Variable thermal conductivity approach for bioheat transfer during thermal ablation

References

• Akbar, N. S., Raza, M., & Ellahi, R. (2016a). Anti-bacterial application for new thermal conductivity model in arteries with CNT suspended nanofluid. Journal of Mechanics in Medicine and Biology, 16(5), 1650063. doi: 10.1142/S0219519416500639
   Web of Science ®Google Scholar
• Akbar, N. S., Raza, M., & Ellahi, R. (2016b). Endoscopic effects with entropy generation analysis in peristalsis for the thermal conductivity of H2O+Cu nanofluid. Journal of Applied Mathematics and Mechanics, 9(4), 1721–1730.
   Google Scholar
• Arpaci, V. S. (1996). Conduction heat transfer. Reading, MA: Addison-Wesley Publishing Co.
   Google Scholar
• Bhattacharya, A., & Mahajan, R. L. (2003). Temperature dependence of thermal conductivity of biological tissues. Physiological Measurement, 24(3), 769–783. doi: 10.1088/0967-3334/24/3/312
   PubMed Web of Science ®Google Scholar
• Bhatti, M. M., Zeeshan, A., & Ellahi, R. (2017). Electromagnetohydrodynamic (EMHD) peristaltic flow of solid particles in a third-grade fluid with heat transfer. Mechanics & Industry, 18(3), 314. doi: 10.1051/meca/2016061
   Web of Science ®Google Scholar
• Bhatti, M. M., Zeeshan, A., Ellahi, R., & Shit, G. C. (2018). Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy–Brinkman–Forchheimer porous medium. Advanced Powder Technology, 29(5), 1189–1197. doi: 10.1016/j.apt.2018.02.010
   Web of Science ®Google Scholar
• Bhatti, M. M., Zeeshan, A., Tripathi, D., & Ellahi, R. (2018). Thermally developed peristaltic propulsion of magnetic solid particles in biorheological fluids. Indian Journal of Physics, 92(4), 423–430. doi: 10.1007/s12648-017-1132-x
   Web of Science ®Google Scholar
• Cattaneo, C. (1958). A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Compte Rendus, 247, 431–433.
   Google Scholar
• Ellahi, R., Alamri, Sultan, Z., Basit, A., & Majeed, A. (2018). Effects of MHD and slip on heat transfer boundary layer flow over a moving plate based on specific entropy generation. Journal of Taibah University for Science, 12(4), 476–482. doi: 10.1080/16583655.2018.1483795
   Web of Science ®Google Scholar
• Ellahi, R., Zeeshan, A., Shehzad, N., & Alamri, S. Z. (2018). Structural impact of kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: Application of cooling process. Journal of Molecular Liquids, 264, 607–615. doi: 10.1016/j.molliq.2018.05.103
   Web of Science ®Google Scholar
• Guntur, S. R., & Choi, M. J. (2015). Influence of temperature-dependent thermal parameters on temperature elevation of tissue exposed to high-intensity focused ultrasound: Numerical simulation. Ultrasound in Medicine and Biology, 41(3), 806–813. doi: 10.1016/j.ultrasmedbio.2014.10.008
   PubMed Web of Science ®Google Scholar
• Guntur, S. R., Lee, K. I., Paeng, D. G., Coleman, A. J., & Choi, M. J. (2013). Temperature-dependent thermal properties of ex vivo liver undergoing thermal ablation. Ultrasound in Medicine and Biology, 39, 1–14.
   Web of Science ®Google Scholar
• Gupta, P. K., Singh, J., & Rai, K. N. (2010). Numerical simulation for heat transfer in tissues during thermal therapy. Journal of Thermal Biology, 35(6), 295–301. doi: 10.1016/j.jtherbio.2010.06.007
   Web of Science ®Google Scholar
• Hassan, M., Marin, M., Ellahi, R., & Alamri, S. Z. (2018). Exploration of convective heat transfer and flow characteristics synthesis by Cu–Ag water hybrid-nanofluids. Heat Transfer Research, 49(18), 1837–1848. doi: 10.1615/HeatTransRes.2018025569
   Web of Science ®Google Scholar
• Hetnarski, R. B. (1986). Thermal Stresses, Vol. I. North-Holland, Amsterdam: Taylor and Francis Group.
   Google Scholar
• Ijaz, N., Zeeshan, A., Bhatti, M. M., & Ellahi, R. (2018). Analytical study on liquid-solid particles interaction in the presence of heat and mass transfer through a wavy channel. Journal of Molecular Liquids, 250, 80–87. doi: 10.1016/j.molliq.2017.11.123
   Web of Science ®Google Scholar
• Kashcooli, M., Salimpour, M. R., & Shirani, E. (2017). Heat transfer analysis of skin during thermal therapy using thermal wave equation. Journal of Thermal Biology, 64, 7–18. doi: 10.1016/j.jtherbio.2016.12.007
   PubMed Web of Science ®Google Scholar
• Kumar, D., & Rai, K. N. (2017). Numerical simulation of time fractional dual-phase-lag model of heat transfer within skin tissue during thermal therapy. Journal of Thermal Biology, 67, 49–58. doi: 10.1016/j.jtherbio.2017.05.001
   PubMed Web of Science ®Google Scholar
• Kumar, D., Kumar, P., & Rai, K. N. (2015a). Numerical Study on non-Fourier bioheat transfer during thermal ablation. Procedia Engineering, 127, 1300–1307. doi: 10.1016/j.proeng.2015.11.487
   Google Scholar
• Kumar, D., Singh, S., Sharma, N., & Rai, K. N. (2018). Verified non-linear DPL model with experimental data for analyzing heat transfer in tissue during thermal therapy. International Journal of Thermal Sciences, 133, 320–329. doi: 10.1016/j.ijthermalsci.2018.07.031
   Web of Science ®Google Scholar
• Kumar, P., Kumar, D., & Rai, K. N. (2015b). A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment. Journal of Thermal Biology, 49–50, 98–105. doi: 10.1016/j.jtherbio.2015.02.008
   PubMed Web of Science ®Google Scholar
• Kumar, P., Kumar, D., & Rai, K. N. (2016). Non-linear dual-phase-lag model for analyzing heat transfer phenomena in living tissues during thermal ablation. Journal of Thermal Biology, 20, 204–212. doi: 10.1016/j.jtherbio.2016.07.017
   Google Scholar
• Kumar, S., Damor, R. S., & Shukla, A. K. (2018). Numerical study on thermal therapy of triple layer skin tissue using fractional bioheat model. International Journal of Biomathematics, 11(04), 1850052. doi: 10.1142/S1793524518500523
   Google Scholar
• Pennes, H. H. (1948). Analysis of tissue and arterial blood temperature in the resting forearm. Journal of Applied Physiology, 1(2), 93–122. doi: 10.1152/jappl.1948.1.2.93
   PubMed Web of Science ®Google Scholar
• Razzaghi, M., & Yousefi, S. (2001). The Legendre wavelets operational matrix of integration. International Journal of Systems Science, 32(4), 495–502. doi: 10.1080/002077201300080910
   Web of Science ®Google Scholar
• Rossmann, C., & Haemmerich, D. (2014). Review of temperature dependence of thermal properties, dielectric properties, and perfusion of biological tissues at hyperthermic and ablation temperatures. Critical Reviews in Biomedical Engineering, 42, 467–492. doi: 10.1615/CritRevBiomedEng.2015012486
   PubMedGoogle Scholar
• Tan, Q., Zou, X., Dong, H., Ding, Y., & Zhao, X. (2018). Influence of blood vessels on temperature during high-intensity focused ultrasound hyperthermia based on the thermal wave model of bioheat transfer. Advances in Condensed Matter Physics, 2018, 5018460. doi: 10.1155/2018/5018460
   Web of Science ®Google Scholar
• Trujillo, M., & Berjano, E. (2013). Review of the mathematical functions used to model the temperature dependence of electrical and thermal conductivities of biological tissues in radiofrequency ablation. International Journal of Hyperthermia, 29(6), 590–597. doi: 10.3109/02656736.2013.807438
   PubMed Web of Science ®Google Scholar
• Valvano, J. W., Cochran, J. R., & Diller, K. R. (1985). Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors. International Journal of Thermophysics, 6(3), 301–311. doi: 10.1007/BF00522151
   Web of Science ®Google Scholar
• Vernotte, P. (1958). Les paradoxes de la theorie continue de l’equation de la chaleur. Compte Rendus, 246, 3154–3155.
   Google Scholar
• Watanabe, H., Kobayashi, Y., Hashiszume, M., & Fujie, M. G. (2009). Modeling the temperature dependence of thermophysical properties: Study on the effect of temperature dependence for RFA, 31st Annual International Conference of the IEEE EMBS Minneapolis, Minnesota, USA, September 2–6.
   Google Scholar
• Yadav, S., Kumar, D., & Rai, K. N. (2014). Finite element Legendre wavelet Galerkin approach to inward solidification in simple body under most generalized boundary condition. Zeitschrift für Naturforschung, 69a, 501–510.
   Google Scholar