Bone microarchitecture in human fetuses: Investigation of bone microarchitecture

Imaging techniques

The reference technique for the investigation of bone microar-chitecture has for long been histomorphometry, which consists in analyzing histological slices. The bone sample has to be embedded in a resina and a slice with a thickness of a few micrometer is cut. This slice is then examined under a light microscope, and processed using specific quantification methods as described in the next section.

However, since the last decade, quantification based on x-ray microtomography (micro-CT) has considerably increased due to the amazing progresses made by this technique, and the availability of commercial systems. Micro-CT is a high resolution version of CT, used in clinical routine at the hospital. Its principle is to measure the attenua-tion of x-rays in a slice (or a volume) under different angles of view; then these measures are numerically processed to reconstruct a digital image (or volume). Conversely to histomorphometry which requires the cutting of the bone sample to be analyzed, micro-CT is a non destructive technique requiring no special preparation for the sample. In addition, micro-CT may provide three-dimensional images that are difficult to obtain by using serial histological slices due to slice deformations or deteriorations during cutting. The quantification of bone mor- phometry may then be directly performed from three-dimen-sional images, which presents some advantages over bi-di- mensional analysis, as will be highlighted in the next section. Though the accuracy of quantitative microarchitecture parameters is strongly related to image quality in terms of spatial resolution and signal to noise ratio. Spatial resolution refers to the size of the smallest detail that can be observed in the image. It is admitted that for the analysis of adult human trabecular bone a spatial resolution of 10-15 |jm is sufficient to get accurate quantification. Spatial resolution is not necessarily equal to the pixel (picture element) size in the image, although there is often some confusion in these terms. The signal to noise ratio in the micro-CT image is another important parameter with respect to the quantification accuracy since a noisy image makes it difficult the separation of bone from background. However, this segmentation is crucial since it is the first step of quantification and strongly influences the subsequent measurements. Keeping the same signal to noise ratio when spatial resolution increases is a technical difficulty to which micro-CT is confronted. A solution to get high signal to noise ratio in limited acquisi-tion time, is to use x-rays with high photon fluxes. X-rays with such characteristics may be produced by synchrotron sources, and synchrotron radiation (SR) micro-CT systems have been developed in a few synchrotron facilities in the world. A SR micro-CT system has been developed on beam-line ID19 at the ESRF (European Synchrotron Radiation Facility). The system provides three-dimensional images with spatial resolution between 15 and 0.5 |jm, this last resolution being still unachieved by micro-CT systems based on standard x-ray sources. The system has been used for the quantification of bone microarchitecture in human adults, animal models and human fetal bone. A significant advantage of this system over standard micro-CT is that it enables the simultaneous quantification of bone microarchitecture and tissue mineralization, which is possible thanks to the use of monochromatic x-ray beams with sufficient photon fluxes.

Quantification of bone microarchitecture

The nomenclature used for quantifying bone microarchitecture in trabecular or cortical bone has been standardized in a reference paper of Parfitt. In order to infer three-dimensional parameters of bone organization from bi-dimensional slices (provided by histology), geometric assumptions on the organization of bone have to be hypothesized. Usually the bone network is supposed to be organized in a parallel plate model (Parfitt's model). Under this assumption, stereology-de- rived methods allow estimating a number of morphometric parameters from two measures: the percentage of trabecular bone in the sample (Pp) and the normalized number of inter-sections of bone with a set of regularly spaced parallel test lines measured for various orientations (Pl). The following parameters may then be calculated: Trabecular Bone Volume fraction (BV/TV, where TV stands for total bone sample volume), Bone Surface on Bone Volume ratio (BS/BV), Trabecular Thickness (Tb.Th), Trabecular Number (Tb.N), and Trabecular Separation (Tb.Sp). These parameters are typically computed by using the MIL (Mean Intercept Length) method, which was initially proposed for 2D images, and later generalized for 3D images. In this case, the same relationships are used but the test lines are considered in the whole 3D space. Such a method may be applied for the quantification of three-dimensional images provided by micro-CT.

However the so-called derived architectural parameters, have the drawback to rely on a geometrical model of bone structures which is obviously not completely appropriate in all situations. Fortunately this model is no more necessary when three-dimensional images are available. A direct or model-independent method requiring no prior assumption has been proposed to calculate trabecular thickness.

A theoretical local thickness is defined at each point of the volume as the diameter of the maximal sphere including that point. Similarly, all microarchitectural parameters may be obtained via model-independent methods when using 3D images. The parameters are denoted with a star (for instance Tb.Th*) so as to differentiate them from their standard homonyms. Don't blow your budget on pharmacy items where to buy cialis now

We proposed a method for computing the local thickness of 3D discrete images based on discrete geometry. A medial axis of the bone structure, defined as the center of maximal balls, is derived from the local maxima of a 3D discrete distance map. The discrete thickness map is then obtained by propagating the sorted values of the diameter of the maximal balls to the entire balls. We typically use a 3D Chanfrein distance which provides a good approximation of the Euclidian distance. This method provides a thickness value at each point of the bone volume, and thus makes available the distribution of thickness over the entire volume. Statistical results such as the histogram of thickness, and the mean, median, and standard deviation of the distribution are computed. Three-dimensional images may also be used to get information on the orientation and anisotropy of the structure, as well as on the topology of the bone network. Orientation and anisotropy may be obtained from the MIL method by fitting the points defined by each direction and the normalized number of intersections in this direction, by an ellipsoid in 3D space. The degree of anisotropy (DA) is estimated by the ratio of the largest to the smallest axis value. The main orientation of the ellipsoid gives an estimate of the orientation of the structure. Topologic parameters include the Euler number, used to quantify the connectivity of the network, or other characteristics calculated from skeletons like the number of branches, number of connections...

Finally, the global geometry of bone structure in term of platelike or rod-like model may be estimated globally by the SMI (Structure Model Index). We recently proposed new geometrical indices based on a local classification of bone structures to describe more accurately the percentage of plate and rod volumes. The technique is based on an original idea of making a local topological analysis in the neighborhood of each point in order to classify the voxels of the bone structure. We used this classification to label four types of points: boundary, branch, plate and rod points. This initial classification is then re-labeled by re-affecting the boundary type which is not relevant to that of their closest neighbors. After this step, the 3-classes labeled image is used for counting the percentage of branch, plate and rod points in the bone volume, that we respectively denote NV/BV, PV/BV, and RV/BV.