OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 2 — Mar. 4, 2013
« Show journal navigation

Probing multifractality in tissue refractive index: prospects for precancer detection

Nandan Das, Subhasri Chatterjee, Jalpa Soni, Jaidip Jagtap, Asima Pradhan, Tapas K. Sengupta, Prasanta K. Panigrahi, I. Alex Vitkin, and Nirmalya Ghosh  »View Author Affiliations


Optics Letters, Vol. 38, Issue 2, pp. 211-213 (2013)
http://dx.doi.org/10.1364/OL.38.000211


View Full Text Article

Acrobat PDF (380 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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

Light scattering in biological tissue originates from spatial fluctuations of local refractive index (RI) in both the cellular and the extracellular compartments, with the spatial scale of fluctuations ranging from several nanometers to several micrometers [1

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

4

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

]. For many types of tissues, the spatial-scaling distribution of RI exhibits statistical self-similarity (fractality), and accordingly the scale-invariant inverse-power-law dependence of the elastic scattering signal (on either the wavelength or the angular variation of scattering) has been attributed to this self-similarity [2

2. J. M. Schmitt and G. Kumar, Opt. Lett. 21, 1310 (1996). [CrossRef]

5

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]

]. Recent studies have explored light-scattering models for quantification of the fractal micro-optical properties, namely, Hurst exponent (H) and fractal dimension (Df), for their potential applications in precancer detection [5

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]

8

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

]. Such models are usually based on a monofractal hypothesis, which assumes that the scaling properties of the RI spatial fluctuations are the same over the entire tissue region probed. However, considering the wide range of dimensions of inhomogeneities and the complex nature of the spatial correlations, the monofractal approximation may be unrealistic for many tissues. It is thus desirable to study and quantify the nature of multifractality of tissue RI (spatial) variations using a more general type of statistical multiresolution analysis. A multifractal signal is typically characterized by long-range correlations, nonstationarity in fluctuations, and different local scaling behavior [9

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]

]. This type of multiresolution analysis may yield additional diagnostic information, and the multifractal parameters may potentially serve as useful metrics for precancer detection. Moreover, information obtained from such studies may help in developing appropriate models for extraction and quantification of tissue multifractality from light-scattering signals.

We have therefore analyzed the spatial RI variations of human cervical tissues (in epithelium and connective-tissue layers) having different grades of precancers by a state-of-the-art tool for multifractal research, the multifractal detrended fluctuation analysis (MFDFA) [9

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]

]. In addition to exploring the well-accepted malignant progression of the epithelial cellular compartment of most tumors, our investigations on the connective tissue (stroma) morphology are motivated by the recent findings that the progression of cancer involves altered interactions between epithelial cells and the underlying stroma, and changes in stromal biology may precede and stimulate neoplastic progression in preinvasive disease [10

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

]. Quantification of the complex fractal-like architecture of stromal fibrous network may thus prove to be beneficial for this purpose.

We used a differential interference contrast (DIC) microscope (Olympus IX81, USA) to measure the spatial distribution of tissue RI. The tissues were histopathologically characterized (CIN or dysplasia grade I, II, and III) biopsy samples of human cervical tissues obtained from G. S. V. M. Medical College and Hospital in Kanpur, India. The unstained tissue sections (thickness 5μm, lateral dimension 4mm×6mm) were prepared on glass slides. The standard method employed was tissue dehydration, embedding in wax, sectioning under a rotary microtome, and subsequent dewaxing. Images were obtained separately from the epithelium and the connective tissue regions at a magnification of 60× and recorded using a CCD camera (ORCA-ERG, Hamamatsu) having 1344×1024 pixels (pixel dimension 6.45 μm). The width of the point spread function of the microscope was 0.36μm. The recorded images were unfolded (pixelwise) in one linear direction to obtain one-dimensional fluctuation series representing the spatial variation of tissue RI. These were then analyzed through (1) Fourier analysis and (2) MFDFA.

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.

Briefly, the profile Y(i) (spatial series of length N, i=1N) is first generated from the one-dimensional spatial index fluctuations. The profile is then divided into Ns=int(N/s) nonoverlapping segments b of equal length s. The local trend of the series (yb(i)) is determined for each segment b by least-square polynomial fitting and then subtracted from the segmented profiles to yield the detrended fluctuations. The resulting variance is determined for each segment as
F2(b,s)=1si=1s[Y{(b1)s+i}yb(i)]2.
(1)

The moment (q) dependent fluctuation function is then extracted by averaging over all the segments as
Fq(s)={12Nsb=12Ns[F2(b,s)]q/2N}1/q.
(2)

The procedure was performed twice on the series, starting from either end of the series [9

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]

]. The scaling behavior is subsequently determined by analyzing the variations of Fq(s) versus s for each value of q, assuming the general scaling function as
Fq(s)sh(q).
(3)

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. 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.

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

table-icon
View This Table

References

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]

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics
(290.0290) Scattering : Scattering
(170.6935) Medical optics and biotechnology : Tissue characterization

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: October 8, 2012
Revised Manuscript: December 11, 2012
Manuscript Accepted: December 11, 2012
Published: January 14, 2013

Virtual Issues
Vol. 8, Iss. 2 Virtual Journal for Biomedical Optics

Citation
Nandan Das, Subhasri Chatterjee, Jalpa Soni, Jaidip Jagtap, Asima Pradhan, Tapas K. Sengupta, Prasanta K. Panigrahi, I. Alex Vitkin, and Nirmalya Ghosh, "Probing multifractality in tissue refractive index: prospects for precancer detection," Opt. Lett. 38, 211-213 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ol-38-2-211


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1. Fig. 2. Fig. 3.
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited