Stokes polarization imaging applied for monitoring dynamic tissue optical clearing

: We propose a continuous Stokes imaging system with a refresh rate of several seconds, instead of a traditional Mueller measurement setup, to quickly track the microstructural changes of tissues during the optical clearing process. The effectiveness of this fast Stokes imaging applied in monitoring the dynamic process is first validated by three designed experiments with a polarization state that changes continuously and rapidly, and is further confirmed by gradual changes in polarization image contrast and resolution with clearing. By comparison with experiments from different tissue samples with the same agent, the fast Stokes response curve can improve the analysis ability of photon polarization behavior connected with the complicated changes of tissue characteristics.


Introduction
Mueller polarimetry has become an emerging new tool to characterize microstructural biological features, not only because of its sensitivity to the microstructural changes in biological tissues [1], but also due to its capability to improve the imaging quality and the contrast [2,3]. Information extraction based on Muller matrix, for example, Mueller matrix polar decomposition (MMPD), can establish the relationship between polarization parameters and optical processes in tissues [4,5]. These polarization characterization parameters, such as linear retardance, depolarization and dichroism, can effectively highlight certain tissue microstructures without damaging the specimen in a non-invasive, non-staining way, and have been proved to be important indicators to differentiate various abnormal tissues ex-vivo [6][7][8][9][10][11][12], including liver cirrhosis and cancer [9], basal cell carcinoma [8], cervical carcinoma [7,11], papillary thyroid carcinoma [7], breast ductal carcinoma [6], etc.
Tissue optical clearing (TOC) was first proposed by Tuchin and coworkers [13][14][15], and recently has become more and more prominent in biomedical applications due to its great contribution to optical penetration depth and image quality [14,16,17]. The simplest clearing method is to immerse tissue samples into optical clearing agents (OCAs) and after few minutes, the transparency significantly increases. To further enhance the clearing effects or accelerate the process, many researchers have investigated the mechanisms and the process of TOC by various optical imaging methods, such as laser speckle contrast imaging (LSCI) [18], photoacoustic microscopy [19], two-photon microscopy [20] and optical coherence tomography [21]. Several factors are considered to work together during optical clearing [22,23], including the refractive index matching inside and outside cells, hyperosmotic agents induced tissue dehydration, the decrease of tissue thickness, the changes of collagen fiber content and the arrangement of tissue fibrils in a more regular fashion [24][25][26][27].
Our previous work based on Mueller polarimetry has successfully observed the microstructural changes with clearing and given some possible explanations by combination with Monte Carlo simulations [28][29][30]. Based on our sphere-cylinder birefringence model (SCBM) combined with our Monto Carlo simulations, we explained the variations of MMPD parameters and the polarization characteristics related to depth resolution during the clearing process of mouse skin. Also, we compare their different influences on tissue microstructures of two optical clearing agents according to Mueller matrix imaging features. These preliminary studies confirm the feasibility of polarization characterization as a good way to understand the interaction between clearing agents and tissues.
However, traditional Mueller measurements based on mechanical dual-rotated waveplate is time-consuming, it takes about 3 minutes to collect 30 polarization images at different positions and then calculate the Mueller matrix [31], which is inaccurate to describe the changes of dynamic samples. Stokes vector with 4 elements is another form of polarization description, can be obtained quickly compared with Mueller matrix. However, for total polarization measurement, no matter Mueller matrix or Stokes vector group, cannot meet the requirement for rapid dynamic physiological monitoring.
In this paper, we propose a method to achieve continuous Stokes images on the scale of several seconds based on traditional Mueller measurement configuration, and present the application in tissue characterization with clearing process. The average Stokes imaging time can be adjusted by changing the number of overlapping images, the fastest imaging mode takes only 4.8s while the Mueller matrix imaging time is 192s under the same condition [31]. We first validate the feasibility of sequential Stokes imaging on three different types of dynamic samples, then we present the application on tissue clearing especially in the first few minutes by characterizing the changes of resolution and contrast. Besides, we qualitatively demonstrate and compare the dynamic polarization changes induced by different tissues with clearing time, which lay the foundation for the follow-up research on quantitative interpretation of tissue microstructure during clearing based on fast Stokes imaging.

Tissue sample preparation
In this study, we take bovine skeletal muscle and porcine skin whose adipose layer is removed as samples, the specimens are cut in advance in 1.5cm×1.5cm squares by slicing machine (Leica VT1200S), and the thickness is 600 microns for the muscle and 500 microns for the skin specimen. These two samples have different microscopic characteristics, the skeletal muscle is an anisotropic sample due to the arrangement of collagen fibers, while the skin is a sample between anisotropic and isotropic. Before experiments, tissue samples are stored at 4°C in phosphate buffered saline (PBS), then they are let stand a while to equilibrate to room temperature. During experiments, tissue samples are immersed in 100% glycerol and imaged by forward Stokes measurement system at the same time. The white-light images of 600 microns bovine skeletal muscle before and after 16-minute clearing with a resolution board beneath the sample as reference are shown in Fig. 1.

Experiment setup
As shown in Fig. 2, the setup for the Stokes imaging developed by us is similar in appearance to the setup for Muller polarimetry [32]. Illuminating light from the LED source (3W, 620-640nm, Xlamp XP-E, Cree) passes through the polarization states generator (PSG) consisting a polarizer with horizontal polarization direction (P1, extinction ratio 1000:1, Union Optic, China) and a quarter-waveplate (R1, Daheng Optics, China). After the light beam transmits the sample on the stage and the objective lens, the beam is analyzed by the polarization states analyzer (PSA) consisting of a rotatable quarter-waveplate (R2, Daheng Optics, China) and another polarizer with horizontal polarization direction (P2, extinction ratio 1000:1, Union Optic, China), and finally polarization images are captured by a 12-bit CCD camera (Qimaging R6). During experiments, the dynamic tissue clearing process is imaged synchronously by Stokes measurement system, greatly reducing the error caused by moving samples. The photograph and schematic of the configuration for microscopic imaging is shown in Fig. 2. Here we use a 12 microns unstained slice of colon tissue as an example, and show the comparison between the HE-stained slice image and the Stokes and the derived linear retardance images.

Image processing
The flow chart of our imaging processing is shown in Fig. 3: In this paper, we modulate the position of the first quarter-waveplate to ensure that the incident light is right-circularly polarized. Circular polarized light has shown potential in studies of turbid media in many previous works [33][34][35][36], especially for complex biological tissue. Considering the fact that circular polarization state does not have specific orientations and will not be affected by anisotropy axis of tissues, circularly polarized illumination is used to probe the characteristics of the sample. Firstly, we collect a series of polarization images, according to the Mueller expressions of the polarizing components, the light intensity with a rotating quarter-waveplate and a horizontal polarizer can be expressed as follows: In Eq. (1), S 0 is the total intensity, S 1 , S 2 and S 3 represent the differences between the intensities of horizontal and vertical, 45 degree and 135 degree, right and left handed circular polarization components respectively. θ represents the angle between the fast axis direction and the horizontal direction, We define the scattered polarizations by s 1 , s 2 , s 3 given in Eq. (2) to describe the polarization parts of the Stokes vector.
To solve the Stokes vector of the sample, we need at least four polarization intensity images. Actually, considering the solution accuracy and stability, we generally use six polarization images to acquire one 2D Stokes image.
Next, we obtain continuous Stokes images with a faster refresh rate by overlapping, as shown in Fig. 3. For example, we get the Stokes image with the incident circular polarized light based on the original polarization image group including the first to sixth polarization images corresponding to the second quarter-waveplate at the position 0°, 30°, 60°, 120°, 150°. And then the second Stokes image is solved by adding the seventh polarization image where the second quarter-waveplate is set at 180°into the image group and removing the first image. The measurement speed can be greatly increased with this improved method, and also can be adjusted by changing the overlaps. The minimum acquisition time for Stokes vectors is about 4.8s.
Subsequently, based on a series of temporal Stokes images, we can describe the polarization changes on the Poincare sphere, and derive various polarization parameters including the degree of polarization (DoP), the degree of linear polarization (DoLP), the degree of circular polarization (DoCP), linear retardance (δ) and circular depolarization (∆ c ). Among these parameters, the first three are Stokes parameters, and the last two can be derived under the right-circular polarization.
The parameters we use in this paper are listed in the Table 1 below, among these parameters, linear-retardance is one of the most important polarization characterization parameters, and is sensitive to fibrous structure and birefringence. Due to linear-retardance, part of the circularly polarized incident light is converted to linearly polarized light, which explains the increasing linear polarized photons emerging from the sample, presented as the angle between the incident polarization state vector (that is, S 3 axis) and the output polarization state vector on the Poincare sphere [37]. The total depolarization calculated in the case of right-circular polarization reflects the part of the emergent light that does not maintain circular polarization state, equal to the bottom right element in the depolarization matrix calculated from MMPD, to better compared with the parameters obtained from Mueller matrix, we refer it as circular depolarization [4].
The Stokes image is under the condition of right-circular polarized incident light, corresponding to the fourth column of the Mueller matrix. Two typical polarization characterization parameters, circular depolarization and linear retardance are extracted respectively to investigate the microstructural behavior of the sample, both of which can be derived by Mueller matrix and Stokes vector using different expressions in Table 1. Here we use two samples, one is tape, we stack the tapes stretched with different strengths together to construct a sample with uneven linear retardance, the other is completely dehydrated bovine skeletal muscle, which has a strong depolarization ability. In Fig. 4, the good agreement of the derived polarization parameters linear retardance and circular depolarization from Mueller matrix and Stokes vector imaging respectively, not only confirms the feasibility of the overlapping method to calculate Stokes vectors, but also validates the polarization characterization parameters obtained from Stoke vector imaging.

Experimental verification
To demonstrate the advantages of our experimental setup in monitoring dynamic polarization changes compared with minute level Mueller matrix imaging, we use the combination of rotating half-waveplate and quarter-waveplate to design three cases of controllable polarization changes and then monitor these different polarization modulation for 12 minutes. For the first case, the position of the quarter-waveplate is fixed and the angular stepping variation of rotating half-waveplate is 1°, leading to the continuous change of ellipticity of the fully polarized light, the corresponding trajectory on the Poincare sphere is meridian. For the second case, to achieve the continuous changes in azimuth, we keep the speed ratio of the quarter-waveplate and half-waveplate at 2:1(ω 2 = 2ω 1 ), the stepping degrees for two waveplates are set as 2°and 1°r espectively, corresponding to the line of latitude on the Poincare sphere. Thirdly, we control the speed ratio at 24:1(ω 2 =24ω 1 ) with 6°and 0.25°respectively to change the ellipticity and azimuth simultaneously. As shown in Fig. 5(c-e), the dynamic polarization tracking at a time interval of 4.8s is in good agreement with the theoretical calculation in our verification experiment. By comparison, experimental results using Mueller matrix measurement setup are marked by stars in Fig. 5(f-h). When the sample changes slowly as in Fig. 5(c)(d), Mueller matrix measurement can still track the overall trends in spite of losing the details of the variation, however, the Mueller measurement can hardly reflect the characteristics of the samples as the variation speed of the samples increase, as shown in Fig. 5(e).
By using the overlapping calculation method, the time resolution of Stokes vector is improved, leading to a good description of the dynamic samples. However, due to the changes of sample properties during the long measurement, the results of Mueller polarimetry lose much information about the dynamic changes. Apparently, improved Stokes imaging method has advantage in calculating speed and accuracy in tracking the change of polarization parameters in dynamic process.

Dynamic observation of tissue clearing
The process of tissue optical clearing is not necessarily steady and uniform especially in the first several minutes, our fast refresh polarization imaging is good for tracking the microstructural variation in the early stage of clearing. To quantitatively evaluate the tissue changes with clearing, we use a resolution board in the following tissue clearing experiments. Specifically, a bovine skeletal muscle sample with a thickness of 600 microns is put on the resolution plate (Type: 1951USAF), and is immersed into the glycerol on a quartz plate, the quartz plate is chosen instead of a plastic plate to reduce the impact of the container on polarization parameters. Group 0, Element 6 (the corresponding line width is 281 microns) area on the resolution plate is chosen as the imaging region to study the changes of imaging contrast during optical tissue clearing, about 3mm×3mm. We continuously capture 240 polarization images and then calculated 235 Stokes images within 16 minutes after the beginning of clearing, the average calculation time for one Stokes image is only 4.8s, making it possible to track more changes of dynamic samples in detail.
Stokes images at the beginning, middle, and end of the 16-minute clearing process have been shown respectively in Fig. 6(a), where the pixel values at the position of the resolution indicator lines is almost zero. Obviously with the clearing, the s 1 , s 2 , s 3 values range of the tissue sample is expanded from −0.5 to 0.5 and the resolution lines beneath the tissue as references are highlighted.
Then, we map and analyze the trajectory of the Stokes vector on the Poincare sphere, the radius of the two spheres in the Fig. 6(b) are 0.12 and 0.19 respectively, as the clearing going on, the degree of polarization of the sample increases significantly, and the Stokes vectors move gradually from the surface of the small sphere to the large sphere. Each local pixel of tissue sample is unlikely under a completely consistent clearing status, to extract stable tissue polarization characteristics, Fig. 6(c) shows the average values of s 1 , s 2 and s 3 in the imaging area without a resolution board background, where s 2 and s 3 increase with tissue clearing while the s 1 shows a slight decrease. Also, the variance of each element of Stokes vector increases significantly, which is possible related to the increased difference between the transparent part and the shading part of the resolution board. Figure 6(d) clearly shows the quantitative trend of s 1 , s 2 and s 3 , respectively. Stokes vectors arise from three polarization differences in experimental measurements, not directly corresponding to specific microstructures or physical phenomena. Therefore, we usually analyze the polarization characterization parameters derived from Stokes vector, such as degree of polarization (DoP) and linear retardance. Intuitively, as shown in Table 1, the overall degree of polarization depends on the square sum of s 1 , s 2 and s 3 . Among them the absolute value of s 3 describes the polarization degree of circularly polarized light and the square sum of s 1 and s 2 determines the polarization degree of linear polarized light. Therefore, the above experimental results indicate that the cleared skeletal muscle shows an enhanced linear polarization and decreased circular polarization. The corresponding polarization change due to clearing can be supported by the following Fig. 7(c), where the image contrast with the help of resolution board is improved for DoLP and weaken for DoCP. The major mechanisms of optical clearing are tissue dehydration due to osmotic phenomenon and refractive index matching caused by agents penetrating into the intercellular space, which reduces the depolarization phenomenon by light scattering and improves the light transmission. Based on DoP and DoLP images with tissue clearing, we can observe the image contrast and resolution during the clearing process. The imaging area in resolution plate is marked by the red frame as shown in Fig. 7(a). Figure 7(b) indicates that at the early stage of clearing, the difference between the transmittance and shading area of the resolution plate is not obvious. With the optical clearing process, the DoP values of the shading part almost remain stable, while those from the transmittance part corresponding to the tissue characteristics increase significantly. For further quantifying the polarization imaging changes by the clearing, we calculate the contrast with Eq. (3) shown in Fig. 7(c). It can be seen that both the image contrasts for DoP and DoLP are enhanced. Specifically, DoP contrast is increased by clearing mainly in the first 5minutes, and then remains the same between 8minutes and 16 minutes, which can be explained by the uneven optical-clearing effect, quickly change in the first several minutes then become slower, consistent with other research works [23]. The continuous improvements of DoLP contrast imply that there are some other mechanisms accompanied by refractive index matching, especially about 8 minutes later after clearing, for example, changes in collagen fiber content or arrangement. However, the variation of DoCP contrast is small compared to DoP and DoLP, referring to the expression of DoCP, it shows that the quantitative ability of derived polarization parameters is better than the original Stokes vector. Figure 7(d-f) show the polarization images of the resolution board within 16mins at 5 equal intervals, which reveals clearly that the image contrasts of DoP and DoLP increase with tissue clearing while there is no obvious change in DoCP, similar with (b)(c).
Similarly, to demonstrate the influence of clearing on DoP image contrast, series of continuous polarization images are used to monitor the tissue clearing of 500 microns porcine skin. Compared with bovine skeletal muscle, the porcine skin has been severe deformed after 16-minute clearing. Therefore, to make sure that the imaging region is the same, the total monitoring timeline is shortened to about 12 minutes and the corresponding number of 2D Stokes images is 178. For 500 microns porcine skin, the overall trends of DoP and DoLP is similar as that of bovine skeletal muscle. However, the dynamic changes of DoCP from two types of tissue samples by the same agent show different regularities. Accordingly, in the initial stage of tissue clearing, the difference between DoP and DoLP is more obvious in skeletal muscle, and the improvement of image contrast by clearing shows a slower gradient in skin sample. Considering the different micro characteristic of these two samples, such as the content and alignment of fibrous microstructures, the fast-continuous observation of dynamic variation of polarization parameters can be used as a way of information extraction to explain the interaction between tissues and clearing agents.
Imaging resolution is the ability to visually differentiate between two adjacent objects in the image, according to the Raleigh's criterion, only if the intensity of valley region I min is less than or equal to 8/π 2 (∼0.81) times the maximum intensity of the peaks, the imaging region is thought to be resolved [38]. By clearing, the improvement of polarization contrast promotes the enhancement of tissue imaging resolution. According to various tag lines on the resolution plate, we can evaluate the resolution limit at different stages of optical clearing.
As shown in Fig. 9, before optical clearing, the numerical resolution limit according to the Raleigh's criterion is Group 0, Elements 3, where the line width is 397 microns. However, due to the poor penetration of the uncleared tissue, the transmission intensity of valley region is too small to analyze polarization parameters. After tissue immersed in OCAs for 8 minutes, the contrast of polarization parameters has improved a lot, it is easy to distinguish three tag lines in the target area from Fig. 9(d). It can be seen and the resolution limit moves to Group 1, Element 1, where the line width is 250 microns. As clearing goes further, the resolution is increased gradually and the final limit is 198 microns, Group1, Element 3 after 16-minute immersion. The process of tissue optical clearing can cause gradual tissue changes, however, our previous work using Mueller matrix imaging can track polarization features at a slower refresh rate, usually 3minutes. Especially in the first several minutes, the sparse polarization image extraction is possible to miss some significant dynamic variations of tissue characteristics with clearing. Stokes imaging improved by us can realize a relatively fast acquisition of polarization features of tissue samples, suitable for revealing and characterize the microstructural details with tissue clearing.
To illustrate the advantages of the method proposed in section 2, we take the process of a 5-minute optical clearing as an example. To quantitatively evaluate the polarization variations, we adopt the central moment method for statistical analysis of frequency distributions of image features [39][40][41]. Since the imaging region of sample is fixed during experiments, the frequency distribution histograms (FDHs) can describe such image changes effectively. The images of δ and DoP before and after optical clearing have been shown in Fig. 10(a), the more detailed variations in the 5 minutes of clearing period can be demonstrated by FDHs of polarization images containing 601×601 pixels, as shown in Fig. 10(b)(c). As shown in Fig. 10(d), the detailed time curves confirm the trend of Stokes elements has a similar regularity with Fig. 6(d).
In Table 2 and Table 3, we calculate four statistical distribution parameters of δ and DOP images to quantitatively describe the dynamic change of polarization features by clearing process. During the optical clearing samples immersed in glycerol, the P1 value of linear retardance decreases significantly from 101.66°to 84.67°while that of DoP increases steadily from 0.19 to 0.28. The two average values reflect the overall impact on scattering suppression and optical anisotropy by the clearing.
Relatively, the changes of P2, P3, P4 parameters of δ images seem a little more complicated than DoP images. Apparently, the skewness of linear retardance changes a lot from a right-skewed distribution to left-skewed, and the corresponding skewness of depolarization experiences a slight adjustment of getting smaller first and then bigger. Compared with the monotonous increasing P2 and decreasing P4 values of DoP with clearing, it also can be noticed that the P2 and P4 values of δ show different trends in the early and late stages of clearing. These interesting phenomena maybe imply some different clearing mechanisms and penetration stages, and we are considering to extract more detailed characterization information from these dynamic polarization parameter distributions in the follow-up study using continuous and rapid Stokes tissue imaging system.
We use sliding window method to obtain continuous Stokes vector, and then improve the tracking ability to tissue dynamic changes like a clearing process. Considering that six sequential light intensity images are needed for calculation, the extraction of polarization parameters presents an average time series trend, which maybe limit its application in some special cases of transient changes in tissue characteristics. The new proposed Stokes polarization imaging system using a polarization camera can realize a real-time refresh rate [42,43], however, the current commercial polarization camera still lacks the ability of circular polarization detection. Compared with polarization characterization based on Mueller matrix system, the new setup can extract the temporal gradual change of tissue depolarization and linear retardance with clearing time with a refresh rate of about 5s. This technique is suitable to online explore some dynamic tissue processes and present some findings on polarization evolution connected with physical and chemical stimulations like clearing. Also based on the time curve of fast Stokes imaging, we can obtain detailed and accurate gradual changes of polarization image contrast and resolution. These polarization characteristic time curves can not only demonstrate the influence of clearing on polarization imaging quality, but also can be connected to the microstructural differences of different tissue types cleared by the same agent. In our ongoing research, with the help of the fast acquisition of temporal polarization images, we are trying to reveal the time nodes, the main mechanisms and their polarization characterization corresponding to different tissue clearing stages.

Conclusion
Polarization imaging has been proved to be a powerful tool for revealing microscopic features of biological tissues. The time consuming of a general Mueller matrix imaging system is not enough to keep up with the dynamic changes of tissue properties in some cases, for example, tissue clearing. In this paper, we demonstrate the configuration and image analysis of continuous Stokes imaging system developed by us. The Stokes imaging interval can be adjusted by changing the number of overlapping images, and the fastest refresh time is only 4.8s while the Mueller matrix imaging time is 192s under the same condition.
Firstly, the good agreement between Mueller matrix imaging and rapid Stokes imaging method can be shown by experiments of the same tape and tissue samples, which validates the image recognition and the computational effectiveness of polarization parameters based on Stokes images. Next, to demonstrate the necessity and accuracy of continuous Stokes polarization analysis, we design three dynamic polarization modulation processes using a combination of rotating half-waveplate and quarter-waveplate. No matter what kind of polarization changing trajectory on the Poincare sphere, the experimental results clearly show the accurate dynamic polarization response analysis based on Stokes imaging sequence, and the insufficient information extraction based on traditional Mueller imaging. Then this paper presents the gradual contrast and resolution of tissue polarization images during the clearing process and further confirms the feasibility of this method to track real tissue characteristics. Finally, we demonstrate the dynamic changes of depolarization and linear retardance from a cleared tissue sample using basic statistical distribution parameters. These polarization characteristic time curves, as some kind of tissue response characteristics during polarization scattering processes, can not only demonstrate the influence of clearing on polarization imaging quality, but also can be connected to the microstructural differences of different tissue types cleared by the same agent. The continuous fast Stokes imaging method and the feature extraction of time series polarization response have the potential of tissue microstructural monitoring and detailed interpretation, and can be further applied in evaluating optical clearing and other drug delivery process.

Disclosures. The authors declare no conflicts of interest.
Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.