Abstract

Multiresolution analysis on the spatial refractive index inhomogeneities in the epithelium and connective tissue regions of a human cervix reveals a clear signature of multifractality. Importantly, the derived multifractal parameters, namely, the generalized Hurst exponent and the width of the singularity spectrum, derived via multifractal detrended fluctuation analysis, shows interesting differences between tissues having different grades of precancers. The refractive-index fluctuations are found to be more anticorrelated, and the strength of multifractality is observed to be considerably stronger in the higher grades of precancers. These observations on the multifractal nature of tissue refractive-index variations may prove to be valuable for developing light-scattering approaches for noninvasive diagnosis of precancer and early-stage cancer.

© 2013 Optical Society of America

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References

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  1. V. V. Tuchin, L. Wang, and D. À. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).
  2. J. M. Schmitt and G. Kumar, Opt. Lett. 21, 1310 (1996).
    [CrossRef]
  3. N. N. Boustany, S. A. Boppart, and V. Backman, Annu. Rev. Biomed. Eng. 12, 285 (2010).
    [CrossRef]
  4. A. Wax and V. Backman, eds., Biomedical Applications of Light Scattering (McGraw-Hill, 2009).
  5. M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
    [CrossRef]
  6. M. Xu and R. R. Alfano, Opt. Lett. 30, 3051 (2005).
    [CrossRef]
  7. C. J. R. Sheppard, Opt. Lett. 32, 142 (2007).
    [CrossRef]
  8. I. R. Capoglu, J. D. Rogers, A. Taflove, and V. Backman, Opt. Lett. 34, 2679 (2009).
    [CrossRef]
  9. J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
    [CrossRef]
  10. N. Thekkek and R. Richards-Kortum, Nat. Rev. Cancer 8, 725 (2008).
    [CrossRef]

2010 (1)

N. N. Boustany, S. A. Boppart, and V. Backman, Annu. Rev. Biomed. Eng. 12, 285 (2010).
[CrossRef]

2009 (1)

2008 (1)

N. Thekkek and R. Richards-Kortum, Nat. Rev. Cancer 8, 725 (2008).
[CrossRef]

2007 (1)

2006 (1)

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

2005 (1)

2002 (1)

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

1996 (1)

Alfano, R. R.

Backman, V.

N. N. Boustany, S. A. Boppart, and V. Backman, Annu. Rev. Biomed. Eng. 12, 285 (2010).
[CrossRef]

I. R. Capoglu, J. D. Rogers, A. Taflove, and V. Backman, Opt. Lett. 34, 2679 (2009).
[CrossRef]

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Badizadegan, K.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Boone, C. W.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Boppart, S. A.

N. N. Boustany, S. A. Boppart, and V. Backman, Annu. Rev. Biomed. Eng. 12, 285 (2010).
[CrossRef]

Boustany, N. N.

N. N. Boustany, S. A. Boppart, and V. Backman, Annu. Rev. Biomed. Eng. 12, 285 (2010).
[CrossRef]

Bunde, A.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

Capoglu, I. R.

Feld, M. S.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Gopal, V.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Havlin, S.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

Hunter, M.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Kalashnikov, M.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Kantelhardt, J. W.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

Koscielny-Bunde, E.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

Kumar, G.

Popescu, G.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Richards-Kortum, R.

N. Thekkek and R. Richards-Kortum, Nat. Rev. Cancer 8, 725 (2008).
[CrossRef]

Rogers, J. D.

Schmitt, J. M.

Sheppard, C. J. R.

Stanley, H. E.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

Stoner, G. D.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Taflove, A.

Thekkek, N.

N. Thekkek and R. Richards-Kortum, Nat. Rev. Cancer 8, 725 (2008).
[CrossRef]

Tuchin, V. V.

V. V. Tuchin, L. Wang, and D. À. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

Wang, L.

V. V. Tuchin, L. Wang, and D. À. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

Wax, A.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Xu, M.

Zimnyakov, D. À.

V. V. Tuchin, L. Wang, and D. À. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

Zschiegner, S. A.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

Annu. Rev. Biomed. Eng. (1)

N. N. Boustany, S. A. Boppart, and V. Backman, Annu. Rev. Biomed. Eng. 12, 285 (2010).
[CrossRef]

Nat. Rev. Cancer (1)

N. Thekkek and R. Richards-Kortum, Nat. Rev. Cancer 8, 725 (2008).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, Phys. Rev. Lett. 97, 138102 (2006).
[CrossRef]

Physica A (1)

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, S. Havlin, and H. E. Stanley, Physica A 316, 87 (2002).
[CrossRef]

Other (2)

V. V. Tuchin, L. Wang, and D. À. Zimnyakov, Optical Polarization in Biomedical Applications (Springer-Verlag, 2006).

A. Wax and V. Backman, eds., Biomedical Applications of Light Scattering (McGraw-Hill, 2009).

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Figures (3)

Fig. 1.
Fig. 1.

DIC images of typical (a) grade I and (c) grade III dysplastic connective tissues. The corresponding Fourier power spectra are shown in (b) and (d), respectively (in natural logarithm scale). The two different selected ν ranges (lower and higher) exhibiting different power-law scaling are shown by red and green colors. The fits at the lower ν range (blue line), at the higher ν range (red line), and the overall fit (black line). The values for the power-law coefficients (slope β) and the corresponding estimate for the average Hurst exponents H (for overall fitting) are noted.

Fig. 2.
Fig. 2.

MFDFA analysis for grade I dysplastic connective tissue. The profile Y(i) (green dashed curve) and the local polynomial fit yb(i) of Eq. (1) (black solid curve), polynomial of degree 1, is shown here for a particular segment corresponding to a typical window size s=65 (top panel). The detrended fluctuations (for s=65) is displayed in the middle panel. The x axis represents the actual length scale (in micrometers). The log–log (natural logarithm) plot of the moment (q=6 to +6) dependent fluctuation function Fq(s) versus s [derived using Eq. (2)] is shown in the bottom panel.

Fig. 3.
Fig. 3.

Comparison of the variation of (a) generalized Hurst exponent h(q), derived (using Eq. 3), (b) classical multifractal scaling exponent τ(q) (derived via Eq. 4), and (c) the singularity spectrum f(α)(derived using Eq. 5) for grade I and grade III dysplastic connective tissues.

Tables (1)

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Table 1. Summary of MFDFA Analysis on RI Fluctuations of Cervical Tissues

Equations (5)

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

F2(b,s)=1si=1s[Y{(b1)s+i}yb(i)]2.
Fq(s)={12Nsb=12Ns[F2(b,s)]q/2N}1/q.
Fq(s)sh(q).
τ(q)=qh(q)1.
α=dτdq,f(α)=qατ(q),

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