Comparative study of differential matrix and extended polar decomposition formalisms for polarimetric characterization of complex tissue-like turbid media

Abstract

Development of methodologies for quantification/unique interpretation of the intrinsic polarimetry characteristics of biological tissues are important for various applications involving tissue characterization/diagnosis. A detailed comparative evaluation of the polar decomposition and the differential matrix decomposition of Mueller matrices for extraction/quantification of the intrinsic polarimetry characteristics (with special emphasis on linear retardance δ, optical rotation Ψ and depolarization Δ parameters was performed, because these are the most prominent tissue polarimetry effects) from complex tissue-like turbid media exhibiting simultaneous scattering and polarization effects. The results suggest that for media exhibiting simultaneous linear retardance and optical rotation polarization events, the use of retarder polar decomposition with its associated analysis which assumes sequential occurrence of these effects, results in systematic underestimation of δ and overestimation of Ψ parameters. Analytical relationships between the polarization parameters (δ, Ψ) extracted from both the retarder polar decomposition and the differential matrix decomposition for either simultaneous or sequential occurrence of the linear retardance and optical rotation effects were derived. The self-consistency of both decompositions is validated on experimental Mueller matrices recorded from tissue-simulating phantoms (whose polarization properties are controlled, known a-priori, and exhibited simultaneously) of increasing biological complexity. Additional theoretical validation tests were performed on Monte Carlo-generated Mueller matrices from analogous turbid media exhibiting simultaneous depolarization (Δ), linear retardance (δ) and optical rotation (Ψ) effects. After successful evaluation, the potential advantage of the differential matrix decomposition over the polar decomposition formalism was explored for monitoring of myocardial tissue regeneration following stem cell therapy.

Physical model of differential Mueller matrix for depolarizing uniform media

“…This effect is even more important in the backscattering geometry as compared to forward scattering geometry. As noted in [18], this scattering-induced diattenuation effect is not exhibited in a completely distributed fashion leading to an equivalent diattenuation parameter in the differential matrix model. We can conclude from the value of the k 1 parameter and Eq.…”

Mueller polarimetric imaging for surgical and diagnostic applications: a review

“…For a medium with depolarization, the polarization parameters can be then determined from L m and L u , summarised in [119,143] Magnitude of diattenuation:…”

Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment

“…Some studies suggest that differential decomposition may be closer to tissue reality compared with polar decomposition, since it does not operate sequentially. [47][48][49] To test this hypothesis, using Pol-MC code, we recently modeled many bilayered Mueller matrices of heterogeneous birefringent turbid media, with different orientation or value of anisotropy in the layers. 46 The resultant Mueller matrices were then decomposed with both polar and differential decompositions.…”