2.1.

Basis of SHG Origin in Biological Media

Second-order nonlinear polarization of dielectric material effectively occurs when electromagnetic radiation with an oscillating electric field strength greater than ${10}^5\mathrm{W}/{\mathrm{cm}}^2$ interacts with noncentrosymmetric media.²⁷ In general, electromagnetic radiation-induced polarization of material system can be expressed as

This formula accounts for the transition frequency ${\omega }_{\mathrm{ge}}$, the oscillator strength derived from an integral of absorption spectrum $f_{\mathrm{ge}}$, the and change in dipole moment $\mathrm{\Delta }{\mu }_{\mathrm{ge}}$ of ground and excited states, in which $e$ is the constant of electric charge and $h$ is the Planck constant. Macroscopic second-order susceptibility ${\chi }^{(2)}$ is proportionally related to $\beta$,¹⁹ as shown in the following expression:

Since 1986, the application of scanning second harmonic microscopy has revealed polarization of filamentous, columnar structures of collagen fibril in native rat tail tendons, which exhibit the directionality that permeate the tendon cross-section.³⁷ Since then, SHG microscopy, a complementary, structure-sensitive tool to MPFM, has found enormous usefulness in optical tissue biopsy and reconstruction of intact structure of mammalian tissues, as well as in the study of local cellular membrane morphology and its dynamics, which were previously unattainable with conventional histology.^38–40 A mixture of type I and V collagen emulating the state of human breast cancer has been quantifiably diagnosed with SHG intensity measurement, which deceases in parallel with an increase in the content of Col V; mixture with lower Col V is also characterized by longer fibers and a higher emission ratio of Forward SHG to Backward SHG FSHG/BSHG.⁴¹ A similar investigation on breast cancer using SHG microscopy also clarified the relationship between collagen density and carcinogenesis. In that investigation, three tumor-associated collagen signatures were observed and defined based on density, shape, and orientation of collagen fibers, which may provide novel markers for locating and characterizing tumors.⁴² Another study concerning ovarian cancer used the integration of three-dimensional (3D) SHG intensity and bulk optical measurements, as well as Monte Carlo simulations, to investigate the remodeling of structure of ovarian extracellular matrix in a cancerous state. This study revealed lower cell density, denser collagen, and higher regularity at both fibril and fiber levels in malignant tissues.⁴³ When used in combination with Monte Carlo simulations or an assessment computation algorithm, SHG microscopy is also capable of identifying the diseased state osteogenesis imperfect, as well as discriminating different collagen types in kidney tissue.^44,45

Furthermore, manual and acoustooptical polarization-swept fs light sources can help determine the detailed content within the subsurface of tissues.^46,47 Polarization signature of tissues, such as skin and cartilage, has added an additional contrast mechanism to intensity-based investigation and has allowed differentiation of normal and morphologically variant tissues.^9,28,48 For instance, variations of collagen fiber organization and orientation in normal cartilage were revealed and differentiated from degenerated cartilage using polarization-sensitive SHG and ratio of intensities of two orthogonally polarization-resolved SHG signals.⁴⁹ Previously, using polarization-resolved SHG microscopy, Nucciotti et al. assigned a unique value of polarization anisotropy to each physiological/biochemical state of myosin structural conformation, which helped discriminate between attached and detached myosin heads in a contracting intact fiber.⁵⁰

Polarization-sensitive SHG microscopy has been used to investigate structure and molecular composition of tissues such as corneal stroma and skeletal muscle tissues.^51,52 In addition, specific polarization properties of collagen and myosin were distinguished using polarization-selective SHG intensities and their ratios.^53,54 Researchers have applied polarization-sensitive SHG measurements to enable second-order susceptibility tensor-based quantification for numerical analysis of biological tissues. To show this quantification approach, Fig. 1 illustrates the relationship of a linearly polarized laser beam with a propagation vector along the $y$-axis and the orientation of collagen fibril $({\mathrm{\Phi }}_F)$, together with the direction of laser polarization $({\mathrm{\Phi }}_L)$, which are defined as relative angles with respect to the vertical $z$-axis on the plane of the $xz$-coordinate system. The relative angular difference $\phi ={\mathrm{\Phi }}_F-{\mathrm{\Phi }}_L$ is used in numerical analysis.⁵⁵ Under the assumption of cylindrical symmetry, elements of second-harmonic susceptibility tensor reduce to four independent elements.⁵⁶ With the angular definition of $\phi$, the induced SHG intensity can be expressed⁵⁵ as

Fig. 1

Illustration of laser polarization and fiber orientation in a coordination system. ${\mathrm{\Phi }}_F$ is the angle of fiber orientation relative to the $z$-axis, and $({\mathrm{\Phi }}_L)$ is the polarization angle of the electric field vector of an incoming laser with a propagation vector along the $y$-axis.⁵⁵

Equation (6) can be used to fit the SHG intensity as a function of $\phi$. As a result, ${\chi }_{xzx}/{\chi }_{zxx}$, ${\chi }_{zzz}/{\chi }_{zxx}$, fiber orientation ${\mathrm{\Phi }}_F$, and the overall proportionality constant can be determined. These parameters would then allow the quantitative characterization of noncentrosymmetric biological tissues. For instance, averaged ratios of ${\chi }_{zzz}/{\chi }_{zxx}=1.40\mp 0.04$ and ${\chi }_{xzx}/{\chi }_{zxx}=0.53\mp 0.10$ were previously determined as a footprint indicating type I collagen of rat tail tendon;⁵⁷ validity of these ratios is discussed from experimental aspects in the following sections.

3.1.

Clinical Dermatology

Skin, as the outermost protective organ, separates internal soft tissue from external environment and biochemically plays a major role in immunoregulation and maintenance of physiological homeostasis.⁵⁸ The composition of skin can be divided mainly into three sections: epidermis, dermis, and hypodermis. The basal layer, the deepest layer of epidermis, is essentially composed of basal and other cells and is responsible for the synthesis and division of newly formed keratinocytes, which migrate superficially and form spinous and granular layers in the ascending order of cellular maturity with corneum, a lamina of anucleate cells, residing in the outermost layer. The dermis lies immediately underneath the epidermis and consists of an extracellular matrix containing collagen and elastic fibers. Depending on sections of superficial skin, the thickness of the epidermis and dermis range from 50 to 1,500 μm and 100 to 500 μm, respectively.⁵² The subcutaneous depth ranges are measurable using optical imaging modalities and have proven to be readily accessible for diagnostic purposes.⁵⁹ Dermatological science has made significant progress in parallel with advancements in optical microscopy, which have helped resolve cellular and molecular constituents of subcutaneous tissues in applications such as in vivo monitoring of lesions, presurgical illustration of basal cell carcinoma,⁶⁰ and noninvasive assessment of the skin’s microvascular function⁶¹ and related dermatological diseases such as atopic dermatitis.⁶² While confocal fluorescence microscopy can visualize cellular components of the stratum corneum and discriminate the junction of the dermis and epidermis, upon reflection, multiphoton microscopy capable of probing depths greater than a few hundred microns is inherently more suitable for interrogating physical and biochemical properties of deep tissue.⁶³ At the junction between the dermis and epidermis, the laminar structure of epidermal cells, melanin, elastin, and collagen fibers was observed instantaneously with a combined imaging modality of spectra of autofluorescence (AF) and SHG microscopy.⁶⁴ A combination of AF and SHG measurements has also proven invaluable in assessing characteristics of skin aging and pathological conditions in vivo.⁶⁵ In addition, early detection of alterations in the physical and biochemical properties of subcutaneous cellular constituents and structural lamination within human skin biopsy has been demonstrated utilizing an imaging system combining OCT and MPM.⁶⁶ Change in collagenous structure-induced SHG response has helped discriminate normal derma from basal cell carcinoma and has allowed in vivo, guidance for basal cell carcinoma removal.⁶⁷ Likewise, merits of second-order susceptibility imaging lie not only in assessment of tissues with polarization-dependent intensities, but also in providing quantification at a pixel-by-pixel level that serves as a metric for differentiating types, composition, and physiopathological states of tissues. Pixel-level analysis of polarization-dependent SHG measurements has successfully revealed structures of different muscle cells of living Caenorhabditis elegans (C. Elegans) nematodes, as well as differentiated fibrillar collagen and skeletal muscle in mammalian tissues.^68,69 Additionally, development on 1D Fourier and the gray-level co-occurrence matrix analyzes of polarization-sensitive SHG measurements have helped enhance the contrast of images and increase imaging speed nearly five-fold, respectively.^70,71

In our study, molecular origins of SHG sources were quantitatively distinguished in collagen-rich human dermis and the muscle-tendon junction of chicken wings rich in both collagen and myosin using second-order susceptibility imaging.²⁴

Before obtaining second-order susceptibility tensors from human dermis, SHG tensors analysis was performed on the muscle-tendon junction, making sure that results of the imaging technique were valid and capable of discriminating between different SHG origins.

Figure 2 shows single-pixel-resolved mapping of the second-order susceptibility tensor ratios ${\chi }_{zzz}/{\chi }_{zxx}$ and ${\chi }_{xzx}/{\chi }_{zxx}$ derived from polarization-dependent SHG signal by imaging the muscle-tendon junction of chicken wings. The SHG intensity value of each pixel was taken as an average with eight surrounding pixels for enhancing visual impression by smoothing out color-code transition between pixels before image processing, which does not signify any quantitative manipulation to the original data. The tomography of the tensor ratios ${\chi }_{zzz}/{\chi }_{zxx}$ and ${\chi }_{xzx}/{\chi }_{zxx}$ indicates morphological difference between muscle and tendon; tendon is a much stronger SHG emitter than muscle, so image contrast revealed the boundary of the junction. The polarization-dependent SHG intensity at 21 different excitation polarization angles over an angular range of 0 deg to 180 deg were measured to determine ${\chi }_{zzz}/{\chi }_{zxx}$, ${\chi }_{xzx}/{\chi }_{zxx}$, fiber angle ${\mathrm{\Phi }}_F$, and the proportionality constant by least-square-fitting of Eq. (6) and construct image maps of ${\chi }_{zzz}/{\chi }_{zxx}$ and ${\chi }_{xzx}/{\chi }_{zxx}$, which are illustrated in Fig. 2(a) and 2(b), respectively. As can be seen from Fig. 2(a), ${\chi }_{zzz}/{\chi }_{zxx}$ clearly elucidates the contrast between muscle and tendon, whereas such clear distinction is not presented in tomography of ${\chi }_{xzx}/{\chi }_{zxx}$. Figure 2(e) delineates the variation of normalized SHG intensity as a function of polarization angle relative to fiber angle for pixels 1 and 2 marked on Fig. 2(a), and error bars were taken over three repeated images. The respective peak values of ${\chi }_{zzz}/{\chi }_{zxx}$ are $1.04\pm 0.08$ (dashed arrow) and $1.34\pm 0.07$ (solid arrow) for the muscle and tendon, as shown in Fig. 2(c), which demonstrated the effectiveness of SOSM as an imaging contrast mechanism for differentiating the SHG origin of muscle and tendon. Also, note that the dual-peak profile in the histogram of Fig. 2(c) illustrates clear differences of ${\chi }_{zzz}/{\chi }_{zxx}$ for muscle and tendon. On the other hand, as with previous results for rat tail tendons, ${\chi }_{xzx}/{\chi }_{zxx}$, shown in Fig. 2(d), is not close to 1 and does not show such two-peak distinction. Since Eq. (6) was derived under the assumptions of Kleinman and cylindrical symmetries, which reduce the number of second-order susceptibility tensors, the ratio of ${\chi }_{xzx}/{\chi }_{zxx}$ is theoretically set to 1 when assumptions are applied to lossless media with the excitation frequencies being far away from absorption frequencies of the media.⁷² Although the validity of these assumptions was verified by Stoller et al. for the reason that the first electronic transition in collagen (at 310 nm) is far away from the SHG wavelength at 400 nm, other experimental groups have found their results of ${\chi }_{xzx}/{\chi }_{zxx}$ slightly deviated from theory.²³ Both Chu et al. and Plotnikov et al. have made the similar argument that their laser excitation and SHG frequencies were not too far away from the resonant frequency of muscle, which may attribute to a slight deviation from Kleinman symmetry.^9,73 Under the context of the assumption discussed here, the affinity of our SHG wavelength (390 nm) to the resonant wavelength of collagen at 350 to 380 nm may well contribute to a slight deviation from Kleinman symmetry. In addition, a wavelength of 900 nm has been used by other experimental groups to excite myosin molecules of mice leg muscles, as well as mice tail tendon fascia and muscle fascia, which render an SHG emission of 450 nm and thus confirm the contribution of SHG resonance to the deviation from Kleinman symmetry.^54,74 Another possible explanation for such a ratio deviation is the chirality of collagen, which is known to enhance SHG radiation and thus may vary the $\chi$ ratio contribution accordingly.^75,76

Fig. 2

Quantitative analysis of second-order susceptibility tensor ratios on the muscle-tendon junction a of chicken wing. Tomography of (a) ${\chi }_{zzz}/{\chi }_{zxx}$ and (b) ${\chi }_{xzx}/{\chi }_{zxx}$ are illustrated along with histograms of occurrence count for (c) ${\chi }_{zzz}/{\chi }_{zxx}$ and (d) ${\chi }_{xzx}/{\chi }_{zxx}$. Variation of SHG intensity as a function of relative angle between fiber direction and laser polarization for pixel locations 1 and 2 are shown in (a).²⁴

Following the same analytic procedures, SOSM was used to examine human dermis. Figure 3 shows a second-order susceptibility analysis of polarization-sensitive SHG intensity images. SHG intensity images shown in Fig. 3(a), 3(b), and 3(c) delineate the single-pixel-resolved tomography of polarization-dependent SHG intensity, ${\chi }_{zzz}/{\chi }_{zxx}$, and ${\chi }_{xzx}/{\chi }_{zxx}$, respectively. The results of immunohistology revealed collagen I as the main component of fibril bundles in human dermis, which is consistent with analysis of second-order susceptibility within the encircled region of Fig. 3(b); the averaged ${\chi }_{zzz}/{\chi }_{zxx}$ was determined to be $1.34\pm 0.07$. The histogram of ${\chi }_{zzz}/{\chi }_{zxx}$ is presented in Fig. 3(d), where the first peak value of $1.23\pm 0.09$ corresponds to collagen type I, while the second peak value of $0.92\pm 0.08$ could be attributed to collagen type III, another major constituent of the dermis. Furthermore, as reported previously, ${\chi }_{zzz}/{\chi }_{zxx}$ was used for differentiating human dermis under different pathological conditions: keloid, morphea, and dermal elastolysis, which were characterized by peak ${\chi }_{zzz}/{\chi }_{zxx}$ values of $1.67\pm 0.29$, $1.79\pm 0.30$, and $1.75\pm 0.31$, respectively.²⁵

Fig. 3

Second-order susceptibility analysis of SHG images of human dermis. (a) An SHG intensity image. (b) Single-pixel-resolved mapping of ${\chi }_{zzz}/{\chi }_{zxx}$. (c) Single-pixel-resolved mapping of ${\chi }_{xzx}/{\chi }_{zxx}$. (d) Occurrence count for ${\chi }_{zzz}/{\chi }_{zxx}$.²⁴

3.2.

Basic Studies and Tissue Engineering Applications

Connective tissues of a variety of mammalian and amphibian species have been found to be made of different types of collagen.^77,78 Fibrillar collagen, such as type I, exhibits SHG radiation attributing to coherent effects of the high-density and quasicrystalline structure of collagen fibril, and it has been explored for intensity-based characterization of tissue properties. Specifically, through the use of polarization-sensitive SHG and MPF measurement, normal and degenerate equine articular cartilage were differentiated, and it was suggested that numerical models are required for quantification of depth-dependent polarization measurement.⁴⁹ In another study, unraveling endogenously hidden myosin-rich and collagen-rich tissues in amphibian and mammals was achieved.⁷⁹ Furthermore, polarization-sensitive SHG measurements were used to characterize the orientation angle of myosin in collagen I and collagen III.⁷⁷ Hyper-Raileigh scattering experiments were carried out, and peptide bonds were found to be the molecular origin of SHG in proteins.⁸⁰ Using sum-frequency generation vibrational spectroscopy, it was found that molecular SHG also originated from the methylene group associated with Fermi resonance between the fundamental symmetric stretch and the bonding overtone of methylene, and that carbonyl and peptide groups associated with the amide I band are the dominant SHG contributors.⁸¹ Our study revealed that the molecular origin of collagen-rendered second-order susceptibility not only is attributed to the peptide groups in the backbone of the collagen $\alpha$-helix but may also be attributed to the methylene groups in the pyrrolidine rings.⁸² With this work, we demonstrated the visualization and differentiation of different SHG origins, namely, different types of collagen.

These results allow the construction of $\chi$ tensor ratio maps. A peptide pitch-angle ${\theta }^{(p)}$ of $45.82\pm 0.46\text{deg}$ and a methylene pitch-angle ${\theta }^{(m)}$ of $94.80\pm 0.97$ for collagen I from rat tail tendons were estimated, which comply with previous results of x-ray diffraction upon collagen-like peptide. Moreover, collagen II from rat trachea cartilage yielded similar results for ${\theta }^{(p)}$ of $45.75\pm 1.17\text{deg}$, whereas ${\theta }^{(m)}$ of $97.87\pm 1.79\text{deg}$ was slightly different from that of collagen I. Figure 4 shows tomographic images of ${\chi }_{zzz}/{\chi }_{zxx}$, ${\chi }_{xzx}/{\chi }_{zxx}$, ${\theta }^{(p)}$, and ${\theta }^{(m)}$ for type I and II collagens, with type I on the top row (a-d) and type II on the bottom (e-h). Likewise, the histogram of ${\chi }_{zzz}/{\chi }_{zxx}$, ${\chi }_{xzx}/{\chi }_{zxx}$, ${\theta }^{(p)}$, and ${\theta }^{(m)}$ for both type I and II collagens is shown in Fig. 5(a) to 5(d). These results demonstrate the capability of SOSM for identifying different molecular origins of SHG radiation.

Fig. 4

An analysis of second-order susceptibility tensors with collagen I from rat tail tendons and collagen II from rat trachea cartilage. ${\chi }_{zzz}/{\chi }_{zxx}$, ${\chi }_{xzx}/{\chi }_{zxx}$, ${\theta }^{(p)}$, and ${\theta }^{(m)}$ for collagen I and II are shown on the top row (a-d) and the bottom row (e-h), respectively.⁸²

Fig. 5

An analysis of second-order susceptibility tensors. Occurrence-count histograms of (a) ${\chi }_{zzz}/{\chi }_{zxx}$, (b) ${\chi }_{xzx}/{\chi }_{zxx}$, (c) ${\theta }^{(p)}$, and (d) ${\theta }^{(m)}$ for type I and type II collagen, delineating comparison between these types of collagen.⁸²

SOSM imaging has also been used to probe engineered cartilage tissue containing both type I and II collagens; in contrast, native cartilage is mainly composed of type II.⁵⁷ The results of second-order susceptibility tensor analysis from a polarization-dependent SHG image are shown in Fig. 6(a). Immunochemical staining was performed to confirm the presence of collagen I and II, as shown in Fig. 6(b) and 6(c), respectively. Figure 6(d) and 6(e) are the corresponding images of peptide pitch-angle and mythelene pitch-angle. Second-order susceptibility tensor analysis, performed within the dashed encircled regions of Fig. 6(d) and 6(e) are presented, respectively, in Fig. 6(f) and 6(g), illustrating the histograms of peptide- and mythelene pitch-angles for type I and II collagens. These results are summarized in Fig. 6(h), which shows a table of numerical data for ${\theta }^{(p)}$ and ${\theta }^{(m)}$ characterizing type I and II collagens. Clearly, with these results, the validity of SOSM in identifying type I and II collagens in a mixture of engineered cartilage has been verified.

Fig. 6

An MPM image analysis on the selected region for identifying collagen type I and II in a sample of engineered cartilage. (a) The polarization-dependent MPM image. Immunochemical staining confirms the presence of (b) collagen type I and (c) collagen type II. Tomography of (d) ${\theta }^{(p)}$ and (e) ${\theta }^{(m)}$, along with color bars, illustrate the results of second-order susceptibility analysis and single-pixel-resolution of SOSM images. The encircled regions of (d) and (e) are analyzed for distribution of occurrence counts of (f) ${\theta }^{(p)}$ and (g) ${\theta }^{(m)}$, indicating characteristics of collagen type I and II. (h) The characteristics are tabulated in a table.⁸²