Fig. 1. Definition of spatial orientation of fiber-like structure. (a) Two-dimensional orientation of fiber is described by a single azimuthal angle θ; (b) three-dimensional orientation is described by both azimuthal angle θ and polar angle φ

Fig. 2. Two-dimensional orientation analysis approaches for fiber-like structures. Approach based on opening operator^[15]: (a) second harmonic generation (SHG) image of collagen fibers from cervical biopsy section; (b) fibers demonstrate the maximum intensity if they align parallel to the direction of the opening operator; (c) acquired orientation map from the opening operator. Approach based on two-dimensional Fourier transform^{[Download full size}

Fig. 3. Three-dimensional (3D) orientation analysis approaches for fiber-like structures. Approach based on 3D Fourier transform^[18]: (a) representative SHG image of porcine tendon; (b) 3D reconstruction of SHG images; (c) acquired 3D orientation in each ROI; (d) distribution histograms of φ; (e) distribution histograms of θ. Approach based on weighted vector summation^[19]: (f) definition of

Fig. 4. Applications of orientation analysis in wound healing. Wound healing in rat skin after burns^[21]:(a) image of the histological section of the wound and adjacent tissues; (b) fiber density map; (c) 2D directional variance map, indicating a high level of fiber alignment in the wound region versus adjacent tissues. Wound healing in rats after heart infarction^[22]: multi-photon images of the rat heart

Fig. 5. Application of orientation analysis in osteoarthritis of mice^[19,24]. DMM: destabilization of the medial meniscus (osteoarthritis model); Sham: ligament being exposed but not severed; NS-Ctrl: non-surgery control. (a) Schematic of the cartilage with layered structures; (b) a representative multi-photon image of cartilage, with the magenta signal corresponding to SHG image of collagen fibers; (c) based on the

Fig. 6. Application of 3D orientation analysis in the breast cancer in mice model^[19]. (a) Multi-photon image of normal tissue; (b) multi-photon image of tumor tissue; (c) 3D reconstructions of normal tissue; (f) 3D reconstruction of tumor multi-photon image; representative collagen SHG intensity images of (d) normal and (g) tumor tissues, and the insets are schematics of spatial structure of collagen; (e) 3D directional variance map of normal tissue; (h

Fig. 7. Application of 3D orientation analysis in human peritoneal metastases^[19]. (a) Multi-photon image of healthy parietal peritoneum;(b) multi-photon image of pancreatic neoplastic tissue; (c) 3D reconstruction of multi-photon image of healthy parietal peritoneum; (d) 3D reconstruction of multi-photon image of pancreatic neoplastic tissue; (e) 3D directional variance map of healthy parietal peritoneum; (g) 3D directional variance map of pancreatic ne

Fig. 8. Application of 3D orientation analysis in the injury model of engineered brain-like tissues^[19]. (a) “Donut model” of engineered brain-like tissues; (b) schematic of the controlled cortical impact set-up; (c) 3D reconstruction of two-photon excited fluorescence (TPEF) image of neuronal axons; (d) 3D directional variance of the uninjured and injured tissues as a function of distance away from the injury site; representative TPEF images of (e) unin

Fig. 9. Applications of 3D orientation analysis in pulmonary fibroblasts and collagen fibers in engineered tissues^[31]. (a) Schematic of engineered tissue culture and 3D angle definition; (b) cell spreading as a function of culturing time; (c) 3D directional variance of pulmonary fibroblasts (green) and collagen fibers (red) as a function of time; (d) representative images of cells and collagen fibers, as well as distribution histograms of 3D orientation

Fig. 10. Application of 3D orientation analysis in the study of hormone effects in engineered breast tissues^[32]. (a) 3D reconstructions of TPEF images of cell spheroids in response to different hormone treatments; (b) 3D reconstructions of engineered breast tissues including both cells and collagen fibers; (c) one representative frame from 3D constructions; (d) distribution histograms of 3D orientations under different hormone treatments; (e) 3D directio