Abstract

A novel method, condensed Monte Carlo simulation, is presented that applies the results of a single Monte Carlo simulation for a given albedo μs/(μa + μs) to obtaining results for other albedos; μs and μa are the scattering and absorption coefficients, respectively. The method requires only the storage of the number of interactions of each photon with the medium. The reflectance and transmittance of turbid slabs can thus be found from a limited number of condensed Monte Carlo simulations. We can use an inversion procedure to obtain the absorption and scattering coefficients from the total reflectance and total transmittance of slabs. Remitted photon densities from a semi-infinite medium as a function of the distance between the light source and the detector for all albedos can be found even from the results of a single condensed Monte Carlo simulation. The application of similarity rules may reduce further the number of Monte Carlo simulations that are needed to describe the influence of the distribution of scattering angles on the results.

© 1993 Optical Society of America

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1993 (1)

1992 (1)

1991 (1)

B. C. Chance, “Optical method,” Ann. Rev. Biophys. Biochem. 20, 1–28 (1991).
[Crossref]

1990 (4)

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[Crossref]

H. W. Jentink, F. F. M. de Mul, R. G. A. M. Hermsen, R. Graaff, J. Greve, “Monte Carlo simulations of laser Doppler blood flow measurements in tissue,” Appl. Opt. 29, 2371–2381 (1990).
[Crossref] [PubMed]

J. M. Schmitt, G. X. Zhou, E. C. Walker, R. T. Wall, “Multilayer model for photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).
[Crossref] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

1989 (3)

1988 (4)

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical path length,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

S. Takatani, H. Noda, H. Takano, T. Akutsu, “A miniature hybrid reflection type optical sensor for measurement of hemoglobin content and oxygen saturation of whole blood,” IEEE Trans., Biomed. Eng. BME-35, 187–198 (1988).
[Crossref]

J. M. Steinke, A. P. Shepherd, “Diffusion model of the optical absorbance of whole blood,” J. Opt. Soc. Am. A 5, 813–822 (1988).
[Crossref] [PubMed]

1987 (2)

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
[Crossref] [PubMed]

W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “New trends in photobiology,” J. Photochem. Photobiol. B 1, 149–167 (1987).
[Crossref] [PubMed]

1986 (1)

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in-vivo measurement of blood oxygenation,” IEEE Trans., Biomed. Eng. BME-33, 98–107 (1986).
[Crossref]

1984 (1)

J. M. Maarek, G. Jarry, B. de Losnac, A. Lansiart, B. M. Hung, “A simulation method for the study of laser transillumination of biological tissues,” Ann. Biomed. Eng. 12, 281–284 (1984).
[Crossref] [PubMed]

1983 (2)

1979 (1)

S. Takatani, M. D. Graham, “Analysis of diffuse reflectance from a two layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[Crossref]

1977 (1)

1976 (1)

1972 (1)

1971 (1)

1968 (1)

H. C. van de Hulst, “Asymptotic fitting, a method for solving anisotropic transfer problems in thick layers,” J. Comput. Phys. 3, 291–306 (1968).
[Crossref]

1961 (1)

J. R. Mika, “Neutron transport with anisotropic scattering,” Nucl. Sci. Eng. 11, 415–427 (1961).

1956 (1)

J. D. Hardy, H. T. Hammel, D. Murgatroyd, “Spectral transmission and reflectance of excised human skin,” J. Appl. Physiol. 9, 257–264 (1956).
[PubMed]

1955 (1)

R. G. Giovanelli, “Reflection by semi-infinite diffusers,” Opt. Acta 2, 153–162 (1955).
[Crossref]

1931 (1)

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Aarnoudse, J. G.

R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis inυitro and inυiυo,” Appl. Opt. 32, 435–447 (1993).
[Crossref] [PubMed]

R. Graaff, J. G. Aarnoudse, J. R. Zijp, P. M. A. Sloot, F. F. M. de Mul, J. Greve, M. H. Koelink, “Reduced light scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. 31, 1370–1376 (1992).
[Crossref] [PubMed]

R. Graaff, J. G. Aarnoudse, F. F. M. de Mul, H. W. Jentink, “Light propagation parameters for anisotropically scattering media, based on a rigorous solution of the transport equation,” Appl. Opt. 28, 2273–2279 (1989).
[Crossref] [PubMed]

R. Graaff, J. G. Aarnoudse, F. F. M. de Mul, H. W. Jentink, “Improved expression for anisotropic scattering in absorbing media,” in Scattering and Diffraction, H. A. Ferwerda, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1029, 103–110 (1989).

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Monte Carlo simulations and measurements of signals in laser Doppler flowmetry on human skin,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.63–72 (1991).

R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

Akutsu, T.

S. Takatani, H. Noda, H. Takano, T. Akutsu, “A miniature hybrid reflection type optical sensor for measurement of hemoglobin content and oxygen saturation of whole blood,” IEEE Trans., Biomed. Eng. BME-35, 187–198 (1988).
[Crossref]

Anderson, R. R.

R. R. Anderson, J. A. Parrish, “Optical properties of human skin,” in The Science of Photomedicine, J. D. Regan, J. A. Parrish, eds. (Plenum, New York, 1982), pp. 147–194.
[Crossref]

Arridge, S.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical path length,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Bays, R.

R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
[Crossref]

Bolt, R. A.

R. A. Bolt, J. J. Ten Bosch, “A method for measuring position-dependent volume reflection,” Appl. Opt. (to be published).

Bonner, R. F.

R. F. Bonner, R. Nossal, S. Havlin, G. H. Weiss, “Model of photon migration in turbid biological media,” J. Opt. Soc. Am. A 4, 423–432 (1987).
[Crossref] [PubMed]

R. F. Bonner, R. Nossal, “Principles of laser Doppler flowmetry,” in Laser Doppler Blood Flowmetry, A. P. Shepherd, P. A. Öberg, eds. (Kluwer, Boston, Mass., 1990), pp. 17–45.

Braichotte, D.

R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
[Crossref]

Burckhardt, C. W.

R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
[Crossref]

Case, K. M.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Chance, B.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref] [PubMed]

Chance, B. C.

B. C. Chance, “Optical method,” Ann. Rev. Biophys. Biochem. 20, 1–28 (1991).
[Crossref]

Châtelain, A.

R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
[Crossref]

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[Crossref]

Cope, M.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical path length,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

P. van der Zee, M. Essenpreis, D. T. Delpy, M. Cope, “Accurate determination of optical properties of biological tissues using a Monte Carlo inversion technique,” in Proceedings of the Topical Meeting on Atmospheric, Volume, and Surface Scattering and PropagationA. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 125–128.

Dassel, A. C. M.

R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis inυitro and inυiυo,” Appl. Opt. 32, 435–447 (1993).
[Crossref] [PubMed]

R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Monte Carlo simulations and measurements of signals in laser Doppler flowmetry on human skin,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.63–72 (1991).

de Losnac, B.

J. M. Maarek, G. Jarry, B. de Losnac, A. Lansiart, B. M. Hung, “A simulation method for the study of laser transillumination of biological tissues,” Ann. Biomed. Eng. 12, 281–284 (1984).
[Crossref] [PubMed]

de Mul, F. F. M.

R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis inυitro and inυiυo,” Appl. Opt. 32, 435–447 (1993).
[Crossref] [PubMed]

R. Graaff, J. G. Aarnoudse, J. R. Zijp, P. M. A. Sloot, F. F. M. de Mul, J. Greve, M. H. Koelink, “Reduced light scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. 31, 1370–1376 (1992).
[Crossref] [PubMed]

H. W. Jentink, F. F. M. de Mul, R. G. A. M. Hermsen, R. Graaff, J. Greve, “Monte Carlo simulations of laser Doppler blood flow measurements in tissue,” Appl. Opt. 29, 2371–2381 (1990).
[Crossref] [PubMed]

R. Graaff, J. G. Aarnoudse, F. F. M. de Mul, H. W. Jentink, “Light propagation parameters for anisotropically scattering media, based on a rigorous solution of the transport equation,” Appl. Opt. 28, 2273–2279 (1989).
[Crossref] [PubMed]

R. Graaff, J. G. Aarnoudse, F. F. M. de Mul, H. W. Jentink, “Improved expression for anisotropic scattering in absorbing media,” in Scattering and Diffraction, H. A. Ferwerda, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1029, 103–110 (1989).

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Monte Carlo simulations and measurements of signals in laser Doppler flowmetry on human skin,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.63–72 (1991).

R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

Delpy, D. T.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical path length,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

P. van der Zee, M. Essenpreis, D. T. Delpy, M. Cope, “Accurate determination of optical properties of biological tissues using a Monte Carlo inversion technique,” in Proceedings of the Topical Meeting on Atmospheric, Volume, and Surface Scattering and PropagationA. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 125–128.

Essenpreis, M.

P. van der Zee, M. Essenpreis, D. T. Delpy, M. Cope, “Accurate determination of optical properties of biological tissues using a Monte Carlo inversion technique,” in Proceedings of the Topical Meeting on Atmospheric, Volume, and Surface Scattering and PropagationA. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 125–128.

Ferwerda, H. A.

Fountain, M.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref] [PubMed]

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[Crossref] [PubMed]

Funakubo, H.

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H. W. Jentink, F. F. M. de Mul, R. G. A. M. Hermsen, R. Graaff, J. Greve, “Monte Carlo simulations of laser Doppler blood flow measurements in tissue,” Appl. Opt. 29, 2371–2381 (1990).
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R. Graaff, J. G. Aarnoudse, F. F. M. de Mul, H. W. Jentink, “Light propagation parameters for anisotropically scattering media, based on a rigorous solution of the transport equation,” Appl. Opt. 28, 2273–2279 (1989).
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R. Graaff, J. G. Aarnoudse, F. F. M. de Mul, H. W. Jentink, “Improved expression for anisotropic scattering in absorbing media,” in Scattering and Diffraction, H. A. Ferwerda, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1029, 103–110 (1989).

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Monte Carlo simulations and measurements of signals in laser Doppler flowmetry on human skin,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.63–72 (1991).

R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

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S. Takatani, M. D. Graham, “Analysis of diffuse reflectance from a two layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
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B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
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R. Graaff, J. G. Aarnoudse, J. R. Zijp, P. M. A. Sloot, F. F. M. de Mul, J. Greve, M. H. Koelink, “Reduced light scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. 31, 1370–1376 (1992).
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H. W. Jentink, F. F. M. de Mul, R. G. A. M. Hermsen, R. Graaff, J. Greve, “Monte Carlo simulations of laser Doppler blood flow measurements in tissue,” Appl. Opt. 29, 2371–2381 (1990).
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R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Monte Carlo simulations and measurements of signals in laser Doppler flowmetry on human skin,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.63–72 (1991).

Groenhuis, R. A. J.

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Havlin, S.

Heida, P.

R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

Hemenger, R. P.

Hermsen, R. G. A. M.

Holtom, G.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
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J. M. Maarek, G. Jarry, B. de Losnac, A. Lansiart, B. M. Hung, “A simulation method for the study of laser transillumination of biological tissues,” Ann. Biomed. Eng. 12, 281–284 (1984).
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Jacques, S. L.

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Jarry, G.

J. M. Maarek, G. Jarry, B. de Losnac, A. Lansiart, B. M. Hung, “A simulation method for the study of laser transillumination of biological tissues,” Ann. Biomed. Eng. 12, 281–284 (1984).
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Johnson, C.

Keijzer, M.

S. L. Jacques, M. Keijzer, “Dosimetry for lasers and light in dermatology: Monte Carlo simulations of 577-nm pulsed laser penetration into cutaneous vessels,” in Lasers in Dermatology and Tissue Welding, O. T. Tan, R. A. White, J. V. White, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1422, 2–13 (1991).

Kent, J.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
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Klier, K.

Koelink, M. H.

R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis inυitro and inυiυo,” Appl. Opt. 32, 435–447 (1993).
[Crossref] [PubMed]

R. Graaff, J. G. Aarnoudse, J. R. Zijp, P. M. A. Sloot, F. F. M. de Mul, J. Greve, M. H. Koelink, “Reduced light scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. 31, 1370–1376 (1992).
[Crossref] [PubMed]

R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

M. H. Koelink, F. F. M. de Mul, J. Greve, R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, “Monte Carlo simulations and measurements of signals in laser Doppler flowmetry on human skin,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. Soc. Photo-Opt. Instrum. Eng.63–72 (1991).

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P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

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J. M. Maarek, G. Jarry, B. de Losnac, A. Lansiart, B. M. Hung, “A simulation method for the study of laser transillumination of biological tissues,” Ann. Biomed. Eng. 12, 281–284 (1984).
[Crossref] [PubMed]

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J. M. Maarek, G. Jarry, B. de Losnac, A. Lansiart, B. M. Hung, “A simulation method for the study of laser transillumination of biological tissues,” Ann. Biomed. Eng. 12, 281–284 (1984).
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Marijnissen, J. P. A.

McCully, K.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
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J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in-vivo measurement of blood oxygenation,” IEEE Trans., Biomed. Eng. BME-33, 98–107 (1986).
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Mihm, F. G.

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in-vivo measurement of blood oxygenation,” IEEE Trans., Biomed. Eng. BME-33, 98–107 (1986).
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J. R. Mika, “Neutron transport with anisotropic scattering,” Nucl. Sci. Eng. 11, 415–427 (1961).

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R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
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W. G. Zijlstra, G. A. Mook, Medical Reflection Oximetry (Van Gorcum, Assen, The Netherlands, 1962).

Mudgett, P. S.

Munk, F.

P. Kubelka, F. Munk, “Ein Beitrag zur Optik der Farbanstriche,” Z. Tech. Phys. 12, 593–601 (1931).

Murgatroyd, D.

J. D. Hardy, H. T. Hammel, D. Murgatroyd, “Spectral transmission and reflectance of excised human skin,” J. Appl. Physiol. 9, 257–264 (1956).
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Nioka, S.

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
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S. Takatani, H. Noda, H. Takano, T. Akutsu, “A miniature hybrid reflection type optical sensor for measurement of hemoglobin content and oxygen saturation of whole blood,” IEEE Trans., Biomed. Eng. BME-35, 187–198 (1988).
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R. F. Bonner, R. Nossal, “Principles of laser Doppler flowmetry,” in Laser Doppler Blood Flowmetry, A. P. Shepherd, P. A. Öberg, eds. (Kluwer, Boston, Mass., 1990), pp. 17–45.

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R. R. Anderson, J. A. Parrish, “Optical properties of human skin,” in The Science of Photomedicine, J. D. Regan, J. A. Parrish, eds. (Plenum, New York, 1982), pp. 147–194.
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V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
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M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflection spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, P. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
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R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
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J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in-vivo measurement of blood oxygenation,” IEEE Trans., Biomed. Eng. BME-33, 98–107 (1986).
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Schwartz, E.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflection spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, P. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

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Sloot, P. M. A.

Star, W. M.

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Svaasand, L.

R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
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Takano, H.

S. Takatani, H. Noda, H. Takano, T. Akutsu, “A miniature hybrid reflection type optical sensor for measurement of hemoglobin content and oxygen saturation of whole blood,” IEEE Trans., Biomed. Eng. BME-35, 187–198 (1988).
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Takatani, S.

S. Takatani, H. Noda, H. Takano, T. Akutsu, “A miniature hybrid reflection type optical sensor for measurement of hemoglobin content and oxygen saturation of whole blood,” IEEE Trans., Biomed. Eng. BME-35, 187–198 (1988).
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S. Takatani, M. D. Graham, “Analysis of diffuse reflectance from a two layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
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R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
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D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical path length,” Phys. Med. Biol. 33, 1433–1442 (1988).
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P. van der Zee, M. Essenpreis, D. T. Delpy, M. Cope, “Accurate determination of optical properties of biological tissues using a Monte Carlo inversion technique,” in Proceedings of the Topical Meeting on Atmospheric, Volume, and Surface Scattering and PropagationA. Consortini, ed. (ICO Secretariat, Florence, Italy, 1991), pp. 125–128.

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W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “New trends in photobiology,” J. Photochem. Photobiol. B 1, 149–167 (1987).
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Wagnières, G.

R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
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Walker, E. C.

Wall, R. T.

Weiss, G. H.

Welch, A. J.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
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Wilson, B. C.

M. S. Patterson, E. Schwartz, B. C. Wilson, “Quantitative reflection spectrophotometry for the noninvasive measurement of photosensitizer concentration in tissue during photodynamic therapy,” in Photodynamic Therapy: Mechanisms, P. Dougherty, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1065, 115–122 (1989).

Winterhalter, L.

R. Bays, L. Winterhalter, H. Funakubo, Ph. Monnier, M. Savary, G. Wagnières, D. Braichotte, A. Châtelain, H. van den Bergh, L. Svaasand, C. W. Burckhardt, “Clinical optical dose measurement for PDT: invasive and noninvasive techniques,” in Future Trends in Biomedical Applications of Lasers, L. O. Svaasand, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1525, 397–408 (1991).
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D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical path length,” Phys. Med. Biol. 33, 1433–1442 (1988).
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Wyatt, J.

D. T. Delpy, M. Cope, P. van der Zee, S. Arridge, S. Wray, J. Wyatt, “Estimation of optical path length,” Phys. Med. Biol. 33, 1433–1442 (1988).
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Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
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Zhou, G. X.

Zijlstra, W. G.

R. Graaff, A. C. M. Dassel, M. H. Koelink, F. F. M. de Mul, J. G. Aarnoudse, W. G. Zijlstra, “Optical properties of human dermis inυitro and inυiυo,” Appl. Opt. 32, 435–447 (1993).
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W. G. Zijlstra, G. A. Mook, Medical Reflection Oximetry (Van Gorcum, Assen, The Netherlands, 1962).

R. Graaff, A. C. M. Dassel, J. G. Aarnoudse, W. G. Zijlstra, P. Heida, F. F. M. de Mul, M. H. Koelink, J. Greve, “Biophysical aspects of reflection pulse oximetry,” in Proceedings of the Fourth International Conference on Fetal and Neonatal Physiological Measurements, H. N. Lafeber, J. G. Aarnoudse, H. W. Jongsma, eds. (Elsevier, Amsterdam, 1991).

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Zweifel, P. F.

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Anal. Biochem. (1)

B. Chance, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref] [PubMed]

Ann. Biomed. Eng. (1)

J. M. Maarek, G. Jarry, B. de Losnac, A. Lansiart, B. M. Hung, “A simulation method for the study of laser transillumination of biological tissues,” Ann. Biomed. Eng. 12, 281–284 (1984).
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B. C. Chance, “Optical method,” Ann. Rev. Biophys. Biochem. 20, 1–28 (1991).
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[Crossref] [PubMed]

H. W. Jentink, F. F. M. de Mul, R. G. A. M. Hermsen, R. Graaff, J. Greve, “Monte Carlo simulations of laser Doppler blood flow measurements in tissue,” Appl. Opt. 29, 2371–2381 (1990).
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R. Graaff, J. G. Aarnoudse, J. R. Zijp, P. M. A. Sloot, F. F. M. de Mul, J. Greve, M. H. Koelink, “Reduced light scattering properties for mixtures of spherical particles: a simple approximation derived from Mie calculations,” Appl. Opt. 31, 1370–1376 (1992).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

S. Takatani, M. D. Graham, “Analysis of diffuse reflectance from a two layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[Crossref]

IEEE Trans., Biomed. Eng. (2)

J. M. Schmitt, J. D. Meindl, F. G. Mihm, “An integrated circuit-based optical sensor for in-vivo measurement of blood oxygenation,” IEEE Trans., Biomed. Eng. BME-33, 98–107 (1986).
[Crossref]

S. Takatani, H. Noda, H. Takano, T. Akutsu, “A miniature hybrid reflection type optical sensor for measurement of hemoglobin content and oxygen saturation of whole blood,” IEEE Trans., Biomed. Eng. BME-35, 187–198 (1988).
[Crossref]

J. Appl. Physiol. (1)

J. D. Hardy, H. T. Hammel, D. Murgatroyd, “Spectral transmission and reflectance of excised human skin,” J. Appl. Physiol. 9, 257–264 (1956).
[PubMed]

J. Comput. Phys. (1)

H. C. van de Hulst, “Asymptotic fitting, a method for solving anisotropic transfer problems in thick layers,” J. Comput. Phys. 3, 291–306 (1968).
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J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Photochem. Photobiol. B (1)

W. M. Star, J. P. A. Marijnissen, M. J. C. Van Gemert, “New trends in photobiology,” J. Photochem. Photobiol. B 1, 149–167 (1987).
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Nucl. Sci. Eng. (1)

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[Crossref]

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[Crossref]

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Figures (6)

Fig. 1
Fig. 1

Intensity decay of a collimated beam caused by absorption and scattering.

Fig. 2
Fig. 2

Monte Carlo simulations used to predict the relative reflectance expressed per unit of mean free path squared at the surface of a semi-infinite medium with known absorption and scattering coefficients as a function of μtr (a). For finite slabs the results are also a function of μtd (b).

Fig. 3
Fig. 3

Relative reflectance at the surface of a semi-infinite medium as a function of rμt for different values of the albedo c. The relative reflectances were derived from two different condensed Monte Carlo simulations: ○, csim = 0.995, +, csim = 0.99999. Isotropic scattering, nrefr = 1.4.

Fig. 4
Fig. 4

Total transmission for slabs with Henyey–Greenstein scatterers (g = 0.875) between glass slides as a function of slab thickness. Calculations for reduced albedo c′ = 0.99, 0.95, 0.90, and 0.80. Refractive index (air/glass/sample/glass/air): 1.0/1.5/1.4/1.5/1.0.

Fig. 5
Fig. 5

Sum of total transmission and total reflectance for slabs with Henyey–Greenstein scatterers (g = 0.875) between glass slides as a function of slab thickness. Calculations for reduced albedo c′ = 0.99, 0.95, 0.90, and 0.80. Refractive index (air/glass/sample/glass/air): 1.0/1.5/1.4/1.5/1.0.

Fig. 6
Fig. 6

Similarity test for reduced dimensionless relative reflectances at the surface of a semi-infinite medium as a function of rμt′ for different values of the reduced albedo c′. The dimensionless relative reflectances were multiplied by (rμt′)2 and were derived from condensed Monte Carlo simulations with different phase functions: Henyey–Greenstein scattering with ■, gHG = 0, Δ, gHG = 0.75; ○, gHG = 0.875; ⋄, gHG = 0.95, nrefr = 1.4. The dotted lines indicate the slope predicted by Eq. (18).

Tables (4)

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Table 1 Total Reflection and Total Transmission for Slabs with Henyey–Greenstein Scatterers between Glass Slides, gHG = 0.875, c = 0.99a

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Table 2 Number of Photons Transmitted and Reflected After j Interactions with the Mediuma

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Table 3 Total Transmission Ttot for Optically Thin Slabs between Glass Slides Investigated for Henyey–Greenstein Scattering with g = 0.875, g = 0.75, and g = 0a

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Table 4 Total Reflection Rtot for Optically Thin Slabs between Glass Slides Investigated for Henyey–Greenstein Scattering with g = 0.875, g = 0.75, and g = 0a

Equations (20)

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p t ( z ) = I ( z ) I ( 0 ) = exp ( μ a z ) exp ( μ s z ) = exp [ ( μ a + μ s ) z ] = exp ( μ t z ) .
p t ( z ) p t ( z + d z ) = μ t exp ( μ t z ) d z .
p s ( z ) p s ( z + d z ) = μ s exp ( μ t z ) d z ,
l s = 0 1 l d p s ( l ) 0 1 d p s ( l ) = 0 l μ s exp ( μ t l ) d l 0 μ s exp ( μ t l ) d l ,
l s = μ s / μ t 2 μ s / μ t = 1 μ t = l t .
l t = 1 μ t ln ( ) .
r ( i ) μ t = r sim ( i ) μ t , sim ,
R d l ( μ t r ) = R ( r ) / μ t 2 .
R d l [ μ t r ( j ) ] R d l ( j ) = N ( j ) N tot A d l ( j ) ,
A d l ( j ) = π [ r outer 2 ( j ) r inner 2 ( j ) ] μ t 2 ,
μ t d = μ t , sim d sim ,
p ( i ) = ( c / c sim ) N ( i ) .
T tot = j = 0 N table N trans ( j ) ( c c sim ) j ,
R tot = j = 0 N table N refl ( j ) ( c c sim ) j ,
μ a = μ a , sim ,
μ s = μ s ( 1 g ) = μ s , sim ( 1 g sim ) ,
R d l ( μ t r ) R ( r ) / ( μ t ) 2 .
R ( r ) = const exp ( α r ) / r 2 ,
α diff = ( 3 μ a μ t ) 1 / 2 .
μ t d = ( μ a / μ t + μ s / [ ( 1 g ) μ t ] ) μ t d = ( 1 + 7 c ) μ t d .

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