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Assessment of thermal models for human eye

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Abstract

With the increase in laser technology for ophthalmic surgeries, the knowledge of the heat transfer mechanism in the human eye becomes increasingly important. The accuracy in predicting thermal behavior is linked to the use of adequate thermal and numerical methods. In this way, this study presents the results of two two-dimensional models, cartesian and axisymmetric in cylindrical coordinate, to calculate transient temperature of the human eye. Heat transfer was modeled using the Pennes’ thermal model, and the mechanism of heat conduction was assessed through two different approaches, classical Fourier law and non-Fourier law also known as Cattaneo and Vernotee modification. The Fourier and non-Fourier bio-heat equations were solved using the finite element method and the numerical solutions were compared to solutions reported in the literature, as well as numerical results were presented under various conditions to evaluate the differences between the two approaches to predict the diffusion of heat inside the retinal region of human eye subjected intentionally and accidentally to heat sources.

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References

  1. Ng EYK, Ooi EH (2007) Ocular surface temperature: a 3D FEM prediction using bioheat equation. Comput Biol Med 37:829–835. https://doi.org/10.1016/j.compbiomed.2006.08.023

    Article  Google Scholar 

  2. Flyckt VMM, Raaymakers BW, Lagendijk JJW (2006) Modelling the impact of blood flow on the temperature distribution in the human eye and the orbit: fixed heat transfer coefficients versus the Pennes bioheat model versus discrete blood vessels. Phys Med Biol 51:5007–5021. https://doi.org/10.1088/0031-9155/51/19/018

    Article  Google Scholar 

  3. Emery AF, Kramar P, Guy JCL (1995) Microwave 466 induced temperature rises in rabbit eyes in cataract research. J Heat Transf 97:123–128

    Article  Google Scholar 

  4. Lagendijk JJW (1982) A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment. Phys Med Biol 27:1301

    Article  Google Scholar 

  5. Firoozan MS, Porkhial S, Nejad AS (2015) Effect of tissue and atmosphere’s parameters on human eye temperature distribution. J Therm Biol 47:51–58. https://doi.org/10.1016/j.jtherbio.2014.11.001

    Article  Google Scholar 

  6. Gokul KC, Gurung DB, Adhikary PR (2014) Thermal effects of eyelid in human eye temperature model. J Appl Math Informatics 32:649–663. https://doi.org/10.14317/jami.2014.649

    Article  MathSciNet  MATH  Google Scholar 

  7. Shafahi M, Vafai K (2010) Human eye response to thermal disturbances. J Heat Transf 133:011009–011009. https://doi.org/10.1115/1.4002360

    Article  Google Scholar 

  8. Garcia OP, Lyra PRM, Fernandes A, de Lima R. de CF (2019). The influence of the vitreous humor viscosity during laser-induced thermal damage in choroidal melanomas. Int J Therm Sci 136: 444–456. https://doi.org/10.1016/j.ijthermalsci.2018.10.020

  9. Herzog C, Thomsen O, Schmarbeck B et al (2018) Temperature-controlled laser therapy of the retina via robust adaptive H ∞ {\mathcal{H}_{\infty }}-control. at - Automatisierungstechnik 66:1051–1063. https://doi.org/10.1515/auto-2018-0066

    Article  Google Scholar 

  10. Semenyuk V (2018) Prediction of temperature and damage in an irradiated human eye during retinal photocoagulation. Int J Heat Mass Transf 126:306–316. https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.019

    Article  Google Scholar 

  11. Mishra SC, Sahai H (2012) Analyses of non-Fourier heat conduction in 1-D cylindrical and spherical geometry – an application of the lattice Boltzmann method. Int J Heat Mass Transf 55:7015–7023. https://doi.org/10.1016/j.ijheatmasstransfer.2012.07.014

    Article  Google Scholar 

  12. Ali YM, Zhang LC (2005) Relativistic heat conduction. Int J Heat Mass Transf 48:2397–2406. https://doi.org/10.1016/j.ijheatmasstransfer.2005.02.003

    Article  MATH  Google Scholar 

  13. Cattaneo C (1958) A form of heat conduction equation which eliminates the paradox of instantaneous propagation. Comptes Rendus 247:431–433

    MATH  Google Scholar 

  14. Vernott P (1958) Les paradoxes de la theorie continue de léquation de la chaleur. C R Acad Sci 246:3154–3155

    MathSciNet  Google Scholar 

  15. Taitel Y (1972) On the parabolic, hyperbolic and discrete formulation of the heat conduction equation. Int J Heat Mass Transf 15:369–371. https://doi.org/10.1016/0017-9310(72)90085-3

    Article  Google Scholar 

  16. Pennes HH (1948) Analysis of tissue and arterial blood temperatures in the resting human forearm. J Appl Physiol 1:93–122

    Article  Google Scholar 

  17. Mishra SC, Sahai H (2013) Analysis of non-Fourier conduction and radiation in a cylindrical medium using lattice Boltzmann method and finite volume method. Int J Heat Mass Transf 61:41–55. https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.073

    Article  Google Scholar 

  18. Narasimhan A, Sadasivam S (2013) Non-Fourier bio heat transfer modelling of thermal damage during retinal laser irradiation. Int J Heat Mass Transf 60:591–597. https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.010

    Article  Google Scholar 

  19. Tzou DY (2015) Macro- to Microscale Heat Transfer: the Lagging Behavior. John Wiley and Sons

  20. Narasimhan A, Jha KK, Gopal L (2010) Transient simulations of heat transfer in human eye undergoing laser surgery. Int J Heat Mass Transf 53:482–490. https://doi.org/10.1016/j.ijheatmasstransfer.2009.09.007

    Article  MATH  Google Scholar 

  21. Paruch M (2007) Numerical simulation of bioheat transfer process in the human eye using finite element method. Sci Res Inst Math Comput Sci 6:199–204

  22. Ng EYK, Ooi EH (2006) FEM simulation of the eye structure with bioheat analysis. Comput Methods Prog Biomed 82:268–276. https://doi.org/10.1016/j.cmpb.2006.04.001

    Article  Google Scholar 

  23. Scott JA (1988) A finite element model of heat transport in the human eye. Phys Med Biol 33:227

    Article  Google Scholar 

  24. Amara EH (1995) Numerical investigations on thermal effects of laser-ocular media interaction. Int J Heat Mass Transf 38:2479–2488. https://doi.org/10.1016/0017-9310(94)00353-W

    Article  MATH  Google Scholar 

  25. Moritz AR, Henriques FC Jr (1947) Studies of thermal injury. Am J Pathol 23:695–720

    Google Scholar 

  26. Welch AJ, Polhamus GD (1984) Measurement and prediction of thermal injury in the retina of the rhesus monkey. IEEE Trans Biomed Eng 31:633–643. https://doi.org/10.1109/TBME.1984.325313

    Article  Google Scholar 

  27. Dodson B, Hammett P, Klerx R (2014) Probabilistic design for optimization and robustness for engineers. John Wiley and Sons, Chichester

  28. Fanksouser F, Kwasniewska S, eds (2003) Lasers in Ophthalmology: Basic, Diagnostic and Surgical Aspects. Kugler Publications, Hague

  29. Ströher GR, Ströher GL (2014) Numerical thermal analysis of skin tissue using parabolic and hyperbolic approaches. Int Commun Heat Mass Transf 57:193–199. https://doi.org/10.1016/j.icheatmasstransfer.2014.07.026

    Article  Google Scholar 

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Correspondence to Gylles Ricardo Ströher.

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Ströher, G.R., de Andrade, C.R. & Ströher, G.L. Assessment of thermal models for human eye. Heat Mass Transfer 56, 2135–2143 (2020). https://doi.org/10.1007/s00231-020-02845-6

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  • DOI: https://doi.org/10.1007/s00231-020-02845-6

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