Abstract

The scattering anisotropy, g, of tissue can be a powerful metric of tissue structure, and is most directly measured via goniometry and fitting to the Henyey-Greenstein phase function. We present a method based on an independent attenuation measurement of the scattering coefficient along with Monte Carlo simulations to account for multiple scattering, allowing the accurate determination of measurement of g for tissues of thickness within the quasi-ballistic regime. Simulations incorporating the experimental geometry and bulk optical properties show that significant errors occur in extraction of g values, even for tissues of thickness less than one scattering length without modeling corrections. Experimental validation is provided by determination of g in mouse muscle tissues and it is shown that the obtained values are independent of thickness. In addition we present a simple deconvolution-based method and show that it provides excellent estimates for high anisotropy values (above 0.95) when coupled with an independent attenuation measurement.

© 2012 OSA

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2012 (2)

S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express3(6), 1162–1172 (2012).
[CrossRef] [PubMed]

M. G. Giacomelli and A. Wax, “Imaging Contrast and Resolution in Multiply Scattered Low Coherence Interferometry,” IEEE J. Sel. Top. Quantum Electron.18(3), 1050–1058 (2012).
[CrossRef]

2011 (4)

H. F. Ding, Z. Wang, X. Liang, S. A. Boppart, K. Tangella, and G. Popescu, “Measuring the scattering parameters of tissues from quantitative phase imaging of thin slices,” Opt. Lett.36(12), 2281–2283 (2011).
[CrossRef] [PubMed]

V. Turzhitsky, N. N. Mutyal, A. J. Radosevich, and V. Backman, “Multiple scattering model for the penetration depth of low-coherence enhanced backscattering,” J. Biomed. Opt.16(9), 097006 (2011).
[CrossRef] [PubMed]

J. Piskozub and D. McKee, “Effective scattering phase functions for the multiple scattering regime,” Opt. Express19(5), 4786–4794 (2011).
[CrossRef] [PubMed]

L. I. Chaikovskaya, O. V. Tsarjuk, I. V. Belotserkovsky, and M. A. Vozmitel, “Determination of optical properties of tissues,” J. Quant. Spectrosc. Radiat. Transf.112(13), 2128–2133 (2011).
[CrossRef]

2010 (2)

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by Second Harmonic Generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

V. Turzhitsky, A. Radosevich, J. D. Rogers, A. Taflove, and V. Backman, “A predictive model of backscattering at subdiffusion length scales,” Biomed. Opt. Express1(3), 1034–1046 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (3)

R. LaComb, O. Nadiarnykh, and P. J. Campagnola, “Quantitative second harmonic generation imaging of the diseased state osteogenesis imperfecta: experiment and simulation,” Biophys. J.94(11), 4504–4514 (2008).
[CrossRef] [PubMed]

R. Samatham, S. L. Jacques, and P. J. Campagnola, “Optical properties of mutant versus wild-type mouse skin measured by reflectance-mode confocal scanning laser microscopy (rCSLM),” J. Biomed. Opt.13(4), 041309 (2008).
[CrossRef] [PubMed]

N. Pfeiffer and G. H. Chapman, “Successive order, multiple scattering of two-term Henyey-Greenstein phase functions,” Opt. Express16(18), 13637–13642 (2008).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

K. W. Dunn and P. A. Young, “Principles of multiphoton microscopy,” Nephron, Exp. Nephrol.103(2), e33–e40 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (3)

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

I. Turcu, “Effective phase function for light scattered by disperse systems–the small-angle approximation,”. Opt. A Pure App. Opt.6(6), 537–543 (2004).
[CrossRef]

R. Elaloufi, R. Carminati, and J. J. Greffet, “Diffusive-to-ballistic transition in dynamic light transmission through thin scattering slabs: a radiative transfer approach,” J. Opt. Soc. Am. A21(8), 1430–1437 (2004).
[CrossRef] [PubMed]

2001 (1)

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

2000 (1)

L. V. Wang and S. L. Jacques, “Source of error in calculation of optical diffuse reflectance from turbid media using diffusion theory,” Comput. Methods Programs Biomed.61(3), 163–170 (2000).
[CrossRef] [PubMed]

1998 (1)

1996 (1)

1995 (3)

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed.47(2), 131–146 (1995).
[CrossRef] [PubMed]

A. Yodh and B. Chance, “Spectroscopy and Imaging with Diffusing Light,” Phys. Today48(3), 34–40 (1995).
[CrossRef]

I. S. Saidi, S. L. Jacques, and F. K. Tittel, “Mie and Rayleigh modeling of visible-light scattering in neonatal skin,” Appl. Opt.34(31), 7410–7418 (1995).
[CrossRef] [PubMed]

1994 (1)

P. Y. Liu, “A new phase function approximating to Mie scattering for radiative transport equations,” Phys. Med. Biol.39(6), 1025–1036 (1994).
[CrossRef] [PubMed]

1991 (1)

M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci.6(2), 155–168 (1991).
[CrossRef]

1990 (1)

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical-Properties of Biological Tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

1989 (1)

1987 (1)

S. L. Jacques, C. Alter, and S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci.1, 309–333 (1987).

Alfano, R. R.

Alter, C.

S. L. Jacques, C. Alter, and S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci.1, 309–333 (1987).

Andersson-Engels, S.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

Andreola, S.

Backman, V.

Bassi, A.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

Belotserkovsky, I. V.

L. I. Chaikovskaya, O. V. Tsarjuk, I. V. Belotserkovsky, and M. A. Vozmitel, “Determination of optical properties of tissues,” J. Quant. Spectrosc. Radiat. Transf.112(13), 2128–2133 (2011).
[CrossRef]

Berger, A. J.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

Bertoni, A.

Bevilacqua, F.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

Boppart, S. A.

Brewer, M. A.

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by Second Harmonic Generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

Butler, J.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

Campagnola, P. J.

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by Second Harmonic Generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

R. LaComb, O. Nadiarnykh, and P. J. Campagnola, “Quantitative second harmonic generation imaging of the diseased state osteogenesis imperfecta: experiment and simulation,” Biophys. J.94(11), 4504–4514 (2008).
[CrossRef] [PubMed]

R. Samatham, S. L. Jacques, and P. J. Campagnola, “Optical properties of mutant versus wild-type mouse skin measured by reflectance-mode confocal scanning laser microscopy (rCSLM),” J. Biomed. Opt.13(4), 041309 (2008).
[CrossRef] [PubMed]

Capoglu, I. R.

Çapoglu, I. R.

Carminati, R.

Cerussi, A. E.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

Chaikovskaya, L. I.

L. I. Chaikovskaya, O. V. Tsarjuk, I. V. Belotserkovsky, and M. A. Vozmitel, “Determination of optical properties of tissues,” J. Quant. Spectrosc. Radiat. Transf.112(13), 2128–2133 (2011).
[CrossRef]

Chance, B.

A. Yodh and B. Chance, “Spectroscopy and Imaging with Diffusing Light,” Phys. Today48(3), 34–40 (1995).
[CrossRef]

Chapman, G. H.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical-Properties of Biological Tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

Chikoidze, E.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

Cubeddu, R.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

Ding, H. F.

Dunn, K. W.

K. W. Dunn and P. A. Young, “Principles of multiphoton microscopy,” Nephron, Exp. Nephrol.103(2), e33–e40 (2006).
[CrossRef] [PubMed]

Elaloufi, R.

Giacomelli, M. G.

M. G. Giacomelli and A. Wax, “Imaging Contrast and Resolution in Multiply Scattered Low Coherence Interferometry,” IEEE J. Sel. Top. Quantum Electron.18(3), 1050–1058 (2012).
[CrossRef]

Greffet, J. J.

Holcombe, R. F.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

Jacques, S. L.

S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express3(6), 1162–1172 (2012).
[CrossRef] [PubMed]

R. Samatham, S. L. Jacques, and P. J. Campagnola, “Optical properties of mutant versus wild-type mouse skin measured by reflectance-mode confocal scanning laser microscopy (rCSLM),” J. Biomed. Opt.13(4), 041309 (2008).
[CrossRef] [PubMed]

L. V. Wang and S. L. Jacques, “Source of error in calculation of optical diffuse reflectance from turbid media using diffusion theory,” Comput. Methods Programs Biomed.61(3), 163–170 (2000).
[CrossRef] [PubMed]

I. S. Saidi, S. L. Jacques, and F. K. Tittel, “Mie and Rayleigh modeling of visible-light scattering in neonatal skin,” Appl. Opt.34(31), 7410–7418 (1995).
[CrossRef] [PubMed]

L. Wang, S. L. Jacques, and L. Zheng, “MCML--Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed.47(2), 131–146 (1995).
[CrossRef] [PubMed]

S. L. Jacques, C. Alter, and S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci.1, 309–333 (1987).

Jakubowski, D.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

Kumar, G.

LaComb, R.

R. LaComb, O. Nadiarnykh, and P. J. Campagnola, “Quantitative second harmonic generation imaging of the diseased state osteogenesis imperfecta: experiment and simulation,” Biophys. J.94(11), 4504–4514 (2008).
[CrossRef] [PubMed]

LaComb, R. B.

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by Second Harmonic Generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

Li, H.

Liang, X.

Liu, P. Y.

P. Y. Liu, “A new phase function approximating to Mie scattering for radiative transport equations,” Phys. Med. Biol.39(6), 1025–1036 (1994).
[CrossRef] [PubMed]

Marchesini, R.

McKee, D.

Melloni, E.

Mutyal, N. N.

V. Turzhitsky, N. N. Mutyal, A. J. Radosevich, and V. Backman, “Multiple scattering model for the penetration depth of low-coherence enhanced backscattering,” J. Biomed. Opt.16(9), 097006 (2011).
[CrossRef] [PubMed]

Nadiarnykh, O.

O. Nadiarnykh, R. B. LaComb, M. A. Brewer, and P. J. Campagnola, “Alterations of the extracellular matrix in ovarian cancer studied by Second Harmonic Generation imaging microscopy,” BMC Cancer10(1), 94 (2010).
[CrossRef] [PubMed]

R. LaComb, O. Nadiarnykh, and P. J. Campagnola, “Quantitative second harmonic generation imaging of the diseased state osteogenesis imperfecta: experiment and simulation,” Biophys. J.94(11), 4504–4514 (2008).
[CrossRef] [PubMed]

Patterson, M. S.

M. S. Patterson, B. C. Wilson, and D. R. Wyman, “The propagation of optical radiation in tissue I. Models of radiation transport and their application,” Lasers Med. Sci.6(2), 155–168 (1991).
[CrossRef]

Pfeiffer, N.

Pifferi, A.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

Piskozub, J.

Popescu, G.

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, “A Review of the Optical-Properties of Biological Tissues,” IEEE J. Quantum Electron.26(12), 2166–2185 (1990).
[CrossRef]

S. L. Jacques, C. Alter, and S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci.1, 309–333 (1987).

Radosevich, A.

Radosevich, A. J.

V. Turzhitsky, N. N. Mutyal, A. J. Radosevich, and V. Backman, “Multiple scattering model for the penetration depth of low-coherence enhanced backscattering,” J. Biomed. Opt.16(9), 097006 (2011).
[CrossRef] [PubMed]

Rogers, J. D.

Saidi, I. S.

Samatham, R.

S. L. Jacques, B. Wang, and R. Samatham, “Reflectance confocal microscopy of optical phantoms,” Biomed. Opt. Express3(6), 1162–1172 (2012).
[CrossRef] [PubMed]

R. Samatham, S. L. Jacques, and P. J. Campagnola, “Optical properties of mutant versus wild-type mouse skin measured by reflectance-mode confocal scanning laser microscopy (rCSLM),” J. Biomed. Opt.13(4), 041309 (2008).
[CrossRef] [PubMed]

Schmitt, J. M.

Shah, N.

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
[CrossRef] [PubMed]

Sheppard, C. J.

Sichirollo, A. E.

Swartling, J.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

Taflove, A.

Tangella, K.

Taroni, P.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
[CrossRef] [PubMed]

Tittel, F. K.

Torricelli, A.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt.9(6), 1143–1151 (2004).
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I. Turcu, “Effective phase function for light scattered by disperse systems–the small-angle approximation,”. Opt. A Pure App. Opt.6(6), 537–543 (2004).
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Acad. Radiol. (1)

A. E. Cerussi, A. J. Berger, F. Bevilacqua, N. Shah, D. Jakubowski, J. Butler, R. F. Holcombe, and B. J. Tromberg, “Sources of absorption and scattering contrast for near-infrared optical mammography,” Acad. Radiol.8(3), 211–218 (2001).
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Appl. Opt. (4)

Biomed. Opt. Express (2)

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J. Quant. Spectrosc. Radiat. Transf. (1)

L. I. Chaikovskaya, O. V. Tsarjuk, I. V. Belotserkovsky, and M. A. Vozmitel, “Determination of optical properties of tissues,” J. Quant. Spectrosc. Radiat. Transf.112(13), 2128–2133 (2011).
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Figures (6)

Fig. 1
Fig. 1

(a) Experimental setup, (b) Flowchart for obtaining the single scattering anisotropy gsingle from measurements of geff and μsd, (c) Geometry for Monte Carlo simulation.

Fig. 2
Fig. 2

Validation of simulations. (a) Examples of angular distributions for different g values. (b) Snell’s law applied to correct for refracted angle. (c) Dependence of effective anisotropy on scattering length. (d) Wet cell geometry and validation of its minimal effect on the measured effective anisotropy.

Fig. 3
Fig. 3

Extraction of the single scattering anisotropy coefficient (gsingle) for mouse muscle tissue of thickness 200 microns.

Fig. 4
Fig. 4

The wavelength dependency of the reduced scattering coefficient for mouse muscle and rat tail tendon fitted to a power law relation.

Fig. 5
Fig. 5

Effect of absorption on the angular scattering distribution for a fixed g.

Fig. 6
Fig. 6

Effect of increased µsd on the effective phase function, and evaluation of goodness of fit (R2) of the HG function for multiply scattered data.

Tables (6)

Tables Icon

Table 1 Uncertainty relations between geff and gsingle for ranges of gsingle and μsd

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Table 2 Refractive index of the muscle tissue measured over a wavelength range 445–1000 nm

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Table 3 Single scattering anisotropy values extracted from different thickness slices of mouse muscle tissue

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Table 4 Optical properties of rat tail tendon of diameter ~170 microns

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Table 5 Evaluation of deconvolution-based method based approach for obtaining gsingle via Eq. (6)

Tables Icon

Table 6 Effect of absorption on effective anisotropy for a range of g values for two scattering lengths, µsd = 1 and 4a

Equations (6)

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

I = α I 0 e d ( μ s + μ a )
μ s 1 d ln ( I α I 0 )
P ( θ ) = a 1 g 2 ( 1 + g 2 2 g cos θ ) 3 / 2
g eff = ( g single ) N
N avg = { 1 μ s d < 1 μ s d μ s d 1
g single ( g eff ) 1 / N avg

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