Abstract

We investigated the ability of mathematical models to predict temperature rises in biological tissue during laser irradiation by comparing calculated values with experimental measurements. Samples of normal human aorta, beef myocardium, and polyacrylamide gel were irradiated in air with an argon laser beam, while surface temperatures were monitored with an IR camera. The effects of different surface boundary conditions in the model predictions were examined and compared with the experimental data. It was observed that, before a temperature of 60°C was reached, the current mathematical models were capable of predicting tissue-surface temperature rises with an accuracy of 90% for a purely absorbing medium and with an accuracy of 75% for biological tissue (a scattering medium). Above 60°C, however, the models greatly overestimated temperature rises in both cases. It was concluded that the discrepancies were mainly a result of surface water vaporization, which was not considered in current models and which was by far the most significant surface-heat-loss mechanism for laser irradiation in air. The inclusion of surface water vaporization in the mathematical models provided a much better match between predicted temperatures and experimental results.

© 1993 Optical Society of America

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  1. M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, “Transient thermal behavior in biological systems,” Bull. Math. Biophys. 32, 303–314 (1970).
    [CrossRef]
  2. E. H. Wissler, “An analysis of chorioretinal thermal response to intense light exposure,” IEEE Trans. Biomed. Eng. BME-23, 207–215 (1976).
    [CrossRef]
  3. A. N. Takata, L. Zaneveld, W. Richter, Laser-Induced Thermal Damage of Skin (Aerospace Medical Division, Brooks Air Force Base, Tex., 1977).
  4. R. Birngruber, “Thermal modeling in biological tissue,” in Lasers in Biology and Medicine, F. Hillencamp, R. Pratesi, C. A. Sacchi, eds. (Plenum, New York, 1980), pp. 77–97.
    [CrossRef]
  5. A. J. Welch, E. H. Wissler, L. A. Priebe, “Significance of blood flow in calculations of temperature in laser irradiated tissue,” IEEE Trans. Biomed. Eng. BME-27, 164–166 (1980).
    [CrossRef]
  6. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  7. W. Brutsaert, Evaporation into the Atmosphere, Theory, History and Applications, (Reidel, Dordrecht, The Netherlands, 1982).
  8. F P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, New York, 1985), Chap. 6.
  9. P. R. Goth, “Temperature history of canine gastric tissue in response to Nd:YAG laser exposure, M. S. thesis (University of Texas at Austin, Austin, Tex., 1980).
  10. A. J. Welch, “Laser irradiation in tissue,” in Heat Transfer in Medicine and Biology, A. Shitzer, R. C. Eberheart, eds. (Plenum, New York, 1985), pp. 135–183.
    [CrossRef]
  11. G. Yoon, A. J. Welch, M. Motamedi, M. C. J. van Gemert, “Development and application of a three dimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23, 1721–1733 (1987).
    [CrossRef]
  12. G. Yoon, “Absorption and scattering of laser light in biological media—mathematical modeling and methods for determining the optical properties,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988).
  13. S. Chandrasekar, Radiative Transfer (Oxford U. Press, London, 1960).
  14. S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex.1988).
  15. R. A. J. Groenhuis, H. A. Ferwerda, J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements,” Appl. Opt. 13, 236–238 (1983).
  16. T. Togawa, “Skin emissivity measurement using the unsteady state immediately after removing a zero-heat-flow thermometer probe,” presented at the joint Fourteenth International Conference on Medical and Biological Engineering and Seventh International Conference on Medical Physics, Espoo, Finland, 1985.
  17. T. Togawa, “Noncontact skin emissivity measurement by switching two shades of different temperatures,” Phys. Med. Biol. 33, Suppl. 1, 409 (A) (1988).
  18. J. Khosrofian, B. Garetz, “Measurement of Gaussian laser beam diameter through direct inversion of knife-edge data,” Appl. Opt. 22, 3406–3410 (1983).
    [CrossRef] [PubMed]
  19. J. W. Valvano, B. Chitsabesan, “Thermal conductivity and diffusivity of arterial wall and atherosclerotic plaque,” Lasers Life Sci. 1, 219–229 (1987).
  20. S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
    [CrossRef] [PubMed]
  21. I. Çilesiz, A. J. Welch, “Light dosimetry: effects of dehydration and thermal damage on optical properties of human aorta,” Appl. Opt. 32, 477–487 (1993).
    [CrossRef] [PubMed]
  22. S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).
  23. W. F. Cheong, M. Motamedi, A. J. Welch, “Optical modeling of laser photocoagulation of bladder tissue,” Lasers Surg. Med. 7, 72 (A) (1987).
  24. M. J. C. van Gemert, A. J. Welch, “Time constants in thermal laser medicine,” Lasers Surg. Med. 9, 405–421 (1989).
    [CrossRef] [PubMed]
  25. J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors,” Int. J. Thermophys. 6, 301–311 (1985).
    [CrossRef]
  26. J. H. Torres, “Thermal response of arterial wall to continuous wave laser irradiation and contact probe application,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1991).
  27. R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).
  28. R. Agah, M. Motamedi, P. Dalmia, “Changes in optical constants of thermally damaged arterial tissue as a function of wavelength,” Lasers Surg. Med. Suppl. 2, 15 (A) (1990).
  29. A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

1993 (1)

1991 (1)

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

1990 (1)

R. Agah, M. Motamedi, P. Dalmia, “Changes in optical constants of thermally damaged arterial tissue as a function of wavelength,” Lasers Surg. Med. Suppl. 2, 15 (A) (1990).

1989 (1)

M. J. C. van Gemert, A. J. Welch, “Time constants in thermal laser medicine,” Lasers Surg. Med. 9, 405–421 (1989).
[CrossRef] [PubMed]

1988 (1)

T. Togawa, “Noncontact skin emissivity measurement by switching two shades of different temperatures,” Phys. Med. Biol. 33, Suppl. 1, 409 (A) (1988).

1987 (5)

J. W. Valvano, B. Chitsabesan, “Thermal conductivity and diffusivity of arterial wall and atherosclerotic plaque,” Lasers Life Sci. 1, 219–229 (1987).

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

W. F. Cheong, M. Motamedi, A. J. Welch, “Optical modeling of laser photocoagulation of bladder tissue,” Lasers Surg. Med. 7, 72 (A) (1987).

G. Yoon, A. J. Welch, M. Motamedi, M. C. J. van Gemert, “Development and application of a three dimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23, 1721–1733 (1987).
[CrossRef]

1985 (1)

J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors,” Int. J. Thermophys. 6, 301–311 (1985).
[CrossRef]

1983 (2)

1980 (1)

A. J. Welch, E. H. Wissler, L. A. Priebe, “Significance of blood flow in calculations of temperature in laser irradiated tissue,” IEEE Trans. Biomed. Eng. BME-27, 164–166 (1980).
[CrossRef]

1976 (1)

E. H. Wissler, “An analysis of chorioretinal thermal response to intense light exposure,” IEEE Trans. Biomed. Eng. BME-23, 207–215 (1976).
[CrossRef]

1970 (1)

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, “Transient thermal behavior in biological systems,” Bull. Math. Biophys. 32, 303–314 (1970).
[CrossRef]

Agah, R.

R. Agah, M. Motamedi, P. Dalmia, “Changes in optical constants of thermally damaged arterial tissue as a function of wavelength,” Lasers Surg. Med. Suppl. 2, 15 (A) (1990).

R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).

Alter, C. A.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Birngruber, R.

R. Birngruber, “Thermal modeling in biological tissue,” in Lasers in Biology and Medicine, F. Hillencamp, R. Pratesi, C. A. Sacchi, eds. (Plenum, New York, 1980), pp. 77–97.
[CrossRef]

Bosch, J. J. T.

Brutsaert, W.

W. Brutsaert, Evaporation into the Atmosphere, Theory, History and Applications, (Reidel, Dordrecht, The Netherlands, 1982).

Chandrasekar, S.

S. Chandrasekar, Radiative Transfer (Oxford U. Press, London, 1960).

Cheong, W. F.

W. F. Cheong, M. Motamedi, A. J. Welch, “Optical modeling of laser photocoagulation of bladder tissue,” Lasers Surg. Med. 7, 72 (A) (1987).

Chitsabesan, B.

J. W. Valvano, B. Chitsabesan, “Thermal conductivity and diffusivity of arterial wall and atherosclerotic plaque,” Lasers Life Sci. 1, 219–229 (1987).

Çilesiz, I.

Cochran, J. R.

J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors,” Int. J. Thermophys. 6, 301–311 (1985).
[CrossRef]

Dalmia, P.

R. Agah, M. Motamedi, P. Dalmia, “Changes in optical constants of thermally damaged arterial tissue as a function of wavelength,” Lasers Surg. Med. Suppl. 2, 15 (A) (1990).

R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).

DeWitt, D. P.

F P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, New York, 1985), Chap. 6.

Diller, K. R.

J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors,” Int. J. Thermophys. 6, 301–311 (1985).
[CrossRef]

Ettedgui, E.

R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).

Ferwerda, H. A.

Garetz, B.

Goth, P. R.

P. R. Goth, “Temperature history of canine gastric tissue in response to Nd:YAG laser exposure, M. S. thesis (University of Texas at Austin, Austin, Tex., 1980).

Groenhuis, R. A. J.

Henry, P. D.

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

Incropera, F P.

F P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, New York, 1985), Chap. 6.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

Jacques, S. L.

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Khosrofian, J.

Mainster, M. A.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, “Transient thermal behavior in biological systems,” Bull. Math. Biophys. 32, 303–314 (1970).
[CrossRef]

Motamedi, M.

R. Agah, M. Motamedi, P. Dalmia, “Changes in optical constants of thermally damaged arterial tissue as a function of wavelength,” Lasers Surg. Med. Suppl. 2, 15 (A) (1990).

G. Yoon, A. J. Welch, M. Motamedi, M. C. J. van Gemert, “Development and application of a three dimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23, 1721–1733 (1987).
[CrossRef]

W. F. Cheong, M. Motamedi, A. J. Welch, “Optical modeling of laser photocoagulation of bladder tissue,” Lasers Surg. Med. 7, 72 (A) (1987).

R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).

Oraevsky, A. A.

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

Pettit, G. H.

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

Prahl, S. A.

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex.1988).

Priebe, L. A.

A. J. Welch, E. H. Wissler, L. A. Priebe, “Significance of blood flow in calculations of temperature in laser irradiated tissue,” IEEE Trans. Biomed. Eng. BME-27, 164–166 (1980).
[CrossRef]

Richter, W.

A. N. Takata, L. Zaneveld, W. Richter, Laser-Induced Thermal Damage of Skin (Aerospace Medical Division, Brooks Air Force Base, Tex., 1977).

Saidi, I. S.

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

Sauerbrey, R. A.

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

Song, L.

R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).

Spears, J. R.

R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).

Takata, A. N.

A. N. Takata, L. Zaneveld, W. Richter, Laser-Induced Thermal Damage of Skin (Aerospace Medical Division, Brooks Air Force Base, Tex., 1977).

Tips, J. H.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, “Transient thermal behavior in biological systems,” Bull. Math. Biophys. 32, 303–314 (1970).
[CrossRef]

Tittel, F. K.

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

Togawa, T.

T. Togawa, “Noncontact skin emissivity measurement by switching two shades of different temperatures,” Phys. Med. Biol. 33, Suppl. 1, 409 (A) (1988).

T. Togawa, “Skin emissivity measurement using the unsteady state immediately after removing a zero-heat-flow thermometer probe,” presented at the joint Fourteenth International Conference on Medical and Biological Engineering and Seventh International Conference on Medical Physics, Espoo, Finland, 1985.

Torres, J. H.

J. H. Torres, “Thermal response of arterial wall to continuous wave laser irradiation and contact probe application,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1991).

Valvano, J. W.

J. W. Valvano, B. Chitsabesan, “Thermal conductivity and diffusivity of arterial wall and atherosclerotic plaque,” Lasers Life Sci. 1, 219–229 (1987).

J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors,” Int. J. Thermophys. 6, 301–311 (1985).
[CrossRef]

van Gemert, M. C. J.

G. Yoon, A. J. Welch, M. Motamedi, M. C. J. van Gemert, “Development and application of a three dimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23, 1721–1733 (1987).
[CrossRef]

van Gemert, M. J. C.

M. J. C. van Gemert, A. J. Welch, “Time constants in thermal laser medicine,” Lasers Surg. Med. 9, 405–421 (1989).
[CrossRef] [PubMed]

Welch, A. J.

I. Çilesiz, A. J. Welch, “Light dosimetry: effects of dehydration and thermal damage on optical properties of human aorta,” Appl. Opt. 32, 477–487 (1993).
[CrossRef] [PubMed]

M. J. C. van Gemert, A. J. Welch, “Time constants in thermal laser medicine,” Lasers Surg. Med. 9, 405–421 (1989).
[CrossRef] [PubMed]

G. Yoon, A. J. Welch, M. Motamedi, M. C. J. van Gemert, “Development and application of a three dimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23, 1721–1733 (1987).
[CrossRef]

W. F. Cheong, M. Motamedi, A. J. Welch, “Optical modeling of laser photocoagulation of bladder tissue,” Lasers Surg. Med. 7, 72 (A) (1987).

A. J. Welch, E. H. Wissler, L. A. Priebe, “Significance of blood flow in calculations of temperature in laser irradiated tissue,” IEEE Trans. Biomed. Eng. BME-27, 164–166 (1980).
[CrossRef]

A. J. Welch, “Laser irradiation in tissue,” in Heat Transfer in Medicine and Biology, A. Shitzer, R. C. Eberheart, eds. (Plenum, New York, 1985), pp. 135–183.
[CrossRef]

White, T. J.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, “Transient thermal behavior in biological systems,” Bull. Math. Biophys. 32, 303–314 (1970).
[CrossRef]

Wilson, P. W.

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, “Transient thermal behavior in biological systems,” Bull. Math. Biophys. 32, 303–314 (1970).
[CrossRef]

Wissler, E. H.

A. J. Welch, E. H. Wissler, L. A. Priebe, “Significance of blood flow in calculations of temperature in laser irradiated tissue,” IEEE Trans. Biomed. Eng. BME-27, 164–166 (1980).
[CrossRef]

E. H. Wissler, “An analysis of chorioretinal thermal response to intense light exposure,” IEEE Trans. Biomed. Eng. BME-23, 207–215 (1976).
[CrossRef]

Yoon, G.

G. Yoon, A. J. Welch, M. Motamedi, M. C. J. van Gemert, “Development and application of a three dimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23, 1721–1733 (1987).
[CrossRef]

G. Yoon, “Absorption and scattering of laser light in biological media—mathematical modeling and methods for determining the optical properties,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988).

Zaneveld, L.

A. N. Takata, L. Zaneveld, W. Richter, Laser-Induced Thermal Damage of Skin (Aerospace Medical Division, Brooks Air Force Base, Tex., 1977).

Appl. Opt. (3)

Bull. Math. Biophys. (1)

M. A. Mainster, T. J. White, J. H. Tips, P. W. Wilson, “Transient thermal behavior in biological systems,” Bull. Math. Biophys. 32, 303–314 (1970).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Yoon, A. J. Welch, M. Motamedi, M. C. J. van Gemert, “Development and application of a three dimensional light distribution model for laser irradiated tissue,” IEEE J. Quantum Electron. QE-23, 1721–1733 (1987).
[CrossRef]

IEEE Trans. Biomed. Eng. (2)

E. H. Wissler, “An analysis of chorioretinal thermal response to intense light exposure,” IEEE Trans. Biomed. Eng. BME-23, 207–215 (1976).
[CrossRef]

A. J. Welch, E. H. Wissler, L. A. Priebe, “Significance of blood flow in calculations of temperature in laser irradiated tissue,” IEEE Trans. Biomed. Eng. BME-27, 164–166 (1980).
[CrossRef]

Int. J. Thermophys. (1)

J. W. Valvano, J. R. Cochran, K. R. Diller, “Thermal conductivity and diffusivity of biomaterials measured with self-heated thermistors,” Int. J. Thermophys. 6, 301–311 (1985).
[CrossRef]

Lasers Life Sci. (2)

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

J. W. Valvano, B. Chitsabesan, “Thermal conductivity and diffusivity of arterial wall and atherosclerotic plaque,” Lasers Life Sci. 1, 219–229 (1987).

Lasers Surg. Med. (3)

S. L. Jacques, S. A. Prahl, “Modeling optical and thermal distributions in tissue during laser irradiation,” Lasers Surg. Med. 6, 494–503 (1987).
[CrossRef] [PubMed]

W. F. Cheong, M. Motamedi, A. J. Welch, “Optical modeling of laser photocoagulation of bladder tissue,” Lasers Surg. Med. 7, 72 (A) (1987).

M. J. C. van Gemert, A. J. Welch, “Time constants in thermal laser medicine,” Lasers Surg. Med. 9, 405–421 (1989).
[CrossRef] [PubMed]

Lasers Surg. Med. Suppl. (2)

R. Agah, M. Motamedi, P. Dalmia, “Changes in optical constants of thermally damaged arterial tissue as a function of wavelength,” Lasers Surg. Med. Suppl. 2, 15 (A) (1990).

A. A. Oraevsky, S. L. Jacques, I. S. Saidi, G. H. Pettit, R. A. Sauerbrey, F. K. Tittel, P. D. Henry, “Optical properties and energy pathways during XeCl excimer laser irradiation of atherosclerotic aorta,” Lasers Surg. Med. Suppl. 3, 5 (A) (1991).

Phys. Med. Biol. (1)

T. Togawa, “Noncontact skin emissivity measurement by switching two shades of different temperatures,” Phys. Med. Biol. 33, Suppl. 1, 409 (A) (1988).

Other (13)

T. Togawa, “Skin emissivity measurement using the unsteady state immediately after removing a zero-heat-flow thermometer probe,” presented at the joint Fourteenth International Conference on Medical and Biological Engineering and Seventh International Conference on Medical Physics, Espoo, Finland, 1985.

J. H. Torres, “Thermal response of arterial wall to continuous wave laser irradiation and contact probe application,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1991).

R. Agah, M. Motamedi, P. Dalmia, E. Ettedgui, L. Song, J. R. Spears, “Potential role of collagen in optical behavior of arterial tissue during laser irradiation,” in Laser-Tissue Interaction, S. L. Jacques, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1202, 246–252 (1990).

G. Yoon, “Absorption and scattering of laser light in biological media—mathematical modeling and methods for determining the optical properties,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988).

S. Chandrasekar, Radiative Transfer (Oxford U. Press, London, 1960).

S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex.1988).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.

W. Brutsaert, Evaporation into the Atmosphere, Theory, History and Applications, (Reidel, Dordrecht, The Netherlands, 1982).

F P. Incropera, D. P. DeWitt, Fundamentals of Heat and Mass Transfer (Wiley, New York, 1985), Chap. 6.

P. R. Goth, “Temperature history of canine gastric tissue in response to Nd:YAG laser exposure, M. S. thesis (University of Texas at Austin, Austin, Tex., 1980).

A. J. Welch, “Laser irradiation in tissue,” in Heat Transfer in Medicine and Biology, A. Shitzer, R. C. Eberheart, eds. (Plenum, New York, 1985), pp. 135–183.
[CrossRef]

A. N. Takata, L. Zaneveld, W. Richter, Laser-Induced Thermal Damage of Skin (Aerospace Medical Division, Brooks Air Force Base, Tex., 1977).

R. Birngruber, “Thermal modeling in biological tissue,” in Lasers in Biology and Medicine, F. Hillencamp, R. Pratesi, C. A. Sacchi, eds. (Plenum, New York, 1980), pp. 77–97.
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Experimental setup. An IR camera monitored the temperature of the tissue surface during the argon laser irradiation.

Fig. 2
Fig. 2

Peak surface temperature of aortic tissue during argon laser irradiation with (a) 2 W on a 1.8-mm spot for 3 s and (b) 5 W on a 9-mm spot for over 20 s. The temperature increase slows after 70°C. The curve represents a typical pattern of tissue thermal response.

Fig. 3
Fig. 3

Comparison of temperatures predicted by the Takata–Yoon model with those measured experimentally during irradiation of the aortic wall with (a) 2 W of laser power on a 2.0-mm spot and (b) 4 W on a 2.14-mm spot. The following optical properties were used in the modeling: μa = 1.2/cm, μs′ = μs(1 − g) = 48/cm, g = 0.9, μs = 480/cm. The measured temperature histories of two irradiated samples are shown in each case.

Fig. 4
Fig. 4

Surface temperature during the argon laser irradiation of a polyacrylamide gel with a water content of 85% and a μa of 25/cm for (a) an incident power of 1 W and (b) an incident power of 0.5 W. The spot size was 2.0 mm. The measured temperatures deviated from model predictions at 65–70°C.

Fig. 5
Fig. 5

Surface temperature during the irradiation of polyacryl-amide gel with an incident power of 0.5 W on a 2.0-mm spot. The absorption coefficient of the gel was in this case 18/cm. Two of the samples shown in the figure were irradiated after their surface was covered with a transparent plastic wrap of known transmission characteristics. Above 60°C temperatures measured in the samples covered with the plastic wrap were much closer to model predictions than those measured in the samples exposed to air. In other words the rate of the temperature rise did not change dramatically at 65°C for the covered samples.

Fig. 6
Fig. 6

Surface temperature during argon laser irradiation of polyacrylamide gel with a water content of 85% and μa of 25/cm. In this case the incident power is 1 W, and the spot size is 2 mm. The surface center-line data for two experiments are shown by squares and circles. Line A shows the adiabatic heating rate (the hypothetical case of no conduction and no losses, only heat generation by the laser), 369°C/s from Qs = 1540 W/cm3. Curve B has Fourier thermal conduction. Curve C (coincident) has surface convection added with coefficient h = 25 W/m2 K (the maximum expected for free convection from a flat plate).8 Curve D shows surface radiation added with ɛ = 0.95 (coincident). Curve E (dashed curve) shows the predicted temperature with surface vaporization added according to Eq. (4). Curve F includes the correction of calculated temperatures for the thermal-camera IFOV.

Fig. 7
Fig. 7

Surface temperature during the irradiation of polyacrylamide gel with an incident power of 0.5 W on a 2-mm spot. The gel absorption coefficient was 18/cm in this case. Four experiments are plotted, two with plastic wrap covering the surface and two exposed to air. Line A is the adiabatic heating rate (133°C/s from Qs = 555 W/cm3). Curve B is the model result for no surface vaporization (with the boiling phase change intact at 100°C), which falls nearly coincident with the experimental data. Curve C includes surface vaporization (based on Stelling’s formula for water evaporation from a pond).

Fig. 8
Fig. 8

Same as Fig. 5 but water vaporization in a 90-μm layer from the surface of the gel is added. We calculated the water vaporization by using a heat and mass transfer boundary-layer analogy (the Lewis analogy). The match between the model and experiments is excellent when vaporization is assumed to take place up to the depth indicated above. This assumption is based on previous experimental studies.26

Fig. 9
Fig. 9

Surface temperature during the irradiation of fresh beef myocardium with an incident power of 0.5 W on a 2-mm spot. Four experiments are plotted; two samples were covered with plastic wrap and two were exposed to air. In the samples exposed to air the rate of the temperature rise decreases at 60°C, as in the cases of the human aorta and polyacrylamide gel, indicating a general trend for tissues.

Equations (10)

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ρ c d T / d t = ( k T ) + Q s + Q p + Q m ,
Q s ( r ) = μ a ( r ) ϕ ( r ) ,
k T z = h e ( T T e ) + σε ( θ 4 θ e 4 ) + Q vap at z = 0 ,
ζ = ( A s + B s u ) [ P s ( T ) P s ( T e , RH ) ] ,
Q vap = h f g h m [ ρ υ , sat ( T s ) ρ υ , ] ,
h m = h e / ( ρ a c a Le 2 / 3 ) ,
2 π, u 0 L d ( r , s ) ( s · z ) d ω = r i 2 π, u 0 L d ( r , s ) ( z · s ) d ω at z = 0 ,
2 π, u 0 L d ( r , s ) ( z · s ) d ω = r i 2 π, u 0 L d ( r , s ) ( s · z ) d ω at z = d ,
k ( T / r ) = 0 , r = 0 , t > 0 ,
T = T 0 for r and / or z large .

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