This study aimed to evaluate the microstructural changes in the peri-implant bone in patients with short implants in terms of the implant survival status by using fractal analysis measurements.
In this study, a significant difference was found in the FD1 and FD2 values between the implant survival groups, and the mean FD1 and FD2 values of the success group were significantly higher than those of the failure group. This result indicates that the assessment of fractal analysis at 3 months after implant insertion may be useful to determine the probability of cases of implant failure. According to our results, the fractal analysis values of the peri-implant bones of cases of implant failure were significantly lower at 0–1 month (FD1) and 1–2 months (FD2) after implantation. This may have contributed to the reduction of trabecular bone density in the bone around the implantation site.
In our study, the ratio of crown-implant length showed no statistically significant difference compared to the success rate of implantation for post-loading implants; however, the small sample size may have contributed to this result. In addition, the values of mean crown-implant ratio were higher in the failure group than in the success group; this finding could be interpreted as an indicator of clinical significance. There was no clinically significant correlation between the crown-implant ratio and FD3 and FD4 values measured after implant loading.
Some studies have stated that measurements of fractal analysis are affected by image noise and exposure parameters, and therefore, these analyses should be applied to standardized radiographs [16, 24]. In contrast, other reports indicate that image acquisition and exposure parameters do not significantly affect measurements of fractal analysis [14, 15, 19, 20].
Ibrahim et al.  performed fractal analysis measurements with CBCT and demonstrated high accuracy of measurements as compared to dental radiographs for the diagnosis and follow-up of implant. However, the effective exposure dose during dental tomography is considerably higher than that during dental radiography. Therefore, CBCT is not indicated for the assessment of implant follow-up for all cases of implantation .
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.  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.  found that the fractal analysis determined the differences between the bones affected and not affected by periodontal diseases.
Coşgunarslan et al.  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 . Moreover, the quality of trabecular bone architecture can be determined with fractal analysis on direct digital dental radiographs.
Zeytinoğlu et al.  reported significantly reduced mean FD values of the peri-implant trabecular bone at 6 months after prosthetic loading. Contrastingly, Mu et al.  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 .