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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 20 — Sep. 26, 2011
  • pp: 19717–19730
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Differing self-similarity in light scattering spectra: a potential tool for pre-cancer detection

Sayantan Ghosh, Jalpa Soni, Harsh Purwar, Jaidip Jagtap, Asima Pradhan, Nirmalya Ghosh, and Prasanta K. Panigrahi  »View Author Affiliations


Optics Express, Vol. 19, Issue 20, pp. 19717-19730 (2011)
http://dx.doi.org/10.1364/OE.19.019717


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Abstract

The fluctuations in the elastic light scattering spectra of normal and dysplastic human cervical tissues analyzed through wavelet transform based techniques reveal clear signatures of self-similar behavior in the spectral fluctuations. The values of the scaling exponent observed for these tissues indicate the differences in the self-similarity for dysplastic tissues and their normal counterparts. The strong dependence of the elastic light scattering on the size distribution of the scatterers manifests in the angular variation of the scaling exponent. Interestingly, the spectral fluctuations in both these tissues showed multi-fractality (non-stationarity in fluctuations), the degree of multi-fractality being marginally higher in the case of dysplastic tissues. These findings using the multi-resolution analysis capability of the discrete wavelet transform can contribute to the recent surge in the exploration for non-invasive optical tools for pre-cancer detection.

© 2011 OSA

1. Introduction

The use of optical techniques for the study of biomedical systems is a rapidly developing field that has seen a dramatic expansion in the recent years, partly due to tremendous progress in the field of lasers, fiber optics and associated technologies. Both medicine and biotechnology require appropriate instrumentation to analyze and monitor biological systems for deviations from normality. Optical methods, due to their non-invasive nature, are providing novel approaches for medical imaging, diagnosis and therapy. Considerable efforts have been made in the recent past to use optical techniques such as fluorescence spectroscopy [1

1. N. Ramanujam, “Fluorescence spectroscopy of neoplastic and non-neoplastic tissues,” Neoplasia 2, 89–117 (2000). [CrossRef] [PubMed]

6

6. N. Ghosh, S. K. Majumder, and P. K. Gupta, “Polarized fluorescence spectroscopy of human tissues,” Opt. Lett. 27, 2007–2009 (2002). [CrossRef]

], Raman spectroscopy [7

7. A. S. Haka, K. E. Shafer-Peltier, M. Fitzmaurice, J. Crowe, R. R. Dasari, and M. S. Feld, “Diagnosing breast cancer by using Raman spectroscopy,” Proc. Natl. Acad. Sci. (USA) 102, 12371–12376 (2005). [CrossRef]

] and elastic scattering spectroscopy [8

8. N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. 12, 285–314 (2010). [CrossRef] [PubMed]

] for quantitative and early diagnosis of various diseases. Several optical imaging techniques like coherence gated imaging, polarization gated imaging and diffuse optical tomography are also being actively pursued for obtaining high resolution (micron scale) images of biological objects and their underlying structure [9

9. J. Fujimoto, “Optical coherence tomography for ultrahigh resolution in vivo imaging,” Nat. Biotechnol. 21, 1361–1367 (2003). [CrossRef] [PubMed]

13

13. S. L. Jacques, J. C. Ramella-Roman, and K. Lee, “Imaging skin pathology with polarized light,” J. Biomed. Opt. 7, 329–340 (2002). [CrossRef] [PubMed]

].

For optical diagnosis, elastic and inelastic light scattering spectra from tissues are exploited. The in-elastically scattered light (via processes like fluorescence and Raman) contain useful biochemical information about the sample that can be employed for probing subtle biochemical changes as signatures of disease progression. On the other hand, elastically scattered light from biological tissues contain rich morphological and functional information of potential biomedical importance [8

8. N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. 12, 285–314 (2010). [CrossRef] [PubMed]

, 14

14. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4, 717–719 (2007). [CrossRef] [PubMed]

27

27. C.-C. Yu, C. Lau, G. O’Donoghue, J. Mirkovic, S. McGee, L. Galindo, A. Elackattu, E. Stier, G. Grillone, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Quantitative spectroscopic imaging for non-invasive early cancer detection,” Opt. Express 16, 16227–16239 (2008). [CrossRef] [PubMed]

]. Both the angular and wavelength dependence of the elastically scattered light from tissue can be analyzed to extract and quantify subtle morphological changes taking place during progression of a disease [16

16. M. Kalashnikov, W. Choi, C.-C. Yu, Y. Sung, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Assessing light scattering of intracellular organelles in single intact living cells,” Opt. Express 17, 19674–19681 (2009). [CrossRef] [PubMed]

20

20. L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine structure in reflectance from biological tissue: a new technique for measuring nuclear size distribution,” Phys. Rev. Lett. 80, 627–630 (1998). [CrossRef]

, 23

23. N. Ghosh, P. Buddhiwant, A. Uppal, S. K. Majumder, H. S. Patel, and P. K. Gupta, “Simultaneous determination of size and refractive index of red blood cells by light scattering measurements,” Appl. Phys. Lett. 88, 084101 (2006). [CrossRef]

, 24

24. N. Ghosh, S. K. Mohanty, S. K. Majumder, and P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissue,” Appl. Opt. 40, 176–184 (2001). [CrossRef]

], and thus may be explored as a sensitive tool for early diagnosis. This would however involve appropriate modeling of light scattering in complex random media like tissues, and the development of suitable approaches to extract/interpret the morphological information contained in the elastic light scattering signal.

The spatial fluctuation of the refractive index in biological tissues arising from scatterers ranging in sizes from a few nanometers to a few micrometers give rise to elastic scattering [8

8. N. N. Boustany, S. A. Boppart, and V. Backman, “Microscopic imaging and spectroscopy with scattered light,” Annu. Rev. Biomed. Eng. 12, 285–314 (2010). [CrossRef] [PubMed]

, 22

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

]. The lack of sufficient knowledge about the complex dielectric fluctuations in the tissues pose a formidable problem in the exact modeling of light scattering. Nevertheless, several efforts have been made in the recent years using electromagnetic (EM) theory based approaches like Mie theory and Born approximation to model and understand the scattering process from biological tissues [28

28. İ. R. Çapoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett. 34, 2679–2681 (2009). [CrossRef] [PubMed]

32

32. T. T. Wu, J. Y. Qu, and M. Xu, “Unified Mie and fractal scattering by biological cells and subcellular structures,” Opt. Lett. 32, 2324–2326 (2007). [CrossRef] [PubMed]

]. It has also been shown that the refractive index fluctuations in biological tissues are fractal in nature which can be used to understand the structural changes in tissues induced by diseases [18

18. R. Graf and A. Wax, “Nuclear morphology measurements using Fourier domain low coherence interferometry,” Opt. Express 13, 4693–4698 (2005). [CrossRef]

, 29

29. M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006). [CrossRef] [PubMed]

, 33

33. W. Gao, “Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light,” J. Biomed. Opt. 15, 030502 (2010). [CrossRef] [PubMed]

35

35. J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21, 1310–1312 (1996). [CrossRef] [PubMed]

].

Since the tissue morphology dependent refractive index fluctuations are recorded in the elastic scattering spectra [36

36. L. Perelman, “Optical diagnostic technology based on light scattering spectroscopy for early cancer detection,” Expert Rev. Med. Devices 3, 787–803 (2006). [CrossRef]

], analysis of elastically scattered spectral fluctuations using sophisticated fluctuation analysis tools might facilitate extraction and quantification of subtle morphological changes associated with early stages of cancer. The scaling behavior which is generally assumed to be global (mono-fractal), has been shown to manifest in the local fluctuations in various physical processes [37

37. H. Hurst, “Long-term storage capacity of reservoirs,” Trans. Am. Soc. Civ. Eng. 116, 770–808 (1951).

, 38

38. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).

] and has been characterized using Multi-Fractal De-trended Fluctuation Analysis(for example see [39

39. J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley, “Multifractal detrended fluctuation analysis of nonstationary time series,” Physica A 316, 87–114 (2002). [CrossRef]

]). Wavelet Based Multi-Fractal Detrended Fluctuation Analysis (WB-MFDFA) is one other state-of-the-art technique that can be used for extracting and quantifying the self similarity at varying length scales associated with the structural changes associated with cancer progression due to the inherent use of fractal like transformation kernels.

This article is organized as follows: Fourier and power spectrum analysis is reviewed in 2.1, discrete wavelet transform in 2.2, wavelet based power law analysis in 2.3, wavelet based multi-fractal de-trended fluctuation analysis in 2.4 and correlation based analysis in 2.5. Sec. 3 describes the experimental methods for light scattering measurements from tissues. Sec. 4 deals with our findings from the analysis and contains a discussion of the same in the context of the differences between the normal and dysplastic samples. In Sec. 5 we conclude with the prospect of pre-cancer detection using light scattering techniques combined with novel fluctuation analysis methods.

2. Theory

2.1. Fourier analysis and power law spectrum

2.2. A brief review of wavelet transforms

Wavelet Transforms [47

47. I. Daubechies, Ten Lectures on Wavelets, 1st ed., CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM: Society for Industrial and Applied Mathematics, 1992). [CrossRef]

50

50. S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell.11, 674–693 (1989). [CrossRef]

], in both the forms of Discrete and Continuous transforms in the recent years have emerged as an invaluable tool in the field of data analysis and interpretation. Here, we will briefly review the Discrete Wavelet Transform (DWT).

In DWT, two functions, namely, ϕ(n) and ψ(n), called the father and the mother wavelets respectively, form the kernels. They satisfy the admissibility conditions: ∫ ϕ(n)dn < ∞, ∫ ψ(n)dn = 0, ∫ ϕ *(n)ψ(n)dn = 0, ∫ |ϕ(n)|2 dn = ∫ |ψ(n)|2 dn = 1. The scaled and translated versions of the mother wavelet ψ(n) are called the daughter wavelets
ψs,m(n)=2s/2ψ(2snm),m,s+,
(4)
which form a complete set and differ from the former in terms of their height and width. At the sth scale, the height and width of the daughter wavelet are 2s and 2s/2 of that of the mother wavelet respectively. s and m are the scaling and translation parameters.

The DWT for a function f(t) is given by,
f(t)=m=amϕm(t)+m=s0lds,mψs,m(t),
(5)
the coefficient am (called the approximation coefficient) extracts the trend and d s,m (called the detail coefficient) extracts the details or fluctuations from the signal. Here, l = ⌊log(N)/log(2)⌋ is the upper bound for taking the maximum scale for analysis above which the edge effects corrupt the wavelet coefficients giving rise to spurious results. This mathematical artifact is explained by the cone of influence [49

49. C. Torrence and G. Compo, “A practical guide to wavelet analysis,” Bull. Am. Meteorol. Soc. 79, 61–78 (1998). [CrossRef]

].

2.3. Wavelet Fluctuation Power Law Analysis

Fig. 1 Schematic representation of the fluctuation extraction algorithm (adapted from [51]).

2.4. Wavelet Based Multi Fractal De-trended Fluctuation Analysis

2.5. Correlation based analysis

3. Experimental materials and methods

Pathologically graded (CIN or dysplastic) biopsy samples of human cervical tissues cut into slices were used for light scattering measurements and analysis. The tissue sections (thickness ∼ 5μm, lateral dimension ∼ 4mm ×6mm) were prepared on glass slides. The standard method employed for the preparation of the sections is tissue dehydration, embedding in wax and subsequent sectioning under a rotary microtome [55

55. J. D. Bancroft and M. Gamble, Theory and Practice of Histopathological Techniques, 5th ed. (Churchill Livingstone, 2002).

]. The prepared slides were then examined under the microscope by the pathologists for histopathological characterization. The normal counterparts were obtained from the adjacent normal area of the resected tissues. The tissue samples were obtained from G.S.V.M. Medical College and Hospital, Kanpur, India. A total number of fifteen tissue samples were collected from patients in the age group 35 – 60 years. Out of these, eight samples were included in the spectroscopic study. Among these, four were histopathologically characterized as dysplastic and the other four samples were pathologically normal. All the cervical tissues included in this study were squamous type.

A schematic representation of the experimental set-up is shown in Fig. 2. The angle resolved elastic scattering spectra were recorded using a goniometric arrangement for angular range θ : 10° – 150° at 10° intervals. White light output from a Xe-lamp (Newport USA, 50 – 5000 W) was collimated using a combination of lenses and were made incident on the sample kept at the center of the goniometer. The spot-size incident on the sample was controlled by a variable aperture (∼ 1mm). The scattered light from the sample was collimated by a pair of lenses and was then focused into a collecting fiber probe, the distal end of which was coupled to a spectrometer (Ocean Optics HR2000).

Fig. 2 (Color Online) Schematic representation of the experimental set-up for the light scattering measurement. The sample mounted on a goniometer is illuminated by a white light collimated from a Xe-source and the scattered light is then collimated using two lenses (L 2 and L 3) and recorded using a Fiber-Optic Spectrometer. The θf represents the forward scattering angle, while θb is the backward scattering angle. The forward and backward scattering process are represented by red and blue lines respectively while the Fiber-Optic Spectrometer set-up is shown in green. 0 ≤ θ ≤ 180° is the scattering angle at which the spectra were recorded. Note that the rectangular shape of the glass slides prevented acquiring spectra in the angular range 80° – 110°.

The resolution of the spectrometer was 1.8 nm (∼ 4 pixel resolution, spectral coverage 200 – 1100 nm, number of pixels −2048). Note that the analyzed spectral fluctuation window (in nm) was always larger than the resolution of the spectrometer. This follows because in our analysis, we have used Db – 4 wavelets and the minimum window size (corresponding to level 1) was 8, which in term of wavelength was ∼ 3.5nm. The spectroscopic data for the wavelength range 400 −800 nm was used in fluctuation analysis.

The selection of the angular interval (Δθ = 10°) in our angle-resolved elastic scattering spectroscopic studies, was based on the range of scattering vector ( q=2×2πλsin(θ2)) spanned by the varying wavelength and scattering angles (λmin = 400 nm, λmax = 800 nm, Δλ = 400 nm; θmin = 10°, θmax = 150°; resulting in Δq ∼ 29μm −1). The idea was to cover the entire range of variation of Δq by varying scattering angle θ. For the smallest scattering angle used in our study (θmin = 10°), the required angular interval Δθ was found to be ∼ 10°. Note that at larger scattering angles, one may not need to acquire spectra at angular interval of 10°, to capture the range of variation Δq. However, in order to be consistent, the angular interval of Δθ = 10° was used for the range of scattering angles studied. The scattering spectra recorded from the tissue samples at each scattering angles were normalized by the lamp spectra recorded from the glass slides alone. Since for fluctuation analysis spectral shape rather than the absolute intensity information is important, the angle-resolved scattering spectra were not normalized for absolute scattered intensities. Thus normalized angle-resolved scattering spectra were then subjected to the fluctuation analysis.

4. Results and discussions

Typical peak normalized elastic light scattering spectra recorded from normal and dysplastic tissues are shown in Fig. 3. Representative spectra for forward and back-scattering are shown for θ = 10° and θ = 150° in Figs. 3(a) and 3(b) respectively. The broader structures observed in the scattering spectra possibly originates due to contributions of the regular and large scale scattering inhomogeneities (such as epithelial cell nuclei) [15

15. R. S. Gurjar, V. Backman, L. T. Perelman, I. Georgakoudi, K. Badizadegan, I. Itzkan, R. R. Dasari, and M. S. Feld, “Imaging human epithelial properties with polarized light-scattering spectroscopy,” Nat. Med. 7, 1245–1248 (2001). [CrossRef] [PubMed]

]. In contrast, the signatures of the small scale inhomogeneities (index variations in the sub-cellular micro-structures or intracellular organelles) manifest as much more complex and finer fluctuations in the scattering spectra and are thus difficult to identify. Never-the-less the apparent changes in the spectral shape between the forward and the backward scattering angles underscores the fact that the larger and the smaller sized scattering structures contribute differently to the scattering spectra recorded at the forward and the backward scattering angles. Indeed, it has been shown that the contribution of larger scatterers (like cells, nuclei) are more dominant in the spectra recorded at forward angles, whereas the spectra recorded at back-scattering angles are typically more influenced by the smaller sized scatterers [26

26. 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]

].

Fig. 3 Typical peak normalized elastic light scattering spectra recorded from normal and dysplastic tissues at scattering angles (a) θ = 10° and (b) θ = 150°.

Although it is difficult to make a one-to-one correspondence between the intensity fluctuations and local refractive index fluctuations in the morphological structures, some information about the morphology can still be inferred from the light scattering spectral fluctuations. It has been shown that with Born approximation, the light scattering spectrum can be represented as a Fourier transform power spectrum of the local refractive index fluctuations. Thus, the observed spectral fluctuations contain information about the corresponding refractive index fluctuations in the Fourier domain as discussed below.

The results of the Fourier analysis (following Sec. 2.1) on the light scattering spectra for different scattering angles are shown in Fig. 4. The variation of the determined scaling exponent α(θ) as a function of scattering angle θ for normal and dysplastic tissues are shown in this figure. The values are the average values over the sample size and the error bars represent standard deviations. Interesting differences can be noted in the values for α between the normal and the dysplastic tissues. While the value for α for the dysplastic tissues are higher at forward scattering angles, the reverse is the trend in backscattering angles. For example, in the forward scattering angles (10° – 70°), the dysplastic tissues show ∼ 1.186 ≤ αc ≤ 1.322, in the same region however, the normal tissues show ∼ 1.106 ≤ αn ≤ 1.242. Similarly, in the backscattering angles (130° – 150°), the values for α lie in the range ∼ 1.338 ≤ αn ≤ 1.397 for normal, and ∼ 1.119 ≤ αc ≤ 1.251 for dysplastic tissues. The higher values of the power-law coefficient α corresponds to higher values of the Hurst scaling exponent H, indicative of “coarseness” of the fluctuations tending towards sub-fractal behavior; whereas at higher angles (130° – 150°), α values are observed to be smaller in dysplastic samples than that for normal samples in the same region indicating more “roughness” in the fluctuations, signifying a trend towards extreme fractality.

Fig. 4 The variation of the mean values of the scaling exponent α(θ) as a function of scattering angle θ for normal and dysplastic tissues, as determined from Fourier analysis. The error bars represent standard deviations.

Fig. 5 The variation of the mean values of the power law exponent α with the wavelet scale s at representative forward and backward scattering angles θ for (a) normal and (b) dysplastic tissues. The error bars represent standard deviations.

As discussed in Sec. 2.4, we have depicted the mean values of the Hurst exponent (H = h(q = 2)) as a function of the scattering angle θ in Fig. 6; the error bars representing standard deviations. Once again the average values for H are found to be higher for dysplastic tissues in the forward scattering angles (0.214 ±0.003 ≤ Hc ≤ 0.332 ±0.009 and 0.187 ±0.038 ≤ Hn ≤ 0.308 ± 0.062). In contrast, the values for H of the normal tissues are higher in the backscattering angles (0.284 ±0.027 ≤ Hn ≤ 0.312 ±0.003 and 0.251 ±0.003 ≤ Hc ≤ 0.264 ±0.032). This is consistent with the results presented in Figs. 4 and 5.

Fig. 6 The variation of the mean values for the Hurst parameter, H = h(q = 2) as a function of the scattering angle θ for normal and dysplastic tissues, as determined from WB-MFDFA analysis. The error bars represent standard deviations.

Fig. 8 The singularity spectrum f(β) plotted against β at all scattering angles θ for (a) typical normal tissue and (b) typical dysplastic tissue.
Fig. 7 The scaling function h(q) at different forward and backward scattering angles for (a) typical normal tissue and (b) typical dysplastic tissue. The weaker q dependence of h(q) for normal samples in the forward scattering angles (50° – 70°) is indicative of a trend towards mono-fractality, while the stronger dependence of the scaling function on the order of moments for dysplastic sample is indicative of a multi-fractal trend.

The spectral correlation matrices are shown for typical normal and dysplastic tissues (same tissues, the results of which are used in Figs. 7 and 8) in Fig. 9, following Sec. 2.5. It is clear from Figs. 9(a) and 9(b) that though the normal tissues do not show any distinct correlation sectors in this domain, other than the expected correlation that would occur at neighboring wavelengths; dysplastic tissues show the presence of three dominant sectors. It must also be noted that the range of correlation increases from 0.70 – 1.00 for normal to 0.97 – 1.00 for dysplasia. This indicates a higher correlated behavior of the dysplastic tissues than the normal tissues in addition to domain formations in the spectral range. This possibly arises due to the fact that during dysplastic progression, the homogeneous cell morphology gives way to a more fragmented and heterogeneous structure.

Fig. 9 (Color Online) The correlation matrices in the wavelength domain for (a) typical normal tissue and (b) typical dysplastic tissue. The results are shown for the same tissues whose results were presented in Figs. 7 and 8.

5. Conclusion

In conclusion, we have applied a combined Fourier based and discrete wavelet based analysis on the fluctuations extracted from the elastic light scattering spectra of normal and dysplastic human cervical tissues. This approach clearly revealed otherwise hidden signatures of self-similarity in spectral fluctuation for both normal and dysplastic tissues, with interesting differences in the nature of self-similarity. Wavelet Based Multi-Fractal De-trended Fluctuation Analysis (WB-MFDFA) of these fluctuations indicated the existence of multi-fractal nature. Dysplastic tissues showed marginally higher multi-fractality compared to their normal counterparts. The scaling exponent was observed to have angular dependence, possibly arising from the size distribution of the scatterers present in such complex systems. Interestingly, while the value for the fractal scaling exponent α and the Hurst parameter H for the dysplastic tissues were higher at forward scattering angles (20° – 60°), the reverse was the trend in backscattering angles (120° – 150°). Initial results of this study thus show that the fractal scaling exponent (α), Hurst parameter (H) and the strength of multi-fractality of light scattering spectral fluctuations, derived and quantified via the multi-resolution fluctuation analysis, hold promise as potentially useful diagnostic parameters. We should however, note that the initial results presented in this manuscript are based on data acquired from a limited number of tissue samples. A more rigorous study on larger population of samples is currently underway to evaluate the diagnostic potential of this approach. Extraction and quantification of the multi-fractal nature of fluctuations in tissue using such multi-resolution analysis combined with appropriately designed light scattering measurement methods may ultimately lead to the development of non-invasive optical tools for pre-cancer detection.

Acknowledgments

The authors would like to acknowledge Dr. Asha Agarwal, G. S. V. M. Medical College and Hospital, Kanpur, for providing the tissue slides and for fruitful discussions. SG and JS would like to thank P. Manimaran for helpful discussions. HP would like to thank IIT-K where a part of the work was performed. Corresponding author’s phone: +913473279130 (extn: 206).

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N. Ghosh, P. Buddhiwant, A. Uppal, S. K. Majumder, H. S. Patel, and P. K. Gupta, “Simultaneous determination of size and refractive index of red blood cells by light scattering measurements,” Appl. Phys. Lett. 88, 084101 (2006). [CrossRef]

24.

N. Ghosh, S. K. Mohanty, S. K. Majumder, and P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissue,” Appl. Opt. 40, 176–184 (2001). [CrossRef]

25.

Y. L. Kim, V. M. Turzhitsky, Y. Liu, H. Subramanian, and P. Pradhan, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt. 11, 041125 (2006). [CrossRef] [PubMed]

26.

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]

27.

C.-C. Yu, C. Lau, G. O’Donoghue, J. Mirkovic, S. McGee, L. Galindo, A. Elackattu, E. Stier, G. Grillone, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Quantitative spectroscopic imaging for non-invasive early cancer detection,” Opt. Express 16, 16227–16239 (2008). [CrossRef] [PubMed]

28.

İ. R. Çapoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett. 34, 2679–2681 (2009). [CrossRef] [PubMed]

29.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006). [CrossRef] [PubMed]

30.

M. Xu and R. R. Alfano, “Fractal mechanisms of light scattering in biological tissue and cells,” Opt. Lett. 30, 3051–3053 (2005). [CrossRef] [PubMed]

31.

C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett. 32, 142–144 (2007). [CrossRef]

32.

T. T. Wu, J. Y. Qu, and M. Xu, “Unified Mie and fractal scattering by biological cells and subcellular structures,” Opt. Lett. 32, 2324–2326 (2007). [CrossRef] [PubMed]

33.

W. Gao, “Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light,” J. Biomed. Opt. 15, 030502 (2010). [CrossRef] [PubMed]

34.

A. Wax, C. Yang, M. G. Mller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, and M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res. 63, 3556–3559 (2003). [PubMed]

35.

J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett. 21, 1310–1312 (1996). [CrossRef] [PubMed]

36.

L. Perelman, “Optical diagnostic technology based on light scattering spectroscopy for early cancer detection,” Expert Rev. Med. Devices 3, 787–803 (2006). [CrossRef]

37.

H. Hurst, “Long-term storage capacity of reservoirs,” Trans. Am. Soc. Civ. Eng. 116, 770–808 (1951).

38.

B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).

39.

J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley, “Multifractal detrended fluctuation analysis of nonstationary time series,” Physica A 316, 87–114 (2002). [CrossRef]

40.

P. Manimaran, P. K. Panigrahi, and J. C. Parikh, “Wavelet analysis and scaling properties of time series,” Phys. Rev. E 72, 046120 (2005). [CrossRef]

41.

P. Manimaran, P. Panigrahi, and J. Parikh, “Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets,” Physica A 388, 2306–2314 (2009). [CrossRef]

42.

S. Gupta, M. Nair, A. Pradhan, N. Biswal, N. Agarwal, A. Agarwal, and P. Panigrahi, “Wavelet-based characterization of spectral fluctuations in normal, benign, and cancerous human breast tissues,” J. Biomed. Opt. 10, 054012 (2005). [CrossRef] [PubMed]

43.

N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron. 9, 154–161 (2003). [CrossRef]

44.

A. Gharekhan, S. Arora, K. Mayya, P. Panigrahi, M. Sureshkumar, and A. Pradhan, “Characterizing breast cancer tissues through the spectral correlation properties of polarized fluorescence,” J. Biomed. Opt. 13, 054063 (2008). [CrossRef] [PubMed]

45.

A. Gharekhan, S. Arora, P. Panigrahi, and A. Pradhan, “Distinguishing cancer and normal breast tissue autofluorescence using continuous wavelet transform,” IEEE J. Sel. Top. Quantum Electron. 16, 893–899 (2010). [CrossRef]

46.

A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt. 16, 087003 (2011). [CrossRef] [PubMed]

47.

I. Daubechies, Ten Lectures on Wavelets, 1st ed., CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM: Society for Industrial and Applied Mathematics, 1992). [CrossRef]

48.

M. Farge, “Wavelet transforms and their applications to turbulence,” Annu. Rev. Fluid Mech. 24, 395–458 (1992). [CrossRef]

49.

C. Torrence and G. Compo, “A practical guide to wavelet analysis,” Bull. Am. Meteorol. Soc. 79, 61–78 (1998). [CrossRef]

50.

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell.11, 674–693 (1989). [CrossRef]

51.

S. Ghosh, P. Manimaran, and P. K. Panigrahi, “Characterizing multi-scale self-similar behavior and non-statistical properties of financial time series,” Physica A 390, 4304–4316 (2011). [CrossRef]

52.

A. Eke, P. Herman, L. Kocsis, and L. R. Kozak, “Fractal characterization of complexity in temporal physiological signals,” Physiol. Meas. 23, R1–R38 (2002). [CrossRef] [PubMed]

53.

H. E. Stanley and P. Meakin, “Multifractal phenomena in physics and chemistry,” Nature 335, 405–409 (1988). [CrossRef]

54.

P. Šeba, “Random matrix analysis of human EEG data,” Phys. Rev. Lett. 91, 198104 (2003).

55.

J. D. Bancroft and M. Gamble, Theory and Practice of Histopathological Techniques, 5th ed. (Churchill Livingstone, 2002).

OCIS Codes
(100.7410) Image processing : Wavelets
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(290.0290) Scattering : Scattering
(170.6935) Medical optics and biotechnology : Tissue characterization

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: July 14, 2011
Revised Manuscript: August 23, 2011
Manuscript Accepted: August 25, 2011
Published: September 23, 2011

Virtual Issues
Vol. 6, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Sayantan Ghosh, Jalpa Soni, Harsh Purwar, Jaidip Jagtap, Asima Pradhan, Nirmalya Ghosh, and Prasanta K. Panigrahi, "Differing self-similarity in light scattering spectra: a potential tool for pre-cancer detection," Opt. Express 19, 19717-19730 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-20-19717


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  24. N. Ghosh, S. K. Mohanty, S. K. Majumder, and P. K. Gupta, “Measurement of optical transport properties of normal and malignant human breast tissue,” Appl. Opt.40, 176–184 (2001). [CrossRef]
  25. Y. L. Kim, V. M. Turzhitsky, Y. Liu, H. Subramanian, and P. Pradhan, “Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening,” J. Biomed. Opt.11, 041125 (2006). [CrossRef] [PubMed]
  26. 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]
  27. C.-C. Yu, C. Lau, G. O’Donoghue, J. Mirkovic, S. McGee, L. Galindo, A. Elackattu, E. Stier, G. Grillone, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Quantitative spectroscopic imaging for non-invasive early cancer detection,” Opt. Express16, 16227–16239 (2008). [CrossRef] [PubMed]
  28. İ. R. Çapoğlu, J. D. Rogers, A. Taflove, and V. Backman, “Accuracy of the Born approximation in calculating the scattering coefficient of biological continuous random media,” Opt. Lett.34, 2679–2681 (2009). [CrossRef] [PubMed]
  29. M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the born approximation: a new model for precancer detection,” Phys. Rev. Lett.97, 138102 (2006). [CrossRef] [PubMed]
  30. M. Xu and R. R. Alfano, “Fractal mechanisms of light scattering in biological tissue and cells,” Opt. Lett.30, 3051–3053 (2005). [CrossRef] [PubMed]
  31. C. J. R. Sheppard, “Fractal model of light scattering in biological tissue and cells,” Opt. Lett.32, 142–144 (2007). [CrossRef]
  32. T. T. Wu, J. Y. Qu, and M. Xu, “Unified Mie and fractal scattering by biological cells and subcellular structures,” Opt. Lett.32, 2324–2326 (2007). [CrossRef] [PubMed]
  33. W. Gao, “Square law between spatial frequency of spatial correlation function of scattering potential of tissue and spectrum of scattered light,” J. Biomed. Opt.15, 030502 (2010). [CrossRef] [PubMed]
  34. A. Wax, C. Yang, M. G. Mller, R. Nines, C. W. Boone, V. E. Steele, G. D. Stoner, R. R. Dasari, and M. S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Res.63, 3556–3559 (2003). [PubMed]
  35. J. M. Schmitt and G. Kumar, “Turbulent nature of refractive-index variations in biological tissue,” Opt. Lett.21, 1310–1312 (1996). [CrossRef] [PubMed]
  36. L. Perelman, “Optical diagnostic technology based on light scattering spectroscopy for early cancer detection,” Expert Rev. Med. Devices3, 787–803 (2006). [CrossRef]
  37. H. Hurst, “Long-term storage capacity of reservoirs,” Trans. Am. Soc. Civ. Eng.116, 770–808 (1951).
  38. B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, 1982).
  39. J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley, “Multifractal detrended fluctuation analysis of nonstationary time series,” Physica A316, 87–114 (2002). [CrossRef]
  40. P. Manimaran, P. K. Panigrahi, and J. C. Parikh, “Wavelet analysis and scaling properties of time series,” Phys. Rev. E72, 046120 (2005). [CrossRef]
  41. P. Manimaran, P. Panigrahi, and J. Parikh, “Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets,” Physica A388, 2306–2314 (2009). [CrossRef]
  42. S. Gupta, M. Nair, A. Pradhan, N. Biswal, N. Agarwal, A. Agarwal, and P. Panigrahi, “Wavelet-based characterization of spectral fluctuations in normal, benign, and cancerous human breast tissues,” J. Biomed. Opt.10, 054012 (2005). [CrossRef] [PubMed]
  43. N. Agarwal, S. Gupta, A. Pradhan, K. Vishwanathan, and P. Panigrahi, “Wavelet transform of breast tissue fluorescence spectra: a technique for diagnosis of tumors,” IEEE J. Sel. Top. Quantum Electron.9, 154–161 (2003). [CrossRef]
  44. A. Gharekhan, S. Arora, K. Mayya, P. Panigrahi, M. Sureshkumar, and A. Pradhan, “Characterizing breast cancer tissues through the spectral correlation properties of polarized fluorescence,” J. Biomed. Opt.13, 054063 (2008). [CrossRef] [PubMed]
  45. A. Gharekhan, S. Arora, P. Panigrahi, and A. Pradhan, “Distinguishing cancer and normal breast tissue autofluorescence using continuous wavelet transform,” IEEE J. Sel. Top. Quantum Electron.16, 893–899 (2010). [CrossRef]
  46. A. H. Gharekhan, S. Arora, A. N. Oza, M. B. Sureshkumar, A. Pradhan, and P. K. Panigrahi, “Distinguishing autofluorescence of normal, benign, and cancerous breast tissues through wavelet domain correlation studies,” J. Biomed. Opt.16, 087003 (2011). [CrossRef] [PubMed]
  47. I. Daubechies, Ten Lectures on Wavelets, 1st ed., CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM: Society for Industrial and Applied Mathematics, 1992). [CrossRef]
  48. M. Farge, “Wavelet transforms and their applications to turbulence,” Annu. Rev. Fluid Mech.24, 395–458 (1992). [CrossRef]
  49. C. Torrence and G. Compo, “A practical guide to wavelet analysis,” Bull. Am. Meteorol. Soc.79, 61–78 (1998). [CrossRef]
  50. S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell.11, 674–693 (1989). [CrossRef]
  51. S. Ghosh, P. Manimaran, and P. K. Panigrahi, “Characterizing multi-scale self-similar behavior and non-statistical properties of financial time series,” Physica A390, 4304–4316 (2011). [CrossRef]
  52. A. Eke, P. Herman, L. Kocsis, and L. R. Kozak, “Fractal characterization of complexity in temporal physiological signals,” Physiol. Meas.23, R1–R38 (2002). [CrossRef] [PubMed]
  53. H. E. Stanley and P. Meakin, “Multifractal phenomena in physics and chemistry,” Nature335, 405–409 (1988). [CrossRef]
  54. P. Šeba, “Random matrix analysis of human EEG data,” Phys. Rev. Lett.91, 198104 (2003).
  55. J. D. Bancroft and M. Gamble, Theory and Practice of Histopathological Techniques, 5th ed. (Churchill Livingstone, 2002).

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