Polarization-Sensitive Second Harmonic Generation Microscopy for Investigations of Diseased Collagenous Tissues

The advancement of non-invasive quantitative optical diagnosis techniques such as polarization-sensitive second harmonic generation microscopy (PSHG) for diseases such as cancer presents opportunities for improving disease understanding and survival rates. Here, novel and developing techniques in PSHG microscopy applied for the differentiation of cancerous or diseased tissues are presented, including circular dichroism, modulation of laser linear polarization, detection of outgoing linear laser polarization, and double-Stokes Mueller. Typically, initial cancer diagnosis is performed by visual inspection of stained biopsy or surgical resection tissue sections under bright-field microscopy, however, early diagnosis is challenging due to variability in morphological interpretation of the tissues, and because cancer initiation regions can be small and easy to miss. Therefore, pathologists could benefit in identifying cancer on biopsy or surgical resection sections by using unbiased quantitative automated technologies with high spatial resolution and improved disease specificity that can check the entire slide pixel-by-pixel. Second harmonic generation microscopy offers the opportunity to measure ultrastructural alterations in collagenous scaffolds of organ tissues virtually background free on submicron-sized tissue regions. The approach is particularly interesting for cancer diagnosis applications, because during cancer initiation and progression, the collagen in the affected tissue extracellular matrix is often deregulated and becomes disorganized. This mini-review contains a thorough summary of PSHG techniques that have interrogated diseased tissues, and discusses their technical variations and successes in disease discrimination.


INTRODUCTION
Second harmonic generation (SHG) or frequency doubling is a nonlinear optical process which occurs efficiently in a microscope when two laser photons of wavelength λ interact with matter to produce light at λ/2 ( Figure 1B). Only non-central symmetric materials at both molecular and macromolecular scales can produce SHG and therefore, microcrystalline structures are required for SHG. In animals, most SHG occurs from fibrous collagenous connective tissues or myosin in muscle tissues, both having a non-central microcrystalline structure. Since the SHG is emitted due to the presence and ultrastructure of the muscle or collagen interacting with the laser, no dyes or sample modification procedures are needed, and the signal can be interpreted as a direct indicator of structural sample changes.
SHG is energy conserving and consequently does not photobleach, differing significantly from non-parametric processes, such as fluorescence, where absorbed Stokes energy often leads to sample damage and photobleaching.
For biological imaging, lasers with wavelength outside of the tissue absorption spectrum are typically chosen, therefore reduced heat is deposited into the sample allowing for long duration functional in vivo studies.
The SHG intensity and polarization can be written: , where ":" is the tensor product, E . is the intensity and polarization of the laser electric field, and χ (2) FIGURE 1 | Typical microscope schematics for forward-(A) and epi-detection (C) configurations for polarization-sensitive second harmonic generation (SHG) microscopy. The energy state diagram of SHG (B) along with the coordinate system, where Z-X is the image plane and the laser propagates along Y, for an arbitrarily oriented fiber (D) is shown. Abbreviations: SM-scanning mirrors, PSG-polarization state generator, EO-excitation microscope objective, CO-collection microscope objective, PSA-polarization state analyzer, F-filter, PMT-photomultiplier tube detector and DM-dichroic mirror. Example images obtained using PI-SHG (E), CD-SHG (F), DSMP-SHG (G) and PIPO-SHG (H). SHG intensity (E-i), fitted ρ (E-ii) and fitted ρ distribution width (E-iii) are shown for normal and fibrotic liver [14]. SHG images (F) of normal skin and osteogenesis imperfecta (O-i) skin tissues using right-handed circularly polarized light (RHCP), left-handed circularly polarized light (LHCP) and CD-SHG (CD) where red and blue show positive and negative values, respectively [43]. Laboratory-frame χ (2) values (G) of normal and double + breast tissue using DSMP-SHG [44]. Brightfield (H-i), SHG (H-ii), ρ (H-iii), δ orientation (H-iv) and DOLP (H-v) images of normal, triple +, double +, ++-, and triple-breast tissue [44]. Images E-H were adapted with permission from [14,43,44]  is the second-order nonlinear optical susceptibility tensor, containing up to 18 unique elements, describing the sample. The equation shows that intensity and polarization of SHG depends on the sample orientation and ultrastructure, encoded in χ (2) , and on the polarization and intensity of the laser. Kleinman symmetry [1,2], where K χ (2) zxx / χ (2) xxz 1, as well as cylindrical C 6v symmetry are typically assumed, resulting in only two unique χ (2) elements whose ratio is historically designated ρ χ (2) zzz /χ (2) zxx [3]. Since E . is controlled and I . SHG is measured, ρ, and the inplane projection of the orientation angle of collagen, δ, can be extracted via PSHG measurements (see Figure 1D for coordinate system). This review is focused on polarizationsensitive SHG approaches specifically used for discriminating diseased collagenous tissues, and thus many great papers using SHG microscopy are regretfully not included.

Historical Interpretation of the PSHG Parameters Pertaining to Collagen
Researchers, Freund et al. [3][4][5][6], pioneered the use of SHG to investigate the structure of collagenous biological tissue by utilizing different laser polarizations. They focused a Q-switched Nd:YAG laser onto rat tail tendon, collecting SHG in the forward direction, similar to Figure 1A, but without scan mirrors and at different scattering angles. They found an SHG peak at the 0°scattering angle, indicative of the macroscopic ordered polar structure of collagen, and found that χ (2) of tendon exhibited cylindrical symmetry, since rotation about the tendon axis did not appreciably change SHG parameters. They attributed the signal predominantly to C-N bonds in the amino acids, arguing these are the likely dominant polarizable, noncentrosymmetric and non-mobile candidates. They used a polarization state analyzer (PSA) consisting of a polarizer to directly measure ρ for tendons from rats of different age groups, and showed this parameter distinguishes the variation in the developing biological structure.
Noting the important SHG theoretical work of Dick [7], two groups, Plotnikov et al. [8] and Tiaho et al. [9], attributed ρ to the helical pitch (θ) of the protein triple helix via ρ/(2 + ρ) cos θ. However, it is likely that all the levels of the collagen tissue hierarchy can contribute to the polarization-dependent SHG parameters [10]. Therefore, the question of which hierarchical levels of collagen in different tissues are expressed in PSHG microscopy remains open. It also presents an opportunity to investigate which disease states affect the quantitative imaging results. Since the dyes used for standard staining of histopathology samples in hospitals, hematoxylin and eosin Y, seem to be compatible with PSHG microscopy [10], therefore PSHG capability could be added to existing histopathology slide scanners enabling the new modality without altering standard hospital sample preparation procedures. The resulting automated quantitative analysis could yield pathologists with an additional quantitative marker for improved diagnosis and evaluation.

Polarization-In SHG Microscopy
Pioneered in 1979, polarization-in SHG (PI-SHG) microscopy utilizes a polarization state generator (PSG) to rotate the laser linear polarization state. One method is to use a half-wave plate (HWP) in a motorized rotating mount, located before the excitation objective lens ( Figures 1A,C). An SHG intensity image is recorded at each HWP angle, typically with 10-30 steps in the range 0°-90°. Since SHG is predominantly forward-directed, most epi-detected photons require backscattering, which is less efficient than forward-detection [11], and results in depolarization of a fraction of the SHG. Parameters ρ and δ can be found using this methodology by performing nonlinear data fitting.
PI-SHG microscopy was used to distinguish normal and diseased tissue regions in several tissues ( Table 1) with statistical significance, via the χ (2) zzz values of osteosarcoma, breast cancer and melanoma tissues [12], as well as the ρ and θ values of fibrotic and control liver vessels [13,14]. A significant increase in the ρ value was also found between breast cancer biopsy tissues [15,16], and during thermal denaturation of corneal stroma [17]. Several other studies were performed using this technique, including on liver fibrosis [18], osteoarthritis [19], and keratoconus [20,21].
To avoid delays due to nonlinear data fitting, a fast Fourier transform (FFT) algorithm has been developed to extract ρ values quickly [22]. It was used in the study of normal and keratoconic human corneas [23], human breast carcinoma samples [16,24] and to investigate mechanical load in energy storing versus positional collagen fibrils [25]. The FFT approach has also allowed use of a generic structural model, where rather than assuming a particular symmetry, the second-order FFT coefficients (I 2 and ϕ 2 ), which quantify the modulation depth of the polarization SHG response (I 2 ) and its phase (ϕ 2 ), are reported and compared. This approach was used for a survey on cartilage in osteo-arthritic tissue [26,27], for a study of ageing via investigating ribose-glycated fibrils isolated from rat tail [28], and to investigate needle puncture damage in bovine annulus fibrosus [29].
Several groups have also investigated the excitation anisotropy (α) for distinguishing diseased tissues, α I v − I H /I v + I H , where I v and I H are the SHG intensities when the incident light is vertically and horizontally polarized, respectively. α is related to δ, and was measured in skin exposed to UVB [30,31], and using a fast motion-artefact free implementation in cheek and eye corner skin at two ages [32].
Polarization analysis of the outgoing SHG has also been incorporated using a PSA typically located after the collection objective in a forward-detection geometry ( Figure 1A), or after a dichroic mirror that separates SHG in epi-detection ( Figure 1C). While variable PSAs are reviewed in Double Stokes Mueller Polarimetric SHG (DSMP-SHG) Microscopy and Polarization-In, Polarization-Out SHG (PIPO-SHG) Microscopy sections, stationary PSAs are also used. In one implementation, SHG intensity through a polarizer parallel (I || ) and perpendicular (I ⊥ ) to the laser linear polarization is recorded allowing the SHG anisotropy (β) to be calculated: β I || − I ⊥ /I || + 2I ⊥ . A study of dysplastic human skin showed that optimization of the selection of linear laser polarization orientations using a Fourier algorithm on the SHG intensity obtained with circularly polarized light allowed β values to distinguish diseased areas more effectively [33], while in rat skin, β significantly changed during ageing [34]. In another study, the β values of femurs from wild-type mice and oim mice, a model for human osteogenesis imperfecta, were similar [35] while different β values are reported for dysplasia and colon cancer [36] as well as ovarian cancer tissue [37]. Stationary PSAs where the collagen axis is aligned to the laboratory polarization axis have also been used for investigating effects of mechanical load [38] and irradiation with high intensity infra-red light [39].
Interestingly, analysis of the PSHG data has also been achieved through Fourier projection of the PSHG image stacks onto two phasor plots referred to as microscopic multiparametric analysis by phasor projection of PSHG (µMAPPS). This technique has been used to compare the ρ values of SHG data taken from biopsies of the left flank of mice days after implantation of melanoma [40], colon carcinoma and breast cancer cells [41].
PI-SHG microscopy was also used to image submucosa of esophageal squamous cell carcinoma (ESCC). The ρ values from 4 stages of ESCC showed few differences between one another, and authors concluded that PI-SHG microscopy cannot be used for staging ESCC because the structural changes are likely of macromolecular rather than micromolecular origin [42].

Circular Dichroism Second Harmonic Generation Microscopy
In circular dichroism SHG (CD-SHG) microscopy, two SHG images are obtained using left-handed (I L ) and right-handed (I R ) circularly polarized laser light, with no PSA in the SHG detection path (Figures 1A,C). The CD-SHG intensity (I CD-SHG ) is the normalized difference of the two quantities, I CD−SHG 2(I L − I R )/(I L + I R ). One way to implement CD-SHG is via a liquid-crystal rotator (LCR) followed by a quarter-wave plate (QWP) as the PSG [45]. I CD-SHG is a complicated parameter when expressed in terms of the sample susceptibility, and according to equation 12 in [46], only measures structures with nonzero chirality (χ (2) xyz ), nonzero phase between χ (2) elements, and nonzero angle to the imaging plane (ψ in Figure 1D). Nonzero phase between tensor elements can occur due to a resonance transition near the laser wavelength and/or the SHG wavelength, due to a molecular magnetic dipole or due to an electric quadrupole rather than dipolar interaction [46]. CD-SHG microscopy was applied to determine differences between normal and osteogenesis imperfecta skin tissues as well as idiopathic pulmonary fibrosis human lung tissue where variations in I CD-SHG were statistically significant [43,47,48]. Another study used CD-SHG microscopy to find differences between 4 ovarian tissue classifications. The mean I CD-SHG value for normal ovarian tissue was significantly higher than the other tissues [49]. , where M is a double Mueller matrix which can be characterized via measurement. One such implementation using a single detector required 54 measurements. A PSG produced linearly polarized states at angles 0°, ±45°, 90°, 157.5°, two elliptical states, and two circularly polarized states, while at each PSG state, 6 SHG polarization intensities are measured to obtain a Stokes vector using the PSA. Both the PSG and PSA consisted of a polarizer, HWP and QWP at the laser and SHG wavelengths, respectively, with waveplates in mechanical rotation mounts ( Figures  1A,C) [44].

Double Stokes Mueller Polarimetric SHG Microscopy
DSMP-SHG has the advantage that 6 laboratory frame susceptibility components can be extracted from double Mueller matrix components: zxz (calculated relative to one component), and for each component, the real ( Figure 1G) and imaginary parts can be extracted, for each pixel of the image. Figure 1G can be used to compare tensor components for each pixel of the image [44]. Additionally, one can obtain the degree of polarization (DOP), degree of linear polarization (DOLP) and degree of circular polarization (DOCP) at each input polarization. DSMP-SHG microscopy was used to study microarray slides of human breast cancer types, finding that components of χ (2) are predominantly real and validating Kleinman symmetry [44]. When the χ (2) components are real and birefringence is negligible, the polarization of the SHG signal will not have a circular component, hence a reduced polarimetric measurement with only linearly polarized incoming and outgoing states known as polarization-in, polarization-out SHG microscopy can be performed [50][51][52].

Polarization-In, Polarization-Out SHG Microscopy
Polarization-in, polarization-out SHG (PIPO-SHG) uses a simplified PSA compared to DSMP-SHG as well as the same PSG as in the PI-SHG technique, and hence is typically implemented using a forward-detection geometry ( Figure 1A). The PSA measures the linear polarization state of the SHG signal at different angles of the linear polarization of the laser. The simplest PSA consists of a linear polarizer in a motorized rotation mount. SHG images are typically captured with at least 8 PSG angles and 8 PSA angles, hence at least 64 images are recorded for the technique, resulting in ∼20 min acquisition times in comparison to PI-SHG which takes ∼1.5 min [53]. The additional dimensionality of the data is thought to produce higher accuracy fitting, although at the time of writing this manuscript no study has performed the comparison with the other techniques. Fitting of the SHG intensity versus PSA and PSG angles yields δ and ρ. When the more generalized C 6 symmetry is assumed, χ (2) xyz appears, and can be measured as the chirality ratio (C χ (2) xyz /χ (2) zxx ) [54]. The PIPO-SHG measurements also allow the DOLP of the SHG signal to be obtained, where the SHG light is fully linearly polarized when DOLP 1, and increasingly depolarized or circularly polarized as it approaches 0. DOLP measurements were performed at 8 incident laser polarizations (θ 0˚, 22.5˚, 45˚, 67.5˚, 90˚, 112.5˚, 135˚, 157.5˚) and for each one, two DOLP calculations were averaged, one using measurements at analyzer angles 0˚, 45˚, 90˚, 135˚and another at 22.5˚, 67.5˚, 112.5˚, 157.5˚ [55]. An improved DOLP is obtained when structures with δ orientations closest to the normal of the crystal axis are ignored, since they have the lowest signal in collagen imaging, which can result in a low signalto-noise ratio [44]. Lower DOLP values can occur due to ultrastructural disorder of collagen, or due to fragmentation of collagen within the focal volume, where SHG is emitted from uncorrelated domains [56].
A PIPO-SHG microscopy study of pathology slides of lung samples from patients with non-small cell lung carcinoma revealed significant differences in the mean ρ values [57]. A more recent study of that disease showed that the median ρ and the median average distribution (MAD) of δ could differentiate stages II and III from normal tissue, while the MAD of C and DOLP could differentiate stage I [56]. Human thyroid tissues were also investigated with PIPO-SHG, and revealed significant differences in the average DOLP values between normal thyroid tissue and follicular variant of papillary thyroid carcinoma, classical papillary thyroid carcinoma, follicular nodular disease, Grave's disease, and anaplastic or undifferentiated carcinoma. This was also true for the mean ρ values except for insular thyroid tissues [58,59]. Pancreatic ductal adenocarcinoma tissue was also investigated with PIPO-SHG and demonstrated significant differences between the mean ρ values of tumor tissue and the periductal, lobular and parenchymal regions of normal pancreatic tissue. The DOLP values of the pancreatic tumor regions were only significantly different from normal periductal and parenchymal tissues [60] while the C values in diseased thyroid and pancreas were not significantly different from normal tissues [58][59][60].
PIPO-SHG microscopy was also applied to study a microarray slide containing 3 pathological human breast cancer types ( Figure 1H) with the overexpression/absence of estrogen receptor, progesterone receptor, and human epidermal growth factor receptor 2: triple +, double +, and triple -. The mean and median ρ values of triple + and double + as well as the mean and median DOLP values for double + were significantly different from normal breast tissue [44]. Bone cancer was also investigated and the ρ values of bone adjacent to tumor was found to be significantly different to bone adjacent to normal marrow [61]. Polarization-out SHG (PO-SHG) microscopy was also attempted by varying the angle of an analyzer before the detector, as in PIPO-SHG, but with only one linear input polarization state, however, it did not achieve differentiation between normal and diseased tissue [62,63].

DISCUSSION
Automated digital histopathology using PSHG microscopy is a promising technology for diagnosis of disease in histopathological samples, however, implementation requires fast imaging and data analysis balanced with maintaining high measurement accuracy to obtain diagnosis based on the fewest amount of analyzed pixels. To reduce imaging time due to the different laser polarizations needed, liquid crystal or electro-optic modulators can be used [64][65][66], or beams with different polarizations can be interleaved. The clever use of fewer input polarizations could also be used, such as in Stokes-Mueller SHG [67] which uses four polarizations in a PI-SHG setup, or advanced polarimeters with multiple detectors can be used for simultaneous detection of the SHG polarization states [68]. In another technique, polarimetry analysis can also be performed using circularly polarized laser excitation, only requiring a single scan [53,69]. Fourier techniques could be used for faster data analysis [16,23,24], while imaging rates can be increased using higher repetition rate pulsed lasers combined with faster scanners such as spinning mirrors, or by increasing the field of view using a wide-field imaging approach [70]. With these developments, it is reasonable that PSHG microscopy may be implemented in a modified hospital pathology slide scanner. Furthermore, since SHG requires no dyes, it can be implemented as an epi-detection setup in an endoscope for in vivo quantitative imaging as a biopsy tool [71][72][73].
It is evident that PSHG imaging can quantitatively differentiate certain diseased tissues based on their ultrastructure in pathological sample slides however, care must be given to PSHG image quality and the image analysis methods used. For instance, when assessing the quality of PSHG images, it has been found that using SHG intensity as a criterion is only suitable in specific instances [74]. Furthermore, while statistical discrimination based on many samples has been validated in different tissues, the efficacy of diagnosis in individual regions remains unclear and must be addressed. Improved differentiation could be obtained via additional implementation of complementary SHG intensity analysis techniques, such as texture analysis [56,[75][76][77], the Hough transform [78] and the structure tensor [79,80]. These analysis techniques could be extended to PSHG ρ or δ images. Additional information about diseased tissues can be obtained by coupling complementary techniques, such as polarizationsensitive two-photon excitation fluorescence microscopy [81], and polarization-sensitive third harmonic generation microscopy [82]. The idealized scanning system could find potential hotspots and report them to the pathologist who could confirm the diagnosis, aiding in the difficult task of finding small diseased regions in comparatively large samples, saving pathologists time and lives by pinpointing regions of interest.

AUTHOR CONTRIBUTIONS
The authors contributed to manuscript writing (RC, DT) and editing (RC, AJ, MH, DT).