Hierarchical Model of Fibrillar Collagen Organization for Interpreting the Second-Order Susceptibility Tensors in Biological Tissue

Abstract

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.

Imaging the Nonlinear Susceptibility Tensor of Collagen by Nonlinear Optical Stokes Ellipsometry

“…The validity of the symmetry-additive model has been confirmed with experimental hyper-Rayleigh scattering experiments of polypeptides (43), and has been used previously for SHG measurements of collagen (35). If the triple helices are all perfectly aligned within a collagen fiber, c ð2Þ l is directly proportional to b ð2Þ and consequently straight fibers (those with triple-helices aligned and ordered with respect to the fiber axis) should have measured relative values of c ð2Þ l that are similar to theoretically predicted values of b ð2Þ (20,33).…”

“…A study of fibril structures in cornea using electron tomography found that microfibril substructures adopted tilt angles of 15 with respect to the fibril axis (41). Constant tilt angles between 0 and 19 for collagen helices and/or fibrils within collagen fibers have been measured for several different collagen structures using a variety of techniques (20,33,38,41). This discrepancy indicates that the simple d-function distribution is not sufficient to compare the average experimental local-frame tensor elements to the molecular level ab initio calculations.…”

“…The algorithm iterates between solving for the sample orientation at each pixel and solving for the global set of tensor elements most consistent with the collective polarization-dependent SHG response. In the first step, the unique collagen tensor elements (c ð2Þ xxz , c ð2Þ zxx , and c ð2Þ zzz ) can be assumed explicitly, based on reported literature values (20,21,32,33), and a nonlinear least-squares fit to sample orientation is performed at each individual pixel. Initial guess values for f were determined by image analysis using the OrientationJ plug-in for ImageJ (34), and initial guess values for q were chosen arbitrarily to be 40 .…”

“…2, which describes the relative local-frame tensor elements of the structures (37). From the breadth of work on analysis of collagen fiber substructure (20,33,(38)(39)(40)(41), it is apparent that a distribution of tilt angles of collagen …”

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

“…Collagen is the major constituent of the ECM. It can be readily visualized with second harmonic generation (SHG) microscopy in histology sections and its organization can be probed with SHG polarization measurement [4][5][6]. We recently showed that structural details of collagen organization in the tissue can be studied with polarizationin, polarization-out (PIPO) SHG microscopy, where for each orientation of incoming laser polarization a set of outgoing SHG polarizations is measured [7].…”