Abstract

A random nonspherical model for biological tissue and cells permits a better description of their optical properties. Rough surface nonspherical particles have been employed to model biological tissue and cells. The phase function, the anisotropy factor of scattering, and the reduced scattering coefficient are derived. The effect of different size distributions is also discussed. The theoretical results show good agreement with experimental data.

© 2009 Optical Society of America

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References

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    [CrossRef]
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2008 (1)

2007 (2)

G. I. Ruban, S. M. Kosmacheva, N. V. Goncharova, D. V. Bockstaele, and V. A. Loiko, “Investigation of morphometric parameters for granulocytes and lymphocytes as applied to a solution of direct and inverse light-scattering problems,” J. Biomed. Opt. 12, 044017 (2007).
[CrossRef] [PubMed]

C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett. 32, 142-144 (2007).
[CrossRef]

2006 (1)

Y. S. Fawzy, M. Petek, M. Tercelj, and H. S. Zeng, “In vivo assessment and evaluation of lung tissue morphologic and physiological changes from non-contact endoscopic reflectance spectroscopy for improving lung cancer detection,” J. Biomed. Opt. 11, 044003 (2006).
[CrossRef] [PubMed]

2005 (1)

2001 (1)

2000 (1)

R. K. Wang, “Modelling optical properties of soft tissue by fractal distribution of scatters,” J. Mod. Opt. 47, 103-120 (2000).

1998 (2)

1997 (1)

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831-18847 (1997).
[CrossRef]

1993 (1)

1989 (1)

1984 (1)

J. Lenoble and C. Brogniez, “A comparative review of radiation aerosol models,” Beitr. Phys. Atmos. 57, 1-20 (1984).

Alberts, A.

A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland, 1994), pp. 18-19.

Alfano, R. R.

Bockstaele, D. V.

G. I. Ruban, S. M. Kosmacheva, N. V. Goncharova, D. V. Bockstaele, and V. A. Loiko, “Investigation of morphometric parameters for granulocytes and lymphocytes as applied to a solution of direct and inverse light-scattering problems,” J. Biomed. Opt. 12, 044017 (2007).
[CrossRef] [PubMed]

Bray, D.

A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland, 1994), pp. 18-19.

Brogniez, C.

J. Lenoble and C. Brogniez, “A comparative review of radiation aerosol models,” Beitr. Phys. Atmos. 57, 1-20 (1984).

Eick, A. A.

Fawzy, Y. S.

Y. S. Fawzy, M. Petek, M. Tercelj, and H. S. Zeng, “In vivo assessment and evaluation of lung tissue morphologic and physiological changes from non-contact endoscopic reflectance spectroscopy for improving lung cancer detection,” J. Biomed. Opt. 11, 044003 (2006).
[CrossRef] [PubMed]

Freyer, J. P.

Goncharova, N. V.

G. I. Ruban, S. M. Kosmacheva, N. V. Goncharova, D. V. Bockstaele, and V. A. Loiko, “Investigation of morphometric parameters for granulocytes and lymphocytes as applied to a solution of direct and inverse light-scattering problems,” J. Biomed. Opt. 12, 044017 (2007).
[CrossRef] [PubMed]

Gong, W.

Hielscher, A. H.

Irvine, W. M.

Johnson, T. M.

Kahn, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831-18847 (1997).
[CrossRef]

Keller, J. B.

Kerker, M.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), p. 351.

Kosmacheva, S. M.

G. I. Ruban, S. M. Kosmacheva, N. V. Goncharova, D. V. Bockstaele, and V. A. Loiko, “Investigation of morphometric parameters for granulocytes and lymphocytes as applied to a solution of direct and inverse light-scattering problems,” J. Biomed. Opt. 12, 044017 (2007).
[CrossRef] [PubMed]

Kumar, G.

Lacis, A. A.

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Lenoble, J.

J. Lenoble and C. Brogniez, “A comparative review of radiation aerosol models,” Beitr. Phys. Atmos. 57, 1-20 (1984).

Lewis, J.

A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland, 1994), pp. 18-19.

Loiko, V. A.

G. I. Ruban, S. M. Kosmacheva, N. V. Goncharova, D. V. Bockstaele, and V. A. Loiko, “Investigation of morphometric parameters for granulocytes and lymphocytes as applied to a solution of direct and inverse light-scattering problems,” J. Biomed. Opt. 12, 044017 (2007).
[CrossRef] [PubMed]

Lumme, K.

Macke, A.

Mishchenko, M. I.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831-18847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Moscoso, M.

Mourant, J. R.

Muinonen, K.

Palade, G. E.

G. E. Palade, “An electron microscope study of the mitochondrial structure,” in Mitochondria, E. Sato, ed., Vol. 10 of Selected Papers in Biochemistry (University Park, 1972), pp. 35-58.

Papanicolaou, G.

Peltoniemi, J.

Petek, M.

Y. S. Fawzy, M. Petek, M. Tercelj, and H. S. Zeng, “In vivo assessment and evaluation of lung tissue morphologic and physiological changes from non-contact endoscopic reflectance spectroscopy for improving lung cancer detection,” J. Biomed. Opt. 11, 044003 (2006).
[CrossRef] [PubMed]

Raff, M.

A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland, 1994), pp. 18-19.

Roberts, K.

A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland, 1994), pp. 18-19.

Ruban, G. I.

G. I. Ruban, S. M. Kosmacheva, N. V. Goncharova, D. V. Bockstaele, and V. A. Loiko, “Investigation of morphometric parameters for granulocytes and lymphocytes as applied to a solution of direct and inverse light-scattering problems,” J. Biomed. Opt. 12, 044017 (2007).
[CrossRef] [PubMed]

Schmitt, J. M.

Shen, D.

Sheppard, C. J. R.

Si, K.

Tercelj, M.

Y. S. Fawzy, M. Petek, M. Tercelj, and H. S. Zeng, “In vivo assessment and evaluation of lung tissue morphologic and physiological changes from non-contact endoscopic reflectance spectroscopy for improving lung cancer detection,” J. Biomed. Opt. 11, 044003 (2006).
[CrossRef] [PubMed]

Travis, L. D.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831-18847 (1997).
[CrossRef]

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

Tuan, V. D.

V. D. Tuan, Biomedical Photonics Handbook (CRC Press, 2003).

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering (Academic, 1980), p. 739.

Wang, R. K.

R. K. Wang, “Modelling optical properties of soft tissue by fractal distribution of scatters,” J. Mod. Opt. 47, 103-120 (2000).

Watson, J. D.

A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland, 1994), pp. 18-19.

West, R. A.

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831-18847 (1997).
[CrossRef]

Xu, M.

Zeng, H. S.

Y. S. Fawzy, M. Petek, M. Tercelj, and H. S. Zeng, “In vivo assessment and evaluation of lung tissue morphologic and physiological changes from non-contact endoscopic reflectance spectroscopy for improving lung cancer detection,” J. Biomed. Opt. 11, 044003 (2006).
[CrossRef] [PubMed]

Appl. Opt. (4)

Beitr. Phys. Atmos. (1)

J. Lenoble and C. Brogniez, “A comparative review of radiation aerosol models,” Beitr. Phys. Atmos. 57, 1-20 (1984).

J. Biomed. Opt. (2)

G. I. Ruban, S. M. Kosmacheva, N. V. Goncharova, D. V. Bockstaele, and V. A. Loiko, “Investigation of morphometric parameters for granulocytes and lymphocytes as applied to a solution of direct and inverse light-scattering problems,” J. Biomed. Opt. 12, 044017 (2007).
[CrossRef] [PubMed]

Y. S. Fawzy, M. Petek, M. Tercelj, and H. S. Zeng, “In vivo assessment and evaluation of lung tissue morphologic and physiological changes from non-contact endoscopic reflectance spectroscopy for improving lung cancer detection,” J. Biomed. Opt. 11, 044003 (2006).
[CrossRef] [PubMed]

J. Geophys. Res. (1)

M. I. Mishchenko, L. D. Travis, R. A. Kahn, and R. A. West, “Modeling phase functions for dustlike tropospheric aerosols using a mixture of randomly oriented polydisperse spheroids,” J. Geophys. Res. 102, 16831-18847 (1997).
[CrossRef]

J. Mod. Opt. (1)

R. K. Wang, “Modelling optical properties of soft tissue by fractal distribution of scatters,” J. Mod. Opt. 47, 103-120 (2000).

J. Opt. Soc. Am. A (1)

Opt. Lett. (3)

Other (6)

V. D. Tuan, Biomedical Photonics Handbook (CRC Press, 2003).

M. I. Mishchenko, L. D. Travis, and A. A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (Cambridge U. Press, 2002).

H. C. van de Hulst, Multiple Light Scattering (Academic, 1980), p. 739.

M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, 1969), p. 351.

A. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell (Garland, 1994), pp. 18-19.

G. E. Palade, “An electron microscope study of the mitochondrial structure,” in Mitochondria, E. Sato, ed., Vol. 10 of Selected Papers in Biochemistry (University Park, 1972), pp. 35-58.

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Figures (5)

Fig. 1
Fig. 1

3D structure of the random nonspherical particles with respect to the mean value r ¯ = 1 , with roughness parameter σ = 0.2 , and a span of the window W = 1 . Different shapes can be obtained by changing the parameters K, τ, and the display window’s center CP. (a)  K = 2 , τ = 0.38 , CP = 0.5 ; (b), (c)  K = 2 , τ = 0.3 , CP = 0.5 ; (d)  K = 2 , τ = 0.36 , CP = 0.5 with r ¯ = 0.5 .

Fig. 2
Fig. 2

Phase functions with different size distribution functions with the same r eff = 3.36 and v eff = 0.12 and the same shape parameters ( K = 2 , τ = 0.7 , CP = 0.5 ) at incident wavelength 1100 nm .

Fig. 3
Fig. 3

Phase functions for randomly oriented slightly rough prolate (solid curves) and oblate (dashed curves) spheroids with different aspect ratios of 1.2, 2.4, and equal-projected-area spheres with different effective size parameter S eff . (a)  S eff = 15 , (b)  S eff = 8 .

Fig. 4
Fig. 4

Phase functions for suspensions of rat embryo fibroblast cells (M1) with spherical and nonspherical models with an effective size parameter of S eff = 15.5 and experimental results. The particles were chosen as a combination of Figs. 1c, 1d.

Fig. 5
Fig. 5

Phase functions for suspensions of mitochondria with the random nonspherical model and the spherical model with an effective size parameter of S eff = 10.3 and experimental results. The particles are chosen as a combination of Figs. 1c, 1d.

Tables (1)

Tables Icon

Table 1 Anisotropy Factors and Reduced Scattering Coefficients for M1 Cells and Mitochondria a

Equations (12)

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

S ( θ ) = [ P ( θ ) b 1 ( θ ) 0 0 b 1 ( θ ) a 2 ( θ ) 0 0 0 0 a 3 ( θ ) b 2 ( θ ) 0 0 b 2 ( θ ) a 4 ( θ ) ] .
P ( θ ) = i = 0 i max ω i P i ( cos θ ) ,
ω i = 1 M C sca m = 1 M n = 1 N f ' ( r n ) ω i ( r n ) C sca m ( r n ) w n ,
g = μ P ( θ ) d Ω / P ( θ ) d Ω ,
μ s = ( 1 μ ) P ( θ ) d Ω .
f 1 ( r ) = c 0 r 3 D f ,
f 2 ( r ) = 1 / ( 2 π σ m ) · exp [ ( r r m ) 2 / ( 2 σ m 2 ) ] ,
f 3 ( r ) = c n r n exp [ ( ln r ln r n ) 2 / ( 2 σ n 2 ) ] ,
f i ( r ) = { c i , f i ( r ) , for for r r min r min r r max , i = 1 , 2 , 3 ,
r eff = 1 S r min r max π r 3 f i ( r ) d r ,
v eff = 1 S · r eff 2 r min r max π r 2 ( r r eff ) 2 f i ( r ) d r ,
S = r min r max π r 2 f i ( r ) d r .

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