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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 tau. 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 tau cluster around 1 when the fibers are straight, and the range increases up to 1.5 when wavier fibers are present. (C) The Authors. Published by SPIE under a Creative Commons Attribution 4.0 International License. Published version