## 3 Results and Discussion
### Impact of Decalcification on the Hard Tissue Microstructure  
The preparation of histological sections from distracted jaws generally requires the decalcification of the jawbone. SRuCT obtained after the decalcification process, but before physical sectioning, could be helpful in identifying the slices of interest, because both hard and soft tissues are three-dimensionally visible. The impact of decalcification can be evaluated by means of a bi-variate histogram. For this purpose, tomographic datasets must be well registered and the common volume extracted. Composition and shape changes as a result of decalcification, led to a challenging registration problem, so we applied a semi-automatic approach, whereby registration was optimized with respect to selected corresponding landmark pairs, denoted as LM1, and image similarity. Figure 4 shows the spatial distribution of the selected landmarks and two examples of uCT volumes in regions surrounding the corresponding landmarks. Figure 4: **(a)** Spatial distribution of corresponding landmark pairs, with landmarks LM1 used for registration (shown in blue) and landmarks LM2 for determining registration accuracy (shown in red). Lines connect the manually selected landmark positions in the decalcified tissue (marked by a rectangle) with the corresponding position in the non-decalcified tissue—as determined by non-rigid image registration. This can be compared to the manually selected landmark position marked by circles. (**b**,**c**) Orthogonal slices at the manually selected landmark pairs are marked with thick lines in (**a**). These are at point features within (top) a tooth and (bottom) a lacuna in newly formed bone. Figure 3: Three-dimensional representation of the distracted jaw generated from tomography data before decalcification, illustrating bone formation and the location of the holes used for the distractor screws. Since conventional \(\upmu\)CT data only reveals calcified tissues, we investigated if a rigid-and-isotropic-scaling registration with seven parameters (three for translation, three for rotation, one for scaling), abbreviated in the text below by 'rigid', would yield the desired fit. The selected virtual cut displayed in Figure 5, however, clearly proves that such a rigid transformation does not account for decalcification-induced local shrinkages. In the first row of Figure 5, the virtual cut of the non-decalcified bone from the conventional tomography data is presented in turquoise and compared with decalcified tissue covering the grayscale on the central and left images. The superposition of the turquoise-colored edges and the grayscale image clearly indicate non-uniform shrinkage. Figure 5: A selected virtual cut through the tomography data indicates registration quality. Rigid registration displayed in the first row does not provide a reasonable alignment between (**left**) non-decalcified bone and (**right**) decalcified tissue. The employed non-rigid registration enabled the quantification of local shrinkage, represented by the color bar (**bottom right**). The dashed-line box marks the region cropped for the data in Figure 6.  
The second row of images in Figure 5 shows that the non-rigid procedure applied resulted in reasonable fitting (see the orange-colored edge representation overlaid on the grayscale slice from the synchrotron radiation-based tomography data). The related three-dimensional strain field is given by a color bar ranging from yellow (0%) to blue (50% shrinkage). The largest strain values were above 40% and are found in mature bone related to the highest calcium content. The content of the box represented by the dashed lines in Figure 5 is also shown in Figure 6, top row. The second and third rows in Figure 6 contain orthogonal virtual cuts for the rigid and non-rigid approaches. Hence, these data help to gain a three-dimensional impression of the local strain fields, i.e., shrinkage induced by decalcification and paraffin embedding. They also reflect the necessity to apply non-rigid registration.