Coupled systems mechanics

  • 제13권1호
  • /
  • Pages.61-72
  • /
  • 2024
  • /
  • 2234-2184(pISSN)
  • /
  • 2234-2192(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

The effects of thermo-mechanical behavior of living tissues under thermal loading without energy dispassion

  • Ibrahim Abbas (Department of Mathematics, Faculty of Science, Sohag University) ;
  • M. Saif AlDien (Department of Mathematics, Turabah University College, Taif University) ;
  • Mawahib Elamin (Department of Mathematics, College of Science and Arts Qassim University) ;
  • Alaa El-Bary (Basic and Applied Science Institute, Arab Academy for Science, Technology and Maritime Transport)
  • 투고 : 2023.10.15
  • 심사 : 2023.10.26
  • 발행 : 2024.02.25
⟨ 이전 논문 다음 논문 ⟩

초록

This study seeks to develop analytical solutions for the biothermoelastic model without accounting for energy dissipation. These solutions are then applied to estimate the temperature changes induced by external heating sources by integrating relevant empirical data characterizing the biological tissue of interest. The distributions of temperature, displacement, and strain were obtained by utilizing the eigenvalues approach with the Laplace transforms and numerical inverse transforms method. The impacts of the rate of blood perfusion and the metabolic activity parameter on thermoelastic behaviors were discussed specifically. The temperature, displacement, and thermal strain results are visually represented through graphical representations.

키워드

과제정보

The researchers would like to acknowledge Deanship of Scientific Research, Taif University for funding this work.

참고문헌

  1. Abbas, I., Hobiny, A. and Marin, M. (2020), "Photo-thermal interactions in a semi-conductor material with cylindrical cavities and variable thermal conductivity", J. Taibah Univ. Sci., 14(1), 1369-1376. https://doi.org/10.1080/16583655.2020.1824465.
  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., Abdalla, A.E.N.N., Alzahrani, F.S. and Spagnuolo, M. (2016), "Wave propagation in a generalized thermoelastic plate using eigenvalue approach", J. Therm. Stress., 39(11), 1367-1377. https://doi.org/10.1080/01495739.2016.1218229.
  4. Baksi, A., Roy, B.K. and Bera, R.K. (2006), "Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension", Math. Comput. Model., 44(11-12), 1069-1079. https://doi.org/10.1016/j.mcm.2006.03.010.
  5. Das, N.C., Lahiri, A. and Giri, R.R. (1997), "Eigenvalue approach to generalized thermoelasticity", Ind. J. Pure Appl. Math., 28(12), 1573-1594.
  6. Diaz, S.H., Nelson, J.S. and Wong, B.J. (2002), "Rate process analysis of thermal damage in cartilage", Phys. Medic. Biol., 48(1), 19. https://doi.org/10.1088/0031-9155/48/1/302.
  7. Dillenseger, J.L. and Esneault, S. (2010), "Fast FFT-based bioheat transfer equation computation", Comput. Biol. Medic., 40(2), 119-123. https://doi.org/10.1016/j.compbiomed.2009.11.008.
  8. Fahmy, M.A. (2019), "Boundary element modeling and simulation of biothermomechanical behavior in anisotropic laser-induced tissue hyperthermia", Eng. Anal. Bound. Elem., 101, 156-164. https://doi.org/10.1016/j.enganabound.2019.01.006.
  9. Gabay, I., Abergel, A., Vasilyev, T., Rabi, Y., Fliss, D.M. and Katzir, A. (2011), "Temperature-controlled two-wavelength laser soldering of tissues", Laser. Surgery Medic., 43(9), 907-913. https://doi.org/10.1002/lsm.21123
  10. Ghanmi, A. and Abbas, I.A. (2019), "An analytical study on the fractional transient heating within the skin tissue during the thermal therapy", J. Therm. Biol., 82, 229-233. https://doi.org/10.1016/j.jtherbio.2019.04.003.
  11. Green, A. and Naghdi, P. (1992), "On undamped heat waves in an elastic solid", J. Therm. Stress., 15(2), 253-264. https://doi.org/10.1080/01495739208946136.
  12. Green, A. and Naghdi, P. (1993), "Thermoelasticity without energy dissipation", J. Elastic., 31(3), 189-208. https://doi.org/10.1007/BF00044969.
  13. Green, A.E. and Naghdi, P.M. (1991), "A re-examination of the basic postulates of thermomechanics", Proc. Roy. Soc. London. Ser. A: Math. Phys. Sci., 432(1885), 171-194. https://doi.org/10.1098/rspa.1991.0012.
  14. Gupta, N.D. and Das, N.C. (2016), "Eigenvalue approach to fractional order generalized thermoelasticity with line heat source in an infinite medium", J. Therm. Stress., 39(8), 977-990. https://doi.org/10.1080/01495739.2016.1187987.
  15. Gupta, P.K., Singh, J. and Rai, K. (2010), "Numerical simulation for heat transfer in tissues during thermal therapy", J. Therm. Biol., 35(6), 295-301. https://doi.org/10.1016/j.jtherbio.2010.06.007.
  16. Gupta, P.K., Singh, J., Rai, K. and Rai, S. (2013), "Solution of the heat transfer problem in tissues during hyperthermia by finite difference-decomposition method", Appl. Math. Comput., 219(12), 6882-6892. https://doi.org/10.1016/j.amc.2013.01.020.
  17. Hobiny, A. and Abbas, I. (2019), "A GN model on photothermal interactions in a two-dimensions semiconductor half space", Result. Phys., 15, 102588. https://doi.org/10.1016/j.rinp.2019.102588.
  18. Hobiny, A. and Abbas, I. (2021), "Analytical solutions of fractional bioheat model in a spherical tissue", Mech. Bas. Des. Struct. Mach., 49(3), 430-439. https://doi.org/10.1080/15397734.2019.1702055.
  19. Kim, J.Y., Jang, K., Yang, S.J., Baek, J.H., Park, J.R., Yeom, D.I., ... & Chung, S.C. (2016), "Simulation study of the thermal and the thermoelastic effects induced by pulsed laser absorption in human skin", J. Korean Phys. Soc., 68, 979-988. https://doi.org/10.3938/jkps.68.979.
  20. Kumar, P., Kumar, D. and Rai, K. (2015), "A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment", J. Therm. Biol., 49, 98-105. https://doi.org/10.1016/j.jtherbio.2015.02.008.
  21. Kumar, R., Miglani, A. and Rani, R. (2016), "Analysis of micropolar porous thermoelastic circular plate by eigenvalue approach", Arch. Mech., 68(6), 423-439.
  22. Kumar, R., Miglani, A. and Rani, R. (2017), "Eigenvalue formulation to micropolar porous thermoelastic circular plate using dual phase lag model", Multidisc. Model. Mater. Struct., 13(2), 347-362. https://doi.org/10.1108/mmms-08-2016-0038.
  23. Lata, P. (2019), "Thermomechanical interactions in transversely isotropic magneto thermoelastic solid with two temperatures and without energy dissipation", Steel Compos. Struct., 32(6), 779-793. https://doi.org/10.12989/scs.2019.32.6.779.
  24. Lata, P. and Kaur, H. (2022), "Effect of two temperature and energy dissipation in an axisymmetric modified couple stress isotropic thermoelastic solid", Couple. Syst. Mech., 11(3), 199-215. https://doi.org/10.12989/csm.2022.11.3.199.
  25. Li, X., Li, C., Xue, Z. and Tian, X. (2018), "Analytical study of transient thermo-mechanical responses of dual-layer skin tissue with variable thermal material properties", Int. J. Therm. Sci., 124, 459-466. https://doi.org/10.1016/j.ijthermalsci.2017.11.002.
  26. Li, X., Li, C., Xue, Z. and Tian, X. (2019), "Investigation of transient thermo-mechanical responses on the triple-layered skin tissue with temperature dependent blood perfusion rate", Int. J. Therm. Sci., 139, 339-349. https://doi.org/10.1016/j.ijthermalsci.2019.02.022.
  27. Li, X., Qin, Q.H. and Tian, X. (2019), "Thermomechanical response of porous biological tissue based on local thermal non-equilibrium", J. Therm. Stress., 42(12), 1481-1498. https://doi.org/10.1080/01495739.2019.1660599.
  28. 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.
  29. Mahjoob, S. and Vafai, K. (2009), "Analytical characterization of heat transport through biological media incorporating hyperthermia treatment", Int. J. Heat Mass Transf., 52(5-6), 1608-1618. https://doi.org/10.1016/j.ijheatmasstransfer.2008.07.038.
  30. Marin, M. (2010), "Some estimates on vibrations in thermoelasticity of dipolar bodies", J. Vib. Control, 16(1), 33-47. https://doi.org/10.1177/1077546309103419.
  31. Marin, M., Hobiny, A. and Abbas, I. (2021), "Finite element analysis of nonlinear bioheat model in skin tissue due to external thermal sources", Math., 9(13), 1459. https://doi.org/10.3390/math9131459.
  32. Marin, M., Hobiny, A. and Abbas, I. (2021), "The effects of fractional time derivatives in porothermoelastic materials using finite element method", Math., 9(14), 1606. https://doi.org/10.3390/math9141606.
  33. Marin, M., Seadawy, A., Vlase, S. and Chirila, A. (2022), "On mixed problem in thermoelasticity of type III for Cosserat media", J. Taibah Univ. Sci., 16(1), 1264-1274. https://doi.org/10.1080/16583655.2022.2160290.
  34. 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.
  35. Mohammed, B.N. and Ismael, D.S. (2022), "A computational model for temperature monitoring during human liver treatment by Nd: YaG Laser Interstitial Thermal Therapy (LITT)", Aro-Scientif. J. Koya Univ., 10(2), 38-44. http://doi.org/10.14500/aro.10949.
  36. Naik, N.S. and Sayyad, A.S. (2020), "1D thermal analysis of laminated composite and sandwich plates using a new fifth order shear and normal deformation theory", Mater. Today: Proc., 21, 1084-1088. https://doi.org/10.1016/j.matpr.2020.01.009.
  37. Othman, M.I., Fekry, M. and Marin, M. (2020), "Plane waves in generalized magneto-thermo-viscoelastic medium with voids under the effect of initial stress and laser pulse heating", Struct. Eng. Mech., 73(6), 621-629. https://doi.org/10.12989/sem.2020.73.6.621.
  38. 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.
  39. Santra, S., Lahiri, A. and Das, N.C. (2014), "Eigenvalue approach on thermoelastic interactions in an infinite elastic solid with voids", J. Therm. Stress., 37(4), 440-454. https://doi.org/10.1080/01495739.2013.870854.
  40. Shen, W., Zhang, J. and Yang, F. (2005), "Modeling and numerical simulation of bioheat transfer and biomechanics in soft tissue", Math. Comput. Model., 41(11-12), 1251-1265. https://doi.org/10.1016/j.mcm.2004.09.006.
  41. Singh, S. and Lata, P. (2023), "Effect of two temperature and nonlocality in an isotropic thermoelastic thick circular plate without energy dissipation", Part. Diff. Equ. Appl. Math., 7, 100512. https://doi.org/10.1016/j.padiff.2023.100512.
  42. Sobhy, M. and Zenkour, A.M. (2022), "Refined lord-shulman theory for 1D response of skin tissue under ramp-type heat", Mater. (Basel), 15(18), 6292. https://doi.org/10.3390/ma15186292.
  43. Stehfest, H. (1970), "Algorithm 368: Numerical inversion of Laplace transforms [D5]", Commun. ACM, 13(1), 47-49. https://doi.org/10.1145/361953.361969.
  44. Xu, F., Lu, T.J. and Seffen, K.A. (2008a), "Biothermomechanics of skin tissues", J. Mech. Phys. Solid., 56(5), 1852-1884. https://doi.org/10.1016/j.jmps.2007.11.011.
  45. Xu, F., Seffen, K.A. and Lu, T.J. (2008b), "Non-Fourier analysis of skin biothermomechanics", Int. J. Heat Mass Transf., 51(9-10), 2237-2259. https://doi.org/10.1016/j.ijheatmasstransfer.2007.10.024.
  46. Xu, F., Wen, T., Lu, T.J. and Seffen, K.A. (2008c), "Skin biothermomechanics for medical treatments", J. Mech. Behav. Biomed. Mater., 1(2), 172-187. https://doi.org/10.1016/j.jmbbm.2007.09.001.
  47. Yadav, S., Kumar, D. and Rai, K.N. (2014), "Finite element legendre wavelet Galerkin approch to inward solidification in simple body under most generalized boundary condition", Zeitschrift fur Naturforschung A, 69(10-11), 501-510. https://doi.org/10.5560/zna.2014-0052.
  48. Youssef, H.M. and Alghamdi, N.A. (2020), "Modeling of one-dimensional thermoelastic dual-phase-lag skin tissue subjected to different types of thermal loading", Sci. Rep., 10(1), 3399. https://doi.org/10.1038/s41598-020-60342-6.
  49. 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.
  50. Zhou, J., Chen, J. and Zhang, Y. (2009), "Dual-phase lag effects on thermal damage to biological tissues caused by laser irradiation", Comput. Biol. Medic., 39(3), 286-293. https://doi.org/10.1016/j.compbiomed.2009.01.002.
  51. Zhu, D., Luo, Q., Zhu, G. and Liu, W. (2002), "Kinetic thermal response and damage in laser coagulation of tissue", Laser. Surgery Medic., 31(5), 313-321. https://doi.org/10.1002/lsm.10108.