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Probing Dynamic Variation of Layered Microstructure Using Backscattering Polarization Imaging

Probing Dynamic Variation of Layered Microstructure Using Backscattering Polarization Imaging hv photonics Article Probing Dynamic Variation of Layered Microstructure Using Backscattering Polarization Imaging 1 , † 2 , † 3 4 1 5 5 Tongjun Bu , Conghui Shao , Yuanhuan Zhu , Tongyu Huang , Qianhao Zhao , Yanan Sun , Yi Wang 1 , 2 , 3 , 4 , and Hui Ma * Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China; btj20@mails.tsinghua.edu.cn (T.B.); zqh20@mails.tsinghua.edu.cn (Q.Z.) Department of Physics, Tsinghua University, Beijing 100084, China; sch18@mails.tsinghua.edu.cn Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen 518055, China; zhu-yh16@mails.tsinghua.edu.cn Department of Biomedical Engineering, Tsinghua University, Beijing 100084, China; hty19@mails.tsinghua.edu.cn Experimental Research Center, China Academy of Chinese Medicine Science, Beijing 100091, China; sunyanan@merc.ac.cn (Y.S.); wangyi@merc.ac.cn (Y.W.) * Correspondence: mahui@tsinghua.edu.cn † These authors contributed equally to this work. Abstract: Polarization imaging can quantitatively probe the microscopic structure of biological tissues which can be complex and consist of layered structures. In this paper, we established a fast-backscattering Mueller matrix imaging system to characterize the dynamic variation in the microstructure of single-layer and double-layer tissues as glycerin solution penetrated into the samples. The characteristic response of Mueller matrix elements, as well as polarization parameters with clearer physics meanings, show that polarization imaging can capture the dynamic variation in the layered microstructure. The experimental results are confirmed by Monte Carlo simulations. Further examination on the accuracy of Mueller matrix measurements also shows that much faster speed has to be considered when backscattering Mueller matrix imaging is applied to living samples. Citation: Bu, T.; Shao, C.; Zhu, Y.; Keywords: dynamics; polarization; backscattering; Mueller matrix Huang, T.; Zhao, Q.; Sun, Y.; Wang, Y.; Ma, H. Probing Dynamic Variation of Layered Microstructure Using Backscattering Polarization Imaging. Photonics 2022, 9, 153. https:// 1. Introduction doi.org/10.3390/photonics9030153 Polarization imaging has many advantages such as being non-invasive, sensitive to microstructural features [1–7], and capable of quantitative detection of microstructural Received: 31 December 2021 features in biological tissues [8–10]. Polarization imaging can be achieved by adding Accepted: 28 January 2022 a polarization states generator and analyzer to existing optical systems. For example, Published: 4 March 2022 common optical microscopes can be upgraded for polarization imaging [11]. Compared Publisher’s Note: MDPI stays neutral with traditional non-polarized optical methods, a polarization measurement can provide with regard to jurisdictional claims in much richer information on the microstructure of scattering samples such as biological published maps and institutional affil- tissues [12]. Such measurements are label-free and non-invasive and are therefore attractive iations. tools for monitoring dynamic processes in living samples. The states of polarization of light can be described by a four-dimensional Stokes vector S. The polarization property of the sample can be characterized by a 4  4 Mueller Copyright: © 2022 by the authors. matrix [12]. As shown in Equation (1), the Mueller matrix is the transformation matrix of Licensee MDPI, Basel, Switzerland. polarization states. This article is an open access article S = MS out in 2 3 distributed under the terms and M11 M12 M13 M14 conditions of the Creative Commons 6 7 M21 M22 M23 M24 (1) 6 7 M = Attribution (CC BY) license (https:// 4 5 M31 M32 M33 M34 creativecommons.org/licenses/by/ M41 M42 M43 M44 4.0/). Photonics 2022, 9, 153. https://doi.org/10.3390/photonics9030153 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 153 2 of 13 Stacking two layers of simple optical properties can result in Mueller matrices (MM) of much more complicated forms [13,14]. Identifying the characteristic behavior of a layered structure can be very helpful to characterize the microstructure of complex tissues. In our previous works, we used multi-color backscattering Mueller matrix imaging (MMI) based on dual rotating retarders (DRRs) [15] to probe the layered skin of mice, since different wavelengths reach different penetration depths [16]. Using experiments on fabricated samples mimicking a layered structure and Monte Carlo simulations based on the sphere-cylinder birefringence model (SCBM), it was proved that specific polarization parameters can be used to identify layered tissues and extract quantitative information on the layers. Tissue optical clearing (TOC) is a convenient technique to increase the penetration depth of thick tissues [17–22]. The replacement of free water with optical clearing agents of higher refractive index, such as glycerin, causes refractive index matching between the scatterers and their surrounding media to reduce the scattering coefficient of biological tissues, which is often considered as one of the major mechanisms of TOC [23–25]. In fact, the optical properties of skins can be affected in many medical practices, such as the application of cosmetics or transdermal drug delivery [26,27]. MMI provide attractive tools for quantitative characterization of the skin conditions. However, in previous works using DRRs backscattering Mueller matrix imaging, we found that the TOC process in double-layer tissues can be complex. The DRRs system took 30 polarization component images in more than 3 min, which appeared too slow to capture the response of the TOC dynamics and could contain significant errors in the measurements. In this paper, we use TOC by glycerin to generate dynamic variations of microstructure and penetration depths in single-layer and double-layer tissues. We established a fast- backscattering Mueller matrix imaging device based on division of focal plane polarimeters (DoFP) [11] with much faster speed and improved measurement accuracy. The device takes 17 s for each MMI measurement, compared with the backscattering MMI device based on DRRs, which takes 192 s [11]. In addition, to investigate the origin for the instability of the experimental results from the DRRs system, we examine in detail how the errors in the MM elements increase for longer intervals between successive measurements of polarization components or Stokes. By monitoring the TOC dynamics on double-layer and monolayer samples, we demonstrate that some MM elements and polarization parameters can characterize the double-layer features during TOC, which demonstrate that the fast- backscattering Mueller matrix imaging can be a powerful tool to probe and understand the dynamics variations in the microstructure of layered tissues. 2. Materials and Methods 2.1. Experimental Setup The backscattering MMI system is based on DoFP which was successfully used in an upright transmission Mueller matrix microscope for fast MMI of tissue slides and cells [11]. In the system, as shown in Figure 1a, all cage system accessories were provided by RayCage(Zhenjiang) Photoelectric Technol-ogy Co., Ltd. Diffusing light from LED source (10 W, 633 nm, Cree) is collimated by a lens (L1, Daheng Optic, Beijing, China) and then modulated by the polarization states generator (PSG) which consists of a polarizer (P1, extinction ratio >1000:1, Daheng Optic, Beijing, China) and a quarter-wave plate (R1, LBTEK Optic, Changsha, China) fixed on a motorized rotation stage (PRM1/Z8, Thorlabs, Newton, NJ, USA). The backscattering photons from the sample are collected by a lens (L2, LBTEK Optic, China) and detected by polarization states analyzer (PSA), which includes 50:50 non-polarized beam splitter prism (NPBS, Thorlab, Newton, NJ, USA) and two DoFP polarimeters (DoFP 1 and DoFP2, Lucid Vision Labs, Canada) installed on the transmission and reflection ends of the NPBS, respectively. A quarter-wave plate (R1, LBTEK Optic, China) is installed between DoFP1 and the transmission end of the prism. The incident angle  is about 15 degrees to avoid the surface reflection from the sample. The resolution Photonics 2022, 9, x FOR PEER REVIEW 3 of 13 Photonics 2022, 9, x FOR PEER REVIEW 3 of 13 50:50 non-polarized beam splitter prism (NPBS, Thorlab, Newton, New Jersey, USA) and two DoFP polarimeters (DoFP 1 and DoFP2, Lucid Vision Labs, Canada) installed on the transmission and reflection ends of the NPBS, respectively. A quarter-wave plate (R1, 50:50 non-polarized beam splitter prism (NPBS, Thorlab, Newton, New Jersey, USA) and LBTEK Optic, China) is installed between DoFP1 and the transmission end of the prism. two DoFP polarimeters (DoFP 1 and DoFP2, Lucid Vision Labs, Canada) installed on the Photonics 2022, 9, 153 The incident angle θ is about 15 degrees to avoid the surface reflection from the sam 3p of le13 . transmission and reflection ends of the NPBS, respectively. A quarter-wave plate (R1, The resolution of the DoFP polarimeters is 2448 × 2048 pixels for 1.2 × 1.0 cm imaging area. LBTEK Optic, China) is installed between DoFP1 and the transmission end of the prism. Maximum errors among the matrix elements of standard samples are less than 1%. The incident angle θ is about 15 degrees to avoid the surface reflection from the sample. of the DoFP The resol polarimeters ution of the DoF is 2448 P po lar2048 imetepixels rs is 2448 for × 1.2 2048 pi 1.0 xels cm for imaging 1.2 × 1.0 cm ar ea. imag Maximum ing area. Maximum errors among the matrix elements of standard samples are less than 1%. errors among the matrix elements of standard samples are less than 1%. DoFP1 DoFP1 R2 DoFP2 R2 DoFP2 L2 L2 Sample Sample (a) ( (a) ( b) b) Figure 1. Photograph (a) and configuration (b) of the fast-backscattering Mueller matrix system Figure 1. Photograph (a) and configuration (b) of the fast-backscattering Mueller matrix system Figure 1. Photograph (a) and configuration (b) of the fast-backscattering Mueller matrix system based on dual division of focal plane (DoFP) polarimeters. based on dual division of focal plane (DoFP) polarimeters. based on dual division of focal plane (DoFP) polarimeters. 2.2. Tissue Samples Preparation 2.2. Tissue Samples Preparation 2.2. Tissue Samples Preparation As shown in Figure 2, we use human wrist inner skin (in vivo), single layer fresh As shown in Figure 2, we use human wrist inner skin (in vivo), single layer fresh tissue As shown in Figure 2, we use human wrist inner skin (in vivo), single layer fresh tissue (ex vivo) and double-layer fresh tissue (ex vivo) as samples. The human skin (Figure (ex vivo) and double-layer fresh tissue (ex vivo) as samples. The human skin (Figure 2a) tissue (ex vivo) and double-layer fresh tissue (ex vivo) as samples. The human skin (Figure 2a) was marked before experiments to ensure that the same position was measured each was marked before experiments to ensure that the same position was measured each time. 2a) was marked before experiments to ensure that the same position was measured each time. We applied 10% glycerin evenly on the mark area for 20 s, then cleaned the surface We applied 10% glycerin evenly on the mark area for 20 s, then cleaned the surface glycerin time. We applied 10% glycerin evenly on the mark area for 20 s, then cleaned the surface glycerin and took MMI on the same area once every 2 min over one hour. and took MMI on the same area once every 2 min over one hour. glycerin and took MMI on the same area once every 2 min over one hour. (a) (b) Photonics 2022, 9, x FOR PEER REVIEW 4 of 13 (a) (b) (c) (d) Figure 2. Tissue samples: (a) human inner wrist skin (anterior face), (b) single-layer tissue consisting Figure 2. Tissue samples: (a) human inner wrist skin (anterior face), (b) single-layer tissue consisting of adipose layer, (c,d) double-layer tissue consisting of porcine skin and adipose layer. of adipose layer, (c,d) double-layer tissue consisting of porcine skin and adipose layer. The single layer and double-layer tissues used in this study were taken from the re- gion of porcine hind legs, which were prepared 2 h after the porcine was butchered. The double-layer tissue (Figure 2c) consists of 0.5 cm thick porcine skin and 0.5 cm thick adi- pose layer. The single layer tissue (Figure 2b) was cut into a 1.5 × 1.5 cm cube of 1 cm thickness. The double-layer tissue (Figure 2c), consisting of 0.5 cm thick porcine skin and 0.5 cm thick adipose layer, was also cut into the same size as the single layer tissue, then was cut into two equal parts with a piece of plastic wrap between them (Figure 2d). Dur- ing experiments, the double-layer sample were turned upside down with the adipose layer at the top and the porcine skin at the bottom. For TOC, 10% glycerin was applied evenly to the single layer tissue and one side of the bilayer tissue for 20 s. The other side of the double-layer tissue served as a control group, since the plastic wrap prevented lat- eral diffusion of the glycerin. For both single-layer and double-layer tissues, we cleaned the surface glycerin and measured them continuously for one hour. 2.3. Polarization Parameters Our previous work has demonstrated that Mueller matrix and polarization parame- ters can be used as effective tools to study the microstructural variation due to interaction between clearing agents and biological tissues [28,29]. The elements of MM contain abun- dant polarization information of tissue. However, the relationship of a single MM element to a particular microstructure is unclear, so it is useful to extract polarization parameters from MM elements to quantitatively characterize the microstructure information of the sample [12,30]. In this work, we adopted Mueller matrix transformation (MMT) parameter b [31] to reflect the process of TOC, which relates to depolarization. Parameter b has been used in monitoring microstructural variations of fresh skeletal muscle tissues [32], probing lay- ered structures by multi-color backscattering polarimetry [16]. In addition, we also ap- plied MMT parameter t1 and Mueller matrix polar decomposition (MMPD) parameter D to the error analysis at different times of single MM measurements, which respectively represent anisotropy and diattenuation of the sample [33]. The equation expressions for the polarization parameter are shown in Equation (2). 𝑀22 𝑀33 𝑏 = 𝑀22 𝑀33 𝑀23 𝑀32 (2) 𝑡1 = 𝐷 = 𝑀12 𝑀13 𝑀14 2.4. Monte Carlo (MC) Simulation Due to the complexity of biological tissues, Monte Carlo (MC) simulation has been widely used in previous works to help us understand the microstructural changes and the Photonics 2022, 9, 153 4 of 13 The single layer and double-layer tissues used in this study were taken from the region of porcine hind legs, which were prepared 2 h after the porcine was butchered. The double-layer tissue (Figure 2c) consists of 0.5 cm thick porcine skin and 0.5 cm thick adipose layer. The single layer tissue (Figure 2b) was cut into a 1.5  1.5 cm cube of 1 cm thickness. The double-layer tissue (Figure 2c), consisting of 0.5 cm thick porcine skin and 0.5 cm thick adipose layer, was also cut into the same size as the single layer tissue, then was cut into two equal parts with a piece of plastic wrap between them (Figure 2d). During experiments, the double-layer sample were turned upside down with the adipose layer at the top and the porcine skin at the bottom. For TOC, 10% glycerin was applied evenly to the single layer tissue and one side of the bilayer tissue for 20 s. The other side of the double-layer tissue served as a control group, since the plastic wrap prevented lateral diffusion of the glycerin. For both single-layer and double-layer tissues, we cleaned the surface glycerin and measured them continuously for one hour. 2.3. Polarization Parameters Our previous work has demonstrated that Mueller matrix and polarization parameters can be used as effective tools to study the microstructural variation due to interaction be- tween clearing agents and biological tissues [28,29]. The elements of MM contain abundant polarization information of tissue. However, the relationship of a single MM element to a particular microstructure is unclear, so it is useful to extract polarization parame- ters from MM elements to quantitatively characterize the microstructure information of the sample [12,30]. In this work, we adopted Mueller matrix transformation (MMT) parameter b [31] to reflect the process of TOC, which relates to depolarization. Parameter b has been used in monitoring microstructural variations of fresh skeletal muscle tissues [32], probing layered structures by multi-color backscattering polarimetry [16]. In addition, we also applied MMT parameter t1 and Mueller matrix polar decomposition (MMPD) parameter D to the error analysis at different times of single MM measurements, which respectively represent anisotropy and diattenuation of the sample [33]. The equation expressions for the polarization parameter are shown in Equation (2). M22+M33 b = 2 2 (M22M33) +(M23+M32) (2) t1 = 2 2 2 D = M12 + M13 + M14 2.4. Monte Carlo (MC) Simulation Due to the complexity of biological tissues, Monte Carlo (MC) simulation has been widely used in previous works to help us understand the microstructural changes and the optical properties of biological tissues [34,35]. In order to further understand the possible microstructural changes during TOC, Monte Carlo simulations based on the sphere-cylinder birefringence model (SCBM) are chosen to simulate the trajectory of photon scattering in tissues and the changes of their polarization states. The detailed parameters used in the MC simulations will be introduced in the following section. 3. Results and Discussions 3.1. TOC Dynamics of Human Skin For backscattering MMI of human skin, only the diagonal elements of MM showed significant response during TOC. As shown in Figure 3, values of M22, M33 and M44 decrease for the first 35 min, then gradually increase and eventually level off with the experimental time. Such a clear turn during TOC indicates that the skin sample is a layered structure because the polarization features change sharply as photons penetrate to another layer of very different optical properties. The sensitive response of diagonal elements M22, M33 and M44 indicates that TOC affects mainly depolarization of human skin. Smaller values of the diagonal elements mean stronger depolarization. The difference between Photonics 2022, 9, x FOR PEER REVIEW 5 of 13 optical properties of biological tissues [34,35]. In order to further understand the possible microstructural changes during TOC, Monte Carlo simulations based on the sphere-cyl- inder birefringence model (SCBM) are chosen to simulate the trajectory of photon scatter- ing in tissues and the changes of their polarization states. The detailed parameters used in the MC simulations will be introduced in the following section. 3. Results and Discussions 3.1. TOC Dynamics of Human Skin For backscattering MMI of human skin, only the diagonal elements of MM showed significant response during TOC. As shown in Figure 3, values of M22, M33 and M44 decrease for the first 35 min, then gradually increase and eventually level off with the experimental time. Such a clear turn during TOC indicates that the skin sample is a lay- ered structure because the polarization features change sharply as photons penetrate to Photonics 2022, 9, 153 5 of 13 another layer of very different optical properties. The sensitive response of diagonal ele- ments M22, M33 and M44 indicates that TOC affects mainly depolarization of human skin. Smaller values of the diagonal elements mean stronger depolarization. The difference be- M22 and M33 is small and the non-diagonal MM elements values are small, both of which tween M22 and M33 is small and the non-diagonal MM elements values are small, both indicate that human skin samples tend to be isotropic [32]. of which indicate that human skin samples tend to be isotropic [32]. 0.21 M22 M33 0.205 0.2 0.195 0.19 0.185 0.18 0 10 203040 5060 Time(min) (a) (b) Figure 3. Average values and standard deviations of the MM diagonal elements of human skin: (a) Figure 3. Average values and standard deviations of the MM diagonal elements of human skin: M22, M33 and (b) M44. The horizontal axes represent the time after the application of 10% glycerin. (a) M22, M33 and (b) M44. The horizontal axes represent the time after the application of 10% glycerin. Since it is Since it d isifficult to difficult to keep the keep the wrist wrist stat stationary ionary for a forlo a ng long tim time, e, we p werpr epepar ared ani ed animal mal tissu tissue e sample samples s for for dedetailed tailed stud studies ies in the in the folfollowing lowing wo works. rks. 3.2. Error Analysis at Different Time of Single MM Measurement 3.2. Error Analysis at Different Time of Single MM Measurement Before using a Mueller matrix device based on DoFP, we have taken MMI of human Before using a Mueller matrix device based on DoFP, we have taken MMI of human skin during TOC by dual rotating retarders (DRRs) Mueller matrix imaging, which recorded skin during TOC by dual rotating retarders (DRRs) Mueller matrix imaging, which rec- 30 polarization component images in about 3 min to derive the MM image. It was found orded 30 polarization component images in about 3 min to derive the MM image. It was that the experimental results were very unstable, unlike what was obtained with the DoFP- found that the experimental results were very unstable, unlike what was obtained with based device. Since the characteristic time scale of TOC for the human skin sample is over the DoFP-based device. Since the characteristic time scale of TOC for the human skin sam- 20 min, we speculate that the instability of experimentally obtained MM is due to the high ple is over 20 min, we speculate that the instability of experimentally obtained MM is due sensitivity of MMI to the duration component measurements. to the high sensitivity of MMI to the duration component measurements. To test the relationship between MMI accuracy and the duration between Stokes imag- To test the relationship between MMI accuracy and the duration between Stokes im- ing, we varied the time between successive Stokes measurements, DT , and compared Stokes aging, we varied the time between successive Stokes measurements, DTStokes, and com- the variation and error of the MM elements. The DoFP-based device takes a Stokes image pared the variation and error of the MM elements. The DoFP-based device takes a Stokes in a snapshot but completes a MM measurement by rotating the quarter wave plate R1 to image in a snapshot but completes a MM measurement by rotating the quarter wave plate four different angles to generate four incident polarization states [11]. Using angle  data R1 to four different angles to generate four incident polarization states [11]. Using angle of first measurement, angle  data of the second measurement, angle  data of the third 2 3 ζ1 data of first measurement, angle ζ2 data of the second measurement, angle ζ3 data of the measurement and angle  data of the fourth measurement, we derive an MM image with third measurement and angle ζ4 data of the fourth measurement, we derive an MM image four times longer intervals in Stokes imaging, DT . In the same way, we can further Stokes with four times longer intervals in Stokes imaging, DTStokes. In the same way, we can fur- extend the time interval by factors of 8, 12 and 16. The device takes 17 s minimum for each ther extend the time interval by factors of 8, 12 and 16. The device takes 17 s minimum for MM measurement, so we can extend the MM imaging time, DT , to 68, 136, 204 and 272 s. MM Figure 4 shows the average value of MM elements at different DT during TOC of the MM double-layer tissue. The MM elements demonstrate larger errors as DT increase: (1) the MM curves of the elements M13, M23 and M32 show significant differences as DT increases, MM while other non-diagonal elements remain almost constant. It indicates that the structural information related to elements M13, M23 and M32 will be affected, such as diattenuation and anisotropy; (2) the peak variations of diagonal elements M22, M33 and M44 indicate that the time error of probing deep information increases with the increase in DT ; and MM (3) the element M22 and M33 gradually fails to probe deeper information of double-layer tissue as DT increases. When the time is greater than 204 s, the characterization of deep MM information by M22 and M33 becomes less obvious, which can be a reasonable explanation for the instability of the experimental results from the DRRs system. It should be noted that, due to the difference in DT , the starting points of the curves in the figure are different. MM Photonics 2022, 9, x FOR PEER REVIEW 6 of 13 each MM measurement, so we can extend the MM imaging time, DTMM, to 68, 136, 204 and 272 s. Figure 4 shows the average value of MM elements at different DTMM during TOC of the double-layer tissue. The MM elements demonstrate larger errors as DTMM increase: (1) the curves of the elements M13, M23 and M32 show significant differences as DTMM in- creases, while other non-diagonal elements remain almost constant. It indicates that the structural information related to elements M13, M23 and M32 will be affected, such as diattenuation and anisotropy; (2) the peak variations of diagonal elements M22, M33 and M44 indicate that the time error of probing deep information increases with the increase in DTMM; and (3) the element M22 and M33 gradually fails to probe deeper information of double-layer tissue as DTMM increases. When the time is greater than 204 s, the character- ization of deep information by M22 and M33 becomes less obvious, which can be a rea- sonable explanation for the instability of the experimental results from the DRRs system. Photonics 2022, 9, 153 6 of 13 It should be noted that, due to the difference in DTMM, the starting points of the curves in the figure are different. 2 0.05 0.05 0.05 17s 68s 136s 1 204s 0 0 0 272s 0 -0.05 -0.05 -0.05 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 0.05 0.05 0.05 0.22 0.2 0 0 0 0.18 0.16 -0.05 0.14 -0.05 -0.05 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 0.05 0.05 0.05 0.22 0.2 0 0 0 0.18 0.16 -0.05 -0.05 0.14 -0.05 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 0.05 0.05 0.05 0.14 0.12 0.1 0 0 0 0.08 0.06 -0.05 -0.05 -0.05 0.04 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 Time(min) Time(min) Time(min) Time(min) Figure 4. Average value of the MM elements for double-layer tissue at different times of single Figure 4. Average value of the MM elements for double-layer tissue at different times of single measurement: 17 s (the purple line), 68 s (the yellow line), 136 s (the blue line), 204 s (the green line) measurement: 17 s (the purple line), 68 s (the yellow line), 136 s (the blue line), 204 s (the green line) and 272 s (the red line). The horizontal axis represents the time after application of 10% glycerin to and 272 s (the red line). The horizontal axis represents the time after application of 10% glycerin to the double-layer tissue. the double-layer tissue. To further examine how the error of MM elements of MM vary with increasing DTMM, To further examine how the error of MM elements of MM vary with increasing DT , MM we set the MM values at the minimum 17 s as the true value and those at other DTMM as we set the MM values at the minimum 17 s as the true value and those at other DT MM the test value. As shown in Figure 5, we calculated factorized errors as the differences as the test value. As shown in Figure 5, we calculated factorized errors as the differences between the true and test values of the MM elements divided by the rate of change of the between the true and test values of the MM elements divided by the rate of change of the true value itself at different DTMM. The equation expressions for the MMError parameter are true value itself at different DT . The equation expressions for the MM parameter MM Error shown in Equation (3). are shown in Equation (3). MM MM Measurement Ture MM = (3) Error dMM /dt Ture The result shows that such errors are always much bigger than the unit, which means that the MM element errors induced by slow acquisition of individual Stokes images, or DT = DT /4, are much more sensitive than the variation of MM elements themselves. stokes MM For reliable measurements of the dynamic processes using Mueller polarimetry, the Stokes imaging time has to be much faster than the time scales of the processes. 3.3. TOC Dynamics of Double-Layer Tissue 3.3.1. Mueller Matrix Elements of Double-Layer Tissue Since TOC experiments on human skin showed layered phenomenon and it is difficult to take high quality long-time measurements on living skins, we prepared a double-layer tissue sample consisting of porcine skin and an adipose layer. Compared to measurements on human skins which took data at 2-min intervals, the double-layer tissue can be sampled Photonics 2022, 9, x FOR PEER REVIEW 7 of 13 𝑀𝑀 = (3) 𝑑𝑀𝑀 𝑑𝑡 Photonics 2022, 9, 153 7 of 13 The result shows that such errors are always much bigger than the unit, which means that the MM element errors induced by slow acquisition of individual Stokes images, or DTstokes = DTMM/4, are much more sensitive than the variation of MM elements themselves. continuously at a minimum interval of 17 s for each measurement, so that more points can For reliable measurements of the dynamic processes using Mueller polarimetry, the be obtained under the same experimental conditions. Stokes imaging time has to be much faster than the time scales of the processes. Figure 5. Relationship between the error of true value and test value and the rate of change of true Figure 5. Relationship between the error of true value and test value and the rate of change of true value itself at different times of single measurement: 17 s (the purple line), 68 s (the yellow line), 136 value itself at different times of single measurement: 17 s (the purple line), 68 s (the yellow line), 136 s s (the blue line), 204 s (the green line) and 272 s (the red line). The horizontal axis represents the time (the blue line), 204 s (the green line) and 272 s (the red line). The horizontal axis represents the time after application of 10% glycerin to the double-layer tissue and the vertical axis represents the value after application of 10% glycerin to the double-layer tissue and the vertical axis represents the value of the error value between the true and test values of the Mueller matrix element divided by the rate of the error value between the true and test values of the Mueller matrix element divided by the rate of change of the true value itself at different measurement times. of change of the true value itself at different measurement times. 3.3. TOC Dynamics of Double-Layer Tissue Figure 6 shows the MM images of double-layer tissue at different treatment in 8, 25 and 3.58 3.1. min, Mue respectively ller Matrix E . Figur lements e 7 of Do showsub the le-L mean ayervalues Tissueof MM elements of double-layer tissue with or without the application of 10% glycerin. The experimental results show that: Since TOC experiments on human skin showed layered phenomenon and it is diffi- (1) the values of all the three diagonal MM elements first decrease and then increase, which cult to take high quality long-time measurements on living skins, we prepared a double- indicates depolarization power first increases and then decreases; (2) the small difference layer tissue sample consisting of porcine skin and an adipose layer. Compared to meas- between M22 and M33 represents that the samples are mainly isotropic; (3) the values of urements on human skins which took data at 2-min intervals, the double-layer tissue can the non-diagonal elements are small and barely change over the experimental time, which be sampled continuously at a minimum interval of 17 s for each measurement, so that also indicates that depolarization plays a major role in the TOC process, whereas other more points can be obtained under the same experimental conditions. factors such as birefringence and linear retardance make limited contributions; and (4) Figure 6 shows the MM images of double-layer tissue at different treatment in 8, 25 the characteristic trends of the MM diagonal elements during TOC also display a layered and 58 min, respectively. Figure 7 shows the mean values of MM elements of double-layer feature which is similar to the human skin. tissue with or without the application of 10% glycerin. The experimental results show that: (1) the values of all the three diagonal MM elements first decrease and then increase, 𝑀𝑀 𝑀𝑀 Photonics 2022, 9, x FOR PEER REVIEW 8 of 13 Photonics 2022, 9, x FOR PEER REVIEW 8 of 13 which indicates depolarization power first increases and then decreases; (2) the small dif- which indicates depolarization power first increases and then decreases; (2) the small dif- ference between M22 and M33 represents that the samples are mainly isotropic; (3) the ference between M22 and M33 represents that the samples are mainly isotropic; (3) the values of the non-diagonal elements are small and barely change over the experimental values of the non-diagonal elements are small and barely change over the experimental time, which also indicates that depolarization plays a major role in the TOC process, time, which also indicates that depolarization plays a major role in the TOC process, whereas other factors such as birefringence and linear retardance make limited contribu- Photonics 2022, 9, 153 8 of 13 whereas other factors such as birefringence and linear retardance make limited contribu- tions; and (4) the characteristic trends of the MM diagonal elements during TOC also dis- tions; and (4) the characteristic trends of the MM diagonal elements during TOC also dis- play a layered feature which is similar to the human skin. play a layered feature which is similar to the human skin. (a) (b) (c) (a) (b) (c) Figure 6. Images of Mueller matrices of double-layer tissue consisting of porcine skin and adipose Figure 6. Images of Mueller matrices of double-layer tissue consisting of porcine skin and adipose Figure 6. Images of Mueller matrices of double-layer tissue consisting of porcine skin and adipose layer in one-hour experimental time: (a) 8, (b) 25, (c) 58 min. Among the 16 matrix element images layer in one-hour experimental time: (a) 8, (b) 25, (c) 58 min. Among the 16 matrix element images of layer in one-hour experimental time: (a) 8, (b) 25, (c) 58 min. Among the 16 matrix element images of the three MM images, the left half represents tissue with application of 10% glycerin and the right of the the thr three M ee MM M images, images, the the left left half half r represe epresents nts ti tissue ssue with with application application of of 1 10% 0% g glycerin lycerin an and d the the rig right ht half represents the control group. half represents the control group. half represents the control group. Figure 7. Average values elements of MM of double-layer tissue at different treatment: application of 10% glycerin (blue lines) and control group (red line). The horizontal axis represents the time after different treatment. 3.3.2. Polarization Parameters of Single-Layer and Double-Layer Tissues We have found that MM elements can probe the double-layer tissue [16], but they may not clearly display the microstructure of the tissues. Polarization parameters with clearer physics meanings, such as b, are more suitable to probe layered tissue during TOC. Particularly, b is negatively correlated depolarization [31]. To further verify that the sharp Photonics 2022, 9, x FOR PEER REVIEW 9 of 13 Figure 7. Average values elements of MM of double-layer tissue at different treatment: application of 10% glycerin (blue lines) and control group (red line). The horizontal axis represents the time after different treatment. 3.3.2. Polarization Parameters of Single-Layer and Double-Layer Tissues Photonics 2022, 9, 153 9 of 13 We have found that MM elements can probe the double-layer tissue [16], but they may not clearly display the microstructure of the tissues. Polarization parameters with clearer physics meanings, such as b, are more suitable to probe layered tissue during TOC. Particularly, b is negatively correlated depolarization [31]. To further verify that the sharp turn at approximately 25 min after TOC was a characteristic feature for layered structure, turn at approximately 25 min after TOC was a characteristic feature for layered structure, we measured TOC using single-layer adipose tissue of the same size and thickness as we measured TOC using single-layer adipose tissue of the same size and thickness as double-layer tissue with 10% glycerin. Figure 5 shows average values of parameter b for double-layer tissue with 10% glycerin. Figure 5 shows average values of parameter b for different samples. different samples. As shown in Figure 8a, for double-layer tissue, the result shows that the structural As shown in Figure 8a, for double-layer tissue, the result shows that the structural variation can be divided into four stages. The 10 min after application of 10% glycerin variation can be divided into four stages. The 10 min after application of 10% glycerin can can be considered as the first stage when b remains almost constant. The second stage be considered as the first stage when b remains almost constant. The second stage is from is from 10 to 25 min when parameter b decreases significantly, which indicates that the 10 to 25 min when parameter b decreases significantly, which indicates that the depolari- depolarization power increases. From 25 to 30 min can be regarded as the third stage when zation power increases. From 25 to 30 min can be regarded as the third stage when pa- parameter b increases. In addition, the fourth stage is from 30 to 60 min when parameter b rameter b increases. In addition, the fourth stage is from 30 to 60 min when parameter b remains nearly constant. By comparing the variation of parameters with single-layer and remains nearly constant. By comparing the variation of parameters with single-layer and double-layer tissue as TOC proceeds, we found a clear peak at 25 min for double-layer double-layer tissue as TOC proceeds, we found a clear peak at 25 min for double-layer tissue and none for single-layer tissue. The different trends in parameters for different tissue and none for single-layer tissue. The different trends in parameters for different samples indicate the ability of parameter b to probe deep information in the TOC process. samples indicate the ability of parameter b to probe deep information in the TOC process. (a) (b) (c) (d) Figure 8. (a)Average values of MMT parameter b of different samples: double-layer tissue (porcine Figure 8. (a) Average values of MMT parameter b of different samples: double-layer tissue (porcine skin and adipose layer) with application of 10% glycerin (the blue line), double-layer tissue (porcine skin and adipose layer) with application of 10% glycerin (the blue line), double-layer tissue (porcine skin and adipose layer) without glycerin (the red line) as control and single-layer tissue (adipose skin and adipose layer) without glycerin (the red line) as control and single-layer tissue (adipose layer) layer) with application of 10% glycerin (the yellow line). Average value of parameters for double- with application of 10% glycerin (the yellow line). Average value of parameters for double-layer tissue at different DT : (b) MMT parameter b, (c) MMT parameter t1 and (d) MMPD parameter D. MM The horizontal axis represents the time after application of 10% glycerin to the double-layer tissue. In this section, we also compared the variations of polarization parameters at different DT . Figure 8b–d shows the average values of MM elements at different DT during MM MM TOC of the double-layer tissue: (1) the variation of parameter b shows that the position of sharp turn at approximately 25 min is gradually delayed as DT increases, indicating MM the time error increase by degrees; (2) the above analysis proves that the sample tends to be isotropic, indicating both anisotropy (MMT parameter t1) and diattenuation (MMPD parameter D) are in a small range, which are shown in Figure 8c,d. when DT = 17 s. MM However, the illusion of increase appears in both parameters D and t1 with the increase in Photonics 2022, 9, 153 10 of 13 DT , resulting in the wrong experimental phenomenon. The result shows fast MMI is MM necessary in subsequent measurements. 3.3.3. Monte Carlo (MC) Simulations In order to better understand the changes in microstructure of the double-layer sam- ples during TOC, we simulate the backward Mueller matrices of the scatterer model (SSM) and the sphere-cylinder birefringence model (SCBM) with Monte Carlo simulations cor- responding to the samples of different layers, respectively. The simulation results are compared with experimental results to verify their validity. For the double-layer samples constructed from porcine adipose and skin used in this paper, we constructed two different optical models corresponding to the two types of structures. Porcine adipose is a typical optically isotropic sample, so we used the spherical scatterer model (SSM), which is an isotropic scatterer, to simulate it with the following parameters: the diameter of the spherical scatterer changes from 0.2 to 0.25 m with an interval of 0.01 m, the scattering coefficient is 140 cm , the refractive index is 1.49 [36] and the refractive index of the medium is 1.35. The porcine skin is rich in collagen fibers, so we used the sphere-cylinder birefringence model (SCBM) for its simulation. The diameters of the scatterers are 0.2 m for the spheres and 1.5 m for the cylinders. The scattering coefficients for spherical and cylindrical scatterers are 10 and 190 cm , respectively [28]. The azimuth angle of the cylinder scatterer is 0 and the rise and fall varies gradually from 40 at 2 intervals to 34 with the course of the TOC. The zenith angle of the cylinder scatterer is 90 , and the rise and fall is 10 . The refractive indices of both spherical and cylindrical scatterers are 1.43, the birefringence value is 3.0  10 and the refractive index of the medium is 1.35. For both models, the incident light wavelength is 633 nm, the thickness is 0.5 cm and the number of photons for a simulation is 10 . We then combine the experimental and simulated data together to analyze and discuss the possible mechanism of tissue permeability. The refractive index matching between the scatterer and the surrounding interstitial in biological tissues is often considered as one of the major mechanisms of TOC [37]. The high permeability of glycerin solutions leads to an increase in the refractive index of the interstitial mass of biological tissues, resulting in a gradual decrease in the refractive index difference between the scatterer and the interstitial mass, thus reducing scattering from the tissue. For this reason, we gradually change the refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.40 to simulate the refractive index matching process. For the double-layer samples, we discuss them in layers. The first layer consists of porcine adipose cells. There have been many experiments and theories linking the optical properties of biological tissue scatterers to their particle size [38]. Combining the experimental data, it can be clearly observed that when the photons mainly pass through the first layer of samples, before the inflection point appears, M22 > M44 [39], which means that the light we observe is mainly scattered by particles that are small compared to the measured wavelength, so the particle size of the spherical scatterers in the first layer of the SSM is smaller, with a diameter of 0.2 m. Considering that the second layer of porcine skin samples is rich in fibrous structures, such as collagen fibers, a SCBM is used. For the effect of tissue permeability on the double-layer samples, we change the refractive index of the two samples media separately during the simulation as a way to achieve refractive index matching. As can be seen in Figure 9, for the b parameter, the simulation process is similar to that of TOC in the experiment. The line preservation bias gradually decreases when tissue permeabilization is performed for isotropic tissues. When TOC is performed for anisotropic media containing coarse fibers, the refractive index matching is accompanied by the gradual ordering of the cylinder scatterers due to water loss, and their backscattering line preservation gradually increases. When the refractive index matching ends, the b-value tends to stabilize. Photonics 2022, 9, x FOR PEER REVIEW 11 of 13 skin samples is rich in fibrous structures, such as collagen fibers, a SCBM is used. For the effect of tissue permeability on the double-layer samples, we change the refractive index of the two samples media separately during the simulation as a way to achieve refractive index matching. As can be seen in Figure 9, for the b parameter, the simulation process is similar to that of TOC in the experiment. The line preservation bias gradually decreases when tissue permeabilization is performed for isotropic tissues. When TOC is performed for aniso- tropic media containing coarse fibers, the refractive index matching is accompanied by the gradual ordering of the cylinder scatterers due to water loss, and their backscattering Photonics 2022, 9, 153 11 of 13 line preservation gradually increases. When the refractive index matching ends, the b- value tends to stabilize. Figure 9. Average values of MMT parameter b and the result of MC simulations for double-layer Figure 9. Average values of MMT parameter b and the result of MC simulations for double-layer tissue. Layer1: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.40. tissue. Layer1: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.40. Layer2: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.39. Layer2: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.39. 4. Con 4. Conclusions clusions In thi In this s p paper aper,, we se we set t up up a a fast-backscattering fast-backscattering Mue Mueller ller m matrix atrix im imaging aging (M (MMI) MI) de device vice based on based on Do DoFP FP. The . The device device takes take17 s 17 s for s for each each MMI MMI measur meas ement uremen which t which is much is mfaster uch faster than than 192 s 192 s for the for DRRs-based the DRRs-based device. device We used . Wethis used DoFP-based this DoFP-b device ased d to evice examine to extissue amine optical tissue clearing (TOC) on human skins and found that the diagonal elements of MM respond optical clearing (TOC) on human skins and found that the diagonal elements of MM re- sensitively to TOC and display a characteristic sharp turn as TOC proceeds, which is an spond sensitively to TOC and display a characteristic sharp turn as TOC proceeds, which indication that photons penetrate another layer of a different optical property. For further is an indication that photons penetrate another layer of a different optical property. For studies of the TOC process of skin, we established single-layer and double-layer tissue further studies of the TOC process of skin, we established single-layer and double-layer samples. We investigated the reasons for the instability of MMI in previous studies of TOC tissue samples. We investigated the reasons for the instability of MMI in previous studies using the slow DRRs-based device. By varying the time interval between successive Stokes of TOC using the slow DRRs-based device. By varying the time interval between succes- images, from which the MM images are calculated, and examining the corresponding sive Stokes images, from which the MM images are calculated, and examining the corre- errors in the MM elements, we proved that such time interval has significant effects on the sponding errors in the MM elements, we proved that such time interval has significant accuracy of MM elements during TOC process. For reliable measurements of the dynamic effects on the accuracy of MM elements during TOC process. For reliable measurements processes using Mueller polarimetry, the Stokes images have to be captured in much shorter of the dynamic processes using Mueller polarimetry, the Stokes images have to be cap- intervals than the time scales of the dynamic process. We also examined the characteristic tured in much shorter intervals than the time scales of the dynamic process. We also ex- behaviors of Mueller matrix elements and polarization parameters with clear physics amined the characteristic behaviors of Mueller matrix elements and polarization parame- meanings, which demonstrates that the fast backscatter Mueller matrix imaging can be a ters with clear physics meanings, which demonstrates that the fast backscatter Mueller powerful tool to probe dynamics of interaction between clearing agents and layered tissues. matrix imaging can be a powerful tool to probe dynamics of interaction between clearing MC simulations based on SCBM proved that refractive index matching can explain the TOC agents and layered tissues. MC simulations based on SCBM proved that refractive index process of the double-layer tissue using 10% glycerin as a clearing agent. The result shows matching can explain the TOC process of the double-layer tissue using 10% glycerin as a that the samples are nearly isotropic, diagonal elements and parameter b, all of which are clearing agent. The result shows that the samples are nearly isotropic, diagonal elements related to depolarization, respond sensitively to the layered structure during TOC. Author Contributions: Conceptualization, H.M.; data curation, T.B., C.S., Q.Z., Y.Z., Y.S. and Y.W.; method- ology, T.H., Y.Z. and Q.Z.; supervision, H.M.; writing—original draft, T.B. and C.S.; writing—review and editing, T.B., C.S. and H.M. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (Grants: 61527826 and 11974206) and the Shenzhen Bureau of Science and Innovation (Grants: JCYJ20170412170814624 and JCYJ20160818143050110). Institutional Review Board Statement: The study was conducted according to the guidelines of the Declaration of Helsinki, and approved by Ethics Committee of Tsinghua University (Ethics Issue No. 9, 2022). Photonics 2022, 9, 153 12 of 13 Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Written informed consent has been obtained from the patient(s) to publish this paper. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy. Conflicts of Interest: The authors declare no conflict of interest. References 1. Gurjar, R.S.; Backman, V.; Perelman, L.T.; Georgakoudi, I.; Badizadegan, K.; Itzkan, I.; Dasari, R.R.; Feld, M.S. Imaging human epithelial properties with polarized light-scattering spectroscopy. Nat. Med. 2001, 7, 1245–1248. [CrossRef] 2. Kunnen, B.; Macdonald, C.; Doronin, A.; Jacques, S.; Eccles, M.; Meglinski, I. 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Probing Dynamic Variation of Layered Microstructure Using Backscattering Polarization Imaging

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hv photonics Article Probing Dynamic Variation of Layered Microstructure Using Backscattering Polarization Imaging 1 , † 2 , † 3 4 1 5 5 Tongjun Bu , Conghui Shao , Yuanhuan Zhu , Tongyu Huang , Qianhao Zhao , Yanan Sun , Yi Wang 1 , 2 , 3 , 4 , and Hui Ma * Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China; btj20@mails.tsinghua.edu.cn (T.B.); zqh20@mails.tsinghua.edu.cn (Q.Z.) Department of Physics, Tsinghua University, Beijing 100084, China; sch18@mails.tsinghua.edu.cn Tsinghua-Berkeley Shenzhen Institute, Tsinghua University, Shenzhen 518055, China; zhu-yh16@mails.tsinghua.edu.cn Department of Biomedical Engineering, Tsinghua University, Beijing 100084, China; hty19@mails.tsinghua.edu.cn Experimental Research Center, China Academy of Chinese Medicine Science, Beijing 100091, China; sunyanan@merc.ac.cn (Y.S.); wangyi@merc.ac.cn (Y.W.) * Correspondence: mahui@tsinghua.edu.cn † These authors contributed equally to this work. Abstract: Polarization imaging can quantitatively probe the microscopic structure of biological tissues which can be complex and consist of layered structures. In this paper, we established a fast-backscattering Mueller matrix imaging system to characterize the dynamic variation in the microstructure of single-layer and double-layer tissues as glycerin solution penetrated into the samples. The characteristic response of Mueller matrix elements, as well as polarization parameters with clearer physics meanings, show that polarization imaging can capture the dynamic variation in the layered microstructure. The experimental results are confirmed by Monte Carlo simulations. Further examination on the accuracy of Mueller matrix measurements also shows that much faster speed has to be considered when backscattering Mueller matrix imaging is applied to living samples. Citation: Bu, T.; Shao, C.; Zhu, Y.; Keywords: dynamics; polarization; backscattering; Mueller matrix Huang, T.; Zhao, Q.; Sun, Y.; Wang, Y.; Ma, H. Probing Dynamic Variation of Layered Microstructure Using Backscattering Polarization Imaging. Photonics 2022, 9, 153. https:// 1. Introduction doi.org/10.3390/photonics9030153 Polarization imaging has many advantages such as being non-invasive, sensitive to microstructural features [1–7], and capable of quantitative detection of microstructural Received: 31 December 2021 features in biological tissues [8–10]. Polarization imaging can be achieved by adding Accepted: 28 January 2022 a polarization states generator and analyzer to existing optical systems. For example, Published: 4 March 2022 common optical microscopes can be upgraded for polarization imaging [11]. Compared Publisher’s Note: MDPI stays neutral with traditional non-polarized optical methods, a polarization measurement can provide with regard to jurisdictional claims in much richer information on the microstructure of scattering samples such as biological published maps and institutional affil- tissues [12]. Such measurements are label-free and non-invasive and are therefore attractive iations. tools for monitoring dynamic processes in living samples. The states of polarization of light can be described by a four-dimensional Stokes vector S. The polarization property of the sample can be characterized by a 4  4 Mueller Copyright: © 2022 by the authors. matrix [12]. As shown in Equation (1), the Mueller matrix is the transformation matrix of Licensee MDPI, Basel, Switzerland. polarization states. This article is an open access article S = MS out in 2 3 distributed under the terms and M11 M12 M13 M14 conditions of the Creative Commons 6 7 M21 M22 M23 M24 (1) 6 7 M = Attribution (CC BY) license (https:// 4 5 M31 M32 M33 M34 creativecommons.org/licenses/by/ M41 M42 M43 M44 4.0/). Photonics 2022, 9, 153. https://doi.org/10.3390/photonics9030153 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 153 2 of 13 Stacking two layers of simple optical properties can result in Mueller matrices (MM) of much more complicated forms [13,14]. Identifying the characteristic behavior of a layered structure can be very helpful to characterize the microstructure of complex tissues. In our previous works, we used multi-color backscattering Mueller matrix imaging (MMI) based on dual rotating retarders (DRRs) [15] to probe the layered skin of mice, since different wavelengths reach different penetration depths [16]. Using experiments on fabricated samples mimicking a layered structure and Monte Carlo simulations based on the sphere-cylinder birefringence model (SCBM), it was proved that specific polarization parameters can be used to identify layered tissues and extract quantitative information on the layers. Tissue optical clearing (TOC) is a convenient technique to increase the penetration depth of thick tissues [17–22]. The replacement of free water with optical clearing agents of higher refractive index, such as glycerin, causes refractive index matching between the scatterers and their surrounding media to reduce the scattering coefficient of biological tissues, which is often considered as one of the major mechanisms of TOC [23–25]. In fact, the optical properties of skins can be affected in many medical practices, such as the application of cosmetics or transdermal drug delivery [26,27]. MMI provide attractive tools for quantitative characterization of the skin conditions. However, in previous works using DRRs backscattering Mueller matrix imaging, we found that the TOC process in double-layer tissues can be complex. The DRRs system took 30 polarization component images in more than 3 min, which appeared too slow to capture the response of the TOC dynamics and could contain significant errors in the measurements. In this paper, we use TOC by glycerin to generate dynamic variations of microstructure and penetration depths in single-layer and double-layer tissues. We established a fast- backscattering Mueller matrix imaging device based on division of focal plane polarimeters (DoFP) [11] with much faster speed and improved measurement accuracy. The device takes 17 s for each MMI measurement, compared with the backscattering MMI device based on DRRs, which takes 192 s [11]. In addition, to investigate the origin for the instability of the experimental results from the DRRs system, we examine in detail how the errors in the MM elements increase for longer intervals between successive measurements of polarization components or Stokes. By monitoring the TOC dynamics on double-layer and monolayer samples, we demonstrate that some MM elements and polarization parameters can characterize the double-layer features during TOC, which demonstrate that the fast- backscattering Mueller matrix imaging can be a powerful tool to probe and understand the dynamics variations in the microstructure of layered tissues. 2. Materials and Methods 2.1. Experimental Setup The backscattering MMI system is based on DoFP which was successfully used in an upright transmission Mueller matrix microscope for fast MMI of tissue slides and cells [11]. In the system, as shown in Figure 1a, all cage system accessories were provided by RayCage(Zhenjiang) Photoelectric Technol-ogy Co., Ltd. Diffusing light from LED source (10 W, 633 nm, Cree) is collimated by a lens (L1, Daheng Optic, Beijing, China) and then modulated by the polarization states generator (PSG) which consists of a polarizer (P1, extinction ratio >1000:1, Daheng Optic, Beijing, China) and a quarter-wave plate (R1, LBTEK Optic, Changsha, China) fixed on a motorized rotation stage (PRM1/Z8, Thorlabs, Newton, NJ, USA). The backscattering photons from the sample are collected by a lens (L2, LBTEK Optic, China) and detected by polarization states analyzer (PSA), which includes 50:50 non-polarized beam splitter prism (NPBS, Thorlab, Newton, NJ, USA) and two DoFP polarimeters (DoFP 1 and DoFP2, Lucid Vision Labs, Canada) installed on the transmission and reflection ends of the NPBS, respectively. A quarter-wave plate (R1, LBTEK Optic, China) is installed between DoFP1 and the transmission end of the prism. The incident angle  is about 15 degrees to avoid the surface reflection from the sample. The resolution Photonics 2022, 9, x FOR PEER REVIEW 3 of 13 Photonics 2022, 9, x FOR PEER REVIEW 3 of 13 50:50 non-polarized beam splitter prism (NPBS, Thorlab, Newton, New Jersey, USA) and two DoFP polarimeters (DoFP 1 and DoFP2, Lucid Vision Labs, Canada) installed on the transmission and reflection ends of the NPBS, respectively. A quarter-wave plate (R1, 50:50 non-polarized beam splitter prism (NPBS, Thorlab, Newton, New Jersey, USA) and LBTEK Optic, China) is installed between DoFP1 and the transmission end of the prism. two DoFP polarimeters (DoFP 1 and DoFP2, Lucid Vision Labs, Canada) installed on the Photonics 2022, 9, 153 The incident angle θ is about 15 degrees to avoid the surface reflection from the sam 3p of le13 . transmission and reflection ends of the NPBS, respectively. A quarter-wave plate (R1, The resolution of the DoFP polarimeters is 2448 × 2048 pixels for 1.2 × 1.0 cm imaging area. LBTEK Optic, China) is installed between DoFP1 and the transmission end of the prism. Maximum errors among the matrix elements of standard samples are less than 1%. The incident angle θ is about 15 degrees to avoid the surface reflection from the sample. of the DoFP The resol polarimeters ution of the DoF is 2448 P po lar2048 imetepixels rs is 2448 for × 1.2 2048 pi 1.0 xels cm for imaging 1.2 × 1.0 cm ar ea. imag Maximum ing area. Maximum errors among the matrix elements of standard samples are less than 1%. errors among the matrix elements of standard samples are less than 1%. DoFP1 DoFP1 R2 DoFP2 R2 DoFP2 L2 L2 Sample Sample (a) ( (a) ( b) b) Figure 1. Photograph (a) and configuration (b) of the fast-backscattering Mueller matrix system Figure 1. Photograph (a) and configuration (b) of the fast-backscattering Mueller matrix system Figure 1. Photograph (a) and configuration (b) of the fast-backscattering Mueller matrix system based on dual division of focal plane (DoFP) polarimeters. based on dual division of focal plane (DoFP) polarimeters. based on dual division of focal plane (DoFP) polarimeters. 2.2. Tissue Samples Preparation 2.2. Tissue Samples Preparation 2.2. Tissue Samples Preparation As shown in Figure 2, we use human wrist inner skin (in vivo), single layer fresh As shown in Figure 2, we use human wrist inner skin (in vivo), single layer fresh tissue As shown in Figure 2, we use human wrist inner skin (in vivo), single layer fresh tissue (ex vivo) and double-layer fresh tissue (ex vivo) as samples. The human skin (Figure (ex vivo) and double-layer fresh tissue (ex vivo) as samples. The human skin (Figure 2a) tissue (ex vivo) and double-layer fresh tissue (ex vivo) as samples. The human skin (Figure 2a) was marked before experiments to ensure that the same position was measured each was marked before experiments to ensure that the same position was measured each time. 2a) was marked before experiments to ensure that the same position was measured each time. We applied 10% glycerin evenly on the mark area for 20 s, then cleaned the surface We applied 10% glycerin evenly on the mark area for 20 s, then cleaned the surface glycerin time. We applied 10% glycerin evenly on the mark area for 20 s, then cleaned the surface glycerin and took MMI on the same area once every 2 min over one hour. and took MMI on the same area once every 2 min over one hour. glycerin and took MMI on the same area once every 2 min over one hour. (a) (b) Photonics 2022, 9, x FOR PEER REVIEW 4 of 13 (a) (b) (c) (d) Figure 2. Tissue samples: (a) human inner wrist skin (anterior face), (b) single-layer tissue consisting Figure 2. Tissue samples: (a) human inner wrist skin (anterior face), (b) single-layer tissue consisting of adipose layer, (c,d) double-layer tissue consisting of porcine skin and adipose layer. of adipose layer, (c,d) double-layer tissue consisting of porcine skin and adipose layer. The single layer and double-layer tissues used in this study were taken from the re- gion of porcine hind legs, which were prepared 2 h after the porcine was butchered. The double-layer tissue (Figure 2c) consists of 0.5 cm thick porcine skin and 0.5 cm thick adi- pose layer. The single layer tissue (Figure 2b) was cut into a 1.5 × 1.5 cm cube of 1 cm thickness. The double-layer tissue (Figure 2c), consisting of 0.5 cm thick porcine skin and 0.5 cm thick adipose layer, was also cut into the same size as the single layer tissue, then was cut into two equal parts with a piece of plastic wrap between them (Figure 2d). Dur- ing experiments, the double-layer sample were turned upside down with the adipose layer at the top and the porcine skin at the bottom. For TOC, 10% glycerin was applied evenly to the single layer tissue and one side of the bilayer tissue for 20 s. The other side of the double-layer tissue served as a control group, since the plastic wrap prevented lat- eral diffusion of the glycerin. For both single-layer and double-layer tissues, we cleaned the surface glycerin and measured them continuously for one hour. 2.3. Polarization Parameters Our previous work has demonstrated that Mueller matrix and polarization parame- ters can be used as effective tools to study the microstructural variation due to interaction between clearing agents and biological tissues [28,29]. The elements of MM contain abun- dant polarization information of tissue. However, the relationship of a single MM element to a particular microstructure is unclear, so it is useful to extract polarization parameters from MM elements to quantitatively characterize the microstructure information of the sample [12,30]. In this work, we adopted Mueller matrix transformation (MMT) parameter b [31] to reflect the process of TOC, which relates to depolarization. Parameter b has been used in monitoring microstructural variations of fresh skeletal muscle tissues [32], probing lay- ered structures by multi-color backscattering polarimetry [16]. In addition, we also ap- plied MMT parameter t1 and Mueller matrix polar decomposition (MMPD) parameter D to the error analysis at different times of single MM measurements, which respectively represent anisotropy and diattenuation of the sample [33]. The equation expressions for the polarization parameter are shown in Equation (2). 𝑀22 𝑀33 𝑏 = 𝑀22 𝑀33 𝑀23 𝑀32 (2) 𝑡1 = 𝐷 = 𝑀12 𝑀13 𝑀14 2.4. Monte Carlo (MC) Simulation Due to the complexity of biological tissues, Monte Carlo (MC) simulation has been widely used in previous works to help us understand the microstructural changes and the Photonics 2022, 9, 153 4 of 13 The single layer and double-layer tissues used in this study were taken from the region of porcine hind legs, which were prepared 2 h after the porcine was butchered. The double-layer tissue (Figure 2c) consists of 0.5 cm thick porcine skin and 0.5 cm thick adipose layer. The single layer tissue (Figure 2b) was cut into a 1.5  1.5 cm cube of 1 cm thickness. The double-layer tissue (Figure 2c), consisting of 0.5 cm thick porcine skin and 0.5 cm thick adipose layer, was also cut into the same size as the single layer tissue, then was cut into two equal parts with a piece of plastic wrap between them (Figure 2d). During experiments, the double-layer sample were turned upside down with the adipose layer at the top and the porcine skin at the bottom. For TOC, 10% glycerin was applied evenly to the single layer tissue and one side of the bilayer tissue for 20 s. The other side of the double-layer tissue served as a control group, since the plastic wrap prevented lateral diffusion of the glycerin. For both single-layer and double-layer tissues, we cleaned the surface glycerin and measured them continuously for one hour. 2.3. Polarization Parameters Our previous work has demonstrated that Mueller matrix and polarization parameters can be used as effective tools to study the microstructural variation due to interaction be- tween clearing agents and biological tissues [28,29]. The elements of MM contain abundant polarization information of tissue. However, the relationship of a single MM element to a particular microstructure is unclear, so it is useful to extract polarization parame- ters from MM elements to quantitatively characterize the microstructure information of the sample [12,30]. In this work, we adopted Mueller matrix transformation (MMT) parameter b [31] to reflect the process of TOC, which relates to depolarization. Parameter b has been used in monitoring microstructural variations of fresh skeletal muscle tissues [32], probing layered structures by multi-color backscattering polarimetry [16]. In addition, we also applied MMT parameter t1 and Mueller matrix polar decomposition (MMPD) parameter D to the error analysis at different times of single MM measurements, which respectively represent anisotropy and diattenuation of the sample [33]. The equation expressions for the polarization parameter are shown in Equation (2). M22+M33 b = 2 2 (M22M33) +(M23+M32) (2) t1 = 2 2 2 D = M12 + M13 + M14 2.4. Monte Carlo (MC) Simulation Due to the complexity of biological tissues, Monte Carlo (MC) simulation has been widely used in previous works to help us understand the microstructural changes and the optical properties of biological tissues [34,35]. In order to further understand the possible microstructural changes during TOC, Monte Carlo simulations based on the sphere-cylinder birefringence model (SCBM) are chosen to simulate the trajectory of photon scattering in tissues and the changes of their polarization states. The detailed parameters used in the MC simulations will be introduced in the following section. 3. Results and Discussions 3.1. TOC Dynamics of Human Skin For backscattering MMI of human skin, only the diagonal elements of MM showed significant response during TOC. As shown in Figure 3, values of M22, M33 and M44 decrease for the first 35 min, then gradually increase and eventually level off with the experimental time. Such a clear turn during TOC indicates that the skin sample is a layered structure because the polarization features change sharply as photons penetrate to another layer of very different optical properties. The sensitive response of diagonal elements M22, M33 and M44 indicates that TOC affects mainly depolarization of human skin. Smaller values of the diagonal elements mean stronger depolarization. The difference between Photonics 2022, 9, x FOR PEER REVIEW 5 of 13 optical properties of biological tissues [34,35]. In order to further understand the possible microstructural changes during TOC, Monte Carlo simulations based on the sphere-cyl- inder birefringence model (SCBM) are chosen to simulate the trajectory of photon scatter- ing in tissues and the changes of their polarization states. The detailed parameters used in the MC simulations will be introduced in the following section. 3. Results and Discussions 3.1. TOC Dynamics of Human Skin For backscattering MMI of human skin, only the diagonal elements of MM showed significant response during TOC. As shown in Figure 3, values of M22, M33 and M44 decrease for the first 35 min, then gradually increase and eventually level off with the experimental time. Such a clear turn during TOC indicates that the skin sample is a lay- ered structure because the polarization features change sharply as photons penetrate to Photonics 2022, 9, 153 5 of 13 another layer of very different optical properties. The sensitive response of diagonal ele- ments M22, M33 and M44 indicates that TOC affects mainly depolarization of human skin. Smaller values of the diagonal elements mean stronger depolarization. The difference be- M22 and M33 is small and the non-diagonal MM elements values are small, both of which tween M22 and M33 is small and the non-diagonal MM elements values are small, both indicate that human skin samples tend to be isotropic [32]. of which indicate that human skin samples tend to be isotropic [32]. 0.21 M22 M33 0.205 0.2 0.195 0.19 0.185 0.18 0 10 203040 5060 Time(min) (a) (b) Figure 3. Average values and standard deviations of the MM diagonal elements of human skin: (a) Figure 3. Average values and standard deviations of the MM diagonal elements of human skin: M22, M33 and (b) M44. The horizontal axes represent the time after the application of 10% glycerin. (a) M22, M33 and (b) M44. The horizontal axes represent the time after the application of 10% glycerin. Since it is Since it d isifficult to difficult to keep the keep the wrist wrist stat stationary ionary for a forlo a ng long tim time, e, we p werpr epepar ared ani ed animal mal tissu tissue e sample samples s for for dedetailed tailed stud studies ies in the in the folfollowing lowing wo works. rks. 3.2. Error Analysis at Different Time of Single MM Measurement 3.2. Error Analysis at Different Time of Single MM Measurement Before using a Mueller matrix device based on DoFP, we have taken MMI of human Before using a Mueller matrix device based on DoFP, we have taken MMI of human skin during TOC by dual rotating retarders (DRRs) Mueller matrix imaging, which recorded skin during TOC by dual rotating retarders (DRRs) Mueller matrix imaging, which rec- 30 polarization component images in about 3 min to derive the MM image. It was found orded 30 polarization component images in about 3 min to derive the MM image. It was that the experimental results were very unstable, unlike what was obtained with the DoFP- found that the experimental results were very unstable, unlike what was obtained with based device. Since the characteristic time scale of TOC for the human skin sample is over the DoFP-based device. Since the characteristic time scale of TOC for the human skin sam- 20 min, we speculate that the instability of experimentally obtained MM is due to the high ple is over 20 min, we speculate that the instability of experimentally obtained MM is due sensitivity of MMI to the duration component measurements. to the high sensitivity of MMI to the duration component measurements. To test the relationship between MMI accuracy and the duration between Stokes imag- To test the relationship between MMI accuracy and the duration between Stokes im- ing, we varied the time between successive Stokes measurements, DT , and compared Stokes aging, we varied the time between successive Stokes measurements, DTStokes, and com- the variation and error of the MM elements. The DoFP-based device takes a Stokes image pared the variation and error of the MM elements. The DoFP-based device takes a Stokes in a snapshot but completes a MM measurement by rotating the quarter wave plate R1 to image in a snapshot but completes a MM measurement by rotating the quarter wave plate four different angles to generate four incident polarization states [11]. Using angle  data R1 to four different angles to generate four incident polarization states [11]. Using angle of first measurement, angle  data of the second measurement, angle  data of the third 2 3 ζ1 data of first measurement, angle ζ2 data of the second measurement, angle ζ3 data of the measurement and angle  data of the fourth measurement, we derive an MM image with third measurement and angle ζ4 data of the fourth measurement, we derive an MM image four times longer intervals in Stokes imaging, DT . In the same way, we can further Stokes with four times longer intervals in Stokes imaging, DTStokes. In the same way, we can fur- extend the time interval by factors of 8, 12 and 16. The device takes 17 s minimum for each ther extend the time interval by factors of 8, 12 and 16. The device takes 17 s minimum for MM measurement, so we can extend the MM imaging time, DT , to 68, 136, 204 and 272 s. MM Figure 4 shows the average value of MM elements at different DT during TOC of the MM double-layer tissue. The MM elements demonstrate larger errors as DT increase: (1) the MM curves of the elements M13, M23 and M32 show significant differences as DT increases, MM while other non-diagonal elements remain almost constant. It indicates that the structural information related to elements M13, M23 and M32 will be affected, such as diattenuation and anisotropy; (2) the peak variations of diagonal elements M22, M33 and M44 indicate that the time error of probing deep information increases with the increase in DT ; and MM (3) the element M22 and M33 gradually fails to probe deeper information of double-layer tissue as DT increases. When the time is greater than 204 s, the characterization of deep MM information by M22 and M33 becomes less obvious, which can be a reasonable explanation for the instability of the experimental results from the DRRs system. It should be noted that, due to the difference in DT , the starting points of the curves in the figure are different. MM Photonics 2022, 9, x FOR PEER REVIEW 6 of 13 each MM measurement, so we can extend the MM imaging time, DTMM, to 68, 136, 204 and 272 s. Figure 4 shows the average value of MM elements at different DTMM during TOC of the double-layer tissue. The MM elements demonstrate larger errors as DTMM increase: (1) the curves of the elements M13, M23 and M32 show significant differences as DTMM in- creases, while other non-diagonal elements remain almost constant. It indicates that the structural information related to elements M13, M23 and M32 will be affected, such as diattenuation and anisotropy; (2) the peak variations of diagonal elements M22, M33 and M44 indicate that the time error of probing deep information increases with the increase in DTMM; and (3) the element M22 and M33 gradually fails to probe deeper information of double-layer tissue as DTMM increases. When the time is greater than 204 s, the character- ization of deep information by M22 and M33 becomes less obvious, which can be a rea- sonable explanation for the instability of the experimental results from the DRRs system. Photonics 2022, 9, 153 6 of 13 It should be noted that, due to the difference in DTMM, the starting points of the curves in the figure are different. 2 0.05 0.05 0.05 17s 68s 136s 1 204s 0 0 0 272s 0 -0.05 -0.05 -0.05 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 0.05 0.05 0.05 0.22 0.2 0 0 0 0.18 0.16 -0.05 0.14 -0.05 -0.05 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 0.05 0.05 0.05 0.22 0.2 0 0 0 0.18 0.16 -0.05 -0.05 0.14 -0.05 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 0.05 0.05 0.05 0.14 0.12 0.1 0 0 0 0.08 0.06 -0.05 -0.05 -0.05 0.04 0 10 2030 405060 0 1020304050 60 0 1020 304050 60 0 10 203040 5060 Time(min) Time(min) Time(min) Time(min) Figure 4. Average value of the MM elements for double-layer tissue at different times of single Figure 4. Average value of the MM elements for double-layer tissue at different times of single measurement: 17 s (the purple line), 68 s (the yellow line), 136 s (the blue line), 204 s (the green line) measurement: 17 s (the purple line), 68 s (the yellow line), 136 s (the blue line), 204 s (the green line) and 272 s (the red line). The horizontal axis represents the time after application of 10% glycerin to and 272 s (the red line). The horizontal axis represents the time after application of 10% glycerin to the double-layer tissue. the double-layer tissue. To further examine how the error of MM elements of MM vary with increasing DTMM, To further examine how the error of MM elements of MM vary with increasing DT , MM we set the MM values at the minimum 17 s as the true value and those at other DTMM as we set the MM values at the minimum 17 s as the true value and those at other DT MM the test value. As shown in Figure 5, we calculated factorized errors as the differences as the test value. As shown in Figure 5, we calculated factorized errors as the differences between the true and test values of the MM elements divided by the rate of change of the between the true and test values of the MM elements divided by the rate of change of the true value itself at different DTMM. The equation expressions for the MMError parameter are true value itself at different DT . The equation expressions for the MM parameter MM Error shown in Equation (3). are shown in Equation (3). MM MM Measurement Ture MM = (3) Error dMM /dt Ture The result shows that such errors are always much bigger than the unit, which means that the MM element errors induced by slow acquisition of individual Stokes images, or DT = DT /4, are much more sensitive than the variation of MM elements themselves. stokes MM For reliable measurements of the dynamic processes using Mueller polarimetry, the Stokes imaging time has to be much faster than the time scales of the processes. 3.3. TOC Dynamics of Double-Layer Tissue 3.3.1. Mueller Matrix Elements of Double-Layer Tissue Since TOC experiments on human skin showed layered phenomenon and it is difficult to take high quality long-time measurements on living skins, we prepared a double-layer tissue sample consisting of porcine skin and an adipose layer. Compared to measurements on human skins which took data at 2-min intervals, the double-layer tissue can be sampled Photonics 2022, 9, x FOR PEER REVIEW 7 of 13 𝑀𝑀 = (3) 𝑑𝑀𝑀 𝑑𝑡 Photonics 2022, 9, 153 7 of 13 The result shows that such errors are always much bigger than the unit, which means that the MM element errors induced by slow acquisition of individual Stokes images, or DTstokes = DTMM/4, are much more sensitive than the variation of MM elements themselves. continuously at a minimum interval of 17 s for each measurement, so that more points can For reliable measurements of the dynamic processes using Mueller polarimetry, the be obtained under the same experimental conditions. Stokes imaging time has to be much faster than the time scales of the processes. Figure 5. Relationship between the error of true value and test value and the rate of change of true Figure 5. Relationship between the error of true value and test value and the rate of change of true value itself at different times of single measurement: 17 s (the purple line), 68 s (the yellow line), 136 value itself at different times of single measurement: 17 s (the purple line), 68 s (the yellow line), 136 s s (the blue line), 204 s (the green line) and 272 s (the red line). The horizontal axis represents the time (the blue line), 204 s (the green line) and 272 s (the red line). The horizontal axis represents the time after application of 10% glycerin to the double-layer tissue and the vertical axis represents the value after application of 10% glycerin to the double-layer tissue and the vertical axis represents the value of the error value between the true and test values of the Mueller matrix element divided by the rate of the error value between the true and test values of the Mueller matrix element divided by the rate of change of the true value itself at different measurement times. of change of the true value itself at different measurement times. 3.3. TOC Dynamics of Double-Layer Tissue Figure 6 shows the MM images of double-layer tissue at different treatment in 8, 25 and 3.58 3.1. min, Mue respectively ller Matrix E . Figur lements e 7 of Do showsub the le-L mean ayervalues Tissueof MM elements of double-layer tissue with or without the application of 10% glycerin. The experimental results show that: Since TOC experiments on human skin showed layered phenomenon and it is diffi- (1) the values of all the three diagonal MM elements first decrease and then increase, which cult to take high quality long-time measurements on living skins, we prepared a double- indicates depolarization power first increases and then decreases; (2) the small difference layer tissue sample consisting of porcine skin and an adipose layer. Compared to meas- between M22 and M33 represents that the samples are mainly isotropic; (3) the values of urements on human skins which took data at 2-min intervals, the double-layer tissue can the non-diagonal elements are small and barely change over the experimental time, which be sampled continuously at a minimum interval of 17 s for each measurement, so that also indicates that depolarization plays a major role in the TOC process, whereas other more points can be obtained under the same experimental conditions. factors such as birefringence and linear retardance make limited contributions; and (4) Figure 6 shows the MM images of double-layer tissue at different treatment in 8, 25 the characteristic trends of the MM diagonal elements during TOC also display a layered and 58 min, respectively. Figure 7 shows the mean values of MM elements of double-layer feature which is similar to the human skin. tissue with or without the application of 10% glycerin. The experimental results show that: (1) the values of all the three diagonal MM elements first decrease and then increase, 𝑀𝑀 𝑀𝑀 Photonics 2022, 9, x FOR PEER REVIEW 8 of 13 Photonics 2022, 9, x FOR PEER REVIEW 8 of 13 which indicates depolarization power first increases and then decreases; (2) the small dif- which indicates depolarization power first increases and then decreases; (2) the small dif- ference between M22 and M33 represents that the samples are mainly isotropic; (3) the ference between M22 and M33 represents that the samples are mainly isotropic; (3) the values of the non-diagonal elements are small and barely change over the experimental values of the non-diagonal elements are small and barely change over the experimental time, which also indicates that depolarization plays a major role in the TOC process, time, which also indicates that depolarization plays a major role in the TOC process, whereas other factors such as birefringence and linear retardance make limited contribu- Photonics 2022, 9, 153 8 of 13 whereas other factors such as birefringence and linear retardance make limited contribu- tions; and (4) the characteristic trends of the MM diagonal elements during TOC also dis- tions; and (4) the characteristic trends of the MM diagonal elements during TOC also dis- play a layered feature which is similar to the human skin. play a layered feature which is similar to the human skin. (a) (b) (c) (a) (b) (c) Figure 6. Images of Mueller matrices of double-layer tissue consisting of porcine skin and adipose Figure 6. Images of Mueller matrices of double-layer tissue consisting of porcine skin and adipose Figure 6. Images of Mueller matrices of double-layer tissue consisting of porcine skin and adipose layer in one-hour experimental time: (a) 8, (b) 25, (c) 58 min. Among the 16 matrix element images layer in one-hour experimental time: (a) 8, (b) 25, (c) 58 min. Among the 16 matrix element images of layer in one-hour experimental time: (a) 8, (b) 25, (c) 58 min. Among the 16 matrix element images of the three MM images, the left half represents tissue with application of 10% glycerin and the right of the the thr three M ee MM M images, images, the the left left half half r represe epresents nts ti tissue ssue with with application application of of 1 10% 0% g glycerin lycerin an and d the the rig right ht half represents the control group. half represents the control group. half represents the control group. Figure 7. Average values elements of MM of double-layer tissue at different treatment: application of 10% glycerin (blue lines) and control group (red line). The horizontal axis represents the time after different treatment. 3.3.2. Polarization Parameters of Single-Layer and Double-Layer Tissues We have found that MM elements can probe the double-layer tissue [16], but they may not clearly display the microstructure of the tissues. Polarization parameters with clearer physics meanings, such as b, are more suitable to probe layered tissue during TOC. Particularly, b is negatively correlated depolarization [31]. To further verify that the sharp Photonics 2022, 9, x FOR PEER REVIEW 9 of 13 Figure 7. Average values elements of MM of double-layer tissue at different treatment: application of 10% glycerin (blue lines) and control group (red line). The horizontal axis represents the time after different treatment. 3.3.2. Polarization Parameters of Single-Layer and Double-Layer Tissues Photonics 2022, 9, 153 9 of 13 We have found that MM elements can probe the double-layer tissue [16], but they may not clearly display the microstructure of the tissues. Polarization parameters with clearer physics meanings, such as b, are more suitable to probe layered tissue during TOC. Particularly, b is negatively correlated depolarization [31]. To further verify that the sharp turn at approximately 25 min after TOC was a characteristic feature for layered structure, turn at approximately 25 min after TOC was a characteristic feature for layered structure, we measured TOC using single-layer adipose tissue of the same size and thickness as we measured TOC using single-layer adipose tissue of the same size and thickness as double-layer tissue with 10% glycerin. Figure 5 shows average values of parameter b for double-layer tissue with 10% glycerin. Figure 5 shows average values of parameter b for different samples. different samples. As shown in Figure 8a, for double-layer tissue, the result shows that the structural As shown in Figure 8a, for double-layer tissue, the result shows that the structural variation can be divided into four stages. The 10 min after application of 10% glycerin variation can be divided into four stages. The 10 min after application of 10% glycerin can can be considered as the first stage when b remains almost constant. The second stage be considered as the first stage when b remains almost constant. The second stage is from is from 10 to 25 min when parameter b decreases significantly, which indicates that the 10 to 25 min when parameter b decreases significantly, which indicates that the depolari- depolarization power increases. From 25 to 30 min can be regarded as the third stage when zation power increases. From 25 to 30 min can be regarded as the third stage when pa- parameter b increases. In addition, the fourth stage is from 30 to 60 min when parameter b rameter b increases. In addition, the fourth stage is from 30 to 60 min when parameter b remains nearly constant. By comparing the variation of parameters with single-layer and remains nearly constant. By comparing the variation of parameters with single-layer and double-layer tissue as TOC proceeds, we found a clear peak at 25 min for double-layer double-layer tissue as TOC proceeds, we found a clear peak at 25 min for double-layer tissue and none for single-layer tissue. The different trends in parameters for different tissue and none for single-layer tissue. The different trends in parameters for different samples indicate the ability of parameter b to probe deep information in the TOC process. samples indicate the ability of parameter b to probe deep information in the TOC process. (a) (b) (c) (d) Figure 8. (a)Average values of MMT parameter b of different samples: double-layer tissue (porcine Figure 8. (a) Average values of MMT parameter b of different samples: double-layer tissue (porcine skin and adipose layer) with application of 10% glycerin (the blue line), double-layer tissue (porcine skin and adipose layer) with application of 10% glycerin (the blue line), double-layer tissue (porcine skin and adipose layer) without glycerin (the red line) as control and single-layer tissue (adipose skin and adipose layer) without glycerin (the red line) as control and single-layer tissue (adipose layer) layer) with application of 10% glycerin (the yellow line). Average value of parameters for double- with application of 10% glycerin (the yellow line). Average value of parameters for double-layer tissue at different DT : (b) MMT parameter b, (c) MMT parameter t1 and (d) MMPD parameter D. MM The horizontal axis represents the time after application of 10% glycerin to the double-layer tissue. In this section, we also compared the variations of polarization parameters at different DT . Figure 8b–d shows the average values of MM elements at different DT during MM MM TOC of the double-layer tissue: (1) the variation of parameter b shows that the position of sharp turn at approximately 25 min is gradually delayed as DT increases, indicating MM the time error increase by degrees; (2) the above analysis proves that the sample tends to be isotropic, indicating both anisotropy (MMT parameter t1) and diattenuation (MMPD parameter D) are in a small range, which are shown in Figure 8c,d. when DT = 17 s. MM However, the illusion of increase appears in both parameters D and t1 with the increase in Photonics 2022, 9, 153 10 of 13 DT , resulting in the wrong experimental phenomenon. The result shows fast MMI is MM necessary in subsequent measurements. 3.3.3. Monte Carlo (MC) Simulations In order to better understand the changes in microstructure of the double-layer sam- ples during TOC, we simulate the backward Mueller matrices of the scatterer model (SSM) and the sphere-cylinder birefringence model (SCBM) with Monte Carlo simulations cor- responding to the samples of different layers, respectively. The simulation results are compared with experimental results to verify their validity. For the double-layer samples constructed from porcine adipose and skin used in this paper, we constructed two different optical models corresponding to the two types of structures. Porcine adipose is a typical optically isotropic sample, so we used the spherical scatterer model (SSM), which is an isotropic scatterer, to simulate it with the following parameters: the diameter of the spherical scatterer changes from 0.2 to 0.25 m with an interval of 0.01 m, the scattering coefficient is 140 cm , the refractive index is 1.49 [36] and the refractive index of the medium is 1.35. The porcine skin is rich in collagen fibers, so we used the sphere-cylinder birefringence model (SCBM) for its simulation. The diameters of the scatterers are 0.2 m for the spheres and 1.5 m for the cylinders. The scattering coefficients for spherical and cylindrical scatterers are 10 and 190 cm , respectively [28]. The azimuth angle of the cylinder scatterer is 0 and the rise and fall varies gradually from 40 at 2 intervals to 34 with the course of the TOC. The zenith angle of the cylinder scatterer is 90 , and the rise and fall is 10 . The refractive indices of both spherical and cylindrical scatterers are 1.43, the birefringence value is 3.0  10 and the refractive index of the medium is 1.35. For both models, the incident light wavelength is 633 nm, the thickness is 0.5 cm and the number of photons for a simulation is 10 . We then combine the experimental and simulated data together to analyze and discuss the possible mechanism of tissue permeability. The refractive index matching between the scatterer and the surrounding interstitial in biological tissues is often considered as one of the major mechanisms of TOC [37]. The high permeability of glycerin solutions leads to an increase in the refractive index of the interstitial mass of biological tissues, resulting in a gradual decrease in the refractive index difference between the scatterer and the interstitial mass, thus reducing scattering from the tissue. For this reason, we gradually change the refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.40 to simulate the refractive index matching process. For the double-layer samples, we discuss them in layers. The first layer consists of porcine adipose cells. There have been many experiments and theories linking the optical properties of biological tissue scatterers to their particle size [38]. Combining the experimental data, it can be clearly observed that when the photons mainly pass through the first layer of samples, before the inflection point appears, M22 > M44 [39], which means that the light we observe is mainly scattered by particles that are small compared to the measured wavelength, so the particle size of the spherical scatterers in the first layer of the SSM is smaller, with a diameter of 0.2 m. Considering that the second layer of porcine skin samples is rich in fibrous structures, such as collagen fibers, a SCBM is used. For the effect of tissue permeability on the double-layer samples, we change the refractive index of the two samples media separately during the simulation as a way to achieve refractive index matching. As can be seen in Figure 9, for the b parameter, the simulation process is similar to that of TOC in the experiment. The line preservation bias gradually decreases when tissue permeabilization is performed for isotropic tissues. When TOC is performed for anisotropic media containing coarse fibers, the refractive index matching is accompanied by the gradual ordering of the cylinder scatterers due to water loss, and their backscattering line preservation gradually increases. When the refractive index matching ends, the b-value tends to stabilize. Photonics 2022, 9, x FOR PEER REVIEW 11 of 13 skin samples is rich in fibrous structures, such as collagen fibers, a SCBM is used. For the effect of tissue permeability on the double-layer samples, we change the refractive index of the two samples media separately during the simulation as a way to achieve refractive index matching. As can be seen in Figure 9, for the b parameter, the simulation process is similar to that of TOC in the experiment. The line preservation bias gradually decreases when tissue permeabilization is performed for isotropic tissues. When TOC is performed for aniso- tropic media containing coarse fibers, the refractive index matching is accompanied by the gradual ordering of the cylinder scatterers due to water loss, and their backscattering Photonics 2022, 9, 153 11 of 13 line preservation gradually increases. When the refractive index matching ends, the b- value tends to stabilize. Figure 9. Average values of MMT parameter b and the result of MC simulations for double-layer Figure 9. Average values of MMT parameter b and the result of MC simulations for double-layer tissue. Layer1: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.40. tissue. Layer1: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.40. Layer2: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.39. Layer2: refractive index of the interstitial mass from 1.35 with 0.01 as an interval to 1.39. 4. Con 4. Conclusions clusions In thi In this s p paper aper,, we se we set t up up a a fast-backscattering fast-backscattering Mue Mueller ller m matrix atrix im imaging aging (M (MMI) MI) de device vice based on based on Do DoFP FP. The . The device device takes take17 s 17 s for s for each each MMI MMI measur meas ement uremen which t which is much is mfaster uch faster than than 192 s 192 s for the for DRRs-based the DRRs-based device. device We used . Wethis used DoFP-based this DoFP-b device ased d to evice examine to extissue amine optical tissue clearing (TOC) on human skins and found that the diagonal elements of MM respond optical clearing (TOC) on human skins and found that the diagonal elements of MM re- sensitively to TOC and display a characteristic sharp turn as TOC proceeds, which is an spond sensitively to TOC and display a characteristic sharp turn as TOC proceeds, which indication that photons penetrate another layer of a different optical property. For further is an indication that photons penetrate another layer of a different optical property. For studies of the TOC process of skin, we established single-layer and double-layer tissue further studies of the TOC process of skin, we established single-layer and double-layer samples. We investigated the reasons for the instability of MMI in previous studies of TOC tissue samples. We investigated the reasons for the instability of MMI in previous studies using the slow DRRs-based device. By varying the time interval between successive Stokes of TOC using the slow DRRs-based device. By varying the time interval between succes- images, from which the MM images are calculated, and examining the corresponding sive Stokes images, from which the MM images are calculated, and examining the corre- errors in the MM elements, we proved that such time interval has significant effects on the sponding errors in the MM elements, we proved that such time interval has significant accuracy of MM elements during TOC process. For reliable measurements of the dynamic effects on the accuracy of MM elements during TOC process. For reliable measurements processes using Mueller polarimetry, the Stokes images have to be captured in much shorter of the dynamic processes using Mueller polarimetry, the Stokes images have to be cap- intervals than the time scales of the dynamic process. We also examined the characteristic tured in much shorter intervals than the time scales of the dynamic process. We also ex- behaviors of Mueller matrix elements and polarization parameters with clear physics amined the characteristic behaviors of Mueller matrix elements and polarization parame- meanings, which demonstrates that the fast backscatter Mueller matrix imaging can be a ters with clear physics meanings, which demonstrates that the fast backscatter Mueller powerful tool to probe dynamics of interaction between clearing agents and layered tissues. matrix imaging can be a powerful tool to probe dynamics of interaction between clearing MC simulations based on SCBM proved that refractive index matching can explain the TOC agents and layered tissues. MC simulations based on SCBM proved that refractive index process of the double-layer tissue using 10% glycerin as a clearing agent. The result shows matching can explain the TOC process of the double-layer tissue using 10% glycerin as a that the samples are nearly isotropic, diagonal elements and parameter b, all of which are clearing agent. The result shows that the samples are nearly isotropic, diagonal elements related to depolarization, respond sensitively to the layered structure during TOC. Author Contributions: Conceptualization, H.M.; data curation, T.B., C.S., Q.Z., Y.Z., Y.S. and Y.W.; method- ology, T.H., Y.Z. and Q.Z.; supervision, H.M.; writing—original draft, T.B. and C.S.; writing—review and editing, T.B., C.S. and H.M. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Natural Science Foundation of China (Grants: 61527826 and 11974206) and the Shenzhen Bureau of Science and Innovation (Grants: JCYJ20170412170814624 and JCYJ20160818143050110). 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Journal

Photonics – Multidisciplinary Digital Publishing Institute

Published: Mar 4, 2022

Keywords: dynamics; polarization; backscattering; Mueller matrix

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