Thickness analysis and reconstruction of trabecular bone and bone substitute microstructure based on fuzzy distance map using both ridge and thinning skeletonization

The accurate geometric analysis of microstructured biological porous media is crucial for an understanding of the geometric changes that result from diseases such as osteoporosis and for the design of bone substitutes for the treatment of cancer patients. This paper presents a methodological development designed to improve the description of the average pore size and thickness of a microstructure's biological media. Specifically, the paper introduces a new skeletonization method based on a ridge skeleton combined with fuzzy distance transform (FDT), which has recently been used in the literature and has shown some advantages compared to the traditional distance transform. The new skeletonization method is applied to trabecular bone excised from healthy and osteoporotic vertebrae, as well as to bone substitutes with small and large pores. These samples are scanned by a micro-computed tomography scanner. The new skeletonization method has been implemented successfully, and an exact algorithm for implementation and reconstruction has been developed. The results show that, compared to widely used thinning methods, the new FDT ridge skeleton generates measurements that are more representative of the microstrucrure of the examined media. It is concluded that the new method can find the ridges of the FDT and produce topologically accurate skeletons, leading to accurate measurement and reconstruction of the microstructured porous media.