Comparative study of the influence of imaging resolution on linear retardance parameters derived from the Mueller matrix

Abstract

Polarization imaging techniques are emerging tools to provide quantitative information of anisotropic structures, such as the density and orientation distribution of fibers in tissue samples. Recently, it is found that when using Mueller matrix polarimetry to obtain the structural features of tissue samples, some information can be revealed by relatively low-resolution polarization parameter images. Thus, to analyze what kinds of anisotropic optical and structural information contained in high-resolution polarization images are preserved in low-resolution ones, here we carry out a comparative study of the influence of imaging resolution on the Mueller matrix derived linear retardance parameters. We measure the microscopic Mueller matrix of human healthy breast duct tissues and ductal carcinoma in situ (DCIS) tissues, which have distinct typical fibrous structures, using objectives with different numerical aperture. Then we quantitatively compare a group of image texture feature parameters of the linear retardance parameters images under high and low imaging resolutions. The results demonstrate that the fibers density information contained in the texture features of linear retardance δ parameter image are preserved well with the decline of imaging resolution. While for the azimuthal orientation parameter θ which closely related to the spatial location, we still need high imaging resolution to obtain quantitative structural information. The study provides an important criterion to decide which information of fibrous structures can be extracted accurately using transmission Mueller matrix microscope with low numerical aperture objectives.

Fig. 1.

Schematic of the study. (a) Flow chart of the experiment. (b) Selected unstained tissue slices under 40$\times$/NA 0.65 objective and their adjacent H&E stained slices. The white scale bar is 50 $\mu$m. (c) Schematic of the Mueller matrix microscope.

Fig. 2.

Imaging and digitally resolution-reduced results from the non-duct area of (a) healthy breast duct tissue samples, (b) DCIS tissue samples. In each group, from left to right of the first row shows the images of adjacent H&E stained slice under 4$\times$/NA 0.1 and 40$\times$/NA 0.65 objectives observation, unpolarized light intensity images of the unstained tissue slice under 4$\times$/NA 0.1 and 40$\times$/NA 0.65 objectives observation. From left to right of the second and third rows show the MMPD $\delta$ and $\theta$ images of the same region under 4$\times$/NA 0.1 and 40$\times$/NA 0.65 objectives observation, the digitally low-pass filtered MMPD $\delta$ and $\theta$ images, and digitally simulate (averaged after low-pass filtering) 4$\times$/NA 0.1 MMPD $\delta$ and $\theta$ images. The units for $\delta$ is radian angle, for $\theta$ is degree of angle. The white scale bar is 50 $\mu$m.

Fig. 3.

Comparative analyzing results of MMPD $\delta$ parameter images of 13 healthy human breast duct tissue samples (blue dots) and 13 DCIS tissue samples (orange dots) between the 4$\times$/NA 0.1 (X-axis) and 40$\times$/NA 0.65 (Y-axis) data sets. (a)-(f) Mean, Entropy, Contrast, Correlation, Energy and Homogeneity. In each panel, the correlation coefficient R between the 40$\times$/NA 0.65 and 4$\times$/NA 0.1 objectives data sets are provided, and the significance P values between healthy and DCIS tissue samples of the 4$\times$/NA 0.1 and 40$\times$/NA 0.65 data sets are also listed in X-axis and Y-axis.

Fig. 4.

Comparative analyzing results of MMPD $\theta$ parameter images of 13 healthy human breast duct tissue samples (blue dots) and 13 DCIS tissue samples (orange dots) between the 4$\times$/NA 0.1 (X-axis) and 40$\times$/NA 0.65 (Y-axis) data sets. (a)-(f) Mean, Entropy, Contrast, Correlation, Energy and Homogeneity. In each panel, the significance P values between healthy and DCIS tissue samples of the 4$\times$/NA 0.1 and 40$\times$/NA 0.65 data sets are provided around X-axis and Y-axis.

Fig. 5.

Images of (a) 4-$\mu$m-thick adjacent H&E stained slice, (b) unpolarized light intensity of unstained slice, (c) MMPD parameters $\delta$, and (d) GLCM parameters of DCIS tissue sample under 4$\times$/NA 0.1 objective. The breast duct, non-duct and the fat tissue area are marked with identifiers of blue triangle, red star and black arrow in (a), respectively. The dashed box in (b) shows the FOV of 40$\times$/NA 0.65 objective. The white dashed lines in (c) show the boundary of the duct. The white scale bar is 500 $\mu$m.