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

Abstract

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.

Dual‐ and single‐shot susceptibility ratio measurements with circular polarizations in second‐harmonic generation microscopy

“…To validate the dual‐ and single‐shot R ‐ratio measurement techniques, DSMP measurements were performed on the muscle sample and the R and C‐ ratios were obtained. Then, using s 0 and s 3 SHG images for RCP and LCP inputs extracted from the DSMP dataset, SHG‐CD and CA CD values were calculated. CA‐values were also calculated separately for right‐ and left‐circularly polarized incident beam (CA R or CA L , respectively).…”

“…The SHG‐CD and CA CD values extracted from the DSMP dataset are presented in Figure 3B,C, respectively. The SHG‐CD histogram shows a normal distribution with a mean 0.02 and a standard deviation of 0.16 indicating that most fibers are in the image plane ( α = 0) . Therefore, the sample structure can be described by a C 6 v model .…”

“…We have previously shown that the achiral molecular χ 2 tensor components are in phase with each other, and therefore, Δ zzz , xxz = Δ zxx , xxz = 0 can be assumed . Furthermore, it is shown that to a good approximation .…”

“…In addition, a dual‐shot measurement involving both RCP and LCP input states can be used to measure the second‐harmonic generation circular dichroism (SHG‐CD), which is defined as the normalized difference in outgoing intensity of SHG when the sample is excited with RCP and LCP light, ( I RCP − I LCP )/([ I RCP + I LCP ]/2). SHG‐CD can be used to determine the presence of chirality and complex‐valued χ 2 tensor contributions as well as a nonzero out‐of‐plane orientation angle α . Similar to CA CD , the SHG‐CD measurement can be described in terms of the measured SHG Stokes vector parameters, which in turn can be expressed in terms of Mueller matrix elements : …”

“… is the susceptibility tensor element for which the generated second harmonic electric field and incident light electric field are along the C 6 symmetry axis of the molecular fiber, such as myofibril or collagen fiber ( z ) and is the susceptibility tensor element for which the SHG electric field is along z ‐axis and the incident light electric field is perpendicular to it. The R ‐ratio has been previously used to characterize different biomaterials such as tendon , bone , muscle , and starch . The R ‐ratio was further used to differentiate between normal and cancerous tissues in various organs such as lung , breast , thyroid , and pancreas .…”