Abstract

High dynamic range optical-to-near-infrared transmission measurements for different parts of human body in the spectral range from 650 to 950 nm have been performed. Experimentally measured spectra are correlated with Monte Carlo simulations using chromaticity coordinates in CIE 1976 L*a*b* color space. Both a qualitative and a quantitative agreement have been found, paving a new way of characterizing human tissues in vivo. The newly developed experimental and computational platform for assessing tissue transmission spectra is anticipated to have a considerable impact on identifying favorable conditions for laser surgery and optical diagnostics, while providing supplementary information about tissue properties.

© 2012 OSA

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2011 (2)

A. Doronin and I. Meglinski, “Online object oriented Monte Carlo computational tool for the needs of biomedical optics,” Biomed. Opt. Express2(9), 2461–2469 (2011).
[CrossRef] [PubMed]

A. Doronin, I. Fine, and I. Meglinski, “Assessment of the calibration curve for transmittance pulse-oximetry,” Laser Phys.21(11), 1972–1977 (2011).
[CrossRef]

2010 (2)

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

2005 (3)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

G. I. Petrov and V. V. Yakovlev, “Enhancing red-shifted white-light continuum generation in optical fibers for applications in nonlinear Raman microscopy,” Opt. Express13(4), 1299–1306 (2005).
[CrossRef] [PubMed]

2004 (1)

G. I. Petrov, V. V. Yakovlev, and N. I. Minkovski, “Broadband nonlinear optical conversion of a high-energy diode-pumped picosecond laser,” Opt. Commun.229, 441–445 (2004).
[CrossRef]

2003 (3)

D. E. J. G. J. Dolmans, D. Fukumura, and R. K. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3(5), 380–387 (2003).
[CrossRef] [PubMed]

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

I. V. Meglinski and S. J. Matcher, “Computer simulation of the skin reflectance spectra,” Comput. Methods Programs Biomed.70(2), 179–186 (2003).
[CrossRef] [PubMed]

2002 (1)

D. B. Sarwer, T. A. Wadden, and L. A. Whitaker, “An investigation of changes in body image following cosmetic surgery,” Plast. Reconstr. Surg.109(1), 363–369, discussion 370–371 (2002).
[CrossRef] [PubMed]

2001 (1)

I. V. Meglinski, “Modeling the reflectance spectra of the optical radiation for random inhomogeneous multi-layered highly scattering and absorbing media by the Monte Carlo technique,” Quantum Electron.31, 1101–1107 (2001).

2000 (1)

1995 (1)

1993 (1)

1991 (1)

H. Key, E. R. Davies, P. C. Jackson, and P. N. T. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol.36(5), 579–590 (1991).
[CrossRef] [PubMed]

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)

Buchmann, E. V.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Chance, B.

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]

Davies, E. R.

H. Key, E. R. Davies, P. C. Jackson, and P. N. T. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol.36(5), 579–590 (1991).
[CrossRef] [PubMed]

Denk, W.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

Denton, M. L.

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

Dolmans, D. E. J. G. J.

D. E. J. G. J. Dolmans, D. Fukumura, and R. K. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3(5), 380–387 (2003).
[CrossRef] [PubMed]

Doronin, A.

A. Doronin and I. Meglinski, “Online object oriented Monte Carlo computational tool for the needs of biomedical optics,” Biomed. Opt. Express2(9), 2461–2469 (2011).
[CrossRef] [PubMed]

A. Doronin, I. Fine, and I. Meglinski, “Assessment of the calibration curve for transmittance pulse-oximetry,” Laser Phys.21(11), 1972–1977 (2011).
[CrossRef]

Eells, J. T.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Fine, I.

A. Doronin, I. Fine, and I. Meglinski, “Assessment of the calibration curve for transmittance pulse-oximetry,” Laser Phys.21(11), 1972–1977 (2011).
[CrossRef]

Fukumura, D.

D. E. J. G. J. Dolmans, D. Fukumura, and R. K. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3(5), 380–387 (2003).
[CrossRef] [PubMed]

Helmchen, F.

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

Henry, M. M.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Jackson, P. C.

H. Key, E. R. Davies, P. C. Jackson, and P. N. T. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol.36(5), 579–590 (1991).
[CrossRef] [PubMed]

Jacques, S. L.

Jain, R. K.

D. E. J. G. J. Dolmans, D. Fukumura, and R. K. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3(5), 380–387 (2003).
[CrossRef] [PubMed]

Kane, M.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Key, H.

H. Key, E. R. Davies, P. C. Jackson, and P. N. T. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol.36(5), 579–590 (1991).
[CrossRef] [PubMed]

Li, H. Y. S.

Matcher, S. J.

I. V. Meglinski and S. J. Matcher, “Computer simulation of the skin reflectance spectra,” Comput. Methods Programs Biomed.70(2), 179–186 (2003).
[CrossRef] [PubMed]

Meglinski, I.

A. Doronin, I. Fine, and I. Meglinski, “Assessment of the calibration curve for transmittance pulse-oximetry,” Laser Phys.21(11), 1972–1977 (2011).
[CrossRef]

A. Doronin and I. Meglinski, “Online object oriented Monte Carlo computational tool for the needs of biomedical optics,” Biomed. Opt. Express2(9), 2461–2469 (2011).
[CrossRef] [PubMed]

Meglinski, I. V.

I. V. Meglinski and S. J. Matcher, “Computer simulation of the skin reflectance spectra,” Comput. Methods Programs Biomed.70(2), 179–186 (2003).
[CrossRef] [PubMed]

I. V. Meglinski, “Modeling the reflectance spectra of the optical radiation for random inhomogeneous multi-layered highly scattering and absorbing media by the Monte Carlo technique,” Quantum Electron.31, 1101–1107 (2001).

Minkovski, N. I.

G. I. Petrov, V. V. Yakovlev, and N. I. Minkovski, “Broadband nonlinear optical conversion of a high-energy diode-pumped picosecond laser,” Opt. Commun.229, 441–445 (2004).
[CrossRef]

Noojin, G. D.

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

Ntziachristos, V.

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

Patterson, M. S.

Petrov, G. I.

G. I. Petrov and V. V. Yakovlev, “Enhancing red-shifted white-light continuum generation in optical fibers for applications in nonlinear Raman microscopy,” Opt. Express13(4), 1299–1306 (2005).
[CrossRef] [PubMed]

G. I. Petrov, V. V. Yakovlev, and N. I. Minkovski, “Broadband nonlinear optical conversion of a high-energy diode-pumped picosecond laser,” Opt. Commun.229, 441–445 (2004).
[CrossRef]

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]

Psaltis, D.

Qiao, Y.

Ranka, J. K.

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

Saidi, I. S.

Sarwer, D. B.

D. B. Sarwer, T. A. Wadden, and L. A. Whitaker, “An investigation of changes in body image following cosmetic surgery,” Plast. Reconstr. Surg.109(1), 363–369, discussion 370–371 (2002).
[CrossRef] [PubMed]

Scully, M. O.

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

Stentz, A. J.

Summerfelt, P.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Thomas, R. J.

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

Tittel, F. K.

Wadden, T. A.

D. B. Sarwer, T. A. Wadden, and L. A. Whitaker, “An investigation of changes in body image following cosmetic surgery,” Plast. Reconstr. Surg.109(1), 363–369, discussion 370–371 (2002).
[CrossRef] [PubMed]

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

Welch, A. J.

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]

Wells, P. N. T.

H. Key, E. R. Davies, P. C. Jackson, and P. N. T. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol.36(5), 579–590 (1991).
[CrossRef] [PubMed]

Whelan, H. T.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Whelan, N. T.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Whitaker, L. A.

D. B. Sarwer, T. A. Wadden, and L. A. Whitaker, “An investigation of changes in body image following cosmetic surgery,” Plast. Reconstr. Surg.109(1), 363–369, discussion 370–371 (2002).
[CrossRef] [PubMed]

Wilson, B. C.

Windeler, R. S.

Wong-Riley, M. T.

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

Yakovlev, V. V.

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

G. I. Petrov and V. V. Yakovlev, “Enhancing red-shifted white-light continuum generation in optical fibers for applications in nonlinear Raman microscopy,” Opt. Express13(4), 1299–1306 (2005).
[CrossRef] [PubMed]

G. I. Petrov, V. V. Yakovlev, and N. I. Minkovski, “Broadband nonlinear optical conversion of a high-energy diode-pumped picosecond laser,” Opt. Commun.229, 441–445 (2004).
[CrossRef]

Zhang, H. F.

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

Appl. Opt. (3)

Biomed. Opt. Express (1)

Comput. Methods Programs Biomed. (1)

I. V. Meglinski and S. J. Matcher, “Computer simulation of the skin reflectance spectra,” Comput. Methods Programs Biomed.70(2), 179–186 (2003).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (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]

Laser Phys. (1)

A. Doronin, I. Fine, and I. Meglinski, “Assessment of the calibration curve for transmittance pulse-oximetry,” Laser Phys.21(11), 1972–1977 (2011).
[CrossRef]

Nat. Biotechnol. (1)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol.23(3), 313–320 (2005).
[CrossRef] [PubMed]

Nat. Methods (2)

F. Helmchen and W. Denk, “Deep tissue two-photon microscopy,” Nat. Methods2(12), 932–940 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7(8), 603–614 (2010).
[CrossRef] [PubMed]

Nat. Rev. Cancer (1)

D. E. J. G. J. Dolmans, D. Fukumura, and R. K. Jain, “Photodynamic therapy for cancer,” Nat. Rev. Cancer3(5), 380–387 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

G. I. Petrov, V. V. Yakovlev, and N. I. Minkovski, “Broadband nonlinear optical conversion of a high-energy diode-pumped picosecond laser,” Opt. Commun.229, 441–445 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Med. Biol. (1)

H. Key, E. R. Davies, P. C. Jackson, and P. N. T. Wells, “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths,” Phys. Med. Biol.36(5), 579–590 (1991).
[CrossRef] [PubMed]

Plast. Reconstr. Surg. (1)

D. B. Sarwer, T. A. Wadden, and L. A. Whitaker, “An investigation of changes in body image following cosmetic surgery,” Plast. Reconstr. Surg.109(1), 363–369, discussion 370–371 (2002).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (2)

J. T. Eells, M. M. Henry, P. Summerfelt, M. T. Wong-Riley, E. V. Buchmann, M. Kane, N. T. Whelan, and H. T. Whelan, “Therapeutic photobiomodulation for methanol-induced retinal toxicity,” Proc. Natl. Acad. Sci. U.S.A.100(6), 3439–3444 (2003).
[CrossRef] [PubMed]

V. V. Yakovlev, H. F. Zhang, G. D. Noojin, M. L. Denton, R. J. Thomas, and M. O. Scully, “Stimulated Raman photoacoustic imaging,” Proc. Natl. Acad. Sci. U.S.A.107(47), 20335–20339 (2010).
[CrossRef] [PubMed]

Quantum Electron. (1)

I. V. Meglinski, “Modeling the reflectance spectra of the optical radiation for random inhomogeneous multi-layered highly scattering and absorbing media by the Monte Carlo technique,” Quantum Electron.31, 1101–1107 (2001).

Other (4)

I. Meglinski and A. Doronin, “Online Monte Carlo for biomedical optics,” SPIE Newsroom, Nov.7, 2011, http://spie.org/x57619.xml .

G. Donner, H. W-Jensen, “A spectral BSSRDF for shading human skin,” EGSR Symposium (2006).

N. V. Tkachenko, Optical Spectroscopy: Methods and Instrumentations (Elsevier Science, 2006).

D. H. Brainard, “Color appearance and color difference specification,” In The Science of Color, S. K. Shevell, ed. (Elsevier, 2003).

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Figures (8)

Fig. 1
Fig. 1

Schematic presentation of the experimental system used in current study.

Fig. 2
Fig. 2

Near-IR spectral transmission measured in vivo for fingernail (1), finger (2), palm (3), wrist (4) and forearm (5).

Fig. 3
Fig. 3

Absorption properties of skin tissues used in the simulation. Left, absorption coefficients of key skin tissues chromophores: 1, oxy-hemoglobin; 2, deoxy-hemoglobin; 3, water; 4, eumelanin [18]; 5, pheomelanin [18]; 6, baseline [18]. Right, absorption coefficients of the human skin layers counted by Eqs. (1)-(3).

Fig. 4
Fig. 4

Rayleigh scattering (1), Mie scattering (2), and combined Rayleigh and Mie scattering (3) by Eqs. (4), (5), and (6), respectively.

Fig. 5
Fig. 5

Chromaticity coordinates for fingernail (1), finger (2), palm (3), wrist (4) and forearm (5): crosses display experimental data and circles—the results of computer MC simulations.

Fig. 6
Fig. 6

The changes of human skin color presented in CIE 1976 L*a*b* color space simulated by the developed MC model (crosses) compared with the results of measurements/observations in vivo (squares) for near-IR light transmitted through the various parts of human body: 1,fingernail; 2, finger; 3, palm; 4, wrist; 5, forearm.

Fig. 7
Fig. 7

The results of MC simulation of human skin spectra (left) and corresponding colors (right) while varying the melanin content in living epidermis: (1), 0%; (2), 2%; (3), 5%; (4), 10%; (5), 20%; (6), 35%; (7), 45%; fraction between eumelanin and pheomelanin is 1:3.

Fig. 8
Fig. 8

The results of MC simulation of human skin spectra (left) and corresponding colors (right) while varying the blood concentration in the layers from papillary dermis to subcutaneous tissue: (1), 0%; (2), 2%; (3), 5%; (4), 10%; (5), 20%; (6), 35%; (7), 70%, respectively. The melanin concentration is 2% and fraction between eumelanin and pheomelanin is 1:3.

Tables (2)

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Table 1 Parameters used for assessment of the absorption coefficients of the layers. Layers 10–17 are the same as layers 1–7 in the reverse order.

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Table 2 Results of the MC simulation of skin color CIE coordinates in L*,a*,b* color spacea

Equations (6)

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μ a S t r a t . c o r n e u m ( λ ) = ( 1 C H 2 O ) μ a b a s e l i n e ( λ ) + C H 2 O μ a w a t e r ( λ )
μ a E p i d e r m i s    ( λ ) = ( 1 C H 2 O ) [ C m e l ( B m e l μ a m e l ( λ ) + ( 1 B m e l ) μ a p h . m e l ( λ ) ) + ( 1 C m e l ) μ a b a s e l i n e    ( λ ) ] + C H 2 O μ a w a t e r ( λ )
μ a L a y e r ( λ ) = ( 1 C H 2 O ) × [ ( C b l o o d F H b F R B C H t ) ( S μ a o x y ( λ ) + ( 1 S ) μ a d e o x y ( λ ) ) ] + ( 1 C H 2 O ) [ ( 1 C b l o o d F H b F R B C H t ) μ a b a s e l i n e ( λ ) ] + + C H 2 O μ a w a t e r ( λ )
μ s R a y l e i g h ( λ ) = 2.2 × 10 11 × λ 4
μ s M i e ( λ ) = 11.74 × λ 0.22
μ s L a y e r ( λ ) = N ( μ s R a y l e i g h ( λ ) + μ s M i e ( λ ) )

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