Media 2: Understanding the twin-image problem in phase retrieval

Originally published in JOSA A on 01 November 2012 (josaa-29-11-2367

Media 3: Understanding the twin-image problem in phase retrieval

Originally published in JOSA A on 01 November 2012 (josaa-29-11-2367

Media 4: Understanding the twin-image problem in phase retrieval

Originally published in JOSA A on 01 November 2012 (josaa-29-11-2367

Media 1: Understanding the twin-image problem in phase retrieval

Originally published in JOSA A on 01 November 2012 (josaa-29-11-2367

Media 1: Quantitative interior x-ray nanotomography by a hybrid imaging technique

Originally published in Optica on 20 March 2015 (optica-2-3-259

Ultrastructure Organization of Human Trabeculae Assessed by 3D sSAXS and Relation to Bone Microarchitecture

<div><p>Although the organization of bone ultrastructure, i.e. the orientation and arrangement of the mineralized collagen fibrils, has been in the focus of research for many years for cortical bone, and many models on the osteonal arrangement have been proposed, limited attention has been paid to trabecular bone ultrastructure. This is surprising because trabeculae play a crucial role for the mechanical strength of several bone sites, including the vertebrae and the femoral head. On this account, we first validated a recently developed method (3D sSAXS or 3D scanning small-angle X-ray scattering) for investigating bone ultrastructure in a quantitative and spatially resolved way, using conventional linearly polarized light microscopy as a gold standard. While both methods are used to analyze thin tissue sections, in contrast to polarized light microscopy, 3D sSAXS has the important advantage that it provides 3D information on the orientation and arrangement of bone ultrastructure. In this first study of its kind, we used 3D sSAXS to investigate the ultrastructural organization of 22 vertebral trabeculae of different alignment, types and sizes, obtained from 4 subjects of different ages. Maps of ultrastructure orientation and arrangement of the trabeculae were retrieved by stacking information from consecutive 20-μm-thick bone sections. The organization of the ultrastructure was analyzed in relation to trabecular microarchitecture obtained from computed tomography and to relevant parameters such as distance to trabecular surface, local curvature or local bone mineralization. We found that (i) ultrastructure organization is similar for all investigated trabeculae independent of their particular characteristics, (ii) bone ultrastructure exhibiting a high degree of orientation was arranged in domains, (iii) highly oriented ultrastructural areas were located closer to the bone surface, (iv) the ultrastructure of the human trabecular bone specimens followed the microarchitecture, being oriented mostly parallel to bone surface, and (v) local surface curvature seems to have an effect on the ultrastructure organization. Further studies that investigate bone ultrastructure orientation and arrangement are needed in order to understand its organization and consequently its relation to bone biology and mechanics.</p></div

Supplement Media 2: Quantitative interior x-ray nanotomography by a hybrid imaging technique

Originally published in Optica on 20 March 2015 (optica-2-3-259

3D scanning small-angle X-ray scattering (3D sSAXS) experimental procedure, providing spatially resolved and quantitative 3D ultrastructure information for trabecular bone.

<p>(A) The histological bone section was mounted on a metal holder, and raster-scanned with a micro-focus X-ray beam, at a step size of 20 μm, for 10 rotation angles <i>ω</i>. The 2D orientation angle <i>χ</i> as well as the 2D degree of orientation (DO) were extracted from each diffraction pattern [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.ref038" target="_blank">38</a>], for a <i>q</i>-range of 37.9–75.8 μm⁻¹ (orange dashed circles), suitable to retrieve the orientation of mineralized collagen fibrils in the bone tissue. The 3D information (polar and azimuthal angles <i>θ</i>_ο and <i>φ</i>_ο and the 3D DO) was derived by fitting the experimental data to sinusoidal equations (red inset), as described in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.ref029" target="_blank">29</a>]. For further experimental details, please consult [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.ref029" target="_blank">29</a>]. The result for all points in the region of interest (ROI) is the orientation map shown at the right, where the ultrastructure arrangement of each 20 × 20 × 20 μm³ bone volume is represented by a vector, whose direction represents the main orientation of the ultrastructure and the length and color stand for the DO. (B) The histological bone section of the investigated ROI is registered to the SR CT-derived volume, to identify the corresponding digital section in the CT volume (gray bone on black background). The X-ray transmission information recorded by a photodiode on site during the 3D sSAXS experiments (red inset) is registered to the digital SR CT section, which allows identifying every point of the ROI within the 3D bone structure, and thereby spatial mapping between ultrastructural information obtained from 3D sSAXS and microstructural information retrieved from SR CT. C) 3D bone structure from SR CT, which corresponds to all the points within the pre-selected ROIs that have been analyzed using 3D sSAXS. A virtual cut (indicated as red surface) has been performed to the structure at the position of the ROI in (A). D) The 3D sSAXS information of the whole trabecula can be plotted as a 3D map that represents the ultrastructure orientation, where the direction of the vectors corresponds to the ultrastructure orientation and the vector length and color indicate the DO in a quantitative fashion (given by the colormap on the right). A virtual cut similar to that in (C) has been performed at the position of the 2D orientation map at the right part of (A).</p

Vertebral specimens of the 4 subjects and trabeculae that have been studied.

<p>(A) Cylindrical vertebral cores from 4 different subjects (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.t001" target="_blank">Table 1</a>), imaged using synchrotron radiation-based computed tomography (SR CT) at 7.4 μm voxel size. The symmetry axis of the cylinder corresponds to the craniocaudal direction. Differences in bone mass are apparent, corresponding to different ages of the donors (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.t001" target="_blank">Table 1</a>). (B) The bone samples selected from the cylindrical cores consisted in sequences of 20-μm-thick histological sections, including the selected regions of interest (red frames), which designate trabeculae analyzed by 3D scanning small-angle X-ray scanning (3D sSAXS). Sample 1c mostly contained trabeculae with their long axis in the craniocaudal direction, while Sample 1p had preferentially trabeculae at a perpendicular direction. Selected trabeculae from Sample 1c were mostly plate-like because this was by far the most common trabecular type found for the craniocaudal direction. On the other hand, perpendicular trabeculae for Sample 1p were mostly rod-like, whereas selected trabeculae from the other subjects (2–4) exhibited more irregular shapes, in-between plates and rods.</p

Validation of 3D small-angle X-ray scattering (3D sSAXS) by correlation with linear polarized light microscopy, in terms of ultrastructure orientation and alignment.

<p>(A) Bright-field image of bone section, which shows one of the regions of interest (red circle) assessed using both linear polarized light microscopy (PLM) and 3D small-angle X-ray scattering (3D sSAXS). The ROI is circular because of the rotation of the sample for the linear PLM experiments, which leads to a loss of the information at the corners (cf. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.g003" target="_blank">Fig 3B</a>). (B) The goodness of the sinusoidal fit required in linear PLM to retrieve the ultrastructure orientation, given by the coefficient of determination (R²). In most areas, the goodness of the fit was high (> 0.8). However, there were also large areas where the goodness of the fit was very low, which corresponded to areas without any predominant ultrastructure orientation, i.e. very low values of DO. (C) In-plane ultrastructure orientation from linear PLM. (D) In-plane ultrastructure orientation from 3D sSAXS. (C-D) Lines indicate the main orientation of the ultrastructure, where the bar length represents the DO. Local ultrastructure orientations, as obtained from linear PLM and from 3D sSAXS, were comparable. (E) Difference of in-plane ultrastructure orientation between linear PLM and 3D sSAXS. For most points (~75%), in-plane ultrastructure orientation was similar (< 10° difference). Larger differences could be explained by low DO values (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.g005" target="_blank">Fig 5F</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0159838#pone.0159838.g005" target="_blank">Fig 5G</a>), characterizing areas without any predominant ultrastructure orientation. (F) DO from linear PLM. (G) DO from 3D sSAXS. (H) Difference of DO between linear PLM and 3D sSAXS. (F-H) PLM and 3D sSAXS agreed regarding the location of high and low DO areas. However, high DO areas were bigger when retrieved from 3D sSAXS.</p