="#c35" class="usa-link" aria-describedby="c35">Clayton and Philo, 2014</a>). Excised larynx studies were conducted as early as the 18th century, including <a href="#c59" class="usa-link" aria-describedby="c59">Ferrein (1741)</a>, who is credited as having been the first to use the term “vocal cords” (<a href="#c16" class="usa-link" aria-describedby="c16">Berke <em>et al.</em>, 1987</a>; <a href="#c120" class="usa-link" aria-describedby="c120">Markatos <em>et al.</em>, 2019</a>). <a href="#c139" class="usa-link" aria-describedby="c139">Müller (1839)</a> reported experiments using excised avian and primate larynges. As summarized by <a href="#c60" class="usa-link" aria-describedby="c60">Flanagan (1972)</a> and <a href="#c56" class="usa-link" aria-describedby="c56">Fagyal (2001)</a>, this time period also saw the development of mechanical devices to synthesize voiced sounds via flow-induced vibration of reeds (e.g., <a href="#c204" class="usa-link" aria-describedby="c204">von Kempelen, 1791</a>). Development of vocal fold-like structures to provide sound for talking robots has continued in modern times (e.g., <a href="#c63" class="usa-link" aria-describedby="c63">Fukui <em>et al.</em>, 2005</a>; <a href="#c61" class="usa-link" aria-describedby="c61">Fukui <em>et al.</em>, 2007</a>; <a href="#c62" class="usa-link" aria-describedby="c62">Fukui <em>et al.</em>, 2008</a>; <a href="#c54" class="usa-link" aria-describedby="c54">Endo <em>et al.</em>, 2014</a>). For additional historical discussion, see <a href="#c16" class="usa-link" aria-describedby="c16">Berke <em>et al.</em> (1987)</a> and <a href="#c120" class="usa-link" aria-describedby="c120">Markatos <em>et al.</em> (2019)</a>.</p>
|
||
<p>Synthetic VF models have also long been used to study the physics of phonation, including static models (e.g., <a href="#c162" class="usa-link" aria-describedby="c162">Scherer <em>et al.</em>, 2001</a>), models with prescribed motion (e.g., <a href="#c132" class="usa-link" aria-describedby="c132">Mongeau <em>et al.</em>, 1997</a>), and self-oscillating models. Self-oscillating VF models mimic the fundamental flow-induced vibration characteristic of human VFs to study coupled fluid, structure, and acoustic interactions and have been designed with varying degrees of fidelity. In addition to his excised larynx studies mentioned previously, <a href="#c139" class="usa-link" aria-describedby="c139">Müller (1839)</a> described synthetic larynx and vocal fold models (see Fig. <a href="#f1" class="usa-link">1</a>). Other early descriptions of synthetic, self-oscillating VF models include <a href="#c55" class="usa-link" aria-describedby="c55">Ewald (1913)</a>, <a href="#c210" class="usa-link" aria-describedby="c210">Wethlo (1918)</a>, and <a href="#c172" class="usa-link" aria-describedby="c172">Smith (1961</a>, <a href="#c173" class="usa-link" aria-describedby="c173">1966)</a>. Since the 1990s, there has been a significant increase in the number of studies using self-oscillating VF models. Scientific advances that have facilitated these increased modeling efforts include the availability of commercial materials with stiffness characteristics suitable for VF modeling; the emergence of modern experimental tools, such as high-speed imaging, particle image velocimetry (PIV), and data acquisition devices; and continued research into laryngeal morphology and function that has driven the need for experimental validation as well as in-depth, systematic exploration.</p>
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<figure class="fig xbox font-sm" id="f1"><h3 class="obj_head">FIG. 1.</h3>
|
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g001.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/5d3f523dd690/JASMAN-000156-001283_1-g001.jpg" loading="lazy" height="627" width="717" alt="FIG. 1."></a></p>
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<figcaption><p>Self-oscillating synthetic vocal fold model. Adapted from Fig. 39 of Müller, J. P. (<strong>1839</strong>). <em>Über die Compensation der physischen Kräfte am menschlichen Stimmorgan: Mit Bemerkungen über die Stimme der Säugethiere, Vögel und Amphibien (On the compensation of the physical forces in the human vocal organ: With remarks on the voice of mammals, birds and amphibians)</em> (A. Hirschwald, Berlin); from the Digital Collections of Weimar University Library.</p></figcaption></figure><p>A review of static, driven, and self-oscillating VF models was published by <a href="#c98" class="usa-link" aria-describedby="c98">Kniesburges <em>et al.</em> (2011)</a>. Since that time, self-oscillating VF modeling has experienced accelerated growth in terms of design, functionality, and application. The purpose of this review is to provide an up-to-date, comprehensive review of synthetic, self-oscillating VF models. This paper is organized as follows. A brief overview of human VF morphology and function is provided, the use of VF models in voice research is introduced, and the two most common types of synthetic, self-oscillating VF models are described in detail. Applications in which these models have been used are surveyed, and experimentation techniques are summarized. Finally, areas for future development are recommended.</p></section><section id="s2"><h2 class="pmc_sec_title">II. VOCAL FOLD MORPHOLOGY AND FUNCTION</h2>
|
||
<p>The structure and function of the human VFs are well-documented (e.g., <a href="#c84" class="usa-link" aria-describedby="c84">Hirano and Sato, 1993</a>; <a href="#c71" class="usa-link" aria-describedby="c71">Gray, 2000</a>; <a href="#c188" class="usa-link" aria-describedby="c188">Titze, 2000</a>; <a href="#c160" class="usa-link" aria-describedby="c160">Sato, 2018</a>). A brief overview of aspects most pertinent to VF modeling is here provided; for a more complete review, see <a href="#c219" class="usa-link" aria-describedby="c219">Zhang (2016)</a>. As illustrated in Fig. <a href="#f2" class="usa-link">2</a>, two opposing VFs are located at the top of the trachea in the respiratory airway within the larynx. The glottis is the space between the VFs, and the spaces above and below are the supraglottic and subglottic regions, respectively. Each VF is comprised of multiple layers of tissue of differing composition and stiffness, including muscle, lamina propria, and epithelium, with the lamina propria consisting of three layers as shown in Fig. <a href="#f2" class="usa-link">2</a>. The intermediate and deep layers of the lamina propria are commonly collectively termed the vocal ligament (<a href="#c83" class="usa-link" aria-describedby="c83">Hirano <em>et al.</em>, 1982</a>).</p>
|
||
<figure class="fig xbox font-sm" id="f2"><h3 class="obj_head">FIG. 2.</h3>
|
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g002.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/0f2d362dc81c/JASMAN-000156-001283_1-g002.jpg" loading="lazy" height="405" width="709" alt="FIG. 2."></a></p>
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<figcaption><p>Frontal cross-sections of the larynx (left; <a href="#c70" class="usa-link" aria-describedby="c70">Gray, 1918</a>) and VF (right; <a href="#c188" class="usa-link" aria-describedby="c188">Titze, 2000</a>). The intermediate and deep layers of the lamina propria are commonly collectively referred to as the vocal ligament, and the muscular region as the vocal fold body. Credits: (Left) Adapted from <a href="#c70" class="usa-link" aria-describedby="c70">Gray, H. (1918)</a>. <em>Anatomy of the Human Body</em>, 20th ed., edited by W. H. Lewis (Lea and Febiger, Philadelphia). (Right) Adapted with permission from Titze, I. R. (<strong>2000</strong>). <em>Principles of Voice Production</em>, Second Printing. (National Center for Voice and Speech, Iowa City). Copyright 2000 National Center for Voice and Speech.</p></figcaption></figure><p>During respiration, the VFs are abducted to allow air exchange between the lungs and mouth. During voicing, the VFs are adducted and air flowing from the lungs initiates and sustains VF flow-induced vibration. This causes periodic interruption of the glottal jet, with the associated pressure fluctuations being the source of sound for voice production. This process is termed phonation.</p>
|
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<p>The relative composition of collagen and elastin fibers causes a variation in stiffness between VF layers (<a href="#c71" class="usa-link" aria-describedby="c71">Gray, 2000</a>; <a href="#c117" class="usa-link" aria-describedby="c117">Madruga de Melo <em>et al.</em> (2003)</a>; <a href="#c179" class="usa-link" aria-describedby="c179">Tateya <em>et al.</em>, 2006</a>; <a href="#c28" class="usa-link" aria-describedby="c28">Chan <em>et al.</em>, 2007</a>). For modeling purposes, key characteristics of the spatial stiffness variation include the following. The muscle, which is also referred to as the VF body, is relatively stiff when active. The ligament consists of the intermediate and deep layers of the lamina propria and is transversely isotropic, with the plane of isotropy being aligned with the frontal anatomical plane and the anterior-posterior (out-of-plane) stiffness exceeding that of the in-plane stiffness. The superficial lamina propria is exceedingly flexible, and the epithelium is thin yet strong enough to withstand vibration. During voicing, the superficial lamina propria and epithelium layers experience the bulk of vibration, although the ligament and body also experience motion.</p></section><section id="s3"><h2 class="pmc_sec_title">III. VOCAL FOLD MODELING</h2>
|
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<p>Phonation involves coupled, complex biological and mechanical phenomena including neurological feedback and control mechanisms, cellular mechanobiological responses, muscle activity, air flow, blood flow, vibrating tissue dynamics, acoustical source-filter interactions, and ultimately sound production. A variety of models have been employed to investigate the underlying mechanical components of phonation, i.e., primarily air flow, tissue dynamics, and acoustics. Such approaches have included <em>in vivo</em> and excised larynx models (<a href="#c50" class="usa-link" aria-describedby="c50">Döllinger <em>et al.</em>, 2011</a>), theoretical and computational models (<a href="#c6" class="usa-link" aria-describedby="c6">Alipour <em>et al.</em>, 2011</a>; <a href="#c51" class="usa-link" aria-describedby="c51">Döllinger <em>et al.</em>, 2023</a>), and synthetic models (<a href="#c98" class="usa-link" aria-describedby="c98">Kniesburges <em>et al.</em>, 2011</a>).</p>
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<p><em>In vivo</em>, excised, computational, and synthetic models constitute a set of approaches with complementary limitations and capabilities. The relative merits of these types of models include the following (portions of which have been adapted from <a href="#c81" class="usa-link" aria-describedby="c81">Hilton and Thomson, 2022</a>). <em>In vivo</em> and excised larynx models are morphologically authentic but limited in terms of repeatability, parameterizability, and longevity. Excised larynges are subject to tissue degradation. The material properties and geometries of computational models can be precisely defined and used to directly generate desired data (e.g., pressure, velocity, flow rate, and vibratory motion) with spatiotemporal resolution commensurate with model fidelity. However, computational models are based on mathematical approximations of highly nonlinear physical phenomena, and high-fidelity simulations require substantial resources of time and hardware to set up, validate, simulate, and post-process. In contrast, the physical phenomena that are only approximated in computational simulations are inherently present within <em>in vivo</em>, excised, and synthetic model experiments; physical experiments are thus necessary to validate computational simulations. Synthetic models typically exhibit greater longevity and are generally more materially and geometrically parameterizable than <em>in vivo</em> and excised larynges but less so than computational models.</p>
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<p>Experiments using synthetic VF models possess several key advantages. First, experimental data are directly measured, as opposed to being modeled in simulations. This is critical owing to complex, nonlinear, and coupled phenomena such as turbulence, flow separation, large deformation and strain, collision, acoustic coupling, and radiated acoustics that are, in many cases, difficult to accurately model theoretically or simulate computationally. This first advantage is shared with <em>in vivo</em>/excised larynx-based experiments. Second, data can be gathered in a benchtop setup that would be more difficult to acquire (if not impossible) than <em>in vivo</em>. This is facilitated by synthetic model longevity as well as greater instrument access than <em>in vivo</em> and that is, in some cases, more convenient than in excised larynx experiments. Third, control over synthetic model stiffness and geometry enables parametric exploration of isolated variables. With <em>in vivo</em> and excised larynges, abduction and adduction can be controlled, but there is only limited control over other parameters such as viscoelasticity and underlying geometry. Further, duplicate synthetic models of the same nominal configuration can be fabricated and tested. Fourth, synthetic VF models can vibrate without interruption for a very long time. For example, the study of <a href="#c52" class="usa-link" aria-describedby="c52">Drechsel and Thomson (2008)</a> required approximately 4.5 h of continuous vibration of a synthetic, self-oscillating VF model, in addition to several additional hours of vibration during experiment preparation. Finally, while synthetic model experimentation requires model fabrication and setup, they can be conducted without excised larynx procurement and preparation, and they do not require heating and humidification of air or periodic specimen hydration.</p>
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<p>The previously noted synthetic VF modeling advantages are common to rigid, driven, and self-oscillating models. The need for self-oscillating models stems from human phonation being, fundamentally, a flow-induced vibratory process in which flow, solid, and acoustic dynamics are tightly coupled. Thus, self-oscillating models offer the advantages of synthetic models with the benefit of providing a phonomimetic platform to facilitate the study of phonatory flow-structure-acoustic interactions.</p>
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<p>Synthetic VF models, and particularly self-oscillating VF models, possess limitations and present unique challenges. First, physiological and neuromuscular processes are not represented. Second, owing to the complex tissue composition of the VFs, developing models that accurately mimic human VF form and function is difficult. For example, VF tissue is materially nonlinear (<a href="#c9" class="usa-link" aria-describedby="c9">Alipour‐Haghighi and Titze, 1991</a>; <a href="#c7" class="usa-link" aria-describedby="c7">Alipour <em>et al.</em>, 2013</a>), anisotropic (<a href="#c5" class="usa-link" aria-describedby="c5">Alipour <em>et al.</em>, 2000</a>; <a href="#c41" class="usa-link" aria-describedby="c41">Cook and Mongeau, 2007</a>; <a href="#c42" class="usa-link" aria-describedby="c42">Cook <em>et al.</em>, 2008</a>; <a href="#c43" class="usa-link" aria-describedby="c43">Cook <em>et al.</em>, 2009</a>), and exhibits variations between tissue types (<a href="#c71" class="usa-link" aria-describedby="c71">Gray, 2000</a>) with concomitant spatial variations in stiffness. On the other hand, synthetic models typically have distinct layer transitions and are comprised of linear, isotropic materials (with a few exceptions, as discussed in the following). Further, the geometries and material properties of the human VFs have yet to be fully defined and are highly variable between individuals, across the lifespan, and according to physiological state (e.g., health, hydration, and vocal conditioning). Fabrication challenges arise due to some human VF tissue layers being exceptionally soft and thin (e.g., <a href="#c83" class="usa-link" aria-describedby="c83">Hirano <em>et al.</em>, 1982</a>, reported cover layer thicknesses of around 0.3 mm and combined intermediate and deep lamina propria layer thicknesses of around 1 mm). Third, achieving synthetic VF model self-oscillation with lifelike characteristics (e.g., mucosal wave and collision) is nontrivial. Finally, whereas the motion of driven synthetic models is known and highly repeatable, the motion of self-oscillating models is unknown and must be measured, is less repeatable, and is subject to temporal and vibration-induced material property changes, such as creep and stress relaxation. In many respects, therefore, self-oscillating models occupy a space between rigid/driven models and excised/<em>in vivo</em> larynges in terms of complexity.</p></section><section id="s4"><h2 class="pmc_sec_title">IV. SYNTHETIC, SELF-OSCILLATING VOCAL FOLD MODELS</h2>
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<p>The advantages and limitations of synthetic, self-oscillating VF models have led to numerous development and application research pursuits. A key underlying premise is that if a model is defined with a spatial distribution of stiffness (i.e., a combination of geometry and material properties) that matches the human VFs, and if the airway configuration is similarly representative of the human airway, then the model will vibrate with frequency, onset pressure, and motion characteristics that are typical of human phonation. However, phenomenological modeling approaches have also proved to be beneficial. While efforts to develop truly phonomimetic models are still ongoing, models with favorable flow-induced responses have been developed and successfully used in a range of applications. In this section, the models are presented in detail, and in Sec. <a href="#s5" class="usa-link">V</a>, applications are surveyed.</p>
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<p>While the different synthetic, self-oscillating VF models described in the literature share varying degrees of structural and functional commonality, most can be classified as being one of two types: those comprised of a thin membrane that encapsulates a liquid or viscoelastic substance (e.g., a water-filled latex tube), and those that are predominantly comprised of soft elastic solid(s) (e.g., ultrasoft silicone formed into a VF-like shape). For convenience, these are here referred to as “membranous” and “elastic solid” types, respectively. Other types of self-oscillating models have been studied, such as collapsible tubes for human phonation (<a href="#c37" class="usa-link" aria-describedby="c37">Conrad, 1980</a>, <a href="#c38" class="usa-link" aria-describedby="c38">1985</a>; <a href="#c15" class="usa-link" aria-describedby="c15">Berke <em>et al.</em>, 1991</a>), avian phonation (<a href="#c53" class="usa-link" aria-describedby="c53">Elemans <em>et al.</em>, 2009</a>), and tracheoesophageal speech (<a href="#c192" class="usa-link" aria-describedby="c192">Tourinho and da Silva, 2023</a>); a spring-supported VF model (<a href="#c170" class="usa-link" aria-describedby="c170">Sidlof <em>et al.</em>, 2011</a>); and a vibrating reed (<a href="#c214" class="usa-link" aria-describedby="c214">Yoshinaga <em>et al.</em>, 2021</a>). The membranous and elastic solid models are the focus of this review owing to their prevalence in recent literature and are discussed in Secs. <a href="#s4A" class="usa-link">IV A</a> and <a href="#s4B" class="usa-link">IV B</a>, respectively.</p>
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<section id="s4A"><h3 class="pmc_sec_title">A. Membranous vocal fold models</h3>
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<p>Membranous VF models are comprised of a vibrating, flexible membrane encapsulating a liquid or viscoelastic substance that occupies the space between the membrane and a rigid body. Several examples are shown in Fig. <a href="#f3" class="usa-link">3</a>. Most commonly, this encapsulated region has been filled with a liquid—most commonly water—although other materials have been used. The undeformed shape of the vibrating portion is primarily dictated by the initial membrane and rigid body geometries as well as the hydrostatic pressure within the encapsulated region.</p>
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<figure class="fig xbox font-sm" id="f3"><h4 class="obj_head">FIG. 3.</h4>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g003.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/a928a5ad66f6/JASMAN-000156-001283_1-g003.jpg" loading="lazy" height="824" width="774" alt="FIG. 3."></a></p>
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<div class="p text-right font-secondary"><a href="figure/f3/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>(Color online) (a) Silicone membrane covering a rigid body with fluid filling the space between the membrane and body. (b) Schematic of pressurized latex tube (PLT) model to represent a brass player's lips, along with top view illustration with flow out of the page (inset region with dashed border). (c) Picture of PLT model of human VFs. (d) PLT model. (e,f) Membranous VF model with latex fitted to wedge-shaped body. Credits: (a) Adapted from Titze, I. R., Schmidt, S. S., and Titze, M. R. (<strong>1995</strong>). “Phonation threshold pressure in a physical model of the vocal fold mucosa,” J. Acoust. Soc. Am. <strong>97</strong>, 3080-3084, with permission of Acoustical Society of America. Copyright 1995 Acoustical Society of America. (b) Adapted from Vilain, C. E., Pelorson, X., Hirschberg, A., Le Marrec, L., Op't Root, W., and Willems, J. (<strong>2003</strong>). “Contribution to the physical modeling of the lips. Influence of the mechanical boundary conditions,” Acta Acust. United Ac. <strong>89</strong>, 882-887, with permission of European Acoustics Association. Copyright 2003 European Acoustics Association. (c) Reproduced from Ruty, N., Van Hirtum, A., Pelorson, X., Lopez, I., and Hirschberg, A. (<strong>2005</strong>). “A mechanical experimental setup to simulate vocal folds vibrations: preliminary results,” ZAS Papers in Linguistics <strong>40</strong>, 161-175; licensed under a Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) license (<a href="https://creativecommons.org/licenses/by-sa/4.0/" class="usa-link usa-link--external" data-ga-action="click_feat_suppl" target="_blank" rel="noopener noreferrer">https://creativecommons.org/licenses/by-sa/4.0/</a>). (d) Used with permission from van Hirtum, A., Ahmad, M., Chottin, R., Pelorson, X. (<strong>2023a</strong>). “A Composite Analogy to study the Linear Elasticity of a Pressurised Latex Tube with application to a mechanical vocal fold replica,” Int. J. Appl. Mech. <strong>15</strong>, 2350068. Copyright 2023 World Scientific Publishing Co., Inc. (e,f) Adapted from Krebs, F., Silva, F., Sciamarella, D., and Artana, G. (<strong>2012</strong>). “A three-dimensional study of the glottal jet,” Exp. Fluids <strong>52</strong>, 1133-1147, with permission from SNCSC. Copyright 2011 Springer-Verlag.</p></figcaption></figure><p><a href="#c189" class="usa-link" aria-describedby="c189">Titze <em>et al.</em> (1995)</a> developed and tested a membranous, self-oscillating VF model to explore a previous theoretical expression for phonation threshold pressure (<a href="#c186" class="usa-link" aria-describedby="c186">Titze, 1988</a>). The model, shown in Fig. <a href="#f3" class="usa-link">3(a)</a>, consisted of a stainless-steel VF “body,” a silicone membrane attached to the body to represent the epithelium, and a liquid or other substance filling the gap between the membrane and body to represent the cover. The application of this model is discussed in Sec. <a href="#s5" class="usa-link">V</a>. This synthetic model concept was subsequently used by <a href="#c30" class="usa-link" aria-describedby="c30">Chan <em>et al.</em> (1997)</a> and <a href="#c29" class="usa-link" aria-describedby="c29">Chan and Titze (2006)</a>.</p>
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<p>Around the same time, another type of membranous model was developed, initially to simulate the flow-induced vibration of a brass musical instrument player's lips. The model concept consisted of two parallel water-filled latex tubes [Figs. <a href="#f3" class="usa-link">3(b)</a> and <a href="#f3" class="usa-link">3(c)</a>], wherein air flow between the tubes excited oscillation of the tube walls, enabling study of vibrating lip aerodynamics, vibrations, and acoustics (<a href="#c66" class="usa-link" aria-describedby="c66">Gilbert and Petiot, 1997a</a>,<a href="#c67" class="usa-link" aria-describedby="c67">b</a>; <a href="#c45" class="usa-link" aria-describedby="c45">Cullen <em>et al.</em>, 1998</a>; <a href="#c68" class="usa-link" aria-describedby="c68">Gilbert <em>et al.</em>, 1998</a>; <a href="#c44" class="usa-link" aria-describedby="c44">Cullen <em>et al.</em>, 2000</a>; <a href="#c25" class="usa-link" aria-describedby="c25">Campbell, 2004</a>; <a href="#c146" class="usa-link" aria-describedby="c146">Newton <em>et al.</em>, 2008</a>; <a href="#c203" class="usa-link" aria-describedby="c203">Vilain <em>et al.</em>, 2003</a>; <a href="#c106" class="usa-link" aria-describedby="c106">Lopez <em>et al.</em>, 2006</a>). The lip model of <a href="#c203" class="usa-link" aria-describedby="c203">Vilain <em>et al.</em> (2003)</a> included a metal cylinder with a section of the cylinder removed, latex stretched over the cylinder [Fig. <a href="#f3" class="usa-link">3(c)</a>], and water within the space between the latex tube and the cylinder. The water was connected to a reservoir with an adjustable elevation to control the water pressure within the models and hence the stiffness of the latex tubes. This approach was adopted by <a href="#c157" class="usa-link" aria-describedby="c157">Ruty <em>et al.</em> (2005)</a> to model human VF vibration, and subsequent modifications of this design incorporated features such as asymmetric stiffness (e.g., <a href="#c156" class="usa-link" aria-describedby="c156">Ruty <em>et al.</em>, 2006</a>; <a href="#c75" class="usa-link" aria-describedby="c75">Haas <em>et al.</em>, 2016</a>; <a href="#c113" class="usa-link" aria-describedby="c113">Lucero <em>et al.</em>, 2020</a>) and separate control over glottal gap and stiffness (e.g., <a href="#c75" class="usa-link" aria-describedby="c75">Haas <em>et al.</em>, 2016</a>). Such models have been used in conjunction with reduced-order numerical models (e.g., <a href="#c155" class="usa-link" aria-describedby="c155">Ruty <em>et al.</em>, 2007</a>; <a href="#c200" class="usa-link" aria-describedby="c200">Van Hirtum <em>et al.</em>, 2007</a>; <a href="#c114" class="usa-link" aria-describedby="c114">Lucero <em>et al.</em>, 2009</a>; <a href="#c10" class="usa-link" aria-describedby="c10">Bailly <em>et al.</em>, 2010</a>; <a href="#c34" class="usa-link" aria-describedby="c34">Cisonni <em>et al.</em>, 2011</a>; <a href="#c111" class="usa-link" aria-describedby="c111">Lucero <em>et al.</em>, 2011</a>) and to explore source-tract acoustic coupling (<a href="#c112" class="usa-link" aria-describedby="c112">Lucero <em>et al.</em>, 2012</a>), the influence of vocal tract constriction on phonation onset (<a href="#c201" class="usa-link" aria-describedby="c201">Van Hirtum and Pelorson, 2015</a>), left-right asymmetry (<a href="#c75" class="usa-link" aria-describedby="c75">Haas <em>et al.</em>, 2016</a>; <a href="#c113" class="usa-link" aria-describedby="c113">Lucero <em>et al.</em>, 2020</a>), nodule-like surface growths (<a href="#c116" class="usa-link" aria-describedby="c116">Luizard and Pelorson, 2017</a>), varying initial condition configurations (<a href="#c202" class="usa-link" aria-describedby="c202">Van Hirtum and Pelorson, 2017</a>), external photoglottography (<a href="#c19" class="usa-link" aria-describedby="c19">Bouvet <em>et al.</em>, 2019</a>), and liquid being sprayed on the model surface (<a href="#c198" class="usa-link" aria-describedby="c198">Van Hirtum <em>et al.</em>, 2019</a>; <a href="#c20" class="usa-link" aria-describedby="c20">Bouvet <em>et al.</em>, 2020a</a>,<a href="#c21" class="usa-link" aria-describedby="c21">b</a>). <a href="#c196" class="usa-link" aria-describedby="c196">Van Hirtum <em>et al.</em> (2023a)</a> discussed material stress-strain considerations of the PLT model [Fig. <a href="#f3" class="usa-link">3(d)</a>].</p>
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<p>Variations of the PLT model have been reported. Water-filled, latex membranes attached to a wedge-shaped (rather than cylindrical) body have been developed and used to study asymmetric VF vibration (<a href="#c156" class="usa-link" aria-describedby="c156">Ruty <em>et al.</em>, 2006</a>), constrictions near the VFs (<a href="#c11" class="usa-link" aria-describedby="c11">Bailly <em>et al.</em>, 2008</a>), and three-dimensional (3D) detailed characteristics of the glottal jet (<a href="#c100" class="usa-link" aria-describedby="c100">Krebs <em>et al.</em>, 2012</a>; <a href="#c165" class="usa-link" aria-describedby="c165">Sciamarella <em>et al.</em>, 2012</a>) [see Figs. <a href="#f3" class="usa-link">3(e)</a> and <a href="#f3" class="usa-link">3(f)</a>]. Finally, it is worth noting the limited use of vibrating membranes without adjacent liquid regions as surrogates for VF vibration (<a href="#c89" class="usa-link" aria-describedby="c89">Isogai <em>et al.</em>, 1988</a>; <a href="#c91" class="usa-link" aria-describedby="c91">Kakita, 1988</a>; <a href="#c129" class="usa-link" aria-describedby="c129">Misun, 2005</a>; <a href="#c131" class="usa-link" aria-describedby="c131">Misun <em>et al.</em>, 2011</a>) (see <a href="#c13" class="usa-link" aria-describedby="c13">Baken and Švec, 2012</a>; <a href="#c130" class="usa-link" aria-describedby="c130">Misun, 2012</a>) as well as for modeling voice-producing element prostheses (<a href="#c178" class="usa-link" aria-describedby="c178">Tack <em>et al.</em>, 2006</a>), the avian syrinx (<a href="#c53" class="usa-link" aria-describedby="c53">Elemans <em>et al.</em>, 2009</a>), and the tracheoesophageal segment (<a href="#c192" class="usa-link" aria-describedby="c192">Tourinho and da Silva, 2023</a>). For modeling the vibration of the human VFs, however, the liquid-filled membranous model concept is superior to the “liquid-less” membrane concept since the former more closely resembles the human VF structure.</p>
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<p>Membranous liquid-filled tube models possess several favorable characteristics for studying VF flow-induced vibration. Their fabrication process is generally simpler and less prone to failure than the elastic solid models discussed in Sec. <a href="#s4B" class="usa-link">IV B</a>. As observed by <a href="#c202" class="usa-link" aria-describedby="c202">Van Hirtum and Pelorson (2017)</a>, different degrees of stiffness can be tested using the same model by varying internal liquid pressure, whereas to explore stiffness variation in elastic solid models, multiple models are needed. Liquid-filled tube models appear to be more readily able to achieve onset pressures typical of human phonation; <a href="#c155" class="usa-link" aria-describedby="c155">Ruty <em>et al.</em> (2007)</a> reported onset pressures as low as approximately 250 Pa, and onset pressures in this range are not uncommon for these models. A range of frequencies has been reported; for example, <a href="#c155" class="usa-link" aria-describedby="c155">Ruty <em>et al.</em> (2007)</a> reported a frequency range of 110 to 170 Hz, <a href="#c116" class="usa-link" aria-describedby="c116">Luizard and Pelorson (2017)</a> reported a range from around 70 to 120 Hz, and the model used by <a href="#c100" class="usa-link" aria-describedby="c100">Krebs <em>et al.</em> (2012)</a> and <a href="#c165" class="usa-link" aria-describedby="c165">Sciamarella <em>et al.</em> (2012)</a> vibrated at approximately 55 Hz. The response with different encapsulated substances can be studied. Finally, these models are robust to sustained, large-amplitude vibration. To the best of this author's knowledge, the longevities of membranous and elastic solid models have not been directly compared. However, based on the compositions of these two types of models, it is postulated that relative to elastic models, liquid-filled latex tube models have longer shelf lives than elastic solid models and can be vibrated for longer periods of time without exhibiting material-related changes in model performance. This hypothesis is based on the tube models typically utilizing commercially available rubber materials, whereas elastic solid models are most commonly fabricated using silicone compounds diluted with significantly larger than recommended quantities of silicone thinner and are thus subject to temporal drifts in material properties (discussed further in Sec. <a href="#s4B2" class="usa-link">IV B 2</a>). Direct comparisons between these two model types are needed to confirm this hypothesis, however.</p>
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<p>A few present limitations of membranous models are here noted. While the shape of membranous models can be influenced by the shape of the mounting surface (e.g., cylindrical; <a href="#c155" class="usa-link" aria-describedby="c155">Ruty <em>et al.</em>, 2007</a>, vs wedge-shaped <a href="#c100" class="usa-link" aria-describedby="c100">Krebs <em>et al.</em>, 2012</a>) and by the interior liquid pressure, control over their shapes is somewhat more limited than for elastic solid models. Further, membranous models with nonlinear and/or anisotropic material properties have not yet appeared in the literature. Finally, the vibratory motion of a membranous model was shown by <a href="#c100" class="usa-link" aria-describedby="c100">Krebs <em>et al.</em> (2012)</a>, but in general, the motion of membranous models has not been extensively compared with that of the human VFs.</p></section><section id="s4B"><h3 class="pmc_sec_title">B. Elastic solid vocal fold models</h3>
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<section id="s4B1"><h4 class="pmc_sec_title">1. Overview</h4>
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<p>Elastic solid models are the second primary type of synthetic, self-oscillating VF models discussed in this review. These models are comprised of ultrasoft polymers formed into a VF-like shape. Casting of silicone has been the most common material and fabrication approach, although cast polyurethanes (e.g., <a href="#c184" class="usa-link" aria-describedby="c184">Thomson <em>et al.</em>, 2005</a>; <a href="#c52" class="usa-link" aria-describedby="c52">Drechsel and Thomson, 2008</a>), cast hydrogels (<a href="#c33" class="usa-link" aria-describedby="c33">Choo <em>et al.</em>, 2010</a>), and 3D-printed silicones (discussed in Sec. <a href="#s4B2" class="usa-link">IV B 2</a>) have also been reported.</p>
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<p>Elastic solid models were developed to enable the testing of self-oscillating VF models with prescribed geometries mimicking those of the human VFs. <a href="#c183" class="usa-link" aria-describedby="c183">Thomson <em>et al.</em> (2003</a>, <a href="#c184" class="usa-link" aria-describedby="c184">2005)</a> and <a href="#c185" class="usa-link" aria-describedby="c185">Thomson <em>et al.</em> (2004)</a> reported a single-material, homogeneous model of the human VFs with a shape based on the so-called “M5” profile of <a href="#c162" class="usa-link" aria-describedby="c162">Scherer <em>et al.</em> (2001)</a> which had been defined based on laminagraphic tracings of the VFs. The model of <a href="#c184" class="usa-link" aria-describedby="c184">Thomson <em>et al.</em> (2005)</a> was fabricated by casting a mixture of the liquid polyurethane rubber compound Evergreen and flexibilizer Everflex (both from Smooth-On, Inc., but no longer commercially available) into a VF-shaped mold as shown in Fig. <a href="#f4" class="usa-link">4(a)</a>. The flexibilizer lowered the cured modulus to where it was comparable to that of human VF tissue. The cured model was demolded and mounted to a clear acrylic plate as shown in Fig. <a href="#f4" class="usa-link">4(b)</a>. <a href="#c184" class="usa-link" aria-describedby="c184">Thomson <em>et al.</em> (2005)</a> reported a model vibration frequency of approximately 120 Hz and an onset pressure of 1.15 kPa. This model thus vibrated at a desirable frequency, subglottal pressure, and amplitude, and the fabrication process was relatively straightforward.</p>
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<figure class="fig xbox font-sm" id="f4"><h5 class="obj_head">FIG. 4.</h5>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g004.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/35f4a7d5faa1/JASMAN-000156-001283_1-g004.jpg" loading="lazy" height="1360" width="782" alt="FIG. 4."></a></p>
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<figcaption><p>(Color online) One-layer VF model mold (a), attachment to mounting plate (b), and vibratory motion (c). (d) Two-layer VF model fabrication process and cross section. (e) “EPI” model design and close-up image. (f) Geometry of multi-layer model with adipose tissue layer and superior surface undercut (dimensions in mm). (g) Superior views and cross-sections of multi-layer models of differing geometries. Credits: (a–c) Adapted from Thomson, S. L., Mongeau, L., and Frankel, S. H. (<strong>2005</strong>). “Aerodynamic transfer of energy to the vocal folds,” J. Acoust. Soc. Am. <strong>118</strong>, 1689-1700, with permission of Acoustical Society of America. Copyright 2005 Acoustical Society of America. (d) Adapted from Riede, T., Tokuda, I. T., Munger, J. B., and Thomson, S. L. (<strong>2008</strong>). “Mammalian laryngeal air sacs add variability to the vocal tract impedance: Physical and computational modeling,” J. Acoust. Soc. Am. <strong>124</strong>, 634-647, with permission of Acoustical Society of America. Copyright 2008 Acoustical Society of America. (e) Adapted from Murray, P. R., and Thomson, S. L. (<strong>2012</strong>). “Vibratory responses of synthetic, self-oscillating vocal fold models,” J. Acoust. Soc. Am. <strong>132</strong>, 3428-3438, with permission of Acoustical Society of America. Copyright 2012 Acoustical Society of America. (f) Adapted from Motie-Shirazi, M., Zañartu, M., Peterson, S. D., Mehta, D. D., Kobler, J. B., Hillman, R. E., and Erath, B. D. (<strong>2019</strong>). “Toward development of a vocal fold contact pressure probe: sensor characterization and validation using synthetic vocal fold models,” Appl. Sci. <strong>9</strong>, 3002; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (<a href="https://creativecommons.org/licenses/by/4.0/" class="usa-link usa-link--external" data-ga-action="click_feat_suppl" target="_blank" rel="noopener noreferrer">https://creativecommons.org/licenses/by/4.0/</a>). (g) Used with permission of Elsevier Science & Technology Journals, from Bouvet, A., Pelorson, X., and Van Hirtum, A. (<strong>2020b</strong>). “Influence of water spraying on an oscillating channel,” J. Fluid. Struct. <strong>93</strong>, 102840. Copyright 2019 Elsevier Science & Technology Journals.</p></figcaption></figure><p>Development of this model introduced the concept of fabricating self-oscillating VF models with geometries that could be controlled by creating molds of the desired shapes and with stiffnesses that could be controlled by adjusting the composition of the cast material. This model was termed a “one-layer” model because of its homogeneous composition. Other one-layer models were subsequently developed and used to study aspects of VF flow-induced vibration, such as mechanisms of irregular vibration (<a href="#c17" class="usa-link" aria-describedby="c17">Berry <em>et al.</em>, 2006</a>), acoustic loading and acoustic vs aerodynamic modes of vibration (<a href="#c223" class="usa-link" aria-describedby="c223">Zhang <em>et al.</em>, 2006a</a>,<a href="#c224" class="usa-link" aria-describedby="c224">b</a>, <a href="#c225" class="usa-link" aria-describedby="c225">2009</a>), glottal jet aerodynamic structures (<a href="#c145" class="usa-link" aria-describedby="c145">Neubauer <em>et al.</em>, 2007</a>), glottal contact pressure (<a href="#c174" class="usa-link" aria-describedby="c174">Spencer <em>et al.</em>, 2008</a>; <a href="#c31" class="usa-link" aria-describedby="c31">Chen and Mongeau, 2011</a>), and fluid-structure and fluid-structure-acoustic interactions (<a href="#c14" class="usa-link" aria-describedby="c14">Becker <em>et al.</em>, 2009</a>; <a href="#c95" class="usa-link" aria-describedby="c95">Kniesburges <em>et al.</em>, 2013</a>).</p>
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<p>The one-layer model typically exhibited “swinging door”-type motion and lacked a mucosal wave, as is evident in Fig. <a href="#f4" class="usa-link">4(c)</a> and video <a href="#v1" class="usa-link">Mm. 1.</a>
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<a href="#c223" class="usa-link" aria-describedby="c223">Zhang <em>et al.</em> (2006a</a>,<a href="#c224" class="usa-link" aria-describedby="c224">b</a>, <a href="#c225" class="usa-link" aria-describedby="c225">2009</a>) reported that the “swinging door”-type motion was due to model vibration being acoustically coupled with the upstream flow supply tube resonance. Further, while one-layer model onset pressures were within the pressure-producing capability of the human lung, they were higher than typical human onset pressures. Low onset pressures in one-layer models were facilitated by strong subglottic tube resonance coupling, which is not expected to occur in this manner during conversational speech owing to the lowest subglottic resonance frequency typically being significantly higher than the VF vibration frequency (e.g., <a href="#c300" class="usa-link" aria-describedby="c300">Sundberg <em>et al.</em>, 2013</a>, reported a subglottal resonance frequency of 496 Hz during a vowel sequence produced at 122 Hz).</p>
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<p>Studies were conducted to create models that retained the advantages of the one-layer model but with more favorable characteristics in terms of onset pressure and/or mucosal wave-like motion. Models comprised of two layers of different stiffness, such as shown in Fig. <a href="#f4" class="usa-link">4(d)</a>, were fabricated to mimic the body-cover concept of <a href="#c82" class="usa-link" aria-describedby="c82">Hirano and Kakita (1985)</a> (<a href="#c153" class="usa-link" aria-describedby="c153">Riede <em>et al.</em>, 2008</a>; <a href="#c52" class="usa-link" aria-describedby="c52">Drechsel and Thomson, 2008</a>; <a href="#c127" class="usa-link" aria-describedby="c127">Mendelsohn and Zhang, 2011</a>), although these models did not produce the desired wave-like motion. <a href="#c218" class="usa-link" aria-describedby="c218">Zhang (2011)</a> found that imposing vertical restraints suppressed the inferior-superior model motion that was typical of one-layer models. <a href="#c167" class="usa-link" aria-describedby="c167">Shaw <em>et al.</em> (2012)</a> and <a href="#c211" class="usa-link" aria-describedby="c211">Xuan and Zhang (2014)</a> added fibers to mimic the material nonlinearity of human VF tissue, the latter also including an epithelial layer. <a href="#c195" class="usa-link" aria-describedby="c195">Tur <em>et al.</em> (2023)</a> added fibers of varying characteristics to the ligament layer. While adding fibers resulted in greater sensitivity of frequency to subglottal pressure (<a href="#c167" class="usa-link" aria-describedby="c167">Shaw <em>et al.</em>, 2012</a>), significant frequency range (<a href="#c195" class="usa-link" aria-describedby="c195">Tur <em>et al.</em>, 2023</a>), and improved glottal closure characteristics (<a href="#c211" class="usa-link" aria-describedby="c211">Xuan and Zhang, 2014</a>), the process for adding fibers has not been refined and fibers are generally not presently incorporated in VF models. Adding fibers may yet yield improved mucosal wave-like motion, however, noting that <a href="#c207" class="usa-link" aria-describedby="c207">Wang <em>et al.</em> (2023)</a> found in computational simulations that superior-inferior fiber orientation in the conus elasticus improved mucosal wave characteristics.</p>
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<p>A model with four silicone layers—epithelium, superficial lamina propria, ligament, and body (muscle)—was developed by <a href="#c141" class="usa-link" aria-describedby="c141">Murray and Thomson (2011</a>, <a href="#c142" class="usa-link" aria-describedby="c142">2012)</a> [see Fig. <a href="#f4" class="usa-link">4(e)</a>]. Additionally, a fiber through the ligament layer modeled the inferior-superior restraining effect of the vocal ligament. This so-called “EPI” model also included more significant rounding of the inferior margin than the M5 model. The model vibrated between approximately 85 and 100 Hz, at an onset pressure of between 0.27 and 0.37 kPa, and with favorable mucosal wave-like motion (<a href="#c140" class="usa-link" aria-describedby="c140">Murray, 2011</a>; <a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson, 2012</a>) as shown in <a href="#v2" class="usa-link">Mm. 2.</a> While these characteristics are favorable and the model continues to be used (e.g., <a href="#c168" class="usa-link" aria-describedby="c168">Shimamura and Tokuda, 2017</a>; <a href="#c79" class="usa-link" aria-describedby="c79">Häsner <em>et al.</em>, 2021</a>; <a href="#c215" class="usa-link" aria-describedby="c215">Yoshinaga <em>et al.</em>, 2023</a>), the multiple layers—particularly the soft superficial lamina propria layer—render this model significantly more difficult to fabricate than one- and two-layer models.</p>
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<figure class="fig xbox font-sm" id="v1"><h5 class="obj_head">Mm. 1.</h5>
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<div class="media-box p text-center margin-x-neg-2 tablet:margin-x-0"><video controls="" preload="none" height="360" width="480" poster="https://cdn.ncbi.nlm.nih.gov/pmc/cms/images/video_poster.png"><source src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/a9f1ae27458e/JASMAN-000156-001283_1-S1-pmcvs_normal.mp4"></source><div class="media-fallback margin-x-2 tablet:margin-x-0">
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<div class="object-id font-xs text-base-dark">DOI: 10.1121/10.0028267.1</div>
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<figcaption><p>Stroboscopic video of vibrating one-layer synthetic model of <a href="#c184" class="usa-link" aria-describedby="c184">Thomson <em>et al.</em> (2005)</a>.</p></figcaption></figure><figure class="fig xbox font-sm" id="v2"><h5 class="obj_head">Mm. 2.</h5>
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<div class="media-box p text-center margin-x-neg-2 tablet:margin-x-0"><video controls="" preload="none" height="360" width="400" poster="https://cdn.ncbi.nlm.nih.gov/pmc/cms/images/video_poster.png"><source src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/27d01d736fe5/JASMAN-000156-001283_1-S2-pmcvs_normal.mp4"></source><div class="media-fallback margin-x-2 tablet:margin-x-0">
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<div class="object-id font-xs text-base-dark">DOI: 10.1121/10.0028267.2</div>
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<figcaption><p>High-speed video of vibrating EPI model of <a href="#c140" class="usa-link" aria-describedby="c140">Murray (2011)</a> in a hemilarynx configuration. Video courtesy of Preston R. Murray.</p></figcaption></figure><p>Other notable adjustments to elastic solid VF models include using magnetic resonance imaging (MRI) to define geometry (<a href="#c149" class="usa-link" aria-describedby="c149">Pickup and Thomson, 2010</a>; <a href="#c21" class="usa-link" aria-describedby="c21">Bouvet <em>et al.</em>, 2020b</a>) [Fig. <a href="#f4" class="usa-link">4(g)</a>], “undercutting” of the superior surface for improved mucosal wave-like motion and glottal contact characteristics (<a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em>, 2019</a>), modeling the paraglottic space (adipose tissue) to lower modal frequency (<a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em>, 2019</a>) [Fig. <a href="#f4" class="usa-link">4(f)</a>], using an optimization approach to define geometry (<a href="#c181" class="usa-link" aria-describedby="c181">Taylor and Thomson, 2022</a>; <a href="#c81" class="usa-link" aria-describedby="c81">Hilton and Thomson, 2022</a>), creating a poroelastic cover layer for quantifying the effects of vibration on perfusion pressure-flow relationships (<a href="#c182" class="usa-link" aria-describedby="c182">Thacker, 2023</a>), and creation of a graphite-filled epithelial layer to create electrically-conductive VF models for measuring glottal closure (<a href="#c177" class="usa-link" aria-describedby="c177">Syndergaard <em>et al.</em>, 2017</a>). This latter approach was utilized by <a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em> (2019)</a> and <a href="#c136" class="usa-link" aria-describedby="c136">Motie-Shirazi <em>et al.</em> (2022)</a> to identify VF model impact location and <a href="#c40" class="usa-link" aria-describedby="c40">Conte <em>et al.</em> (2021b)</a> and <a href="#c39" class="usa-link" aria-describedby="c39">Conte <em>et al.</em> (2021a)</a> to study EGG-like signals in VFs simulating normal and pathologic conditions. Variation in anterior-posterior cross-sectional geometry has been incorporated in MRI-based models (<a href="#c23" class="usa-link" aria-describedby="c23">Bouvet <em>et al.</em>, 2021</a>; <a href="#c79" class="usa-link" aria-describedby="c79">Häsner <em>et al.</em>, 2021</a>; <a href="#c121" class="usa-link" aria-describedby="c121">Matsumoto <em>et al.</em>, 2021</a>; <a href="#c121" class="usa-link" aria-describedby="c121">Matsumoto <em>et al.</em>, 2024</a>; <a href="#c199" class="usa-link" aria-describedby="c199">Van Hirtum <em>et al.</em>, 2022</a>; <a href="#c77" class="usa-link" aria-describedby="c77">Hasegawa <em>et al.</em>, 2022</a>; <a href="#c195" class="usa-link" aria-describedby="c195">Tur <em>et al.</em>, 2023</a>). VF models with control over adduction and/or elongation have been developed (<a href="#c167" class="usa-link" aria-describedby="c167">Shaw <em>et al.</em>, 2012</a>; <a href="#c118" class="usa-link" aria-describedby="c118">Manti <em>et al.</em>, 2015</a>; <a href="#c69" class="usa-link" aria-describedby="c69">Girault <em>et al.</em>, 2021</a>; <a href="#c195" class="usa-link" aria-describedby="c195">Tur <em>et al.</em>, 2023</a>) (see Fig. <a href="#f5" class="usa-link">5</a>). <a href="#c80" class="usa-link" aria-describedby="c80">Hilton (2019)</a> introduced an MRI-compatible posturing device capable of abduction and adduction, and <a href="#c24" class="usa-link" aria-describedby="c24">Burks <em>et al.</em> (2021)</a> described an electromagnetic-based concept for adducting VF models.</p>
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<figure class="fig xbox font-sm" id="f5"><h5 class="obj_head">FIG. 5.</h5>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g005.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/e0c6ec856ff3/JASMAN-000156-001283_1-g005.jpg" loading="lazy" height="501" width="717" alt="FIG. 5."></a></p>
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<div class="p text-right font-secondary"><a href="figure/f5/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>(Color online) Schematic of VF posturing device of <a href="#c195" class="usa-link" aria-describedby="c195">Tur <em>et al.</em> (2023)</a>. Adapted from Tur, B., Gühring, L., Wendler, O., Schlicht, S., Drummer, D., and Kniesburges, S. (<strong>2023</strong>). “Effect of ligament fibers on dynamics of synthetic, self-oscillating vocal folds in a biomimetic larynx model,” Bioengineering <strong>10</strong>, 1130; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (<a href="https://creativecommons.org/licenses/by/4.0/" class="usa-link usa-link--external" data-ga-action="click_feat_suppl" target="_blank" rel="noopener noreferrer">https://creativecommons.org/licenses/by/4.0/</a>).</p></figcaption></figure><p>Due to the importance of matching Reynolds, Strouhal, and Mach numbers for flow, vibration, and acoustic similarity, nearly all elastic solid VF models have been life-sized, although some scaled studies have been performed. <a href="#c170" class="usa-link" aria-describedby="c170">Sidlof <em>et al.</em> (2011)</a> developed a 4× scaled-up model consisting of a relatively stiff silicone mounted on lateral springs; the springs facilitated flow-induced vibration frequencies between 10 and 14 Hz. A one-layer, fully elastic 4× model was reported by <a href="#c180" class="usa-link" aria-describedby="c180">Taylor <em>et al.</em> (2019)</a> that exhibited flow-induced vibration at a frequency of 13 to 15 Hz with an onset pressure of 150 Pa when connected to a 7.88-m long tube. Embedded markers were distributed throughout the frontal midplane during fabrication and MRI was used to image the internal deformation of the vibrating model (Fig. <a href="#f6" class="usa-link">6</a>). This model vibrated with primarily “swinging-door”-type motion since it was coupled to upstream tube subglottal acoustic resonance.</p>
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<figure class="fig xbox font-sm" id="f6"><h5 class="obj_head">FIG. 6.</h5>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g006.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/aee47311f275/JASMAN-000156-001283_1-g006.jpg" loading="lazy" height="682" width="797" alt="FIG. 6."></a></p>
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<div class="p text-right font-secondary"><a href="figure/f6/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>(Color online) (a) Fabrication process of 4× model with MRI fiducial markers placed halfway during model casting. (b) Illustration of model mounted in shroud. (c) Motion of model profile and internal markers obtained via MRI. Adapted from Taylor, C. J., Tarbox, G. J., Bolster, B. D., Bangerter, N. K., and Thomson, S. L. (<strong>2019</strong>). “Magnetic resonance imaging-based measurement of internal deformation of vibrating vocal fold models,” J. Acoust. Soc. Am. <strong>145</strong>, 989-997, with permission of Acoustical Society of America. Copyright 2019 Acoustical Society of America.</p></figcaption></figure></section><section id="s4B2"><h4 class="pmc_sec_title">2. Fabrication and materials</h4>
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<p>Most elastic VF models have been fabricated using a sequential casting process such as that which is illustrated in Figs. <a href="#f4" class="usa-link">4(e)</a> and <a href="#f7" class="usa-link">7</a>. Because this process includes steps and materials that have been customized for VF modeling and that pose unique challenges, an overview and discussion of the processes and materials for fabricating elastic solid VF models is here provided.</p>
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<figure class="fig xbox font-sm" id="f7"><h5 class="obj_head">FIG. 7.</h5>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><img class="graphic" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/6a0d4bcccffd/JASMAN-000156-001283_1-g007.jpg" loading="lazy" height="3154" width="3547" alt="FIG. 7."></p>
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<figcaption><p>(Color online) Sequential casting process for fabricating the multi-layer EPI model. Adapted from Murray, P. R., and Thomson, S. L. (<strong>2012</strong>). “Vibratory responses of synthetic, self-oscillating vocal fold models,” J. Acoust. Soc. Am. <strong>132</strong>, 3428-3438, with permission of Acoustical Society of America. Copyright 2012 Acoustical Society of America.</p></figcaption></figure><p>The EPI model was fabricated as follows and as illustrated in Fig. <a href="#f7" class="usa-link">7</a>. Individual negative molds for the body, ligament, and cover layers were created by pouring liquid rubber (Smooth-Sil 950, Smooth-On, Inc., Macungie, PA) around respective 3D-printed positives. The body layer was then created by pouring Ecoflex (EF) 00–30 at a ratio of 1:1:1 into the body mold (i.e., one part EF 00–30 A, one part EF 00–30 B, and one part Silicone Thinner, by weight; all Smooth-On, Inc. products). After the body layer was cured, an acrylic thread was inserted into the ligament mold, EF 00–30 1:1:4 was poured into the ligament mold, and the cured body layer was inserted into the ligament mold for ligament layer formation. Provided that the body layer exterior surface was free from contaminants such as dust, oil, or release agent, the ligament layer naturally bonded to the body layer. After ligament layer curing, EF 00–30 1:1:9 was poured into the superficial lamina propria (SLP) layer mold, and the cured, combined ligament-body structure was inserted into the SLP mold, with the SLP layer then naturally adhering to the ligament and body layers. The cured part was then removed and Dragon Skin (Smooth-On, Inc.) at a ratio of 1:1:1 was poured over the SLP layer to form the epithelial layer, and once cured, the model was trimmed to remove molding guide sections. Powder was applied to the model surface prior to testing to minimize surface tackiness that would cause the model to tear with vibratory collision. Note that the influence of powder applied to candidate silicones for VF modeling was documented by <a href="#c65" class="usa-link" aria-describedby="c65">Gabriel <em>et al.</em> (2019)</a>.</p>
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<p>Commercial materials used to fabricate elastic solid VF models include Evergreen (Smooth-On, Inc.), a now-discontinued two-component polyurethane product; Ecoflex and Solaris, addition-cure families of silicones (Smooth-On, Inc.); Silopren UV Electro 225-1 (Momentive Performance Materials, Inc.), an ultraviolet-cure silicone; and the urethane rubber Vytaflex (Smooth-On, Inc.) Of these, Ecoflex has been the most widely used and is discussed in more detail in the following. The use of Solaris has recently been explored (<a href="#c133" class="usa-link" aria-describedby="c133">Motie-Shirazi, 2022</a>) because it is optically transparent, whereas Ecoflex is only translucent. Silopren UV Electro is also transparent but differs from the other materials in that it cures upon exposure to ultraviolet light. This feature has led to its use in 3D-printed VF models (discussed in the following), but it can also be cast. However, Silopren UV Electro is only distributed in expensive large quantities, thus availability is, at present, a major limitation. Vytaflex has been reported in only one study (<a href="#c88" class="usa-link" aria-describedby="c88">Horacek <em>et al.</em>, 2011</a>), and its potential for VF modeling has not been thoroughly investigated. The addition-cure silicone Dragon Skin (Smooth-On, Inc.) is compatible with the aforementioned silicones and has been used for some VF layers but is generally too stiff for the superficial lamina propria layer. Ecoflex and Dragon Skin are two-component liquid silicone rubber materials available in different formulations with varying pre-cured viscosities and stiffnesses. Ecoflex 00–30 is the most commonly used product in the elastic solid VF models surveyed in this paper. In addition to its use in VF modeling, Ecoflex has been used in numerous other applications, such as wearable devices (e.g., <a href="#c206" class="usa-link" aria-describedby="c206">Wang <em>et al.</em>, 2019</a>), organ phantoms (e.g., <a href="#c1" class="usa-link" aria-describedby="c1">Adams <em>et al.</em>, 2017</a>), and soft robotics (e.g., <a href="#c205" class="usa-link" aria-describedby="c205">Wang <em>et al.</em>, 2021</a>).</p>
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<p>The pre-cured viscosity and post-cured modulus of Ecoflex, as well as the other silicone materials, can be lowered by adding Silicone Thinner or other silicone oils (<a href="#c169" class="usa-link" aria-describedby="c169">Shivapooja <em>et al.</em>, 2016</a>). Silicone Thinner has been used almost exclusively in VF modeling for this purpose. This ability to tune stiffness by varying the amount of Silicone Thinner enables the fabrication of VF models with layers of differing stiffness. As discussed in the following, researchers have reported that EF 00–30 with a mixing ratio of 1:1:0 (part A:part B:thinner, by weight) has a modulus on the order of 60 kPa. The manufacturer recommends a maximum added Silicone Thinner quantity of 10% of the combined weight of parts A and B, or a mixing ratio of 1:1:0.2; however, significantly greater quantities of Silicone Thinner are commonly used in VF modeling. For example, <a href="#c174" class="usa-link" aria-describedby="c174">Spencer <em>et al.</em> (2008)</a> reported a modulus of 6 kPa for a mixing ratio of 1:1:4 (i.e., 200% of the combined weight of parts A and B), and <a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson (2012)</a> reported a modulus of 0.2 kPa for a mixing ratio of 1:1:9 (450% of the combined weight of parts A and B). Models with these higher-than-recommended ratios have been successfully fabricated and used, but drawbacks include difficulties with demolding, leeching, and curing. Other difficulties arising from oversaturation have been recently studied and documented (<a href="#c78" class="usa-link" aria-describedby="c78">Häsner and Birkholz, 2023</a>). Curing can be improved by eliminating or limiting the amount of release agent used when preparing molds (discussed further in the following), curing and/or post-curing in an oven (<a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson, 2012</a>), and curing in a microwave (<a href="#c72" class="usa-link" aria-describedby="c72">Greenwood and Thomson, 2021</a>). The latter results in much faster curing than oven curing, although care must be taken to avoid overheating. Further, reproducibility is a challenge in VF modeling because curability and cured stiffness vary with factors such as silicone liquid component age, gradual separation and settling of silicone liquid material while sitting for extended periods of time, and other environmental factors (e.g., humidity and temperature). Because of such variations, geometric and material properties of fabricated models should be measured, ideally as close as possible to when experiments (e.g., flow-induced vibration tests) are conducted. For in-depth study of some of these effects, see <a href="#c78" class="usa-link" aria-describedby="c78">Häsner and Birkholz (2023)</a>.</p>
|
||
<p>Elastic properties of Ecoflex and other similar materials have been reported elsewhere (e.g., <a href="#c26" class="usa-link" aria-describedby="c26">Case <em>et al.</em>, 2015</a>; <a href="#c147" class="usa-link" aria-describedby="c147">Park <em>et al.</em>, 2018</a>; <a href="#c119" class="usa-link" aria-describedby="c119">Marechal <em>et al.</em>, 2021</a>; <a href="#c46" class="usa-link" aria-describedby="c46">Darby <em>et al.</em>, 2022</a>). The stress-strain response of Ecoflex and Dragon Skin is generally linear at moderately low strains (e.g., <a href="#c167" class="usa-link" aria-describedby="c167">Shaw <em>et al.</em>, 2012</a>; <a href="#c24" class="usa-link" aria-describedby="c24">Burks <em>et al.</em>, 2021</a>; <a href="#c4" class="usa-link" aria-describedby="c4">Ahmad <em>et al.</em>, 2023</a>), but nonlinearity at higher strains has been reported (<a href="#c4" class="usa-link" aria-describedby="c4">Ahmad <em>et al.</em>, 2023</a>). Ecoflex 00–30 modulus of elasticity values from a selection of VF- related publications are listed in Table <a href="#t1" class="usa-link">I</a>; these are included here given the larger range of Silicone Thinner ratios used in VF modeling compared to what is typical in other applications such as those listed previously. These values are representative of those found in the human VFs (e.g., <a href="#c193" class="usa-link" aria-describedby="c193">Tran <em>et al.</em>, 1993</a>; <a href="#c28" class="usa-link" aria-describedby="c28">Chan <em>et al.</em>, 2007</a>; <a href="#c8" class="usa-link" aria-describedby="c8">Alipour and Vigmostad, 2012</a>; <a href="#c27" class="usa-link" aria-describedby="c27">Chan, 2018</a>; <a href="#c36" class="usa-link" aria-describedby="c36">Cochereau <em>et al.</em>, 2020</a>). The Ecoflex 00–30 data are also plotted in Fig. <a href="#f8" class="usa-link">8</a> with a curve fit. Significant variations between reported values at given ratios are evident and may be attributable to material properties actually varying due to fabrication environmental and process considerations (e.g., temperature, humidity, time between curing and testing, and pre-mixing settling of material), variations in material testing protocols (e.g., sample geometry, strain rate, applied force in rheometry, engineering vs true stress/strain), and/or different values of Poisson's ratio used when converting shear modulus to tensile modulus. Consequently, it is recommended that standardized testing procedures be followed, specifically <a href="#c280" class="usa-link" aria-describedby="c280">ASTM-D412-16 (2016)</a> for stress vs strain measurement (as was used by <a href="#c119" class="usa-link" aria-describedby="c119">Marechal <em>et al.</em>, 2021</a>). It is also recommended that, in the case of rheological testing, the Poisson's ratio also be measured for transparent conversion from shear to tensile modulus values. Finally, as many synthetic VF models possess multiple layers of differing stiffness, the effective properties of combined layers vs individual layers constitute an important characteristic that should be studied, such as has been reported by <a href="#c2" class="usa-link" aria-describedby="c2">Ahmad <em>et al.</em> (2021)</a>, <a href="#c3" class="usa-link" aria-describedby="c3">Ahmad <em>et al.</em> (2022)</a>, and <a href="#c4" class="usa-link" aria-describedby="c4">Ahmad <em>et al.</em> (2023)</a>, as well as <a href="#c197" class="usa-link" aria-describedby="c197">Van Hirtum <em>et al.</em> (2023b)</a>.</p>
|
||
<section class="tw xbox font-sm" id="t1"><h5 class="obj_head">TABLE I.</h5>
|
||
<div class="caption p"><p>Tensile modulus of Ecoflex 00-30 with various mixing ratios and testing methods reported in a selection of VF modeling-related literature. “0” denotes a mixing ration of 1:1:0 (part A:part B:thinner, by weight), “1” denotes 1:1:1, and so on.</p></div>
|
||
<div class="tbl-box p" tabindex="0"><table class="content" frame="hsides" rules="groups" border="1">
|
||
<colgroup span="1">
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<col align="left" span="1">
|
||
<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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<col align="center" span="1">
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</colgroup>
|
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<thead><tr>
|
||
<th align="left" colspan="1" rowspan="1"></th>
|
||
<th align="center" colspan="1" rowspan="1">0</th>
|
||
<th align="center" colspan="1" rowspan="1">0.5</th>
|
||
<th align="center" colspan="1" rowspan="1">0.8</th>
|
||
<th align="center" colspan="1" rowspan="1">1</th>
|
||
<th align="center" colspan="1" rowspan="1">1.2</th>
|
||
<th align="center" colspan="1" rowspan="1">1.4</th>
|
||
<th align="center" colspan="1" rowspan="1">1.6</th>
|
||
<th align="center" colspan="1" rowspan="1">1.8</th>
|
||
<th align="center" colspan="1" rowspan="1">2</th>
|
||
<th align="center" colspan="1" rowspan="1">3</th>
|
||
<th align="center" colspan="1" rowspan="1">4</th>
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||
<th align="center" colspan="1" rowspan="1">5</th>
|
||
<th align="center" colspan="1" rowspan="1">5.5</th>
|
||
<th align="center" colspan="1" rowspan="1">6</th>
|
||
<th align="center" colspan="1" rowspan="1">6.5</th>
|
||
<th align="center" colspan="1" rowspan="1">8</th>
|
||
<th align="center" colspan="1" rowspan="1">9</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c153" class="usa-link" aria-describedby="c153">Riede <em>et al.</em> (2008)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">10</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">2</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c174" class="usa-link" aria-describedby="c174">Spencer <em>et al.</em> (2008)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">6</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c148" class="usa-link" aria-describedby="c148">Pickup and Thomson (2009)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">7.8-9.0 <a href="#t1n1" class="usa-link"><sup>a</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">5.2</td>
|
||
<td colspan="1" rowspan="1">2.9-3.3 <a href="#t1n1" class="usa-link"><sup>a</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c149" class="usa-link" aria-describedby="c149">Pickup and Thomson (2010)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">8.5</td>
|
||
<td colspan="1" rowspan="1">5.2</td>
|
||
<td colspan="1" rowspan="1">2.94</td>
|
||
<td colspan="1" rowspan="1">1.5</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c141" class="usa-link" aria-describedby="c141">Murray and Thomson (2011)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">11.8</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">1.6</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.2</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson (2012)</a>
|
||
<a href="#t1n2" class="usa-link">
|
||
<sup>b</sup>
|
||
</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">10.6</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">8.18</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">1.15</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.227</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c167" class="usa-link" aria-describedby="c167">Shaw <em>et al.</em> (2012)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">10.53</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">3.34</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c95" class="usa-link" aria-describedby="c95">Kniesburges <em>et al.</em> (2013)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">4.4</td>
|
||
<td colspan="1" rowspan="1">2.5</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c118" class="usa-link" aria-describedby="c118">Manti <em>et al.</em> (2015)</a>
|
||
<a href="#t1n3" class="usa-link"><sup>c</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">45.9</td>
|
||
<td colspan="1" rowspan="1">38.6</td>
|
||
<td colspan="1" rowspan="1">32.1</td>
|
||
<td colspan="1" rowspan="1">25.1</td>
|
||
<td colspan="1" rowspan="1">20.9</td>
|
||
<td colspan="1" rowspan="1">17.7</td>
|
||
<td colspan="1" rowspan="1">15.2</td>
|
||
<td colspan="1" rowspan="1">11.5</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c209" class="usa-link" aria-describedby="c209">Weiss <em>et al.</em> (2016)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">70.2</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">10.03</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">3.10</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c65" class="usa-link" aria-describedby="c65">Gabriel <em>et al.</em> (2019)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">67</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">1.1</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c76" class="usa-link" aria-describedby="c76">Hadwin <em>et al.</em> (2019)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">11.8</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">2</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.6</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em> (2019)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">17.3</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">6.8</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.95</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c180" class="usa-link" aria-describedby="c180">Taylor <em>et al.</em> (2019)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">2</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c22" class="usa-link" aria-describedby="c22">Bouvet <em>et al.</em> (2020c)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">21.9</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">10.4</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">4.9</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.2</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c24" class="usa-link" aria-describedby="c24">Burks <em>et al.</em> (2021)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">42.9</td>
|
||
<td colspan="1" rowspan="1">27.9</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">20.6</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c134" class="usa-link" aria-describedby="c134">Motie-Shirazi <em>et al.</em> (2021a)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">7.13</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">4.04</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">1.10</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c176" class="usa-link" aria-describedby="c176">Stewart and Erath (2021)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">9.38</td>
|
||
<td colspan="1" rowspan="1">5.78</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">2.22</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c181" class="usa-link" aria-describedby="c181">Taylor and Thomson (2022)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.96</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.63</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c137" class="usa-link" aria-describedby="c137">Motie-Shirazi <em>et al.</em> (2023)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">13.2</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">5.8</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">1.0</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<div class="p text-right font-secondary"><a href="table/t1/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
|
||
<div class="tw-foot p">
|
||
<div class="fn" id="t1n1">
|
||
<sup>
|
||
<sup>a</sup>
|
||
</sup><p class="display-inline">Range provided since multiple values were reported from different specimens.</p>
|
||
</div>
|
||
<div class="fn" id="t1n2">
|
||
<sup>
|
||
<sup>b</sup>
|
||
</sup><p class="display-inline">Values converted from published shear modulus data at 1.26 Hz using the relationship <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M1" display="inline" overflow="linebreak"><mi>E</mi><mo>=</mo><mn>2</mn><mi>G</mi><mo stretchy="false">(</mo><mn>1</mn><mo>+</mo><mi>ν</mi><mo stretchy="false">)</mo></math></span>, with <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M2" display="inline" overflow="linebreak"><mi>ν</mi><mo>=</mo><mn>0.49</mn></math></span>, where <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M3" display="inline" overflow="linebreak"><mi>E</mi></math></span> and <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M4" display="inline" overflow="linebreak"><mi>G</mi></math></span> denote tensile and shear modulus, respectively, and <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M5" display="inline" overflow="linebreak"><mi>ν</mi></math></span> denotes Poisson's ratio.</p>
|
||
</div>
|
||
<div class="fn" id="t1n3">
|
||
<sup>
|
||
<sup>c</sup>
|
||
</sup><p class="display-inline">Values obtained by digitizing the published plot of modulus vs thinner ratio.</p>
|
||
</div>
|
||
</div></section><figure class="fig xbox font-sm" id="f8"><h5 class="obj_head">FIG. 8.</h5>
|
||
<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g008.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/47bbadc61fcf/JASMAN-000156-001283_1-g008.jpg" loading="lazy" height="731" width="777" alt="FIG. 8."></a></p>
|
||
<div class="p text-right font-secondary"><a href="figure/f8/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
|
||
<figcaption><p>Ecoflex 00-30 modulus of elasticity, <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M6" display="inline" overflow="linebreak"><mi>E</mi></math></span>, vs thinner ratio, <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M7" display="inline" overflow="linebreak"><mi>r</mi></math></span>. Note the use of a log scale for the <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M8" display="inline" overflow="linebreak"><mi>y</mi></math></span>-axis. Gray open markers are individual values reported in Table <a href="#t1" class="usa-link">I</a>. Black solid markers are values averaged for each integer ratio from <em>r</em> = 0 to <em>r</em> = 8. The solid line is the rational polynomial <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M9" display="inline" overflow="linebreak"><mi>E</mi><mo>=</mo><mo>(</mo><mn>0.5354</mn><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>9.017</mn><mi>r</mi><mo>+</mo><mn>42.71</mn><mo>)</mo><mo>/</mo><mo>(</mo><mi>r</mi><mo>+</mo><mn>0.5398</mn><mo>)</mo></math></span> with an R-square value of 0.84. The polynomial provides a reasonable fit to the data for <em>r</em> = 1 through <em>r</em> = 8, but poorly for <em>r</em> = 0 and <em>r</em> = 9.</p></figcaption></figure><p>Poisson's ratio data for Ecoflex 00–30 from two VF modeling studies are listed in Table <a href="#t2" class="usa-link">II</a>. Methods for analyzing silicone material properties for VF modeling, including those of composite layers, can be found in <a href="#c2" class="usa-link" aria-describedby="c2">Ahmad <em>et al.</em> (2021)</a>, <a href="#c3" class="usa-link" aria-describedby="c3">Ahmad <em>et al.</em> (2022)</a>, and <a href="#c4" class="usa-link" aria-describedby="c4">Ahmad <em>et al.</em> (2023)</a>, as well as <a href="#c197" class="usa-link" aria-describedby="c197">Van Hirtum <em>et al.</em> (2023b)</a>. Additionally, two surface characteristics, tackiness and waviness, of various silicones that could be used for VF modeling, including Ecoflex 00–30, were explored by <a href="#c65" class="usa-link" aria-describedby="c65">Gabriel <em>et al.</em> (2019)</a>.</p>
|
||
<section class="tw xbox font-sm" id="t2"><h5 class="obj_head">TABLE II.</h5>
|
||
<div class="caption p"><p>Poisson's ratio for different mixing ratios of Ecoflex 00-30 and thinner.</p></div>
|
||
<div class="tbl-box p" tabindex="0"><table class="content" frame="hsides" rules="groups" border="1">
|
||
<colgroup span="1">
|
||
<col align="left" span="1">
|
||
<col align="char" char="." span="1">
|
||
<col align="char" char="." span="1">
|
||
<col align="char" char="." span="1">
|
||
<col align="char" char="." span="1">
|
||
<col align="char" char="." span="1">
|
||
</colgroup>
|
||
<thead><tr>
|
||
<th align="left" colspan="1" rowspan="1"></th>
|
||
<th align="center" colspan="1" rowspan="1">1:1:0</th>
|
||
<th align="center" colspan="1" rowspan="1">1:1:0.5</th>
|
||
<th align="center" colspan="1" rowspan="1">1:1:1</th>
|
||
<th align="center" colspan="1" rowspan="1">1:1:2</th>
|
||
<th align="center" colspan="1" rowspan="1">1:1:4</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c209" class="usa-link" aria-describedby="c209">Weiss <em>et al.</em> (2016)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.475</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1">0.457</td>
|
||
<td colspan="1" rowspan="1">0.460</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1">
|
||
<a href="#c24" class="usa-link" aria-describedby="c24">Burks <em>et al.</em> (2021)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.46</td>
|
||
<td colspan="1" rowspan="1">0.45</td>
|
||
<td colspan="1" rowspan="1">0.44</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<div class="p text-right font-secondary"><a href="table/t2/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div></section><p>Common difficulties encountered when casting elastic solid VF models include inconsistency over time of uncured material composition due to long-term sedimentation while not being used, inadequate mixing of material parts, entrainment of air bubbles during mixing and pouring, incomplete curing after mixing, and material tearing during demolding. Effects of sedimentation can be mitigated by thoroughly mixing each individual material—including scraping the container bottom—prior to weighing out amounts for mixing. Complete mixing can be most effectively and efficiently achieved using dual axis centrifugal mixers, also termed planetary centrifugal mixers (e.g., FlackTek, Inc., Landrum, SC, USA; THINKY U.S.A., Inc., Laguna Hills, CA, USA; Torrey Hills Technology, San Diego, SC, USA). Air bubbles formed during mixing can be removed by vacuum degassing, and air entrainment during pouring can be avoided by employing proper pouring techniques.</p>
|
||
<p>Incomplete curing and material tearing during the demolding of ultrasoft silicones are largely due to the use of large quantities of thinner. Consequently, some models are prone to low yield when fabricating ultrasoft layers (such as the superficial lamina propria layer of the EPI model). Post-cure oven treatment improves, but does not always guarantee, curing. Release agent is typically applied to molds to facilitate demolding. However, insufficient release agent leads to cured material sticking to the mold, and too much release agent inhibits curing. Alternative fabrication processes have therefore been explored. One such approach has been the use of soluble molds or mold negatives. In <a href="#c208" class="usa-link" aria-describedby="c208">Ward (2014)</a>, VF models were cast into molds comprised of compacted powdered sugar blocks that had been milled into the desired shape. After the silicone had been poured and cured in the molds, the molds were dissolved with water. This process required the creation of a new set of molds for each model but did not require a release agent and was immune to the primary demolding difficulties associated with casting silicone in traditional molds. <a href="#c79" class="usa-link" aria-describedby="c79">Häsner <em>et al.</em> (2021)</a> demonstrated the use of water-soluble 3D-printed negatives using polyvinyl alcohol (PVA) [see Fig. <a href="#f9" class="usa-link">9(a)</a>]. This method holds significant promise for VF modeling owing to the speed and flexibility of various 3D printing techniques for mold and mold negative fabrication. Additionally, methods for 3D printing VF models have been reported, including homogeneous models with a poured epithelial layer (<a href="#c154" class="usa-link" aria-describedby="c154">Romero <em>et al.</em>, 2021</a>) as well as multi-layer models with discrete layers of different stiffness (<a href="#c72" class="usa-link" aria-describedby="c72">Greenwood and Thomson, 2021</a>) and with material stiffness gradients (<a href="#c216" class="usa-link" aria-describedby="c216">Young <em>et al.</em>, 2024</a>) [see Figs. <a href="#f9" class="usa-link">9(b)–9(d)</a>]. In these methods, liquid silicone (Ecoflex or UV Electro) is extruded into a gel-like support matrix as is illustrated in Figs. <a href="#f9" class="usa-link">9(c)</a> and <a href="#f9" class="usa-link">9(d)</a> and as can be seen in <a href="#v3" class="usa-link">Mm. 3.</a> Advantages of 3D printing VF models include omission of the demolding step, ability to efficiently print new geometries without making new molds, possible control over anisotropy by varying print orientation, alternative methods of creating spatial stiffness variations, and potential ability to 3D print geometries that could not be cast. Disadvantages include coarser spatial resolution than casting, the need for specialized hardware and software tools, and the fact that 3D printing ultrasoft silicone is a relatively immature technology.</p>
|
||
<figure class="fig xbox font-sm" id="f9"><h5 class="obj_head">FIG. 9.</h5>
|
||
<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g009.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/2839b5726dd2/JASMAN-000156-001283_1-g009.jpg" loading="lazy" height="1857" width="797" alt="FIG. 9."></a></p>
|
||
<div class="p text-right font-secondary"><a href="figure/f9/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>(Color online) Water-soluble (a) and additive manufacturing (b-d) techniques for fabricating elastic solid VF models. (a) Combination of non-water-soluble and water-soluble 3D-printed molds and mold negatives. (b) One-layer model pictured at three instances during printing. (c) Multi-layer model fabricated using embedded 3D printing. (d) Multi-layer model with stiffness gradient fabricated using functionally graded 3D printing. Credits: (a) Adapted with permission from Häsner, P., Prescher, A. and Birkholz, P. (<strong>2021</strong>). “Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds,” J. Acoust. Soc. Am. <strong>149</strong>, 466-475. Copyright 2021 Acoustical Society of America. (b) Adapted from Romero, R. G. T., Colton, M. B., and Thomson, S. L. (<strong>2020</strong>). “3D-printed synthetic vocal fold models,” J. Voice <strong>35</strong>, 685-694, Copyright 2020 The Voice Foundation. (c) Adapted with permission from Greenwood, T. E. and Thomson, S. L. (<strong>2021</strong>). “Embedded 3D printing of multi-layer, self-oscillating vocal fold models,” J. Biomech. <strong>121</strong>, 110388. Copyright 2021, Elsevier. (d) Adapted from Young, C. A., O'Bannon, M., Thomson, S. L. (<strong>2024</strong>). “Three-dimensional printing of ultrasoft silicone with a functional stiffness gradient,” 3D Print. Addit. Manuf. <strong>11</strong>, 435-445; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (<a href="https://creativecommons.org/licenses/by/4.0/" class="usa-link usa-link--external" data-ga-action="click_feat_suppl" target="_blank" rel="noopener noreferrer">https://creativecommons.org/licenses/by/4.0/</a>).</p></figcaption></figure><figure class="fig xbox font-sm" id="v3"><h5 class="obj_head">Mm. 3.</h5>
|
||
<div class="media-box p text-center margin-x-neg-2 tablet:margin-x-0"><video controls="" preload="none" height="360" width="640" poster="https://cdn.ncbi.nlm.nih.gov/pmc/cms/images/video_poster.png"><source src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/70e5ce539c6c/JASMAN-000156-001283_1-S3-pmcvs_normal.mp4"></source><div class="media-fallback margin-x-2 tablet:margin-x-0">
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||
<div>Your browser is not supporting the HTML5 <video> element.</div>
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<div>You may download that video as a file and play it with a player of you choice.</div>
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<p><a href="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/70e5ce539c6c/JASMAN-000156-001283_1-S3-pmcvs_normal.mp4" class="usa-link">Download video stream</a>.</p>
|
||
</div></video></div>
|
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<div class="media p">
|
||
<div class="caption">
|
||
<a href="/articles/instance/11348498/bin/JASMAN-000156-001283_1-S3.mp4" data-ga-action="click_feat_suppl" class="usa-link">Download video file</a><sup> (58.8MB, mp4) </sup>
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</div>
|
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<div class="object-id font-xs text-base-dark">DOI: 10.1121/10.0028267.3</div>
|
||
</div>
|
||
<div class="p text-right font-secondary"><a href="figure/v3/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>Time-lapse video showing 3D printing of silicone VF model reported by <a href="#c154" class="usa-link" aria-describedby="c154">Romero <em>et al.</em> (2021)</a>. Video courtesy of Taylor E. Greenwood and Ryan G. T. Romero.</p></figcaption></figure><p>Currently, issues with consistency, repeatability, and fabrication yield are the greatest limitations of elastic solid VF modeling, and membranous models are superior in these regards. However, their ability to be fabricated into specific geometries with spatial control over stiffness is a notable strength. Future development in materials and fabrication processes will likely result in elastic solid modeling improvements. Ultimately, given their respective advantages and limitations, it is anticipated that both membranous and elastic solid models will continue to be used in phonation research in the foreseeable future.</p></section></section></section><section id="s5"><h2 class="pmc_sec_title">V. APPLICATIONS</h2>
|
||
<p>Synthetic VF models have been used for a wide variety of purposes, ranging from theoretical model validation to experimental exploration of complex fluid, solid, and acoustic phenomena. In this section, examples of such applications are discussed. Additionally, values for measures of primary relevance to phonation are summarized in Table <a href="#t3" class="usa-link">III</a> for membranous and elastic solid VF models along with corresponding human <em>in vivo</em> values.</p>
|
||
<section class="tw xbox font-sm" id="t3"><h3 class="obj_head">TABLE III.</h3>
|
||
<div class="caption p"><p>Values for primary phonatory measures from selected membranous and elastic solid VF model studies, along with typical values for human speech. Some values are approximate owing to their having been obtained from figures in the original sources.</p></div>
|
||
<div class="tbl-box p" tabindex="0"><table class="content" frame="hsides" rules="groups" border="1">
|
||
<colgroup span="1">
|
||
<col align="left" span="1">
|
||
<col align="center" span="1">
|
||
<col align="center" span="1">
|
||
<col align="center" span="1">
|
||
</colgroup>
|
||
<thead><tr>
|
||
<th align="left" colspan="1" rowspan="1"></th>
|
||
<th align="center" colspan="1" rowspan="1">Onset pressure (kPa)</th>
|
||
<th align="center" colspan="1" rowspan="1">Frequency (Hz)</th>
|
||
<th align="center" colspan="1" rowspan="1">Maximum glottal width (mm)</th>
|
||
</tr></thead>
|
||
<tbody>
|
||
<tr>
|
||
<td colspan="1" rowspan="2">
|
||
<strong>Human VFs (in vivo)</strong>
|
||
</td>
|
||
<td colspan="1" rowspan="2">0.29–0.49 <a href="#t3n1" class="usa-link"><sup>a</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">100–136 (male) <a href="#t3n1" class="usa-link"><sup>a</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="2">2 <a href="#t3n2" class="usa-link"><sup>b</sup></a>
|
||
</td>
|
||
</tr>
|
||
<tr><td colspan="1" rowspan="1">189–224 (female) <a href="#t3n1" class="usa-link"><sup>a</sup></a>
|
||
</td></tr>
|
||
<tr><td colspan="4" rowspan="1">Membranous models</td></tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c155" class="usa-link" aria-describedby="c155">Ruty <em>et al.</em> (2007)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.27–0.97</td>
|
||
<td colspan="1" rowspan="1">107-168</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c11" class="usa-link" aria-describedby="c11">Bailly <em>et al.</em> (2008)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.47–1.7</td>
|
||
<td colspan="1" rowspan="1">153-180</td>
|
||
<td colspan="1" rowspan="1">1.9</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c116" class="usa-link" aria-describedby="c116">Luizard and Pelorson (2017)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.37–1.0<a href="#t3n3" class="usa-link"><sup>c</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">75–226<a href="#t3n3" class="usa-link"><sup>c</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr><td colspan="4" rowspan="1">Elastic solid models</td></tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson (2012)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.27–1.68</td>
|
||
<td colspan="1" rowspan="1">86–136</td>
|
||
<td colspan="1" rowspan="1">1.2-4.2</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c225" class="usa-link" aria-describedby="c225">Zhang <em>et al.</em> (2009)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.7–2.7</td>
|
||
<td colspan="1" rowspan="1">105–162</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em> (2019)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">1.6</td>
|
||
<td colspan="1" rowspan="1">168</td>
|
||
<td colspan="1" rowspan="1">1.48 <a href="#t3n4" class="usa-link"><sup>d</sup></a>
|
||
</td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c191" class="usa-link" aria-describedby="c191">Tokuda and Shimamura (2017)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">0.4–0.77</td>
|
||
<td colspan="1" rowspan="1">70–126<a href="#t3n5" class="usa-link"><sup>e</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
<tr>
|
||
<td colspan="1" rowspan="1"> <a href="#c195" class="usa-link" aria-describedby="c195">Tur <em>et al.</em> (2023)</a>
|
||
</td>
|
||
<td colspan="1" rowspan="1">1.6–4.8</td>
|
||
<td colspan="1" rowspan="1">227–454<a href="#t3n5" class="usa-link"><sup>e</sup></a>
|
||
</td>
|
||
<td colspan="1" rowspan="1"></td>
|
||
</tr>
|
||
</tbody>
|
||
</table></div>
|
||
<div class="p text-right font-secondary"><a href="table/t3/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
|
||
<div class="tw-foot p">
|
||
<div class="fn" id="t3n1">
|
||
<sup>
|
||
<sup>a</sup>
|
||
</sup><p class="display-inline"><a href="#c12" class="usa-link" aria-describedby="c12">Baken and Orlikoff (2000)</a>.</p>
|
||
</div>
|
||
<div class="fn" id="t3n2">
|
||
<sup>
|
||
<sup>b</sup>
|
||
</sup><p class="display-inline"><a href="#c164" class="usa-link" aria-describedby="c164">Schuberth <em>et al.</em> (2002)</a>.</p>
|
||
</div>
|
||
<div class="fn" id="t3n3">
|
||
<sup>
|
||
<sup>c</sup>
|
||
</sup><p class="display-inline">Study included VF models with and without nodule-like masses; values reported here are without.</p>
|
||
</div>
|
||
<div class="fn" id="t3n4">
|
||
<sup>
|
||
<sup>d</sup>
|
||
</sup><p class="display-inline">Study used a single VF model in a hemilarynx position. The maximum glottal width value listed here is double their reported value of 0.74 mm.</p>
|
||
</div>
|
||
<div class="fn" id="t3n5">
|
||
<sup>
|
||
<sup>e</sup>
|
||
</sup><p class="display-inline">Values reported here are at onset.</p>
|
||
</div>
|
||
</div></section><p><a href="#c186" class="usa-link" aria-describedby="c186">Titze (1988)</a> developed a theoretical expression for phonation onset pressure, <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M10" display="inline" overflow="linebreak"><msub><mrow><mi>P</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msub></math></span>,
|
||
</p>
|
||
<table class="disp-formula p" id="d1"><tr>
|
||
<td class="formula"><math id="M11" display="block" overflow="linebreak"><msub><mrow><mi>P</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msub><mo>=</mo><mfenced close=")" open="(" separators="|"><mrow><mfrac><mrow><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub></mrow><mrow><mi>T</mi></mrow></mfrac></mrow></mfenced><mi>B</mi><mi>c</mi><msub><mrow><mi>ξ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></td>
|
||
<td class="label">(1)</td>
|
||
</tr></table>
|
||
<p>where <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M12" display="inline" overflow="linebreak"><msub><mrow><mi>k</mi></mrow><mrow><mi>t</mi></mrow></msub></math></span> is the transglottal pressure coefficient, <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M13" display="inline" overflow="linebreak"><mi>T</mi></math></span> is the vocal fold thickness, <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M14" display="inline" overflow="linebreak"><mi>B</mi></math></span> is a viscous damping coefficient, <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M15" display="inline" overflow="linebreak"><mi>c</mi></math></span> is the mucosal wave velocity, and <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M16" display="inline" overflow="linebreak"><msub><mrow><mi>ξ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is the pre-phonatory glottal half-width. <a href="#c189" class="usa-link" aria-describedby="c189">Titze <em>et al.</em> (1995)</a> used the membranous VF model shown in Fig. <a href="#f3" class="usa-link">3(a)</a> to test the predicted linear relationships between <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M17" display="inline" overflow="linebreak"><msub><mrow><mi>P</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msub></math></span> and <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M18" display="inline" overflow="linebreak"><msub><mrow><mi>ξ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> and between <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M19" display="inline" overflow="linebreak"><msub><mrow><mi>P</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msub></math></span> and <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M20" display="inline" overflow="linebreak"><mi>B</mi></math></span>. Onset and offset pressures were measured for varying degrees of pre-phonatory glottal half-width and different fluids, with the lowest onset pressures being on the order of 0.4 kPa for water and from around 0.45 to 0.5 kPa for higher-viscosity fluids. The expected linear relationship between <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M21" display="inline" overflow="linebreak"><msub><mrow><mi>P</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msub></math></span> and <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M22" display="inline" overflow="linebreak"><mi>B</mi></math></span> was confirmed. However, while a portion of the <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M23" display="inline" overflow="linebreak"><msub><mrow><mi>P</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msub></math></span> vs <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M24" display="inline" overflow="linebreak"><msub><mrow><mi>ξ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> data were linear, the data also suggested the presence of an optimal non-zero pre-phonatory glottal gap for minimum <span xmlns:mml="http://www.w3.org/1998/Math/MathML">
|
||
<math id="M25" display="inline" overflow="linebreak"><msub><mrow><mi>P</mi></mrow><mrow><mi>t</mi><mi>h</mi></mrow></msub></math></span> and showed consistent hysteresis between onset and offset threshold pressures (Fig. <a href="#f10" class="usa-link">10</a>). These trends and other associated phenomena were subsequently explored by <a href="#c107" class="usa-link" aria-describedby="c107">Lucero (1995</a>, <a href="#c108" class="usa-link" aria-describedby="c108">1996</a>, <a href="#c109" class="usa-link" aria-describedby="c109">1998</a>, <a href="#c110" class="usa-link" aria-describedby="c110">1999</a>, <a href="#c114" class="usa-link" aria-describedby="c114">2009)</a>, <a href="#c64" class="usa-link" aria-describedby="c64">Fulcher <em>et al.</em> (2019)</a>, and <a href="#c113" class="usa-link" aria-describedby="c113">Lucero <em>et al.</em> (2020)</a>. Additional studies using synthetic models based on that of <a href="#c189" class="usa-link" aria-describedby="c189">Titze <em>et al.</em> (1995)</a> were conducted by <a href="#c30" class="usa-link" aria-describedby="c30">Chan <em>et al.</em> (1997)</a> and <a href="#c29" class="usa-link" aria-describedby="c29">Chan and Titze (2006)</a> to explore relationships between threshold pressure and prephonatory angle, membrane thickness, vocal tract inertance, and other cover materials, including fat, hyaluronic acid, and fibronectin.</p>
|
||
<figure class="fig xbox font-sm" id="f10"><h3 class="obj_head">FIG. 10.</h3>
|
||
<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g010.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/a417c1da9717/JASMAN-000156-001283_1-g010.jpg" loading="lazy" height="728" width="737" alt="FIG. 10."></a></p>
|
||
<div class="p text-right font-secondary"><a href="figure/f10/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
|
||
<figcaption><p>Measured threshold pressure vs pre-phonatory glottal half-width at onset (open circles) and offset (closed circles). Reproduced with permission from Titze, I. R., Schmidt, S. S., and Titze, M. R. (<strong>1995</strong>). “Phonation threshold pressure in a physical model of the vocal fold mucosa,” J. Acoust. Soc. Am. <strong>97</strong>, 3080–3084. Copyright 1995 Acoustical Society of America.</p></figcaption></figure><p>Physical models have also been used for the development, validation, and exploration of theoretical and low-order models of VF flow-induced vibration (e.g., <a href="#c155" class="usa-link" aria-describedby="c155">Ruty <em>et al.</em>, 2007</a>; <a href="#c200" class="usa-link" aria-describedby="c200">Van Hirtum <em>et al.</em>, 2007</a>; <a href="#c201" class="usa-link" aria-describedby="c201">Van Hirtum and Pelorson, 2015</a>; <a href="#c191" class="usa-link" aria-describedby="c191">Tokuda and Shimamura, 2017</a>; <a href="#c113" class="usa-link" aria-describedby="c113">Lucero <em>et al.</em>, 2020</a>; <a href="#c213" class="usa-link" aria-describedby="c213">Yokota <em>et al.</em>, 2021</a>) as well as for high-fidelity computational model development, validation, and comparison (<a href="#c58" class="usa-link" aria-describedby="c58">Farahani and Zhang, 2016</a>; <a href="#c158" class="usa-link" aria-describedby="c158">Sadeghi <em>et al.</em>, 2019</a>; <a href="#c163" class="usa-link" aria-describedby="c163">Schoder <em>et al.</em>, 2020</a>; <a href="#c57" class="usa-link" aria-describedby="c57">Falk <em>et al.</em>, 2021</a>). Regarding the latter, however, synthetic VF models remain relatively underutilized as a tool for providing data for development and validation of high-fidelity computational models.</p>
|
||
<p>Because repeated collision of opposing vocal folds is thought to be an important contributor to the etiology of voice disorders (<a href="#c187" class="usa-link" aria-describedby="c187">Titze, 1994</a>; <a href="#c73" class="usa-link" aria-describedby="c73">Gunter, 2003</a>; <a href="#c74" class="usa-link" aria-describedby="c74">Gunter <em>et al.</em>, 2005</a>; <a href="#c137" class="usa-link" aria-describedby="c137">Motie-Shirazi <em>et al.</em>, 2023</a>), methods to predict and measure contact stress have been of considerable interest. Synthetic VF models have been used to develop such methods. <a href="#c174" class="usa-link" aria-describedby="c174">Spencer <em>et al.</em> (2008)</a> used digital image correlation to measure stress and strain on the superior surface of a VF model, and then used a Hertzian impact model to estimate the collision stress. <a href="#c49" class="usa-link" aria-describedby="c49">Diaz-Cadiz <em>et al.</em> (2019)</a> proposed a first-order approximation for estimating collision stress from high-speed videoendoscopy, and using a synthetic VF model, compared the approximation to the actual collision pressure measured using a pressure sensor. Direct measurements of synthetic VF model impact stress have been obtained using a probe microphone mounted in a hemilarynx wall (<a href="#c31" class="usa-link" aria-describedby="c31">Chen and Mongeau, 2011</a>), a contact sensor placed between opposing VF models (<a href="#c85" class="usa-link" aria-describedby="c85">Horacek <em>et al.</em>, 2016</a>), a pressure sensor array using an electromechanical film transducer (<a href="#c209" class="usa-link" aria-describedby="c209">Weiss <em>et al.</em>, 2016</a>), and a contact pressure transducer mounted in a hemilarynx wall with inferior-superior sliding capability (<a href="#c49" class="usa-link" aria-describedby="c49">Diaz-Cadiz <em>et al.</em>, 2019</a>; <a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em>, 2019</a>; <a href="#c134" class="usa-link" aria-describedby="c134">Motie-Shirazi <em>et al.</em>, 2021a</a>,<a href="#c135" class="usa-link" aria-describedby="c135">b</a>; <a href="#c136" class="usa-link" aria-describedby="c136">Motie-Shirazi <em>et al.</em>, 2022</a>, <a href="#c137" class="usa-link" aria-describedby="c137">Motie-Shirazi <em>et al.</em>, 2023</a>).</p>
|
||
<p>Synthetic VF models have been used as initial test beds for development activities related to excised larynx or <em>in vivo</em> quantitative phonation instruments. For example, the synthetic model contact pressure study of <a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em> (2019)</a> was a precursor to the excised larynx intraglottal pressure study of <a href="#c125" class="usa-link" aria-describedby="c125">Mehta <em>et al.</em> (2019)</a>. Other examples include the development of an endoscopic two-point laser projection device for measuring glottal width (<a href="#c150" class="usa-link" aria-describedby="c150">Popolo and Titze, 2008</a>), a laser grid projection system for acquiring 3D measurements of the vibrating superior surface of the VFs (<a href="#c115" class="usa-link" aria-describedby="c115">Luegmair <em>et al.</em>, 2010</a>), and validation of stereo-endoscopic high-speed imaging (<a href="#c175" class="usa-link" aria-describedby="c175">Stevens <em>et al.</em>, 2016</a>).</p>
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<p>Fluid-structure-acoustic interactions are at the core of the mechanics of phonation. Consequently, characterization and study of the glottal jet and other flow-structure-acoustic effects and interactions have led to greater understanding of the fundamental physics of phonation. Owing to their longevity, ability to be parameterized, and similar dependence on flow-structure-acoustic interactions, self-oscillating synthetic VF models have been used for this purpose. <a href="#c145" class="usa-link" aria-describedby="c145">Neubauer <em>et al.</em> (2007)</a> used flow visualization of the glottal jet in a synthetic VF model to describe aspects of an unconfined supraglottal jet and identify flow structures that could be of relevance during phonation (see Fig. <a href="#f11" class="usa-link">11</a>). Studies on the confined supraglottal jet using PIV have been conducted with (e.g., <a href="#c52" class="usa-link" aria-describedby="c52">Drechsel and Thomson, 2008</a>; <a href="#c11" class="usa-link" aria-describedby="c11">Bailly <em>et al.</em>, 2008</a>; <a href="#c94" class="usa-link" aria-describedby="c94">Kniesburges <em>et al.</em>, 2017</a>) and without (e.g., <a href="#c14" class="usa-link" aria-describedby="c14">Becker <em>et al.</em>, 2009</a>; <a href="#c170" class="usa-link" aria-describedby="c170">Sidlof <em>et al.</em>, 2011</a>; <a href="#c165" class="usa-link" aria-describedby="c165">Sciamarella <em>et al.</em>, 2012</a>; <a href="#c95" class="usa-link" aria-describedby="c95">Kniesburges <em>et al.</em>, 2013</a>; <a href="#c103" class="usa-link" aria-describedby="c103">Lodermeyer <em>et al.</em>, 2015</a>; <a href="#c144" class="usa-link" aria-describedby="c144">Näger <em>et al.</em>, 2023</a>) ventricular folds. In the case of <a href="#c165" class="usa-link" aria-describedby="c165">Sciamarella <em>et al.</em> (2012)</a>, the phenomenon of axis switching was evident in the confined tube downstream of the VFs. However, the presence of axis switching and other flow structures and phenomena identified by these authors has yet to be experimentally verified using realistic vocal tract models. Other studies involving interactions between fluid flow, structural motion, and/or acoustics include the role of supraglottal flow structures on acoustic production (<a href="#c222" class="usa-link" aria-describedby="c222">Zhang and Neubauer, 2010</a>); source-tract interactions using straight (<a href="#c128" class="usa-link" aria-describedby="c128">Migimatsu and Tokuda, 2019</a>) and MRI-based vocal tract models (<a href="#c151" class="usa-link" aria-describedby="c151">Probst <em>et al.</em>, 2019</a>), as well as using vocal tract models with varying degrees of constriction (<a href="#c123" class="usa-link" aria-describedby="c123">May and Scherer, 2023</a>) and of varying lengths (<a href="#c99" class="usa-link" aria-describedby="c99">Kraxberger <em>et al.</em>, 2023</a>); the role of model closure on sound generation (<a href="#c97" class="usa-link" aria-describedby="c97">Kniesburges <em>et al.</em>, 2020</a>); and the use of PIV to identify aeroacoustic sound sources during phonation (<a href="#c105" class="usa-link" aria-describedby="c105">Lodermeyer <em>et al.</em>, 2018</a>; <a href="#c124" class="usa-link" aria-describedby="c124">McPhail <em>et al.</em>, 2019</a>; <a href="#c102" class="usa-link" aria-describedby="c102">Lodermeyer <em>et al.</em>, 2021</a>).</p>
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<figure class="fig xbox font-sm" id="f11"><h3 class="obj_head">FIG. 11.</h3>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g011.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/d0cde96bdeff/JASMAN-000156-001283_1-g011.jpg" loading="lazy" height="782" width="797" alt="FIG. 11."></a></p>
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<div class="p text-right font-secondary"><a href="figure/f11/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>(Color online) Visualization of supraglottal jet exiting a self-oscillating, synthetic VF model, with distinguishable flow features labeled. Reproduced with permission from Neubauer, J., Zhang, Z., Miraghaie, R. and Berry, D.A. (<strong>2007</strong>). “Coherent structures of the near field flow in a self-oscillating physical model of the vocal folds,” J. Acoust. Soc. Am. <strong>121</strong>, 1102-1118. Copyright 2007 Acoustical Society of America.</p></figcaption></figure><p>While a degree of asymmetry in VF motion is not uncommon in normal phonation (e.g., <a href="#c166" class="usa-link" aria-describedby="c166">Shaw and Deliyski, 2008</a>; <a href="#c18" class="usa-link" aria-describedby="c18">Bonilha and Deliyski, 2008</a>; <a href="#c93" class="usa-link" aria-describedby="c93">Kendall, 2009</a>; <a href="#c32" class="usa-link" aria-describedby="c32">Chen <em>et al.</em>, 2014</a>), significant asymmetries concomitant with some voice disorders (e.g., paralysis, paresis, or asymmetric lesions) may result in impaired voicing. Since synthetic VF models can be fabricated and tested with pre-determined asymmetries in geometry, material properties, and/or tension, they may be used to understand the effects of asymmetry on phonation, the degree to which various asymmetric conditions cause asymmetric motion, and the potential effects of phonosurgical interventions to repair asymmetry. For example, left-right stiffness asymmetry has been studied in membranous models by varying internal liquid pressure (<a href="#c156" class="usa-link" aria-describedby="c156">Ruty <em>et al.</em>, 2006</a>; <a href="#c75" class="usa-link" aria-describedby="c75">Haas <em>et al.</em>, 2016</a>; <a href="#c113" class="usa-link" aria-describedby="c113">Lucero <em>et al.</em>, 2020</a>) and in cast synthetic VF models by varying material stiffness (<a href="#c148" class="usa-link" aria-describedby="c148">Pickup and Thomson, 2009</a>; <a href="#c217" class="usa-link" aria-describedby="c217">Zhang, 2010</a>; <a href="#c220" class="usa-link" aria-describedby="c220">Zhang and Hieu Luu, 2012</a>; <a href="#c221" class="usa-link" aria-describedby="c221">Zhang <em>et al.</em>, 2013</a>; <a href="#c171" class="usa-link" aria-describedby="c171">Signorello <em>et al.</em>, 2016</a>). Geometric asymmetries that have been explored using synthetic VF models include (see Fig. <a href="#f12" class="usa-link">12</a>) simulated unilateral cordectomy (<a href="#c126" class="usa-link" aria-describedby="c126">Mendelsohn <em>et al.</em>, 2014</a>), left-right vertical asymmetry (<a href="#c168" class="usa-link" aria-describedby="c168">Shimamura and Tokuda, 2017</a>; <a href="#c191" class="usa-link" aria-describedby="c191">Tokuda and Shimamura, 2017</a>; <a href="#c22" class="usa-link" aria-describedby="c22">Bouvet <em>et al.</em>, 2020c</a>; <a href="#c23" class="usa-link" aria-describedby="c23">Bouvet <em>et al.</em>, 2021</a>), surface masses such as polyps and nodules (<a href="#c116" class="usa-link" aria-describedby="c116">Luizard and Pelorson, 2017</a>; <a href="#c40" class="usa-link" aria-describedby="c40">Conte <em>et al.</em>, 2021b</a>; <a href="#c137" class="usa-link" aria-describedby="c137">Motie-Shirazi <em>et al.</em>, 2023</a>), and augmentation injection to correct for vocal bowing (<a href="#c143" class="usa-link" aria-describedby="c143">Murray <em>et al.</em>, 2014</a>).</p>
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<figure class="fig xbox font-sm" id="f12"><h3 class="obj_head">FIG. 12.</h3>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g012.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/9b17f438ac54/JASMAN-000156-001283_1-g012.jpg" loading="lazy" height="690" width="774" alt="FIG. 12."></a></p>
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<div class="p text-right font-secondary"><a href="figure/f12/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>(Color online) Synthetic VF models with geometric asymmetry. (a) Inferior-superior left-right level difference. (b) Left-right asymmetry via rotation about medial-lateral axis. (c) Unilateral nodules using membranous models. (d) Bowed VF model with injection holes placed laterally in the mounting plate for medialization via augmentation injections. Credits: (a) Reproduced with permission from Tokuda, I. T., and Shimamura, R. (<strong>2017</strong>). “Effect of level difference between left and right vocal folds on phonation: Physical experiment and theoretical study,” J. Acoust. Soc. Am. <strong>142</strong>, 482-492. Copyright 2017 Acoustical Society of America. (b) Adapted with permission from Bouvet, A., Tokuda, I., Pelorson, X. and Van Hirtum, A. (<strong>2021</strong>). “Imaging of auto-oscillating vocal folds replicas with left–right level difference due to angular asymmetry,” Biomed. Signal Proces. <strong>63</strong>, 102154. Copyright 2021, Elsevier. (c) Adapted with permission from Luizard, P. and Pelorson, X. (<strong>2017</strong>). “Threshold of oscillation of a vocal fold replica with unilateral surface growths,” J. Acoust. Soc. Am. <strong>141</strong>, 3050-3058. Copyright 2017 Acoustical Society of America. (d) Reprinted with permission from Murray, P. R., Thomson, S. L., and Smith, M. E. (<strong>2014</strong>). “A synthetic self-oscillating vocal fold model platform for studying augmentation injection,” J. Voice <strong>28</strong>, 133–143. Copyright 2014 The Voice Foundation.</p></figcaption></figure><p>Brief mention is here made of other applications. These include spatiotemporal analysis using empirical eigenfunctions to explore irregular vibration, including subharmonic phonation and biphonation (<a href="#c17" class="usa-link" aria-describedby="c17">Berry <em>et al.</em>, 2006</a>); subharmonic tone generation (<a href="#c96" class="usa-link" aria-describedby="c96">Kniesburges <em>et al.</em>, 2016</a>); the effects of surface liquid on vibration [<a href="#c198" class="usa-link" aria-describedby="c198">Van Hirtum <em>et al.</em>, 2019</a>; <a href="#c20" class="usa-link" aria-describedby="c20">Bouvet <em>et al.</em>, 2020a</a>,<a href="#c21" class="usa-link" aria-describedby="c21">b</a>; <a href="#c215" class="usa-link" aria-describedby="c215">Yoshinaga <em>et al.</em>, 2023</a>; see Fig. <a href="#f13" class="usa-link">13(a)</a>]; the response of an injectable biomaterial to vibration in a phonomimetic bioreactor system [<a href="#c101" class="usa-link" aria-describedby="c101">Latifi <em>et al.</em>, 2016</a>; see Fig. <a href="#f13" class="usa-link">13(b)</a>]; water resistance voice therapy (<a href="#c86" class="usa-link" aria-describedby="c86">Horacek <em>et al.</em>, 2019a</a>,<a href="#c87" class="usa-link" aria-describedby="c87">b</a>); development of a surgical training model [<a href="#c159" class="usa-link" aria-describedby="c159">Saliba and Barros, 2023</a>; Fig. <a href="#f13" class="usa-link">13(c)</a>]; and coupling synthetic VF model data with finite element data for estimating VF material properties (<a href="#c76" class="usa-link" aria-describedby="c76">Hadwin <em>et al.</em>, 2019</a>). Finally, synthetic VF models have been used to explore non-human vocalization, including mammalian air sacs (<a href="#c153" class="usa-link" aria-describedby="c153">Riede <em>et al.</em>, 2008</a>), the vocal membrane of non-human mammalian species (<a href="#c92" class="usa-link" aria-describedby="c92">Kanaya <em>et al.</em>, 2022</a>) [Fig. <a href="#f13" class="usa-link">13(d)</a>], and the avian syrinx (<a href="#c53" class="usa-link" aria-describedby="c53">Elemans <em>et al.</em>, 2009</a>; <a href="#c152" class="usa-link" aria-describedby="c152">Riede <em>et al.</em>, 2019</a>) [Fig. <a href="#f13" class="usa-link">13(e)</a>].</p>
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<figure class="fig xbox font-sm" id="f13"><h3 class="obj_head">FIG. 13.</h3>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g013.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/1bc39a4bd263/JASMAN-000156-001283_1-g013.jpg" loading="lazy" height="635" width="740" alt="FIG. 13."></a></p>
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<figcaption><p>(Color online) (a) Setup for using an optical particle sizer (OPS) to measure aerosol particle formation by self-oscillating synthetic VF models. (b) Phonomimetic bioreactor with cell-scaffold mixture imbedded within VF models. (c) Surgical training model. (d) Physical model of non-human mammalian vocal membrane. (e) Membranous structure mimicking the avian syrinx. Credits: (a) Reproduced with permission from Yoshinaga, T., Yamaya, Y., Minami, T., Obata, H., Tsuchida, H., Yoshitani, T., Tokuda, I. T., and Iida, A., “Effects of vocal fold oscillation characteristics on the aerosol droplet production,” J. Aerosol Sci. <strong>174</strong>, 106251. Copyright 2023 Elsevier. (b) Adapted from Latifi N., Heris, H. K., Thomson, S. L., Taher, R., Kazemirad, S., Sheibani, S., Li-Jessen N. Y. K., Vali, H., Mongeau, L. (<strong>2016</strong>). “A flow perfusion bioreactor system for vocal fold tissue engineering applications,” Tissue Eng. Part C.-ME. <strong>22</strong>, 823-838. Copyright 2016 Mary Ann Liebert, Inc. (c) Reproduced from Saliba, T. V., and Barros, R. S. M. D. (<strong>2023</strong>). “Development and validation of a 3D laryngeal model in surgical skills training,” Braz. J. Otorhinolar. <strong>89</strong>, 128-135; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (<a href="https://creativecommons.org/licenses/by/4.0/" class="usa-link usa-link--external" data-ga-action="click_feat_suppl" target="_blank" rel="noopener noreferrer">https://creativecommons.org/licenses/by/4.0/</a>). (d) Adapted from Kanaya, M., Matsumoto, T., Uemura, T., Kawabata, R., Nishimura, T., and Tokuda, I. T. (<strong>2022</strong>). “Physical modeling of the vocal membranes and their influence on animal voice production,” JASA Express Lett. <strong>2</strong>, 111201; licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (<a href="https://creativecommons.org/licenses/by/4.0/" class="usa-link usa-link--external" data-ga-action="click_feat_suppl" target="_blank" rel="noopener noreferrer">https://creativecommons.org/licenses/by/4.0/</a>). (e) Reproduced with permission Elemans, C. P. H., Muller, M., Larsen, O. N., and van Leeuwen, J. L. (<strong>2009</strong>). “Amplitude and frequency modulation control of sound production in a mechanical model of the avian syrinx,” J. Exp. Biol. 212, 1212-1224. Copyright 2009 Company of Biologists Ltd.</p></figcaption></figure></section><section id="s6"><h2 class="pmc_sec_title">VI. EXPERIMENTAL TECHNIQUES</h2>
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<p>With the development of synthetic VF models has been the development and application of numerous experimental techniques for their study. In this section, an overview of experimental methods specifically used for studying VF model flow, motion, and acoustics is given.</p>
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<p>In all cases, self-oscillating VF model studies require a flow supply; see Fig. <a href="#f14" class="usa-link">14</a> for representative cases. This is typically provided by means of compressed air from a building supply or a standalone air tank. In contrast to excised larynx setups, neither heating nor humidification of the flow supply is required to maintain health of the VF model, although such would not be inherently problematic. As with excised larynx experiments, flow conditioning, such as a large square box plenum (e.g., Fig. <a href="#f14" class="usa-link">14</a>), is often used to settle airflow prior to entering the subglottic tube and, in some cases if desired, to create an area difference between the subglottic tube and the plenum to create a well-defined, reflective acoustic boundary. Hemilarynx as well as full larynx configurations have been used in synthetic VF model experiments, with and without vocal tracts.</p>
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<figure class="fig xbox font-sm" id="f14"><h3 class="obj_head">FIG. 14.</h3>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g014.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/e9a8707967a5/JASMAN-000156-001283_1-g014.jpg" loading="lazy" height="808" width="777" alt="FIG. 14."></a></p>
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<figcaption><p>(Color online) Illustrations of experimental setups for membranous (a–c) and elastic solid (d–f) models. (a,b) Air supplied to large plenum with laser diode and laser sensor to measure orifice opening. Reservoir of adjustable height provided symmetric pressure to opposing liquid-filled tubes representing VFs. (c) Similar to (a,b) but with separate pressures applied to opposing VF models to create medial-lateral asymmetry. (d) Air supplied through plenum, through subglottal tube, to VF models. Vocal tract model with ventricular folds included. (e) Setup with acoustic treatment of subglottal regions. (f) Acoustical treatment of subglottal system (inset region with dashed border) and supraglottal setup for using PIV to measure flow within supraglottal channel. Credits: (a) Reproduced with permission from Ruty, N., Pelorson, X., Van Hirtum, A., Lopez-Arteaga, I., and Hirschberg, A. (<strong>2007</strong>). “An <em>in vitro</em> setup to test the relevance and the accuracy of low-order vocal folds models,” J. Acoust. Soc. Am. <strong>121</strong>, 479–490. Copyright 2007 Acoustical Society of America. (b) Reproduced with permission from Bailly, L., Pelorson, X., Henrich, N., and Ruty, N. (<strong>2008</strong>). “Influence of a constriction in the near field of the vocal folds: Physical modeling and experimental validation,” J. Acoust. Soc. Am. <strong>124</strong>, 3296–3308. Copyright 2008 Acoustical Society of America. (c) Reproduced with permission from Haas, J., Luizard, P., Pelorson, X., and Lucero, J. C. (<strong>2016</strong>). “Study of the effect of a moderate asymmetry on a replica of the vocal folds,” Acta Acust. United Ac. <strong>102</strong>, 230–239. Copyright 2016 European Acoustics Association. (d) Reproduced with permission from Drechsel, J. S, and Thomson, S. L. (<strong>2008</strong>). “Influence of supraglottal structures on the glottal jet exiting a two-layer synthetic, self-oscillating vocal fold model,” J. Acoust. Soc. Am. <strong>123</strong>, 4434–4445. Copyright 2008 Acoustical Society of America. (e) Reproduced with permission from Häsner, P., Prescher, A. and Birkholz, P. (<strong>2021</strong>). “Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds,” J. Acoust. Soc. Am. <strong>149</strong>, 466–475. Copyright 2021 Acoustical Society of America. (f) Adapted from Lodermeyer, A., Becker, S., Döllinger, M., and Kniesburges, S. (<strong>2015</strong>). “Phase-locked flow field analysis in a synthetic human larynx model,” Exp. Fluids <strong>56</strong>, 13, with permission from SNCSC. Copyright 2015 Springer-Verlag.</p></figcaption></figure><p>A characteristic of VF models is the potential for coupling with subglottal acoustics to drive or assist model vibration. <a href="#c224" class="usa-link" aria-describedby="c224">Zhang <em>et al.</em> (2006b)</a> first identified this issue with elastic solid models in a study involving subglottic tubes of varying lengths. It was shown that the one-layer model followed quarter-wavelength resonance theory, demonstrating the importance of appropriately taking into consideration subglottic tube length [see Fig. <a href="#f15" class="usa-link">15(a)</a>]. Distinct vibratory shapes for aerodynamic vs acoustically driven vibration modes were observed by <a href="#c223" class="usa-link" aria-describedby="c223">Zhang <em>et al.</em> (2006a)</a> [see Fig. <a href="#f15" class="usa-link">15(b)</a>]. Acoustically coupled modes exhibited a “swinging-door”-type motion characterized by large inferior-superior motion, whereas aerodynamic modes were characterized by limited inferior-superior motion and greater medial-lateral motion, the latter being more characteristic of the human VF mucosal wave. Further, in general, longer tubes and VF models that produce acoustically driven modes of vibration often yield significantly lower onset pressures, but at the cost of increased vertical motion and reduced wave-like motion. The roles of VF model stiffness and acoustic loading were studied by <a href="#c225" class="usa-link" aria-describedby="c225">Zhang <em>et al.</em> (2009)</a>, and acoustic and aerodynamic coupling was further explored by <a href="#c151" class="usa-link" aria-describedby="c151">Probst <em>et al.</em> (2019)</a> with a synthetic VF model and an MRI-based vocal tract replica. Given these studies which have shown the potential for model vibration to couple with subglottic resonance, it is important that studies using self-oscillating, synthetic VF models—membranous as well as elastic solid—should describe in detail the subglottic setup and address whether the model vibration was acoustically or aerodynamically coupled.</p>
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<figure class="fig xbox font-sm" id="f15"><h3 class="obj_head">FIG. 15.</h3>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g015.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/bf934cc73dd7/JASMAN-000156-001283_1-g015.jpg" loading="lazy" height="1193" width="780" alt="FIG. 15."></a></p>
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<div class="p text-right font-secondary"><a href="figure/f15/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>(Color online) (a) Frequency vs subglottic tube length for one-layer elastic solid VF model. Closed symbols: measured model onset frequencies; open symbols: subglottal tube resonance frequencies; solid lines: theory. Adapted with permission from Zhang, Z., Neubauer, J. and Berry, D. A. (<strong>2006a</strong>). “The influence of subglottal acoustics on laboratory models of phonation,” J. Acoust. Soc. Am. <strong>120</strong>, 1558-1569. Copyright 2006 Acoustical Society of America. (b) Trajectories of points on homogeneous elastic solid VF model undergoing aerodynamic (left) and acoustic (right) modes of vibration. Adapted with permission from Zhang, Z., Neubauer, J., and Berry, D. A. (<strong>2006a</strong>). “Aerodynamically and acoustically driven modes of vibration in a physical model of the vocal folds,” J. Acoust. Soc. Am. <strong>120</strong>, 2841-2849. Copyright 2006, Acoustical Society of America.</p></figcaption></figure><p>A diverse array of experimental techniques has been incorporated to study acoustics, fluid dynamics, and structural motion of self-oscillating VF models. In addition to well-known methods of processing microphone signal data to analyze radiated acoustics, human listener evaluations of model-generated acoustic data have been used to assess perceptual effects caused by changing body stiffness (<a href="#c221" class="usa-link" aria-describedby="c221">Zhang <em>et al.</em>, 2013</a>, <a href="#c171" class="usa-link" aria-describedby="c171">Signorello <em>et al.</em>, 2016</a>). Flow measurement techniques that have been employed include hot-wire anemometry (<a href="#c184" class="usa-link" aria-describedby="c184">Thomson <em>et al.</em>, 2005</a>; <a href="#c14" class="usa-link" aria-describedby="c14">Becker <em>et al.</em>, 2009</a>), laser Doppler velocimetry (<a href="#c14" class="usa-link" aria-describedby="c14">Becker <em>et al.</em>, 2009</a>), flow visualization (<a href="#c145" class="usa-link" aria-describedby="c145">Neubauer <em>et al.</em>, 2007</a>; <a href="#c52" class="usa-link" aria-describedby="c52">Drechsel and Thomson, 2008</a>; <a href="#c88" class="usa-link" aria-describedby="c88">Horacek <em>et al.</em>, 2011</a>; <a href="#c131" class="usa-link" aria-describedby="c131">Misun <em>et al.</em>, 2011</a>; <a href="#c95" class="usa-link" aria-describedby="c95">Kniesburges <em>et al.</em>, 2013</a>; <a href="#c64" class="usa-link" aria-describedby="c64">Fulcher <em>et al.</em>, 2019</a>), and PIV (<a href="#c145" class="usa-link" aria-describedby="c145">Neubauer <em>et al.</em>, 2007</a>; <a href="#c52" class="usa-link" aria-describedby="c52">Drechsel and Thomson, 2008</a>; <a href="#c14" class="usa-link" aria-describedby="c14">Becker <em>et al.</em>, 2009</a>; <a href="#c148" class="usa-link" aria-describedby="c148">Pickup and Thomson, 2009</a>; <a href="#c100" class="usa-link" aria-describedby="c100">Krebs <em>et al.</em>, 2012</a>; <a href="#c165" class="usa-link" aria-describedby="c165">Sciamarella <em>et al.</em>, 2012</a>; <a href="#c103" class="usa-link" aria-describedby="c103">Lodermeyer <em>et al.</em>, 2015</a>; <a href="#c105" class="usa-link" aria-describedby="c105">Lodermeyer <em>et al.</em>, 2018</a>; <a href="#c102" class="usa-link" aria-describedby="c102">Lodermeyer <em>et al.</em>, 2021</a>; <a href="#c158" class="usa-link" aria-describedby="c158">Sadeghi <em>et al.</em>, 2019</a>). In a study comparing high-speed vs phase-averaged PIV, it was shown that phase-averaging can yield useful flow information, although aeroacoustic sound generation exploration via PIV requires high-speed interrogation (<a href="#c104" class="usa-link" aria-describedby="c104">Lodermeyer <em>et al.</em>, 2016</a>). Principal component analysis (PCA) has been a means of identifying coherent flow structures (<a href="#c145" class="usa-link" aria-describedby="c145">Neubauer <em>et al.</em>, 2007</a>; <a href="#c96" class="usa-link" aria-describedby="c96">Kniesburges <em>et al.</em>, 2016</a>). Analysis techniques for measuring motion of synthetic VF models include videokymography (<a href="#c150" class="usa-link" aria-describedby="c150">Popolo and Titze, 2008</a>; <a href="#c174" class="usa-link" aria-describedby="c174">Spencer <em>et al.</em>, 2008</a>; <a href="#c148" class="usa-link" aria-describedby="c148">Pickup and Thomson, 2009</a>, <a href="#c149" class="usa-link" aria-describedby="c149">2010</a>; <a href="#c115" class="usa-link" aria-describedby="c115">Luegmair <em>et al.</em>, 2010</a>; <a href="#c141" class="usa-link" aria-describedby="c141">Murray and Thomson, 2011</a>, <a href="#c142" class="usa-link" aria-describedby="c142">2012</a>; <a href="#c220" class="usa-link" aria-describedby="c220">Zhang and Hieu Luu, 2012</a>; <a href="#c191" class="usa-link" aria-describedby="c191">Tokuda and Shimamura, 2017</a>; <a href="#c128" class="usa-link" aria-describedby="c128">Migimatsu and Tokuda, 2019</a>; <a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em>, 2019</a>; <a href="#c23" class="usa-link" aria-describedby="c23">Bouvet <em>et al.</em>, 2021</a>; <a href="#c72" class="usa-link" aria-describedby="c72">Greenwood and Thomson, 2021</a>; <a href="#c121" class="usa-link" aria-describedby="c121">Matsumoto <em>et al.</em>, 2021</a>; <a href="#c122" class="usa-link" aria-describedby="c122">Matsumoto <em>et al.</em>, 2024</a>; <a href="#c176" class="usa-link" aria-describedby="c176">Stewart and Erath, 2021</a>; <a href="#c181" class="usa-link" aria-describedby="c181">Taylor and Thomson, 2022</a>; <a href="#c77" class="usa-link" aria-describedby="c77">Hasegawa <em>et al.</em>, 2022</a>), modal decomposition techniques (<a href="#c17" class="usa-link" aria-describedby="c17">Berry <em>et al.</em>, 2006</a>; <a href="#c223" class="usa-link" aria-describedby="c223">Zhang <em>et al.</em>, 2006a</a>,<a href="#c224" class="usa-link" aria-describedby="c224">b</a>; <a href="#c202" class="usa-link" aria-describedby="c202">Van Hirtum and Pelorson, 2017</a>), direct linear transformation (DLT) to track small numbers of points on model medial surfaces (<a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson, 2012</a>; <a href="#c143" class="usa-link" aria-describedby="c143">Murray <em>et al.</em>, 2014</a>; <a href="#c175" class="usa-link" aria-describedby="c175">Stevens <em>et al.</em>, 2016</a>), laser dot projection to measure superior surface motion (<a href="#c115" class="usa-link" aria-describedby="c115">Luegmair <em>et al.</em>, 2010</a>), digital image correlation (DIC, a solid domain counterpart to PIV) to track model motion via randomly-distributed dot patterns (<a href="#c174" class="usa-link" aria-describedby="c174"><em>Spencer <em>et al.</em></em>, 2008</a>; <a href="#c31" class="usa-link" aria-describedby="c31">Chen and Mongeau, 2011</a>), MRI for simultaneous internal and external motion (<a href="#c180" class="usa-link" aria-describedby="c180">Taylor <em>et al.</em>, 2019</a>), internal motion using optically transparent VF model materials (<a href="#c133" class="usa-link" aria-describedby="c133">Motie-Shirazi, 2022</a>), and laser Doppler vibrometry for model velocity (<a href="#c174" class="usa-link" aria-describedby="c174">Spencer <em>et al.</em>, 2008</a>; <a href="#c14" class="usa-link" aria-describedby="c14">Becker <em>et al.</em>, 2009</a>; <a href="#c53" class="usa-link" aria-describedby="c53">Elemans <em>et al.</em>, 2009</a>; <a href="#c102" class="usa-link" aria-describedby="c102">Lodermeyer <em>et al.</em>, 2021</a>; <a href="#c99" class="usa-link" aria-describedby="c99">Kraxberger <em>et al.</em>, 2023</a>) and model frequency response (<a href="#c116" class="usa-link" aria-describedby="c116">Luizard and Pelorson, 2017</a>; <a href="#c152" class="usa-link" aria-describedby="c152">Riede <em>et al.</em>, 2019</a>).</p>
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<p>Some pitfalls and considerations of particular relevance to synthetic VF model experimentation are here noted. As discussed previously, models mounted on long subglottal tubes that produce quarter wavelengths on the order of the model <em>in vacuo</em> modal frequencies are prone to acoustic coupling. In some cases, acoustic coupling may be acceptable, but in studies where mucosal wave-like characteristics are central to the research question, shorter subglottal tubes for aerodynamic coupling should be utilized. In all cases, the geometric characteristics of the subglottic system should be reported because of model susceptibility to acoustic coupling.</p>
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<p>The use of a vocal tract is an important consideration. <a href="#c79" class="usa-link" aria-describedby="c79">Häsner <em>et al.</em> (2021)</a> studied the influence of smooth vs wavy subglottal tube profile on flow and vibratory characteristics, including subglottal pressure, onset pressure, pulmonary power, and vibratory frequency (see Fig. <a href="#f16" class="usa-link">16</a>). VF models with different anterior-posterior cross-sectional shapes (round, quadrilateral, and triangular) were employed along with different degrees of tracheal wall waviness and the presence or absence of a vocal tract model. They reported that including a vocal tract model decreased onset pressure by around 400 to 500 Pa, which is a significant reduction. Slight decreases in pulmonary power with waviness depth were seen. Waviness minimally affected pressures measured at the low end of the trachea at vibration onset, but significantly reduced the corresponding onset pressures at the upper end of the trachea. Model vibration frequencies were significantly higher with a vocal tract model than without, but they did not vary with waviness depth. This study demonstrated the potential influence of a vocal tract model on synthetic VF model response. Pitfalls of extrapolating conclusions based on acoustical data obtained without a vocal tract to a configuration with a vocal tract were highlighted by <a href="#c171" class="usa-link" aria-describedby="c171">Signorello <em>et al.</em> (2016)</a>. Given these findings, the presence or absence of a vocal tract model should always be documented when presenting results using synthetic VF models, and it is recommended that vocal tract models be included where possible.</p>
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<figure class="fig xbox font-sm" id="f16"><h3 class="obj_head">FIG. 16.</h3>
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<p class="img-box line-height-none margin-x-neg-2 tablet:margin-x-0 text-center"><a class="tileshop" target="_blank" href="https://www.ncbi.nlm.nih.gov/core/lw/2.0/html/tileshop_pmc/tileshop_pmc_inline.html?title=Click%20on%20image%20to%20zoom&p=PMC3&id=11348498_JASMAN-000156-001283_1-g016.jpg"><img class="graphic zoom-in" src="https://cdn.ncbi.nlm.nih.gov/pmc/blobs/fde2/11348498/774379d9dd67/JASMAN-000156-001283_1-g016.jpg" loading="lazy" height="572" width="752" alt="FIG. 16."></a></p>
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<div class="p text-right font-secondary"><a href="figure/f16/" class="usa-link" target="_blank" rel="noopener noreferrer">Open in a new tab</a></div>
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<figcaption><p>Top: Configuration for measuring effects on phonatory output of tracheal waviness, VF shape (round, quadrilateral, and triangular), and presence of vocal tract. Dimensions in mm. Bottom: Onset (solid lines) and offset (dashed lines) pressures measured at the upper pressure tap vs waviness depth for different VF shapes, with (left) and without (right) a vocal tract model, showing significant reduction in threshold pressures with a vocal tract model. Corresponding pressures measured at the lower pressure tap were affected to a significantly lesser degree by waviness. Adapted with permission from Häsner, P., Prescher, A. and Birkholz, P. (<strong>2021</strong>). “Effect of wavy trachea walls on the oscillation onset pressure of silicone vocal folds,” J. Acoust. Soc. Am. <strong>149</strong>, 466-475. Copyright 2021 Acoustical Society of America.</p></figcaption></figure><p>For VF models themselves, environmental and temporal factors that affect properties, and hence vibratory characteristics, should be carefully observed and controlled where possible. These include model heating from intense illumination for high-speed imaging, material creep and relaxation, potential leeching of silicone thinner to adjacent regions of cured silicone in multi-layer elastic solid VF models, and changing of model geometry over time. For example, <a href="#c182" class="usa-link" aria-describedby="c182">Thacker (2023)</a> demonstrated silicone swelling/shrinking when immersed in water/mineral oil, respectively. <a href="#c78" class="usa-link" aria-describedby="c78">Häsner and Birkholz (2023)</a> systematically studied changes in elastic solid VF model vibration caused by aging over an eight-week period, finding significant variability in phonatory response measures over such an extended time. Finally, silicone is gas permeable, a potentially significant characteristic when using silicone VF models in conjunction with biological, bioengineered, or hydrogel components. Owing to considerations such as these, authors of studies using synthetic VF models should take great care to report relevant fabrication, experimental setup, and experimental procedure details.</p></section><section id="s7"><h2 class="pmc_sec_title">VII. CONCLUSIONS AND FUTURE WORK</h2>
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<p>A comprehensive review of synthetic, self-oscillating VF models for voice production research has been provided. The designs, capabilities, and limitations of the two most common types of such models have been presented, the two types being membranous models (e.g., water-filled latex tubes), and elastic solid models (e.g., ultrasoft silicones formed into VF-like shapes). Materials and fabrication processes unique to the implementation of elastic solid models have been discussed. Applications and experimental configurations associated with both types of models have been provided. Recommendations for future studies have been given, including comparing the vibratory motion of liquid-filled elastic tube models to that of human VFs; pursuing membranous models with nonlinear and/or anisotropic material properties; further exploring the use of fibers in elastic solid VF models; using ASTM D412 for acquiring stress-strain data of synthetic model materials; acquiring Poisson's ratio data of synthetic model materials; including vocal tract models whenever possible; carefully reporting model fabrication and experimental setup and procedure details, particularly regarding subglottic configurations and resonance characteristics; measuring model geometric and material properties, ideally close to the time of model testing; and increasing utilization of synthetic VF model data for development and validation of high-fidelity computational models of phonation.</p>
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<p>In addition to the previous recommendations, while significant progress has been made in recent decades to create and use models to study the biomechanical underpinnings of phonation, there remain significant opportunities to develop models with ever increasing lifelike motion that can produce even more clinically relevant results. To date, most synthetic VF models have been based on the adult human male. Female morphological characteristics, as well as those of children, remain underrepresented in VF modeling studies. Future VF modeling efforts should fill this important gap. Additionally, key success measures of modeling VF vibration include low onset pressure, mucosal wave-like motion, and glottal closure. Factors that affect these characteristics include geometric definitions, boundary conditions, and the spatial distribution of stiffness. The “M5” geometric profile of <a href="#c162" class="usa-link" aria-describedby="c162">Scherer <em>et al.</em> (2001)</a> has been widely used, in part because it provided the basis for early elastic solid synthetic model studies (<a href="#c184" class="usa-link" aria-describedby="c184">Thomson <em>et al.</em>, 2005</a>) and in part because of its well-defined shape. However, more lifelike geometries can improve model response (<a href="#c148" class="usa-link" aria-describedby="c148">Pickup and Thomson, 2009</a>; <a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson, 2012</a>). Notably, while shape variation along the anterior-posterior direction exists in the human VFs (e.g., <a href="#c190" class="usa-link" aria-describedby="c190">Titze and Talkin, 1979</a>), most synthetic VF models have been defined using uniform cross-sections. Some exceptions to this include studies by <a href="#c148" class="usa-link" aria-describedby="c148">Pickup and Thomson (2009)</a>, <a href="#c142" class="usa-link" aria-describedby="c142">Murray and Thomson (2012)</a>, <a href="#c23" class="usa-link" aria-describedby="c23">Bouvet <em>et al.</em> (2021)</a>, <a href="#c79" class="usa-link" aria-describedby="c79">Häsner <em>et al.</em> (2021)</a>, <a href="#c121" class="usa-link" aria-describedby="c121">Matsumoto <em>et al.</em> (2021)</a>, <a href="#c122" class="usa-link" aria-describedby="c122">Matsumoto <em>et al.</em> (2024)</a>, <a href="#c199" class="usa-link" aria-describedby="c199">Van Hirtum <em>et al.</em> (2022)</a>, <a href="#c77" class="usa-link" aria-describedby="c77">Hasegawa <em>et al.</em> (2022)</a>, and <a href="#c195" class="usa-link" aria-describedby="c195">Tur <em>et al.</em> (2023)</a>. The fabrication of models with non-uniform cross-sections is slightly more complex, particularly with multi-layer models; however, this important aspect of human VF shape should be routinely incorporated in VF models. Research to quantify VF exterior profile and layer geometries with greater detail to enable more accurate modeling is needed. More lifelike boundary conditions, as opposed to rigid mounting plates, may also improve model response; see the computational study by <a href="#c90" class="usa-link" aria-describedby="c90">Jones <em>et al.</em> (2015)</a> and experimental incorporation by <a href="#c138" class="usa-link" aria-describedby="c138">Motie-Shirazi <em>et al.</em> (2019)</a>, <a href="#c134" class="usa-link" aria-describedby="c134">Motie-Shirazi <em>et al.</em> (2021a</a>,<a href="#c135" class="usa-link" aria-describedby="c135">b)</a>, <a href="#c136" class="usa-link" aria-describedby="c136">Motie-Shirazi <em>et al.</em> (2022)</a>, <a href="#c137" class="usa-link" aria-describedby="c137">Motie-Shirazi <em>et al.</em> (2023)</a>, and <a href="#c176" class="usa-link" aria-describedby="c176">Stewart and Erath (2021)</a>. Furthermore, while elastic solid models that achieve complete closure and realistic open quotient values have been reported (e.g., <a href="#c218" class="usa-link" aria-describedby="c218">Zhang, 2011</a>; <a href="#c134" class="usa-link" aria-describedby="c134">Motie-Shirazi <em>et al.</em>, 2021a</a>,<a href="#c135" class="usa-link" aria-describedby="c135">b</a>; <a href="#c181" class="usa-link" aria-describedby="c181">Taylor and Thomson, 2022</a>), fabrication of these models that consistently produce desired levels of glottal closure remains somewhat elusive. Owing to the significant role of collision in phonation and phonotrauma, a mature understanding of the mechanisms that govern glottal closure, followed by application in VF modeling efforts, is needed. The degree to which the epithelium layer affects VF vibration has been explored using excised human larynges and computational simulations (see <a href="#c194" class="usa-link" aria-describedby="c194">Tse <em>et al.</em>, 2015</a>, and <a href="#c48" class="usa-link" aria-describedby="c48">Deng and Peterson, 2023</a>, respectively) but has yet to be studied using synthetic models. Methods for creating consistent and repeatable transverse isotropy and material nonlinearity are two advancements that would significantly improve VF models. Finally, neuromuscular control of the larynx plays a significant role in phonation due to the effects of intrinsic muscle activity on VF position, stiffness, and shape. VF models with artificial, soft muscle activation do not yet appear to have been reported in the literature. Consequently, this area presents a significant opportunity for VF model development, in particular by drawing upon the extensive existing studies on artificial soft actuators for robotics applications (e.g., <a href="#c212" class="usa-link" aria-describedby="c212">Yang and Wang, 2024</a>).</p></section><section id="ack1" class="ack"><h2 class="pmc_sec_title">ACKNOWLEDGMENTS</h2>
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<p>The author respectfully acknowledges the contributions of the numerous students and researchers worldwide who have contributed to the ongoing advancement of synthetic, self-oscillating vocal fold models, many of whose works are cited herein. This publication was supported by the National Institute On Deafness and Other Communication Disorders (NIDCD) of the National Institutes of Health (NIH) under Award Nos. R01DC009616 and R01DC018577. The content is solely the responsibility of the author and does not necessarily represent the official views of the NIH.</p></section><section id="fn-group1" class="fn-group"><div class="fn-group p font-secondary-light font-sm"><div class="fn p" id="tr1">
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<sup>a)</sup><p class="display-inline">Portions of this review were completed while previously affiliated with the Department of Mechanical Engineering, Brigham Young University, Provo, UT 84602, USA.</p>
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</div></div></section><section id="sec12"><h2 class="pmc_sec_title">AUTHOR DECLARATIONS</h2>
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<section id="sec13"><h3 class="pmc_sec_title">Conflict of Interest</h3>
|
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<p>The author has no conflict of interest to declare.</p></section></section><section id="sec14"><h2 class="pmc_sec_title">DATA AVAILABILITY</h2>
|
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<p>The data that support the findings of this study are available from the corresponding author upon reasonable request.</p></section><section id="ref-list1" class="ref-list"><h2 class="pmc_sec_title">References</h2>
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