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This pre-print is available under a Creative Commons License (Attribution 4.0 International), CC BY 4.0, as described at http://creativecommons.org/licenses/by/4.0/" /> <meta name="DC.AccessRights" content="restricted" /> <meta name="DC.Description" content="Using thermal imaging for cryoablation and cryotherapy is a convenient technique but it does not allow for visualization of what is inside. We model thermal field distribution which can help relate surface thermal field images to in-depth temperature field dynamics that show freezing and thawing processes dynamics. We consider the spatio-temporal distribution of temperature using examples of hydrogel and living tissue subjected to a cryoprobe. Freezing in the hydrogel is compared with the measurements using visual morphometry. Such studies can be useful for comparing in-vitro and in-vivo thermal field dynamics and for estimating the correct timing for cryoapplication. ### Competing Interest Statement The authors have declared no competing interest." /> <meta name="DC.Contributor" content="O. V. Ivakhnenko" /> <meta name="DC.Contributor" content="O. F. Todrin" /> <meta name="DC.Contributor" content="V.Yu. Globa" /> <meta name="DC.Contributor" content="M.O. Chyzh" /> <meta name="DC.Contributor" content="G.O. Kovalov" /> <meta name="DC.Contributor" content="S.N. Shevchenko" /> <meta name="article:published_time" content="2024-11-13" /> <meta name="article:section" content="New Results" /> <meta name="citation_title" content="Mathematical modeling of the frozen zone dynamics: towards using thermal imagers in cryotherapy" /> <meta name="citation_abstract" lang="en" content="<p>Using thermal imaging for cryoablation and cryotherapy is a convenient technique but it does not allow for visualization of what is inside. We model thermal field distribution which can help relate surface thermal field images to in-depth temperature field dynamics that show freezing and thawing processes dynamics. We consider the spatio-temporal distribution of temperature using examples of hydrogel and living tissue subjected to a cryoprobe. Freezing in the hydrogel is compared with the measurements using visual morphometry. Such studies can be useful for comparing in-vitro and in-vivo thermal field dynamics and for estimating the correct timing for cryoapplication.</p>" /> <meta name="citation_journal_title" content="bioRxiv" /> <meta name="citation_publisher" content="Cold Spring Harbor Laboratory" /> <meta name="citation_publication_date" content="2024/01/01" /> <meta name="citation_mjid" content="biorxiv;2024.10.19.619201v2" /> <meta name="citation_id" content="2024.10.19.619201v2" /> <meta name="citation_public_url" content="https://www.biorxiv.org/content/10.1101/2024.10.19.619201v2" /> <meta name="citation_abstract_html_url" content="https://www.biorxiv.org/content/10.1101/2024.10.19.619201v2.abstract" /> <meta name="citation_full_html_url" content="https://www.biorxiv.org/content/10.1101/2024.10.19.619201v2.full" /> <meta name="citation_pdf_url" content="https://www.biorxiv.org/content/biorxiv/early/2024/11/13/2024.10.19.619201.full.pdf" /> <meta name="citation_doi" content="10.1101/2024.10.19.619201" /> <meta name="citation_num_pages" content="39" /> <meta name="citation_article_type" content="Article" /> <meta name="citation_section" content="New Results" /> <meta name="citation_firstpage" content="2024.10.19.619201" /> <meta name="citation_author" content="O. V. Ivakhnenko" /> <meta name="citation_author_institution" content="B. Verkin Institute for Low Temperature Physics and Engineering" /> <meta name="citation_author_institution" content="Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research" /> <meta name="citation_author" content="O. F. Todrin" /> <meta name="citation_author_institution" content="Institute for Problems of Cryobiology and Cryomedicine" /> <meta name="citation_author" content="V.Yu. Globa" /> <meta name="citation_author_institution" content="Institute for Problems of Cryobiology and Cryomedicine" /> <meta name="citation_author" content="M.O. Chyzh" /> <meta name="citation_author_institution" content="Institute for Problems of Cryobiology and Cryomedicine" /> <meta name="citation_author" content="G.O. Kovalov" /> <meta name="citation_author_institution" content="Institute for Problems of Cryobiology and Cryomedicine" /> <meta name="citation_author" content="S.N. 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We model thermal field distribution which can help relate surface thermal field images to in-depth temperature field dynamics that show freezing and thawing processes dynamics. We consider the spatio-temporal distribution of temperature using examples of hydrogel and living tissue subjected to a cryoprobe. Freezing in the hydrogel is compared with the measurements using visual morphometry. Such studies can be useful for comparing in-vitro and in-vivo thermal field dynamics and for estimating the correct timing for cryoapplication. ### Competing Interest Statement The authors have declared no competing interest." /> <meta name="og-title" property="og:title" content="Mathematical modeling of the frozen zone dynamics: towards using thermal imagers in cryotherapy" /> <meta name="og-url" property="og:url" content="https://www.biorxiv.org/content/10.1101/2024.10.19.619201v2" /> <meta name="og-site-name" property="og:site_name" content="bioRxiv" /> <meta name="og-description" property="og:description" content="Using thermal imaging for cryoablation and cryotherapy is a convenient technique but it does not allow for visualization of what is inside. We model thermal field distribution which can help relate surface thermal field images to in-depth temperature field dynamics that show freezing and thawing processes dynamics. We consider the spatio-temporal distribution of temperature using examples of hydrogel and living tissue subjected to a cryoprobe. Freezing in the hydrogel is compared with the measurements using visual morphometry. Such studies can be useful for comparing in-vitro and in-vivo thermal field dynamics and for estimating the correct timing for cryoapplication. ### Competing Interest Statement The authors have declared no competing interest." /> <meta name="og-type" property="og:type" content="article" /> <meta name="og-image" property="og:image" content="https://www.biorxiv.org/sites/default/files/images/biorxiv_logo_homepage7-5-small.png" /> <meta name="citation_date" content="2024-11-13" /> <link rel="alternate" type="application/vnd.ms-powerpoint" title="Powerpoint" href="/content/10.1101/2024.10.19.619201v2.ppt" /> <meta name="description" content="bioRxiv - the preprint server for biology, operated by Cold Spring Harbor Laboratory, a research and educational institution" /> <meta name="generator" content="Drupal 7 (http://drupal.org)" /> <link rel="canonical" href="https://www.biorxiv.org/content/10.1101/2024.10.19.619201v2" /> <link rel="shortlink" href="https://www.biorxiv.org/node/4218609" /> 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class="highwire-article-citation highwire-citation-type-highwire-article node4218609" data-node-nid="4218609" id="node-4218609--21747972230" data-pisa="biorxiv;2024.10.19.619201v2" data-pisa-master="biorxiv;2024.10.19.619201" data-apath="/biorxiv/early/2024/11/13/2024.10.19.619201.atom" data-hw-author-tooltip-instance="highwire_author_tooltip"><div class="highwire-cite highwire-cite-highwire-article highwire-citation-biorxiv-article-top clearfix has-author-tooltip" > <span class="biorxiv-article-type"> New Results </span> <h1 class="highwire-cite-title" id="page-title">Mathematical modeling of the frozen zone dynamics: towards using thermal imagers in cryotherapy</h1> <div class="highwire-cite-authors" ><span class="highwire-citation-authors"><span class="highwire-citation-author first" data-delta="0"><span class="nlm-given-names">O. V.</span> <span class="nlm-surname">Ivakhnenko</span></span>, <span class="highwire-citation-author" data-delta="1"><span class="nlm-given-names">O. F.</span> <span class="nlm-surname">Todrin</span></span>, <span class="highwire-citation-author" data-delta="2"><span class="nlm-given-names">V.Yu.</span> <span class="nlm-surname">Globa</span></span>, <span class="highwire-citation-author" data-delta="3"><span class="nlm-given-names">M.O.</span> <span class="nlm-surname">Chyzh</span></span>, <span class="highwire-citation-author" data-delta="4"><span class="nlm-given-names">G.O.</span> <span class="nlm-surname">Kovalov</span></span>, <span class="highwire-citation-author hw-author-orcid-logo-wrapper" data-delta="5"><a href="http://orcid.org/0000-0003-3655-0365" target="_blank" class="hw-author-orcid-logo link-icon-only link-icon"><span class="hw-icon-orcid hw-icon-color-orcid"></span> <span class="title element-invisible">View ORCID Profile</span></a><span class="nlm-given-names">S.N.</span> <span class="nlm-surname">Shevchenko</span></span></span></div> <div class="highwire-cite-metadata" ><span class="highwire-cite-metadata-doi highwire-cite-metadata"><span class="label">doi:</span> https://doi.org/10.1101/2024.10.19.619201 </span></div> </div> <div id="hw-article-author-popups-node-4218609--21747972230" style="display: none;"><div class="author-tooltip-0"><div class="author-tooltip-name">O. V. Ivakhnenko </div><div class="author-tooltip-affiliation"><span class="author-tooltip-text"><div class='author-affiliation'><span class='nlm-sup'>1</span><span class='nlm-institution'>B. Verkin Institute for Low Temperature Physics and Engineering</span>, Kharkiv 61103, <span class='nlm-country'>Ukraine</span></div><div class='author-affiliation'><span class='nlm-sup'>2</span><span class='nlm-institution'>Theoretical Quantum Physics Laboratory, Cluster for Pioneering Research</span>, RIKEN, Wako, Saitama, 351-0198, <span class='nlm-country'>Japan</span></div></span></div><ul class="author-tooltip-find-more"><li class="author-tooltip-gs-link first"><a href="/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=O.%2BV.%2BIvakhnenko%2B" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on Google Scholar</a></li><li class="author-tooltip-pubmed-link"><a href="/lookup/external-ref?access_num=Ivakhnenko%20OV&link_type=AUTHORSEARCH" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on PubMed</a></li><li class="author-site-search-link last"><a href="/search/author1%3AO.%2BV.%2BIvakhnenko%2B" rel="nofollow" class="" data-icon-position="" data-hide-link-title="0">Search for this author on this site</a></li></ul></div><div class="author-tooltip-1"><div class="author-tooltip-name">O. F. Todrin </div><div class="author-tooltip-affiliation"><span class="author-tooltip-text"><div class='author-affiliation'><span class='nlm-sup'>3</span><span class='nlm-institution'>Institute for Problems of Cryobiology and Cryomedicine</span>, 61016 Kharkiv, <span class='nlm-country'>Ukraine</span></div></span></div><ul class="author-tooltip-find-more"><li class="author-tooltip-gs-link first"><a href="/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=O.%2BF.%2BTodrin%2B" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on Google Scholar</a></li><li class="author-tooltip-pubmed-link"><a href="/lookup/external-ref?access_num=Todrin%20OF&link_type=AUTHORSEARCH" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on PubMed</a></li><li class="author-site-search-link last"><a href="/search/author1%3AO.%2BF.%2BTodrin%2B" rel="nofollow" class="" data-icon-position="" data-hide-link-title="0">Search for this author on this site</a></li></ul></div><div class="author-tooltip-2"><div class="author-tooltip-name">V.Yu. Globa </div><div class="author-tooltip-affiliation"><span class="author-tooltip-text"><div class='author-affiliation'><span class='nlm-sup'>3</span><span class='nlm-institution'>Institute for Problems of Cryobiology and Cryomedicine</span>, 61016 Kharkiv, <span class='nlm-country'>Ukraine</span></div></span></div><ul class="author-tooltip-find-more"><li class="author-tooltip-gs-link first"><a href="/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=V.Yu.%2BGloba%2B" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on Google Scholar</a></li><li class="author-tooltip-pubmed-link"><a href="/lookup/external-ref?access_num=Globa%20V&link_type=AUTHORSEARCH" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on PubMed</a></li><li class="author-site-search-link last"><a href="/search/author1%3AV.Yu.%2BGloba%2B" rel="nofollow" class="" data-icon-position="" data-hide-link-title="0">Search for this author on this site</a></li></ul></div><div class="author-tooltip-3"><div class="author-tooltip-name">M.O. Chyzh </div><div class="author-tooltip-affiliation"><span class="author-tooltip-text"><div class='author-affiliation'><span class='nlm-sup'>3</span><span class='nlm-institution'>Institute for Problems of Cryobiology and Cryomedicine</span>, 61016 Kharkiv, <span class='nlm-country'>Ukraine</span></div></span></div><ul class="author-tooltip-find-more"><li class="author-tooltip-gs-link first"><a href="/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=M.O.%2BChyzh%2B" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on Google Scholar</a></li><li class="author-tooltip-pubmed-link"><a href="/lookup/external-ref?access_num=Chyzh%20M&link_type=AUTHORSEARCH" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on PubMed</a></li><li class="author-site-search-link last"><a href="/search/author1%3AM.O.%2BChyzh%2B" rel="nofollow" class="" data-icon-position="" data-hide-link-title="0">Search for this author on this site</a></li></ul></div><div class="author-tooltip-4"><div class="author-tooltip-name">G.O. Kovalov </div><div class="author-tooltip-affiliation"><span class="author-tooltip-text"><div class='author-affiliation'><span class='nlm-sup'>3</span><span class='nlm-institution'>Institute for Problems of Cryobiology and Cryomedicine</span>, 61016 Kharkiv, <span class='nlm-country'>Ukraine</span></div></span></div><ul class="author-tooltip-find-more"><li class="author-tooltip-gs-link first"><a href="/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=G.O.%2BKovalov%2B" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on Google Scholar</a></li><li class="author-tooltip-pubmed-link"><a href="/lookup/external-ref?access_num=Kovalov%20G&link_type=AUTHORSEARCH" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on PubMed</a></li><li class="author-site-search-link last"><a href="/search/author1%3AG.O.%2BKovalov%2B" rel="nofollow" class="" data-icon-position="" data-hide-link-title="0">Search for this author on this site</a></li></ul></div><div class="author-tooltip-5"><div class="author-tooltip-name">S.N. Shevchenko </div><div class="author-tooltip-affiliation"><span class="author-tooltip-text"><div class='author-affiliation'><span class='nlm-sup'>1</span><span class='nlm-institution'>B. Verkin Institute for Low Temperature Physics and Engineering</span>, Kharkiv 61103, <span class='nlm-country'>Ukraine</span></div></span></div><ul class="author-tooltip-find-more"><li class="author-tooltip-gs-link first"><a href="/lookup/google-scholar?link_type=googlescholar&gs_type=author&author%5B0%5D=S.N.%2BShevchenko%2B" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on Google Scholar</a></li><li class="author-tooltip-pubmed-link"><a href="/lookup/external-ref?access_num=Shevchenko%20S&link_type=AUTHORSEARCH" target="_blank" class="" data-icon-position="" data-hide-link-title="0">Find this author on PubMed</a></li><li class="author-site-search-link"><a href="/search/author1%3AS.N.%2BShevchenko%2B" rel="nofollow" class="" data-icon-position="" data-hide-link-title="0">Search for this author on this site</a></li><li class="author-orcid-link"><a href="http://orcid.org/0000-0003-3655-0365" target="_blank" class="" data-icon-position="" data-hide-link-title="0">ORCID record for S.N. Shevchenko</a></li><li class="author-corresp-email-link last"><span>For correspondence: <a href="mailto:sshevchenko@ilt.kharkov.ua" class="" data-icon-position="" data-hide-link-title="0">sshevchenko@ilt.kharkov.ua</a></span></li></ul></div></div></div> </div> </div> <div class="panel-separator"></div><div class="panel-pane pane-highwire-panel-tabs pane-panels-ajax-tab-tabs" > <div class="pane-content"> <div class="item-list"><ul class="tabs inline panels-ajax-tab"><li class="first"><a href="/content/10.1101/2024.10.19.619201v2" class="panels-ajax-tab-tab" data-panel-name="biorxiv_tab_art" data-target-id="highwire_article_tabs" data-entity-context="node:4218609" data-trigger="" data-url-enabled="1">Abstract</a><a href="/panels_ajax_tab/biorxiv_tab_art/node:4218609/1" rel="nofollow" style="display:none" class="js-crawler-link"></a></li><li><a href="/content/10.1101/2024.10.19.619201v2.full-text" class="panels-ajax-tab-tab" data-panel-name="article_tab_full_text" data-target-id="highwire_article_tabs" data-entity-context="node:4218609" data-trigger="full-text" data-url-enabled="1">Full Text</a><a href="/panels_ajax_tab/article_tab_full_text/node:4218609/1" rel="nofollow" style="display:none" class="js-crawler-link"></a></li><li><a href="/content/10.1101/2024.10.19.619201v2.article-info" class="panels-ajax-tab-tab" data-panel-name="biorxiv_tab_info" data-target-id="highwire_article_tabs" data-entity-context="node:4218609" data-trigger="article-info" data-url-enabled="1">Info/History</a><a href="/panels_ajax_tab/biorxiv_tab_info/node:4218609/1" rel="nofollow" style="display:none" class="js-crawler-link"></a></li><li><a href="/content/10.1101/2024.10.19.619201v2.article-metrics" class="panels-ajax-tab-tab" data-panel-name="article_tab_metrics" data-target-id="highwire_article_tabs" data-entity-context="node:4218609" data-trigger="article-metrics" data-url-enabled="1">Metrics</a><a href="/panels_ajax_tab/article_tab_metrics/node:4218609/1" rel="nofollow" style="display:none" class="js-crawler-link"></a></li><li class="last"><a href="/content/10.1101/2024.10.19.619201v2.full.pdf+html" class="panels-ajax-tab-tab" data-panel-name="biorxiv_tab_pdf" data-target-id="highwire_article_tabs" data-entity-context="node:4218609" data-trigger="full.pdf+html" data-url-enabled="1"><i class="icon-file-alt"></i> Preview PDF</a><a href="/panels_ajax_tab/biorxiv_tab_pdf/node:4218609/1" rel="nofollow" style="display:none" class="js-crawler-link"></a></li></ul></div> </div> </div> <div class="panel-separator"></div><div class="panel-pane pane-highwire-panel-tabs-container" > <div class="pane-content"> <div data-panels-ajax-tab-preloaded="biorxiv_tab_art" id="panels-ajax-tab-container-highwire_article_tabs" class="panels-ajax-tab-container"><div class="panels-ajax-tab-loading" style ="display:none"><img class="loading" src="https://www.biorxiv.org/sites/all/modules/contrib/panels_ajax_tab/images/loading.gif" alt="Loading" title="Loading" /></div><div class="panels-ajax-tab-wrap-biorxiv_tab_art"><div class="panel-display panel-1col clearfix" > <div class="panel-panel panel-col"> <div><div class="panel-pane pane-highwire-markup" > <div class="pane-content"> <div class="highwire-markup"><div xmlns="http://www.w3.org/1999/xhtml" data-highwire-cite-ref-tooltip-instance="highwire_reflinks_tooltip" class="content-block-markup" xmlns:xhtml="http://www.w3.org/1999/xhtml"><div class="article abstract-view "><span class="highwire-journal-article-marker-start"></span><div class="section abstract" id="abstract-1"><h2 class="">Abstract</h2><p id="p-2">Using thermal imaging for cryoablation and cryotherapy is a convenient technique but it does not allow for visualization of what is inside. We model thermal field distribution which can help relate surface thermal field images to in-depth temperature field dynamics that show freezing and thawing processes dynamics. We consider the spatio-temporal distribution of temperature using examples of hydrogel and living tissue subjected to a cryoprobe. Freezing in the hydrogel is compared with the measurements using visual morphometry. Such studies can be useful for comparing <em>in-vitro</em> and <em>in-vivo</em> thermal field dynamics and for estimating the correct timing for cryoapplication.</p></div><h3>Competing Interest Statement</h3><p id="p-3">The authors have declared no competing interest.</p><div class="section fn-group" id="fn-group-1"><h2>Footnotes</h2><ul><li class="fn-update fn-group-summary-of-updates" id="fn-1"><p id="p-4">Figures placed on their place; For all the figures.</p></li></ul></div><span class="highwire-journal-article-marker-end"></span></div><span class="related-urls"></span></div></div> </div> </div> <div class="panel-separator"></div><div class="panel-pane pane-biorxiv-copyright" > <div class="pane-content"> <div class="field field-name-field-highwire-copyright field-type-text field-label-inline clearfix"><div class="field-label">Copyright </div><div class="field-items"><div class="field-item even">The copyright holder for this preprint is the author/funder, who has granted bioRxiv a 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