## 3 Fibrous Structures
### Bone  
The collagen microfibrils discussed in the previous section form fibers and are modified by specific tissues with either proteoglycans or mineral depositions to form bone [9; 59]. Bone is a biological, hierarchical composite of hydroxyapatite and collagen [72]. Figure 4a shows the hierarchical structure of a human cortical bone, starting with collagen molecules and the collagen fibrils preferentially aligned along the longitudinal direction, thus contributing to bone stiffness as the bone carries the load in the longitudinal direction [73]. Hydroxyapatite crystals nucleate on the c-axis parallel to the fibrils in the gaps between the ends of the tropocollagen molecules, thus mimicking the staggered arrangement of fibrils [72]. Mineralized collagen fibrils arrange themselves alternately to create a lamellae structure. These lamellae surround a central canal, forming osteons that create the cortical bone together [72; 74].  
Figure 4: (a) Hierarchical structure of a compact bone starting with the collagen molecule; reprinted from [PERSON] et al. (1998) [74] with permission from Elsevier. (b) (i) Diffraction pattern in which radial integration regions are shown; the loading axis is indicated by orange arrows. (b) (ii) 1D radial integration of the SAXS pattern shown in (b) (i) reprinted from [PERSON] et al. (2016) [75] with permission from Springer Nature. (c) (i) SAXS pattern for a wild-type bone; c denotes the collagen peak, (d) denotes the diffuse scattering from the minerals, and **e** is the angular integration of I(\(\chi\)), where \(\chi\) is the azimuthal angle. (c) (ii) Diffraction pattern for a GIOP (glucocorticoid-induced osteoporosis) bone. Reprinted from [PERSON] et al. (2021) [76] with permission from Elsevier.  
Figure 4b (i) shows the 2D SAXS pattern of a trabecular bone [75]. The diffuse scattering at the center of the pattern originates from the nanocrystalline hydroxyapatite platelets. A radially integrated scan (Figure 4b (ii)) of the 2D pattern is used to analyze the structure. The first- and third-order peaks seen in this radial scan come from the meridional D-periodicity of collagen. Because the first-order peak has large diffuse scattering, the third-order peak, shown in blue, as seen in Figure 4b (i), is used for analysis [75]. The degree of alignment of the platelets is determined from the azimuthal intensity distribution of the third-order diffraction from collagen. The thickness of the mineral platelets was calculated from the surface-to-volume ratio calculated from the invariant, \(Q=\int q^{2}\cdot I(q)\), and the Porod parameter, the y-intercept in the Porod-Debye plot, I(q). \(q^{4}\) vs. \(q^{4}\)[77].  
Figure 4c shows the SAXS pattern of a wild-type femur of a mouse. Figure 4c (i) is from a healthy bone, and Figure 4c (ii) is from a femur afflicted with a form of arthritis. The diffraction pattern of the healthy bone shows oriented features in the third-order collagen reflection as well as in the scattering due to platelets. In the afflicted bone, the collagen becomes unoriented, and the diffuse scattering shows lower platelet ordering. These broader azimuthal intensity distributions show the random orientation of the fibrils in the afflicted bone compared to the healthy bone. This decrease in ordering resulted in poorer mechanical properties of the afflicted bone [76]. Changes in the collagen structure can also be used to evaluate samples for osteoporosis by monitoring the changes in the position of the collagen peak, which can be related to the strain in the bone and can be evaluated [78].