## 1 Introduction
Micro-CT is considered the gold standard for the assessment of bone morphology, although the high quality of micro-CT, high cost, radiation dose and the need for a bone sample preclude its use as a diagnostic test to assess the relationship between systemic bone turnover and condylar bone microstructure in patients with facial asymmetry [24]. Microstructural evaluation of condyle trabecular bone could also be assessed with the analysis of fractal dimension (FD) [25]. FD analysis is a statistical analysis of tissues used to describe complex figures and structural models that defines the complexity of a structure by measuring with fractal mathematics the similarities present inside the structure [26; 27]. Fractal analysis can be performed with different techniques, such as encompassing multifractal analysis, mass methods, box-counting and lacunarity analysis, and each technique offers a perspective on the fractal characteristics of biological structures [26]. All these techniques applied to radiographic images can quantify complex geometric figures (fractals), therefore enabling a qualitative bone evaluation with a non-invasive method [28]. FD analysis performed with the box-counting method has successively been used to investigate the quantity of trabeculae present inside bone marrow, thereby assessing the integrity and quality of bone [29]. In the literature, studies about the FD accuracy agree that FD is a valid technique when compared to the bone mineral density screening test using periapical and panoramic X-rays [30; 31]; therefore, it has been applied to evaluate modifications of the periapical bone region after endodontic therapy [27]. The FD value increases with an increase in a structure's complexity; therefore, a higher FD value indicates that the structure is more complex. Bone measurable characteristics are the trabecular distribution, bone thickness and bone density [26; 27]. The structure and distribution of bone trabeculae is determined by the porosity, bone thickness and anisotropy. Trapecular bone structure analysis to evaluate bone health has found important applications in medical areas [26]. FD can distinguish different densities in bone areas with a linear correlation between bone density and FD on histological samples [25]. FD in orthodontics was applied to evaluate bone structure. [PERSON] et al. [32] analyzed CBCT scans of patients with maxillary impacted amines and found an increase in maxillary bone around the unilateral impacted amines compared to the non-impacted side; however, the FD differences were not statistically significant. [PERSON] et al. [33] also used FD to study the trabecular structure of the mandible as an indicator of possible orthodontic relapse in patients undergoing orthodontic treatment, and a statistically nonsignificant difference in the FD of the bone structure emerged between the relapse and stability groups. Furthermore, [PERSON] et al. [34] found a statistically significant difference in FD when the authors analyzed 51 CBCT scans to investigate the correlation between FD and the maturation stages of the midpalatal suture; their results revealed a 100% sensitivity, 93.7% specificity, 9.5% false positive rate and 0% false negative rate of FD analysis for predicting midpalatal suture maturation, concluding that it represents a valid tool to stage the maturation of the midpalatal suture. FD to evaluate condylar bone structure was applied to panoramic X-rays and to Cone Beam Computed Tomography (CBCT) scans, and different dimensions and different methods have been used to analyze the images; however, the most used methods to calculate FD are represented by the Image [6] software and the box-counting method [26]. The evaluation of FD in asymmetrical patients with condylar hyperplasia has not yet been studied, and it might be useful to assess whether the FD value of the hyperplastic condyle differs from that of the contralateral one in patients with active condylar hyperplasia, to define a non-invasive screening method.