Advertisement

Solution of the Heat Conduction Equation

  • Johann Roider
  • Reginald Birngruber
Part of the Lasers, Photonics, and Electro-Optics book series (LPEO)

Abstract

During laser irradiation of biological tissue several steps have to be considered: (a) propagation of light in tissue including reflection and scattering, (b) transformation of laser light into photochemical, acoustic, or thermal energy, depending primarily on the absorber, pulse energy, and pulse duration, (c) propagation of the spatial temperature profile for the fraction of light energy that was transformed into thermal energy, and propagation of acoustic transients for the fraction of light energy that was converted into mechanical energy, and (d) the dependency between temperature elevation and tissue damage, which can be described by the Arrhenius law.

Keywords

Retinal Pigment Epithelium Heat Conduction Equation Melanin Granule Heat Diffusion Equation Laser Beam Axis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abramowitz M, Stegun IA. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Applied Mathematics Series 55, National Bureau of Standards, 1970.Google Scholar
  2. 2.
    ADINAT Users Manual, A Finite Element Program for Automatic Dynamic Nonlinear Analysis of Temperatures, Adina Engineering Inc., Report AE -81–2, Watertown, MA, 1981.Google Scholar
  3. 3.
    Birngruber R, Hillenkamp F, Gabel V-P. Experimentelle und theoretische Untersuchungen zur thermischen Schadigung des Augenhintergrunds durch Laserstrahlung, GSF-Report, AO 251, Gesellschaft für Strahlen-und Umweltforschung m.b.H, Munchen, 1978.Google Scholar
  4. 4.
    Birngruber R, Hillenkamp F, Gabel V-P. “Theoretical investigations of laser thermal retinal injury,” Health Phys. 48(6): 781–796 (1985).CrossRefGoogle Scholar
  5. 5.
    Bimgruber R. “Choroidal circulation and heat convection at the fundus of the eye—Implications for the laser coagulation and the stabilization of retinal temperature,” in Wolbarsht ML (ed.), Laser Applications in Medicine and Biology, Plenum Press, New York, London, 1991.Google Scholar
  6. 6.
    Carslaw FHS, Jaeger JC. Conduction of Heat in Solids, 2nd ed., Oxford University Press, New York (1959).Google Scholar
  7. 7.
    Douglas, J, Gunn J. “A general formulation of alternating direction methods, I.,” Numer. Math. 6: 428–453 (1964).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Gabay S, Kremer I, Ben-Sira, I, Erez G. “Retinal thermal response to copper-vapor laser exposure,” Lasers Surg. Med. 8: 418–427 (1988).CrossRefGoogle Scholar
  9. 9.
    Gabel VP, Bimgruber R, Hillencamp F. “Visible and near infrared light absorption in pigment epithelium and choroid,” in Int. Cong. Series No. 450, III Concilium Ophthal., Kyoto, Excerpta Med. 658–662 (1978).Google Scholar
  10. 10.
    Gemert MJC van, Kleijn WJA de, Hulsbergen Henning JP. “Temperature behaviour of a model port-wine stain during argon laser coagulation,” Phys. Med. Biol. 27: 1089–1104 (1982).CrossRefGoogle Scholar
  11. 11.
    Hansen WP, Fine S. “Melanin granule models for pulsed induced retinal injury,” Appl. Opt. 7(1): 155–159 (1968).Google Scholar
  12. 12.
    Hayes JR, Wolbarsht M. “Thermal model for retinal damage induced by pulsed lasers,” Aerosp. Med. 39: 474 (1968).Google Scholar
  13. 13.
    Mainster MA, White TJ, Wilson PW. “Transient thermal behaviour in biological systems,” Bull. Math. Biophys. 32: 303–314 (1970).MATHCrossRefGoogle Scholar
  14. 14.
    Mainster MA, White TJ, Tips JH, Wilson PW. “Refined temperatures produced by intense light sources,” J. Opt. Soc. Am. 60: 264–270 (1970).ADSCrossRefGoogle Scholar
  15. 16.
    Roider J. “Modellrechnungen zum Wärmeeinstrom in das Korpergewebe bei Applikation verschiedener Peloidpackungen,” Dissertation, Universität Munchen, 1989.Google Scholar
  16. 17.
    Roider J, Hillenkamp F, Flotte T, Birngruber R. “Microphotocoagulation: selective effects of repetitive short laser pulses.” Proc. Natl. Acad. Sci. USA, 90: 8643–8647 (1993).ADSCrossRefGoogle Scholar
  17. 18.
    Peaceman DW, Rachford HH Jr. “The numerical solution of parabolic and elliptic differential equations,” J. Soc. Ind. Appl. Math. 3: 28–41 (1955).MathSciNetMATHCrossRefGoogle Scholar
  18. 19.
    Scott JA. “A finite-element model of heat transport in the human eye,” Phys. Med. Biol. 33: 227–241 (1988).CrossRefGoogle Scholar
  19. 20.
    Scott JA. “The computation of temperature rises in the human eye induced by infrared radiation,” Phys. Med. Biol. 33: 243–257 (1988).CrossRefGoogle Scholar
  20. 21.
    Schwarz HR. Methoden der finiten Elemente, Teubner, Stuttgart, 1984.CrossRefGoogle Scholar
  21. 22.
    Takata AN, Goldfinch L, Hinds JK, Kuan LP, Thomopoulis N, Weigendt A. Thermal Model of Laser Induced Eye Damage, Final Tech. Rep., IITR1, J-TR 74–6324, Oct. 1974.Google Scholar
  22. 23.
    Takata AN, Zaneveld L, Richter W. Laser-Induced Thermal Damage in Skin, USAF School Aerospace Med., Brooks AFB, TX Rep. SAM-TR-77–38, 1977.Google Scholar
  23. 24.
    Vassiliadis A. “Ocular damage from laser radiation,” in Wolbarsht ML (ed.), Laser Applications in Medicine and Biology, Plenum Press, London, 1971, pp. 125–162.CrossRefGoogle Scholar
  24. 25.
    Welch AJ, Priebe LA, Polhamus GO, Mistry GD. Model of Thermal Injury Based on Temperature Rise in Fundus Exposed to Laser Radiation, USAF School Aerospace Med., Final Rep. F41609–74-C-0025, 1976.Google Scholar
  25. 26.
    Welch AJ, Wissler EH, Priebe LA. “Significance of blood flow in calculations of temperature in laser irradiated tissue,” IEEE Trans. Biomed. Eng. 27: 164–166 (1980).CrossRefGoogle Scholar
  26. 27.
    White TJ, Mainster MA, Tips JH, Wilson PW. “Chorioretinal thermal behaviour,” Bull. Math. Biophys. 32: 315–322 (1970).CrossRefGoogle Scholar
  27. 28.
    Wissler EH. “An analysis of chorioretinal thermal response to intense light exposures,” IEEE Biomed. Eng. 23: 207–215 (1976).CrossRefGoogle Scholar
  28. 29.
    Wissler EH, Gorish W. “A mathematical model for predicting thermal responses in the neighborhood of arteries and veins during laser irradiation,” in Mow V(ed.), Advances in Biomedical Engineering, ASME, New York, 1980.Google Scholar
  29. 30.
    Wray LJ. Model for Prediction of Retinal Burns, Defense Atomic Support Agency, Report No. 1282, 1962.Google Scholar
  30. 31.
    Yoon G, Welch AJ, Motamedi M, Gemert MCJ van. “Development and application of threedimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23(10): 1721–1733 (1987).Google Scholar
  31. 32.
    Zienkiewicz OC. The Finite-Element Method in Engineering Science, 3rd ed., McGraw-Hill, London, 1977.Google Scholar

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Johann Roider
    • 1
  • Reginald Birngruber
    • 1
  1. 1.Wellman Laboratories of Photomedicine, Massachusetts General HospitalHarvard Medical SchoolBostonUSA

Personalised recommendations