Abstract

Here light propagation and radiation transfer of ultrafast laser pulses in heterogeneous biological tissues are simulated by use of the discrete-ordinates method (DOM). Formulations for solving the time-dependent radiation-transfer equation are deduced for three-dimensional geometries incorporating the Fresnel specularly reflecting boundary condition and characteristics of ultrafast laser pulses. The present method can treat both the incident laser intensity and the scattered radiation intensity from the walls of the targeted tissue as two components, i.e., a diffuse part and a specular part. Reflectivity at the tissue-air interface is calculated by use of Snell’s law and the Fresnel equation. The high-order S10 DOM method is found to be adequate for describing the propagation and transfer of ultrafast laser radiation in heterogeneous tissues. The time-dependent radiation field in the tissue as well as the temporal radiation intensity profiles at the boundaries can be obtained simultaneously. The absolute values of the logarithmic slope of the temporal reflectance and transmittance at various detector positions are found to converge to a constant value in a homogeneous tissue model. With the inclusion of a small inhomogeneity, such a value will change in line with the property of the embedded inhomogeneity. The orientation of heterogeneity of the tissues also substantially affects the radiation intensity at the boundaries. The effect of the Fresnel boundary in the modeling is pronounced. The simulated transmitted signals are broadened and amplified under specularly reflecting boundary condition as compared with those under diffusely reflecting boundary conditions.

© 2003 Optical Society of America

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  1. S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
    [CrossRef] [PubMed]
  2. R. R. Alfano, S. G. Demos, S. K. Gayen, “Advances in optical imaging of biomedical media,” Ann. N.Y. Acad. Sci. 820, 248–270 (1997).
    [CrossRef] [PubMed]
  3. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  4. S. L. Jacques, “Time resolved propagation of ultrashort laser pulses within turbid tissues,” Appl. Opt. 28, 2223–2229 (1989).
    [CrossRef] [PubMed]
  5. D. M. Rector, R. F. Rogers, J. S. George, “A focusing image probe for assessing neural activity in vivo,” J. Neurosci. Methods 91, 135–145 (1999).
    [CrossRef] [PubMed]
  6. A. D. Klose, U. Netz, J. Beuthan, A. H. Hielsher, “Optical tomography using the time-independent equation of radiative transfer. 1. Forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).
    [CrossRef]
  7. F. H. Loesel, F. P. Fisher, H. Suhan, J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B 66, 121–128 (1998).
  8. K. M. McNally, B. S. Sorg, A. J. Welch, J. M. Dawes, E. R. Owen, “Photothermal effects of laser tissue soldering,” Phys. Med. Biol. 44, 983–1002 (1999).
    [CrossRef] [PubMed]
  9. S. Grapengiesser, F. Gudmundsson, O. Larko, M. Ericson, A. Rosen, A. M. Wennberg, “Pain caused by photodynamic therapy of skin cancer,” Clin. Exp. Dermatol. 27, 493–497 (2002).
    [CrossRef] [PubMed]
  10. A. Obana, Y. Gohto, “Scanning laser system for photodynamic therapy of choroidal neovascularization,” Lasers Surg. Med. 30, 370–375 (2002).
    [CrossRef] [PubMed]
  11. E. J. Seibel, Q. Y. J. Smithwick, “Unique features of optical scanning, single fiber endoscopy,” Lasers Surg. Med. 30, 177–183 (2002).
    [CrossRef] [PubMed]
  12. S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 10, 826–831 (2002).
    [CrossRef]
  13. S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues. I. Prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
    [CrossRef] [PubMed]
  14. D. A. Boas, J. P. Culver, J. J. Stott, A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10, 159–170 (2002), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  15. Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer 14, 504–511 (2000).
    [CrossRef]
  16. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1987).
  17. K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
    [CrossRef] [PubMed]
  18. M. F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 1993), Chap. 15.
  19. W. A. Fiveland, “The selection of discrete ordinate quadrature sets for anisotropic scattering,” American Society of Mechanical Engineers, Heat Transfer Division 72, 89–96 (1991).
  20. K. D. Lathrop, “Spatial differencing of the transport equation: positive vs accuracy,” J. Comput. Phys. 4, 475–498 (1968).
    [CrossRef]
  21. K. D. Lathrop, F. W. Brinkley, “TWOTRAN-II code,” Los Alamos Scientific Laboratory Rep. #LA-4848-MS (Los Alamos Scientific Laboratory, Los Alamos, N. Mex., 1973).
  22. S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
    [CrossRef]
  23. K. Mitra, S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. 38, 188–196 (1999).
    [CrossRef]
  24. Z. Guo, S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt. 40, 3156–3163 (2001).
    [CrossRef]
  25. Z. Guo, S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
    [CrossRef]
  26. J. C. Chai, H. S. Lee, S. V. Patankar, “Ray effect and false scattering in the discrete ordinates method,” Numer. Heat Transfer Part B 24, 373–389 (1993).
    [CrossRef]
  27. A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
    [CrossRef] [PubMed]
  28. Z. Guo, S. Kumar, “Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media,” Appl. Opt. 39, 4411–4417 (2000).
    [CrossRef]
  29. S. K. Wan, Z. Guo, S. Kumar, J. Aber, B. A. Garetz, “Detecting inhomogeneities in a turbid medium,” presented at Eurotherm 73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 15–17 April 2003.

2002 (7)

A. D. Klose, U. Netz, J. Beuthan, A. H. Hielsher, “Optical tomography using the time-independent equation of radiative transfer. 1. Forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).
[CrossRef]

S. Grapengiesser, F. Gudmundsson, O. Larko, M. Ericson, A. Rosen, A. M. Wennberg, “Pain caused by photodynamic therapy of skin cancer,” Clin. Exp. Dermatol. 27, 493–497 (2002).
[CrossRef] [PubMed]

A. Obana, Y. Gohto, “Scanning laser system for photodynamic therapy of choroidal neovascularization,” Lasers Surg. Med. 30, 370–375 (2002).
[CrossRef] [PubMed]

E. J. Seibel, Q. Y. J. Smithwick, “Unique features of optical scanning, single fiber endoscopy,” Lasers Surg. Med. 30, 177–183 (2002).
[CrossRef] [PubMed]

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 10, 826–831 (2002).
[CrossRef]

D. A. Boas, J. P. Culver, J. J. Stott, A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10, 159–170 (2002), http://www.opticsexpress.org .
[CrossRef] [PubMed]

Z. Guo, S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
[CrossRef]

2001 (1)

2000 (2)

Z. Guo, S. Kumar, “Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media,” Appl. Opt. 39, 4411–4417 (2000).
[CrossRef]

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer 14, 504–511 (2000).
[CrossRef]

1999 (3)

D. M. Rector, R. F. Rogers, J. S. George, “A focusing image probe for assessing neural activity in vivo,” J. Neurosci. Methods 91, 135–145 (1999).
[CrossRef] [PubMed]

K. M. McNally, B. S. Sorg, A. J. Welch, J. M. Dawes, E. R. Owen, “Photothermal effects of laser tissue soldering,” Phys. Med. Biol. 44, 983–1002 (1999).
[CrossRef] [PubMed]

K. Mitra, S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. 38, 188–196 (1999).
[CrossRef]

1998 (3)

S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
[CrossRef]

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

F. H. Loesel, F. P. Fisher, H. Suhan, J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B 66, 121–128 (1998).

1997 (2)

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

R. R. Alfano, S. G. Demos, S. K. Gayen, “Advances in optical imaging of biomedical media,” Ann. N.Y. Acad. Sci. 820, 248–270 (1997).
[CrossRef] [PubMed]

1993 (1)

J. C. Chai, H. S. Lee, S. V. Patankar, “Ray effect and false scattering in the discrete ordinates method,” Numer. Heat Transfer Part B 24, 373–389 (1993).
[CrossRef]

1991 (1)

W. A. Fiveland, “The selection of discrete ordinate quadrature sets for anisotropic scattering,” American Society of Mechanical Engineers, Heat Transfer Division 72, 89–96 (1991).

1990 (1)

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

1989 (3)

1968 (1)

K. D. Lathrop, “Spatial differencing of the transport equation: positive vs accuracy,” J. Comput. Phys. 4, 475–498 (1968).
[CrossRef]

Aber, J.

S. K. Wan, Z. Guo, S. Kumar, J. Aber, B. A. Garetz, “Detecting inhomogeneities in a turbid medium,” presented at Eurotherm 73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 15–17 April 2003.

Alcouffe, R. E.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Alfano, R. R.

R. R. Alfano, S. G. Demos, S. K. Gayen, “Advances in optical imaging of biomedical media,” Ann. N.Y. Acad. Sci. 820, 248–270 (1997).
[CrossRef] [PubMed]

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Arridge, S. R.

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Barbour, R. L.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Beuthan, J.

A. D. Klose, U. Netz, J. Beuthan, A. H. Hielsher, “Optical tomography using the time-independent equation of radiative transfer. 1. Forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).
[CrossRef]

Bille, J. F.

F. H. Loesel, F. P. Fisher, H. Suhan, J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B 66, 121–128 (1998).

Bindokas, V. P.

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 10, 826–831 (2002).
[CrossRef]

Boas, D. A.

Brinkley, F. W.

K. D. Lathrop, F. W. Brinkley, “TWOTRAN-II code,” Los Alamos Scientific Laboratory Rep. #LA-4848-MS (Los Alamos Scientific Laboratory, Los Alamos, N. Mex., 1973).

Chai, J. C.

J. C. Chai, H. S. Lee, S. V. Patankar, “Ray effect and false scattering in the discrete ordinates method,” Numer. Heat Transfer Part B 24, 373–389 (1993).
[CrossRef]

Chance, B.

Culver, J. P.

Dawes, J. M.

K. M. McNally, B. S. Sorg, A. J. Welch, J. M. Dawes, E. R. Owen, “Photothermal effects of laser tissue soldering,” Phys. Med. Biol. 44, 983–1002 (1999).
[CrossRef] [PubMed]

Demos, S. G.

R. R. Alfano, S. G. Demos, S. K. Gayen, “Advances in optical imaging of biomedical media,” Ann. N.Y. Acad. Sci. 820, 248–270 (1997).
[CrossRef] [PubMed]

Dunn, A. K.

Ericson, M.

S. Grapengiesser, F. Gudmundsson, O. Larko, M. Ericson, A. Rosen, A. M. Wennberg, “Pain caused by photodynamic therapy of skin cancer,” Clin. Exp. Dermatol. 27, 493–497 (2002).
[CrossRef] [PubMed]

Fisher, F. P.

F. H. Loesel, F. P. Fisher, H. Suhan, J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B 66, 121–128 (1998).

Fiveland, W. A.

W. A. Fiveland, “The selection of discrete ordinate quadrature sets for anisotropic scattering,” American Society of Mechanical Engineers, Heat Transfer Division 72, 89–96 (1991).

Flock, S. T.

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues. I. Prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

Garetz, B. A.

S. K. Wan, Z. Guo, S. Kumar, J. Aber, B. A. Garetz, “Detecting inhomogeneities in a turbid medium,” presented at Eurotherm 73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 15–17 April 2003.

Gayen, S. K.

R. R. Alfano, S. G. Demos, S. K. Gayen, “Advances in optical imaging of biomedical media,” Ann. N.Y. Acad. Sci. 820, 248–270 (1997).
[CrossRef] [PubMed]

George, J. S.

D. M. Rector, R. F. Rogers, J. S. George, “A focusing image probe for assessing neural activity in vivo,” J. Neurosci. Methods 91, 135–145 (1999).
[CrossRef] [PubMed]

Gohto, Y.

A. Obana, Y. Gohto, “Scanning laser system for photodynamic therapy of choroidal neovascularization,” Lasers Surg. Med. 30, 370–375 (2002).
[CrossRef] [PubMed]

Grapengiesser, S.

S. Grapengiesser, F. Gudmundsson, O. Larko, M. Ericson, A. Rosen, A. M. Wennberg, “Pain caused by photodynamic therapy of skin cancer,” Clin. Exp. Dermatol. 27, 493–497 (2002).
[CrossRef] [PubMed]

Gudmundsson, F.

S. Grapengiesser, F. Gudmundsson, O. Larko, M. Ericson, A. Rosen, A. M. Wennberg, “Pain caused by photodynamic therapy of skin cancer,” Clin. Exp. Dermatol. 27, 493–497 (2002).
[CrossRef] [PubMed]

Guo, Z.

Z. Guo, S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
[CrossRef]

Z. Guo, S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt. 40, 3156–3163 (2001).
[CrossRef]

Z. Guo, S. Kumar, “Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media,” Appl. Opt. 39, 4411–4417 (2000).
[CrossRef]

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer 14, 504–511 (2000).
[CrossRef]

S. K. Wan, Z. Guo, S. Kumar, J. Aber, B. A. Garetz, “Detecting inhomogeneities in a turbid medium,” presented at Eurotherm 73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 15–17 April 2003.

Hebden, J. C.

S. R. Arridge, J. C. Hebden, “Optical imaging in medicine. II. modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).
[CrossRef] [PubMed]

Hielsher, A. H.

A. D. Klose, U. Netz, J. Beuthan, A. H. Hielsher, “Optical tomography using the time-independent equation of radiative transfer. 1. Forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1987).

Jacques, S. L.

Kim, S.

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 10, 826–831 (2002).
[CrossRef]

Kitagawa, K.

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 10, 826–831 (2002).
[CrossRef]

Klose, A. D.

A. D. Klose, U. Netz, J. Beuthan, A. H. Hielsher, “Optical tomography using the time-independent equation of radiative transfer. 1. Forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).
[CrossRef]

Kumar, S.

Z. Guo, S. Kumar, “Three-dimensional discrete ordinates method in transient radiative transfer,” J. Thermophys. Heat Transfer 16, 289–296 (2002).
[CrossRef]

Z. Guo, S. Kumar, “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media,” Appl. Opt. 40, 3156–3163 (2001).
[CrossRef]

Z. Guo, S. Kumar, “Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media,” Appl. Opt. 39, 4411–4417 (2000).
[CrossRef]

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer 14, 504–511 (2000).
[CrossRef]

K. Mitra, S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. 38, 188–196 (1999).
[CrossRef]

S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
[CrossRef]

S. K. Wan, Z. Guo, S. Kumar, J. Aber, B. A. Garetz, “Detecting inhomogeneities in a turbid medium,” presented at Eurotherm 73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 15–17 April 2003.

Larko, O.

S. Grapengiesser, F. Gudmundsson, O. Larko, M. Ericson, A. Rosen, A. M. Wennberg, “Pain caused by photodynamic therapy of skin cancer,” Clin. Exp. Dermatol. 27, 493–497 (2002).
[CrossRef] [PubMed]

Lathrop, K. D.

K. D. Lathrop, “Spatial differencing of the transport equation: positive vs accuracy,” J. Comput. Phys. 4, 475–498 (1968).
[CrossRef]

K. D. Lathrop, F. W. Brinkley, “TWOTRAN-II code,” Los Alamos Scientific Laboratory Rep. #LA-4848-MS (Los Alamos Scientific Laboratory, Los Alamos, N. Mex., 1973).

Lee, H. S.

J. C. Chai, H. S. Lee, S. V. Patankar, “Ray effect and false scattering in the discrete ordinates method,” Numer. Heat Transfer Part B 24, 373–389 (1993).
[CrossRef]

Liu, F.

K. M. Yoo, F. Liu, R. R. Alfano, “When does the diffusion approximation fail to describe photon transport in random media,” Phys. Rev. Lett. 64, 2647–2650 (1990).
[CrossRef] [PubMed]

Loesel, F. H.

F. H. Loesel, F. P. Fisher, H. Suhan, J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B 66, 121–128 (1998).

McNally, K. M.

K. M. McNally, B. S. Sorg, A. J. Welch, J. M. Dawes, E. R. Owen, “Photothermal effects of laser tissue soldering,” Phys. Med. Biol. 44, 983–1002 (1999).
[CrossRef] [PubMed]

Mitra, K.

K. Mitra, S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. 38, 188–196 (1999).
[CrossRef]

S. Kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Adv. Heat Transfer 33, 187–294 (1998).
[CrossRef]

Modest, M. F.

M. F. Modest, Radiative Heat Transfer (McGraw-Hill, New York, 1993), Chap. 15.

Morimoto, R. I.

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 10, 826–831 (2002).
[CrossRef]

Netz, U.

A. D. Klose, U. Netz, J. Beuthan, A. H. Hielsher, “Optical tomography using the time-independent equation of radiative transfer. 1. Forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).
[CrossRef]

Nollen, E. A. A.

S. Kim, E. A. A. Nollen, K. Kitagawa, V. P. Bindokas, R. I. Morimoto, “Polyglutamine protein aggregates are dynamic,” Nat. Cell Biol. 10, 826–831 (2002).
[CrossRef]

Obana, A.

A. Obana, Y. Gohto, “Scanning laser system for photodynamic therapy of choroidal neovascularization,” Lasers Surg. Med. 30, 370–375 (2002).
[CrossRef] [PubMed]

Owen, E. R.

K. M. McNally, B. S. Sorg, A. J. Welch, J. M. Dawes, E. R. Owen, “Photothermal effects of laser tissue soldering,” Phys. Med. Biol. 44, 983–1002 (1999).
[CrossRef] [PubMed]

Patankar, S. V.

J. C. Chai, H. S. Lee, S. V. Patankar, “Ray effect and false scattering in the discrete ordinates method,” Numer. Heat Transfer Part B 24, 373–389 (1993).
[CrossRef]

Patterson, M. S.

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte-Carlo modeling of light propagation in highly scattering tissues. I. Prediction and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

Rector, D. M.

D. M. Rector, R. F. Rogers, J. S. George, “A focusing image probe for assessing neural activity in vivo,” J. Neurosci. Methods 91, 135–145 (1999).
[CrossRef] [PubMed]

Rogers, R. F.

D. M. Rector, R. F. Rogers, J. S. George, “A focusing image probe for assessing neural activity in vivo,” J. Neurosci. Methods 91, 135–145 (1999).
[CrossRef] [PubMed]

Rosen, A.

S. Grapengiesser, F. Gudmundsson, O. Larko, M. Ericson, A. Rosen, A. M. Wennberg, “Pain caused by photodynamic therapy of skin cancer,” Clin. Exp. Dermatol. 27, 493–497 (2002).
[CrossRef] [PubMed]

San, K.-C.

Z. Guo, S. Kumar, K.-C. San, “Multi-dimensional Monte Carlo simulation of short pulse laser radiation transport in scattering media,” J. Thermophys. Heat Transfer 14, 504–511 (2000).
[CrossRef]

Seibel, E. J.

E. J. Seibel, Q. Y. J. Smithwick, “Unique features of optical scanning, single fiber endoscopy,” Lasers Surg. Med. 30, 177–183 (2002).
[CrossRef] [PubMed]

Smithwick, Q. Y. J.

E. J. Seibel, Q. Y. J. Smithwick, “Unique features of optical scanning, single fiber endoscopy,” Lasers Surg. Med. 30, 177–183 (2002).
[CrossRef] [PubMed]

Sorg, B. S.

K. M. McNally, B. S. Sorg, A. J. Welch, J. M. Dawes, E. R. Owen, “Photothermal effects of laser tissue soldering,” Phys. Med. Biol. 44, 983–1002 (1999).
[CrossRef] [PubMed]

Stott, J. J.

Suhan, H.

F. H. Loesel, F. P. Fisher, H. Suhan, J. F. Bille, “Non-thermal ablation of neural tissue with femtosecond laser pulses,” Appl. Phys. B 66, 121–128 (1998).

Wan, S. K.

S. K. Wan, Z. Guo, S. Kumar, J. Aber, B. A. Garetz, “Detecting inhomogeneities in a turbid medium,” presented at Eurotherm 73 on Computational Thermal Radiation in Participating Media, Mons, Belgium, 15–17 April 2003.

Welch, A. J.

K. M. McNally, B. S. Sorg, A. J. Welch, J. M. Dawes, E. R. Owen, “Photothermal effects of laser tissue soldering,” Phys. Med. Biol. 44, 983–1002 (1999).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

Three-dimensional geometry and coordinates system.

Fig. 2
Fig. 2

Two-dimensional multilayered configurations: (a) configuration I, (b) configuration II.

Fig. 3
Fig. 3

Benchmark comparisons of temporal distributions of transmittances between DOM S4 and S10 methods, DA, and MC method for ultrafast laser transport in 2D multilayered configuration I.

Fig. 4
Fig. 4

Comparison of temporal transmittances between the Fresnel specular boundary and diffuse boundary conditions for configuration I.

Fig. 5
Fig. 5

Comparison of temporal reflectance and transmittance between configuration I and II.

Fig. 6
Fig. 6

Comparison of temporal reflectance and transmittance between homogeneous model and inhomogeneous model with a small inhomogeneity (σ a = 0.50 mm-1).

Fig. 7
Fig. 7

Effect of absorption coefficient of the inhomogeneity on the temporal transmittance profiles.

Fig. 8
Fig. 8

Absolute value of log slopes of reflectance and transmittance at different detector positions for both homogeneous model and inhomogeneous model with a small inhomogeneity (σ a = 0.50 mm-1).

Fig. 9
Fig. 9

Relationship between AVLS and absorption coefficient in the inhomogeneity.

Fig. 10
Fig. 10

Contour plots of divergence of radiative heat flux in Y–Z planes for inhomogeneous model with a small inhomogeneity (σ a = 0.10 mm-1) at the center.

Fig. 11
Fig. 11

Comparison of temporal profiles of divergence of radiative heat flux at different optical axis locations with different absorption coefficients in the inhomogeneity.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

1cIlt+ξlIlx+ηlIly+μlIlz+σeIl=σeSl, l=1, 2, , n,
Sl=1-ωIb+ ω4πi=1nwiΦilIi+Scl, l=1, 2, , n,
Scl= ω4π IcΦξcξl+ηcηl+μcμl,
Icx, y, z, ξc, t=I0x=0, y, z, t-x/cξc×exp-σex/ξcδξc-1,
ρ= 12tan2θi-θrtan2θi+θr+ sin2θi-θrsin2θi+θr,
Iwd=wIbw+ ρwdπξl <0n/2 wlIl|ξl|,
Iwl=ρwsl I-1.

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