Mueller-matrix imaging polarimetry elevated by wavelet decomposition and polarization-singular processing for analysis of specific cancerous tissue pathology

Abstract

Significance: Mueller-matrix polarimetry is a powerful method allowing for the visualization of malformations in biological tissues and quantitative evaluation of alterations associated with the progression of various diseases. This approach, in fact, is limited in observation of spatial localization and scale-selective changes in the poly-crystalline compound of tissue samples.

Aim: We aimed to improve the Mueller-matrix polarimetry approach by implementing the wavelet decomposition accompanied with the polarization-singular processing for express differential diagnosis of local changes in the poly-crystalline structure of tissue samples with various pathology.

Approach: Mueller-matrix maps obtained experimentally in transmitted mode are processed utilizing a combination of a topological singular polarization approach and scale-selective wavelet analysis for quantitative assessment of the adenoma and carcinoma histological sections of the prostate tissues.

Results: A relationship between the characteristic values of the Mueller-matrix elements and singular states of linear and circular polarization is established within the framework of the phase anisotropy phenomenological model in terms of linear birefringence. A robust method for expedited (up to $\sim 15\min$) polarimetric-based differential diagnosis of local variations in the poly-crystalline structure of tissue samples containing various pathology abnormalities is introduced.

Conclusions: The benign and malignant states of the prostate tissue are identified and assessed quantitatively with a superior accuracy provided by the developed Mueller-matrix polarimetry approach.

Keywords: Mueller-matrix; birefringence; cancer; imaging polarimetry; polarization-singular; polarized light; wavelet decomposition.

Fig. 1

Experimental setup. (1) He–Ne laser, (2) collimator, (3) stationary quarter-wave plate, (5), (8) mechanically movable quarter-wave plates, (4), (9) polarizer and analyzer, (6) histological section, (7) polarizing microobjective, (10) CCD camera.

Fig. 2

Spatial distributions of characteristic values of the MM images $f_{44}(x,y)$ of histological sections of prostate adenoma (a) and carcinoma (b). Illustrative linear dependences of $N(L,x)$, $N(C,x)$, $N(L,y)$, and $N(C,y)$, respectively, for prostate adenoma (c), (e), (g), (i) and carcinoma (d), (f), (h), (j). See further details in the text.

Fig. 3

Spatial distributions of characteristic values of the MM images $f_{44}(x,y)$ of histological sections of prostate adenoma (a) and carcinoma (b). Illustrative linear dependences of $N(L,x)$, $N(C,x)$, $N(L,y)$, and $N(C,y)$, respectively, for prostate adenoma (c), (e), (g), (i) and carcinoma (d), (f), (h), (j). See further details in the text.

Fig. 4

Wavelet transform of distributions $N(L,x)$ and $N(C,x)$ for (a) adenoma and (b) carcinoma tissues. Linear dependencies of the amplitudes of the wavelet coefficients $Q_{A^{*}}(L,b)$ and $Q_{A^{*}}(C,b)$ on the optimal scale $A^{*}$ of the MHAT function ${\mathrm{\Omega }}_{ab}$ of MM image characteristic values $f_{44}(x,y)$ for (c), (e) adenoma and (d), (f) carcinoma tissues, respectively.

Fig. 5

Wavelet transform of distributions $N(L,x)$ and $N(C,x)$ for (a) adenoma and (b) carcinoma tissues. Linear dependencies of the amplitudes of the wavelet coefficients $Q_{A^{*}}(L,b)$ and $Q_{A^{*}}(C,b)$ on the optimal scale $A^{*}$ of the MHAT function ${\mathrm{\Omega }}_{ab}$ of MM image characteristic values $f_{44}(x,y)$ for (c), (e) myoma and (d), (f) endometriosis tissues, respectively.