Use of fractal analysis in dental images for osteoporosis detection: a systematic review and meta-analysis

Osteoporosis is a major and growing health problem worldwide. It is a skeletal systemic disease characterized by low bone mass and deterioration of the microarchitectural structure of the bone which results in the increased risk of fractures [1]. On 1994, World Health Organization (WHO) provided diagnostic criteria on the assessment of fracture risk and its application for screening the postmenopausal osteoporosis. These criteria are based on the measurement of bone mineral density (BMD) [1], which is the amount of the bone mass per unit volume (volumetric density, g/cm³), or per unit area (areal density, g/cm²). BMD is assessed by dual-energy X-ray absorptiometry (DEXA) and it is recommended for all women who come to menopause age [2]. Osteoporosis is diagnosed if the patient’s femoral neck BMD is 2.5 standard deviations (SDs) below the average of a young and healthy individual (T-score). Low BMD, or osteopenia, is defined as a BMD value of more than 1 SD but 2.5 SDs below the normal range.

At present, the assessment of BMD is the only aspect that is readily measured in clinical practice which forms the cornerstone for the general management, risk prediction, and treatment of osteoporotic patients (OP) [3, 4]. Ideally, the clinical assessment of the skeleton should also capture other features of the bone, since other abnormalities such as micro-architectural deterioration can also contribute to skeletal fragility. The only BMD cannot capture all these assessments. As a consequence, it sometimes happens that there is an overlap in BMD scores of patients who do and do not sustain osteoporotic fractures. For example, patients undergoing a long duration of treatment with bisphosphonates show an increased risk of atypical femur fractures despite a decrease in osteoporotic and hip fractures [5]. Therefore, BMD alone cannot be considered an optimal index to monitor the effects of osteoporosis or treatments and to predict the risk of fracture [6]. Thus, there is a necessity to develop new techniques for better assessment of trabecular structures and cortical bone [7‐9].

Dental radiographs are cheap and routinely taken during periodic dental examinations and checkups on a large population. Dental radiographs may provide a window into the composition and condition of the jawbone over a long period with minimal exposure or risk [10] as well as the chance for screening individuals with low BMD or risk of bone fractures. For example, the OSTEODENT project [11‐16] used an image analysis software for automatic quantification of mandibular cortical width (MCW) from dental panoramic X-rays and showed that there is a correlation between MCW and BMD. These results suggest a possible use of dental radiographs for the evaluation of the BMD if acceptable specificity and sensitivity are achieved.

A possible useful method to analyze the radiographs is fractal analysis (FA), a mathematical method describing and analyzing complex shapes and structural patterns such as the bone tissue. Specifically, the fractal dimension (FD) is a quantitative measure of image complexity. Since coining the term fractal by Mandelbrot and devising sets of mathematical approaches to calculate FD [17], FA was applied in different fields including dentistry [18]. FA has been shown to be useful to quantify trabecular changes after jaw bone regeneration [19] and implant positioning [20]; to measure the roughness of implant surfaces [21, 22]; to evaluate the healing process of endodontic lesions after root canal treatment [23, 24]; to assess staging, grading, and survival on histological samples of individuals affected by oral squamous cell carcinoma; to diagnosis caries [25]; and to characterize and diagnose the epithelial-connective tissue interface malignant and premalignant lesions [18, 26]. That being said, the main application of FA in dentistry is the evaluation of the morphological pattern of jawbones and its possible change over time [27]. Some reports have shown the promising application of FD in differentiating healthy individuals (HC) from osteoporotic patients (OP) [10, 28‐30]. The bone is a fractal tissue, and the FA may be the ideal non-invasive method of detecting and quantifying changes in the bone mineral content and architecture of jawbone in OP.

However, there is still a lack of literature on standardized methods to apply FA in radiographic images. There are some reviews in the literature about the FA of medical radiographs; however, these are focused on the application of FD in evaluating the bone microstructure using non-dental radiographs [31‐34] or focused on the broad application of FD obtained from dental images. These reviews did not reach a conclusion about the applicability of dental radiographs for osteoporosis diagnosis [18, 27, 35, 36].

Therefore, this systematic review firstly aimed at evaluating the accuracy of FD obtained from dental radiographs in distinguishing HC from OP. Secondly, the authors intended to identify the appropriate site and technique to differentiate HC from OP by means of FD measurements on dental radiographs with the final goal to suggest a standardized procedure.

To the authors’ knowledge, this is the first systematic review on the application of FD obtained from dental images for the screening and the diagnosis of osteoporosis. Also, unlike previous reviews [18, 27, 33], a comprehensive meta-analysis was conducted which also took into account the role of possible moderators such as ROIs and FD calculation methods. Controversial findings have been reported in the literature for the application of FD as a supportive marker in the diagnosis of osteoporosis. Some authors suggested that with a loss of BMD, the complexity of trabecular structure increases with the consequent increase of FD values [42, 50]. Some other authors, instead, showed a correlation between simulated model of osteoporosis and decreased FD values [57] and also decreased FD with low BMD [10, 53, 58]. The ability to screen possible OP in dental settings is of great importance since dental check-ups are performed routinely, and dental radiographs are an inseparable part of it. Dental radiographs are noninvasive, inexpensive, and widely available; therefore, if the obtained FD values were found to be reliable and with high values of sensibility and specificity, it would be considered a supportive tool in the identification of OP and in the progression of osteoporosis.

The overall analysis of the included studies in our review showed that to date FD cannot be used to identify patients affected by osteoporosis. In addition, the heterogeneity of the studies suggests the necessity for the standardization of the whole procedure for the calculation of FD from dental images. The conflicting findings among studies may be explained by differences in ROIs size, shape, and location; dissimilar images processing methods (which can lead to difficulties in controlling magnification/distortion), anatomical variations, discrepancies between two-dimensional or three-dimensional images, different methods for FD measurements [59], and non-consistent FD output for cortical and trabecular bone [30].

The numerical representation of FA is not affected by variations in X-ray exposure and small variations in beam alignment, but the image pre-processing before FD evaluation and the choice of the ROI (i.e., shape and size) can affect the final results [60, 61]. There was high variability in the size, shape, and sites of the ROIs in the included studies. To overcome these differences in our meta-analysis, a general categorization was done based on the most common sites: mandible, maxilla, and condyles. Mandible region was the most used site for the measurement of FD; indeed eleven studies reported FD values from mandible and only 2 studies chose maxilla and condyle. However, taking the mandible region as a whole, the overall effect of meta-analysis showed no evidence of a possible significant difference between HC and OP because the studies reported conflicting results. Indeed, 5 studies [41, 50, 51, 54, 56] showed that FD values were higher in OP than in HC and 6 studies [30, 45, 47, 49, 52, 55] showed the opposite. The lack of consensus among studies on FD result can be partly explained by differences of trabecular and cortical regions architecture which were not be taken into account. The lack of an adequate number of studies on maxilla and condyle cannot allow us to infer any conclusion about these regions and their reliability for the computation of FD values. Nevertheless, when adjusted on the ROIs sites, dividing maxilla into three subregions (i.e., molar, premolar, and canine), more consistent results were found among FD measurements. Indeed, for molar subregion of maxilla, 5 studies [30, 45, 49, 52, 55] showed a slightly lower value of FD in OP than in HC group whereas only 1 study [54] showed the opposite. Some previous studies found that small changes in X-ray exposure, beam alignment, and ROI position do not change FD values calculated from digital radiographic images significantly, and hence, exact positioning of ROIs may not be necessary [61]. Our results agree with these previous findings showing the same trend for different studies on the measures in the same subregions of the mandible.

When using the term FD, it is important to keep in mind that it is not something unique or absolute since the FD values depend on several factors such as processing and calculation methods [18]. On the other side, FD can overcome the limitations related to unequal magnification and geometric distortion produced by different equipment. However, to analyze the dental radiographs, first, a ROI is selected using appropriate software such as NIH’s ImageJ (Image J; US National Institutes of Health, Bethesda, MD). Then, fractals may be calculated from digitalized images after a mandatory pre-processing analysis. Steps, such as cropping of the ROI, duplication of the ROI and removal of large-scale variations in brightness with a blurred Gaussian filter, the subtraction of ROI from the original image, and the addition of 128 gray values to each pixel location, binarization, erosion, dilatation, inversion, and skeletonization, should be taken before evaluating the FD [61]. Most of the authors used the proposal of White and Rudolph [62].

After pre-processing, several methods can be used for FD calculation such as the power spectral density, triangular prism surface area, blanket method, intensity difference scaling or variogram, and the box-counting algorithm [62]. However, calculation and interpretation of FD are always challenging since all the calculation methods work based on estimation, and since each method has its theoretical basis, different FD values may be obtained for the same region [63]. Also, since there is no gold standard for the estimators, the best approach is to consider the relative discrepancies of all estimators together to form the best understanding [59]. Among all the methods, box counting seems to be the most commonly used probably due to its simplicity and availability [30, 44]. However, similar to other methods, there are some limitations to box counting including difficulty in obtaining error bounds [64], possibility of overestimation or underestimation [65], construction of empty boxes, box-size dependency of the FD computation, grid effect, process of signal binarization required for this method [63], and lengthy computation time [65]. Moreover, box counting is not appropriate for rough-textured surfaces since it has limitations in covering the image surface completely [66]. Our meta-analysis showed that the results of studies that applied box counting, which was the most common method for calculating FD, were not in line with each other, meaning that other possible factors might have played role in the final results.

Finally, panoramic was the most common imaging modality followed by periapical X-ray and CBCT. However, a comparison of the results between studies with different imaging modalities was not feasible since FD can only be reliably compared when the imaging systems have the same spatial resolution [67]. For example, a previous study on rat bones found that FD values obtained from digitized film radiographs were higher than direct digital images [68]. Also, more studies with CBCT as imaging modality is needed since three-dimensional and high-resolution images are considered more accurate than panoramic in evaluating bone quality because of the low dose of radiation, minimized distortion, and the opportunity to work with real-size images. However, only three studies in our review [28, 46, 51] used CBCT as the method of choice.

BMD results were used to separate the OP from HC group in most of the studies evaluating FD on dental radiographs, but it would be even more interesting to explore the association of FD with the risk of fractures. These studies may lead in the future to the development of a tool that calculates FD values from dental radiographs with a standardized pipeline. In this manner, the measurement could be more accessible for the practitioner to evaluate the diagnostic potential of FD measures on dental radiographs in the evaluation and/or progression of osteoporosis.

In conclusion, from the current evidence, the applicability of FD should be very carefully considered since the average methodological quality of the studies is low and none of them complied with all 4 QUADAS domains. Moreover, the wide heterogeneity of the results strongly suggested standardizing the protocol used for FD calculation.