## 4 Micro-CT Bone Structure Analysis in OP-Related Studies
### Bone and Tissue Mineral Density Measurement  
According to [PERSON]'s law (\(I_{x}=I_{0}e^{-\mu x}\)), the X-ray attenuation by an object (\(I_{x}/I_{0}\)) is dependent on its thickness \(x\) and on its linear attenuation coefficient \(\mu\), which in turn depends on the source energy and the material constituting the sample [74]. Therefore, the greyscale level of every voxel assigned during the reconstruction phase is strictly related to the material composition and, consequently, to its density. According to this, information about the sample density can be obtained from the micro-CT analysis by comparing its X-ray attenuation to those measured from two calibration phantoms with a known density. In order to have a reliable attenuation comparison, the phantoms should have dimensions similar to that of the sample analysed and should undergo the same scanning and reconstruction processes. In this way, the X-ray attenuation will depend exclusively on the sample density and not on the other parameters of the Lambert-Beer law (i.e., object thickness  
Figure 13: Histogram method for the segmentation threshold choice. and source energy). Considering that the X-ray attenuation phenomenon in the bone tissue is mainly dominated by the inorganic phase, to obtain information about the sample density, phantoms of known hydroxyapatite concentration are commonly used. In the past, BMD constituted the principal value used to estimate the bone failure risk. In micro-CT analyses, BMD represents the grey level of the entire volume of the sample, including porosity and soft tissue contributions, in addition to the bone tissue one. Therefore, BMD represents an indicator of apparent bone density. For a long time, the BMD value was used as a predictor for bone strength at the macroscopic level. However, due to its strong dependence on the volume and porosity of the sample analysed, the measure of BMD as a bone density marker presents some limitations. In fact, an inferior BMD can be the result of a decrease in real bone density (depending exclusively on bone material properties) as well as of an increase in the bone porosity fraction. Therefore, the contribution of the compositional variations of bone tissue in the BMD value cannot be distinguished from the architectural ones. In addition, the numerical value of BMD is strongly dependent on the instrument used and on the experimental conditions adopted and cannot be compared between different studies. In recent years, thanks to the development of the up-to-date experimental CT scanners working at very high resolutions, tissue mineral density (TMD) has been introduced as a better indicator of bone density due to the exclusion of the porosity and soft tissue contributions. It is worth mentioning that the TMD value provides an indication of real bone density, expressed in mg of hydroxyapatite per cm\({}^{3}\). However, TMD cannot be directly compared with the material bone density obtained through the more traditional gravimetric methods (e.g., through the application of Archimedes' principle) [75]. [PERSON] and collaborators formulated an equation in order to obtain the real tissue density starting from the TMD value calculated through micro-CT measurements [76]. However, to formulate this equation, they assumed that the bone tissue is constituted by three phases (i.e., water, organic and inorganic) and that the organic volume ratio is always equal to 36%. Since this value can change among patients and among bones of the same individual, the equation formulated by [PERSON] and collaborators presents some limitations and should be applied with caution. In general, TMD is useful to make comparisons between the real density of healthy and osteoporotic bone samples subjected to the same scanning and calibration procedures, as reported by the authors of a recent work [26].