Significance: The spatial organization of collagen fibers has been used as a biomarker for assessing injury and disease progression. However, quantifying this organization for complex structures is challenging.
Aim: To quantify and classify complex collagen fiber organizations.
Approach: Using quantitative second-harmonic generation (SHG) microscopy, we show that collagen-fiber orientation can be viewed as pseudovector fields. Subsequently, we analyze them using fluid mechanic metrics, such as energy U, enstrophy E, and tortuosity τ.
Results: We show that metrics used in fluid mechanics for analyzing fluid flow can be adapted to analyze complex collagen fiber organization. As examples, we consider SHG images of collagenous tissue for straight, wavy, and circular fiber structures.
Conclusions: The results of this study show the utility of the chosen metrics to distinguish diverse and complex collagen organizations. We find that the distribution of values for E and U increases with collagen fiber disorganization, where they divide between low and high values corresponding to uniformly aligned fibers and disorganized collagen fibers, respectively. We also confirm that the values of τ cluster around 1 when the fibers are straight, and the range increases up to 1.5 when wavier fibers are present.
Multiphoton microscopy provides a suitable technique for imaging biological tissues with submicrometer resolution. Usually a Gaussian beam (GB) is used for illumination, leading to a reduced power efficiency in the multiphoton response and vignetting for a square-shaped imaging area. A flat-top beam (FTB) provides a uniform spatial intensity distribution that equalizes the probability of a multiphoton effect across the imaging area. We employ a customized widefield multiphoton microscope to compare the performance of a square-shaped FTB illumination with that based on using a GB, for both two-photon fluorescence (TPF) and second-harmonic generation (SHG) imaging. The variation in signal-to-noise ratio across TPF images of fluorescent dyes spans ∼5.6 dB for the GB and ∼1.2 dB for the FTB illumination, respectively. For the GB modality, TPF images of mouse colon and Convallaria root, and SHG images of chicken tendon and human breast biopsy tissue showcase ∼20 % area that are not imaged due to either insufficient or lack of illumination. For quantitative analysis that depends on the illuminated area, this effect can potentially lead to inaccuracies. This work emphasizes the applicability of FTB illumination to multiphoton applications.
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