## 2 Materials and Methods
### Histology and Immune-Histochemical Preparation  
For histological assessment, the rat mandible specimens were cut in the horizontal plane to attain sections that included both osteotomy sites and the complete distraction gap zone. The paraffin-embedded sections selected for histological processing were sliced to 2 \(\upmu\)m thickness with a microtome Leica SM2010R (Leica Instruments GmbH, Nussloch, Germany). Hematoxylin and eosin (H&E) was used as a surface stain for the decalcified bone sections.  
Selected sections were used to identify human mesenchymal stromal cells (hMSCs) by means of human-specific repetitive _Arthobacter luteus_ (Alu) sequences as well as immunostaining for a human leukocyte antigen Class 1 (HLA-1). To detect repetitive human-specific Alu sequences, chromogenic in situ hybridization was performed on paraffin sections, as described by [PERSON] [21]. To improve probe binding, one base of the sequence was changed from 59-cgggggtggcatgatggt-39, reverse 59-ttttttggacgggatctcgc-39 to 59-cgagggggtgccatysis. The laboratory-based tomography data only show the bony structures, whereas the synchrotron radiation-based measurement after decalcification includes soft-tissue components with similar X-ray absorption to the decalcified bone. Furthermore, an affine transformation was insufficient, as the bony structures shrunk and were non-uniformly deformed during decalcification. As a consequence, the three-dimensional data were semi-automatically registered. Specifically, the data were pre-aligned based on an affine transformation determined from eight manually selected landmarks in both datasets. Subsequently, 50 corresponding landmark pairs were identified in the pre-aligned datasets by an image-processing specialist. These landmark pairs were employed for registration guidance and have been denoted as LM1. An oral and maxillofacial surgeon independently selected 50 corresponding landmark pairs (denoted as LM2), which were employed to determine registration accuracy. Landmarks were manually selected by navigating to corresponding 3D image locations in two independent itk-SNAP viewers (version 3.6.0) [22] showing orthogonal slices. Furthermore, masks were automatically created by thresholding and extracting the largest connected components to focus registration on the foreground regions. Note: these masks included bony tissue for the non-decalcified data and all tissue components of the decalcified data.  
The elastix image registration software version 4.9 was employed [23; 24], as this well-established approach supports the use of masks for defining image regions to be matched and allows the combination of image dissimilarity measures and landmark distances in the cost function. Registration was optimized by maximizing normalized cross-correlation within the overlapping region of the masks with weight one and minimizing the Euclidean distance of the 50 LM1 landmark pairs with weight ten. Spatial transformations were restricted to either (i) affine or (ii) affine followed by a three-level cubic B-Spline transformation with a final grid spacing of 32 voxels, termed non-rigid. Full sampling was used for more stable convergence behavior.