Slope-based segmentation of articular cartilage using polarization-sensitive optical coherence tomography phase retardation image

Abstract. A segmentation method based on phase retardation measurements from polarization-sensitive optical coherence tomography (PS-OCT) is developed to differentiate the structural zones of articular cartilage. The organization of collagen matrix in articular cartilage varies over the different structural zones, generating different tissue birefringence. Analyzing the slope of the accumulated phase retardation at different depths can detect the variation in tissue birefringence and be used to segment the structural zones. The method is validated on phantoms composed of layers of different materials. Articular cartilage samples from adult swine are segmented with the method. The characteristics in each segmented zone are also examined by histology and high-resolution second-harmonic generation imaging, showing distinctive properties that match with the anatomical structure of articular cartilage. The segmentation algorithm is also applied on PS-OCT images acquired at multiple illumination angles, where the angular dependence of tissue birefringence in the deep zone is detected. This method offers a noninvasive imaging approach to differentiating the structural zones of articular cartilage, as well as a quantification approach based on the phase retardation measurements of PS-OCT. This method has great potential in studying depth-related progression of cartilage degeneration.


Introduction
Articular cartilage is the tissue that covers the ends of bones in joints and facilitates the transmission of loads. It is composed of a dense extracellular matrix (ECM) of collagen. From the joint surface to the bone, articular cartilage can be divided into four structural zones: superficial zone, transitional zone, deep zone, and calcified zone. 1 Superficial zone makes up 10% to 20% of the cartilage thickness. It is the only zone that contains type I collagen which forms large fiber bundles aligned in parallel to the articular surface. Transitional (or middle) zone covers 40% to 60% of the cartilage thickness. It contains mostly type II collagen which forms collagen fibrils oriented obliquely to the surface. Deep zone and calcified zone together cover 20% to 50% of the cartilage thickness. Deep zone is composed mostly of type II collagen which forms small fibrils aligned perpendicularly to the articular surface. Calcified zone serves as an interface between hard bone and soft cartilage. It is also composed mostly of type II collagen, but with higher degree of mineralization. 2 Osteoarthritis (OA) is the most common form of joint disease and is associated with the degeneration of cartilage ECM. The destruction and structural damage of ECM progress gradually from superficial zone toward deep zone as the severity of degeneration increases. 3 To diagnose the severity of cartilage degeneration, it is important to differentiate the different cartilage structural zones. An imaging and segmentation method that can detect the different structural zones can have many applications in diagnosing and repairing OA. Radiography and arthroscopy are the current standard imaging methods for diagnosing OA. Radiography measures joint space width, which can indicate the loss of cartilage. However, it lacks sufficient resolution for detecting early alterations in cartilage. Arthroscopy can only image cartilage surface but is unable to assess subsurface structures. Those current methods lack diagnostic accuracy, especially for early stage articular cartilage degeneration.
Optical coherence tomography (OCT) is a noninvasive realtime imaging technique, which can acquire the cross-sectional view of tissues. It has micrometer-scale spatial resolution and several millimeters of penetration depth. OCT detects tissue morphology through backscattered light. Using conventional OCT imaging, degenerative cartilage was found to show higher surface irregularity, less tissue homogeneity, and less penetration depth than healthy cartilage. 4,5 However, those morphological changes only occur when the degeneration is already severe. Using conventional OCT, Rogowska et al. 6 segmented the boundary between cartilage and bone. As conventional OCT only measures the intensity image of optical reflectivity in tissue, it cannot differentiate collagen variations in the different structural zones and thus lacks the sensitivity for detecting early cartilage degeneration.
Polarization-sensitive optical coherence tomography (PS-OCT) is a functional extension of conventional OCT. PS-OCT can characterize tissue birefringence by phase retardation measurement. [7][8][9][10] Tissue birefringence occurs in fibrous structures such as collagen fibers, where the optical refractive index along or perpendicular to the fiber direction is different. Such birefringence causes phase retardation between light polarized in those two orientations as light propagates through tissue.
Tissue birefringence is very sensitive to collagen fiber organization, such as diameter, orientation, alignment, etc. As the organization of collagen ECM varies over different structural zones in articular cartilage, the tissue birefringence should also differ from zone to zone. Since PS-OCT has the capability to detect tissue birefringence, it has the potential to differentiate the structural zones.
In some early studies, reduced tissue birefringence was detected in degenerated cartilage due to severe alterations in collagen organization. 11,12 Those studies were still based on conventional OCT where the detection of reduced birefringence was qualitative and indirect. Later on, Ugryumova et al. 13 applied PS-OCT to image articular cartilage and measured tissue birefringence more directly by accumulated phase retardation. Xie et al. 3 utilized PS-OCT to image articular cartilage at different stages of degenerative joint disease (DJD), but found it was yet unable to distinguish the disease stage by qualitative observations from the PS-OCT phase retardation results. By PS-OCT, the tissue birefringence in articular cartilage was found to depend on not only the healthy states, but also the light illumination direction 14 and topographical location. 15 Therefore, a more comprehensive quantitative method is needed to distinguish the different severities of DJD. Brill et al. 16 quantified the features in the banding pattern of phase retardation image, such as the width and height of the bands and the total number of bands. Banding pattern appears when the phase retardation accumulates every π phase shift. This approach is limited to tissues with strong birefringence as those with relatively weak birefringence cannot show the banding pattern, which makes it unsuitable for detecting early cartilage degenerations. Shyu et al. 17 utilized the slope of phase retardation image to quantify birefringence in articular cartilage. A single slope was quantified without the differentiation of structural zones. Multiple regions of interest (ROIs) over the cartilage tissue were analyzed, and the statistical results demonstrated different slope distributions for different disease states. However, there were still difficulties in detecting the specific characterizations and identifying the severity.
As the organization of collagen fibers varies over the different zones in articular cartilage, a better approach can be developed to detect such changes by characterizing the depth variation of tissue birefringence. A similar variation was observed in PS-OCT imaging of retina, where Duan et al. 18 detected almost constant phase retardation in choroid but rapid increase of phase retardation in sclera. They further segmented the chorio-scleral interface based on the change of the phase retardation slope. A theoretical study was carried out by Fanjul-Vélez and Arce-Diego 19 to simulate tissue birefringence in a layered structure using extended Jones matrix calculus. They built an ideal three-layer model for articular cartilage, where the collagen fibers were modeled as exactly parallel to the tissue surface in the superficial zone, in an arched shape in the transitional zone, and exactly perpendicular to the surface in the deep zone. Kasaragod et al. 20 adopted this model and compared experimental data with simulation. By fitting the experimental data with the simulation model, they obtained tissue parameters such as the thickness of the zones, birefringence, and the quadratic function representing the fiber orientation in the transitional zone. Their work showed that the three-layered cartilage structural zones could be extracted from PS-OCT phase retardation image. Nevertheless, their model system assumed ideal conditions of collagen fiber organization, which might not be realistic in practical conditions.
In this study, a segmentation method based on the slope of phase retardation is developed to differentiate the structural zones in articular cartilage from PS-OCT measurements. The method is validated on phantoms composed of multiple layers of materials with different birefringence. The method is then applied on swine articular cartilage to segment the superficial, transitional, and deep zones. The thickness and mean birefringence of each zone are quantified. The effect of illumination angle on the segmentation is also investigated. The characteristics of each segmented zone are further examined by histology and second-harmonic generation (SHG) imaging, which show distinctive features that match with the anatomical structure of articular cartilage. It is shown that this method is capable of differentiating the structural zones in articular cartilage, which can potentially improve the detection of early degeneration in articular cartilage.

Phantom Design
The purpose of a phantom study is to validate the segmentation method on phantoms made by well-defined layers of materials with different birefringence. Two phantoms are developed. Phantom 1 is made by tightly taping three layers of removable tape (Scotch ® Magic™, 3M, 811) around a piece of cover glass (Fisherbrand™, 12-542-C). Removable tape has moderate birefringence, whereas cover glass has no birefringence. The thickness of a single layer of the tape is measured to be 53 AE 1 μm by an electronic digital caliper (Marathon, CO 030200). Phantom 2 is made by covering two layers of removable tape on top of chicken breast muscle. The birefringence of chicken breast muscle is typically two to three times higher than that of tape.

Cartilage Tissue Preparation
Articular bones from the knee joint of adult swine are obtained from a local farm and imaged within 24 h. Cartilage tissue blocks are extracted from the articular bone and cut into cubic blocks with edge length of around 3 to 5 mm. The top of the cubic tissue is the intact natural surface. In this study, PS-OCT imaging on five samples (S1 to S5) extracted from four animals is reported. The sample locations are illustrated in Fig. 1(a). All the samples are extracted from the distal femoral condyle. Samples S1, S2, S4, and S5 are extracted from the medial central location (position 1) of four different animals. Sample S3 is extracted from the lateral central location (position 2) of the same animal as S2. Thus, samples S2 and S3 compare two symmetric locations on the femoral condyle.

Polarization-Sensitive Optical Coherence
Tomography Imaging PS-OCT imaging is conducted on a previously reported PS-OCT system. 10 The schematic of the system is shown in Fig. 2 passive polarization delay unit, two orthogonal polarization states of light are separated and delayed in time. The light then passes through a 75:25 fiber coupler, and the 25% port is sent to illuminate the sample. The backscattered signal from the sample passes through the fiber coupler again, and the 75% port is sent to the detection unit. Light from the sample arm and the reference arm are guided to a polarization diversity (PD) detection unit. The polarization sensitive features are measured by a Jones-matrix-based method. 8,10 The average power on sample is around 2 mW. The depth resolution is ∼8.1 μm in air, and the lateral resolution is ∼19.2 μm.
The illumination and scanning geometry of PS-OCT imaging are shown in Fig. 1(b). The laser beam illuminates on the natural tissue surface from top. The incident angle θ is the angle between the laser beam and the normal of the tissue surface. Sample is attached on a tilting mount so that the incident angle θ can be adjusted in the azimuth plane (XZ plane). At near normal incidence, θ is close to zero, and the beam is almost perpendicular to the tissue surface (XY plane). At tilted illumination, θ is rotated around Y axis. PS-OCT scanning is performed by scanning the laser beam in X (fast scan) and Y (slow scan) directions, with which a 3-D volume can be  acquired. Each B-scan image shows a cross-sectional view in the XZ plane.
In the PS-OCT system, two orthogonal input polarization states are illuminated on the sample, and two PD detectors measure the corresponding OCT output signals. Thus, the OCT output signals at each depth location z can be written as a 2 × 2 matrix: E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 1 ; 6 3 ; 6 7 5 E out ðzÞ ¼ (1) where the superscripts 1 and 2 indicate the response to the input polarization states 1 and 2, respectively, and the subscripts A and B indicate the PD detectors A and B, respectively. A surface segmentation is then applied to obtain the depth position z 0 of the sample surface and the corresponding E out ðz 0 Þ. A similar matrix M of the round-trip Jones matrix of the sample can be constructed as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 6 3 ; 5 4 where J s is the round-trip Jones matrix of the sample, J out is the Jones matrix from the sample surface to the PD detection unit, and χ represents the imperfection of the PD detection. By calculating the similar matrix M, the effect from the matrix J out and χ, which can be regarded as the system-induced polarization impact, can be eliminated. The eigenvalues of J s should be the same eigenvalues λ 1;2 of M due to the property of similar matrix.
The round-trip phase retardation of the sample, δðzÞ, is then obtained as the phase difference between the two eigenvalues as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 3 2 6 ; 7 3 0

Second-Harmonic Generation Imaging
Details about the SHG imaging system can be found in Ref. 21. A femtosecond Ti:sapphire laser is used to excite the nonlinear signal. A 60× objective lens with NA ¼ 1.2 (UPLSAP060XW, Olympus) is used to acquire high-resolution imaging. The lateral resolution of the SHG imaging is 0.4 μm. Each SHG image frame is acquired in the XY plane as marked by the blue rectangles in Fig. 1(b). The field of view is ∼130 μm × 130 μm. Two image stacks are acquired along the tissue depth (Z axis) by depth scanning. One stack is taken from the natural tissue surface into ∼200-μm depth, and the other stack is taken after a ∼0.5 mm of the top layer of the tissue is removed.

Phantom Study
The slope-based segmentation is first tested on phantoms composed of layers of different materials. Figure 3 shows the PS-OCT results for phantom 1, which contains three layers of tape, a piece of cover glass, and three layers of tape again. By PS-OCT imaging, coregistered intensity image and phase retardation image are obtained simultaneously. The intensity B-scan image is shown in Fig. 3(a). For each individual layer of tape, relatively strong back reflection can be obtained from both its upper and lower boundaries. Three zones that are tape-glass-tape can be clearly distinguished in Fig. 3(a). In the top and bottom tape zones, three layers of tape can be seen. Figure 3(b) shows an averaged A-line profile. The peaks correspond to strong back reflection from each layer of the tape in the top and bottom tape zones, respectively. Therefore, from the intensity image, the boundaries between the zones can be clearly visualized.
The corresponding coregistered phase retardation B-scan image is shown in Fig. 3(c), and an averaged A-line profile of the accumulated phase retardation is shown in Fig. 3(d). In Fig. 3(d), it can be observed that the phase retardation increases linearly at the beginning, plateaus in the middle, and increases linearly again. The two linear regions correspond to the top and bottom tape zones, respectively, which show moderate birefringence. Phase retardation accumulates consistently and linearly in those two tape zones. On the other hand, cover glass has no birefringence, and the plateau profile in the middle region shows no accumulation of phase retardation. A ∼1.6-rad phase retardation bias is observed in the plateau area. This kind of bias has also been reported by other groups 22 and is likely caused by averaging random-phase noise in a low signal-tonoise ratio (SNR) region, such as in the glass.
Slope-based segmentation is applied on the phase retardation A-line to find the boundaries between the zones. The two linear regions are segmented by searching the sudden change points (peaks in the second derivative curve) along a phase retardation A-line. The segmentation is obtained from each A-line for a ROI of 3 mm × 3 mm. The segmented boundaries are marked by the dashed lines in Fig. 3(c), corresponding to the phantom surface, boundary between the top tape zone and the cover glass, and boundary between the cover glass and the bottom tape zone, respectively. The same segmented boundaries are also marked in Fig. 3(a) and compared with the intensity image. As we can see, the segmented boundaries match very well with the visible interfaces in the intensity image. The averaged slope is found to be 0.178 AE 0.023 deg ∕μm in the top tape zone and 0.206 AE 0.029 deg ∕μm in the lower tape zone, respectively. The cover glass has no birefringence, where the phase retardation curve is fitted by a flat line. The thickness of the top tape zone (assuming n ¼ 1.3686) is 162.1 AE 6.4 μm from the segmentation results, which is consistent with the measured value of ∼159 μm by the caliper. The thickness of the cover glass (assuming n ¼ 1.5001) is 154.1 AE 9.9 μm from the segmentation results, which matches well with the measured value of ∼155 μm by the caliper.  boundary between the tape and chicken tissue. The slope is found to be 0.183 AE 0.029 deg ∕μm in the tape zone and 0.573 AE 0.097 deg ∕μm in the chicken breast tissue, respectively. The birefringence in the chicken breast tissue is about three times higher than that in the tape. Through the phantom study, it is validated that phase retardation slope can be utilized to segment structural zones with different birefringence.

Cartilage Imaging
The slope-based segmentation method is next applied to cartilage tissues. The various zones in articular cartilage have different collagen organizations, which can result in different birefringence. Thus, multiple layers could be differentiated and segmented based on this property.

Data Processing of Slope-Based Segmentation
The segmentation algorithm is demonstrated on cartilage sample S1 as shown in Fig. 5. Figures 5(a) and 5(b) show the intensity and phase retardation image, respectively. The phase retardation is calculated based on the method described in Sec. 2.3. Details about the data processing are explained below.
Preprocessing: In Fig. 5(a), the tissue surface is clearly shown in the intensity image due to strong backscattering. The tissue surface is identified based on the intensity image and marked as S in the coregistered phase retardation image, as shown in Fig. 5(b). The origin of each A-line is defined at the surface of the tissue. Each A-line in the phase retardation image is then shifted up to flatten the surface. Running averaging is performed on each A-line by averaging it with its surrounding A-lines. The averaging window is selected as 21 A-lines by 11 B-scans by trial and error. Figure 5(c) shows a representative averaged phase retardation A-line, which shows a characteristic feature of multiple linear regions along the depth. From Fig. 5(c), three regions can be observed. The first region has a relatively flat slope and is located at the depth <200 μm; the second region has a slow slope and is located around the depth 200 to 400 μm; and the third region has a fast slope and is located at the depth >450 μm. A multisegment linear fitting will be used to fit the phase retardation A-line.
Reliability thresholding: In the intensity images, SNR drops significantly at deep depth due to light attenuation, which can affect the reliability of the analysis. Effective signal-to-noise ratio (ESNR) is specific for Jones-matrix-based PS-OCT imaging, 22 which balances the SNR in the four channels acquired using two input polarization states and two PD detectors (2 × 2 ¼ 4). To ensure reliable calculation, thresholding is applied and pixels with ESNR <10 dB in the phase retardation image are removed.
Slope-based segmentation: Segmentation of the multiple linear regions is demonstrated on the phase retardation Aline shown in Fig. 5(c) as an example. In the segmentation process, the pixel positions S, B0, B1, B2, and T are solved for each phase retardation A-line, where S is the tissue surface, B0 and T are the starting and ending point, respectively, of the reliable phase retardation accumulation, B1 is the boundary between the superficial and transitional zone, and B2 is the boundary between the transitional and deep zone. Several assumptions are applied in the algorithm based on prior knowledge about articular cartilage: articular cartilage contains three structural zones, the superficial zone has a thickness <200 μm, and the PS-OCT imaging depth can reach the deep zone. Here, B0 is introduced to exclude the first, a few pixels which are highly fluctuating due to surface effect and artifacts. The following steps are taken in the segmentation algorithm: 1. Tissue surface S is extracted by an automatic surface segmentation algorithm applied on the intensity Bscan image. The position of S is then defined as the origin (pixel number 0) in the averaged A-line. From the segmentation, three regions with different phase retardation slopes can be distinguished as R-1 (S − B1), R-2 (B1-B2), and R-3 (B2 − T), corresponding to superficial, transitional, and deep zone, respectively.
Quantification of birefringence: The depth position and thickness of each region can be extracted and quantified from the segmentation. Birefringence is quantified by the slope of the phase retardation curve. For tissue of thickness z, the round-trip phase retardation accumulation can be expressed as δðzÞ ¼ 4πΔn · z∕λ 0 , where λ 0 is the central wavelength. From the linear fitting, the slope of the phase retardation accumulation can be extracted. The slope of the phase retardation is related to the birefringence Δn, as slope ¼ dδðzÞ dz ¼ 4πΔn λ 0 . 9,14 In this study, the optic axis of the collagen fiber is unknown. Thus, the obtained birefringence should be apparent birefringence, which will be discussed in more details later. By analyzing the accumulated phase retardation and quantifying its slope over a sufficient depth range, the accumulative properties of birefringence will be obtained and used to distinguish different structural zones.  Figure 6 shows the results from sample S2 (left column) and S3 (right column). From top to bottom, the intensity image, phase retardation image, and phase retardation A-line are shown, respectively. The segmented boundaries are marked by the dashed lines in the phase retardation images. Comparing Figs. 5 and 6, we can see that samples S2 and S3 show similar features as S1, where the superficial zone has a relatively flat slope and the deep zone has a faster slope than the transitional zone.

Slope-Based Segmentation in Articular Cartilage
The averaged thickness and slope of each segmented region from the 3-D volume of the samples S1 to S3 are summarized in Table 1. Thickness is converted from optical path length by assuming an average refractive index n ¼ 1.444 in articular cartilage. 23 For sample S1, region R-1 is relatively thin with a thickness of ∼125 μm. Region R-2 is twice thicker than R-1, which is consistent with the anatomical knowledge about the thickness of superficial and transitional zones. 1,2 Region R-3 is ∼560-μm thick, and it may not represent the full thickness of the deep zone as the maximum reliable depth is limited by the light penetration. In relatively deep depth (>1 mm), the phase retardation computation becomes less reliable due to low SNR. 24 All the three samples have similar thickness division over the three regions. Especially, samples S2 and S3 show very close thickness in both regions R-1 and R-2. This indicates that the symmetric locations on the same cartilage sample have similar structural zone thickness.
In Table 1, the slopes of samples S1, S2, and S3 show some common characteristics. The slope increases from region R-1 to R-3. The slope in region R-1 is close to zero, with a large standard deviation that is higher than its mean value. This indicates that the phase retardation cannot accumulate sufficiently in region R-1, due to the frequent change of collagen fiber orientations in the superficial zone at different depths. The slope in region R-2 is higher than that in R-1 as collagen fibers become obliquely aligned in the transitional zone. The slope in region R-3 is about 3 to 4 times higher than that in R-2.
Other cases have also been observed where the slope in the deep zone is relatively low, which are likely caused by variations in the topographical locations and illumination angles. More discussions will be provided in Sec. 5.  In our investigation, region R-2 normally shows higher fitting error than the other regions. For the phase retardation slope, the relative standard deviation compared with its average value is also higher in region R-2 than in region R-3. Those information may imply that the collagen orientation in the transitional zone is more random than that in the deep zone. The standard deviation in the superficial zone is high, likely due to a combination of several reasons, such as uneven surface, strong surface reflection, and large fiber bundles with alternating orientations at different depths.

Validation with Histology Image
The PS-OCT segmentation is also compared with histology. In this experiment, sample S4 is imaged by PS-OCT. Afterward, the sample is sent to a histology lab to obtain the histology image. The PS-OCT phase retardation image is shown in Fig. 7(a). Three regions R-1, R-2, and R-3 can be differentiated and segmented based on the slope of the phase retardation measurement. The segmentation boundaries are marked by the dashed lines. The histology image of the same sample is shown in Fig. 7(b). Although the histology image does not have sufficient resolution to resolve collagen fibers, the shape and orientation of chondrocytes can be visualized, showing distinct features in different structural zones. Based on the averaged segmentation depth identified in the phase retardation image, the regions are marked by the brackets on the left side of Fig. 7(b). From the regions R-1, R-2, and R-3, different features of the chondrocytes can be observed. Zoomed-in images from a representative area selected from each region are shown in Figs. 7(c)-7(e), respectively. In Fig. 7(c), the chondrocytes are flattened and aligned almost parallel to the tissue surface. In Fig. 7(d), the chondrocytes are more rounded than in Fig. 7(c), and oriented obliquely. In Fig. 7(e), the chondrocytes are aligned in columns (the dashed lines indicate the approximate alignment of the chondrocytes). Those features in each selected region match with the common features of chondrocytes in the superficial, transitional, and deep zone of articular cartilage, respectively. 1,25 Thus, with the evidence from the histology results, the three segmented regions correspond to the superficial zone (R-1), transitional zone (R-2), and deep zone (R-3).

PS-OCT Imaging Under Various Illumination Angles
PS-OCT measurement has been reported to be sensitive to the illumination angle with respect to the collagen fiber orientation. 13,14,24,26 A multiple illumination angle study is performed on Sample S5 to further verify the multisegment slopebased segmentation in PS-OCT. Figure 8 shows show that the tissue birefringence becomes higher as the illumination angle increases from 0 deg to larger angles.
To verify how the slope-based segmentation can also be applied to tilted illumination, three A-line profiles and the corresponding multisegment linear fitting are shown in Figs. 9(a)-9(c), at illumination angles of around 0 deg, −25 deg, and −40 deg, respectively. The locations of the corresponding Alines are marked by the arrows in the phase retardation images shown in Figs. 8(a), 8(c), and 8(e), respectively. In Fig. 9, the multisegment linear fitting works very well, and three regions are successfully segmented for each case at different illumination angles. From the surface to deep location, the phase retardation slope shows a minimum slope in region R-1, a slow slope in region R-2, and a fast slope in region R-3. Furthermore, the slope in region R-3 is sensitive to the illumination angle and it increases monotonically as the illumination angle increases from 0 deg to −25 deg and −40 deg.
The segmentation algorithm is applied on 3-D volume data at different illumination angles. The averaged segmentation depth and slope for each region are shown in Figs. 10(a) and 10(b), respectively. The averaged segmentation depth for B1, B2, and T are ∼100, 500, and 1100 μm, respectively. Thus, the thickness of R-1, R-2, and R-3 are ∼100, 400, and 600 μm, respectively. In tilted illumination, light travels through a slightly longer path length in a layered structure compared with normal illumination. For the maximum tilting angle of AE40 deg, this difference is calculated to be ∼10% by considering refraction. In  Fig. 10(a), this small difference is not observed in the segmented layer thickness at different illumination angles likely because the variation of the structural zone thickness caused by topographical variation and tissue heterogeneity is >10%. Thus, in this study, the thickness is defined in the direction of the beam illumination for simplicity. At large tilting angles, the SNR is lower and the penetration depth is reduced, which can also be seen in the intensity images. The averaged slopes of the different regions are shown in Fig. 10(b). Region R-3 has a larger slope than regions R-1 and R-2. It indicates that region R-3 has higher tissue birefringence. This is consistent with the anatomical fact that collagen fibers in the deep zone are densely packed and highly aligned. 2,25 The slope of region R-3 shows high sensitivity to the illumination angle. At 0 deg to 15 deg illumination angle, the slope is minimum at ∼0.15 deg ∕μm. At AE40 deg, the slope is increased to ∼0.4 deg ∕μm.
To understand the birefringence measured at different illumination angles, collagen fiber can be modeled as a uniaxial crystal. In a uniaxial crystal, the identical principal indices of refraction are called the ordinary index, n o , and the distinctive index of refraction is called the extraordinary index, n e . The index of refraction for the ordinary wave is simply n o . The index of refraction for the extraordinary wave depends on the angle θ c and is given as 27 where θ c is the angle between the direction of propagation and the optic axis. The true birefringence is defined as jn e − n o j. The apparent birefringence is defined as Δn ¼ n e ðθ c Þ − n o . In this study, the exact orientation of the optic axis is unknown and thus the measured birefringence should be apparent birefringence. When θ c is 0 deg (propagating along the optic axis), the apparent birefringence becomes zero and no birefringence will be observed. When θ c is 90 deg (propagating perpendicular to optic axis), the apparent birefringence reaches a maximum value which is the same as true birefringence.
In the deep zone, collagen fibers are aligned approximately in the perpendicular direction to the surface. When the illumination angle increases, a larger slope is observed, indicating higher apparent birefringence. As the collagen fibers may not be perfectly aligned and exactly parallel with the illumination light even at 0 deg tilting angle, some birefringence is still observed near normal illumination in our experiments. The  slopes in regions R-1 and R-2 are found to be not sensitive to the illumination angle. This is likely because the collagen fibers in the superficial zone change orientation at different depths, and the collagen fibers in the transitional zone are bent with some randomness.

MPM Imaging of Articular Cartilage
Although PS-OCT does not have sufficient resolution to directly visualize collagen fibers, SHG imaging is a high-resolution microscopy technique that can visualize the organization of collagen fibers. SHG imaging is carried out on sample S1 to examine the microscopic features at different depth regions. The microscopic features from the SHG imaging are then compared with the birefringence features measured by the PS-OCT for each structural zone. Figure 11 shows the SHG images from approximately the three depths marked by 1, 2, and 3 in Fig. 5(b). Figures 11(a)- 11(d) show SHG images at depth range 10 to 40 μm, near the tissue surface in region R-1. Large fiber bundles are clearly distinguished, and the fibers are almost parallel to the tissue surface. The fiber orientation changes from frame to frame at different depths. Those features match with the collagen properties in the superficial zone. With the fiber orientation changing frequently within a short depth range, the phase retardation cannot accumulate and the measured birefringence in this layer would be low. This is consistent with the relatively flat slope in region R-1 in the PS-OCT slope-based analysis. Figures 11(i)-11(l) show SHG images at depth around 500 to 600 μm, inside region R-3. The collagen in this region is found to form small fibrils that are densely packed. The dark circular holes correspond to chondrocytes that lack SHG contrast. Those features are consistent with the collagen properties in the deep zone, where type II collagen forms fibrils and the collagen density is high. 1 The orientation of the fibrils is hard to distinguish as limited by the resolution of the SHG imaging system. Figures 11(e)-11(h) show SHG images at depth range around 80 to 140 μm, in the transitional area from R-1 to R-2. The fibers are much smaller than those in the superficial zone, and they are not orientated in parallel with the surface, an indication of oblique orientation. The collagen density seems to be lower than that in the region R-3. Those features are consistent with the properties of the transitional zone. Thus, with the supportive evidence from high-resolution SHG imaging, the segmentations R-1, R-2, and R-3 from the PS-OCT analysis are shown to match with the characteristics of the superficial, transitional, and deep zone, respectively, in articular cartilage.

Discussion
In this study, relatively high birefringence is observed in the deep zone. Similar observations have also been reported by others that the phase retardation in the deep area may accumulate relatively fast in some locations of cartilage samples. 15,26 However, in some other reported literature, 14,16,20 low birefringence has been found in deep zone at normal incidence. The difference in the results shows that the quantification of birefringence in the deep zone is quite sensitive, and it may depend on the types of samples, topographical locations, illumination angles, etc. In our study, the knee joints of swine (4-to 6-months old) were used. In Ref. 14, the samples were extracted from the proximal tibia of adult Holstein dairy cows (5-to 7-years old). In Ref. 16, moderately degenerated cartilage samples were obtained from the central lateral femoral condyles of human patients. In an ideal model where the collagen fibers are aligned perfectly perpendicular to the tissue surface in the deep zone, the birefringence should be low in the deep zone when the incident light is exactly parallel with the fiber orientation under normal incidence. However, in practice, real samples may differ from the ideal model. Studies with multiple measurement locations have shown that the major direction of collagen fibers is not exactly perpendicular to the surface and the angle may vary over locations. 13,15,28 From the measurements over a large area on joint surface, the orientation of collagen fibers in articular cartilage was observed to vary topographically, 28 where the collagen fibers in the deep area were not perpendicular to the tissue surface in the peripheral areas of the joint. Xie et al. 15 demonstrated similar topographical variations by measuring 30 locations on nine healthy bovine tibia samples by PS-OCT and polarized light microscopy (PLM). Among the 30 locations, 16 had shown relatively high birefringence in the deep area. Those samples were found to have tilted fiber orientation in the deep zone (not exactly perpendicular to the surface) observed by PLM. Ugryumova et al. 26 also found that the major collagen fiber orientation in the deep zone was not exactly perpendicular to the tissue surface.
In our experiment, the incident beam cannot be controlled to be aligned exactly parallel with the fiber orientation in the deep zone because the exact fiber orientation is unknown. Thus, it is likely that there is a nonzero angle between the illumination beam and the major collagen fiber orientation in the deep zone. Considering that the collagen fibers in the deep zone are highly aligned and densely packed, even a small angle could possibly result in a relatively high birefringence in the deep zone, which could still be higher than that in the transitional zone, depending on the fiber alignment and packing density in the two zones. From our measurements on multiple swine knee joints, the measured birefringence in the deep zone is usually higher than that in the transitional zone, which may represent a tilted collagen fiber orientation in the deep zone. Cases with relatively low measured birefringence in the deep zone are also observed but rare. It sometimes occurs in the central part of femoral cartilage but is usually limited within a localized area. For the locations demonstrated in this study, we have found similar segmentation results. They consistently show higher slope in deep zone than that in transitional zone. Noticeably, very tilted collagen fiber orientation was also reported from the articular cartilage of swine knee joint, 29 which is consistent with the cases in our study. Collagen fiber orientation in articular cartilage is complex and depends on the types of specimen and age, 29,30 joint and sampling location, 15,28 and other factors such as physical exercise and loading conditions. More studies are required to figure out the details in the future.
In this study, the measured phase retardation slope is related to the apparent birefringence, which is shown to be capable of differentiating the different structural zones in articular cartilage. Several references have reported on detecting the orientation of optic axis and true birefringence. 26,31 Reference 26 used a multiple angle illuminating strategy for measuring the optic axis in cartilage, where measurements with precisely symmetrical incident angles were required. Reference 31 measured the 3-D optic axis in cornea by utilizing extended Jones matrix formalism and prior knowledge of fiber orientation distribution in the sample. Both studies were based on free-space systems, with complex and precise control on the polarization state. Controlling polarization state in fiber-based system is more challenging. For future work, it will be interesting to investigate the detection of optic axis and true birefringence in articular cartilage using fiber-based PS-OCT system.

Conclusion
A segmentation method based on the slope of PS-OCT phase retardation measurement is developed to differentiate the structural zones of articular cartilage. The method is validated on phantoms composed of layers of different materials. Swine articular cartilage samples are segmented to differentiate the different structural zones. Typically, the superficial zone shows a relatively flat slope, the transitional zone shows a slow slope, and the deep zone shows a fast slope. The segmentation regions are further examined by histology and high-resolution SHG imaging, which show distinctive properties that match with the anatomical structures. The slope in the deep zone is found to be sensitive to the illumination angle, where the slope increases significantly with the illumination angle. As the slope of phase retardation is sensitive to and quantifies the tissue birefringence, this approach can detect changes in collagen ECM and thus segment the structural zones based on tissue birefringence. This method has great potential to characterize the progression of depth-dependent articular cartilage degeneration.

Disclosures
The authors have no financial interests or potential conflict of interest to disclose concerning this work.