Mechanical stability of polarization signatures in biological tissue characterization

Mueller matrix imaging polarimetry (MMIP) is a promising technique for investigating structural abnormalities in pathological diagnosis. The characterization stability of polarization signatures, described by Mueller matrix parameters (MMPs), correlates with the mechanical state of the biological medium. In this study, we developed an MMIP system capable of applying quantitative forces to samples and measuring the resulting polarization signatures. Mechanical stretching experiments were conducted on a mimicking phantom and a tissue sample at different force scales. We analyzed the textural features and data distribution of MMP images and evaluated the force effect on the characterization of MMPs using the structural similarity index. The results demonstrate that changes in the mechanical microenvironment (CMM) can cause textural fluctuations in MMP images, interfering with the stability of polarization signatures. Specifically, parameters of anisotropic orientation, retardance, and optical rotation are the most sensitive to CMM, inducing a dramatic change in the overall image texture, while other parameters (e.g., polarization, diattenuation, and depolarization) exhibit locality in their response to CMM. For some MMPs, CMM can enhance regional textural contrasts. This study elucidates the mechanical stability of polarization signatures in biological tissue characterization and provides a valuable reference for further research toward minimizing CMM influence.


Abstract:
This document provides supplemental information to "Mechanical stability of polarization signatures in biological tissue characterization".

Content of sections
1. Construction process of the mimicking phantom 2. Analyses of the textural features and data distributions for VPs images

Figure S1
Image textures of diattenuation vector under increasing forces

Figure S2
Image textures of polarization vector under increasing forces

Figure S3
Image textures of retardance vector under increasing forces

Figure S4
Image textures of polarization vector in depolarizer matrix under increasing forces

Figure S5
Data distributions of diattenuation vector under increasing forces

Figure S6
Data distributions of polarization vector under different forces

Figure S7
Data distributions of retardance vector under different forces

Figure S8
Data distributions of polarization vector in depolarizer matrix under increasing forces

Figure S9
MSSIM of VPs images under increasing forces

Figure S10
MSSIM summarization of VPs images under increasing forces

Construction process of the mimicking phantom
The construction process of the mimicking phantom is as follows: (1) Tinfoil tape was used to make an uncovered cube around the slide, with the slide as the bottom surface.(2) A small amount of silk fibers was wrapped around a cylinder with a diameter of 1 mm, after which the looped silk fibers were removed with a tweezer and placed in the middle of the tinfoil cube.
(3) The PDMS solution and the curing agent were mixed in the ratio of 10:1, and then the powder of polystyrene microspheres was put into the PDMS solution for uniform mixing, and then the solution was poured into the tinfoil cube.(4) The tinfoil cube was placed on a flat surface that had been leveled, and cured for 48 hours at room temperature.(5) After curing, the PDMS was peeled off the slide with the tinfoil removed, and the excess PDMS was cut off with a razor blade.(6) The final phantom dimensions were 2 mm in thickness, 2 cm in width, and 7 cm in length.Excluding the clamped portions, the actual length of the phantom involved in the stretching was 2 cm.The construction process was carried out in an ultra-clean laboratory to prevent dust particles from entering the PDMS solution and affecting the scattering coefficient.And gloves were worn throughout the construction process to prevent fingerprints from sticking to the phantom after the PDMS had cured, which could lead to a change in the polarization state of the incident light when the sample was illuminated.
We compared and analyzed the textural features, data distributions, and MSSIM values of VPs images.Each pseudo-color image in Supplemental Figs.S1-S4 is employed by the same color bar.With the force increasing, the textural changes of VPs images exhibit some obvious trends as well, which can be quantitatively described by the data distributions in Supplemental Figs.S5-S10.These results also demonstrate that changes in the mechanical environment within biological tissues will generate fluctuations in the textural contrasts of MMPs images.With the force increasing, for P norm images, the overall values decrease gradually, with reduced textural consistency and enhanced contrast, but the values in the lower-left corner increase abnormally at 6 N and 7 N.For P H images, the overall values gradually increase, with improved textural consistency and diminished contrast, but the values on the left side gradually decrease at 6 N and 7 N.For P 45 images, the overall values gradually increase, with enhanced textural consistency, however, at 6 N and 7 N, the values in the upper and lower left corners show an unusual decrease and increase, respectively.For P C images, the overall values gradually increase, with enhanced contrast, however, at 6 N and 7 N, the values in the upper left and lower left corners show an abnormal increase and decrease, respectively.With the force increasing, for P norm images, the median and lower outliers decrease basically, it should be noted that the smaller lower outliers at 1 N correspond to the upper-right corner of the pseudo-color map, and that the larger upper outliers at 6 N and 7 N correspond to the lower-left corner of the pseudo-color map.For P H images, median and upper outliers gradually increase, but at 7 N they decrease slightly.And the lower outliers at 7 N also decrease significantly, corresponding to the left region in the pseudo-color map.For P 45 images, there are small increases and fluctuations in the median and lower outliers, respectively, corresponding to changes in textural fragments in the pseudo-color map.For P C images, median and upper outliers increase, while lower outliers decrease.With the force increasing, for R H images, the increase in the number of upper outliers causes the divergence of the median, which corresponds to the textural fragmentation in the upper region of the pseudo-color map, while the lower outliers gradually decrease.For R 45 images, median and upper outliers decrease, and the number of lower outliers gradually increases, corresponding to the textural fragments in the upper region of the pseudo-color map.For R C images, median, upper and lower outliers increase, reflecting the overall change of the textures in the pseudo-color map.For P ΔH images, median and upper outliers decrease, while there are fluctuations in lower outliers, reflecting variations in the blue textures in the pseudo-color map.For P Δ45 images, median and upper outliers increase, while there are small fluctuations in the lower outliers, reflecting changes of the blue textures in the pseudo-color map, such as those in the upper-left region.For P ΔC images, median, upper and lower outliers fluctuate and there is randomness in the textural change trend.

Fig. S1 .
Fig. S1.Image textures of diattenuation vector under increasing forces.(a) D norm images; (b) D H images; (c) D 45 images; (d) D C images.With the force increasing, for D norm images, the overall values tend to decrease, with improved textural fragments and enhanced contrast, but the values on the left side appear to increase abnormally at 7 N.For D H images, the overall values gradually increase, with improved textural consistency and diminished contrast, but the values on the left side at 7 N appear to decrease abnormally.For D 45 images, the textural distribution is basically stable.For D C images, the values gradually decrease in the upper part but fluctuate in the lower part.

Fig. S2 .
Fig. S2.Image textures of polarization vector under increasing forces.(a) P norm images; (b) P H images; (c) P 45 images; (d) P C images.With the force increasing, for P norm images, the overall values decrease gradually, with reduced textural consistency and enhanced contrast, but the values in the lower-left corner increase abnormally at 6 N and 7 N.For P H images, the overall values gradually increase, with improved textural consistency and diminished contrast, but the values on the left side gradually decrease at 6 N and 7 N.For P 45 images, the overall values gradually increase, with enhanced textural consistency, however, at 6 N and 7 N, the values in the upper and lower left corners show an unusual decrease and increase, respectively.For P C images, the overall values gradually increase, with enhanced contrast, however, at 6 N and 7 N, the values in the upper left and lower left corners show an abnormal increase and decrease, respectively.

Fig. S3 .
Fig. S3.Image textures of retardance vector under increasing forces.(a) R H images; (b) R 45 images; (c) R C images.With the force increasing, for R H images, the values in the upper part gradually increase, with reduced textural consistency and enhanced contrast.For R 45 images, the values in the upper part gradually decrease, with reduced textural consistency and enhanced contrast.For R C images, the overall values gradually increase, and the contrast first diminishes and then increases.

Fig. S4 .
Fig. S4.Image textures of polarization vector in depolarizer matrix under increasing forces.(a) P Δnorm images; (b) P ΔH images; (c) P Δ45 images; (d) P ΔC images.With the force increasing, for P Δnorm images and P ΔH images, the overall values decrease gradually, with reduced textural consistency and enhanced contrast.For P Δ45 images, the overall values gradually increase, with improved textural consistency and diminished contrast.For P ΔC images, the overall values are stable, but the textural consistency and contrast fluctuate.

Fig. S5 .
Fig. S5.Data distributions of diattenuation vector under increasing forces.(a) D norm images; (b) D H images; (c) D 45 images; (d) D C images.With the force increasing, for D norm images, the median, upper and lower outliers show a decreasing trend, however, the upper outliers at 7 N increase abnormally, corresponding to the left region in the pseudocolored map.For D H images, the median, upper and lower outliers show an increasing trend, but decrease abnormally at 7 N, corresponding to the left region in the pseudo-colored map.For D 45 images, median, upper and lower outliers are basically stable.For D C images, median and lower outliers decrease, while upper outliers show small fluctuations, corresponding to the lower region in the pseudo-colored map.

Fig. S6 .
Fig. S6.Data distributions of polarization vector under different forces.(a) P norm images; (b) P H images; (c) P 45 images; (d) P C images.With the force increasing, for P norm images, the median and lower outliers decrease basically, it should be noted that the smaller lower outliers at 1 N correspond to the upper-right corner of the pseudo-color map, and that the larger upper outliers at 6 N and 7 N correspond to the lower-left corner of the pseudo-color map.For P H images, median and upper outliers gradually increase, but at 7 N they decrease slightly.And the lower outliers at 7 N also decrease significantly, corresponding to the left region in the pseudo-color map.For P 45 images, there are small increases and fluctuations in the median and lower outliers, respectively, corresponding to changes in textural fragments in the pseudo-color map.For P C images, median and upper outliers increase, while lower outliers decrease.

Fig. S7 .
Fig. S7.Data distributions of retardance vector under different forces.(a) R H images; (b) R 45 images; (c) R C images.With the force increasing, for R H images, the increase in the number of upper outliers causes the divergence of the median, which corresponds to the textural fragmentation in the upper region of the pseudo-color map, while the lower outliers gradually decrease.For R 45 images, median and upper outliers decrease, and the number of lower outliers gradually increases, corresponding to the textural fragments in the upper region of the pseudo-color map.For R C images, median, upper and lower outliers increase, reflecting the overall change of the textures in the pseudo-color map.

Fig. S8 .
Fig. S8.Data distributions of polarization vector in depolarizer matrix under increasing forces.(a) P Δnorm images; (b) P ΔH images; (c) P Δ45 images; (d) P ΔC images.With the force increasing, for P Δnorm images, the median and lower outliers decrease, while the upper outliers fluctuate, corresponding to the orange textural fragments in the pseudo-color map.For P ΔH images, median and upper outliers decrease, while there are fluctuations in lower outliers, reflecting variations in the blue textures in the pseudo-color map.For P Δ45 images, median and upper outliers increase, while there are small fluctuations in the lower outliers, reflecting changes of the blue textures in the pseudo-color map, such as those in the upper-left region.For P ΔC images, median, upper and lower outliers fluctuate and there is randomness in the textural change trend.

Fig. S9 .
Fig. S9.MSSIM of VPs images under increasing forces.(a) diattenuation vector; (b) polarization vector; (c) retardance vector; (d) polarization vector in depolarizer matrix.For each VP, the MSSIM value exhibits a tendency under the influence of force, such as the obvious trend of monotonous decreasing in (a), (c), and (d).These tendencies indicate that differences in mechanical status can lead to instability in texture-based pathological diagnosis.Meanwhile, the MSSIM-based relationship between each vector and force is summarized in Fig. S10.

Fig. S10 .
Fig. S10.MSSIM summarization of VPs images under increasing forces.(a) diattenuation vector; (b) polarization vector; (c) retardance vector; (d) polarization vector in depolarizer matrix.For each vector, the sum of MSSIM decreases with increasing force.Meanwhile, R H and P Δ45 have the maximum (4.41) and the minimum (0.36) sum of MSSIM, respectively.Although force affects R H the most, other VPs also have a large sum of MSSIM, such as D norm (4.37) and P norm (2.88), which indicates that applied force can interfere with other optical properties (e.g.diattenuation and polarization) of the tissue besides anisotropy or birefringence.The results indicate that changes in the mechanical environment within biological tissues will generate fluctuations in the textural contrasts of MMIPs images, causing instability in texture-based pathological diagnosis.