Fractal analysis of bone microstructure on dental radiographs may be useful for diagnostic applications; however, the histological microstructures of the bone cannot be visualized by any clinical imaging modality. Corpas et al. [12] stated that minor changes in bone occurring over a short-term period can be followed up with digital intraoral radiography; however, the results of radiographic fractal analysis did not match that of histological fractal analysis.

The box counting method quantitatively describes the severity of bone disease and can be used to improve the current diagnostic techniques. Updike et al. [10] found that the fractal analysis determined the differences between the bones affected and not affected by periodontal diseases.

Coşgunarslan et al. [11] evaluated 240 DPRs of lactating (3–6 months duration) and nulliparous women by the fractal box counting method and found a significant difference between the FD values of the cancellous bone but no significant difference between the FD values of the cortical bones. This observation may have resulted from the fact that fractals affect cortical bone much later than the cancellous bone. Further study is needed to assess fractal analysis of the cortical bones.

Fractal dimension values on dental radiographs have been reported to differ between dentate and edentulous patients [19]. Moreover, the quality of trabecular bone architecture can be determined with fractal analysis on direct digital dental radiographs.

Zeytinoğlu et al. [15] reported significantly reduced mean FD values of the peri-implant trabecular bone at 6 months after prosthetic loading. Contrastingly, Mu et al. [14] found significant increase in the mean fractal dimension at 12 months after prosthetic loading. According to our results, the mean fractal dimension values decreased at 6–12 months after implant loading, but no significant difference was found.

There are some limitations of this study. One of them is the limited sample number of the failed implants. To assess the required sample size, power analyses were conducted. Unfortunately, we have limited number of follow-up radiographs of patients with failed implants. This study may be useful as a pilot study for further studies with much more sample size. Second, although periapical radiography is a high-resolution intraoral imaging method for FD analysis, panoramic radiographs were used because this study was retrospective. Finally, in this study, the ROI selection was not a specific frame size. The effect of ROI position and size on FD measurements is unclear. It has been proved that determining the exact ROI location and size may not make a significant difference, but there is no consensus on this idea [26].