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

Theoretical Foundation for Interface-Specific Hyper-Rayleigh Scattering in Uniaxial Chiral Assemblies

The role of incoherence is considered in polarization-dependent second harmonic generation (SHG) measurements of uniaxially oriented assemblies. SHG microscopy continues to find growing utility for tissue, powders, and materials analysis, all of which exhibit structural heterogeneity over length scales comparable to the optical wavelength. In these cases, the detected SHG signal will generally exhibit partial decoherence, invalidating polarization analyses that implicitly assume purely polarized signal detection. The primary goal of the present study is to develop a mathematical framework for interpreting the incoherent component of the SHG signals produced in such instances. While formulas for describing hyper-Rayleigh scattering (HRS) from isotropic systems are reasonably well established, practical systems encountered experimentally in SHG microscopy measurements are often of lower symmetry. The next lowest symmetry below isotropic, and therefore the next most common samples likely to be encountered experimentally, are uniaxial assemblies, in which one spatial axis is unique from the other two. Such systems include surface assemblies, poled films, stretched polymers, lipid bilayers, most collagenous tendons, and numerous other naturally occurring biological structures. In this work, the general theory for HRS of uniaxially oriented assemblies is developed, including both achiral and chiral uniaxial assemblies. Intriguingly, this analysis predicts the possible observation of large electric dipole-allowed chiral-specific observables within just the incoherent component of the SHG response of chiral assemblies exhibiting with polar, uniaxial ensemble symmetry. The incoherent chiral contributions exhibit distinctly different symmetry than the established chiral sensitivity of coherent SHG in uniaxial assemblies, which is independent of polar order. These predictions provide context for the prior reports of chiral-specific SHG microscopy of tissues and suggest new experimental strategies for performing surface-specific and chiral-specific nonlinear optical analysis of chiral assemblies.

Zonal Characteristics of Collagen Ultrastructure and Responses to Mechanical Loading in Articular Cartilage

The biomechanical properties of articular cartilage arise from a complex bioenvironment comprising hierarchically organised collagen networks within the extracellular matrix (ECM) that interact with the proteoglycan-rich interstitial fluid. This network features a depth-dependent fibril organisation across different zones. Understanding how collagen fibrils respond to external loading is key to elucidating the mechanisms behind lesion formation and managing degenerative conditions like osteoarthritis. This study employs polarisation-resolved second harmonic generation (pSHG) microscopy to quantify the ultrastructural organisation of collagen fibrils and their spatial gradient along the depth of bone-cartilage explants under a close-to-in vivo condition. By combining with in-situ loading, we examined the responses of collagen fibrils by quantifying changes in their principal orientation and degree of alignment. The spatial gradient and heterogeneity of collagen organisation were captured at high resolution (1 μm) along the longitudinal plane of explants (0.5 mm by 2 mm). Zone-specific ultrastructural characteristics were quantified to aid in defining zonal borders, revealing consistent zonal proportions with varying overall thicknesses. Under compression, the transitional zone exhibited the most significant re-organisation of collagen fibrils. It initially allowed large deformation through the re-orientation of fibrils, which then tightened fibril alignment to prevent excessive deformation, indicating a dynamic adaptation mechanism in response to increasing strain levels. Our results provide comprehensive, zone-specific baselines of cartilage ultrastructure and micromechanics, crucial for investigating the onset and progression of degenerative conditions, setting therapeutic intervention targets, and guiding cartilage repair and regeneration efforts. STATEMENT OF SIGNIFICANCE: Achieved unprecedented quantification of the spatial gradient and heterogeneity of collagen ultrastructural organisation at a high resolution (1 μm) along the full depth of the longitudinal plane of osteochondral explants (0.5 mm by 2 mm) under close-to-in vivo condition. Suggested new anatomical landmarks based on ultrastructural features for determining zonal borders and found consistent zonal proportions in explants with different overall thicknesses. Demonstrated that collagen fibrils initially respond by reorienting themselves at low strain levels, playing a significant role in cartilage deformation, particularly within the transitional zone. At higher strain levels, more collagen fibrils re-aligned, indicating a dynamic shift in the response mechanism at varying strain levels.

Effect of out of plane orientation on polarization second harmonic generation of single collagen fibrils

Second harmonic generation (SHG) microscopy has emerged as a powerful technique for visualizing collagen organization within tissues. Amongst the many advantages of SHG is its sensitivity to collagen nanoscale organization, and its presumed sensitivity to the relative out of plane polarity of fibrils. Recent results have shown that circular dichroism SHG (CD-SHG), a technique that has been commonly assumed to reveal the relative out of plane polarity of collagen fibrils, is actually insensitive to changes in fibril polarity. However, results from another research group seem to contradict this conclusion. Both previous results have been based on SHG imaging of collagen fibrils within tissues, therefore, to gain a definitive understanding of the sensitivity of SHG to relative out of plane polarity, the results from individual fibrils are desirable. Here we present polarization resolved SHG microscopy (PSHG) data from individual collagen fibrils oriented out of the image plane by buckling on an elastic substrate. We show through correlation with atomic force microscopy measurements that SHG intensity can be used to estimate the out of plane angle of individual fibrils. We then compare the sensitivity of two PSHG techniques, CD-SHG and polarization-in, polarization-out SHG (PIPO-SHG), to the relative out of plane polarity of individual fibrils. We find that for single fibrils CD-SHG is insensitive to relative out of polarity and we also demonstrate the first direct experimental confirmation that PIPO-SHG reveals the relative out of plane polarity of individual collagen fibrils.