Skip to main content
SpringerLink
Log in

The propagation of optical radiation in tissue I. Models of radiation transport and their application

  • Published:
Lasers in Medical Science Aims and scope Submit manuscript

Abstract

This paper is the first of two reviewing the propagation of electromagnetic radiation of wavelength 0.25–10μm in tissue. After a brief discussion of light/tissue interactions, a mathematical description of light propagation in terms of radiative transfer is developed. Formal solutions of the resulting equation are outlined, but the emphasis is on approximate method of solution—namely the discrete ordinates method, the technique of functional expansion and Monte Carlo simulation. The application of the simplest of these approximate methods, namely the 2-flux and diffusion models, to tissue optics is discussed in some detail. The second paper deals with the optical properties of tissue and the salient characteristics of light fluence distributions in these tissues.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Patterson MS, Wilson BC, Wyman DR. The propagation of optical radiation in tissue II. Optical properties of tissues and resulting fluence distributions.Lasers Med Sci (in press).

  2. Boulnois JL. Photophysical processes in recent medical laser developments: a review.Lasers Med Sci 1986,1:47–66

    Article  Google Scholar 

  3. Ishimaru A.Wave propagation and scattering in random media. New York: Academic Press, 1978

    Google Scholar 

  4. Wilksch PA, Jacka F, Blake AJ. Studies of light propagation through tissue. In: Doiron DR, Gomer CJ (eds)Porphyrin localization and treatment of tumors. New York: Liss, 1984, 149–61

    Google Scholar 

  5. Patterson MS, Wilson BC, Chance B. Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties.Appl Opt 1989,28:2331–6

    Google Scholar 

  6. Hansen JE, Travis LD. Light scattering in planetary atmospheres.Space Sci Rev 1974,16:527–613

    Article  Google Scholar 

  7. Svaasand LO, Gomer CJ. Optics in tissue. In: Muller GJ, Sliney DH (eds)Dosimetry of laser radiation in medicine and biology, Vol. IS-5. Bellingham: SPIE Optical Engineering 1990:114–32

    Google Scholar 

  8. Fante RL. Relationship between radiative-transport theory and Maxwell's equations in dielectric media.J Opt Soc Am 1981,71:460–8

    Google Scholar 

  9. Yoo KM, Liu F, Alfano RR. Biological materials probed by the temporal and angular profiles of the backscattered ultrafast laser pulses.J Opt Soc Am B 1990,7:1685–93

    Google Scholar 

  10. van de Hulst HC.Multiple light scattering tables, formulas and applications. New York: Academic Press, 1980

    Google Scholar 

  11. Jerlov NG.Marine Optics. Amsterdam: Elsevier, 1976

    Google Scholar 

  12. Duderstadt JJ, Hamilton LJ.Nuclear reactor analysis. New York: Wiley, 1976

    Google Scholar 

  13. Irvine WM. Multiple scattering in planetary atmospheres.Icarus 1975,25:175–204

    Article  Google Scholar 

  14. Hunt GE. A review of computational techniques for analysing the transfer of radiation through a model cloudy atmosphere.J. Quant Spectrosc Radiat Transfer 1971,11:665–90

    Google Scholar 

  15. van de Hulst HC, Irvine WM. General report on radiation transfer in planets: scattering in model planetary atmospheres.Mem Soc Roy Sci Liege 15th Ser 7 1962,78

  16. Irvine WM. The formation of absorption bands and the distribution of photon optical paths in a scattering atmosphere.Bull Astron Inst Neth 1964,17:266–79

    Google Scholar 

  17. Chandrasekhar S.Radiative transfer. New York: Dover, 1960

    Google Scholar 

  18. Sobolev VV.Light scattering in planetary atmospheres. Oxford: Pergamon, 1975

    Google Scholar 

  19. Case KM, Zweifel PF.Linear transport theory. Reading: Addison Wesley, 1967

    Google Scholar 

  20. van de Hulst.A new look at multiple scattering. Unnumbered mimeographed report, NASA Institute for Space Science, New York, 1963

    Google Scholar 

  21. Anderson RR, Hu J, Parrish JA. Optical radiation transfer in the human skin and applications in in vivo remittance spectroscopy. In Marks R, Payne PA (eds)Bioengineering and the skin. Lancaster: MTP, 1981:253–65

    Google Scholar 

  22. Ambartsumian VA.Dokl Akad Nauk SSSR 1943,38:257

    Google Scholar 

  23. Moaveni MK, Razani A. Application of invariant imbedding for the study of optical transmission and reflection by blood: Part I—Theory.Ind J Biochem Biophys 1974,11:25–9

    Google Scholar 

  24. Orchard SW. Reflection and transmission of light by diffusing suspensions.J Opt Soc Am 1969,59:1584–97

    Google Scholar 

  25. Mudgett PS, Richards LW. Multiple scattering calculations for technology.Appl Opt 1971,10:1485–502

    Google Scholar 

  26. Schuster A. Radiation through a foggy atmosphere.Astrophys J 1905,21:1–22

    Article  Google Scholar 

  27. Kubelka P, Munk F. Ein Beitrag zur Optik der Farbanstriche.Z Tech Phys 1931,12:593–601

    Google Scholar 

  28. Kubelka P. New contributions to the optics of intensely light-scattering materials, Part I.J Opt Soc Am 1948,38:448–57

    Google Scholar 

  29. van Gemert MJC, Star WM. Relations between the Kubelka-Munk and the transport equation models for anisotropic scattering.Lasers Life Sci 1987,1:287–98

    Google Scholar 

  30. Mudgett PS and Richards LW. Multiple scattering calculations for technology II.J Coll Interface Sci 1972,39:551–67

    Article  Google Scholar 

  31. Reichman J. Determination of absorption and scattering coefficients for nonhomogeneous media. 1. Theory.Appl Opt 1973,12:1811–5

    Google Scholar 

  32. Klier K. Absorption and scattering in plane parallel turbid media.J Opt Soc Am 1972,62:882–5

    Google Scholar 

  33. Brinkworth BJ. Interpretation of the Kubelka-Munk coefficients in reflection theory.Appl Opt 1972,11:1434–5

    Google Scholar 

  34. Meador WE, Weaver WR. Diffusion approximation for large absorption in radiative transfer.Appl Opt 1979,18:1204–8

    Google Scholar 

  35. Welch AJ, Yoon G, van Gemert MJC. Practical models for light distribution in laser-irradiated tissues.Lasers Surg Med 1987,6:488–93

    PubMed  Google Scholar 

  36. Star WM, Marijnissen JPA, van Gemert MJC. Light dosimetry in optical phantoms and in tissues I. Multiple flux and transport theory.Phys Med Biol 1988,33:437–54

    Article  PubMed  Google Scholar 

  37. Reynolds L, Johnson C, Ishimaru A. Diffuse reflectance from a finite blood medium: applications to the modeling of fiber optic catheters.Appl Opt 1976,15:2059–67

    Google Scholar 

  38. Takatani S, Graham MD. Theoretical analysis of diffuse reflectance from a two-layer tissue model.IEEE Trans Biomed Eng 1979,BME-26:656–64

    PubMed  Google Scholar 

  39. Hemenger RP. Optical properties of turbid media with specularly reflecting boundaries: applications to biological problems.Appl Opt 1977,16:2007–12

    Google Scholar 

  40. Groenhuis RAJ, Ferwerda HA, Ten Bosch JJ. Scattering and absorption of turbid materials determined from reflection measurements. 1. Theory.Appl Opt 1983,22:2456–62

    Google Scholar 

  41. Jacques SL, Prahl SA. Modeling optical and thermal distributions in tissue during laser irradiation.Lasers Surg Med 1987,7:494–503

    Google Scholar 

  42. McKenzie AL. How may external and interstitial illumination be compared in laser photodynamic therapy:Phys Med Biol 1985,30:455–60

    Article  PubMed  Google Scholar 

  43. Storchi PRM. Application of the Pn method to the calculation of the angular flux of gamma rays.J. Comp Phys 1984,55:81–97

    Article  Google Scholar 

  44. Moulton JD.Diffusion modelling of light propagation in turbid media. M. Eng. Thesis, McMaster University, Canada, 1990

    Google Scholar 

  45. Carter LL, Cashwell ED.Particle transport simulation with the Monte Carlo method. Technical Information Center, Office of Public Affairs, U.S. Energy Research and Development Administration, 1975

  46. Levitt LB. The use of self-optimized exponential biasing in obtaining Monte Carlo estimates of transmission probabilities.Nucl Sci Eng 1968,31:500–4

    Google Scholar 

  47. Wilson BC, Adam G. A Monte Carlo model for the absorption and flux distributions of light in tissue.Med Phys 1983,10:824–30

    Article  PubMed  Google Scholar 

  48. Flock ST, Wilson BC, Patterson MS. Hybrid Monte Carlo—diffusion theory modelling of light distributions in tissue. In:Laser interaction with tissue, SPIE 1988,908:20–8

    Google Scholar 

  49. Peters VG, Wyman DR, Patterson MS, Frank GL. Optical properties of normal and diseased human tissue in the visible and near infrared.Phy Med Biol 1990,35:1317–34

    Article  Google Scholar 

  50. Wilson BC, Patterson MS, Flock ST, Wyman DR. Tissue optical properties in relation to models for light propagation and in vivo dosimetry. In: Chance B (ed.)Photon migration in tissue. New York: Plenum 1990, 24–42

    Google Scholar 

  51. Jacques SL. Time resolved propagation of ultrashort laser pulses within turbid tissues.Appl Opt 1989,28:2223–9

    Google Scholar 

  52. Hebden JC, Kruger RA. Transillumination imaging performance: spatial resolution simulation studies.Med Phys 1990,17:41–7

    Article  PubMed  Google Scholar 

  53. Bonner RF, Nossal R, Havlin S, Weiss GH. Model for photon migration in turbid biological media.J Opt Soc Am A 1987,4:423–32

    PubMed  Google Scholar 

  54. Nossal R, Kiefer J, Weiss GH et al. Photon migration in layered media.Appl Opt 1988,27:3382–91

    Google Scholar 

  55. Weiss GH, Nossal R, Bonner RF. Statistics of penetration depth of photons re-emitted from irradiated tissue.J Mod Optics 1989,36:349–59

    Google Scholar 

  56. Taitlebaum H, Havlin S, Weiss GH. Approximate theory of photon migration in a two-layer medium.Appl Opt 1989,28:2245–9

    Google Scholar 

  57. Chandrasekhar S. Stochastic problems in physics and astronomy.Rev Mod Phys 1943,15:1–88

    Article  Google Scholar 

  58. Herman M, Lenoble J. Asymptotic radiation in a scattering and absorbing medium.J Quant Spectrosc Radiat Transfer 1968,8:355–67

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Hamilton Regional Cancer Centre and McMaster University, 711 Concession Street, L8V 1C3, Hamilton, Ontario, Canada

    Michael S. Patterson, Brian C. Wilson & Douglas R. Wyman

Authors
  1. Michael S. Patterson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Brian C. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Douglas R. Wyman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Patterson, M.S., Wilson, B.C. & Wyman, D.R. The propagation of optical radiation in tissue I. Models of radiation transport and their application. Laser Med Sci 6, 155–168 (1991). https://doi.org/10.1007/BF02032543

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02032543

Key words

Search

Navigation