Analytical Breakthrough of Pennes’ Bioheat Model in Malignant Tissues Exposed to Thermal Radiation: In Silico Investigation with Fractional-Order Three-Phase Lag

This research article proposes an advanced approach to examine the thermal properties of bioheat transfer to the malignant tissues due to exposure of direct thermal radiations. In order to carry such novel investigations for living beings, an inventive one-dimensional (1-D) bioheat model has incorporated with fractional-order three-phase lag (FOTPL), including time-delay parameter α for the Pennes’ bioheat transfer equation, and employed to dissect the thermal properties of the malignant tissues. This unique problem is resolved using the Laplace transform technique. Both the thermal and temperature damages to the malignant cells exposed to bioheat transfer with thermal radiation are determined in physical form by using proper simulation environment. The various effects of fractional-order three-phase lag parameter are represented graphically and analyzed. Basically, this research paper has been divided into six sections. Section 1 describes the use of bioheat and their related thermal processes to study the pattern and blood flow mechanism for the transfer of bioheat in healthy and cancerous cells by eliminating thermal damage in the malignant cells; Sect. 2 analyzes the existing literature in the field of bioheat transfer; Sect. 3 critically elaborates the basic equations to model bioheat transfer with instant surface heating due to thermal or laser radiations; Sect. 4 formulates the complete resolution of the problem with different temperature variations in the biological tissues with their surface heating by applying the thermal source; Sect. 5 exhibits the numerical results on the specific values of different parameter, including the variation of bioheat transfer, different values of memory-dependent derivatives and thermal damage to the malignant tissues; and finally, Sect. 6 concludes the research and presents the future direction which may be extended to analyze the bioheat transfer in different kind of tissues.