Theoretical simulation study of linearly polarized light on microscopic second-harmonic generation in collagen type I

Abstract

A theoretical model is established for dealing with second-harmonic generation (SHG) in type I collagen excited by linearly polarized light focused by a microscope. With this model, the effects of the polarization angle alpha, numerical aperture (NA), as well as the ratio of hyperpolarizability rho=beta(xxx)beta(xyy) on SHG emission have been investigated. Simulation results reveal that SHG emission power changes periodically as alpha. The use of lower NA leads to weaker SHG emission but is more concentrated in two closer lobes, whereas more distributed emission in two detached lobes appear at higher NA. As the introduction of polarization direction, which is not along with the fiber axis (alpha not equal0 deg), one more element beta(xyy) is valid in our case than beta(xxx) alone, while their ratio rho plays a very important role for collagen features characterization. SHG emission with rho shows complicated modality that SHG emission is different at different alpha and not symmetric at +/-rho except at alpha=0 deg, suggesting the important impact of polarization working on rho for SHG emission. Our theoretical simulation results provide useful clues for experimental study of microscopic SHG emission in collagen excited by linearly polarized beam.

Polarization response of second-harmonic images for different collagen spatial distributions

“…Although it is well known that collagen fibers might present a variety of distributions, 13,14 numerical models were only able to explain the behavior of sets of quasialigned fibers. 1,9,11 This work dealt with the analysis of the SHG signal response to polarization for different organizations of the collagen fibers. This collagen distribution of the samples has been classified by means of the structure tensor.…”

“…5,[21][22][23] It has been shown that the modulation of the SHG signal with polarization can be characterized by this ratio ρ, a parameter related to the internal collagen structure, 9,11 which decreases with collagen aging and loss of regular distribution (i.e., denaturation). 9,15,21,24,25 An objective tool to evaluate the external collagen organization (fiber distribution) in SHG images has recently been reported. This is the so-called structure tensor, 26,27 which consists of a matrix of partial derivatives along the main spatial directions providing information about the orientation of every pixel of an SHG image.…”

“…1,2 In particular, the dependence of second-harmonic generation (SHG) microscopy images of collagen-based tissues with incident polarization has been reported to better visualize certain features [3][4][5] and provide valuable information related to the structure and type of collagen fibers. [6][7][8] Although it is well known that polarization modulates the spatial distribution of the SHG signal from collagen fibers, this has only been analyzed in detail for regular patterns [9][10][11] (i.e., when the fibers are aligned along a preferential direction and the SHG signal is coherently produced). 12 However, the spatial distribution is not always uniform 13,14 and can be modified with aging, 3,15,16 mechanical damage, 17 and pathological processes [18][19][20] among others.…”

Characterization of excitation beam on second-harmonic generation in fibrillous type I collagen

“…Accordingly, three components of SHG intensity based on the coordinates x-, y-, and zaxes have been obtained (as for collimated light, we represent the excited SHG by the x and y components; for focused light, we present it in our previous paper [13] by the components perpendicular (s) and parallel ( p) to the emission plane). In order to compare the SHG by focused light to that from collimated light, we project the components in the p and s directions to the x, y, and z directions.…”

“…Accordingly, how focused light influences SHG in fibrillous collagen type I has not been comprehensively compared to that of collimated light before. Therefore, based on our newly established theoretical model to deal with the SHG excited by a linearly polarized focused beam in type I collagen [13], in this paper, we further characterize the differences between SHG emissions in type I collagen excited by collimated and focused light. In particular, the effects of the linear polarization angle (α) and the fibril polarity characterized by the parameter of hyperpolarizability ratio (ρ) on SHG emission have been compared under collimated and focused beam excitation, respectively.…”