{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:01:19Z","timestamp":1792785679035,"version":"4.5.0"},"reference-count":34,"publisher":"IOP Publishing","issue":"19","license":[{"start":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T00:00:00Z","timestamp":1791417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,10,8]],"date-time":"2026-10-08T00:00:00Z","timestamp":1791417600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"funder":[{"name":"Youth Science Fund Project","award":["12402221"],"award-info":[{"award-number":["12402221"]}]},{"name":"NSERC Discovery Grants Program","award":["RGPIN-2026-07599"],"award-info":[{"award-number":["RGPIN-2026-07599"]}]},{"name":"Canada Foundation for Innovation Research Chairs Program","award":["950-230876"],"award-info":[{"award-number":["950-230876"]}],"id":[{"id":"https:\/\/ror.org\/000az4664","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Phys. Med. Biol."],"published-print":{"date-parts":[[2026,10,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    <jats:italic>Objective.<\/jats:italic>\n                    Depth-dependent heterogeneity in perfusion and thermophysical properties remains a major obstacle to accurate non-invasive measurement of tissue thermal parameters. The objective was to develop an analytical photothermal model that encodes such spatial heterogeneity into a time-dependent effective thermal response coefficient (ETRC) for tissue characterization and early tumor detection.\n                    <jats:italic>Approach.<\/jats:italic>\n                    A finite-window ETRC framework was formulated using the scaling relationship between thermal diffusion depth and time. The ETRC was represented directly by a power series in time and truncated after the first-order term for experimental fitting,\n                    <jats:italic>\u03b2<\/jats:italic>\n                    (\n                    <jats:italic>t<\/jats:italic>\n                    )\u2248\n                    <jats:italic>\u03b2<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    +\n                    <jats:italic>\u03b2<\/jats:italic>\n                    <jats:sub>1<\/jats:sub>\n                    <jats:italic>t<\/jats:italic>\n                    . The fitted ETRC was constrained to remain non-negative throughout each cooling window. An explicit analytical solution was then derived for this constrained finite-window representation through variable substitution.\n                    <jats:italic>Main results.<\/jats:italic>\n                    The proposed model achieved the lowest root-mean-square error in the cooling phase among the tested models. Pixel-wise fitting generated maps of the effective thermal diffusivity\n                    <jats:italic>\u03b1. In vivo, \u03b1<\/jats:italic>\n                    in the peritumoral vascular region decreased progressively from day 3 after inoculation and differed significantly from the pre-inoculation baseline by day 6 (\n                    <jats:italic>p<\/jats:italic>\n                    &lt; 0.01), approximately 3\u20134 d before tumors became palpable. The area under the receiver operating characteristic curve reached 0.94 on day 12.\n                    <jats:italic>Significance.<\/jats:italic>\n                    An interpretable and computationally efficient approach is provided for estimating effective depth-weighted thermal diffusivity from surface-temperature decay while accounting for depth-dependent heterogeneity, without requiring pre-assumed tissue layers. The proposed method may support longitudinal non-invasive thermal imaging, early tumor detection and functional monitoring of tumor development.\n                  <\/jats:p>","DOI":"10.1088\/1361-6560\/aea7f3","type":"journal-article","created":{"date-parts":[[2026,9,15]],"date-time":"2026-09-15T22:54:35Z","timestamp":1789512875000},"page":"195026","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Encoding depth heterogeneity into time: a finite-window power-series thermal response model for non-invasive tissue characterization and early tumor detection"],"prefix":"10.1088","volume":"71","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-4131-6852","authenticated-orcid":true,"given":"Hong","family":"Tang","sequence":"first","affiliation":[{"name":"Northeastern University"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Cong","family":"Zhang","sequence":"additional","affiliation":[{"name":"The First Hospital, Harbin Medical University"},{"name":"Harbin Medical University"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"data-curation","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"}]},{"given":"Hai","family":"Zhang","sequence":"additional","affiliation":[{"name":"Harbin Institute of Technology"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]},{"given":"Andreas","family":"Mandelis","sequence":"additional","affiliation":[{"name":"University of Toronto"},{"name":"University of Toronto"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"investigation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"}]}],"member":"266","published-online":{"date-parts":[[2026,10,8]]},"reference":[{"key":"pmbaea7f3bib1","doi-asserted-by":"publisher","first-page":"196","DOI":"10.18280\/mmep.070204","type":"journal-article","article-title":"Heat exchange within the surrounding biological tissue during magnetic hyperthermia","volume":"7","author":"Abu-Bakr","year":"2020","journal-title":"Math. 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