Abstract

Canonical correlation analysis, a multivariate statistical technique, was used to investigate the degree of association between tissue optical properties and spatially resolved reflectance signals. Monte Carlo modeling was employed to simulate signals corresponding to different combinations of optical properties and these data sets were fed as input to statistical analysis. The results show that it is possible to adjust the separation and angular orientation of source and detector fibers such that the effect of a particular optical property will be augmented among coincident variations in other properties. The trends observed exhibit differences when compared with a conventional univariate sensitivity analysis in which only a single property is varied whereas all other parameters of interest are kept constant.

© 2010 Optical Society of America

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  1. N. Thekkek and R. Richards-Kortum, “Optical imaging for cervical cancer detection: solutions for a continuing global problem,” Nat. Rev. Cancer 8, 725–731 (2008).
    [CrossRef]
  2. J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV–visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20, 119–131 (2009).
    [CrossRef] [PubMed]
  3. C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
    [CrossRef] [PubMed]
  4. D. Hidovic-Rowe and E. Claridge, “Modelling and validation of spectral reflectance for the colon,” Phys. Med. Biol. 50, 1071–1093 (2005).
    [CrossRef] [PubMed]
  5. D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11, 064027 (2006).
    [CrossRef]
  6. O. P. Kaspers, H. J. C. M. Sterenborg, and A. Amelink, “Controlling the optical path length in turbid media using differential path-length spectroscopy: fiber diameter dependence,” Appl. Opt. 47, 365–371 (2008).
    [CrossRef] [PubMed]
  7. I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
    [CrossRef]
  8. J. R. Mourant, I. J. Bigio, D. A. Jack, T. M. Johnson, and H. D. Miller, “Measuring absorption coefficients in small volumes of highly scattering media: source-detector separations for which path lengths do not depend on scattering properties,” Appl. Opt. 36, 5655–5661 (1997).
    [CrossRef] [PubMed]
  9. G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45, 1062–1071 (2006).
    [CrossRef] [PubMed]
  10. G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
    [CrossRef] [PubMed]
  11. B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
    [CrossRef]
  12. Q. Wang, H. Yang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Measurement of internal tissue optical properties at ultraviolet and visible wavelengths: development and implementation of a fiberoptic-based system,” Opt. Express 16, 8685–8703(2008).
    [CrossRef] [PubMed]
  13. N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
    [CrossRef] [PubMed]
  14. U. Utzinger and R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
    [CrossRef] [PubMed]
  15. A. Wang, V. Nammalavar, and R. Drezek, “Experimental evaluation of angularly variable fiber geometry for targeting depth-resolved reflectance from layered epithelial tissue phantoms,” J. Biomed. Opt. 12, 044011 (2007).
    [CrossRef] [PubMed]
  16. J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
    [CrossRef] [PubMed]
  17. L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
    [CrossRef] [PubMed]
  18. W. J. Conover, Practical Nonparametric Statistics (Wiley, 1999).
  19. W. R. Dillon and M. Goldstein, Multivariate Analysis: Methods and Applications (Wiley, 1984).
  20. R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).
  21. J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. 37, 3586–3593 (1998).
    [CrossRef]
  22. R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
    [CrossRef] [PubMed]
  23. T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy,” Appl. Opt. 44, 2072–2081 (2005).
    [CrossRef] [PubMed]
  24. D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J. 92, 3260–3274 (2007).
    [CrossRef] [PubMed]
  25. 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, 6628–6637 (1999).
    [CrossRef]
  26. 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, 879–888 (1992).
    [CrossRef] [PubMed]
  27. E. L. Hull and T. H. Foster, “Steady-state reflectance spectroscopy in the P3 approximation,” J. Opt. Soc. Am. A 18, 584–599 (2001).
    [CrossRef]
  28. J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. 45, 8152–8162 (2006).
    [CrossRef] [PubMed]
  29. C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
    [CrossRef]
  30. A. Amelink, H. J. C. M. Sterenborg, M. P. L. Bard, and S. A. Burgers, “In vivo measurement of the local optical properties of tissue by use of differential path-length spectroscopy,” Opt. Lett. 29, 1087–1089 (2004).
    [CrossRef] [PubMed]
  31. P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
    [CrossRef] [PubMed]
  32. G. Zonios and A. Dimou, “Modeling diffuse reflectance from semi-infinite turbid media: application to the study of skin optical properties,” Opt. Express 14, 8661–8674 (2006).
    [CrossRef] [PubMed]
  33. R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46, 7317–7328 (2007).
    [CrossRef] [PubMed]
  34. P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
    [CrossRef] [PubMed]
  35. J. Ramachandran, T. M. Powers, S. Carpenter, A. Garcia-Lopez, J. P. Freyer, and J. R. Mourant, “Light scattering and microarchitectural differences between tumorigenic and non-tumorigenic cell models of tissue,” Opt. Express 15, 4039–4053 (2007).
    [CrossRef] [PubMed]
  36. J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys J. 88, 2929–2938(2005).
    [CrossRef] [PubMed]
  37. J. D. Wilson, B. R. Giesselman, S. Mitra, and T. H. Foster, “Lysosome-damage-induced scattering changes coincide with release of cytochrome c,” Opt. Lett. 32, 2517–2519 (2007).
    [CrossRef] [PubMed]
  38. P. M. Pilarski, X. Su, D. M. Glerum, W. Rozmus, and C. J. Backhouse, “Rapid simulation of wide-angle scattering from mitochondria in single cells,” Opt. Express 16, 12819–12834(2008).
    [CrossRef] [PubMed]
  39. C. K. Hayakawa, B. Y. Hill, J. S. You, F. Bevilacqua, J. Spanier, and V. Venugopalan, “Use of the δ-P1 approximation for recovery of optical absorption, scattering, and asymmetry coefficients in turbid media,” Appl. Opt. 43, 4677–4684 (2004).
    [CrossRef] [PubMed]
  40. S. Menon, Q. Su, and R. Grobe, “Determination of g and μ using multiply scattered light in turbid media,” Phys. Rev. Lett. 94, 153904 (2005).
    [CrossRef] [PubMed]
  41. N. Joshi, C. Donner, and H. W. Jensen, “Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination,” Opt. Lett. 31, 936–938 (2006).
    [CrossRef] [PubMed]
  42. A.J.Welch and M.J. C.van Gemert, eds., Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).
  43. J. R. Mourant, J. Boyer, A. H. Hielscher, and I. J. Bigio, “Influence of the scattering phase function on light transport measurements in turbid media performed with small source-detector separations,” Opt. Lett. 21, 546–548 (1996).
    [CrossRef] [PubMed]
  44. A. Kienle, F. K. Forster, and R. Hibst, “Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance,” Opt. Lett. 26, 1571–1573 (2001).
    [CrossRef]
  45. H. Tian, Y. Liu, and L. Wang, “Influence of the third-order parameter on diffuse reflectance at small source-detector separations,” Opt. Lett. 31, 933–935 (2006).
    [CrossRef] [PubMed]
  46. C. Kortun, Y. R. Hijazi, and D. Arifler, “Combined Monte Carlo and finite-difference time-domain modeling for biophotonic analysis: implications on reflectance-based diagnosis of epithelial precancer,” J. Biomed. Opt. 13, 034014 (2008).
    [CrossRef] [PubMed]

2009 (1)

J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV–visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20, 119–131 (2009).
[CrossRef] [PubMed]

2008 (10)

N. Thekkek and R. Richards-Kortum, “Optical imaging for cervical cancer detection: solutions for a continuing global problem,” Nat. Rev. Cancer 8, 725–731 (2008).
[CrossRef]

O. P. Kaspers, H. J. C. M. Sterenborg, and A. Amelink, “Controlling the optical path length in turbid media using differential path-length spectroscopy: fiber diameter dependence,” Appl. Opt. 47, 365–371 (2008).
[CrossRef] [PubMed]

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

Q. Wang, H. Yang, A. Agrawal, N. S. Wang, and T. J. Pfefer, “Measurement of internal tissue optical properties at ultraviolet and visible wavelengths: development and implementation of a fiberoptic-based system,” Opt. Express 16, 8685–8703(2008).
[CrossRef] [PubMed]

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
[CrossRef] [PubMed]

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

P. M. Pilarski, X. Su, D. M. Glerum, W. Rozmus, and C. J. Backhouse, “Rapid simulation of wide-angle scattering from mitochondria in single cells,” Opt. Express 16, 12819–12834(2008).
[CrossRef] [PubMed]

C. Kortun, Y. R. Hijazi, and D. Arifler, “Combined Monte Carlo and finite-difference time-domain modeling for biophotonic analysis: implications on reflectance-based diagnosis of epithelial precancer,” J. Biomed. Opt. 13, 034014 (2008).
[CrossRef] [PubMed]

2007 (6)

J. D. Wilson, B. R. Giesselman, S. Mitra, and T. H. Foster, “Lysosome-damage-induced scattering changes coincide with release of cytochrome c,” Opt. Lett. 32, 2517–2519 (2007).
[CrossRef] [PubMed]

J. Ramachandran, T. M. Powers, S. Carpenter, A. Garcia-Lopez, J. P. Freyer, and J. R. Mourant, “Light scattering and microarchitectural differences between tumorigenic and non-tumorigenic cell models of tissue,” Opt. Express 15, 4039–4053 (2007).
[CrossRef] [PubMed]

R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46, 7317–7328 (2007).
[CrossRef] [PubMed]

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J. 92, 3260–3274 (2007).
[CrossRef] [PubMed]

A. Wang, V. Nammalavar, and R. Drezek, “Experimental evaluation of angularly variable fiber geometry for targeting depth-resolved reflectance from layered epithelial tissue phantoms,” J. Biomed. Opt. 12, 044011 (2007).
[CrossRef] [PubMed]

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

2006 (7)

G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45, 1062–1071 (2006).
[CrossRef] [PubMed]

G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
[CrossRef] [PubMed]

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11, 064027 (2006).
[CrossRef]

J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. 45, 8152–8162 (2006).
[CrossRef] [PubMed]

G. Zonios and A. Dimou, “Modeling diffuse reflectance from semi-infinite turbid media: application to the study of skin optical properties,” Opt. Express 14, 8661–8674 (2006).
[CrossRef] [PubMed]

N. Joshi, C. Donner, and H. W. Jensen, “Noninvasive measurement of scattering anisotropy in turbid materials by nonnormal incident illumination,” Opt. Lett. 31, 936–938 (2006).
[CrossRef] [PubMed]

H. Tian, Y. Liu, and L. Wang, “Influence of the third-order parameter on diffuse reflectance at small source-detector separations,” Opt. Lett. 31, 933–935 (2006).
[CrossRef] [PubMed]

2005 (6)

S. Menon, Q. Su, and R. Grobe, “Determination of g and μ using multiply scattered light in turbid media,” Phys. Rev. Lett. 94, 153904 (2005).
[CrossRef] [PubMed]

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys J. 88, 2929–2938(2005).
[CrossRef] [PubMed]

T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy,” Appl. Opt. 44, 2072–2081 (2005).
[CrossRef] [PubMed]

C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
[CrossRef] [PubMed]

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

2004 (2)

2003 (3)

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

U. Utzinger and R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
[CrossRef] [PubMed]

2001 (2)

1999 (1)

1998 (1)

1997 (1)

1996 (1)

1992 (1)

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, 879–888 (1992).
[CrossRef] [PubMed]

A’Amar, O.

Agrawal, A.

Amelink, A.

Arifler, D.

C. Kortun, Y. R. Hijazi, and D. Arifler, “Combined Monte Carlo and finite-difference time-domain modeling for biophotonic analysis: implications on reflectance-based diagnosis of epithelial precancer,” J. Biomed. Opt. 13, 034014 (2008).
[CrossRef] [PubMed]

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J. 92, 3260–3274 (2007).
[CrossRef] [PubMed]

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11, 064027 (2006).
[CrossRef]

Atkinson, E. N.

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

Backhouse, C. J.

Backman, V.

Bard, M. P. L.

Bargo, P. R.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

Bender, J. E.

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

Bevilacqua, F.

C. K. Hayakawa, B. Y. Hill, J. S. You, F. Bevilacqua, J. Spanier, and V. Venugopalan, “Use of the δ-P1 approximation for recovery of optical absorption, scattering, and asymmetry coefficients in turbid media,” Appl. Opt. 43, 4677–4684 (2004).
[CrossRef] [PubMed]

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Bigelow, C. E.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys J. 88, 2929–2938(2005).
[CrossRef] [PubMed]

Bigio, I. J.

Blair, G.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

Bocklage, T. J.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Boiko, I.

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

Boyer, J.

Breslin, T. M.

G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
[CrossRef] [PubMed]

C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
[CrossRef] [PubMed]

Brown, J. Q.

J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV–visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20, 119–131 (2009).
[CrossRef] [PubMed]

Bullock, K. L.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Burgers, S. A.

Calkins, D. J.

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys J. 88, 2929–2938(2005).
[CrossRef] [PubMed]

Carpenter, S.

Charvet, I.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Claridge, E.

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

Collier, T.

T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy,” Appl. Opt. 44, 2072–2081 (2005).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

Conover, W. J.

W. J. Conover, Practical Nonparametric Statistics (Wiley, 1999).

Cox, D. D.

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

Depeursinge, C.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Dillon, W. R.

W. R. Dillon and M. Goldstein, Multivariate Analysis: Methods and Applications (Wiley, 1984).

Dimou, A.

Donner, C.

Dorin, M. H.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Drezek, R.

A. Wang, V. Nammalavar, and R. Drezek, “Experimental evaluation of angularly variable fiber geometry for targeting depth-resolved reflectance from layered epithelial tissue phantoms,” J. Biomed. Opt. 12, 044011 (2007).
[CrossRef] [PubMed]

J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. 45, 8152–8162 (2006).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

Eick, A. A.

El-Naggar, A.

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

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, 879–888 (1992).
[CrossRef] [PubMed]

Feld, M. S.

Fitzmaurice, M.

Follen, M.

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11, 064027 (2006).
[CrossRef]

T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy,” Appl. Opt. 44, 2072–2081 (2005).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

Forster, F. K.

Foster, T. H.

Freyer, J. P.

Fu, K.

Garcia-Lopez, A.

Ghislain, M. St.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Giesselman, B. R.

Gilchrist, K. W.

Gillenwater, A.

L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
[CrossRef] [PubMed]

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J. 92, 3260–3274 (2007).
[CrossRef] [PubMed]

Glerum, D. M.

Goldstein, M.

W. R. Dillon and M. Goldstein, Multivariate Analysis: Methods and Applications (Wiley, 1984).

Goodell, T. T.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

Greene, H. M.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Grobe, R.

S. Menon, Q. Su, and R. Grobe, “Determination of g and μ using multiply scattered light in turbid media,” Phys. Rev. Lett. 94, 153904 (2005).
[CrossRef] [PubMed]

Guillaud, M.

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

Hayakawa, C. K.

Hibst, R.

Hidovic-Rowe, D.

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

Hielscher, A. H.

Hijazi, Y. R.

C. Kortun, Y. R. Hijazi, and D. Arifler, “Combined Monte Carlo and finite-difference time-domain modeling for biophotonic analysis: implications on reflectance-based diagnosis of epithelial precancer,” J. Biomed. Opt. 13, 034014 (2008).
[CrossRef] [PubMed]

Hill, B. Y.

Hull, E. L.

Jack, D. A.

Jacques, S. L.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

Jensen, H. W.

Johnson, R. A.

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).

Johnson, T. M.

Joshi, N.

Kan, C.

L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
[CrossRef] [PubMed]

Kaspers, O. P.

Kienle, A.

Kortun, C.

C. Kortun, Y. R. Hijazi, and D. Arifler, “Combined Monte Carlo and finite-difference time-domain modeling for biophotonic analysis: implications on reflectance-based diagnosis of epithelial precancer,” J. Biomed. Opt. 13, 034014 (2008).
[CrossRef] [PubMed]

Koval, G.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

Kuech, T. F.

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

Lin, A. W. H.

Liu, Y.

Lo, J. Y.

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

MacAulay, C.

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11, 064027 (2006).
[CrossRef]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

Malpica, A.

T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy,” Appl. Opt. 44, 2072–2081 (2005).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

Manoharan, R.

Markey, M. K.

L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
[CrossRef] [PubMed]

Marquet, P.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Marr-Lyon, L. R.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Meda, P.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Menon, S.

S. Menon, Q. Su, and R. Grobe, “Determination of g and μ using multiply scattered light in turbid media,” Phys. Rev. Lett. 94, 153904 (2005).
[CrossRef] [PubMed]

Miller, H. D.

Mitra, S.

Mourant, J. R.

Nammalavar, V.

A. Wang, V. Nammalavar, and R. Drezek, “Experimental evaluation of angularly variable fiber geometry for targeting depth-resolved reflectance from layered epithelial tissue phantoms,” J. Biomed. Opt. 12, 044011 (2007).
[CrossRef] [PubMed]

Nguyen, T. H.

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

Nieman, L. T.

L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
[CrossRef] [PubMed]

Ory, G.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Palmer, G. M.

J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV–visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20, 119–131 (2009).
[CrossRef] [PubMed]

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45, 1062–1071 (2006).
[CrossRef] [PubMed]

G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
[CrossRef] [PubMed]

C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
[CrossRef] [PubMed]

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, 879–888 (1992).
[CrossRef] [PubMed]

Pavlova, I.

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J. 92, 3260–3274 (2007).
[CrossRef] [PubMed]

Perelman, L. T.

Pfefer, T. J.

Pilarski, P. M.

Powers, T. M.

J. Ramachandran, T. M. Powers, S. Carpenter, A. Garcia-Lopez, J. P. Freyer, and J. R. Mourant, “Light scattering and microarchitectural differences between tumorigenic and non-tumorigenic cell models of tissue,” Opt. Express 15, 4039–4053 (2007).
[CrossRef] [PubMed]

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Prahl, S. A.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

Rajaram, N.

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

Ramachandran, J.

Ramanujam, N.

J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV–visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20, 119–131 (2009).
[CrossRef] [PubMed]

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
[CrossRef] [PubMed]

G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45, 1062–1071 (2006).
[CrossRef] [PubMed]

C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
[CrossRef] [PubMed]

Reif, R.

Richards-Kortum, R.

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

N. Thekkek and R. Richards-Kortum, “Optical imaging for cervical cancer detection: solutions for a continuing global problem,” Nat. Rev. Cancer 8, 725–731 (2008).
[CrossRef]

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J. 92, 3260–3274 (2007).
[CrossRef] [PubMed]

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11, 064027 (2006).
[CrossRef]

T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy,” Appl. Opt. 44, 2072–2081 (2005).
[CrossRef] [PubMed]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

U. Utzinger and R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
[CrossRef] [PubMed]

Rozmus, W.

Schwarz, R. A.

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

Shen, D.

Sleven, R. A.

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

Smith, H. O.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Sokolov, K.

L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
[CrossRef] [PubMed]

Spanier, J.

Sterenborg, H. J. C. M.

Su, Q.

S. Menon, Q. Su, and R. Grobe, “Determination of g and μ using multiply scattered light in turbid media,” Phys. Rev. Lett. 94, 153904 (2005).
[CrossRef] [PubMed]

Su, X.

Sun, J.

Thekkek, N.

N. Thekkek and R. Richards-Kortum, “Optical imaging for cervical cancer detection: solutions for a continuing global problem,” Nat. Rev. Cancer 8, 725–731 (2008).
[CrossRef]

Thueler, P.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Tian, H.

Tunnell, J. W.

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

Utzinger, U.

Van Dam, J.

Venugopalan, V.

Vermeulen, B.

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

Vishwanath, K.

J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV–visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20, 119–131 (2009).
[CrossRef] [PubMed]

Wang, A.

A. Wang, V. Nammalavar, and R. Drezek, “Experimental evaluation of angularly variable fiber geometry for targeting depth-resolved reflectance from layered epithelial tissue phantoms,” J. Biomed. Opt. 12, 044011 (2007).
[CrossRef] [PubMed]

J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. 45, 8152–8162 (2006).
[CrossRef] [PubMed]

Wang, L.

Wang, N. S.

Wang, Q.

Waxman, A. G.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Weber, C. R.

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

Wichern, D. W.

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).

Williams, M.

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

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, 879–888 (1992).
[CrossRef] [PubMed]

Wilson, J. D.

J. D. Wilson, B. R. Giesselman, S. Mitra, and T. H. Foster, “Lysosome-damage-induced scattering changes coincide with release of cytochrome c,” Opt. Lett. 32, 2517–2519 (2007).
[CrossRef] [PubMed]

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys J. 88, 2929–2938(2005).
[CrossRef] [PubMed]

Xu, F.

G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
[CrossRef] [PubMed]

C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
[CrossRef] [PubMed]

Yang, H.

You, J. S.

Yu, B.

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

Zhu, C.

G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
[CrossRef] [PubMed]

C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
[CrossRef] [PubMed]

Zonios, G.

Zsemlye, M. M.

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

Appl. Opt. (10)

J. R. Mourant, I. J. Bigio, D. A. Jack, T. M. Johnson, and H. D. Miller, “Measuring absorption coefficients in small volumes of highly scattering media: source-detector separations for which path lengths do not depend on scattering properties,” Appl. Opt. 36, 5655–5661 (1997).
[CrossRef] [PubMed]

G. M. Palmer and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part I: Theory and validation on synthetic phantoms,” Appl. Opt. 45, 1062–1071 (2006).
[CrossRef] [PubMed]

G. M. Palmer, C. Zhu, T. M. Breslin, F. Xu, K. W. Gilchrist, and N. Ramanujam, “Monte Carlo-based inverse model for calculating tissue optical properties. Part II: Application to breast cancer diagnosis,” Appl. Opt. 45, 1072–1078 (2006).
[CrossRef] [PubMed]

O. P. Kaspers, H. J. C. M. Sterenborg, and A. Amelink, “Controlling the optical path length in turbid media using differential path-length spectroscopy: fiber diameter dependence,” Appl. Opt. 47, 365–371 (2008).
[CrossRef] [PubMed]

J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. 37, 3586–3593 (1998).
[CrossRef]

T. Collier, M. Follen, A. Malpica, and R. Richards-Kortum, “Sources of scattering in cervical tissue: determination of the scattering coefficient by confocal microscopy,” Appl. Opt. 44, 2072–2081 (2005).
[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, 6628–6637 (1999).
[CrossRef]

J. Sun, K. Fu, A. Wang, A. W. H. Lin, U. Utzinger, and R. Drezek, “Influence of fiber optic probe geometry on the applicability of inverse models of tissue reflectance spectroscopy: computational models and experimental measurements,” Appl. Opt. 45, 8152–8162 (2006).
[CrossRef] [PubMed]

R. Reif, O. A’Amar, and I. J. Bigio, “Analytical model of light reflectance for extraction of the optical properties in small volumes of turbid media,” Appl. Opt. 46, 7317–7328 (2007).
[CrossRef] [PubMed]

C. K. Hayakawa, B. Y. Hill, J. S. You, F. Bevilacqua, J. Spanier, and V. Venugopalan, “Use of the δ-P1 approximation for recovery of optical absorption, scattering, and asymmetry coefficients in turbid media,” Appl. Opt. 43, 4677–4684 (2004).
[CrossRef] [PubMed]

Biophys J. (1)

J. D. Wilson, C. E. Bigelow, D. J. Calkins, and T. H. Foster, “Light scattering from intact cells reports oxidative-stress-induced mitochondrial swelling,” Biophys J. 88, 2929–2938(2005).
[CrossRef] [PubMed]

Biophys. J. (1)

D. Arifler, I. Pavlova, A. Gillenwater, and R. Richards-Kortum, “Light scattering from collagen fiber networks: micro-optical properties of normal and neoplastic stroma,” Biophys. J. 92, 3260–3274 (2007).
[CrossRef] [PubMed]

Curr. Opin. Biotechnol. (1)

J. Q. Brown, K. Vishwanath, G. M. Palmer, and N. Ramanujam, “Advances in quantitative UV–visible spectroscopy for clinical and pre-clinical application in cancer,” Curr. Opin. Biotechnol. 20, 119–131 (2009).
[CrossRef] [PubMed]

Gynecol. Oncol. (1)

J. R. Mourant, T. J. Bocklage, T. M. Powers, H. M. Greene, K. L. Bullock, L. R. Marr-Lyon, M. H. Dorin, A. G. Waxman, M. M. Zsemlye, and H. O. Smith, “In vivo light scattering measurements for detection of precancerous conditions of the cervix,” Gynecol. Oncol. 105, 439–445 (2007).
[CrossRef] [PubMed]

J. Biomed. Opt. (13)

L. T. Nieman, C. Kan, A. Gillenwater, M. K. Markey, and K. Sokolov, “Probing local changes in the oral cavity for early detection of cancer using oblique polarized reflectance spectroscopy: a pilot clinical trial,” J. Biomed. Opt. 13, 024011 (2008).
[CrossRef] [PubMed]

I. Pavlova, C. R. Weber, R. A. Schwarz, M. Williams, A. El-Naggar, A. Gillenwater, and R. Richards-Kortum, “Monte Carlo model to describe depth selective fluorescence spectra of epithelial tissue: applications for diagnosis of oral precancer,” J. Biomed. Opt. 13, 064012 (2008).
[CrossRef]

N. Rajaram, T. H. Nguyen, and J. W. Tunnell, “Lookup table-based inverse model for determining optical properties of turbid media,” J. Biomed. Opt. 13, 050501 (2008).
[CrossRef] [PubMed]

U. Utzinger and R. Richards-Kortum, “Fiber optic probes for biomedical optical spectroscopy,” J. Biomed. Opt. 8, 121–147(2003).
[CrossRef] [PubMed]

A. Wang, V. Nammalavar, and R. Drezek, “Experimental evaluation of angularly variable fiber geometry for targeting depth-resolved reflectance from layered epithelial tissue phantoms,” J. Biomed. Opt. 12, 044011 (2007).
[CrossRef] [PubMed]

C. Zhu, G. M. Palmer, T. M. Breslin, F. Xu, and N. Ramanujam, “Use of a multiseparation fiber optic probe for the optical diagnosis of breast cancer,” J. Biomed. Opt. 10, 024032 (2005).
[CrossRef] [PubMed]

D. Arifler, C. MacAulay, M. Follen, and R. Richards-Kortum, “Spatially resolved reflectance spectroscopy for diagnosis of cervical precancer: Monte Carlo modeling and comparison to clinical measurements,” J. Biomed. Opt. 11, 064027 (2006).
[CrossRef]

B. Yu, J. Y. Lo, T. F. Kuech, G. M. Palmer, J. E. Bender, and N. Ramanujam, “Cost-effective diffuse reflectance spectroscopy device for quantifying tissue absorption and scattering in vivo,” J. Biomed. Opt. 13, 060505 (2008).
[CrossRef]

R. Drezek, M. Guillaud, T. Collier, I. Boiko, A. Malpica, C. MacAulay, M. Follen, and R. Richards-Kortum, “Light scattering from cervical cells throughout neoplastic progression: influence of nuclear morphology, DNA content, and chromatin texture,” J. Biomed. Opt. 8, 7–16 (2003).
[CrossRef] [PubMed]

C. R. Weber, R. A. Schwarz, E. N. Atkinson, D. D. Cox, C. MacAulay, M. Follen, and R. Richards-Kortum, “Model-based analysis of reflectance and fluorescence spectra for in vivo detection of cervical dysplasia and cancer,” J. Biomed. Opt. 13, 064016 (2008).
[CrossRef]

P. Thueler, I. Charvet, F. Bevilacqua, M. St. Ghislain, G. Ory, P. Marquet, P. Meda, B. Vermeulen, and C. Depeursinge, “In vivo endoscopic tissue diagnostics based on spectroscopic absorption, scattering, and phase function properties,” J. Biomed. Opt. 8, 495–503 (2003).
[CrossRef] [PubMed]

P. R. Bargo, S. A. Prahl, T. T. Goodell, R. A. Sleven, G. Koval, G. Blair, and S. L. Jacques, “In vivo determination of optical properties of normal and tumor tissue with white light reflectance and an empirical light transport model during endoscopy,” J. Biomed. Opt. 10, 034018 (2005).
[CrossRef] [PubMed]

C. Kortun, Y. R. Hijazi, and D. Arifler, “Combined Monte Carlo and finite-difference time-domain modeling for biophotonic analysis: implications on reflectance-based diagnosis of epithelial precancer,” J. Biomed. Opt. 13, 034014 (2008).
[CrossRef] [PubMed]

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

Med. Phys. (1)

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, 879–888 (1992).
[CrossRef] [PubMed]

Nat. Rev. Cancer (1)

N. Thekkek and R. Richards-Kortum, “Optical imaging for cervical cancer detection: solutions for a continuing global problem,” Nat. Rev. Cancer 8, 725–731 (2008).
[CrossRef]

Opt. Express (4)

Opt. Lett. (6)

Phys. Med. Biol. (1)

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

Phys. Rev. Lett. (1)

S. Menon, Q. Su, and R. Grobe, “Determination of g and μ using multiply scattered light in turbid media,” Phys. Rev. Lett. 94, 153904 (2005).
[CrossRef] [PubMed]

Other (4)

A.J.Welch and M.J. C.van Gemert, eds., Optical-Thermal Response of Laser-Irradiated Tissue (Plenum, 1995).

W. J. Conover, Practical Nonparametric Statistics (Wiley, 1999).

W. R. Dillon and M. Goldstein, Multivariate Analysis: Methods and Applications (Wiley, 1984).

R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, 2002).

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Figures (5)

Fig. 1
Fig. 1

Source–detector geometries employed in Monte Carlo simulations. A single source fiber and twelve detector fibers are (a) oriented perpendicular to the tissue surface and (b) tilted toward each other at an angle of α = 30 ° . In both cases, the center-to- center source–detector separations range from 0.25 to 3 mm in increments of 0.25 mm .

Fig. 2
Fig. 2

Partial correlations between (a) μ s and I i , (b) μ a and I i , and (c) g and I i , where the indices i = 1 , 2 , , 12 correspond to source–detector separations ranging from 0.25 to 3 mm in increments of 0.25 mm . The source fiber and the detector fibers are perpendicular to the tissue surface.

Fig. 3
Fig. 3

Canonical loadings R V ^ , z ( 2 ) showing the correlation between (a) V ^ 1 and I i * , (b) V ^ 2 and I i * , and (c) V ^ 3 and I i * , where the indices i = 1 , 2 , , 12 correspond to source–detector separations ranging from 0.25 to 3 mm in increments of 0.25 mm . The source fiber and the detector fibers are perpendicular to the tissue surface.

Fig. 4
Fig. 4

Partial correlations between (a) μ s and I i , (b) μ a and I i , and (c) g and I i , where the indices i = 1 , 2 , , 12 correspond to source–detector separations ranging from 0.25 to 3 mm in increments of 0.25 mm . The source fiber and the detector fibers are tilted toward each other.

Fig. 5
Fig. 5

Canonical loadings R V ^ , z ( 2 ) showing the correlation between (a) V ^ 1 and I i * , (b) V ^ 2 and I i * , and (c) V ^ 3 and I i * , where the indices i = 1 , 2 , , 12 correspond to source–detector separations ranging from 0.25 to 3 mm in increments of 0.25 mm . The source fiber and the detector fibers are tilted toward each other.

Tables (2)

Tables Icon

Table 1 Sample Canonical Correlations for Perpendicular Fibers and the Corresponding Canonical Loadings R U ^ , z ( 1 ) Showing the Correlation Between U ^ k and the Predictor Variables

Tables Icon

Table 2 Sample Canonical Correlations for Tilted Fibers and the Corresponding Canonical Loadings R U ^ , z ( 1 ) Showing the Correlation Between U ^ k and the Predictor Variables

Equations (6)

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

r w 1 w 2 . w 3 = r w 1 w 2 r r w 2 w 3 w 1 w 3 ( 1 r w 1 w 3 2 ) ( 1 r w 2 w 3 2 ) ,
r w 1 w 2 . w 3 w 4 = r w 1 w 2 . w 3 r w 1 w 4 . w 3 r w 2 w 4 . w 3 ( 1 r w 1 w 4 . w 3 2 ) ( 1 r w 2 w 4 . w 3 2 ) ,
r μ s I i . μ a g = r μ s I i . μ a r μ s g . μ a r I i g . μ a ( 1 r μ s g . μ a 2 ) ( 1 r I i g . μ a 2 ) .
R = [ R 11 R 12 ( p × p ) ( p × q ) R 21 R 22 ( q × p ) ( q × q ) ] .
U ^ k = e ^ k R 11 1 / 2 z ( 1 ) ; V ^ k = f ^ k R 22 1 / 2 z ( 2 ) ,
R U ^ , z ( 1 ) = A ^ R 11 ; R V ^ , z ( 2 ) = B ^ R 22 .

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