Polarimetric second harmonic generation microscopy of partially oriented fibers II: Imaging study.

Polarimetric second harmonic generation (SHG) microscopy imaging is employed to investigate the ultrastructural organization of biological and biomimetic partially oriented fibrillar structures. The linear polarization-in polarization-out SHG microscopy measurements are conducted with rat tail tendon, rabbit cornea, pig cartilage, and biomimetic meso-tetra(4-sulfonatophenyl)porphine (TPPS4) cylindrical aggregates, which represent different two- and three-dimensional (2D and 3D) configurations of C6 symmetry fibril structures in the focal volume (voxel) of the microscope. The polarization-in polarization-out imaging of rat tail tendon reveals that SHG intensity is affected by parallel/antiparallel arrangements of the fibers, and achiral (R) and chiral (C) susceptibility component ratio values change by tilting the tendon fibers out of image plane. The R ratio changes for the 2D crossing fibers observed in cornea tissue. The 3D crossing of fibers also affects R ratio in cartilage tissue. The distinctly different dependence of R on crossing and tilting of fibers is demonstrated in collagen and TPPS4 aggregates, due to the achiral molecular susceptibility ratio having values below and above 3, respectively. The polarimetric microscopy results correspond well with the analytical expressions of amplitude and R and C ratios dependence on the crossing angle of the fibers. The experimentally measured SHG intensity and R and C ratio maps are consistent with the computational modeling of various fiber configurations presented in the preceding article. The demonstrated SHG intensity and R and C ratio dependencies on fibril configurations provide the basis for interpreting polarimetric SHG microscopy images in terms of 3D ultrastructural organization of fibers in each voxel of the samples.

Polarimetric second-harmonic generation microscopy of partially oriented fibers I: Digital modeling.

Second-harmonic generation (SHG) in biological tissues originates predominantly from noncentrosymmetric fibrillar structures partially oriented within a focal volume (voxel) of a multiphoton excitation microscope. This study is aimed to elucidate fibrillar organization factors influencing SHG intensity, as well as achiral, R, and chiral, C, nonlinear susceptibility tensor component ratios. SHG response is calculated for various configurations of fibrils in a voxel using the digital nonlinear microscope. The R and C ratios are calculated using linear incident and outgoing polarization states that simulate polarization-in polarization-out polarimetric measurements. The investigation shows strong SHG intensity dependence on parallel/antiparallel fiber organization. The R and C ratios are strongly influenced by the fiber chirality, tilting of the fibers out of the image plane, and crossing of the fibers. The computational modeling provides the basis for the interpretation of polarimetric SHG microscopy images in terms of the ultrastructural organization of fibers in each voxel of the samples. The modeling results are employed in the accompanying paper to investigate the ultrastructures with parallel/antiparallel fibers and two-dimensional and tree-dimensional crossing fibers in biological and biomimetic structures.

Wide-field Stokes polarimetric microscopy for second harmonic generation imaging.

We employ wide-field second harmonic generation (SHG) microscopy together with nonlinear Stokes polarimetry for quick ultrastructural investigation of large sample areas (700 µm × 700 µm) in thin histology sections. The Stokes vector components for SHG are obtained from the polarimetric measurements with incident and outgoing linear and circular polarization states. The Stokes components are used to construct the images of polarimetric parameters and deduce the maps of ultrastructural parameters of achiral and chiral nonlinear susceptibility tensor components ratios and cylindrical axis orientation in fibrillar materials. The large area imaging was employed for lung tumor margin investigations. The imaging shows reduced SHG intensity, increased achiral susceptibility ratio values, and preferential orientation of collagen strands along the boarder of tumor margin. The wide-field Stokes polarimetric SHG microscopy opens a possibility of quick large area imaging of ultrastructural parameters of tissue collagen, which can be used for nonlinear histopathology investigations.

Second harmonic generation theory for a helical macromolecule with high sensitivity to structural disorder.

Microscopic theory for the second harmonic generation in a helical molecular system is developed in the minimal coupling representation including non-local interaction effects. At the second order to the field we find a compact expression which combines dipolar, quadrupolar and magnetic contributions. A detailed derivation of the response is performed to specifically isolate the quadratic coupling terms, which we denote as the K coupling. Applying the theory to a helical macromolecule we find that the dipolar and quadrupolar contributions reflect the symmetry properties of the system and its homogeneity, while the K coupling contribution reveals inhomogeneities of the system.

Complex Susceptibilities and Chiroptical Effects of Collagen Measured with Polarimetric Second-Harmonic Generation Microscopy.

Nonlinear optical properties of collagen type-I are investigated in thin tissue sections of pig tendon as a research model using a complete polarimetric second-harmonic generation (P-SHG) microscopy technique called double Stokes-Mueller polarimetry (DSMP). Three complex-valued molecular susceptibility tensor component ratios are extracted. A significant retardance is observed between the chiral susceptibility component and the achiral components, while the achiral components appear to be in phase with each other. The DSMP formalism and microscopy measurements are further used to explain and experimentally validate the conditions required for SHG circular dichroism (SHG-CD) of collagen to occur. The SHG-CD can be observed with the microscope when: (i) the chiral second-order susceptibility tensor component has a non-zero value, (ii) a phase retardance is present between the chiral and achiral components of the second-order susceptibility tensor and (iii) the collagen fibres are tilted out of the image plane. Both positive and negative areas of SHG-CD are observed in microscopy images, which relates to the anti-parallel arrangement of collagen fibres in different fascicles of the tendon. The theoretical formalism and experimental validation of DSMP imaging technique opens new opportunities for ultrastructural characterisation of chiral molecules, in particular collagen, and provides basis for the interpretation of SHG-CD signals. The nonlinear imaging of chiroptical parameters offers new possibilities to further improve the diagnostic sensitivity and/or specificity of nonlinear label-free histopathology.

Characterization of Pancreatic Cancer Tissue Using Multiphoton Excitation Fluorescence and Polarization-Sensitive Harmonic Generation Microscopy.

Thin tissue sections of normal and tumorous pancreatic tissues stained with hematoxylin and eosin were investigated using multiphoton excitation fluorescence (MPF), second harmonic generation (SHG), and third harmonic generation (THG) microscopies. The cytoplasm, connective tissue, collagen and extracellular structures are visualized with MPF due to the eosin stain, whereas collagen is imaged with endogenous SHG contrast that does not require staining. Cellular structures, including membranous interfaces and nuclear components, are seen with THG due to the aggregation of hematoxylin dye. Changes in the collagen ultrastructure in pancreatic cancer were investigated by a polarization-sensitive SHG microscopy technique, polarization-in, polarization-out (PIPO) SHG. This involves measuring the orientation of the linear polarization of the SHG signal as a function of the linear polarization orientation of the incident laser radiation. From the PIPO SHG data, the second-order non-linear optical susceptibility ratio, χ(2) zzz '/χ(2) zxx ', was obtained that serves as a structural parameter for characterizing the tissue. Furthermore, by assuming C6 symmetry, an additional second-order non-linear optical susceptibility ratio, χ(2) xyz '/χ(2) zxx ', was obtained, which is a measure of the chirality of the collagen fibers. Statistically-significant differences in the χ(2) zzz '/χ(2) zxx ' values were found between tumor and normal pancreatic tissues in periductal, lobular, and parenchymal regions, whereas statistically-significant differences in the full width at half maximum (FWHM) of χ(2) xyz '/χ(2) zxx ' occurrence histograms were found between tumor and normal pancreatic tissues in periductal and parenchymal regions. Additionally, the PIPO SHG data were used to determine the degree of linear polarization (DOLP) of the SHG signal, which indicates the relative linear depolarization of the signal. Statistically-significant differences in DOLP values were found between tumor and normal pancreatic tissues in periductal and parenchymal regions. Hence, the differences observed in the χ(2) zzz '/χ(2) zxx ' values, the FWHM of χ(2) xyz '/χ(2) zxx ' values and the DOLP values could potentially be used to aid pathologists in diagnosing pancreatic cancer.

Collagen chirality and three-dimensional orientation studied with polarimetric second-harmonic generation microscopy.

Polarization-dependent second-harmonic generation (P-SHG) microscopy is used to characterize molecular nonlinear optical properties of collagen and determine a three-dimensional (3D) orientation map of collagen fibers within a pig tendon. C6 symmetry is used to determine the nonlinear susceptibility tensor components ratios in the molecular frame of reference χzzz2/χzxx2 and χxyz2/χzxx2 , where the latter is a newly extracted parameter from the P-SHG images and is related to the chiral structure of collagen. The χxyz2/χzxx2 is observed for collagen fibers tilted out of the image plane, and can have positive or negative values, revealing the relative polarity of collagen fibers within the tissue. The P-SHG imaging was performed using a linear polarization-in polarization-out (PIPO) method on thin sections of pig tendon cut at different angles. The nonlinear chiral properties of collagen can be used to construct the 3D organization of collagen in the tissue and determine the orientation-independent molecular susceptibility ratios of collagen fibers in the molecular frame of reference.

Third-harmonic generation Stokes-Mueller polarimetric microscopy.

An experimental implementation of the nonlinear Stokes-Mueller polarimetric (NSMP) microscopy in third-harmonic generation modality is presented. The technique is able to extract all eight 2D-accessible χ(3) components for any sample from 64 polarization measurements, and can be applied to noninvasive ultrastructural characterization. The polarization signature of an isotropic glass coverslip is presented, and carotenoid crystallites in the root of orange carrot (Daucus carota) are investigated, showing complex χ(3) components with a significant chiral contribution.

Second harmonic generation double stokes Mueller polarimetric microscopy of myofilaments.

The experimental implementation of double Stokes Mueller polarimetric microscopy is presented. This technique enables a model-independent and complete polarimetric characterization of second harmonic generating samples using 36 Stokes parameter measurements at different combinations of incoming and outgoing polarizations. The degree of second harmonic polarization and the molecular nonlinear susceptibility ratio are extracted for individual focal volumes of a fruit fly larva wall muscle.

Second Harmonic Generation Mediated by Aligned Water in Starch Granules.

The origin of second harmonic generation (SHG) in starch granules was investigated using ab initio quantum mechanical modeling and experimentally examined using polarization-in, polarization-out (PIPO) second harmonic generation microscopy. Ab initio calculations revealed that the largest contribution to the SHG signal from A- and B-type allomorphs of starch originates from the anisotropic organization of hydroxide and hydrogen bonds mediated by aligned water found in the polymers. The hypothesis was experimentally tested by imaging maize starch granules under various hydration and heat treatment conditions that alter the hydrogen bond network. The highest SHG intensity was found in fully hydrated starch granules, and heat treatment diminished the SHG intensity. The PIPO SHG imaging showed that dried starch granules have a much higher nonlinear optical susceptibility component ratio than fully hydrated granules. In contrast, deuterated starch granules showed a smaller susceptibility component ratio demonstrating that SHG is highly sensitive to the organization of the hydroxyl and hydrogen bond network. The polarization SHG imaging results of potato starch granules, representing starch allomorph B, were compared to those of maize starch granules representing allomorph A. The results showed that the amount of aligned water was higher in the maize granules. Nonlinear microscopy of starch granules provides evidence that varying hydration conditions leads to significant changes in the nonlinear susceptibility ratio as well as the SHG intensity, supporting the hypothesis from ab initio calculations that the dominant contribution to SHG is due to the ordered hydroxide and hydrogen bond network.

Characterization of collagen in non-small cell lung carcinoma with second harmonic polarization microscopy.

Polarization second harmonic microscopy was used for collagen imaging in human non-small cell lung carcinoma and normal lung tissues ex vivo and revealed significant differences in the nonlinear susceptibility component ratio, demonstrating potential use in cancer diagnosis.

Molecular organization of crystalline ß-carotene in carrots determined with polarization-dependent second and third harmonic generation microscopy.

Polarization-in, polarization-out (PIPO) second harmonic generation (SHG) and third harmonic generation (THG) microscopy was used to study the crystalline organization of ß-carotene molecules within individual aggregates contained in the chromoplasts of orange carrots in vivo. Multimodal PIPO SHG and PIPO THG studies of the aggregates revealed one dominant SHG and THG dipole signifying that ß-carotene molecules are oriented along a single axis. Three-dimensional visualization of the orientation of ß-carotene molecules with respect to the aggregate axis was also performed with both microscopy modalities and revealed organization of the aggregates as ribbon-like structures consisting of twists and folds. Therefore, PIPO SHG and PIPO THG microscopy provides information on the crystalline organization and the orientation of ordered biological structures in vivo where multimodal polarization dependent SHG and THG investigations are particularly advantageous as both noncentrosymmetric and centrosymmetric crystalline organizations can be probed.

Hierarchical model of fibrillar collagen organization for interpreting the second-order susceptibility tensors in biological tissue.

The second-order nonlinear polarization properties of fibrillar collagen in various rat tissues (vertebrae, tibia, tail tendon, dermis, and cornea) are investigated with polarization-dependent second-harmonic generation (P-SHG) microscopy. Three parameters are extracted: the second-order susceptibility ratio, R = [Formula: see text] ; a measure of the fibril distribution asymmetry, |A|; and the weighted-average fibril orientation, <δ>. A hierarchical organizational model of fibrillar collagen is developed to interpret the second-harmonic generation polarization properties. Highlights of the model include: collagen type (e.g., type-I, type-II), fibril internal structure (e.g., straight, constant-tilt), and fibril architecture (e.g., parallel fibers, intertwined, lamellae). Quantifiable differences in internal structure and architecture of the fibrils are observed. Occurrence histograms of R and |A| distinguished parallel from nonparallel fibril distributions. Parallel distributions possessed low parameter values and variability, whereas nonparallel distributions displayed an increase in values and variability. From the P-SHG parameters of vertebrae tissue, a three-dimensional reconstruction of lamellae of intervertebral disk is presented.

Nonlinear optical properties of type I collagen fibers studied by polarization dependent second harmonic generation microscopy.

Collagen (type I) fibers are readily visualized with second harmonic generation (SHG) microscopy though the molecular origin of the signal has not yet been elucidated. In this study, the molecular origin of SHG from type I collagen is investigated using the time-dependent coupled perturbed Hartree-Fock calculations of the hyperpolarizibilities of glycine, proline, and hydroxyproline. Two effective nonlinear dipoles are found to orient in-the-plane of the amino acids, with one of the dipoles aligning close to the pitch orientation in the triple-helix, which provides the dominant contribution to the SHG polarization properties. The calculated hyperpolarizability tensor element ratios for the collagen triple-helix models: [(Gly3)n]3, [(Gly-Pro2)n]3, and [(Gly-Pro-Hyp)n]3, are used to predict the second-order nonlinear susceptibility ratios, χ(zzz)(2)/χ(iiz)(2) and χ(zii)(2)/χ(iiz)(2) of collagen fibers. From SHG microscopy polarization in, polarization out (PIPO) measurements of type I collagen in human lung tissue, a theoretical method is used to extract the triple-helix orientation angle with respect to the collagen fiber. The study shows the dominant role of amino acid orientation in the triple-helix for determining the polarization properties of SHG and provides a method for determining the triple-helix orientation angle in the collagen fibers.

Three-dimensional visualization of the first hyperpolarizability tensor.

With polarization dependent second harmonic generation (SHG) microscopy becoming a more popular method for investigating the structure of biological materials, there is a need to develop tools with which to understand and interpret the observed SHG properties. Quantum mechanical calculations of the hyperpolarizability tensor have become a popular method for understanding the SHG properties of biomolecules. Visualization of the full hyperpolarizability tensor, termed the unit sphere representation, has been developed to provide insight and intuition on the relationship between SHG properties and molecules. A single vector representation is also presented, which approximates the SHG properties of molecules for certain cases, where the anisotropy is negligible.