Tissue multifractality and Born approximation in analysis of light scattering: a novel approach for precancers detection

Abstract

Multifractal, a special class of complex self-affine processes, are under recent intensive investigations because of their fundamental nature and potential applications in diverse physical systems. Here, we report on a novel light scattering-based inverse method for extraction/quantification of multifractality in the spatial distribution of refractive index of biological tissues. The method is based on Fourier domain pre-processing via the Born approximation, followed by the Multifractal Detrended Fluctuation Analysis. The approach is experimentally validated in synthetic multifractal scattering phantoms, and tested on biopsy tissue slices. The derived multifractal properties appear sensitive in detecting cervical precancerous alterations through an increase of multifractality with pathology progression, demonstrating the potential of the developed methodology for novel precancer biomarker identification and tissue diagnostic tool. The novel ability to delineate the multifractal optical properties from light scattering signals may also prove useful for characterizing a wide variety of complex scattering media of non-biological origin.

Fractal propagation method enables realistic optical microscopy simulations in biological tissues

“…Qualitatively, D f dictates the “texture” or degree of fluctuation between neighboring voxels (i.e., smooth or rough), l c dictates the spatial size of the fluctuations, and ${\sigma }_n^2$ dictates the overall magnitude of the fluctuations. This concept, which has been used extensively for modeling atmospheric refractive index turbulence due to temperature fluctuations [39], was first proposed as a model of biological tissue by Schmitt et al and has been subsequently furthered by a number of groups, as well as unified with prior Mie-theory results for light scattering in tissue [28, 34, 40–42]. …”

Submicron scale tissue multifractal anisotropy in polarized laser light scattering

“…with inverse analysis can be used to quantify self-similarity in the spatial distribution of refractive index (RI) of random scattering media (such as biological tissues) [13,14]. Such information on the fractal/multifractal nature of spatial RI fluctuations of tissues has shown promise for early detection of cancer [14,15]. For probing anisotropies in RI variations, one further needs to invoke measurements involving polarization.…”

“…= 2π/λ is the wave vector, λ and  are the wavelength and the scattering angle; Λ ||/⊥ = ⌈n 0 ⌉ ||/⊥ the index fluctuation strengths for orthogonal linear polarizations; η ||/⊥ (r) are the corresponding (along the two orthogonal directions) index inhomogeneity distributions. On practical grounds, we have assumed that -(a) the index variations arise from statistical inhomogeneities having different spatial dimensions, albeit with similar amplitude of fluctuating index δn [15,20] and (b) the index fluctuations exhibit uniaxial anisotropy, i.e., it can be decomposed into two orthogonal components, parallel and perpendicular to the axis of the anisotropy [16,17].…”

Optical diagnosis of colon and cervical cancer by support vector machine

“…The diagnostic feature extractions are performed by biomarkers followed by machine learning tools. Most of the biomarkers were applied in optical diagnosis of cancer till now are wavelets [2][3] , multifractal detrended fluctuation analysis (MFDFA) [2][3][10][11] . Mukhopadhyay et.al., in their recent work demonstrated the utility of s-transform as a marker of precancer detection [12] .…”