1.

Introduction

A ligament is a band of soft fibrous tissue that connects bone to bone. Its primary role is to passively control joint motion in response to muscle forces while transmitting mechanical load between bones.^1–3 Routine daily activities apply repetitive and sustained loads up to 25% of the maximum strength of knee ligaments,^4,5 and excessive external force such as car accidents or sports activities can reach up to four times of the daily applied load.⁴ This can lead to ligament damage and injury,⁶ which is most common in knee injuries in the United Kingdom⁷ and has consistently been increasing among young athletes during the past two decades in the United States.⁸ Therefore, studying the mechanical properties of ligaments is crucial for developing effective injury prevention strategies and for providing improved surgical treatment. One of the main factors that affects the nonlinear mechanical and viscoelastic properties of ligaments is the structural architecture.^9–13 The collagen fiber arrangement, the primary load-bearing component in ligaments, has a structural hierarchy.^14–17 From small to large, collagen molecules aggregate to form microfibrils, which in turn form subfibrils, then fibrils, fibers, fascicles, and eventually gross ligament. Approximately 90% of the collagen content in a ligament comprises type I collagen, which is less than what is found in a tendon.^3,18 The collagen fibers are known to have complex wavy undulation crimp patterns.^19,20 Since crimping strongly affects the nonlinear mechanical response of a ligament,^21–24 it is essential to use appropriate imaging techniques to examine the crimp pattern.

There have been numerous studies using polarized light (PL) microscopy to image the crimp patterns in ligaments.^25–29 PL microscopy captures the birefringence of the sample by sandwiching the sample between a pair of crossed polarizers, and the birefringence intensity becomes maximum when the crossed polarizers are 45 deg with respect to the fiber.³⁰ Occasionally, red first-order compensators are applied to show interference colors indicating fiber orientation, and the variation is observed while rotating the polarizer.^30–32 Under the PL microscope, crimped collagen fibers appear to have extinction bands. Combined with tensile tests, researchers have extracted parameters such as crimp angle and fiber orientation under different loading conditions.^27,28,33 Scanning and transmission electron microscopies have been utilized to observe helical patterns in ligaments, which refers to fiber undulation in different planes.^34–36 This helical fashion is also called “fibrillar crimp.”^37,38 Furthermore, the regional difference between the periphery (anterior, posterior) and core portions within ligaments has been analyzed using metrics such as the number of crimps, fibril diameter, and fiber arrangement.^38,39 However, these approaches have low-axial resolution and require relatively invasive sample preparation stages including fixation, dehydration, and coating with gold.^40,41 In contrast, quantitative second-harmonic generation (SHG) microscopy can provide three-dimensional (3-D) quantitative analysis of type I collagen fiber organization and needs minimum sample preparation. Previous studies have used SHG imaging on ligaments to measure parameters such as fiber density and orientation and have correlated them to the computed mechanical properties to evaluate the effects of smoking,⁴² laser damage,⁴³ and chemicals.⁴⁴

SHG is a second-order nonlinear optical process where the signal generated by the sample is at half the wavelength of the incident optical (excitation) field.^45,46 As a microscopy technique, SHG offers high-intrinsic contrast, submicron spatial resolution, and 3-D optical sectioning.⁴⁷ Collagen type I, being intrinsically noncentrosymmetric, is highly specific to SHG^46,47 and provides an excellent opportunity for 3-D imaging of ligaments. Our group has previously shown that SHG combined with spatial Fourier transform (FT) analysis, FT-SHG, is a simple and powerful tool for analyzing collagen fiber organization in tendon,⁴⁸ bone,⁴⁹ and breast tissue.⁵⁰ Moreover, we have shown how to extend quantitative SHG to analyze 3-D collagen fiber organization.^51,52 In this paper, we apply FT-SHG to analysis of the 3-D collagen fiber spatial arrangement in the posterior cruciate ligament (PCL). While Vidal and Mello^32,53 have previously utilized FT analysis on tendons to detect crimp pattern variability, to the best of our knowledge, the work in this study is the first approach to adopt FT-SHG to analyze 3-D crimp organization in ligament tissue. We believe that our crimp pattern analysis could act as a bridge, providing additional information in biomechanical studies that aim to predict damage or injury in the PCL.

2.

Method

2.1.

Sample Preparation

Five porcine knee PCL specimens (of age six months) are cut into thirds along the proximal-distal ligament direction and embedded in an optimal cutting temperature compound (Fig. 1). The middle region between the proximal and distal portions is sectioned at $100\text{-}\mu \mathrm{m}$ thickness by a cryostat (Leica, CM3050S). The thin sections are collected from between the anterior–posterior regions, thereby neglecting the sheath. The tissue sections are then placed on glass microscope slides and #1.5 coverslips are mounted on top with the aqueous mounting media. Tweezers are used to gently lower the coverslip on the microscope slide to avoid creating any air bubbles. After the samples dry, nail polish is applied on the corners to seal the samples. All ligaments are collected from the Meat Science Laboratory of the University of Illinois at Urbana-Champaign. This study is exempt from the Illinois Institutional Animal Care and Use Committee (IACUC).

Fig. 1

(a) Digital image of PCL anatomy, (b) cutting of the PCL into thirds along the proximal-distal direction, and (c) subsequent sectioning of the middle piece into $100\text{-}\mu \mathrm{m}$ thick slices. (d) Mounting of thin sections on a microscope slide with a coverslip placed on top.

2.3.

Image Analysis

The obtained SHG images are analyzed using a customized MATLAB code to label the crimp patterns in each region (Fig. 2). The type discerning algorithm initially calculates the percentage of the dark pixels in the entire image. Those possessing a lower intensity than the dark threshold are identified as dark pixels, and the dark threshold is a single value applied on the entire image, which segments the background to the SHG signal.⁴¹ If the number of dark pixels in the image is less than 10%, the image is assigned as category A (CAT A) or category B (CAT B); conversely, when the number of dark pixels comprises more than 10% of the region, the image is identified as category C (CAT C). Next, spatial FT analysis is carried out on the image, generating a spatial-frequency domain image, and the corresponding two-dimensional magnitude spectrum is integrated radially from 0 deg to 360 deg with a step size of 1 deg. Radial integration values lower than 30% of the maximum value are removed, while those above this threshold are plotted in a polar angular plot for each angle. If the plotted curve fits strongly with a wrapped Gaussian distribution^55,56 ($r^2>0.95$), it is defined as CAT A. When the correlation is weak ($r^2<0.95$), then it is defined as CAT B. For CAT C, the identical radial integration process is applied. In the range of 0 deg to 180 deg, the polar plot with two distinct peaks is further classified as CAT C-2, whereas a single peak plot is CAT C-1. The two peaks can be verified by fitting a wrapped two-term Gaussian distribution and observing the distance of the two means of each peak. The difference of means for CAT C-1 is narrower than 35 deg and wider than 70 deg for CAT C-2. This classification process is applied to all SHG images in the stack. Once the images have a clear tendency toward one type of crimping throughout the whole stack, the entire region is assigned that type. A polar plot that represents the volume can be generated by adding all the data points from each slice.

Fig. 2

Flowchart of image analysis for differentiating crimp types. Initially, the pixels having a lower intensity than the dark threshold are counted and are used to separate CAT A, B from CAT C. FT analysis is applied followed by radial integration to identify CAT A, B, C-1, and C-2. See text for details.

To look at the effect of helicity, the crimp angle is obtained by measuring the fiber orientation differences of the two neighboring SHG bands in CAT C-2 images. Initially, each bright band is isolated, and then FT analysis is applied to the isolated images to calculate the orientation. The same process is implemented on each band, and the corresponding angle is computed.

3.

Results and Discussion

Based on observation, the SHG images are categorized as CAT A, B, or C as shown in Fig. 3. CAT A is characterized as samples with little or no observed crimps in the fibers. Crimps that are confined in-plane are defined as CAT B. Crimps that are out-of-plane, along the third spatial dimension, are defined as CAT C. We consider the fibrous features on the SHG images as “fibers” due to the diameter coinciding with previous studies,¹⁹ and the probability of each crimp type to be detected in the fibrous regions of the PCL is comparable. We note that conventional sample preparation stages such as dissection and cutting into slices could alter the original, natural fiber structure of ligament. However, structure analysis performed on ex vivo condition is a common methodology conducted by many researchers that has been shown to be of value.^{25,28,37,38,43} The primary focus of this study is to employ SHG imaging to quantify collagen fiber crimping of ligament under ex vivo conditions.

Fig. 3

Three types of collagen fiber structure in the PCL. CAT A has almost no waviness of fibers (crimps) and the majority of them are in a single orientation. CAT B has in-plane crimps spreading the range of possible fiber orientations. CAT C has repeating dark and bright bands perpendicular to the fiber direction illustrating crimps out-of-plane. The scale bar is $20\mu \mathrm{m}$.

Figure 4 shows the results of our FT-SHG analysis on representative crimp patterns for CAT A, B, and C. In Fig. 4(a), we observe the typical SHG images for each type. We confirm that CAT A visually appears to have little to no crimps, whereas CAT B shows an in-plane crimp pattern. We observe in Fig. 4(a) that CAT C images also have crimp patterns but with significantly more dark SHG areas compared to CAT A and B. The dark areas are generated because of the out-of-plane crimps. This is due to the SHG intensity reducing once the fibers go out of the image plane and the signal dropping significantly when the fibers are perpendicular with the image plane.^47,57 For further analysis, CAT C is divided into C-1 and C-2, which exhibit irregular and regular crimp patterns, respectively.

Fig. 4

Representative (a) SHG images and the corresponding (b) FT images for each crimp type (CAT A, B, C-1, C-2). The insets represent a magnified view of low spatial-frequency components (center pixels in the black box). These images are integrated radially across different angles and (c) the resulting integrated values (blue) are plotted in a polar plot format. CAT A and B are fitted with a wrapped Gaussian distribution (red), and the correlation coefficient is calculated. CAT C-1 and C-2 are fitted with a two-term wrapped Gaussian distribution (red), and the number of peaks is detected by measuring the distance between the means of the two peaks. For visualization purposes, the FT images are converted to log scale. The scale bar is $40\mu \mathrm{m}$.

The corresponding spatial-frequency maps (on a log scale) for the aforementioned crimp patterns are shown in Fig. 4(b), where the insets highlight the low spatial-frequency components in the center of the spectrum. For CAT A and CAT B, the dominant preferred fiber orientations observed in Fig. 4(a) images are readily picked up in the spectral data. In the case of CAT C-1, we observe more spatial isotropy regarding collagen fiber preferred orientation and crimp direction. However, the spatial-frequency patterns for CAT C-2 reveal the preferred orientation of the collagen fibers (similar to the cases of CAT A and CAT B), as well as the approximately orthogonal dark bands observed in the CAT C-2 SHG image. The low spatial-frequency components in CAT C-2 are affected by the dark bands.

Figure 4(c) shows the radial integration polar plots, which are the sum of the radial integration (obtained from the spatial-frequency data) from each slice within the volume of images per crimp category. Note that the actual summed intensities for the stack, which would typically be labeled along the radius of the plots, are not shown in Fig. 4(c). The straight fibers in CAT A are characteristic of a single orientation, which corresponds to a wrapped Gaussian distribution^55,56 in the polar plot (red curve) with $r^2>0.95$. The majority of fibers in CAT A are oriented along $\sim 95\mathrm{deg}$ [observed in Fig. 4(a)] as confirmed by the peak of the corresponding plot in Fig. 4(c) being marginally over 90 deg. Conversely, fibers in CAT B are curled in-plane. In this case, the in-plane crimping results in neighboring angles being added to the primary fiber orientation and resulting in a broader peak in the polar plot. It can be observed that the radial integration distribution regarding CAT B deviates from a wrapped Gaussian distribution and has a lower correlation coefficient with $r^2<0.95$. In the case of CAT C, the circular plot from 0 deg to 180 deg has two peaks for CAT C-2. One of the peaks represents the orientation of the fibers in the CAT C-2 SHG image, which is along $\sim 110 \mathrm{deg}$. The other peak results from the direction of the regular out-of-plane crimp pattern and appears almost orthogonal from the fiber orientation. This distance between the peaks is calculated by fitting a wrapped two-term Gaussian distribution and measuring the difference between the means of each term. In terms of CAT C-1, the out-of-plane crimps are not clear enough to appear as a peak on the circular plot, so there is usually one single broad peak. The irregularity of the dark bands in CAT C-1 could be caused by the disorder of the crimps^37,58 and an oblique cut from a regular crimp pattern.

The samples are also imaged by conventional imaging techniques such as bright-field [Fig. 5(a)] and PL microscopy [Fig. 5(b)]. The low contrast in Fig. 5(a) results from the unstained biological samples having inherently little contrast.⁵⁹ These instruments are described elsewhere in more detail⁵⁴ and are used for the purpose of mapping and selecting areas for subsequent SHG imaging. Due to the tissue size ($1.2\times 1.2\mathrm{cm}$), $\sim 450$ images are stitched to generate images with larger fields-of-view. By observing the bright-field images, we choose three fibrous regions per sample and obtain SHG images on the selected regions. As shown in Fig. 5(c), SHG microscopy illustrates the collagen fiber structure variation along the depth ($z$-plane) and the corresponding assigned type. This structure variation also differs by region. For example, in Fig. 5(d), region 2 seems to have irregular out-of-plane crimps on slice 1 (CAT C-1), but $12.5\mu \mathrm{m}$ below the plane the pattern appears to be more organized and is categorized as type CAT C-2. $25\mu \mathrm{m}$ below slice 1, the out-of-plane crimps disappear, and the image is assigned to CAT B. Other regions have less feature variance, and the assigned type does not change along the $z$-axis.

Fig. 5

Images of the entire ligament sample using (a) bright-field and (b) PL microscopy (in yellow pseudocolor). Selected fibrous regions on each sample are imaged with SHG in 3-D stacks with the step size of 500 nm. There is (c) a structure variation along the $z$-axis shown by SHG images. All slices in each stack are distinguished by the flowchart and (d) assigned a crimp type. Scale bar is 2 mm and $40\mu \mathrm{m}$, respectively.

The optical sectioning capability of SHG imaging^46,51,60 allows us to capture the overall 3-D structural variations in ligaments. SHG imaging can also be applied to thick samples by collecting the back-scattered SHG signal.^61,62 There have been studies using PL microscopy quantifying crimp organization by measuring the linear birefringence;³¹ however, low-axial resolution diminishes its ability to observe 3-D structural variation. It is important to note that we focus on the aforementioned advantages of SHG microscopy, which make it suitable for revealing collagen fiber structural information. While an in depth one-to-one comparison between imaging modalities is not our primary aim, a brief qualitative comparison of images obtained using SHG microscopy to other modalities is illustrated in the Appendix.

In the case of CAT C-2 images, we observe a repetitive pattern of alternating fiber orientations [Figs. 6(a)–6(b)]. In other words, the fiber bands in the SHG images have a similar orientation in every other band. For example, in Figs. 6(a)–6(b), the first red arrow from the top along with the third and fifth arrows have comparable directions. This also applies to the second, fourth, and sixth arrows. Thus, we suggest that the fibers are not only out-of-plane crimped but also in a helical crimp pattern [Fig. 6(c)]. This is because helical crimps naturally have an out-of-plane region once the fibers twist and change directions. The direction shift is repetitive, which leads to dark bands and bright bands alternating orientation for CAT C-2 crimps. These dark and bright regions are indicated as blue and yellow boxes, respectively, in Figs. 6(a)–6(b). However, since the low-SHG-signal areas are relatively large, it can be thought that the twist areas have a planar crimp that makes the out-of-plane area extended. We utilize solder wires to replicate the crimp pattern in Fig. 6(c), which also illustrates each individual crimped fiber aligned next to each other forming bundles. These bundles of fibers are stacked in layers maintaining its structure. This can be explained due to no particular change in the crimp pattern throughout the $z$-stack. Features in CAT C-2, such as the bright and dark areas and fiber directions, remained constant even though the depth of focus changes for roughly $20\mu \mathrm{m}$.

Fig. 6

In (a) and (b) CAT C-2 images, fiber orientation shifts in a repetitive pattern. Fibers have a similar orientation in every other bright band. Regions in the yellow rectangle have a high SHG intensity, indicating that the fibers are parallel with the image plane. Regions in the blue rectangle have a low intensity, suggesting that the fibers are oblique or perpendicular with the image plane. (c) Solder wires are used to describe the helical crimp pattern with an out-of-plane crimp. (d) Schematic demonstrating how crimped angle is calculated. The scale bar is $20\mu \mathrm{m}$.

Previous studies conducted using electron microscopy^34–36 and PL microscopy^30,31,63 show similar results of the helical crimp patterns. Electron microscopes were able to image twisted fibers directly from highly magnified images, and PL microscopy revealed the helicity of fibers measuring densitometric features from the birefringence intensity. From the helical structure, researchers have suggested their mechanical roles act like a buffer system-absorbing load to prevent damage that could occur in fibers during elongation.³⁸ The helical model has also been applied to simulation models⁶⁴ and analyzed for applications such as grafts.^35,36 Our results from SHG imaging brings another modality for imaging the helicity of ligament fibers and demonstrates the potential to provide image data for 3-D computational simulations of fiber-based anisotropic materials.

The crimp angle is defined as the angle of the crimp with respect to the horizontal [Fig. 6(d)]; thus, intuitively crimp angle in our case is equivalent to one half of the angle differences between each band. The measured crimp angle (data not shown) matches well with previously published data.^38,64,65

4.

Conclusion

In conclusion, FT-SHG was applied for the first time on the PCL to quantitatively assess collagen fiber organization. The results of our work could be summarized in three major points. First, we were able to identify three types of crimping patterns in PCL samples. A customized code, along with FT analysis, was used to quantitatively distinguish each type. Second, unlike traditional imaging modalities used to analyze the PCL, we demonstrated the 3-D variation of crimp structure using SHG imaging. Third, we verified the helical crimp format of collagen fibers in ligament previously observed by electron and PL microscopes. Our work takes advantage of the label-free, high-contrast, and optical sectioning capabilities of SHG microscopy to highlight its potential to be used to link the fibrous structural information in the PCL with its underlying mechanical properties.