Study on Thermal Damage in <scp>3D</scp> Tumor During Magnetic Nanoparticle Hyperthermia Using Space–Time Fractional Dual Phase Lag Bioheat Model

Magnetic nanoparticles for hyperthermic cancer treatment have gained significant attention in recent years. Magnetic hyperthermia ablates malignant cells by dissipating heat from magnetic nanoparticles (MNPs) when subjected to an alternate magnetic field. Living tissues are highly non-homogeneous, and non-Fourier thermal behavior in biological tissue has been experimentally observed. In the present work, two important treatment parameters-the therapeutic temperature distribution and the degree of thermal damage to a three-dimensional, randomly shaped tumor encompassed by healthy tissue during the MNP hyperthermia treatment procedure-have been determined computationally. A three-dimensional space-time fractional dual-phase lag model has been discussed to simulate heat transmission in the tissues. The considered model is solved using the meshless method based on the RBF function and shifted Chebyshev polynomials in spatial and temporal directions, respectively. The influence of fractional derivatives ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi> <mml:mo>,</mml:mo> <mml:mi>β</mml:mi></mml:mrow> <mml:annotation>$$ \alpha, \beta $$</mml:annotation></mml:semantics> </mml:math> ), phase lag times ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>τ</mml:mi> <mml:mi>q</mml:mi></mml:msub> <mml:mo>,</mml:mo> <mml:msub><mml:mi>τ</mml:mi> <mml:mi>T</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {\tau}_q,{\tau}_T $$</mml:annotation></mml:semantics> </mml:math> ), and heat source parameters ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>ϕ</mml:mi> <mml:mo>,</mml:mo> <mml:msub><mml:mi>H</mml:mi> <mml:mn>0</mml:mn></mml:msub> <mml:mo>,</mml:mo> <mml:mi>f</mml:mi></mml:mrow> <mml:annotation>$$ \phi, {H}_0,f $$</mml:annotation></mml:semantics> </mml:math> ) on the thermal damage in tumors has been investigated, and it has been observed that these parameters have significant effects on the distribution of temperature and thermal damage to the tumor tissue.