## 1 Introduction  
Osteoporosis (OP) is a worldwide skeletal disease affecting the elderly population, with a very high incidence in post-menopausal women. OP causes the overall reduction of bone mass due to an imbalance in the remodelling process toward the resorption phase [1]. This reduction is associated with an increased risk of bone fractures with a consequent decline of patients' quality of life [2]. Nowadays, worldwide, 8.9 million osteoporotic fractures occur annually, more than 1000 fractures every hour (one every 3.5 s), with a remarkable cost for society and health care systems. In the European Union (EU), an osteoporotic fracture occurs every 30 s and with the current demographic shift, the incidence is expected to double in a few decades. Although OP has been for long time considered as a women-only disease, recent data show an incidence of one out of two to three women and one out of five men above fifty years old, with a prognosis for men often being significantly worse. To date, in the EU, approximatively 22 million women and 5.5 million men aged between 50-84 years are estimated to be affected by OP [3]. Since the total population's age along with the life expectancy of the elderly are estimated to increase by more than two-fold over the next 25 years, osteopororotic fractures still represent an important clinical issue with a significant impact on the cost for health care systems. In fact, the economic burden of osteopororotic fractures was estimated at EUR 37 billion, distributed between incident fractures (66% of this cost), long-term fracture care (29%) and pharmacological prevention (5%). These costs are even expected to increase by 25% in 2025 [3]. For this reason, an early OP diagnosis can represent a potent tool for the reduction of fracture occurrence and for the maintenance of a good quality of life, especially in the context of the progressive ageing of a population. To date, the gold standard technique for OP diagnosis is the bone mineral density (BMD) measurement through dual-energy X-ray absorptiometry. However, in recent years, BMD has become a less reliable predictor for bone fracture risk since fractured patients have shown a comparable value of BMD to the control ones in several studies [4; 5]. Therefore, it is possible to hypothesise that OP is responsible for a series of bone feature modifications both at the architectural and compositional level, leading to an overall reduction of bone mechanical strength. The set of architectural and compositional features that can define the healthy or pathologic status of a bone can be gathered in the more general expression of \"bone quality\". Consequently, it is possible to affirm that OP is responsible for an overall reduction of bone quality, leading to a decrease in bone strength. In recent years, numerous research studies have been dedicated to the identification of the best indicators of bone quality and, consequently, of the most accurate fracture risk predictors. In particular, significant architectural and compositional alterations have been observed between healthy and osteopororotic bones in both the trabecular and cortical compartments [6]. In order to investigate these OP-related modifications, several imaging techniques have been adopted both at the clinical and research level. Histomorphetry has been one of the first techniques used to this aim, allowing the measurement of several bone architectural parameters through the analysis of thin histological slices extracted from a small biopsy [7]. However, since the analyses are performed on 2D slices, the information concerning the 3D spatial distribution of bone trabeculae and their eventual modification across the entire bone cannot be assessed through this technique. Furthermore, histomorphometry is a time-consuming analysis due to the long sample preparation procedure, which requires a staining phase in order to highlight the bone structure [8].