Numerical solving of dynamic thermography inverse problem for skin cancer diagnosis based on non-Fourier bioheat model

Horvat, Ivan Dominik (author), Iljaž, Jurij (author)

This paper presents numerical solving of the inverse bioheat problem to estimate four skin cancer parameters; diameter, thickness, blood perfusion rate and thermal relaxation time, based on the thermal response on the skin surface obtained by dynamic thermography and numerical skin cancer model, which can greatly enhance dynamic thermography diagnostics. To describe the heat transfer inside biological tissue and thermal behavior during the dynamic thermography process as realistic as possible, the non-Fourier dual-phase-lag bioheat model was used, as well as skin cancer model has been composed of multilayered healthy skin, embedded skin tumor and subcutaneous fat and muscle. Boundary element method has been used to solve a complex non-Fourier bioheat model to simulate dynamic thermography based on the skin cancer model and guessed searched parameters to obtain the thermal response on the skin surface during the cooling and rewarming phase using a cold air jet provocation, which is needed for the solution of the inverse bioheat problem. The inverse problem has been solved by optimization approach using the hybrid Levenberg-Marquardt optimization method, while the measurement data has been generated numerically with known exact tumor parameters and added noise, to evaluate the accuracy and sensitivity of the solution. Inverse problem solution has been tested for two different thermal responses; absolute temperature and temperature difference response, as well as for two different tumor stages; early stage or Clark II and later stage or Clark IV tumor. All important tumor parameters were successfully retrieved, especially the diameter and relaxation time, even for the high level of noise, while the accuracy of obtained parameters is slightly better using absolute temperature response. The results demonstrate the robustness of the method and a promising way for early diagnosis. The findings contribute to improving bioheat modeling in biological tissues, solving inverse bioheat problems and advancing dynamic thermography as a non-invasive tool for early skin cancer diagnosis.

• Language: English
• Keywords: numerical modeling, dynamic thermography, inverse problem, non-Fourier bioheat transfer, dual-phase-lag model, boundary element method, Levenberg-Marquardt optimization
• Work type: Article
• Typology: 1.08 - Published Scientific Conference Contribution
• Organization: FS - Faculty of Mechanical Engineering
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: Str. 271-283
• Numbering: Vol. 71, no. 9/10
• PID: 20.500.12556/RUL-175983
• UDC: 544.344.016.2:616-006:
• ISSN on article: 2536-3948
• COBISS.SI-ID: 257248771
• Publication date in RUL: 17.11.2025

Record is a part of a journal

• Title: Strojniški vestnik
• Shortened title: Stroj. vestn.
• Publisher: Fakulteta za strojništvo
• ISSN: 2536-3948
• COBISS.SI-ID: 294943232

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian

Abstract

Članek obravnava numerično reševanje inverznega problema prenosa toplote za določitev štirih parametrov kožnega raka: premer, debelino, perfuzijski pretok krvi in relaksacijski čas. Določitev temelji na toplotnem odzivu kože pridobljenim z dinamično termografijo ter numeričnim modelom kožnega raka ki lahko bistveno izboljša diagnostično vrednost termografije. Za čim bolj realističen opis prenosa toplote v tkivu med procesom dinamične termografije je bil uporabljen nefourierov model z dvojnim faznim zamikom. Model kožnega raka je sestavljen iz večplastne kože, podkožne maščobe in mišice ter kožnega raka oziroma tumorja. Za rešitev kompleksnega nefourierovega modela ter simulacije dinamične termografije je bil razvit programski paket na osnovi metode robnih elementov. Simulacija dinamične termografije, ki za temperaturno vzbujanje uporablja curek hladnega zraka, je pomembna za rešitev inverznega problema, saj z njo pridemo do termičnega odziva oziroma temperaturnega kontrasta na površini kože pri predpostavljenih iskanih parametrih ter njene primerjave z meritvijo. Tako je bil inverzni problem rešen s pristopom optimizacije, pri čemer je bil uporabljen Levenberg–Marquardt algoritem. Meritve so bili pri tem generirane numerično z vnaprej znanimi parametri tumorja in dodanim šumom za ovrednotenje natančnost in občutljivost inverzne rešitve. Rešitev inverznega problema je bila pri tem testirana za dva različna temperaturna odziva, in sicer absolutno temperaturo in temperaturno razliko, kakor tudi za dve različni stadija tumorja kot je Clark II, ki predstavlja zgodnji stadij in Clark IV, ki predstavlja pozni stadij. Vsi pomembni parametri tumorja so bili uspešno določeni tudi pri visoki stopnji šuma, zlasti premer in relaksacijski čas, pri čemer je bila natančnost ovrednotenih parametrov nekoliko boljša z uporabo absolutnega temperaturnega odziva. Rezultati kažejo na robustno in obetavno metodo za zgodnjo diagnostiko kožnega raka in pomembno prispevajo na področju modeliranja prenosa toplote v bioloških tkivih, reševanju inverznih problemov ter razvoju dinamične termografije.

• Keywords: numerično reševanje, dinamična termografija, inverzni problem, nefourierov prenos toplote, DPL model, metoda robnih elementov, Levenberg-Marquardt optimizacija

Projects

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: P2-0196
• Name: Raziskave v energetskem, procesnem in okoljskem inženirstvu

• Funder: ARIS - Slovenian Research and Innovation Agency
• Project number: J7-60118
• Name: Izpostavljenost ljudi sevanju zaradi uporabe novih brezžičnih komunikacijskih tehnologij na podlagi naprednih modelov elektromagnetno-termalne dozimetrije