Quantitative analysis of 3D trabecular network images

Purpose and context

The objective is to extract quantitative parameters from the 3D images of the trabecular bone network. With 2D images such as used in histomorphometry, stereology methods allowing to infer 3D parameters from 2D measurements, require a priori models of the investigated structure. Bone micro-architecture is typically assumed to follow a parallel-plate model, which is not necessarily true. With 3D images, such an assumption is no more necessary and model-independent methods may be used. In addition, 3D images allow extracting information about the morphology, the anisotropy and the topology of the trabecular network.

Methods

In addition to standard quantification based on the MIL (Mean Intercept Length) method, several quantification methods were developed. Direct thickness measurement: The measurement of the direct trabecular thickness, proposed by Hildebrand and Ruegsegger in a continuous framework was implemented using 3D discrete distance maps. The method provides a 3D map of the local trabecular thickness. Local geometric analysis : We proposed an original method to evaluate locally the geometry of complex structures. The method is based on 3D medial axis representation followed by topologic analysis (collaboration D. Attali, LIS, Grenoble) [1]. Each point of the medial axis is classified according to a local topological analysis of its neighborhood, the size of which is adapted locally to the studied point [2]. The information is then propagated to the whole volume. After classification, new quantitative parameters of bone micro-architecture characterizing independently plate and rod structures are defined. We thus defined new micro-architecture parameters such as the percentage of “plate” or “rod” voxels, or even the thickness of the “plate” or “rod” structures. .

Results

Direct thickness: 

(a)

(b)

a) Illustration of the local trabecular thickness on a 2D slice extracted from the 3D image : the trabecular thickness at one point is defined as the diameter of the maximal ball including that point. b) Color-coded representation of a slice of the 3D trabecular thicknessl maps

Geometric parameters :

The method allows to classify each voxel of the 3D image according to its geometry. The method was first tested on simulated phantoms made of plates and cylinders, and then applied to experimental data. Despite of the complexity of the trabecular bone network, the method provided good results (see figure below). As compared to previous approaches, the method allows to classify the entire volume and only its skeleton, and it appears to be robust to small irregularities on the bone surface.

 

 

(a)

(b)

Illustration of the local classification of each voxel of a trabecular bone 3D image : a) original image, b) Color-coded representation of the classified image : green : plate , pink : rods, red : nodes

The method was applied to trabecular bone images in human [3], in mice [3], and we plan using it for other cohorts of samples to extract geometric characteristics that are not currently evaluated with standard methods.


References