Abstract

The determination of optical parameters of biological tissues is essential for the application of optical techniques in the diagnosis and treatment of diseases. Diffuse Reflection Spectroscopy is a widely used technique to analyze the optical characteristics of biological tissues. In this paper we show that by using diffuse reflectance spectra and a new mathematical model we can retrieve the optical parameters by applying an adjustment of the data with nonlinear least squares. In our model we represent the spectra using a Fourier series expansion finding mathematical relations between the polynomial coefficients and the optical parameters. In this first paper we use spectra generated by the Monte Carlo Multilayered Technique to simulate the propagation of photons in turbid media. Using these spectra we determine the behavior of Fourier series coefficients when varying the optical parameters of the medium under study. With this procedure we find mathematical relations between Fourier series coefficients and optical parameters. Finally, the results show that our method can retrieve the optical parameters of biological tissues with accuracy that is adequate for medical applications.

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2011

B. Morales Cruzado and S. Vázquez y Montiel, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis.57, 375–381. (2011).

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

2010

2009

J. Qin and R. Lu, “Monte Carlo simulation for quantification of light transport features in apples,” Comput. Electron. Agri.68, 44–51 (2009).
[CrossRef]

2008

I. Seo, C. K. Hayakawa, and V. Venugopalan “Radiative transport in the delta-P1 approximation for semi-infinite turbid media,” Med. Phys.35(2), 681–693 (2008).
[CrossRef] [PubMed]

2007

2003

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

2001

1993

1992

T. J. Farrell, M.S Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4), 879–896 (1992).
[CrossRef] [PubMed]

Amar, O. A.

Backman, V.

Bigio, I. J.

Farrell, T. J.

T. J. Farrell, M.S Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4), 879–896 (1992).
[CrossRef] [PubMed]

Foster, T. H.

Gou, L.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

Hanlon, E. B.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

Hayakawa, C. K.

I. Seo, C. K. Hayakawa, and V. Venugopalan “Radiative transport in the delta-P1 approximation for semi-infinite turbid media,” Med. Phys.35(2), 681–693 (2008).
[CrossRef] [PubMed]

Hull, E. L.

Itzkan, I.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

Jacques, S. L.

Lu, R.

J. Qin and R. Lu, “Monte Carlo simulation for quantification of light transport features in apples,” Comput. Electron. Agri.68, 44–51 (2009).
[CrossRef]

Matcher, S. J.

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

Meglinski, I. V.

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

Morales Cruzado, B.

B. Morales Cruzado and S. Vázquez y Montiel, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis.57, 375–381. (2011).

Patterson, M.S

T. J. Farrell, M.S Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4), 879–896 (1992).
[CrossRef] [PubMed]

Perelman, L. T.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

Qin, J.

J. Qin and R. Lu, “Monte Carlo simulation for quantification of light transport features in apples,” Comput. Electron. Agri.68, 44–51 (2009).
[CrossRef]

Qiu, L.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

Radosevich, A.

Reif, R.

Rogers, J. D.

Seo, I.

I. Seo, C. K. Hayakawa, and V. Venugopalan “Radiative transport in the delta-P1 approximation for semi-infinite turbid media,” Med. Phys.35(2), 681–693 (2008).
[CrossRef] [PubMed]

Taflove, A.

Turzhitsky, V.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

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

Vázquez y Montiel, S.

B. Morales Cruzado and S. Vázquez y Montiel, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis.57, 375–381. (2011).

Venugopalan, V.

I. Seo, C. K. Hayakawa, and V. Venugopalan “Radiative transport in the delta-P1 approximation for semi-infinite turbid media,” Med. Phys.35(2), 681–693 (2008).
[CrossRef] [PubMed]

Vitkin, E.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

Walker, J. S.

J. S. Walker, Fourier Analysis (Oxford University Press, 1988), pp. 5–28.

Wang, L. H.

Wilson, B.

T. J. Farrell, M.S Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4), 879–896 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Biomed. Opt. Express

Comput. Electron. Agri.

J. Qin and R. Lu, “Monte Carlo simulation for quantification of light transport features in apples,” Comput. Electron. Agri.68, 44–51 (2009).
[CrossRef]

Comput. Meth. Programs Bio.

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

J. Opt. Soc. Am. A

Med. Phys.

T. J. Farrell, M.S Patterson, and B. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys.19(4), 879–896 (1992).
[CrossRef] [PubMed]

I. Seo, C. K. Hayakawa, and V. Venugopalan “Radiative transport in the delta-P1 approximation for semi-infinite turbid media,” Med. Phys.35(2), 681–693 (2008).
[CrossRef] [PubMed]

Nat. Commun.

E. Vitkin, V. Turzhitsky, L. Qiu, L. Gou, I. Itzkan, E. B. Hanlon, and L. T. Perelman “Photon diffusion near the point of entry in anisotropically scattering turbid media,” Nat. Commun.2, 587 (2011).
[CrossRef] [PubMed]

Rev. Mex. Fis.

B. Morales Cruzado and S. Vázquez y Montiel, “Obtención de los parámetros ópticos de la piel usando algoritmos genéticos y MCML,” Rev. Mex. Fis.57, 375–381. (2011).

Other

J. S. Walker, Fourier Analysis (Oxford University Press, 1988), pp. 5–28.

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Figures (13)

Fig. 1
Fig. 1

Physical model of the simulation using the Monte Carlo method.

Fig. 2
Fig. 2

Diffuse Reflectance when varying (A) the scattering coefficient (B) the absorption coefficient and (C) the refraction index.

Fig. 3
Fig. 3

Trigonometric fitting of the reflection with radial resolution.

Fig. 4
Fig. 4

Curves adjustments radial reflectance (A)[σSF = 0.9998;σDA = 0.9999],(B)[σSF = 0.9998;σDA = 0.8029], where σ is standard deviation.

Fig. 5
Fig. 5

Variations of the Fourier coefficients a2, a5 and a7 related to the scattering.

Fig. 6
Fig. 6

Variations of the Fourier coefficients a1, a6 and a8 related to the scattering.

Fig. 7
Fig. 7

Variation of the Fourier coefficients a1 in relation to the scattering coefficient.

Fig. 8
Fig. 8

Variations of the Fourier series coefficients b2, b4 and b6 in relation to the scattering coefficient.

Fig. 9
Fig. 9

Increase of reflection when varying the scattering coefficient.

Fig. 10
Fig. 10

Relation of the nominal values of the Fourier series expansion coefficients.

Fig. 11
Fig. 11

Variation of the Fourier coefficient a1 in relation to the absorption coefficient.

Fig. 12
Fig. 12

Variation of the Fourier coefficient (A) an and (B) bn with respect to the absorption coefficient.

Fig. 13
Fig. 13

Variation of the Fourier coefficient (A) an and (B) bn with respect to respect of the refraction index.

Tables (4)

Tables Icon

Table 1 Curve Fitting made for the scattering coefficient

Tables Icon

Table 2 Curve Fitting made for the absorption coefficient

Tables Icon

Table 3 Curve Fitting made for the refraction index

Tables Icon

Table 4 Adjustments of curves of coefficient a1 in function of the refraction index

Equations (1)

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R n ( r ) = a 0 + i = 0 n a i cos ( i ω 0 r ) + i = 0 n b i sin ( i ω 0 r )

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