Linear least square (LLS) method for pixel-resolution analysis of polarization dependent SHG images of collagen fibrils

A linear least square (LLS) method is proposed to process polarization dependent SHG intensity analysis at pixel-resolution level in order to provide an analytic solution of nonlinear susceptibility χ(2) coefficients and of fibril orientation. This model is applicable to fibrils with identical orientation in the excitation volume. It has been validated on type I collagen fibrils from cell-free gel, tendon and extracellular matrix of F1 biliary epithelial cells. LLS is fast (a few hundred milliseconds for a 512 × 512 pixel image) and very easy to perform for non-expert in numerical signal processing. Theoretical simulation highlights the importance of signal to noise ratio for accurate determination of nonlinear susceptibility χ(2) coefficients. The results also suggest that, in addition to the peptide group, a second molecular nonlinear optical hyperpolarizability β contributes to the SHG signal. Finally from fibril orientation analysis, results show that F1 cells remodel extracellular matrix collagen fibrils by changing fibril orientation, which might have important physiological function in cell migration and communication.