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Melanin Granule Models for the Processes of Laser-Induced Thermal Damage in Pigmented Retinal Tissues. I. Modeling of Laser-Induced Heating of Melanosomes and Selective Thermal Processes in Retinal Tissues

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Abstract

The computer modeling was applied for investigation of the processes of laser-induced tissue damage. The melanin granule models for the processes of laser-induced thermal damage and the results of computer modeling of the optical, thermophysical, and thermochemical processes during selective laser interaction with melanoprotein granules (melanosomes) in retinal pigment epithelium are presented in this paper. Physical-mathematical model and system of equations are formulated which describe thermal interaction processes for “short” laser pulses of duration t p<10−6 s and for “long” pulses of duration t p10−6 s. Results of numerical simulation of the processes give the space–time distributions of temperature and degrees of thermodenaturation of the protein molecules inside and around melanosomes and in the volume of irradiated tissues. Energy absorption, heat transfer and thermochemical (thermodenaturation, coagulation) processes occurring during the interaction of laser pulses with pigmented spherical and spheroidal granules in heterogeneous tissues are theoretically investigated. The possibility for selective interaction of short laser pulses with pigmented granules is discussed which results in the formation of denaturation microregions inside and near the pigmented granules (granular thermodenaturation) without origination of a continuous macroscopic thermodenaturation lesion in tissue. Analytical model of heating of single spherical and spheroidal granule under laser pulse is presented. Simple equations for time dependencies of particle temperature are obtained. The presented results are of essential interest for laser applications in and can be used for investigation of laser interaction with pigmented tissues in different fields of laser medicine.

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References

  1. 1 Allen, R.G., Thomas, S.J., Harrison, R.F., Zuclich, J.A., Blankenstein, M.F., 1985. Ocular effects of pulsed Nd laser radiation: Variation of threshold with pulsewidth. Health Phys. 49, 685–692.

    Google Scholar 

  2. 2 Anderson, R.R., Parrish, J.A., 1983. Selective photothermolysis: Precise microsurgery by selective absorption of pulsed radiation. Science 220, 524–527.

    Article  Google Scholar 

  3. 3 Arfken, G., 1967. Mathematical Methods for Physicists, New York: Academic Press, p. 67.

    Google Scholar 

  4. Avdeev, P.S., Berezin, Yu.D., Volkov, V.V., 1982. Biological effect of infrared laser radiation of 1.06 mum wavelength on the retinal tissue. Vestn. Ophthal. N1, 26–32 (in Russian).

  5. 5 Birngruber, R., Hillenkamp, F.H., Gabel, V.P., 1985. Theoretical investigation of laser thermal retinal injury. Health Phys. 48, 781–796.

    Google Scholar 

  6. 6 Bohren, C.F., Huffman, D.R., 1983. Absorprtion and Scattering of Light by Small Granules. Wiley, New York.

    Google Scholar 

  7. 7 Fankhauser, F., Kwasniewska, S. (eds.), 2003. Lasers in Ophthalmology—Basic, Diagnostic and Surgical Aspects. Kugler Publications, The Hague.

    Google Scholar 

  8. 8 Goldenberg, H., Tranter, C.J., 1952. Heat flow in an infinite medium heated by a sphere. Br. J. Appl. Phys. 3, 296–305.

    Article  Google Scholar 

  9. 9 Hansen, W.P., Fine, S., 1968. Melanin granule model for pulsed lasers induced retinal injury. Appl. Opt. 7, 155–159.

    Article  Google Scholar 

  10. 10 Hayes, J.R., Wolbarsht, M., 1968. Thermal model for retinal damage induced by pulsed lasers. Aerosp. Med. 39, 474–479.

    Google Scholar 

  11. 11 Henriques, F.C., 1947. Studies of thermal injury. Arch. Pathol. 43, 489–502.

    Google Scholar 

  12. 12 Jean, B., Bende, T., 1998. Infrared lasers. Therapeutic Applications. Ophthalmolgy Clinics of North America 11, 243–255.

    Article  Google Scholar 

  13. 13 Jean, B., Bende, T., 2003. Mid-IR laser applications in medicine. Topics Appl. Phys. 89, 511–544.

    Google Scholar 

  14. 14 Kreith, F., Black, W.Z., 1980. Basic Heat Transfer. Harper & Row, New York.

    Google Scholar 

  15. 15 Lund, J.D., Beatrice, E.S., 1979. Ocular hazard of short pulse argon laser irradiation. Health Phys. 36, 7–11.

    Article  Google Scholar 

  16. 16 Puliafito, C.A. (ed.), 1996. Laser Surgery and Medicine: Principle and Practice. Wiley, New York.

    Google Scholar 

  17. 17 Pustovalov,V.K., Khorunzhii, I.A., 1986. Selective interaction of short laser radiation pulses with pigmented tissues with regard to their granular structure. Quant. Electron. 16, 957–963.

    Article  Google Scholar 

  18. 18 Pustovalov, V.K., 1992. The interaction of intense laser radiation with laminated tissues of eye. Laser Phys. 2, 358–367.

    Google Scholar 

  19. 19 Pustovalov, V.K., Khorunzhii, I.A., 1994. Thermal processes during the action of laser radiation pulses on pigmented granules in heterogeneous biotissues. Proc. SPIE 2323, 284–289.

    Article  Google Scholar 

  20. 20 Pustovalov, V.K., 1996. Analytical model for heating of single spherical melanosome under laser pulse action. Proc. SPIE 2681, 183–186.

    Google Scholar 

  21. 21 Roider, J., Hillenkamp, F., Flotte, T., Birngruber, R., 1993. Microphotocoagulation: Selective effects of repetitive short laser pulses. Proc. Nat. Acad. Sci. USA 90, 8643–8647.

    Article  Google Scholar 

  22. 22 Roider, J., Lindemann, C., El-Hifnavi, E-S., Laqua, H., Birngruber, R., 1998. Therapeutic range of repetitive nanosecond laser exposures in selective RPE photocoagulation. Graefe’s Arch. Clin. Exp. Ophthal. 236, 213–219.

    Article  Google Scholar 

  23. 23 Thompson, C.R., 1994. Melanin granule model for heating of tissue by laser. Proc. SPIE 2134A, 66–79.

    Google Scholar 

  24. 24 Thopmson, C.R., Gerstman, B.S., Jacques, S.L., Rogers, M.E., 1996. Melanin granule model for laser-induced damage in the retina. Bull. Math. Biol. 58, 513–553.

    Article  Google Scholar 

  25. 25 Till, S.J., Till, J., Milsom, P.K., Rowlands, G., 2003. A new model for laser-induced thermal damage in the retina. Bull. Math. Biol. 65, 731–746.

    Article  Google Scholar 

  26. 26 Toth, C.A., Cain, C.P., Stein, C.D., Noojin, G.J., Stolarski, D.J., Zuclich, J.A., Roach, W.P., 1995. Retinal effects of ultrashort laser pulses in the rabbit eye. Invest. Ophthalm. Vis. Res. 36, 1910–1917.

    Google Scholar 

  27. 27 Welch, A.J., 1984. The thermal response of laser irradiated tissue. IEEE J. Quant. Electron. QE-20, 1471–1482.

    Article  Google Scholar 

  28. 28 Welch, A.J., van Gemert, M.J.C. (eds.), 1995. Optical-Thermal Response of Laser-Irradiated Tissue. Plenum Press, New York.

    Google Scholar 

  29. 29 White, T.J., Mainster, M.A., Tips, J.H., Wilson, P.W., 1970. Chorioretinal thermal behaviour. Bull. Math. Biophys. 32, 315–322.

    Article  Google Scholar 

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Pustovalov, V.K., Jean, B. Melanin Granule Models for the Processes of Laser-Induced Thermal Damage in Pigmented Retinal Tissues. I. Modeling of Laser-Induced Heating of Melanosomes and Selective Thermal Processes in Retinal Tissues. Bull. Math. Biol. 69, 245–263 (2007). https://doi.org/10.1007/s11538-006-9123-7

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