A combination of two techniques — computed tomography and small-angle X-ray scattering — and serious computing power have enabled multi-scale, three-dimensional analysis of bone and tooth tissue. See Letters p.349 & p.353
In this issue, two papers (by Liebi et al.1 and by Schaff et al.2) describe different approaches to visualizing three-dimensional bone and tooth structures on both macroscopic and nanometre scales. The methods derive from computed tomography, a well-established imaging technique that can yield 3D pictures of bones, but which quantifies just one scalar parameter, such as mineral density, in each voxel (3D pixel) of the image. Using the new techniques, each voxel contains information on both the orientation and the size of mineral particles in the bone or tooth specimen.
The strength of bone is determined by its structure on all scales, particularly by local variation in the size, amount and orientation of bone mineral particles3. Formed from calcium phosphate, these mineral platelets are just a few nanometres thick and are embedded in a matrix of collagen molecules (Fig. 1, inset). Because bone tissue is constantly remodelled and adapted, the orientation of mineralized collagen fibrils varies in a complex fashion throughout the tissue4.
Although transmission electron microscopy provides sufficient resolution to visualize the mineral particles, it does not allow them to be mapped over millimetre distances in complete bone sections. For this reason, a technique called small-angle X-ray scattering (SAXS) has been used in a 'scanning' mode since the 1990s to study bone taken from patient biopsies and animals5,6. In this method, a bone specimen is moved in two dimensions (defined by the x and y axes in Fig. 1) across a narrow X-ray beam, and at each position of this scan a SAXS pattern is collected. This allows the simultaneous visualization of two different scales: the structure, particularly the orientation, of the mineralized collagen fibrils in every pixel of the scan; and the variation of fibril orientation across a macroscopic specimen.
When a 2D X-ray detector is used, as in the early implementations of scanning SAXS, it effectively provides 4D information: a macroscopic 2D map of the bone tissue and 2D information about the structure of the mineralized collagen fibrils in every pixel of the map7. It is straightforward to extend this to five dimensions by rotating the bone section around an axis to collect 3D information on the mineralized collagen fibrils in each voxel, while the mapping stays 2D8.
It would be desirable to extend this to six dimensions by enabling 3D macroscopic mapping of the specimen. But the reconstruction of such 6D data is a formidable numerical challenge and can be solved only through the use of certain approximations and substantial computing power. In conventional computed tomography, volumes are reconstructed from 2D images taken in the x–y plane for many rotation angles φ around a given axis (Fig. 1). For SAXS tomography, 2D SAXS data must be collected at each position of the x–y plane and at many rotation angles, not just around one axis but around many axes. This results in a huge number of measurements and requires massive computational effort.
To make such efforts tractable, Liebi et al. (page 349) take advantage of certain symmetries in the mineralized collagen fibrils of bone. More specifically, they assume that the arrangement of mineral particles is rotationally symmetrical — it looks the same after a certain amount of rotation — around the direction in which collagen molecules align in each fibril. This symmetry imposes constraints on the SAXS patterns that aid the reconstruction of 3D images using a procedure sometimes called tensor tomography.
Schaff and colleagues' approach (page 353) assumes that the SAXS signal varies slowly with rotation angle. This means that fewer rotation angles are needed during data collection, because data values between rotation angles can be interpolated. The authors used their technique to study dentine in the interior of a tooth. Both techniques1,2 produce 3D pictures of macroscopic specimens, in which each voxel contains an arrow that represents the direction of the predominant orientation of the mineralized collagen fibrils in the voxel.
A previous attempt9 to develop 3D scanning-SAXS tomography was devised for materials with structures that have rotational symmetry around one axis, such as composite materials based on parallel fibres. This approach is similar to that of Liebi and colleagues, but it assumes that all the fibres point in the same direction throughout the specimen, which is not true for bone. Another recently reported approach10 applies normal scanning SAXS to a series of consecutive thin bone sections cut from one block; by assembling the resulting series of scanning SAXS data, a full 3D image was reconstructed. The obvious disadvantage of that technique compared with the currently reported ones is that the bone sample was destroyed.
Both Liebi et al. and Schaff et al. collected more than one million SAXS patterns for their reconstructions — equating to terabytes of data, an impressive amount. Recording them using a synchrotron X-ray source took about a day, and the computations needed for one tomogram required several days of computing time. This is manageable for proof of principle of the techniques, but would be prohibitive for clinical studies, for which many tomograms would be required.
Nevertheless, the feasibility of the techniques has been demonstrated. With the progress currently foreseeable in the development of X-ray sources, detectors and computing power, one can therefore expect SAXS tomography to become an important tool for the analysis of bone, dentine and other mineralized tissues in biological and medical studies.Footnote 1
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Schaff, F. et al. Nature 527, 353–356 (2015).
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