## 4 Micro-CT Bone Structure Analysis in OP-Related Studies
### Finite Element Method Analyses  
The finite element method (FEM) is a computational method usually applied in tissue engineering studies for the analysis of the mechanical behaviour of a tissue in a non-destructive way. In the bone field, the FEM is mainly used for the prediction of bone failure or bone damage in the case of an external load application. To this aim, the micro-CT-reconstructed bone should be modelled through a mesh constituted by a series of defined geometrical elements (e.g., triangles, tetrahedrons or hexahedrons) whose reference points represent the nodes of the mesh. The mechanical parameter of interest (e.g., the Young's modulus or the ultimate stress) is calculated at each mesh node through a mathematical function exploiting the variation of a known measured parameter (e.g., the material density). The application of an external load is simulated by imposing defined boundary conditions on the model. All the mathematical functions of the nodes are then combined and should converge in order to obtain the overall bone behaviour [10]. Furthermore, FEM analyses can also provide the stress distribution on the bone structure which can be visually represented by means of colour maps, as visible in Figure 14.  
It is evident that the total number of elements of the FE can be considered a key parameter to obtain precise FE models, better approximating the bone behaviour. The most common procedure foresees the conversion of each image voxel in an FE. Therefore, thanks to the very high voxel resolution of micro-CT-derived images, very precise FEM models containing a high number of elements can be obtained, allowing the modelling of bone behaviour even at the microscopic scale. For this reason, the FEM analyses based on micro-CT images are defined as micro-FEM [4, 74]. Micro-FEM analyses can represent a useful future tool to predict bone fractures in osteoporoptic patients, where the fracture occurs at atypical loads due to the altered bone microstructure, as described in the first part of this review. In the literature, several micro-FEM analyses were reported for ex vivo biopsies or rat bones to model the trabecular behaviour after load applications, by considering the density value derived from the micro-CT as the key parameter of node equations [20, 78, 79]. Furthermore, in order to verify the reliability of the models, the real mechanical behaviour of the bone was experimentally tested by applying the same loading conditions of FEM analyses. The FEM models and the experimental tests showed a good correlation, thus confirming the reliability of the FEM simulation results. On the other hand, in the work of [PERSON] and collaborators, the orientation of trabecular rods has been identified as the main parameter used to predict bone failure through FEM analyses, calculated by means of the individual trabecula segmentation technique on vertebral biopsies from donors [29]. Thanks to their model, they confirmed that the reduction in the number of transversal rods, usually associated with OP, is responsible for the most remarkable decrease in the mechanical properties of vertebral trabecular bone. The importance of the FEM analysis in the assessment and prediction of bone features and injuries has been widely supported and reported in several studies that thoroughly describe the investigation of bone biomechanics, starting from micro-CT as well as magnetic resonance images [80, 81]. Despite the high potentiality of FEM analyses in bone fracture prediction, their use in the clinical field is still distant due to the long computational times and the high cost of machines able to run these simulations, as well as to the lack of pre-clinical FEM studies confirming the reliability and the accuracy of FEM results in patients. For a more detailed description of the technique and its application in the assessment of bone tissue pathologies, the authors kindly invite readers to refer to the several reviews present in the literature [82, 83, 84].