2.3 Collagen Waviness.

From the PLM-derived orientations, we measured the waviness of collagen fiber bundles. We quantified the waviness using the circular standard deviation [41] of the collagen fiber orientations along a collagen bundle, as described previously [16]. Briefly, a straight fiber bundle would have a constant angle value, and therefore the waviness would be 0 deg. On the other hand, a wavy fiber bundle would have variable angle values throughout the fiber bundle, and therefore the waviness would be greater than 0 deg. To measure the waviness, we sampled the orientations using line segments placed along the length of a collagen bundle. This same line segments were used to measure the bundle waviness and strain (Fig. ​(Fig.2).2). Analysis was only performed on bundles that were identifiable throughout all stretch levels. To visualize the crimp changes with stretch, we used a previously described algorithm for highlighting the crimp (Figs. 3(b) and 4(b)) [16]. Briefly, pixels were colored purple or yellow (color version online) depending on whether the orientation was larger or smaller than the local average orientation, respectively. In crimped collagen bundles, the result was clear bands of alternating purple and yellow, each corresponding to half a crimp period. Uncrimped, or recruited, bundles show no be clear bands. It is important to note that we have shown that this technique for analyzing collagen fiber crimp does not require discerning fiber undulations or even the edges of the fibers or bundles [10]. The PLM-derived orientation resolved at a pixel encodes subpixel information on fiber orientation. Thus, it is possible to use a straight line along a bundle to derive highly accurate measurements of bundle undulations without the need to distinguish visually the bundle edges or the undulations. This is extremely important at high levels of stretch where edges and undulations become essentially impossible to distinguish, yet the signal remains adequate.