Temperature response in skin tissue during hyperthermia based on three-phase-lag bioheat model using RBF meshfree method

References

• J. Liu, L. Zhu and L. X. Xu, “Studies on the three-dimensional temperature transients in the canine prostate during transurethral microwave thermal therapy,” J. Biomech. Eng., vol. 122, no. 4, pp. 372–379, 2000. DOI: 10.1115/1.1288208.
   PubMed Web of Science ®Google Scholar
• R. L. Magin and A. F. Peterson, “Invited review: Noninvasive microwave phased arrays for local hyperthermia: A review,” Int. J. Hyperthermia, vol. 5, no. 4, pp. 429–450, 1989. DOI: 10.3109/02656738909140470.
   PubMed Web of Science ®Google Scholar
• R. Seip and E. S. Ebbini, “Noninvasive estimation of tissue temperature response to heating fields using diagnostic ultrasound,” IEEE Trans. Biomed. Eng., vol. 42, no. 8, pp. 828–839, 1995. DOI: 10.1109/10.398644.
   PubMed Web of Science ®Google Scholar
• G. Fibich, “Time dispersive effects in ultrashort laser-tissue interactions,” J. Heat Transfer, vol. 322, pp. 27–32, 1995.
   Google Scholar
• W. Whelan and D. Wyman, “Temperature reconstruction by estimating the thermophysical and optical properties of tissues during interstitial laser heating,” Adv. Heat Mass Transfer Biotechnol., vol. 322, pp. 17–26, 1995.
   Google Scholar
• S. Rastegar, A. M. Chard and A. Azeemi, “An analysis of the kinetics of single-rate and multi-rate thermal damage in laser irradiation of biological tissue,” J. Heat Transfer, vol. 268, pp. 137–137, 1993.
   Google Scholar
• Z. Yilbas, M. Sami and T. Patiroglu, “Study into penetration speed during laser cutting of brain tissues,” J. Med. Eng. Technol., vol. 22, no. 6, pp. 274–279, 1998. DOI: 10.3109/03091909809010011.
   PubMed Web of Science ®Google Scholar
• G. L. Valderrama, L. G. Fredin, M. J. Berry, B. Dempsey and G. M. Harpole, “Temperature distributions in laser-irradiated tissues,” in Laser-Tissue Interaction II, vol. 1427, S. L. Jacques, Ed. Los Angeles, CA: SPIE, 1991, pp. 200–213. DOI: 10.1117/12.44104.
   Google Scholar
• V. Pustovalov, “Thermal processes under the action of laser radiation pulse on absorbing granules in heterogeneous biotissues,” Int. J. Heat Mass Transfer, vol. 36, no. 2, pp. 391–399, 1993. DOI: 10.1016/0017-9310(93)80015-M.
   Web of Science ®Google Scholar
• S. Field and N. Bleehen, “Hyperthermia in the treatment of cancer,” Cancer Treat. Rev., vol. 6, no. 2, pp. 63–94, 1979. DOI: 10.1016/S0305-7372(79)80043-2.
   PubMed Web of Science ®Google Scholar
• Z. P. Chen and R. B. Roemer, “The effects of large blood vessels on temperature distributions during simulated hyperthermia,” J. Biomech. Eng., vol. 114, no. 4, pp. 473–481, 1992. DOI: 10.1115/1.2894097.
   PubMed Web of Science ®Google Scholar
• S. T. Clegg and R. B. Roemer, “Reconstruction of experimental hyperthermia temperature distributions: Application of state and parameter estimation,” J. Biomech. Eng., vol. 115, no. 4A, pp. 380–388, 1993. DOI: 10.1115/1.2895501.
   PubMedGoogle Scholar
• H. H. Pennes, “Analysis of tissue and arterial blood temperatures in the resting human forearm,” J. Appl. Physiol., vol. 1, no. 2, pp. 93–122, 1948. DOI: 10.1152/jappl.1948.1.2.93.
   PubMed Web of Science ®Google Scholar
• C. Cattaneo, “A form of heat-conduction equations which eliminates the paradox of instantaneous propagation,” Comptes Rendus, vol. 247, pp. 431, 1958.
   Google Scholar
• P. Vernotte, “Les paradoxes de la theorie continue de l’equation de la chaleur,” Comptes Rendu, vol. 246, pp. 3154–3155, 1958.
   Google Scholar
• D. Y. Tzou, “A unified field approach for heat conduction from macro-to micro-scales,” J. Heat Transfer, vol. 117, no. 1, pp. 8–16, 1995. DOI: 10.1115/1.2822329.
   Web of Science ®Google Scholar
• W. Q. Lu, J. Liu and Y. Zeng, “Simulation of the thermal wave propagation in biological tissues by the dual reciprocity boundary element method,” Eng. Anal. Boundary Elem., vol. 22, no. 3, pp. 167–174, 1998. DOI: 10.1016/S0955-7997(98)00039-3.
   Web of Science ®Google Scholar
• Ş. Özen, S. Helhel and O. Cerezci, “Heat analysis of biological tissue exposed to microwave by using thermal wave model of bio-heat transfer,” Burns, vol. 34, no. 1, pp. 45–49, 2008. DOI: 10.1016/j.burns.2007.01.009.
   PubMed Web of Science ®Google Scholar
• X. Z. Liu, Y. Zhu, F. Zhang and X. F. Gong, “Estimation of temperature elevation generated by ultrasonic irradiation in biological tissues using the thermal wave method,” Chin. Phys. B, vol. 22, no. 2, pp. 024301, 2013. DOI: 10.1088/1674-1056/22/2/024301.
   Web of Science ®Google Scholar
• R. Fazlali and H. Ahmadikia, “Analytical solution of thermal wave models on skin tissue under arbitrary periodic boundary conditions,” Int. J. Thermophys., vol. 34, no. 1, pp. 139–159, 2013. DOI: 10.1007/s10765-013-1396-0.
   Web of Science ®Google Scholar
• M. R. Salimpour and E. Shirani, “Heat transfer analysis of skin during thermal therapy using thermal wave equation,” J. Therm. Biol., vol. 64, pp. 7–18, 2017.
   PubMed Web of Science ®Google Scholar
• B. Deka and J. Dutta, “Finite element methods for non-Fourier thermal wave model of bio heat transfer with an interface,” J. Appl. Math. Comput., vol. 62, no. 1–2, pp. 701–724, 2020. DOI: 10.1007/s12190-019-01304-8.
   Web of Science ®Google Scholar
• J. Zhou, Y. Zhang and J. Chen, “An axisymmetric dual-phase-lag bioheat model for laser heating of living tissues,” Int. J. Therm. Sci., vol. 48, no. 8, pp. 1477–1485, 2009. DOI: 10.1016/j.ijthermalsci.2008.12.012.
   Web of Science ®Google Scholar
• S. Singh and S. Kumar, “Numerical study on triple layer skin tissue freezing using dual phase lag bio-heat model,” Int. J. Therm. Sci., vol. 86, pp. 12–20, 2014. DOI: 10.1016/j.ijthermalsci.2014.06.027.
   Web of Science ®Google Scholar
• H. Askarizadeh and H. Ahmadikia, “Analytical analysis of the dual-phase-lag model of bioheat transfer equation during transient heating of skin tissue,” Heat Mass Transfer, vol. 50, no. 12, pp. 1673–1684, 2014. DOI: 10.1007/s00231-014-1373-6.
   Web of Science ®Google Scholar
• P. Kumar, D. Kumar and K. Rai, “A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment,” J. Therm. Biol., vol. 49, pp. 98–105, 2015.
   PubMed Web of Science ®Google Scholar
• P. Kumar, D. Kumar and K. Rai, “Numerical simulation of dual-phase-lag bioheat transfer model during thermal therapy,” Math. Biosci., vol. 281, pp. 82–91, 2016. DOI: 10.1016/j.mbs.2016.08.013.
   PubMed Web of Science ®Google Scholar
• S. R. Choudhuri, “On a thermoelastic three-phase-lag model,” J. Therm. Stresses, vol. 30, no. 3, pp. 231–238, 2007. DOI: 10.1080/01495730601130919.
   Web of Science ®Google Scholar
• R. Quintanilla and R. Racke, “A note on stability in three-phase-lag heat conduction,” Int. J. Heat Mass Transfer, vol. 51, no. 1-2, pp. 24–29, 2008. DOI: 10.1016/j.ijheatmasstransfer.2007.04.045.
   Web of Science ®Google Scholar
• R. Kumar and V. Chawla, “A study of plane wave propagation in anisotropic three-phase-lag and two-phase-lag model,” Int. Commun. Heat Mass Transfer, vol. 38, no. 9, pp. 1262–1268, 2011. DOI: 10.1016/j.icheatmasstransfer.2011.07.005.
   Web of Science ®Google Scholar
• I. Kaur, P. Lata and K. Handa, “Effects of memory dependent derivative of bio-heat model in skin tissue exposed to laser radiation,” EAI Endorsed Trans. Pervasive Health Technol., vol. 6, no. 22, pp. 164589, 2020. DOI: 10.4108/eai.13-7-2018.164589.
   Google Scholar
• P. Lata, I. Kaur and K. Singh, “Transversely isotropic thin circular plate with multi-dual-phase lag heat transfer,” Steel Compos. Struct. Int. J., vol. 35, no. 3, pp. 343–351, 2020.
   Web of Science ®Google Scholar
• I. Kaur, P. Lata and K. Singh, “Effect of memory dependent derivative on forced transverse vibrations in transversely isotropic thermoelastic cantilever nano-beam with two temperature,” Appl. Math. Modell., vol. 88, pp. 83–105, 2020. DOI: 10.1016/j.apm.2020.06.045.
   Web of Science ®Google Scholar
• P. Lata and H. Kaur, “Interactions in a homogeneous isotropic modified couple stress thermoelastic solid with multi-dual-phase-lag heat transfer and two temperature,” Steel and Composite Structures,” An Int. J., vol. 38, no. 2, pp. 213–221, 2021.
   Google Scholar
• R. Kumar and V. Chawla, “Reflection and refraction of plane wave at the interface between elastic and thermoelastic media with three-phase-lag model,” Int. Commun. Heat Mass Transfer, vol. 48, pp. 53–60, 2013. DOI: 10.1016/j.icheatmasstransfer.2013.08.013.
   Web of Science ®Google Scholar
• A. Akbarzadeh, J. Fu and Z. Chen, “Three-phase-lag heat conduction in a functionally graded hollow cylinder,” Trans. Can. Soc. Mech. Eng., vol. 38, no. 1, pp. 155–171, 2014. DOI: 10.1139/tcsme-2014-0010.
   Web of Science ®Google Scholar
• S. Falahatkar, A. Nouri-Borujerdi, A. Mohammadzadeh and M. Najafi, “Evaluation of heat conduction in a laser irradiated tooth with the three-phase-lag bio-heat transfer model,” Therm. Sci. Eng. Prog., vol. 7, pp. 203–212, 2018. DOI: 10.1016/j.tsep.2018.06.012.
   Google Scholar
• Q. Zhang, Y. Sun and J. Yang, “Bio-heat response of skin tissue based on three-phase-lag model,” Sci. Rep., vol. 10, no. 1, pp. 1–14, 2020.
   PubMedGoogle Scholar
• D. Kumar and K. Rai, “Three-phase-lag bioheat transfer model and its validation with experimental data,” Mech. Based Des. Struct. Mach., vol. 50, no. 7, pp. 2493–2507, 2022.
   Web of Science ®Google Scholar
• A. Hobiny, F. Alzahrani and I. Abbas, “Analytical estimation of temperature in living tissues using the TPL bioheat model with experimental verification,” Mathematics, vol. 8, no. 7, pp. 1188, 2020. DOI: 10.3390/math8071188.
   Web of Science ®Google Scholar
• R. Verma and S. Kumar, “Computational study on skin tissue freezing using three-phase lag bioheat model,” J. Heat Transfer, vol. 143, no. 11, pp. 111201 (9 pages), 2021. DOI: 10.1115/1.4051764.
   Web of Science ®Google Scholar
• M. Zerroukat, H. Power and C. Chen, “A numerical method for heat transfer problems using collocation and radial basis functions,” Int. J. Numer. Meth. Eng., vol. 42, no. 7, pp. 1263–1278, 1998. DOI: 10.1002/(SICI)1097-0207(19980815)42:7<1263::AID-NME431>3.0.CO;2-I.
   Web of Science ®Google Scholar
• L. Cao, Q. H. Qin and N. Zhao, “An RBF–MFS model for analysing thermal behaviour of skin tissues,” Int. J. Heat Mass Transfer, vol. 53, no. 7-8, pp. 1298–1307, 2010. DOI: 10.1016/j.ijheatmasstransfer.2009.12.036.
   Web of Science ®Google Scholar
• M. Jamil and E. Ng, “Evaluation of meshless radial basis collocation method (RBCM) for heterogeneous conduction and simulation of temperature inside the biological tissues,” Int. J. Therm. Sci., vol. 68, pp. 42–52, 2013. DOI: 10.1016/j.ijthermalsci.2013.01.007.
   Web of Science ®Google Scholar
• Z. W. Zhang, H. Wang and Q. H. Qin, “Meshless method with operator splitting technique for transient nonlinear bioheat transfer in two-dimensional skin tissues,” Int. J. Mol. Sci., vol. 16, no. 1, pp. 2001–2019, 2015. DOI: 10.3390/ijms16012001.
   PubMed Web of Science ®Google Scholar
• W. Chen, L. Ye and H. Sun, “Fractional diffusion equations by the Kansa method,” Comput. Math. Appl., vol. 59, no. 5, pp. 1614–1620, 2010. DOI: 10.1016/j.camwa.2009.08.004.
   Web of Science ®Google Scholar
• M. Abbaszadeh and M. Dehghan, “An improved meshless method for solving two-dimensional distributed order time-fractional diffusion-wave equation with error estimate,” Numer. Algorithms, vol. 75, no. 1, pp. 173–211, 2017. DOI: 10.1007/s11075-016-0201-0.
   Web of Science ®Google Scholar
• M. Dehghan, M. Abbaszadeh and A. Mohebbi, “Error estimate for the numerical solution of fractional reaction–subdiffusion process based on a meshless method,” J. Comput. Appl. Math., vol. 280, pp. 14–36, 2015. DOI: 10.1016/j.cam.2014.11.020.
   Web of Science ®Google Scholar
• M. Dehghan, M. Abbaszadeh and A. Mohebbi, “Analysis of a meshless method for the time fractional diffusion-wave equation,” Numer. Algorithms, vol. 73, no. 2, pp. 445–476, 2016. DOI: 10.1007/s11075-016-0103-1.
   Web of Science ®Google Scholar
• A. Esen, F. Bulut and Ö. Oruç, “A unified approach for the numerical solution of time fractional Burgers’ type equations,” Eur. Phys. J. Plus., vol. 131, no. 4, pp. 1–13, 2016. DOI: 10.1140/epjp/i2016-16116-5.
   Web of Science ®Google Scholar
• V. R. Hosseini, E. Shivanian and W. Chen, “Local radial point interpolation (MLRPI) method for solving time fractional diffusion-wave equation with damping,” J. Comput. Phys., vol. 312, pp. 307–332, 2016. DOI: 10.1016/j.jcp.2016.02.030.
   Web of Science ®Google Scholar
• Q. Liu, F. Liu, I. Turner, V. Anh and Y. Gu, “A RBF meshless approach for modeling a fractal mobile/immobile transport model,” Appl. Math. Comput., vol. 226, pp. 336–347, 2014. DOI: 10.1016/j.amc.2013.10.008.
   Web of Science ®Google Scholar
• H. R. Ghehsareh, S. H. Bateni and A. Zaghian, “A meshfree method based on the radial basis functions for solution of two-dimensional fractional evolution equation,” Eng. Anal. Boundary Elem., vol. 61, pp. 52–60, 2015. DOI: 10.1016/j.enganabound.2015.06.009.
   Web of Science ®Google Scholar
• H. R. Ghehsareh, A. Zaghian and M. Raei, “A local weak form meshless method to simulate a variable order time-fractional mobile–immobile transport model,” Eng. Anal. Boundary Elem., vol. 90, pp. 63–75, 2018. DOI: 10.1016/j.enganabound.2018.01.016.
   Web of Science ®Google Scholar
• H. R. Ghehsareh, M. Raei and A. Zaghian, “Application of meshless local Petrov–Galerkin technique to simulate two-dimensional time-fractional Tricomi-type problem,” J. Braz. Soc. Mech. Sci. Eng., vol. 41, no. 6, pp. 1–15, 2019. DOI: 10.1007/s40430-019-1749-0.
   Web of Science ®Google Scholar
• Ö. Oruç, “A meshfree computational approach based on multiple-scale pascal polynomials for numerical solution of a 2D elliptic problem with nonlocal boundary conditions,” Int. J. Comput. Methods, vol. 17, no. 10, pp. 1950080, 2020. DOI: 10.1142/S0219876219500804.
   Web of Science ®Google Scholar
• R. Salehi, “A meshless point collocation method for 2D multi-term time fractional diffusion-wave equation,” Numer. Algorithms, vol. 74, no. 4, pp. 1145–1168, 2017. DOI: 10.1007/s11075-016-0190-z.
   Web of Science ®Google Scholar
• J. C. Mason and D. C. Handscomb, Chebyshev Polynomials. New York, USA: Chapman and Hall/CRC, 2002.
   Google Scholar
• M. D. Buhmann, Radial Basis Functions: Theory and Implementations, vol. 12. Cambridge, UK: Cambridge University Press, 2003.
   Google Scholar
• P. K. Gupta, J. Singh and K. Rai, “Numerical simulation for heat transfer in tissues during thermal therapy,” J. Therm. Biol., vol. 35, no. 6, pp. 295–301, 2010. DOI: 10.1016/j.jtherbio.2010.06.007.
   Web of Science ®Google Scholar
• Z. S. Deng and J. Liu, “Analytical study on bioheat transfer problems with spatial or transient heating on skin surface or inside biological bodies,” J. Biomech. Eng., vol. 124, no. 6, pp. 638–649, 2002. DOI: 10.1115/1.1516810.
   PubMed Web of Science ®Google Scholar