Abstract

Polarimetric imaging is emerging as a viable technique for tumor detection and staging. As a preliminary step towards a thorough understanding of the observed contrasts, we present a set of numerical Monte Carlo simulations of the polarimetric response of multilayer structures representing colon samples in the backscattering geometry. In a first instance, a typical colon sample was modeled as one or two scattering “slabs” with monodisperse non absorbing scatterers representing the most superficial tissue layers (the mucosa and submucosa), above a totally depolarizing Lambertian lumping the contributions of the deeper layers (muscularis and pericolic tissue). The model parameters were the number of layers, their thicknesses and morphology, the sizes and concentrations of the scatterers, the optical index contrast between the scatterers and the surrounding medium, and the Lambertian albedo. With quite similar results for single and double layer structures, this model does not reproduce the experimentally observed stability of the relative magnitudes of the depolarizing powers for incident linear and circular polarizations. This issue was solved by considering bimodal populations including large and small scatterers in a single layer above the Lambertian, a result which shows the importance of taking into account the various types of scatterers (nuclei, collagen fibers and organelles) in the same model.

© 2011 OSA

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2011

A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19(2), 1582–1593 (2011).
[CrossRef] [PubMed]

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE 7895, 78950E (2011).
[CrossRef]

2010

2009

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105(10), 102023 (2009).
[CrossRef]

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[CrossRef] [PubMed]

2008

S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE 6842, 68420I, 68420I-7 (2008).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13(4), 044036 (2008).
[CrossRef] [PubMed]

2007

M. F. G. Wood, X. Guo, and I. A. Vitkin, “Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology,” J. Biomed. Opt. 12(1), 014029 (2007).
[CrossRef] [PubMed]

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications 2, 07018 (2007).
[CrossRef]

2006

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt. 11(4), 041105 (2006).
[CrossRef] [PubMed]

2005

2004

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

2003

A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength: a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
[CrossRef]

2002

I. A. Vitkin, R. D. Laszlo, and C. L. Whyman, “Effects of molecular asymmetry of optically active molecules on the polarization properties of multiply scattered light,” Opt. Express 10(4), 222–229 (2002).
[PubMed]

I. L. Maksimova, S. V. Romanov, and V. F. Izotova, “The effect of multiple scattering in disperse media on polarization characteristics of scattered light,” Opt. Spectrosc. 92(6), 915–923 (2002).
[CrossRef]

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7(3), 300–306 (2002).
[CrossRef] [PubMed]

R. L. P. van Veen, W. Verkruysse, and H. J. C. M. Sterenborg, “Diffuse-reflectance spectroscopy from 500 to 1060 nm by correction for inhomogeneously distributed absorbers,” Opt. Lett. 27(4), 246–248 (2002).
[CrossRef] [PubMed]

2001

2000

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–268 (2000).
[CrossRef]

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

1999

1998

A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt. 37(31), 7392–7400 (1998).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68(2), 141–142 (1998).

1997

1996

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[CrossRef] [PubMed]

S. A. Skinner and P. E. O’Brien, “The microvascular structure of the normal colon in rats and humans,” J. Surg. Res. 61(2), 482–490 (1996).
[CrossRef] [PubMed]

G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996).
[CrossRef] [PubMed]

1995

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

1993

1991

Aarnoudse, J. G.

Alianelli, L.

Anastasiadou, M.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications 2, 07018 (2007).
[CrossRef]

Antonelli, M. R.

Arendt, J. T.

G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996).
[CrossRef] [PubMed]

Backman, V.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. 38(31), 6628–6637 (1999).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Badizadegan, K.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Bashkatov, A. N.

A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength: a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
[CrossRef]

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–268 (2000).
[CrossRef]

Ben Hatit, S.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications 2, 07018 (2007).
[CrossRef]

Benali, A.

Berns, M. W.

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

Bigio, I. J.

Blumetti, C.

Boone, C. W.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Burke, P.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Chaikovskaya, L. I.

Claridge, E.

D. Hidović-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. 50(6), 1071–1093 (2005).
[CrossRef] [PubMed]

Colombo, A.

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. 28(3), 237–243 (2001).
[CrossRef] [PubMed]

Contini, D.

Corkan, L. A.

H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68(2), 141–142 (1998).

Cothren, R. M.

G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996).
[CrossRef] [PubMed]

Crawford, J. M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996).
[CrossRef] [PubMed]

Crum, C. P.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Dasari, R. R.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Dassel, A. C. M.

De Martino, A.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE 7895, 78950E (2011).
[CrossRef]

A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19(2), 1582–1593 (2011).
[CrossRef] [PubMed]

M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express 18(10), 10200–10208 (2010).
[CrossRef] [PubMed]

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications 2, 07018 (2007).
[CrossRef]

de Mul, F. F. M.

Drévillon, B.

Du, H.

H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68(2), 141–142 (1998).

Eick, A. A.

Farina, B.

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. 28(3), 237–243 (2001).
[CrossRef] [PubMed]

Feld, M. S.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. 38(31), 6628–6637 (1999).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996).
[CrossRef] [PubMed]

Fiskerstrand, E. J.

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

Fitzmaurice, M.

Freyer, J. P.

Fuh, R.-C. A.

H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68(2), 141–142 (1998).

Gayet, B.

Genina, E. A.

A. N. Bashkatov and E. A. Genina, “Water refractive index in dependence on temperature and wavelength: a simple approximation,” Proc. SPIE 5068, 393–395 (2003).
[CrossRef]

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–268 (2000).
[CrossRef]

Georgakoudi, I.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Ghosh, N.

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[CrossRef] [PubMed]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105(10), 102023 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13(4), 044036 (2008).
[CrossRef] [PubMed]

Graaff, R.

Guo, X.

M. F. G. Wood, X. Guo, and I. A. Vitkin, “Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology,” J. Biomed. Opt. 12(1), 014029 (2007).
[CrossRef] [PubMed]

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt. 11(4), 041105 (2006).
[CrossRef] [PubMed]

Guyot, S.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications 2, 07018 (2007).
[CrossRef]

Hamano, T.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Hidovic-Rowe, D.

D. Hidović-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. 50(6), 1071–1093 (2005).
[CrossRef] [PubMed]

Hielscher, A. H.

Hillman, L. W.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Isenhath, S.

S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE 6842, 68420I, 68420I-7 (2008).
[CrossRef]

Ismaelli, A.

Itzkan, I.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Izotova, V. F.

I. L. Maksimova, S. V. Romanov, and V. F. Izotova, “The effect of multiple scattering in disperse media on polarization characteristics of scattered light,” Opt. Spectrosc. 92(6), 915–923 (2002).
[CrossRef]

Jacques, S. L.

Kaplan, B.

Katsev, I. L.

Kattawar, G. W.

Keefe, K.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Kienle, A.

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[CrossRef] [PubMed]

Kochubey, V. I.

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–268 (2000).
[CrossRef]

Koelink, M. H.

Kopstad, G.

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

Laszlo, R. D.

Ledanois, G.

Lee, K.

S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE 6842, 68420I, 68420I-7 (2008).
[CrossRef]

Li, J.

H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68(2), 141–142 (1998).

Lima, C.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Lindsey, J. S.

H. Du, R.-C. A. Fuh, J. Li, L. A. Corkan, and J. S. Lindsey, “PhotochemCAD: a computer-aided design and research tool in photochemistry,” Photochem. Photobiol. 68(2), 141–142 (1998).

Lompado, A.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Lualdi, M.

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. 28(3), 237–243 (2001).
[CrossRef] [PubMed]

Maitland, D. J.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7(3), 300–306 (2002).
[CrossRef] [PubMed]

Maksimova, I. L.

I. L. Maksimova, S. V. Romanov, and V. F. Izotova, “The effect of multiple scattering in disperse media on polarization characteristics of scattered light,” Opt. Spectrosc. 92(6), 915–923 (2002).
[CrossRef]

Manhas, S.

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE 7895, 78950E (2011).
[CrossRef]

Manoharan, R.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. 38(31), 6628–6637 (1999).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996).
[CrossRef] [PubMed]

Marchesini, R.

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. 28(3), 237–243 (2001).
[CrossRef] [PubMed]

Martelli, F.

Moes, C. J. M.

Moriyama, E. H.

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[CrossRef] [PubMed]

Mourant, J. R.

Munger, K.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Nelson, J. S.

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

Norvang, L. T.

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

Novikova, T.

Nusrat, A.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

O’Brien, P. E.

S. A. Skinner and P. E. O’Brien, “The microvascular structure of the normal colon in rats and humans,” J. Surg. Res. 61(2), 482–490 (1996).
[CrossRef] [PubMed]

Ossikovski, R.

M. Anastasiadou, S. Ben Hatit, R. Ossikovski, S. Guyot, and A. De Martino, “Experimental validation of the reverse polar decomposition of depolarizing Mueller matrices,” J. European Opt. Soc. Rapid Publications 2, 07018 (2007).
[CrossRef]

Patterson, M. S.

A. Kienle and M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41(10), 2221–2227 (1996).
[CrossRef] [PubMed]

Perelman, L. T.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. 38(31), 6628–6637 (1999).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Pierangelo, A.

Prahl, S. A.

Prikhach, A. S.

Ramella-Roman, J. C.

Romanov, S. V.

I. L. Maksimova, S. V. Romanov, and V. F. Izotova, “The effect of multiple scattering in disperse media on polarization characteristics of scattered light,” Opt. Spectrosc. 92(6), 915–923 (2002).
[CrossRef]

Samatham, R.

S. L. Jacques, R. Samatham, S. Isenhath, and K. Lee, “Polarized light camera to guide surgical excision of skin cancers,” Proc. SPIE 6842, 68420I, 68420I-7 (2008).
[CrossRef]

Sankaran, V.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7(3), 300–306 (2002).
[CrossRef] [PubMed]

Sassaroli, A.

Seiler, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Shapshay, S. M.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Sheets, E. E.

K. Badizadegan, V. Backman, C. W. Boone, C. P. Crum, R. R. Dasari, I. Georgakoudi, K. Keefe, K. Munger, S. M. Shapshay, E. E. Sheets, and M. S. Feld, “Spectroscopic diagnosis and imaging of invisible pre-cancer,” Faraday Discuss. 126, 265–279, discussion 303–311 (2004).
[CrossRef] [PubMed]

Shen, D.

Shields, S.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Skinner, S. A.

S. A. Skinner and P. E. O’Brien, “The microvascular structure of the normal colon in rats and humans,” J. Surg. Res. 61(2), 482–490 (1996).
[CrossRef] [PubMed]

Smith, M.

M. Smith, “Interpreting Mueller matrix images of tissues,” Proc. SPIE 4257, 82–89 (2001).
[CrossRef]

Smith, M. H.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Sterenborg, H. J. C. M.

Svaasand, E. K.

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

Svaasand, L. O.

L. O. Svaasand, E. J. Fiskerstrand, G. Kopstad, L. T. Norvang, E. K. Svaasand, J. S. Nelson, and M. W. Berns, “Therapeutic response during pulsed laser treatment of port-wine stains: dependence on vessel diameter and depth in dermis,” Lasers Med. Sci. 10(4), 235–243 (1995).
[CrossRef]

Tanner, E.

M. H. Smith, P. Burke, A. Lompado, E. Tanner, and L. W. Hillman, “Mueller matrix imaging polarimetry in dermatology,” Proc. SPIE 3911, 210–216 (2000).
[CrossRef]

Tomatis, S.

M. Lualdi, A. Colombo, B. Farina, S. Tomatis, and R. Marchesini, “A phantom with tissue-like optical properties in the visible and near infrared for use in photomedicine,” Lasers Surg. Med. 28(3), 237–243 (2001).
[CrossRef] [PubMed]

Tuchin, V. V.

A. N. Bashkatov, E. A. Genina, V. I. Kochubey, and V. V. Tuchin, “Estimation of wavelength dependence of refractive index of collagen fibers of scleral tissue,” Proc. SPIE 4162, 265–268 (2000).
[CrossRef]

Tynes, H. H.

Validire, P.

A. Pierangelo, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, and A. De Martino, “Ex-vivo characterization of human colon cancer by Mueller polarimetric imaging,” Opt. Express 19(2), 1582–1593 (2011).
[CrossRef] [PubMed]

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE 7895, 78950E (2011).
[CrossRef]

A. Pierangelo, S. Manhas, A. Benali, M. R. Antonelli, T. Novikova, P. Validire, B. Gayet, A. De Martino, and P. Validire, “Use of Mueller imaging for the staging of human colon cancer,” Proc. SPIE 7895, 78950E (2011).
[CrossRef]

M. R. Antonelli, A. Pierangelo, T. Novikova, P. Validire, A. Benali, B. Gayet, and A. De Martino, “Mueller matrix imaging of human colon tissue for cancer diagnostics: how Monte Carlo modeling can help in the interpretation of experimental data,” Opt. Express 18(10), 10200–10208 (2010).
[CrossRef] [PubMed]

Van Dam, J.

G. Zonios, L. T. Perelman, V. Backman, R. Manoharan, M. Fitzmaurice, J. Van Dam, and M. S. Feld, “Diffuse reflectance spectroscopy of human adenomatous colon polyps in vivo,” Appl. Opt. 38(31), 6628–6637 (1999).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

G. I. Zonios, R. M. Cothren, J. T. Arendt, J. Wu, J. Van Dam, J. M. Crawford, R. Manoharan, and M. S. Feld, “Morphological model of human colon tissue fluorescence,” IEEE Trans. Biomed. Eng. 43(2), 113–122 (1996).
[CrossRef] [PubMed]

van Gemert, M. J. C.

van Marie, J.

van Staveren, H. J.

van Veen, R. L. P.

Verkruysse, W.

Vitkin, I. A.

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[CrossRef] [PubMed]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105(10), 102023 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13(4), 044036 (2008).
[CrossRef] [PubMed]

M. F. G. Wood, X. Guo, and I. A. Vitkin, “Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology,” J. Biomed. Opt. 12(1), 014029 (2007).
[CrossRef] [PubMed]

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt. 11(4), 041105 (2006).
[CrossRef] [PubMed]

I. A. Vitkin, R. D. Laszlo, and C. L. Whyman, “Effects of molecular asymmetry of optically active molecules on the polarization properties of multiply scattered light,” Opt. Express 10(4), 222–229 (2002).
[PubMed]

Wallace, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80(3), 627–630 (1998).
[CrossRef]

Walsh, J. T.

V. Sankaran, J. T. Walsh, and D. J. Maitland, “Comparative study of polarized light propagation in biologic tissues,” J. Biomed. Opt. 7(3), 300–306 (2002).
[CrossRef] [PubMed]

Whyman, C. L.

Wilson, B. C.

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[CrossRef] [PubMed]

Wood, M. F. G.

M. F. G. Wood, N. Ghosh, E. H. Moriyama, B. C. Wilson, and I. A. Vitkin, “Proof-of-principle demonstration of a Mueller matrix decomposition method for polarized light tissue characterization in vivo,” J. Biomed. Opt. 14(1), 014029 (2009).
[CrossRef] [PubMed]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Polarimetry in turbid, birefringent, optically active media: a Monte Carlo study of Mueller matrix decomposition in the backscattering geometry,” J. Appl. Phys. 105(10), 102023 (2009).
[CrossRef]

N. Ghosh, M. F. G. Wood, and I. A. Vitkin, “Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence,” J. Biomed. Opt. 13(4), 044036 (2008).
[CrossRef] [PubMed]

M. F. G. Wood, X. Guo, and I. A. Vitkin, “Polarized light propagation in multiply scattering media exhibiting both linear birefringence and optical activity: Monte Carlo model and experimental methodology,” J. Biomed. Opt. 12(1), 014029 (2007).
[CrossRef] [PubMed]

X. Guo, M. F. G. Wood, and I. A. Vitkin, “Angular measurements of light scattered by turbid chiral media using linear Stokes polarimeter,” J. Biomed. Opt. 11(4), 041105 (2006).
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Figures (9)

Fig. 1
Fig. 1

Mueller matrix image of a colon sample, with a healthy part at the bottom left and a cancerous part at the top right. The matrix is shown in normalized form, with all its elements (except M11) divided by M11 and denoted as M*ii (M*ii = Mii/M11, i = 2, 3, 4) onward. The scale of the normalized elements is given by the colorbar. The image was taken at 550 nm [14,19].

Fig. 3
Fig. 3

Absolute values of the diagonal elements |M*ii| of the backscattering Mueller matrix normalized by |M11|, simulated at λ = 633 nm (a) for mono-dispersed scattering medium on a Lambertian substrate, modeling the mucosa on underlying layers. Each parameter was varied while keeping the others constant at the nominal values for the mucosa (r = 200 nm, MFP = 53.7 µm; m = 1.46/1.38, h = 0.5 mm). (b): variation of the sphere radius r with Lambertian albedo a = 0; (c): variation of the scattering parameter with a = 0, (d): variation of the scattering layer thickness with a = 0.3.

Fig. 2
Fig. 2

Left: Microscopic structure of a healthy colon sample, with its different layers: the mucosa (M), the submucosa (SM), the circular muscular tissue (C), the longitudinal muscular tissue (L) and the pericolic tissue (P). The very thin muscularis mucosa (MM) separates M from SM. Right: microscopic structure of a pathological sample, with a budding tumor (T) invading the mucosa and submucosa, with the underlying tissues still intact. From Ref. [19].

Fig. 4
Fig. 4

Absolute values of the diagonal elements of the backscattering Mueller matrix normalized by |M11| simulated at λ = 633 nm. (1): single layer representing the submucosa (r = 1.75 µm, MFP = 19.69 µm, m = 1.38/1.36, h = 0.7 mm) on absorbing substrate (albedo a = 0). (2): two layers representing the submucosa (same parameters as above) and mucosa (r1 = 200 nm, MFP = 53.7 µm, m = 1.46/1.38, h = 0.5 mm) on Lambertian substrate of albedo a = 0.1. (3): same as (2), with a = 0.3.

Fig. 5
Fig. 5

Left: sequence illustrating evolving exophytic growth in colon tissue as uniform (constant thickness) morphological deformation of the superficial layer (mucosa). Right: absolute values of the normalized diagonal elements |M*iiI calculated at λ = 633 nm for the following scatterer parameters r = 200 nm, µs = 93.1 cm−1; m = 1.46/1.38, h = 0.5 mm, albedo a = 0 (a) and 0.3 (b).

Fig. 6
Fig. 6

Left: two illustrations of exophytic growth originating in the mucosa, whose thickness increases in a non-uniform fashion (a, c). Right: absolute values of the normalized diagonal elements |M*ii| of the backscattering Mueller matrix calculated at λ = 633 nm for a single mucosa layer (r = 200 nm, µs = 93.1 cm−1; m = 1.46/1.38, h = 0.5 mm) on absorbing substrate (albedo a = 0), with h s varying from 0 (flat surface) to 2 mm (b); or Rs from 0 to 2.25 mm (d).

Fig. 7
Fig. 7

Normalized diagonal elements of the simulated backscattering Mueller matrices at λ = 633 nm for a single-layer with a bimodal population of scatterers (r 1 = 200 nm; r 2 = 50 nm; m = 1.46/1.38), Lambertian albedo a = 0.3. The images were calculated with r 1-sphere at 12% volume fraction varying the concentration of r2-sphere from 0% (mono-disperse population µ s = 186.202 cm−1) till 1%.

Fig. 8
Fig. 8

Normalized diagonal coefficients of the simulated backscattering Muller matrices at λ = 633 nm for a single-layer with bimodal population of scatterers (r 1 = 200 nm; r 2 = 50 nm; m = 1.46/1.38), Lambertian albedo a = 0.3. The images were calculated at different volume fraction of the r2-sphere (a): 1%; (b): 0.1%; (c): 0.01%; (d): 0.007%, (e): 0.005%; (f): 0.003%.

Fig. 9
Fig. 9

Spectral dependence of normalized diagonal coefficients of the simulated backscattering Mueller matrices images with diffuse light illumination for single layer bimodal population model of colon tissue (r 1 = 200 nm at 12% volume fraction value; r 2 = 50 nm at 0.01% volume fraction value, h = 0.5 mm, Lambertian albedo a = 0.3). The images were calculated using the values of optical index contrast, MFP and absorption coefficient reported in Table 1 in non-absorbing µa(λ) = 0, and absorbing µa(λ) medium.

Tables (1)

Tables Icon

Table 1 Spectrally resolved optical index contrast m, scattering parameter µ s and absorption coefficient µ a of the bimodal population tissue phantom

Equations (11)

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

I ( θ , φ )  d Ω = a Z 0 π cos θ  d Ω
| M 22 * | = | M 33 * | < | M 44 * |
M F P = 1 i N i σ i
μ e = μ s + μ a
β = μ s μ s + μ a
n c o l l a g e n ( λ ) = 1.426 + 19476 λ 2 1131066900 λ 4
μ a ( λ ) = μ a H b ( λ ) + μ a β c a r ( λ ) + μ a w a t e r ( λ )
C d i f f ( λ , b v r ) = { 1 exp [   2   μ a b l o o d ( λ ) ]   b v r 2   μ a b l o o d ( λ )   b v r }
μ a b l o o d ( λ ) = ln ( 10 )   C H b   ( α   ε H b 0 2 ( λ ) + ( 1 α ) ε H b ( λ ) ) / 64500
μ a H b ( λ ) = C d i f f ( λ , b v r )   V H b   μ a b l o o d ( λ )
μ a β c a r ( λ ) = C β c a r   log ( 10 )   ε β c a r ( λ )

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