Advances in materials Research

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The effects of thermal relaxation times in thermo-viscoelastic tissues during hyperthermia treatment

  • Ibrahim A. Abbas (Department of mathematics, Faculty of Science, Sohag University) ;
  • Aboelnour N. Abdalla (Department of mathematics, Faculty of Science, Sohag University) ;
  • Abdelrahman A. Abbas (Department of mathematics, Faculty of Science, Sohag University)
  • Received : 2023.11.01
  • Accepted : 2024.02.29
  • Published : 2024.08.25
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Abstract

The paper is a study on the biothermoelastic analysis in viscoelastic biological tissues in the presence of thermal relaxation times. Using Laplace transforms and related methodologies, we explore how living tissue responds to an exponentially decaying pulse of heat flux at the boundary. The Laplace transformations are reversed using the numerical method. The Tzuo technique was used to measure the reversal. Temperature, displacement, and stress distributions are affected by single-phase and delay relaxation coefficients as well as volume rheological factors, are provided with numerical findings and graphically depicted. In addition, we carry out a parametric analysis to provide assistance in choosing the design variables that are the most successful, which finally results in an improvement in the accuracy of hyperthermia treatments.

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References

  1. Abbas, I.A. (2015), "Generalized thermoelastic interaction in functional graded material with fractional order three-phase lag heat transfer", J. Cent. South Univ., 22(5), 1606-1613. https://doi.org/10.1007/s11771-015-2677-5.
  2. Abbas, I.A. and Kumar, R. (2016), "2D deformation in initially stressed thermoelastic half-space with voids", Steel Compos. Struct., 20(5), 1103-1117. https://doi.org/10.12989/scs.2016.20.5.1103.
  3. Abbas, I.A. and Marin, M. (2017), "Analytical solution of thermoelastic interaction in a half-space by pulsed laser heating", Phys. E: Low Dimens. Syst. Nanostr., 87, 254-260. https://doi.org/10.1016/j.physe.2016.10.048.
  4. Abbas, I.A. and Marin, M. (2018), "Analytical solutions of a two-dimensional generalized thermoelastic diffusions problem due to laser pulse", Iran. J. Sci. Technol. Trans. Mech. Eng., 42, 57-71. https://doi.org/10.1007/s40997-017-0077-1.
  5. Abbas, I.A. and Youssef, H.M. (2012), "A nonlinear generalized thermoelasticity model of temperature-dependent materials using finite element method", Int. J. Thermophys., 33, 1302-1313. https://doi.org/10.1007/s10765-012-1272-3.
  6. Ahmed, H.M., Salem, N.M. and Al-Atabany, W. (2023), "Human cornea thermo-viscoelastic behavior modelling using standard linear solid model", BMC Ophthalmol., 23(1), 250. https://doi.org/10.1186/s12886-023-02985-3.
  7. Alzahrani, F.S. and Abbas, I.A. (2019), "Analytical estimations of temperature in a living tissue generated by laser irradiation using experimental data", J. Therm. Biol., 85, 102421. https://doi.org/10.1016/j.jtherbio.2019.102421.
  8. Cattaneo, C. (1958), "A form of heat-conduction equations which eliminates the paradox of instantaneous propagation", Comptes Rendus, 247, 431.
  9. El-Bary, A.A., Youssef, H.M., Omar, M. and Ramadan, K.T. (2019), "Influence of thermal wave emitted by the cellular devices on the human head", Microsyst. Technol., 25, 413-422. https://doi.org/10.1007/s00542-018-4012-1.
  10. Ezzat, M.A. (2008), "State space approach to solids and fluids", Can. J. Phys., 86(11), 1241-1250.
  11. Ezzat, M.A. (2020), "The effects of thermal and mechanical material properties on tumorous tissue during hyperthermia treatment", J. Therm. Biol., 92, 102649. https://doi.org/10.1016/j.jtherbio.2020.102649.
  12. Ezzat, M.A. (2020), "Fractional thermo-viscoelastic response of biological tissue with variable thermal material properties", J. Therm. Stress., 43(9), 1120-1137. https://doi.org/10.1080/01495739.2020.1770643.
  13. Ezzat, M.A. (2021), "Bio-thermo-mechanics behavior in living viscoelastic tissue under the fractional dual-phase-lag theory", Arch. Appl. Mech., 91(9), 3903-3919. https://doi.org/10.1007/s00419-021-01984-4.
  14. Ezzat, M.A. (2021), "Thermo-mechanical memory responses in a thick tumorous skin tissue during hyperthermia treatment", Waves Random Complex Media, 2021, 1-25. https://doi.org/10.1080/17455030.2021.2004334.
  15. Ezzat, M.A. (2021), "Thermo-mechanical memory responses of biological viscoelastic tissue with variable thermal material properties", Int. J. Numer. Method. Heat Fluid Flow, 31(1), 548-569. https://doi.org/10.1108/HFF-03-2020-0182.
  16. Ezzat, M.A. (2023), "Analytical study of two-dimensional thermo-mechanical responses of viscoelastic skin tissue with temperature-dependent thermal conductivity and rheological properties", Mech. Based Des. Struct. Mach., 51(5), 2776-2793. https://doi.org/10.1080/15397734.2021.1907757.
  17. Ezzat, M.A. and Alabdulhadi, M.H. (2023), "Thermomechanical interactions in viscoelastic skin tissue under different theories", Indian J. Phys., 97(1), 47-60. https://doi.org/10.1007/s12648-021-02261-4.
  18. Ezzat, M.A., El-Bary, A.A. and Al-Sowayan, N.S. (2016), "Tissue responses to fractional transient heating with sinusoidal heat flux condition on skin surface", Anim. Sci. J. 87(10), 1304-1311. https://doi.org/10.1111/asj.12568.
  19. Ezzat, M.A. and El-Karamany, A.S. (2002), "The uniqueness and reciprocity theorems for generalized thermoviscoelasticity with two relaxation times", Int. J. Eng. Sci., 40(11), 1275-1284. https://doi.org/10.1016/s0020-7225(01)00099-4.
  20. Ezzat, M.A., El-Karamany, A.S. and Samaan, A.A. (2001), "State-space formulation to generalized thermoviscoelasticity with thermal relaxation", J. Therm. Stress., 24(9), 823-846. https://doi.org/10.1080/014957301750379612.
  21. Ezzat, M.A. and Lewis, R.W. (2022), "Two-dimensional thermo-mechanical fractional responses to biological tissue with rheological properties", Int. J. Numer. Method. Heat Fluid Flow, 32(6), 1944-1960. https://doi.org/10.1108/HFF-03-2021-0201.
  22. Ezzat, M.A. and Youssef, H.M. (2010), "Stokes' first problem for an electro-conducting micropolar fluid with thermoelectric properties", Can. J. Phys., 88(1), 35-48. https://doi.org/10.1139/P09-100.
  23. Fahmy, M.A. and Almehmadi, M.M. (2023), "Fractional dual-phase-lag model for nonlinear viscoelastic soft tissues", Fract. Fract., 7(1), 66. https://doi.org/10.3390/fractalfract7010066.
  24. Fox, N. (1969), "Generalised thermoelasticity", Int. J. Eng. Sci., 7(4), 437-445. https://doi.org/10.1016/0020-7225(69)90077-9.
  25. Green, A.E. and Lindsay, K. (1972), "Thermoelasticity", J. Elast., 2(1), 1-7.
  26. Hobiny, A. and Abbas, I. (2021), "Analytical solutions of fractional bioheat model in a spherical tissue", Mech. Based Des. Struct. Mach., 49(3), 430-439. https://doi.org/10.1080/15397734.2019.1702055.
  27. Hobiny, A. and Abbas, I.A. (2018), "Analytical solutions of photo-thermo-elastic waves in a non-homogenous semiconducting material", Result. Phys., 10, 385-390. https://doi.org/10.1016/j.rinp.2018.06.035.
  28. Hobiny, A., Alzahrani, F., Abbas, I. and Marin, M. (2020), "The effect of fractional time derivative of bioheat model in skin tissue induced to laser irradiation", Symmetry, 12(4), 602. https://doi.org/10.3390/sym12040602.
  29. Hobiny, A.D. and Abbas, I.A. (2017), "A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity", Mech. Time Depend. Mater., 21, 61-72. https://doi.org/10.1007/s11043-016-9318-8.
  30. Ilioushin, A. and Pobedria, B. (1970), Fundamentals of the Mathematical Theory of Thermal Viscoelasticity, Nauka, Moscow, Russia.
  31. Kaminski, W. (1990), "Hyperbolic heat conduction equation for materials with a nonhomogeneous inner structure", J. Heat Transf., 112(3), 555-560. https://doi.org/10.1115/1.2910422.
  32. Lata, P. (2022), "Effect of rotation on Stoneley waves in orthotropic magneto-thermoelastic media", Wind Struct., 35(6), 395. https://doi.org/10.12989/was.2022.35.6.395.
  33. Lata, P. and Kaur, H. (2023), "Interactions in a transversely isotropic new modified couple stress thermoelastic thick circular plate with two temperature theory", Coupled Syst. Mech., 12(3), 261-276. https://doi.org/10.12989/csm.2023.12.3.261.
  34. Li, X., Xue, Z. and Tian, X. (2018), "A modified fractional order generalized bio-thermoelastic theory with temperature-dependent thermal material properties", Int. J. Therm. Sci., 132, 249-256. https://doi.org/10.1016/j.ijthermalsci.2018.06.007.
  35. Liu, Z. and Bilston, L. (2000), "On the viscoelastic character of liver tissue: Experiments and modelling of the linear behaviour", Biorheol., 37(3), 191-201.
  36. Lord, H.W. and Shulman, Y. (1967), "A generalized dynamical theory of thermoelasticity", J. Mech. Phys. Solids, 15(5), 299-309. https://doi.org/10.1016/0022-5096(67)90024-5.
  37. Lotfy, K., El-Bary, A. and Tantawi, R. (2019), "Effects of variable thermal conductivity of a small semiconductor cavity through the fractional order heat-magneto-photothermal theory", Eur. Phys. J. Plus, 134(6), 280. https://doi.org/10.1140/epjp/i2019-12631-1.
  38. Luikov, A., Shashkov, A., Vasiliev, L. and Fraiman, Y.E. (1968), "Thermal conductivity of porous systems", Int. J. Heat Mass Transf., 11(2), 117-140. https://doi.org/10.1016/0017-9310(68)90144-0.
  39. Marin, M. (2010), "Lagrange identity method for microstretch thermoelastic materials", J. Math. Anal. Appl., 363(1), 275-286. https://doi.org/10.1016/j.jmaa.2009.08.045.
  40. Marin, M., Ellahi, R. and Chirila, A. (2017), "On solutions of Saint-Venant's problem for elastic dipolar bodies with voids", Carpath. J. Math., 33(2), 219-232.
  41. Mitchell, J.W., Galvez, T.L., Hengle, J., Myers, G.E. and Siebecker, K.L. (1970), "Thermal response of human legs during cooling", J. Appl. Physiol., 29(6), 859-865. https://doi.org/10.1152/jappl.1970.29.6.859.
  42. Othman, M.I.A., Ezzat, M.A., Zaki, S.A. and El-Karamany, A.S. (2002), "Generalized thermo-viscoelastic plane waves with two relaxation times", Int. J. Eng. Sci., 40(12), 1329-1347. https://doi.org/10.1016/s0020-7225(02)00023-x.
  43. Pennes, H.H. (1948), "Analysis of tissue and arterial blood temperatures in the resting human forearm", J. Appl. Physiol., 1(2), 93-122. https://doi.org/10.1152/jappl.1948.1.2.93.
  44. Shih, T.C., Yuan, P., Lin, W.L. and Kou, H.S. (2007), "Analytical analysis of the Pennes bioheat transfer equation with sinusoidal heat flux condition on skin surface", Med. Eng. Phys., 29(9), 946-953. https://doi.org/10.1016/j.medengphy.2006.10.008.
  45. Singh, S. and Lata, P. (2023), "Effect of two temperature and nonlocality in an isotropic thermoelastic thick circular plate without energy dissipation", Partial Differ. Equ. Appl. Math., 7, 100512. https://doi.org/10.1016/j.padiff.2023.100512.
  46. Tzou, D.Y. (2014), Macro-to Microscale Heat Transfer: The Lagging Behavior, John Wiley & Sons Ltd, Chichester, UK.
  47. Xu, F., Lu, T.J. and Seffen, K.A. (2009), "Thermally-induced change in the relaxation behavior of skin tissue", J. Biomech. Eng., 131(7), 071001. https://doi.org/10.1115/1.3118766.
  48. Yasein, M.D., Mabrouk, N., Lotfy, K. and El-Bary, A. (2019), "The influence of variable thermal conductivity of semiconductor elastic medium during photothermal excitation subjected to thermal ramp type", Result. Phys., 15, 102766. https://doi.org/10.1016/j.rinp.2019.102766.
  49. Youssef, H.M. and El-Bary, A. (2016), "Two-temperature generalized thermo-elastic medium thermally excited by time exponentially decaying laser pulse", Int. J. Struct. Stab. Dyn., 16(3), 1450102. https://doi.org/10.1142/S0219455414501028.
  50. Zenkour, A., Abouelregal, A., Alnefaie, K., Zhang, X. and Aifantis, E. (2015), " ", J. Therm. Stress., 38(9), 1049-1067. https://doi.org/10.1080/01495739.2015.1038490.
  51. Zenkour, A.M. and Abbas, I.A. (2014), "Nonlinear transient thermal stress analysis of temperature-dependent hollow cylinders using a finite element model", Int. J. Struct. Stab. Dyn., 14(7), https://doi.org/10.1142/S0219455414500254.
  52. Zhang, A., Wang, J. and Wang, B. (2022), "Bio-thermo-viscoelastic behavior in multilayer skin tissue", J. Therm. Stress., 45(7), 559-575. https://doi.org/10.1080/01495739.2022.2073932.