Fractals in dentistry

Efficacy of the CALM® Algorithm in Reducing Motion-Induced Artifacts in CBCT Imaging: A Fractal Dimension Analysis of Trabecular Bone

OBJECTIVE

The primary goal of this investigation was to ascertain the efficacy of the CALM® motion artifact reduction algorithm in diminishing motion-induced blurriness in Cone Beam Computed Tomography [CBCT] images. The assessment was conducted through Fractal Dimension [FD] analysis of the trabecular bone.

METHODS AND MATERIALS

A desiccated human mandible was subjected to Planmeca ProMax 3D® scanning under eight distinct protocols, marked by variations in motion presence [at 5, 10, and 15 degrees] and the deployment of CALM®. In every scan, five distinct regions of interest [ROIs] were designated for FD analysis, meticulously avoiding tooth roots or cortical bone. The FD was computed employing the box-counting method with Image-J 1.53 software.

RESULTS

Our findings reveal that a 5-degree motion does not significantly disrupt FD analysis, while a 10-degree motion and beyond exhibit statistical differences and volatility among the sites and groups. A decreased FD value, signifying a less intricate or "rough" bone structure, correlated with amplified motion blurriness. The utilization of CALM® software seemed to counteract this effect in some instances, reconciling FD values to those akin to the control groups. Nonetheless, CALM®'s efficacy differed across sites and motion degrees. Interestingly, at one site, CALM® application in the absence of motion resulted in FD values considerably higher than all other groups.

CONCLUSION

The study indicates that motion, particularly at 10 degrees or more, can considerably impact the FD analysis of trabecular bone in CBCT images. In some situations, the CALM® motion artifact reduction algorithm can alleviate this impact, though its effectiveness fluctuates depending on the site and degree of motion. This underscores the necessity of factoring in motion and the employment of artifact reduction algorithms during the interpretation of FD analysis outcomes in CBCT imaging. More research is necessary to refine the application of such algorithms and to comprehend their influence on different sites under varying motion degrees.

Evaluation´ of mandibular alveolar bone in patients with different vertical facial patterns : A cross-sectional CBCT study

PURPOSE

The study aimed to investigate the morphological and structural differences of mandibular alveolar bone between different vertical facial patterns (VFP).

METHODS

In all, 66 CBCT scans of patients were selected for the study: 24 were designated as hyperdivergent, 25 as normodivergent, and 17 as hypodivergent. Fractal values of the interdental alveolus were measured at the incisor, canine, premolar, and molar regions. The minimum trabecular bone width (MTBW) of the alveolus, the buccal and lingual cortical bone thicknesses, and the total alveolar width (AW) at the minimum trabecular bone level were measured. One-way analysis of variance and Tukey test were used to compare the groups. The correlations between FMA (Frankfurt mandibular plane angle) and other measurements were analyzed by Pearson analysis.

RESULTS

No significant differences were detected in fractal values and buccal and lingual cortical bone thicknesses between the groups. The MTBW and AW of the hypodivergent individuals were found to be higher in the anterior and premolar interdental sites. FMA was found to be significantly correlated with MTBW and AW.

CONCLUSIONS

The patients with different VFPs did not exhibit significant differences in the trabecular complexity of the mandibular alveolus. Hypodivergent patients tend to have thicker trabecular and alveolar bone widths than normodivergent and hyperdivergent individuals.

Determination of growth and developmental stages in hand-wrist radiographs : Can fractal analysis in combination with artificial intelligence be used?

PURPOSE

The goal of this work was to assess the classification of maturation stage using artificial intelligence (AI) classifiers.

METHODS

Hand-wrist radiographs (HWRs) from 1067 individuals aged between 7 and 18 years were included. Fifteen regions of interest were selected for fractal dimension (FD) analysis. Five predictive models with different inputs were created (model 1: only FD; model 2: FD and Chapman sesamoid stage; model 3: FD, age, and sex; model 4: FD, Chapman sesamoid stage, age, and sex; model 5: Chapman sesamoid stage, age, and sex). The target diagnoses were accelerating growth velocity, very high growth velocity, and decreasing growth velocity. Four AI algorithms were applied: multilayer perceptron (MLP), support vector machine (SVM), gradient boosting machine (GBM) and C 5.0 decision tree classifier.

RESULTS

All AI algorithms except for C 5.0 yielded similar overall predictive accuracies for the five models. In order from lowest to highest, the predictive accuracies of the models were as follows: model 1 < model 3 < model 2 < model 5 < model 4. The highest overall F1 score, which was used instead of accuracy especially for models with unbalanced data, was obtained for models 1, 2, and 3 based on SVM, for model 4 based on MLP, and for model 5 based on C 5.0. Adding Chapman sesamoid stage, chronologic age, and sex as additional inputs to the FD values significantly increased the F1 score.

CONCLUSION

Applying FD analysis to HWRs is not sufficient to predict maturation stage in growing patients but can be considered a growth rate prediction method if combined with the Chapman sesamoid stage, age, and sex.

Assessment of mandibular trabecular structure and cervical vertebral maturation using fractal analysis

BACKGROUND

Changes in bone trabeculae occur during skeletal maturation. Fractal analysis is a technique for assessing changes in the internal structure of the bone.

OBJECTIVE

The aim of this study was to investigate correlation of bone trabeculation measured on panoramic and lateral cephalometric radiographs with cervical vertebral maturation stages (CVMS).

METHODS

CVMS was evaluated on lateral cephalometric radiographs of 120 individuals aged 6 to 18 years. The subjects were divided into 6 groups (n= 20 each) according to CVMS. On panoramic and lateral cephalometric radiographs, fractal dimension (FD) analyses were performed in mandibular corpus, gonial and condylar regions and cervical vertebral bodies (C2, C3, C4).

RESULTS

FD measurements from the mandibular corpus region bilaterally and C2-C4 vertebral bodies showed significant positive correlations with CVMS (r= 0.418, r= 0.412, r= 0.324, r= 0.304, r= 0.263, respectively). Significant differences were found in the FD values of the right/left mandibular corpus and C2 and C3 vertebrae compared to CVMS (P< 0.001, P< 0.001, P= 0.005, P= 0.019, respectively).

CONCLUSION

Significant positive moderate correlations between the FD values of the right and left mandibular corpus and CVMS suggest that fractal analysis may be useful in determining skeletal maturity stage. The significant FD values obtained from the right/left mandibular corpus, and C2 and C3 vertebra indicate that the complexity of the internal trabecular structure increases with maturation.

Evaluation of cortical and trabecular bone structure of the mandible in patients using L-Thyroxine

BACKGROUND

Long-term use of L-Thyroxine (LT4), the synthetic thyroxine hormone used for thyroid hormone replacement therapy, is an important risk factor for osteoporosis. The aim of this study was to investigate the differences between mandibular cortical index (MCI) and trabecular bone fractal dimension (FD) values on panoramic radiographs of patients using LT4 and control subjects.

METHODS

A total of 142 female patients, 71 cases and 71 controls, were analyzed in the study. Ages were matched in case and control groups and the mean age was 36.6 ± 8.2 (18 to 50) years. MCI consisting of C1 (Normal Mandibular Cortex), C2 (Moderately Resorbed Mandibular Cortex) and, C3 (Severely Resorbed Cortex) scores was determined for case and control groups. Fractal analysis was performed using ImageJ on selected regions of interest from the gonial and interdental regions. The box-count method was used to calculate FD values. Wilcoxon signed-rank test, Mann-Whitney U test, and Spearman correlation analysis were applied to compare the measurements. Statistical significance of differences was established at P < 0.05 level.

RESULTS

FD values did not show statistically significant differences between case and control groups (p > 0.05). The mean FD in the right gonial region was 1.38 ± 0.07 in the case group and 1.38 ± 0.08 in the control group (p = 0.715). The mean FD in the right interdental region was 1.37 ± 0.06 in the cases and 1.36 ± 0.06 in the control group (p = 0.373). The mean FD in the left gonial region was 1.39 ± 0.07 in the cases and 1.39 ± 0.07 in the control group (p = 0.865). The mean FD in the left interdental region is 1.37 ± 0.06 in the cases and 1.38 ± 0.05 in the control group (p = 0.369). The most common MCI score was C1, with 62% in the cases and 83.1% in the control group. MCI scores showed a statistically significant difference between cases and controls (p = 0.016, p < 0.05). While the C2 score was higher in the cases, the C1 score was higher in the controls.

CONCLUSIONS

LT4 use was not associated with the FD of mandibular trabecular bone, but was associated with MCI values of cortical bone. Further studies on larger samples with different imaging modalities and image processing methods are needed.

Evaluation of cortical and trabecular bone structure of the mandible in patients with ankylosing spondylitis

This study aimed to examine the difference between the fractal dimension (FD) values of the mandibular trabecular bone and the panoramic mandibular index (PMI), mandibular cortical index (MCI) and mandibular cortical thickness (MCW) of patients with ankylosing spondylitis (AS) and healthy control group. A total of 184 individuals (92 cases, 92 controls), were examined in our study. PMI, MCI, and MCW values were calculated on panoramic images of all individuals. For FD values, the region of interest (ROI) was selected with the size of 100 × 100 pixels from the right-left gonial and interdental regions and 50 × 50 pixels from the condylar region. Degenerative changes in the temporomandibular joint (TMJ) region were recorded. PMI, MCI, and MCW values showed statistically significant differences between the groups (p = 0.000, p < 0.001). The radiological signs of mandibular cortical resorption were more severe in the case group than in the control group. PMI and MCW values were found to be lower in the case group than in the control group. It was determined that the number of C3 and C2 values, among the MCI values, was higher in the case group. Only the FD values of the ROI selected from the condyle region were found to be statistically significant and were lower in the case group (p = 0.026, p < 0.05). Degenerative changes in the TMJ region were significantly more frequent in the case groups (p = 0.000, p < 0.001). The fact that the mandibular cortex shows more resorptive features in individuals with AS may require further evaluation in terms of osteoporosis. Because of the low FD values of the condylar regions of these patients and the more frequent degenerative changes, the TMJ region should be followed carefully. Detailed examination of the mandibular cortex and condylar region is beneficial in patients with AS for screening and following osteoporotic changes in these individuals, which is essential for the patient's life quality.

Assessment of correlation between hand-wrist maturation and cervical vertebral maturation: a fractal analysis study

BACKGROUND

To investigate whether fractal dimension (FD) measurements from hand-wrist radiographs and lateral cephalometric radiographs are correlated with each other and with skeletal maturation stages.

METHODS

In this retrospective study conducted on hand-wrist and lateral cephalometric radiographs obtained from patients between 2017 and 2023, hand-wrist maturation stages (HWMS) and cervical vertebral maturation stages (CVMS) of 144 subjects (6 to 17 years of age) were assessed radiographically. The participants were divided into nine groups (n = 16 each) based on HWMS. Fractal analysis was performed on the radiographs of the radius, the middle finger phalanges (proximal, medial and distal), and the cervical vertebral bodies (C2, C3, C4). Mean and standard deviation values, Spearman's and Pearson correlation analyses, one-way ANOVA, Kruskal-Wallis H tests and Mann-Whitney-U test were used to evaluate the data.

RESULTS

Positive correlations were found between the FD values of the radius and HWMS or CVMS (r = .559, P = .001, r = .528 P = .001 respectively). The FD values of the radius were positively correlated with those of all cervical vertebrae (C2, C3, C4), proximal and medial phalanges as well as age. FD values measured from the proximal phalanx, medial phalanx and radius showed significant differences among both HWMS and CVMS (P < .05). HWMS was strongly correlated with CVMS (r = .929, P = .001). Age was strongly correlated with HWMS (r = .795, P = .001) and CVMS (r = .756, P = .001). There was a significant difference in terms of age distribution among HWMS and CVMS (P < .05).

CONCLUSIONS

FD measurements on hand-wrist radiographs can provide useful information for the assessment of skeletal maturation stage. Especially, FD measurements from the radius are important and more reliable to predict skeletal maturation stage.

Effects of functional orthopedic treatment on mandibular trabecular bone in class II patients using fractal analysis

PURPOSE

The aim of this retrospective study was to evaluate the effects of functional orthopedic treatment on mandibular bone structure using fractal dimension (FD) analysis of panoramic radiographs.

METHODS

The study material consisted of the pre- and posttreatment digital panoramic radiographs of 80 patients (mean age 10.1 ± 2.01 years; 45 girls, 35 boys) with class II malocclusion who were treated with the monoblock or twin block appliances. The following regions of interest (ROI) were selected: ROI1, condylar process; ROI2, angulus mandibulae; ROI3, corpus mandibulae; and ROI4, mental foramen. Pre- and posttreatment FD values were compared for each ROI.

RESULTS

FD values of the mandibular condyle did not change with the functional orthodontic treatment. FD values of the mandibular corpus region had the highest pretreatment values and significantly decreased with treatment (p < 0.05).

CONCLUSION

Functional orthopedic treatment altered the trabeculation of the mandibular bone, but it is speculated that the changes in the occlusal forces seemed to be of primary significance for this effect.

The mandibular bone structure in children by fractal dimension and its correlation with pixel intensity values: a pilot study

OBJECTIVES

To identify a normal pattern of mandibular trabecular bone in children based on the fractal dimension (FD), and its possible correlation with pixel intensity (PI) values, to facilitate the early diagnosis of possible diseases and/or future bone alterations.

MATERIALS AND METHODS

The 50 panoramic images were selected and divided into two groups, according to the children's age: 8-9 (Group 1; n = 25) and 6-7 (Group 2; n = 25). For FD and PI analyses, three regions of interest (ROIs) were selected, and their mean values were evaluated for each ROI, according to each group, using the t test for independent samples and the model of generalized estimation equations (GEE). Subsequently, these mean values were correlated by the Pearson test.

RESULTS

Comparing the groups, FD and PI did not differ from each other for any of the measured regions (p > 0.00). It was observed that in the mandible branch (ROI1), FD and PI means were 1.26 ± 0.01 and 81.0 ± 2.50, respectively. In the mandible angle (ROI2), the means were 1.21 ± 0.02 (FD) and 72.8 ± 2.13 (PI); and in the mandible, cortical (ROI3) values of FD = 1.03 ± 0.01 and PI = 91.3 ± 1.75 were obtained. There was no correlation between FD and PI in any of the analyzed ROI (r < 0.285). The FD means of ROI1 and ROI2 did not differ from each other (p = 0.053), but both were different from ROI3 (p < 0.00). All PI values differed from each other (p < 0.00).

CONCLUSION

The bone trabeculate pattern in 6-9-year-old children presented FD between 1.01 and 1.29. Besides that, there was no significant correlation between FD and PI.

Estimation of Cancellous Changes Using Fractal Analysis in Patients with Periodontitis

Periodontal disease is a broad term given when the periodontium is affected by inflammation. There are several methods to diagnose periodontitis, but no method to quantify the cancellous bone is presently used. For this purpose, a non-invasive tool that is efficient in analyzing bone quality called fractal analysis can be employed. The objective of the study was to utilize fractal dimension (FD) to evaluate cancellous patterns of interproximal alveolar bone using a digital intraoral periapical radiograph (IOPAR) in different clinical presentations of periodontitis classified according to the latest classification by the World Workshop for Periodontal and Peri-Implant Diseases and Conditions, 2017 (WWDC, 2017). The study aimed to numerically calculate the periodontitis changes in the cancellous bone around the affected tooth on an IOPAR using fractal analysis and to provide an additional criterion for the staging of periodontitis. In this cross-sectional observational study, 75 patients were selected and equally allotted to five groups based on the staging system proposed by the WWDC, 2017. The region of interest was selected on the IOPA radiograph of the tooth with the site having the most significant clinical attachment loss, and FD was calculated using Image J analysis. The association of gender and age with stages of periodontitis was studied using the chi-square test of independence. A comparison of % bone loss and fractal dimension among stages was studied by using the non-parametric Kruskal Wallis test. The relationship between % bone loss and fractal dimension within stages and gender was studied by using the Karl Pearson correlation. A receiver operating characteristic (ROC) curve analysis was performed for FD value as a marker of periodontitis patients. We demonstrated that the FD values decreased significantly with the increase in stages (p < 0.0001). The overall relationship between % bone loss and FD showed a significantly strong negative correlation of -0.739 (p < 0.0001), except for stages III and IV. FD can be utilized as a quantitative method for detecting cancellous bone changes in different stages of periodontitis, aiding in diagnosing periodontitis.

Evaluation of bony changes observed in mandibular osteotomy lines and mandibular condyles following bilateral sagittal ramus osteotomy by fractal analysis

OBJECTIVES

This study aimed to evaluate the surgically impacted trabecular changes in mandibular osteotomy lines and mandibular condyles after bilateral sagittal split ramus osteotomy using the fractal analysis method.

MATERIALS AND METHOD

The study population consisted of 30 patients (9 male, 21 female) diagnosed with mandibular prognathism and operated with bilateral sagittal split ramus osteotomy under general anesthesia. Fractal analyses observed the alterations on the trabecular structure of osteotomy lines, and mandibular condyles on panoramic radiographs obtained preoperatively, postoperatively, 1st week, 6th month, and 12th month. The box-counting method was used to evaluate the changes in trabecular structure by fractal analysis. P-values of less than 0.05 were considered significant.

RESULTS

The fractal dimension values in both osteotomy lines and mandibular condyles were significantly decreased on postoperative 1st week regarding preoperative values. However, fractal dimension values commenced increasing in the following postoperative period. The fractal dimension values of the horizontal and vertical osteotomy lines reached their preoperative values on postoperative 6th and 12th month, respectively. The decreased fractal dimension values observed in the early postoperative period in the right and left condyles reached their preoperative values at the 6th postoperative month.

CONCLUSION

Fractal analyses performed postoperatively can provide information about trabecular changes and bone healing of structures such as osteotomy lines directly affected by bilateral sagittal split ramus osteotomy and indirectly affected mandibular condyles. The results support that fractal analysis can be used together with clinical data in the evaluation of bone healing process.

Applicability of Fractal Analysis for Quantitative Evaluation of Midpalatal Suture Maturation

BACKGROUND

The treatment of transversal maxillary deficiency usually aims at skeletal expansion. The treatment option highly depends on the maturation stage of the midpalatal suture (MPS), which may vary between individuals at the same chronological age. Therefore, the individual determination of the MPS maturation is crucial.

AIMS

Our aim was to investigate the applicability of fractal analysis for the quantitative evaluation of MPS maturation.

METHODS

Nine experienced orthodontists were asked to evaluate the MPS maturation on 51 cone beam computed tomography (CBCT) scans according to the Angelieri classification method. Intra- and inter-examiner reliability was measured using Cohen's Kappa coefficient. The stages were agreed upon according to the results of the examiners with the highest strength of agreement. Fractal analysis was then performed on the CBCTs and the correlation between the fractal dimension values and maturation stages was then evaluated. Optimal fractal dimension cut-off values were determined using a receiver operating characteristic curve.

RESULTS

The cut-off point was found at 1.073, at which the use of fractal dimension for predicting MPS maturation showed 100% sensitivity, 93.7% specificity, 9.5% false positive, 0% false negative rate.

CONCLUSION

Our results provided further evidence that fractal analysis is a reliable tool to determine MPS maturation stage.

Evaluation of trabecular changes following advancement genioplasty combined with or without bilateral sagittal split osteotomy by fractal analysis: a retrospective cohort study

BACKGROUND

It is aimed to investigate whether there was a difference in radiographic changes in the operational areas between genioplasty alone and genioplasty combined with mandibular advancement and to evaluate the fractal dimension (FD) to assess trabecular changes after genioplasty surgery.

METHODS

Preoperative-(T0) and postoperative-(T1) panoramic radiographs of 26 patients without any complications who underwent genioplasty combined with bilateral sagittal osteotomy and mandibular advancement or genioplasty alone were selected. In the panoramic radiographs of both groups, the genial segment, mandibular angulus, and surgical osteotomy line were examined using FD. The box-counting method was used for FD evaluation.

RESULTS

It was determined that FD values before and after treatment were similar in both groups for all regions where measurements were made. After surgery, the FD values of the middle region of the genial segment were found to be significantly lower than the other regions. At T1, the FD values at the osteotomy area were found to be significantly higher than those in the middle region of the genial segment.

CONCLUSION

Trabecular structure does not differ in patients undergoing genioplasty alone or in combination with mandibular advancement osteotomy. The middle region of the genial segment heals later than other regions.

Comparison of trabecular bone structure in individuals with healthy periodontium and stage III/IV, grade C periodontitis by fractal analysis

OBJECTIVE

The aim was to perform fractal analysis (FA) to compare differences in trabecular microarchitecture in interdental and antegonial regions on panoramic radiographs in periodontally healthy patients and those with stage III/IV, grade C periodontitis, and to compare the effects of patient age and sex on FA results.

STUDY DESIGN

Clinical and radiographic records from 33 periodontally healthy individuals and 28 individuals with aggressive periodontitis were obtained from the faculty archives. Three regions of interest (ROIs) were chosen bilaterally from interdental bone around the mandibular first molar and canine and the antegonial region. The mean fractal dimension (FD) values of the ROIs were calculated. Significance of differences was established at P < .05.

RESULTS

FD values of all 3 ROIs in the periodontitis group were significantly lower than values in the control group (P ≤ .004). FD was not affected by patient age (P = .357) or sex (P = .216). There were no significant correlations between FD and age in either group (P ≥ .093). FD values differed significantly between sexes in only one ROI.

CONCLUSIONS

FA can effectively detect trabecular microarchitectural differences in patients with aggressive periodontitis compared to periodontally healthy individuals. This technique might be useful in predicting the susceptibility of patients to periodontal disease.

Evaluation of trabecular bone and mandibular cortical thickness in adults with different vertical facial types

OBJECTIVES

This study investigated differences in trabecular structure and mandibular cortical thickness in adults related to vertical facial type (VFT), sex, and their interactions.

STUDY DESIGN

Lateral cephalometric radiographs (LCRs) and panoramic radiographs (PRs) of 256 patients were reviewed. The VFT classification into low-angle, normal, and high-angle groups was determined using angular and linear measurements on LCRs. Fractal dimension (FD) values and mandibular radiomorphometric indices (RMIs) were calculated on PRs.

RESULTS

Two-way analysis of variance revealed significant differences in FD overall among VFT groups in all sites (P < .001), with pairwise comparisons indicating the greatest values in the high-angle group in the condyle (P < .05) but in the low-angle group elsewhere (P < .001). RMIs were significantly different overall regarding VFT only in the posterior mandible (P = .004), with pairwise comparisons revealing low-angle and normal group values greater than high-angle group values (P < .05). Patient sex and the interaction of facial type and sex had no significant effect on any bone measurements.

CONCLUSIONS

VFT had significant effects on trabecular structure at all measured sites, but cortical thickness was affected only in 1 location.

Evaluation of temporomandibular joint components and mandibular bone structure in ankylosing spondylitis patients

OBJECTIVES

The study aimed to investigate the mandible and temporomandibular joint (TMJ) in patients with ankylosing spondylitis (AS) who had no signs or symptoms of TMJ-related disease and compare them with a control group.

STUDY DESIGN

In total, 128 panoramic radiographs (63 patients with AS, 65 controls) were evaluated. Fractal analysis was conducted on the mandibular condyle (ROI1), angle of the mandible (ROI2), and the area adjacent to the mental foramen (ROI3). Articular eminence inclination (AEI) values were measured. Klemetti index (KI) evaluation of the mandibular cortex was also performed.

RESULTS

Fractal dimension (FD) values were significantly lower in the patients with AS than the controls in ROI1 and ROI2 (P = .001), but there were no significant differences between groups for FD in ROI3, AEI, or KI (P ≥ .09). No significant differences were found in any parameters between patients with AS with different disease durations (P ≥ .06).

CONCLUSIONS

Patients with AS displayed significantly lower FD values in condyles and the angle of the mandible and slightly lower AEI values; therefore, they should be examined routinely for TMJ disorders. Clinicians should be aware of the possibility of secondary osteoporosis in patients with AS and consider its probable effects on the mandible.

Novel method to delineate palatal rugae and assess their complexity using fractal analysis

Palatal rugae constitute significant morphological landmarks, with wide clinical applications in forensics, insertion of mini-screws, and superimposition. Their morphology has been studied mainly with indices relevant to their qualitative characteristics. The present paper aims at presenting a new quantitative method to evaluate their complexity, by means of box-counting fractal dimension analysis, and to investigate its inter- and intra-rater reliability. Twenty maxillary plaster models were scanned for the needs of this study. A sequence of steps, including cropping of the mesh, ball pivoting, distance mapping and fractal dimension analysis, performed with Viewbox 4 software, was followed. Box-counting fractal dimensions were calculated as a measure of rugae's complexity. Inter- and intra-rater reliability were investigated, using Bland-Altman analysis. Fractal dimensions ranged from 1.274 to 1.491 (average: 1.412). Bland-Altman analysis of inter- and intra-examiner reliability demonstrated that the 95% limits of agreement ranged from - 0.012 to 0.011 and from - 0.004 to 0.004, respectively. The method is reliable and can be applied in research and forensics. It offers comprehensive evaluation of the rugae's complexity and a complete set of information about their outlines and height profiles, with minimum user intervention.

Evaluating the effects of orthodontic treatment with clear aligners and conventional brackets on mandibular condyle bone quality using fractal dimension analysis of panoramic radiographs

OBJECTIVE

Orthodontic treatment carried out with clear aligners has become a method that is preferred by patients. In this study, the effect following orthodontic treatment with clear aligners and with conventional brackets, on the mandibular condyle trabecular bone formation is aimed to be examined.

MATERIALS AND METHODS

Thirty two individuals (16 females and 16 males) with a mean age of 16.80 ± 3,10 years who received orthodontic treatment with clear aligners and conventional brackets were included in the study. Individuals included in the study from the archive data were divided into two groups according to treatment types. The mandibular condyle bone quality in the panoramic images taken from the patients before orthodontic treatment (T0) and after orthodontic treatment (T1) has been compared retrospectively. This examination is carried out via the fractal analysis method.

RESULT

The mandibular condyle bone density in individuals that have undergone orthodontic treatment with clear aligners, has been reduced following orthodontic treatment. In individuals that have undergone orthodontic treatment with conventional brackets however the mandibular condyle bone density has increased following treatment (T0) in comparison to before being treated (T1). The mandibular condyle bone density change according to different treatment groups has been found to be statistically different.

CONCLUSION

Orthodontic treatment with clear aligners provides several advantages to patients. However, besides determining the effectiveness of the treatment, complications must also be examined. Application of clear aligners in orthodontic treatment may cause a decrease in bone density in the mandibular condyle. When evaluating orthodontic treatments carried out with clear aligners, the change of the mandibular condyle head bone should be taken into consideration.

Fractal dimension analysis on CBCT scans for detecting low bone mineral density in postmenopausal women

Purpose

The aim of this study was to compare the fractal dimension (FD) measured at 2 bone sites (second cervical vertebra and mandible) on cone-beam computed tomography (CBCT). The research question was whether FD could serve as an accessory tool to refer postmenopausal women for densitometric analysis. Therefore, the reliability and accuracy of FD were evaluated.

Materials and Methods

In total, 103 postmenopausal women were evaluated, of whom 52 had normal bone mineral density and 51 had osteoporosis, according to dual X-ray absorptiometry of the lumbar spine and hip. On the CBCT scans, 2 regions of interest were selected for FD analysis: 1 at the second cervical vertebra and 1 located at the mandible. The correlations between both measurements, intra- and inter-observer agreement, and the accuracy of the measurements were calculated. A P value less than 0.05 was considered to indicate statistical significance for all tests.

Results

The mean FD values were significantly lower at the mandibular region of interest in osteoporotic patients than in individuals with normal bone mineral density. The areas under the curve were 0.644 (P=0.008) and 0.531 (P=0.720) for the mandibular and vertebral sites, respectively.

Conclusion

FD at the vertebral site could not be used as an adjuvant tool to refer women for osteoporosis investigation. Although FD differed between women with normal BMD and osteoporosis at the mandibular site, it demonstrated low accuracy and reliability.

Structural complexity of the craniofacial trabecular bone in multiple myeloma assessed by fractal analysis

Purpose

This study aimed to evaluate the structural complexity of craniofacial trabecular bone in multiple myeloma by fractal analysis of panoramic and lateral skull radiography, and to compare the fractal dimension values of healthy patients (HPs), pre-treatment patients (PTPs), and patients during bisphosphonate treatment (DTPs).

Materials and Methods

Pairs of digital panoramic and lateral skull radiographs of 84 PTPs and 72 DTPs were selected. After application of exclusion criteria, 43 panoramic and 84 lateral skull radiographs of PTPs, 56 panoramic and 72 lateral skull radiographs of DTPs, and 99 panoramic radiographs of age- and sex-matched HPs were selected. The fractal dimension values from panoramic radiographs were compared among HPs, PTPs, and DTPs and between anatomical locations within patient groups using analysis of variance with the Tukey test. Fractal dimension values from lateral skull radiographs were compared between PTPs and DTPs using the Student t-test. Pearson correlation coefficients were used to assess the relationship between the mandible from panoramic radiographs and the skull from lateral skull radiographs. Intra-examiner agreement was assessed using intraclass correlation coefficients (α=0.05).

Results

The fractal dimension values were not significantly different among HPs, PTPs, and DTPs on panoramic radiographs or between PTPs and DTPs on lateral skull radiographs (P>0.05). The mandibular body presented the highest fractal dimension values (P≤0.05). The fractal dimension values of the mandible and skull in PTPs and DTPs were not correlated.

Conclusion

Fractal analysis was not sensitive for distinguishing craniofacial trabecular bone complexity in multiple myeloma patients using panoramic and lateral skull radiography.

Application of Texture and Fractal Dimension Analysis to Evaluate Subgingival Cement Surfaces in Terms of Biocompatibility

Biocompatibility is defined as “the ability of a biomaterial, prosthesis, or medical device to perform with an appropriate host response in a specific application”. Biocompatibility is especially important for restorative dentists as they use materials that remain in close contact with living tissues for a long time. The research material involves six types of cement used frequently in the subgingival region: Ketac Fil Plus (3M ESPE, Germany), Riva Self Cure (SDI, Australia) (Glass Ionomer Cements), Breeze (Pentron Clinical, USA) (Resin-based Cement), Adhesor Carbofine (Pentron, Czech Republic), Harvard Polycarboxylat Cement (Harvard Dental, Great Britain) (Zinc polycarboxylate types of cement) and Agatos S (Chema-Elektromet, Poland) (Zinc Phosphate Cement). Texture and fractal dimension analysis was applied. An evaluation of cytotoxicity and cell adhesion was carried out. The fractal dimension of Breeze (Pentron Clinical, USA) differed in each of the tested types of cement. Adhesor Carbofine (Pentron, Czech Republic) cytotoxicity was rated 4 on a 0–4 scale. The Ketac Fil Plus (3M ESPE, Germany) and Riva Self Cure (SDI, Australia) cements showed the most favorable conditions for the adhesion of fibroblasts, despite statistically significant differences in the fractal dimension of their surfaces.

Nonclinical research areas of future importance for clinical therapies: Exploring the concepts of nonlinearity in dentistry

Linear system analysis has been dominating medical and dental research, and most of the research achievements in these fields have come from applying a reductionist view of nature. However, biologic systems are fundamentally nonlinear with highly composite dynamics made up of numerous interacting elements and feedback loops, therefore studying them as linear models may not result in an accurate representation of their true features. The authors reviewed and utilized some of the principles of chaos and nonlinearity and extended them to clinical dentistry, from cracked tooth and flare-up after root canal procedures to the outcome of clinical treatments. Utilization of the concepts of chaos and sensitive dependence on initial conditions, and the concepts of self-organization, stigmergy, and fractals may help us to understand some of the puzzles that have not been solved by conventional linear models. The goal of this paper is to present some areas within nonclinical research that we believe will have important roles in the development of future clinical examination methods and therapies.

Evaluation of mandibular condyle trabecular structure in patients with rheumatoid arthritis using fractal analysis

OBJECTIVES

The aim of this study was to compare the fractal dimension (FD) of trabecular structure of the mandibular condyles in patients with rheumatoid arthritis (RA) to patients without RA. Correlations between condylar FD and bone mineral density T-scores in the femoral neck and lumbar spine were also examined.

STUDY DESIGN

The RA study group patients were divided into 3 categories (33 normal, 33 osteopenic, and 34 osteoporotic) according to T-scores. The control group without RA was sex- and age-matched with the study group. FD was calculated from panoramic radiographs and compared between the study and control groups. The relationships between FD values and femoral neck and L1-L4 lumbar spine T-scores were investigated for study and control groups. Significance was established at P < .05.

RESULTS

The mean FD values of the entire study group and of each category in the study group were significantly lower than those of the control group (P < .001). There were no significant differences in FD values among the 3 RA categories (P > .05). No significant correlations appeared between FD and femoral neck or lumbar spine T-scores (P ≥ .063).

CONCLUSIONS

Fractal analysis of the condyles on panoramic radiographs can distinguish RA from healthy condyles, even if the patients with RA have normal bone mineral density T-scores.

Retrospective fractal analyses of one-year follow-up data obtained after single-visit nonsurgical endodontic retreatment on periapical radiographs

OBJECTIVES

The aim of retrospective study was to evaluate the changes to the periapical bone sites after non-surgical endodontic retreatment by using fractal analysis on periapical radiographs.

MATERIALS AND METHODS

Thirty patients whose teeth had periapical lesions and underwent primary endodontic treatment were selected for nonsurgical single-visit endodontic retreatment. Two radiographs were taken, the first immediately after retreatment and the second at the 1-year follow-up. An identical region of interest close to the infected root apex was selected from each radiograph. FD was measured using the box-counting method. Periapical status was evaluated using the periapical index (PAI). Treatment outcomes were categorized into healed (PAI < 3), or not healed (PAI ≥ 3) based on radiographic criteria.

RESULTS

The mean FD value significantly increased at the 1-year follow-up compared to baseline. No significant sex biases were apparent. According to the PAI, retreatment after 1 year resulted in a 63.3% healed.

CONCLUSION

The extent of periapical trabecular bone evident radiographically increased, as revealed by FD data, 1 year after endodontic retreatment. Clinical relevance The use of fractal analysis as a quantitative method to evaluate changes in periapical trabecular bone (such as healing and inflammation) after endodontic retreatment can be an important marker in determining the prognosis of endodontic retreatment.

Measurement of the trabecular bone structure of the TMJ region in patients with transverse maxillary deficiency: a CBCT fractal analysis study

OBJECTIVE

This study aimed to evaluate the effect of transverse maxillary deficiency on condylar morphology via visual examination and fractal analysis of cone beam computed tomography (CBCT) scans.

STUDY DESIGN

In total, 97 patients with posterior crossbite or maxillary narrowness and 36 control patients were included. The presence of degenerative changes in the bilateral condyles was evaluated with CBCT. Fractal dimension (FD) was calculated on the condylar images using ImageJ.

RESULTS

Degenerative bone changes were discovered in 38 of the 133 scans (28.6%). There was no significant difference between the groups in terms of the incidence of degenerative changes for either the right or left sides (P ≥ .670). In coronal sections and in mean measurements, FD was significantly lower in the control group compared with the other groups in the right condyle (P ≤ .031). No significant differences were found between the mean FD values of the condyles with degenerative bone changes or the mean FD values of the normal condyles (P ≥ .256).

CONCLUSIONS

In the presence of maxillary transverse deficiencies, degenerative bone changes in the mandibular condyle were not significantly different, but the FD of the right condyle was found to be higher compared with the control group.

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

Fractal dimension (FD) calculated on oral radiographs has been proposed as a useful tool to screen for osteoporosis. This systematic review and meta-analysis firstly aimed at assessing the reliability of FD measures in distinguishing osteoporotic patients (OP) from healthy controls (HC), and secondly, to identify a standardized procedure of FD calculation in dental radiographs for the possible use as a surrogate measure of osteoporosis. A comprehensive search was conducted up to September 2020 using PubMed, Web of Science, and SCOPUS databases. The Preferred Reporting Items for Systematic reviews and Meta-Analyses (PRISMA) statement was followed. Meta-analysis was performed on FD values calculated for HC and OP. Overall, 293 articles were identified. After a three steps screening, 19 studies were included in the qualitative appraisal and 12 were considered for meta-analysis. The methodological quality of the retrieved studies was generally low. Most of the studies included used White and Rudolph and box counting to process the images and to calculate FD, respectively. Overall, 51% of the studies found a meaningful difference between HC and OP groups. Meta-analyses showed that to date, FD measures on dental radiographs are not able to distinguish the OP from HC group significantly. From the current evidence, the use of FD for the identification of OP is not reliable, and no clear conclusion can be drawn due to the heterogeneity of studies. The present review revealed the need for further studies and provided the fundamentals to design them in order to find a standardized procedure for FD calculation (regions for FD assessment; images processing technique; methods for FD measurement). More effort should be made to identify osteoporosis using dental images which are cheap and routinely taken during periodic dental examinations.

Trabecular and cortical mandibular bone investigation in familial adenomatous polyposis patients

Mandibular cortical and trabecular bone abnormalities in patients with familial adenomatous polyposis (FAP) were evaluated using dental panoramic radiographs (DPR) radiomorphometric indices and fractal dimension (FD). Sixty DPRs from 15 FAP patients and 45 healthy controls were evaluated. FAP group was composed of 33.3% females and 66.6% males, age_mean = 37.2 years (SD 15.79). The non-FAP group was paired by gender and sex. The parameters analyzed were: FD of the trabecular bone in four regions of interest (ROI), mandibular cortical index (MCI) and width (MCW). FD values were lower for the FAP group. Statistically significance differences were shown by ROI 2 and 3 anteriorly to the mental foramen bilaterally, p = 0.001, and p = 0.006. The ROI 1 and 4, at the mandibular angle trabeculae, indicated statistical significances on the right side (p = 0.036) and no differences on the left side (p = 0.091). There was no significant difference in MCI and MCW when the groups were compared, MCW (L) p = 0.247, and MCW (R) p = 0.070. Fractal values of FAP patients' mandibular trabecular bone were lower than healthy controls. The radiomorphometric indices MCI and MCW were not useful for analyzing the cortical bone pattern. Therefore, FD is a promising tool for detection of abnormal bone structure in DPRs and for supporting the appropriate referral of FAP patients.

Evaluation of mandibular morphologic measurements and trabecular structure among subgroups of impacted mandibular third molars

OBJECTIVE

To investigate mandibular morphologic measurements and trabecular structures that may cause mandibular third molar (MM3) impaction according to MM3 subgroups.

METHODS

A total of 150 MM3 of 2175 panoramic radiographs (PRs) were reviewed. MM3s according to Winter (vertical), Pell & Gregory Class 1 and group: A, B, C on PRs were included in the study group. Fractal dimensions (FD) and mandibular morphologic measurements were evaluated. Statistical analysis for parametric values was performed using one-way analysis of variance (ANOVA). Statistical analysis for non-parametric values was performed using the Kruskal-Wallis H test.

RESULTS

Statistically, a significant difference was found only in terms of angle of impaction among the groups of MM3 (p < 0.05) [Winter (vertical), and Pell & Gregory Class 1 and group A, B, C]. There was no difference among groups A, B, C in mandibular morphology and trabecular structure, but group C showed different characteristics than the other groups only in terms of impaction angle.

CONCLUSION

The trabecular structure and morphometric properties except for the angle of impaction do not affect impacted MM3s with adequate retromolar space and vertical angle.

Fractal analysis as a useful predictor for determining osseointegration of dental implant? A retrospective study

PURPOSE

The present study aimed at evaluating the effectiveness of fractal analysis on determining the osseointegration of dental implants.

MATERIAL AND METHODS

In a single center, retrospective clinical trial, patients with dental implants in the mandibular premolar/molar region, ASA I-II and < 65-year-old patients were included. Orthopantomograph (OPG) were taken before implant surgery (t0), within a week of surgery (t1), and 1 (t2) and 2 (t3) months after surgery, respectively. Three regions of interest (ROIs) from mesial, distal, and apical sites of the implants were chosen and fractal analysis (FA) was conducted with the box-counting algorithm using White and Rudolph's method.

RESULTS

A total of 39 patients 19 women and 20 men, with a mean age of 52.2 years (52.3 and 52.1 years, respectively) were included. The mean, minimum and maximum values of mesial (roi1), distal (roi2), and apical (roi3) surfaces were compared. The fractal dimension (FD) values of t1 were significantly lower compared with t0 as they decreased during the first week. FD values gradually increased after the first week although never exceeded the FD values of t0. Also, difference between mean FD values of t0 and t3 were found statistically significant (p < 0.05).

DISCUSSION

FA is a promising and noninvasive method to predict osseointegration of a dental implant based on dental radiographs, and it can help shorten the total treatment time.

Investigation of mandibular fractal dimension on digital panoramic radiographs in bruxist individuals

OBJECTIVE

This study aimed to evaluate changes in mandibular trabecular bone structure in bruxism using fractal analysis on digital panoramic radiographs obtained with automatic dosing.

STUDY DESIGN

In this prospective study, fractal analysis was performed on radiographs of 126 bruxists and 126 non-bruxists. Eight paired mandibular regions of interest were selected: the bilateral condylar and gonial regions, and the bilateral dentate regions between the apical areas of the first molar and second premolar and between the first premolar and canine. Fractal dimensions (FDs) were calculated at each site.

RESULTS

Mean FD values in the bilateral gonial regions of the bruxists were significantly lower than those of controls (P ≤ .049). In both groups, FD values of the right dentate region anterior to the mental foramen were significantly lower than those on the left side (P ≤ .042). Females exhibited significantly lower FD values in both condylar regions in both groups (P ≤ .039) and in the right dentate regions in the controls (P ≤ .022). Correlations between age and FD in all regions were positive but nonsignificant in both groups (P > .05).

CONCLUSIONS

FD values of mandibular trabecular bone are affected by bruxism in the gonial region and by laterality and sex differences in the condylar and dentate regions.

Quantitative ultrasound assessment of the influence of roughness and healing time on osseointegration phenomena

The evolution of bone tissue quantity and quality in contact with the surface of orthopedic and dental implants is a strong determinant of the surgical outcome but remains difficult to be assessed quantitatively. The aim of this study was to investigate the performance of a quantitative ultrasound (QUS) method to measure bone-implant interface (BII) properties. A dedicated animal model considering coin-shaped titanium implants with two levels of surface roughness (smooth, S_a = 0.49 µm and rough, S_a = 3.5 µm) allowed to work with a reproducible geometry and a planar interface. The implants were inserted in rabbit femurs and tibiae for 7 or 13 weeks. The ultrasonic response of the BII was measured ex vivo, leading to the determination of the 2-D spatial variations of bone in contact with the implant surface. Histological analysis was carried out to determine the bone-implant contact (BIC) ratio. The amplitude of the echo was significantly higher after 7 weeks of healing time compared to 13 weeks, for both smooth (p < 0.01) and rough (p < 0.05) implants. A negative correlation (R = − 0.63) was obtained between the ultrasonic response and the BIC. This QUS technique is more sensitive to changes of BII morphology compared to histological analyses.

Prediction of mechanical properties of human rib cortical bone using fractal dimension

A large number of post mortem human subjects was used to investigate the relation between the micro-structure of rib cortical bone and the mechanical properties using Fractal Dimension. Uniaxial tensile tests were performed on coupons of rib cortical bone. Tensile strength, yield stress, Young's Modulus, maximum strain, and work to fracture were determined for each coupon. Fractal dimension was computed using CT images and Digital Image Correlation procedures. A highly significant effect of fractal dimension in the mechanical properties was found. In addition, the variation in mechanical properties was found to be adequately represented by Generalized Extreme Value type distributions.

Role of fractal analysis in detection of dysplasia in potentially malignant disorders

Background:

Fractal analysis is, a noninvasive method, used to determine the intricate characteristics of the matter. Oral leukoplakia (OL), a potential malignant disorder, has definite propensity to turn in to malignancy. In such lesions, fractal dimension analysis (FDA) could be helpful in the early detection of malignant transformation.

Objectives:

To determine the efficacy of fractal dimension analysis in detecting malignancy potential of oral leukoplakia.

Materials and Methods:

After ethical clearance, we enrolled 121 patients in our study. Lesions were photographed before and after toluidine staining. Image J software was used to analyze fractal dimensions (FDs) of digital image and results were compared with biopsy.

Results:

Fractal dimension value is significantly higher in leukoplakia with dysplastic changes. FD values increase as age of patients increases. FD value in leukoplakia with different tobacco products showed more positive correlation with surti/khaini abusers.

Conclusion:

Fractal dimension analysis is a useful method in determination of complication in OL cases and can be used as an effective, noninvasive screening tool at primary healthcare centers for early intervention.

Prediction of rapid palatal expansion success via fractal analysis in hand-wrist radiographs

INTRODUCTION

This study aimed to evaluate the efficacy of fractal analysis of hand-wrist radiography in the decision of conventional or surgery-assisted rapid palatal expansion (RPE).

METHODS

The study included 48 patients who underwent the RPE procedure. Study groups were as follows: group 1 (successful conventional RPE [n = 24, 5 male and 19 female patients; mean age ± standard deviation, 15.85 ± 0.97 years]) and group 2 (failed conventional RPE [n = 24, 5 male and 19 female patients; mean age ± standard deviation, 15.96 ± 1.08 years]). Fractal dimension (FD) analysis was conducted on hand-wrist radiographs of the patients for 4 different regions: the epiphysis-diaphysis line of the radius bone and the proximal, medial (MP3), and distal (DP3) phalanxes of the middle finger. A Student t test was performed to compare fractal values between the groups. A receiver operating characteristic analysis was applied to determine the optimal cutoff value of FDs. In addition, a Pearson correlation coefficient was calculated to evaluate the relationship between the fractal values and either age or hand-wrist stage in a second sample group (n = 90; age range, 8.7-18.7 years).

RESULTS

Fractal values of the radius, MP3, and DP3 were significantly increased in the failed conventional RPE group (P <0.05). The optimal cutoff value of the FD for predicting the success of conventional RPE was 1.16 in the radius, 1.18 in proximal phalanxes, 1.29 in MP3, and 1.08 in DP3. There was a positive correlation between fractal values of the radius and age or hand-wrist stages (P <0.05).

CONCLUSIONS

Within the limits of this study, results revealed that fractal analysis of hand-wrist radiographs might be considered a significant tool in the prediction of RPE success.

Effect of total edentulism on the internal bone structure of mandibular condyle: a preliminary study

OBJECTIVE

The aim of this study was to assess the internal structure of the mandibular condyles in patients with total edentulism by applying fractal analysis on cone-beam computed tomography (CBCT) images and compare with dentate subjects.

METHODS

A total of 136 mandibular condyles were assessed. All CBCT images were prepared with 0.25-mm slice thickness and maximum magnification. A 64 × 64 pixel region of interest (ROI) within the trabecular bone in the center of the condyle was selected. Fractal analysis was performed using White and Rudolph's box-counting method.

RESULTS

Control and study groups were age and gender-matched. The mean fractal dimension (FD) value of the study group was significantly lower compared to the control group (p < 0.01). In the study group, the mean FD value of the females was significantly lower than males (p = 0.01). For the control group, there was no significant difference between the genders for FD (p = 0.11). There was no significant difference between the age subgroups of the female study group and the male control group for FD (p = 0.22, p = 0.33). The mean FD value of the younger age subgroup was significantly higher compared to the older age subgroup in the female control and male study group (p = 0.03, p = 0.01).

CONCLUSION

The internal bone structure of mandibular condyles in edentulous patients was found to be affected by edentulism. Fractal analysis can be used as an effective method for assessing temporomandibular joint health.

Evaluation of the peri-implant bone trabecular microstructure changes in short implants with fractal analysis

BACKGROUNDS

This study aimed to evaluate the microstructural changes in the peri-implant bone in patients with short implants in terms of implant survival status by using fractal analysis measurements.

RESULTS

Dental panoramic radiographs (DPRs) of 67 patients were examined and included in this study. Fractal analysis and measurement of the crown-implant ratio were performed with ImageJ. The fractal analysis measurement was performed on the DPRs obtained at preoperative (FD0) and in the follow-up periods (after 2 ± 2 weeks (FD1), 2 months ± 2 weeks (FD2), 6 months ± 2 weeks (FD3), and 12 months + (FD4)). A p value < 0.05 was considered statistically significant. Power analyses were conducted for the test results that did not reject null hypothesis. A significant difference was found in the FD1 and FD2 values between the implant survival groups (p < 0.001 and p = 0.023, respectively). The mean FD1 and FD2 values of the success group were significantly higher than those of the failure group.

CONCLUSIONS

Fractal analysis is a useful method to measure the trabecular microstructure of bone in non-standardized dental radiographs. The present study has a low power to reject the null hypothesis because of the low number of cases of implant failure. Therefore, further study with a large sample size is warranted. In clinical practice, the survival of implants may be predicted by analyzing fractal dimension of the surrounding trabecular bone of the implants.

Evaluation of Topographical Co-Cr-Mo Alloy Surface Changes After Various Finishing Treatments

PURPOSE

To quantify the influence of three different finishing treatments on the cobalt-chromium-molybdenum (Co-Cr-Mo) alloy surface based on stereometric analysis parameters.

MATERIALS AND METHODS

Eighteen specimens were casted from an extra-hard alloy (Wironit^®, BEGO, Bremen, Germany). The samples were distributed into three groups (n = 6 samples per group) dependent on different polishing techniques applied, as follows: A group, only electropolished (EP) samples; B group, after EP, an additional mechanical polishing process was applied to the surface by rubber discs and a polishing paste (RP); C group, after EP, an additional mechanical polishing process was completed by rubber discs, polishing paste and finally by a rotating deer leather wheel (RPDL). Samples were imaged by atomic force microscopy (AFM) in a contact mode, in air, at room temperature.

RESULTS

The evaluation of the microtexture of the sample surface was made based on the 3-D roughness parameters. The lowest statistical surface roughness parameters were found in the RP samples, whereas the highest values were obtained from the EP samples.

CONCLUSIONS

The experiments described can help manufacturers identify the most appropriate parameters and their ranges within which optimal surface characteristics can be achieved.

Use of fractal analysis in dental images: a systematic review

OBJECTIVES

This study reviewed the use of fractal analysis (FA) in dental images.

METHODS

A search was performed using PubMed, MEDLINE, LILACS, Web of Science and SCOPUS databases. The inclusion criteria were human studies in the English language, with no date restriction.

RESULTS

78 articles were found in which FA was applied to panoramic radiographs (34), periapical radiographs (21), bitewing radiographs (4), cephalometric radiograph (1), cone beam CT (15), micro-CT (3), sialography (2), and ultrasound (2). Low bone mineral density (21) and systemic or local diseases (22) around the bone of dental implants were the main subjects of the study of FA. Various sizes and sites of the regions of interest were used to evaluate the bone structure. Different ways were used to treat the image and to calculate FA. FA of 43 articles showed significant differences in the comparison of groups, mainly between healthy and sick patients.

CONCLUSIONS

FA in Dentistry has been widely applied to the study of images. Panoramic and periapical radiographs were those most frequently used. The Image J software and the box-counting method were extensively adopted in the studies reviewed herein. Further studies are encouraged to improve clarification of the parameters that directly influence FA.

Bone Texture Fractal Dimension Analysis of Ultrasound-Treated Bone around Implant Site: A Double-Blind Clinical Trial

Objectives

To evaluate the efficacy of bone texture fractal dimension (FD) analysis method in predicting implant stability from intraoral periapical radiographs using two implant protocols.

Materials and Methods

A double-blind clinical trial was conducted on 22 subjects who needed dental implants. The participants were randomized into two groups, the control group with standard implant protocol treatment and the intervention group with added low-intensity power ultrasound treatment (LIPUS) besides the standard implant protocol. The FD values of bone density were carried out on the mesial and distal sides of the implant on digital intraoral radiographs using the box-counting method. Both resonance frequency (RF) and fractal dimension (FD) were assessed in three time intervals: after surgery and before and after loading.

Results

FD on both the mesial and distal sides serve as very good-to-excellent tests with high validity (ROC area exceeding 0.8) in predicting high implant stability (ISQ ≥ 70). The mesial side measurements were consistently better than the distal side among the intervention groups. The optimum cutoff value for the FD-mesial side that predicts a highly stable implant (ISQ ≥ 70) is ≥1.505. At this optimum cutoff value, the mesial side FD is associated with a perfect sensitivity (100%) and fairly high specificity (86.5%).

Conclusion

The FD analysis could be recommended as an adjunctive quantitative method in prediction of the implant stability with very high sensitivity and specificity. This trial is registered with ISRCTN72648040.

Comparison of fractal dimension analysis and panoramic-based radiomorphometric indices in the assessment of mandibular bone changes in patients with type 1 and type 2 diabetes mellitus

OBJECTIVES

This study compared the fractal dimension (FD) and radiomorphometric indices in the assessment of mandibular bone of patients with type 1 (T1 DM) and type 2 diabetes mellitus (T2 DM).

STUDY DESIGN

Panoramic radiographs of 104 patients were evaluated to calculate FD, mandibular cortical width (MCW), panoramic mandibular index (PMI), and mandibular cortical index (MCI) in the mandible.

RESULTS

No statistically significant differences were found in FD when T1 DM and T2 DM groups were compared with controls (P ≥ .168). Patients with T1 DM had significantly lower MCW (P < .001) and PMI (P = .030) compared with controls. Patients with T2 DM had no significant differences in MCW (P = .228) or PMI (P = .137) compared with controls. No significant differences were observed between patients with T1 DM and those with T2 DM for FD, MCW, and PMI (P > .05). In the T1 DM and T2 DM groups, there was a significant correlation between MCW and FD (P ≤ .011). No correlation was observed between FD and PMI in either the T1 DM group or the T2 DM group (P ≥ .142). No significant differences in MCI were observed between the DM groups and controls (P = .740) or between the T1 DM and T2 DM groups (P = 1.000).

CONCLUSIONS

The cortical and trabecular bone architectures of patients with T1 DM and T2 DM were not different. Patients with T1 DM had lower cortical measurements compared with controls.

Evaluation of trabecular pattern of mandible using fractal dimension, bone area fraction, and gray scale value: comparison of cone-beam computed tomography and panoramic radiography

OBJECTIVE

This study was performed to compare the fractal dimension (FD), bone area fraction (BAF), and gray scale value (GSV) on digital panoramic radiography (DPR) and cross-sectional cone-beam computed tomography (CBCT) using image analysis and to determine whether a relationship exists among parameters associated with bone quality.

METHODS

Thirty edentulous human hemimandibles were scanned by DPR and CBCT. Ninety regions of interest (ROIs) were evaluated on DPR and CBCT images to calculate the FD and BAF. The GSV of the ROI on CBCT was also calculated.

RESULTS

Statistically significant differences were observed in the FD values of the ROIs between DPR and CBCT (p = 0.002) and in the BAF values of ROIs between DPR and CBCT (p = 0.017). The Spearman's correlation test revealed a statistically significant high correlation between the FD and BAF values of the ROIs on DPR and between the FD and BAF values of the ROIs on CBCT (p < 0.01). No significant correlations were observed between the GSVs of ROIs on CBCT and the FD values of ROIs on DPR, the BAF values of ROIs on DPR, the FD values of ROIs on CBCT, and the BAF values of ROIs on CBCT (p > 0.05).

CONCLUSIONS

The GSV did not support the FD and BAF. Additionally, DPR and CBCT did not have similar image quality for assessing the FD, BAF, and GSV. In evaluating the trabecular structure, the use of panoramic radiographs should be continued because the image resolution of CBCT is lower and its generalized dose is higher than that of panoramic radiography. These results may serve as a reference for clinical practitioners using dental CBCT to analyze the trabecular structures of alveolar bones.

Radiographic Fractal and Clinical Resonance Frequency Analyses of Posterior Mandibular Dental Implants: Their Possible Association With Mandibular Cortical Index With 12-Month Follow-up

BACKGROUND

The aim of the present study was to investigate whether the mandibular cortical index (MCI) has a relationship with fractal dimension of bone and/or implant stability, and to justify the possible association between MCI, fractal dimension, and stability.

MATERIALS AND METHODS

Eighty-two subjects who received dental implants to replace missing mandibular premolar/molar sites were selected. Three months after surgical placement, implants were restored with fixed ceramic fused metal crowns. MCI was evaluated at baseline; fractal dimensions were measured with fractal analysis (FA) and implant stability quotient (ISQ) with resonance frequency analysis immediately after surgery and 12-month follow-up.

RESULTS

FA at mesial and distal regions for Class 1, Class 2, and Class 3 MCI resulted with significant increases at 12-month follow-up compared to baseline. The ISQ in patients with Class 2 and Class 3 MCI resulted with a significant decrease compared to Class 1 MCI at baseline and at 12 months. All MCI classes evaluated with ISQ and FA at baseline values resulted with significant increases at 12 months. Significant correlations were considered for all mandibular posterior implants between baseline and 12-month measurements for ISQ and FA evaluations.

CONCLUSIONS

Fractal analysis may be a useful method for understanding the healing process around implants and implant stability quotient values. Mandibular cortical index evaluations should be considered before implant procedures, which may provide a presurgical treatment plan and may provide information about the mandibular bone quality.

Novel methodologies and technologies to assess mid-palatal suture maturation: a systematic review

INTRODUCTION

A reliable method to assess midpalatal suture maturation to drive clinical decision-making, towards non-surgical or surgical expansion, in adolescent and young adult patients is needed. The objectives were to systematically review and evaluate what is known regarding contemporary methodologies capable of assessing midpalatal suture maturation in humans.

METHODS

A computerized database search was conducted using Medline, PubMed, Embase and Scopus to search the literature up until October 5, 2016. A supplemental hand search was completed of references from retrieved articles that met the final inclusion criteria.

RESULTS

Twenty-nine abstracts met the initial inclusion criteria. Following assessment of full articles, only five met the final inclusion criteria. The number of subjects involved and quality of studies varied, ranging from an in-vitro study using autopsy material to prospective studies with in vivo human patients. Three types of evaluations were identified: quantitative, semi-quantitative and qualitative evaluations. Four of the five studies utilized computed tomography (CT), while the remaining study utilized non-invasive ultrasonography (US). No methodology was validated against a histological-based reference standard.

CONCLUSIONS

Weak limited evidence exists to support the newest technologies and proposed methodologies to assess midpalatal suture maturation. Due to the lack of reference standard validation, it is advised that clinicians still use a multitude of diagnostic criteria to subjectively assess palatal suture maturation and drive clinical decision-making.

Assessment of the trabecular structure of mandibular condyles in patients with temporomandibular disorders using fractal analysis

OBJECTIVES

The aim of this study was to evaluate changes in the trabecular structure of the mandibular condyle in patients with temporomandibular disorders (TMDs) using fractal analysis.

STUDY DESIGN

A total of 100 patients ages 18 to 73 years were clinically assessed using the Diagnostic Criteria for Temporomandibular Disorders. The control group was age- and sex-matched with the patient group. Panoramic radiographs were obtained using a Kodak 8000 digital device with 73 kVp and 5 mA fixed parameters. The degree of degeneration in the mandibular condyles was calculated. Regions of interest (84 × 84 pixels) were selected within the cortical boundary of the mandibular condyle, and the fractal dimension (FD) was calculated using ImageJ version 1.48.

RESULTS

Radiographic degenerative changes were more frequently present and more severe in the patient group (P < .001). The mean value of FD was 1.22 ± 0.06 in the patient group and 1.25 ± 0.06 in the control group (P = .001). A significant decrease in FD was observed (P = .001) in the left temporomandibular joints of the patient group, whereas a nonsignificant decrease in FD was observed in the right temporomandibular joints (P = .073) as degenerative changes increased.

CONCLUSIONS

Lower FD values were associated with more severe degenerative changes in the patient group. The trabecular structure of condyles in patients with TMD exhibited decreased complexity when erosive and sclerotic changes were evident. As a result, fractal analysis enhanced the use of panoramic radiography in detecting degenerative changes in patients with TMD.

Quantitative evaluation of midpalatal suture maturation via fractal analysis

Objective

The purpose of this study was to determine whether the results of fractal analysis can be used as criteria for midpalatal suture maturation evaluation.

Methods

The study included 131 subjects aged over 18 years of age (range 18.1–53.4 years) who underwent cone-beam computed tomography. Skeletonized images of the midpalatal suture were obtained via image processing software and used to calculate fractal dimensions. Correlations between maturation stage and fractal dimensions were calculated using Spearman's correlation coefficient. Optimal fractal dimension cut-off values were determined using a receiver operating characteristic curve.

Results

The distribution of maturation stages of the midpalatal suture according to the cervical vertebrae maturation index was highly variable, and there was a strong negative correlation between maturation stage and fractal dimension (−0.623, p < 0.001). Fractal dimension was a statistically significant indicator of dichotomous results with regard to maturation stage (area under curve = 0.794, p < 0.001). A test in which fractal dimension was used to predict the resulting variable that splits maturation stages into ABC and D or E yielded an optimal fractal dimension cut-off value of 1.0235.

Conclusions

There was a strong negative correlation between fractal dimension and midpalatal suture maturation. Fractal analysis is an objective quantitative method, and therefore we suggest that it may be useful for the evaluation of midpalatal suture maturation.