1. Introduction

In biological histopathology, digital image processing can enhance image textural quality for better quantitative analysis [1], providing objective and reliable results. As a promising acquisition technique of digital images, polarization imaging has been utilized extensively to investigate the structural abnormality (e.g., collagen remodeling) in pathological diagnosis [2–5], including breast cancer [6], liver fibrosis [7], cervical precancer [8], kidney [9], muscle [10], and others. Moreover, polarization has also been integrated with other imaging modalities for characterization enhancement, such as polarization-sensitive optical coherence tomography (PS-OCT) [11], polarization-sensitive second-harmonic generation (PS-SHG) [12], and polarized fluorescence [13]. Mueller matrix (MM) is a complete mathematical description of the polarization signatures of an object [14], and MM imaging polarimetry (MMIP) has emerged as an essential method for characterizing biological structures, which contains a series of MM parameters (MMPs) [15,16]. Furthermore, several studies have proposed that polarization signatures are correlated with the mechanical properties of biological tissues. For example, mechanical stretching generates birefringence in skin tissues [17], retardation can serve as an index for evaluating cellular contractile force [18], strain-induced optical anisotropy exhibits a difference between the normal and stretched chicken breast [19], and some anisotropic properties are highly related with stretching states [20,21]. However, in these studies, the focus was mainly on the relationship between mechanical properties and limited anisotropy properties without considering the effects of mechanical force on other polarization signatures, such as anisotropy degree [22], diattenuation [23], depolarization [24,25], and fibrous orientation [26], which are also significant MMPs for characterization of biological structures. It has been reported that the image values of circular depolarization can increase after the porcine bladder is stretched for a certain length [27]. Biological tissues typically undergo mechanical processes during histological sample preparation, such as tissue compression generated by the slicer blade and structural shrinkage during staining, potentially leading to changes in the mechanical microenvironment (CMM) [28]. For example, the diameter of histological specimens is generally reduced by an average of 0.2 cm (ranging from 0 to 0.7 cm) compared with the fixed specimens [29]. In accordance with the Poisson effect, strain induced by CMM in tissues exists in three spatial dimensions, e.g., elongation or contraction in one direction may result in contraction or elongation perpendicular to that direction. Thus, the effects of mechanical processes on biological tissues are coupled in multiple spatial dimensions and should be investigated jointly. Cells and tissues respond to CMM at multiple structural scales [30,31], leading to fluctuations in size and spatial distribution of spherical scatterers (e.g., nuclei) and cylindrical scatterers (e.g., fibers). These fluctuations will change the polarization scattering microenvironment (PSM) in biological tissues. According to Mie scattering theory [32], unstable PSM may cause poor characterization stability of polarization signatures for pathological diagnosis. Stretching is a common method for applying mechanical force to biological tissues with viscoelastic characteristics [17,27]. It is important to note that many biological soft tissues (e.g., skin) have viscoelastic properties and are spatially non-homogeneous in their optical and physical properties, and thus changes in PSM during stretching may also exhibit spatial non-homogeneity.

In our previous study [33], we developed an MMIP system for performing MM imaging of biological tissues while applying quantitative stretch. We performed mechanical stretching on an unstained 7 µm-thick section of breast cancer tissue at the mN scale (ranging from 0 to 400 mN in ∼70 mN increments) and measured the resulting polarization signatures. Specifically, diattenuation and depolarization parameters exhibit no significant changes in the image textures of the breast cancer tissue. However, the absolute differences in the average values of these parameters between the cancerous and fibrous regions decrease with mechanical stretching, indicating that forces at the mN scale can affect the MM imaging of biological tissues to a certain extent. Furthermore, it is conceivable that tissues could potentially undergo greater mechanical forces, such as those at the N scale [28], under specific conditions. Therefore, the force scale and MMPs considered in our earlier study require further expansion. This expansion may potentially provide a more comprehensive understanding of how force impacts the characterization stability of polarization signatures.

In this work, we constructed a mimicking phantom to simulate the mechanical stretching process on breast cancer tissue, which served as a basis for conducting extended experiments. Subsequently, we upgraded the previously implemented MMIP system, utilizing avian skin tissue as a demonstration sample. An avian skin tissue sample was chosen for its intrinsic and formal birefringence inherent in collagen as well as scattering properties [17,34], which can provide rich polarization characteristics. Using Mueller matrix transformation (MMT) and Mueller matrix polar decomposition (MMPD) methods [15,16,35], we derived a set of 25 MMPs, comprising 9 scalar parameters (SPs) and 16 vector parameters (VPs). These parameters are crucial in characterizing the polarization signatures of the sample. Finally, we conducted a comparative analysis of the MMPs images obtained from the avian skin tissue under controlled forces ranging from 0 to 7 N in 1 N increments. This investigation aimed to evaluate the influence of CMM on the stability of polarization signatures in biological tissue characterization.

2. Materials and methods

2.1 Mueller matrix imaging system

In this work, the MMIP system was updated and streamlined with fewer moving components compared to its predecessor. The system was assembled with a mechanical stretching platform serving as the sample stage. As shown in Fig. 1, the system comprises three subsystems: a polarization state analyzer (PSA), a polarization state generator (PSG), and a stretching platform integrated with a force-sensing and display circuit.

 

Fig. 1. Schematic diagram of the MMIP system. (a) Optical setup. (b) Hardware setup. (c) Stretching platform. (d)–(f) Schematic diagram of the sample under different stretching forces. (g) A scattering model to describe the sample stretched. LS, light source; P1, polarizer; R1, quarter-wave plate; MT, microscope tube; RL, relay lens; P, polarizer; BSP, beam-splitting prism; R2, quarter-wave plate. (i) Stretch loading module. (ii) Sample clamping module. (iii) Force sensing module. The force-displaying circuit is not shown in this figure. In (d), the black dot is the fixed end, and the red arrow is the stretched end. In (a), the color change from red to blue is used to indicate the transmission path of the light beam from the light source to the camera.

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In PSA shown in Fig. 1(a), there are three beam-splitting prisms (Thorlabs, BS013), four relay lenses (Edmund Optics, #45762), one quarter-wave plate (Thorlabs, AQWP05M-600), four linear polarizers (Edmund Optics, #45667), and four cameras (CatchBEST, MU3E130C). In PSG, a collimator lens positioned behind the white LED restricts the spread of light beams. By manually adjusting the fast-axis direction of a quarter-wave plate (Thorlabs, AQWP05M-580) and the polarization direction of a linear polarizer (Edmund Optics, #45667), different incident polarization states are generated. The incident polarization states include 0° linear polarization, 45° linear polarization, 90° linear polarization, 135° linear polarization, left circular polarization, and right circular polarization. The stretching platform integrates a sample clamping module, a stretch loading module (operated manually and continuously with a single bolt), and a force-sensing module with a range of 0∼50 N and a resolution of 0.01 N. The stretch forces are displayed on an LCD unit within the circuit. During each stretch, the incident light generated by PSG illuminates the sample, and the light exiting from the sample passes through the PSA and is collected by the cameras. The final MMPs images are calculated from 24 images acquired with different combinations of PSG and PSA [36,37]. We have calibrated the inversion error of the Mueller matrix under the condition that the incident light was generated manually, and the average root mean square error of the air Mueller matrix was 0.0265. Table 1 shows the used MMPs, including 9 SPs and 16 VPs.

Table 1. Scalar and vector parameters derived by MMT and MMPD methods

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2.2 Sample preparation and experimental setup

In our previous study [33], we conducted a mechanical stretching experiment on an unstained section of breast cancer tissue (7 µm thick) at a mN scale, varying from 0 to 400 mN in ∼70 mN increments. This experiment demonstrates that forces within the mN scale can affect the MM imaging of tissue sections. Leveraging insights from the prior study, we constructed a mimicking phantom to imitate the mechanical stretching process in breast cancer tissue. The phantom can serve as a foundational tool, offering both theoretical understanding and a basis for further extensive experiments in this work.

As shown in Figs. 2(a) and (b), the breast cancer tissue exhibits obvious ring-like structures, featuring fibrous regions (cylindrical scatterers) surrounding the cancer cell regions (spherical scatterers). In the phantom, we used silk fibers (20∼30 µm in diameter) and polystyrene microspheres (10 µm in diameter) to simulate ring-like cylindrical scatterers and spherical scatterers, respectively. Polydimethylsiloxane (PDMS) was selected to generate the encapsulation medium material. The physical and optical properties of breast tissues and material are summarized in Table 2. The polystyrene microsphere inside the ring-like silk fibers simulated the cancer cell region, while those outside the ring-like silk fibers simulated the normal cell region. The amounts of polystyrene microspheres were calculated according to the scattering coefficients of normal and cancerous breast cell regions, respectively. The final phantom dimensions were 2 mm in thickness, 2 cm in width, and 7 cm in length, with a round view field of 1.8 mm in diameter. Utilizing the MMIP system of the previous version, we subjected the phantom to incremental stretching from 0 to 400 mN in steps of ∼70 mN. A detailed account of the phantom construction process is available in the Supplement 1.

 

Fig. 2. Influence of stretching forces at a mN scale on the mimicking phantom. (a) Section of breast cancer tissue. (b) Mimicking phantom. (c) and (d) Influence of stretching forces on parameter b of cylindrical scatterer and spherical scatterer regions, respectively. (e) and (f) Influence of stretching forces on parameter D of cylindrical scatterer and spherical scatterer regions, respectively. In (a) and (b), cyan five-pointed stars represent the cylindrical scatterer region, while yellow triangles represent the spherical scatterer region. Scale bars in (b) are 2 cm (left) and 500 µm (right), respectively.

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Table 2. Physical and optical properties of breast tissues and materials used in the phantom

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Biological tissues often feature intricate collagen fiber networks, seen in normal and diseased tissues such as those in the breast and skin. Structural alterations in these tissues can influence their polarization signatures. However, subjecting precious human tissue samples to strong stretching at the N scale may cause a risk of wastage, necessitating the use of acceptable alternatives. In this work, an avian skin tissue sample was chosen to generate diverse polarization properties, characterized by a complex network of collagen fibers interwoven with capillaries and nerve endings, exhibiting both anisotropic and isotropic properties [34,38,39]. During the sample preparation, fat was initially removed from the surface of the avian skin tissue. Subsequently, the sample was clamped at both ends using the sample clamping module and subjected to stretching, ranging from 1 to 7 N in 1 N increments. The imaging magnification was set at 9.2×, and the illuminated area of the sample was about 25 mm × 20 mm, with a circle field of view approximately 1.8 mm in diameter. To minimize the effect of the sample’s viscoelastic properties on the stretching process and to avoid drastic deformation during image acquisition, we first pre-stretched the avian skin tissue so that it was in a pre-tensioned state. After pre-tensioning, the avian skin tissue sample was approximately 40 um thick. As the sample underwent mechanical stretching from 1 to 7 N, it exhibited elongation along the direction of stretching and contraction in the vertical direction, which reduced the sample thickness to some extent. According to the Poisson effect, the change in sample thickness is one of the reflections of the effect of mechanical force on the tissue in three dimensions, consequently, the influence of thickness change on the tissue was not discussed separately in this work. Due to the intricate collagen fiber network with viscoelastic properties in the skin sample, tissue deformation was diverse, involving scaling, translation, and torsion at different scales. Given the scarcity of common properties required for global registration due to their disappearance, the varied deformations could cause challenges in image alignment under different stretching. Consequently, relying on the major common textural features in these images, we identified a region of interest (ROI) with a common view field as a benchmark. We then initialized the matching of ROIs to minimize interference with the analysis of MMPs.

We manually conducted the registration of the samples (phantom and avian skin tissue) under various stretching forces and assessed the registration using image cosine similarity (higher values indicating better alignment, with 1 being optimal). The cosine similarity values ranged from 0.935 to 0.998 for the phantom, and from 0.913 to 0.976 for the avian skin tissue. These results indicated that, after registration, the field of view in each image under different stretching forces matched that of the initial image to a high degree.

3. Results and discussions

Figure 2 shows the influence of stretching forces at a mN scale on the mimicking phantom, where we selected the same phantom region under different forces to calculate and analyze MMPs. Specifically, Figs. 2(c)–(f) demonstrate the impact of increasing forces on parameters b. For cylindrical scatterers, both parameters b and D exhibit a decreasing trend, with mean values decreasing from 0.271 and 0.839 to 0.236 and 0.803, respectively, resulting in variations of 12.9% and 4.3%. For spherical scatterers, the mean values of parameter b increase from 0.334 to 0.344, while those of parameter D decrease from 0.704 to 0.694, resulting in variations of 3% and 1.4%, respectively. For parameter b, the spherical scatterer region, characterized by its relatively dense arrangement of small particles, experiences a small change in distribution per unit volume due to the gentle mechanical stretching. Consequently, the values of parameter b exhibit less variation. Conversely, the cylindrical scatterer region, predominantly composed of silk fibers with larger column diameters, undergoes slight loosening of the larger cylindrical scatterers during mechanical stretching. These results in fluctuations cause a larger variation in parameter b. As for parameter D, the spherical scatterer region remains approximately isotropic after stretching, with a small change in light differential absorption. In contrast, the cylindrical scatterer region exhibits anisotropy, with scatterers distributed in a circular pattern. As stretching proceeds, fibers in the stretching direction undergo slight elongation without significant distribution variation. However, fibers in different directions from the stretching direction experience orientation changes, leading to a decrease in the overall orientation consistency of the cylindrical scatterers and a subsequent reduction in anisotropy [21]. This, in turn, causes a decrease in D values.

The results from the phantom experiment are in agreement with our previous study [33], indicating that the optical properties in PSM exhibit statistical variations when influenced by mechanical forces. Due to the moderate strength of the stretching, its incremental values (∼70 mN, ∼20 µm) could be controlled. The results of the phantom experiment provide a foundation for further exploration of the avian skin tissue. For substantial deformations induced by intense stretching, the impact on PSM may be more pronounced. Previous reports indicate that, in comparison to fixed tumors, histological specimens can exhibit an average diameter decrease of 0.2 cm (ranging from 0 to 0.7 cm) [29]. Therefore, it is necessary to extend the stretching scale further, potentially enabling a more comprehensive understanding of the influence of force on the characterization stability of polarization signatures.

Figure 3 shows the textural changes of each SP image under increasing forces. Figure 3(a) is the original images of the ROIs with the applied forces ranging from 1 to 7 N, which shows a high overlapping degree of textural features between each image after ROI alignment. The common textural features are marked by yellow and green arrows, respectively. The ROI size is about 500 µm × 700 µm covered with 272 × 382 pixels. Before ROI alignment, between each stretch increment, the overall shift (in the stretching direction) of the sample approximately ranged from 97 to 250 µm, and the shift degree approximately varied from 10% to 30%. It should be noted that the sample deformation under stretch was holistic, but within the imaging ROIs, the most significant observable deformation occurred in the stretching direction.

 

Fig. 3. Image textures of SPs under increasing forces. (a) original grayscale image ROIs after alignment. (b) b images. (c) A images. (d) x images. (e) d images. (f) D images. (g) R images. (h) δ images. (i) Ψ images. (j) Δ images. Black lines with double arrows indicate the direction of the stretching forces.

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Figures 3(b)–(j) are the pseudo-color images of SPs b, A, x, d, D, R, δ, Ψ, and Δ, respectively, and the images of each SP are pseudo-color shaded with the same color bar. Under increasing forces, the textural changes exhibit some obvious trends. Specifically, the textures show a color alteration from red to green on the left in Fig. 3(d), corresponding to decreasing SPs values, which are similar to those in Figs. 3(e) and (f). Synchronously, the textural distributions show an opposite trend from blue to red in Figs. 3(g)–(i), with increasing SPs values. In addition, the textural changes are mainly distributed on the image edges for SPs b, A, and Δ, specifically the top left corner in Figs. 3(b) and (c), and the bottom left corner in Fig. 3(j), respectively. These results are due to the rearrangement of structures such as collagen fibers in the sample under stretching forces [17], which modifies PSM and the polarization properties of the sample, resulting in textural changes of the SPs images. Thus, the stretching forces exhibit a definite effect on the image textures of MMPs, which can be also indicated by VPs images shown in Supplement 1.

Statistical analysis was conducted to quantitatively assess the fluctuation in the data obtained from SPs images. Figure 4 shows the data distribution of each SP image under increasing forces. The solid black line connects the averages of each violin plot, reflecting a trend similar to that of the medians. With increasing force, the medians for parameters A and D tend to remain close to the top, while near the middle for parameters b, x, d, and Δ. Specifically, for parameters R, δ, and Ψ, the medians shift from the middle to the top of the violin plot. Moreover, both upper and lower outliers exhibit specific trends. For example, the lower outliers first increase and then decrease for parameters A and b, whereas those increase for parameters R and δ. The trends of all medians and outliers presented in Fig. 4 are summarized in Table 3. Figure 4 illustrates that mechanical forces impact both anisotropic parameters and other SPs (e.g., A, x, D, and Ψ). One possible explanation is that the optical properties in PSM undergo statistical variations due to forces, exhibiting overall consistent fluctuations and local randomness. This phenomenon is consistent with the spatial inhomogeneity in the optical properties of the avian skin tissue, as further evidenced by the data distributions of VPs shown in Supplement 1.

 

Fig. 4. Data distributions of SPs images under increasing forces. (a) A images. (b) b images. (c) x images. (d) d images. (e) D images. (f) R images. (g) δ images. (h) Ψ images. (i) Δ images. Changes of medians and outliers reflect the textural fluctuations caused by forces.

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Table 3. Trends in data distributions of SPs used in this study under different forces

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Fig. 5. MSSIM of SPs images under increasing forces. (a) and (c) SPs derived from the MMT method. (b) and (d) SPs derived from the MMPD method. (a) and (b) Distribution trends of the scatters for each SP under increasing forces. (c) and (d) Bidirectional relationships between SPs and forces, where show the statistical information: the impact of different force increments on each SP; and the impact of each force increment on different SPs derived from MMT and MMPD methods, respectively.

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Based on the textural variations and data distributions in MMPs images, integrated analysis can be employed to provide a more comprehensive quantitative assessment. Under increasing forces, MMPs images can be considered as a sequence of image frames transformed through a mechanical image filtering process, including nonlinear image transformations, such as translation, rotation, and scaling at different scales. Images of biological tissues exhibit highly structured characteristics, with strong pixel correlation. Especially in spatially similar conditions, these correlations carry crucial information about the structures of biological tissues in the visual scene. Therefore, the degree of image transformation can be perceived by detecting changes in the structural information of the images. The structural similarity (SSIM) index is a human-intuitive standard for image quality assessment [40], providing a direct method to compare the structural relationship between transformed images (ranging from 2 N to 7 N) and the reference one (under 1 N). SSIM is defined as:

As the sample ROIs under different forces have been aligned based on the major common textural features before calculating the MMPs images, the MSSIM values were calculated without extra ROI alignment. Figure 5 shows the MSSIM of SPs images under increasing forces. In Figs. 5(a) and 5(b), for each data point, the two SPs images used for calculating MSSIM were the reference image (under 1 N) and a transformed image (ranging from 2 N to 7 N). For example, the data point of parameter x in column “5” in Fig. 5(a) was calculated by x images under 1 N and 5 N, where x image under 1 N was the reference image and that under 5 N was the transformed one. For parameters b, A, and d in Fig. 5(a), the MSSIM values vary from 0.5 to 0.61, with a range of 0.06, 0.04, and 0.06, respectively. However, for parameter x, the MSSIM values exhibit a larger range of 0.43 (from -0.02 to 0.41). Also, the overall MSSIM values of parameters b, A, and d are higher than those of parameter x. In Fig. 5(b), parameter D has the highest MSSIM values (greater than 0.7) with the smallest variation range of 0.09. While for parameters R, δ, Ψ, and Δ, the MSSIM values are smaller than 0.55 and vary in a range of 0.37, 0.38, 0.20, and 0.14, respectively. Meanwhile, as the force increases, almost all the MSSIM values of SPs images show decreasing trends. Figures 5(c) and (d) are the bidirectional relationships between SPs and forces, which show the link between SPs, force, and MSSIM. In the bidirectional relationships, one relates to the sensitivity of individual SPs to different forces, and the other relates to the effect of individual forces on different SPs. Additionally, in Figs. 5(c) and (d), the different colors of the arcs reflect different forces, and the width of the arcs indicates the value of MSSIM. As the force increases from 1 to 7 N, the total MSSIM values decrease from 2.16 to 1.61 in Fig. 5(c) and from 2.41 to 1.26 in Fig. 5(d), respectively, indicating an overall decreasing tendency of image structural similarity. For the sum of MSSIM values, parameter D has a value of 4.37, while parameter Ψ has a value of 0.194, corresponding to the minimum and maximum sensitivity to mechanical forces, respectively. These differences between parameters D and Ψ can be also illustrated by the contrasting trends in their pseudo-color image textures and data distributions, as shown in Figs. 3 and 4. The integrated analysis employed with structural similarity provides a comprehensive quantitative assessment, indicating that the structural similarity between the SPs images (ranging from 2 N to 7 N) and the initial reference image (under 1 N) exhibits an overall decreasing trend as the force value increases, but the decreasing trend varies among different SPs. The MSSIM values of VPs images are shown in Supplement 1.

The avian skin tissue features a complex and interwoven fiber network that is viscoelastic, with spatially inhomogeneous optical properties. During the stretching process, the central region of the sample contracts in the direction perpendicular to the stretch, pulling the fiber network on both sides and gradually forming a saddle-shaped distribution pattern. Parameter x is correlated with anisotropic orientation, and the fiber network of avian skin tissue responds significantly to different stretching stages, causing a substantial orientation change of the cylindrical scatterers and a reduction in the consistency of the local fiber orientation. This results in a decrease in structural anisotropy and an increase in depolarization, accompanied by a decrease in the values of x and D, and an increase in Δ values, as shown on the left in Figs. 3(d), (f), and (j). The distribution of cylindrical scatterers and medium birefringence can jointly affect R and δ. Under strong stress birefringence due to stretching, the region with reduced structural anisotropy is accompanied by an increase in optical anisotropy, leading to a substantial overall increase in the values of R and δ, as shown in Figs. 3(g)–(h) and Figs. 4(f)–(g). As stress birefringence does not significantly affect depolarization, the overall Δ values change to a lesser extent, as shown in Fig. 3(j) and Fig. 4(i). Additionally, chiral compounds such as glucose and amino acids, both causing optical rotation, are abundant in biological tissues. Specifically, left-handed amino acid and right-handed sugar molecules predominate [41]. As stretching proceeds, the proportion of left-handed amino acids and right-handed sugar molecules may change in certain localized regions, resulting in altered rotational effects on the polarized light and variations in Ψ values, as shown by the complex textures in Fig. 3(i) and the data distribution in Fig. 4(h).

Both phantom and avian skin experiments demonstrate that CMM caused by forces can affect the stability of polarization signatures in biological tissue characterization. According to the Poisson effect, CMM induces alterations in the PSM of tissues in three dimensions, including both the two-dimensional stretching plane and the thickness direction perpendicular to stretching. In this work, the experimental results indicate the combined impact of CMM on the PSM of tissues in three dimensions. It is crucial to note that alterations in thickness alone can independently influence the PSM of tissues, and the relevant studies can be referred in the Refs. [42,43]. During the derivation of MMPs using MMT and MMPD methods, many of the same MM elements are involved, transmitting or amplifying the CMM impact. Previous studies have predominantly focused on the connection between mechanical force and MMPs in terms of limited anisotropy properties (e.g., retardance and birefringence), neglecting other polarization properties for biological tissue characterization. For instance, diattenuation can highlight the anisotropic scattering of biological tissues in the near-infrared band, offering crucial structural information [23]. It is important to note that MMPs exhibit varied responses to CMM at the N scale. Parameters related to anisotropic orientation, retardance, and optical rotation are highly sensitive to CMM, leading to overall dramatic changes in image textures. In contrast, other parameters (e.g., polarization, diattenuation, and depolarization) respond to CMM in a limited manner. Additionally, certain MMPs may show enhanced textural contrasts under mechanical forces.

It is important to note that different tissues do not respond uniformly to the same preparation process. For example, the effect of formalin fixation on the volume of different tissues can vary considerably, including shrinking of brain tissue [44] and swelling of liver and myocardium tissues [45]. For the two possible volume variation trends, according to the Poisson effect, it can be a suitable method to induce tissue shrinking and swelling simultaneously by mechanical stretching, which can be used to simulate the changes in PSM induced by swelling in the direction of stretching and shrinking in the direction perpendicular to stretching, respectively. To minimize mechanical stress, the frozen sectioning technique may be an effective method, which can eliminate much of the chemical processing involved in preparing paraffin sections, thereby reducing the swelling or shrinking of the samples. For cases where paraffin sections are necessary, the solution ratio and tissue infiltration time in histological processing need accurate control. As manual operation tends to cause uncertainties, the strict control of all steps of histological processing by an automated method will help to minimize the differences in swelling or shrinking of the same type of tissues. In addition, the usage of tough and sharp blades and the optimized automated slicing process can avoid the abnormal deformation caused by the non-consistent squeezing of the blade on the tissue slices. On the other hand, the machine learning technique has shown great potential in fusing multiple polarimetry basis parameters to characterize the microstructural features of biological tissues [46]. Accordingly, the characterization method fusing multiple MMPs based on machine learning techniques may facilitate the mechanical stability improvement of polarization signatures, contributing to revealing structural information more robustly, and related studies will be conducted in the future.

4. Conclusions

In this study, we reported an MMIP system integrated with force loading and sensing modules, enabling 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 force scales of mN and N, respectively. The experimental results of the mimicking phantom provided prior knowledge of the influence of CMM on the characterization stability of polarization signatures. Based on the analysis of textural features and data distributions of MMPs images, using the structural similarity index, we evaluated the response trends of polarization signatures to increasing forces. The results demonstrate that, in addition to parameters related to birefringence or retardance, mechanical forces nonlinearly interfere with other MMPs (e.g., diattenuation, depolarization, anisotropic orientation, and optical rotation) to varying degrees. In certain cases, we observed enhanced textural contrasts in specific MMPs images, particularly evident in the lower image region of parameters x, d, δ, D_H, R_C, and P_ΔC. The textural enhancement can be interpreted as positive mechanical image transformation. The results can be traced back to structural deformation or rearrangement within biological soft tissues, which exhibit viscoelastic properties and spatial non-homogeneity in their optical and physical characteristics. Structural changes impact the PSM within the tissue and alter optical properties, thereby modifying the scattering polarization states of photons and textural contrast.

In summary, the preparation process of biological tissue for pathological diagnosis is complex, and strict control of processing standards and consistency can minimize changes in the mechanical state of tissues caused by external factors, thus eliminating influence on the stability of polarization signatures in biological tissue characterization. In addition, the excised tissue specimen generally does not experience the same mechanical stress as live tissue, and the results of ex-vivo studies should be adequately assessed before being translated into in vivo applications. This study provides a reference for the application of the MMIP technique in pathological diagnosis.