{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:20:45Z","timestamp":1760232045983,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2022,5,5]],"date-time":"2022-05-05T00:00:00Z","timestamp":1651708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11074159","2021TS088"],"award-info":[{"award-number":["11074159","2021TS088"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities","award":["11074159","2021TS088"],"award-info":[{"award-number":["11074159","2021TS088"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJERPH"],"abstract":"<jats:p>The development of appropriate photothermal detection of skin diseases to meet complex clinical demands is an urgent challenge for the prevention and therapy of skin cancer. An extensive body of literature has ignored all high-order harmonics above the second order and their influences on low-order harmonics. In this paper, a new iterative numerical method is developed for solving the nonlinear thermal diffusion equation to improve nonlinear photothermal detection for the noninvasive assessment of the thickness of port-wine stain (PWS). First, based on the anatomical and structural properties of skin tissue of PWS, a nonlinear theoretical model for photothermal detection is established. Second, a corresponding nonlinear thermal diffusion equation is solved by using the new iterative numerical method and taking into account harmonics above the second-order and their effects on lower-order harmonics. Finally, the thickness and excitation light intensity of PWS samples are numerically simulated. The simulation results show that the numerical solution converges fasterand the physical meaning of the solution is clearerwith the new method than with the traditional perturbation method. The rate of change in each harmonic with the sample thickness for the new method is higher than that for the conventional perturbation method, suggesting that the proposed numerical method may provide greater detection sensitivity. The results of the study provide a theoretical basis for the clinical treatment of PWS.<\/jats:p>","DOI":"10.3390\/ijerph19095637","type":"journal-article","created":{"date-parts":[[2022,5,5]],"date-time":"2022-05-05T13:10:26Z","timestamp":1651756226000},"page":"5637","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Nonlinear Photothermal Iterative Theory for Port-Wine Stain Detection"],"prefix":"10.3390","volume":"19","author":[{"given":"Na","family":"Cao","sequence":"first","affiliation":[{"name":"Shaanxi Key Laboratory of Ultrasound, School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongtao","family":"Liang","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Ultrasound, School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruoyu","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Ultrasound, School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanhua","family":"Li","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Ultrasound, School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Cao","sequence":"additional","affiliation":[{"name":"Shaanxi Key Laboratory of Ultrasound, School of Physics and Information Technology, Shaanxi Normal University, Xi\u2019an 710062, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1111\/jdv.15599","article-title":"Port wine stain treatment outcomes have not improved over the past three decades","volume":"33","author":"Raath","year":"2019","journal-title":"J. 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