Fractal analysis for the assessment of trabecular peri-implant alveolar bone using panoramic radiographs

The current overview of the devices of temporary anchorage placed on the palatal bone: CBCT study

Temporary anchorage devices (TADs) are frequently applied to different anatomic areas with different protocols to increase skeletal effects and anchorage in orthodontic treatment planning. It has been reported in many literatures that primary stability for orthodontic TADs is significant for long-term survival rate. For this reason, different areas of the palatal region, which has many indications, have been widely used in the studies. In this evaluation where bone quality and thickness are important, density, bone thickness, and fractal dimension (FD) on cone beam computed tomography (CBCT) will provide more predictable clinical results. The aim of this study was to evaluate bone thickness, density, and FD in the palatal region of the first, and second premolars, and first molars. There was a remarkable difference (p < 0.05) between the parameters of FD, thickness and density of bone in the identified areas in the palatal region. In terms of thickness and FD, the 1st premolar region had significantly higher values than the other regions (p < 0.05). In terms of density, the values in the right 1st molar and right 1st premolar regions were significantly higher (p < 0.05). The 1st premolar region is an ideal site for placement of palatal TADs. CBCT-assisted preliminary evaluation of FD value, bone density, and thickness may increase clinical success when selecting the location of TADs to be applied to the palatal bone.

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 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.

Evaluation of Change in Radiographic Fractal Dimension around Dental Implants Placed with Low-Speed Drilling and Standard Drilling Protocols

Osseointegration is a process that depends on a multitude of factors, including the type of drilling, whether biological or conventional. Objective: Establish box-counting dimension values for radiological images in patients with implants placed with both drilling methods. Material and method: The sample included 129 implants corresponding to 50 patients. A double-blind study of data collection was carried out with the subsequent analysis of the fractal dimension as a comparative value of the state of the trabecular architecture. Results: We found no significant differences (p ≥ 0.05) between the two study groups comparing both drilling techniques. The values for the conventional drilling technique are 0.24 ± 0.07 and for biological drilling: 0.19 ± 0.11 with a p-value of 0.767. Conclusions: The drilling technique does not influence the success of the procedure and the osseointegration process.

Magnetic resonance imaging and fractal analysis findings in temporomandibular joints with disk perforation

OBJECTIVE

This study compared magnetic resonance imaging (MRI) findings and fractal dimension (FD) values in the temporomandibular joints (TMJs) of study patients with disk perforation vs control patients.

STUDY DESIGN

Of 75 TMJs examined with MRI for characteristics of the disk and condyle, 45 were included in the study group and 30 in the control group. MRI findings and FD values were compared for significance of differences between the groups. The frequency of subclassifications was analyzed for differences between the two forms of disk configuration and grades of effusion. Mean FD values were analyzed for differences among subclassifications of MRI findings and between groups.

RESULTS

Examination of MRI variables revealed that the study group had significantly greater frequencies of flattened disks, disk displacement, flattening and combined defects in condylar morphology, and grade 2 effusion (P = .001) Joints with perforated disks had a large percentage of normal disk-condyle relationships (73.3%). Significant differences were discovered between biconcave and flattened disk configuration in the frequencies of internal disk status and condylar morphology. FD values of all patients varied significantly among the subclassifications of disk configuration, internal disk status, and effusion. Mean FD values were significantly lower in the study group with perforated disks (1.07) compared with the control group (1.20, P = .001).

CONCLUSIONS

MRI variables and FD can be useful in investigating intra-articular TMJ status.

The effects of vitamin D deficiency on mandibular bone structure: a retrospective radiological study

OBJECTIVE

The aim of the study was to evaluate the effects of vitamin D deficiency on the mandibular bone structure by fractal analysis and panoramic morphometric indices.

METHODS

Ninety participants were divided into three groups as 30 individuals with severe vitamin D deficiency, 30 individuals with vitamin D deficiency, and 30 individuals with vitamin D sufficiency. Fractal dimension analysis (FD), panoramic mandibular index (PMI), mandibular cortical index (MCI), and mandibular cortical thickness measurement (CTM) were evaluated on panoramic radiographs.

RESULTS

FD values of the patients with vitamin D deficiency were found to be statistically lower than the patients with vitamin D sufficiency (p < 0.05). FD value of supracortical area above the angulus mandible (FD2) in patients with severe vitamin D deficiency was significantly lower than FD values (p = 0.002). There was no statistically significant difference between the groups in the CTM (p > 0.05). PMI was significantly lower in patients with severe vitamin D deficiency (p < 0.001). There was a significant difference in MCI values between the groups (p < 0.05).

CONCLUSION

Vitamin D deficiency causes a decrease in bone mineral density in the mandible, and an increase in alveolar porosity. FD analysis and radiomorphometric indices in panoramic radiographs can be used to assess osteoporotic changes in patients with vitamin D deficiency.

Reliability of Using Texture Analysis of Periapical Radiographs Obtained Using Radiovisiography for Assessing Bone Quality in Dental Implant Planning: A Cross-Sectional Study

Background Pre-prosthetic implant radiographic imaging helps in the quantitative and qualitative analysis of the bone structure and also enables the evaluation of the relationship between critical structures and potential implant sites. Purpose The aim of the study was to define the reliability of utilizing the analysis of textures from the periapical radiographic images obtained through Radiovisiography (RVG) in order to better plan for dental implantations. Methods A cross-sectional study was conducted using 50 intraoral periapical radiographs which were obtained through RVG performed prior to the placement of implants. The radiographs were segregated based on anatomical locations i.e. 12 for the anterior maxilla, nine for the posterior maxilla, seven for the anterior mandible, and 22 for the posterior mandible. Each of the radiographs was visually assessed by four experienced examiners, namely a Prosthodontist E1, Periodontist E2, Oral surgeon E3, and Oral radiologist E4, which was then compared to an experienced operator's tactile perception during a pilot drill for implant placement. As a reference, the Lekholm and Zarb classification was provided to all the examiners for them to qualitatively assess the bone structure in the radiographs. Results The examiners' results were correlated with the assessment provided by the experienced operator. E1 and E4 successfully assessed 42% of the radiographs while E2 had the least success with only 26%. Of the 12 anterior maxillary radiographs, only eight were accurately assessed by E1. With respect to the posterior maxilla, all examiners correctly assessed four radiographs each. Of the seven anterior mandibular radiographs, except for E2, the rest correctly assessed three radiographs each. Of the 22 posterior mandibular radiographs, only nine were accurately assessed by E4. Conclusion Intraoral periapical radiographs obtained through RVG did not meet the desired parameters for assessing the bone quality during the planning stage for implants.

Evaluation of mandibular bone changes in multiple myeloma patients on dental panoramic radiographs

OBJECTIVE

The aim of this study is to assess the mandibular bone structures of multiple myeloma (MM) patients on panoramic radiographs using fractal analysis (FA) and radio-morphometric indices.

METHODS

The study group consisted of 67 MM patients, and the control group consisted of 67 individuals without any systemic disease. The mandibular cortical index (MCI) classification, antegonial index (AGI), gonial index (GI), mandibular cortical width (MCW), panoramic mandibular index (PMI) and fractal dimensions (FD) were evaluated on panoramic radiographs. FD measurements were made by identifying 4 related areas. Shapiro-Wilk test was used to determine the normal distribution of the data. Chi-square and independent t tests were used to compare the findings between the two groups.

RESULTS

The FD values of the study group in ROI1, ROI2, ROI3, ROI4 regions and GI values were found to be statistically significantly lower than the control group (p < 0.001). There was no statistically significant difference between the two groups in terms of AGI, MCW and PMI values (p > 0.05). While C1 was the most common type in the control group, C2 was the most common type in the study group. C2 and C3 were detected more in the study group than in the control group (p < 0.001).

CONCLUSION

Our study showed a consensus with the studies advocating that fractal analysis and radio-morphometric indices are methods that can be used to determine mandibular bone density. The low bone density of MM patients is a condition that physicians should be aware of for interventional dental procedures.

Does Fractal Analysis Have a Role in Diagnosis of Langerhans Cell Histiocytosis?

PURPOSE

Langerhans cell histiocytosis (LCH) of the jaws is a rare disease and is often diagnosed at an advanced stage. This study aims to assess the trabecular pattern of jaws via fractal analysis (FA) on initial panoramic radiographs (OPG) of the patients with LCH to facilitate interpretation of the radiographic changes.

METHODS

A case-control study investigated LCH cases with jaw involvement retrieved from the databases of Istanbul and Kocaeli Universities between 2010 and 2021. Initial OPGs of LCH cases and OPGs of healthy sex- and age-matched controls were investigated with FA. All images were assessed using ImageJ software. On each OPG, a total of 6 regions of interest (ROIs) located on the mandible were investigated bilaterally. The independent variables were the trabecular patterns of jaws of LCH cases and their control matches. The outcome variables were the fractal dimension (FD) values obtained from the ROIs on OPGs. Data were analyzed using the Mann-Whitney U test and Student's t test.

RESULTS

Fifteen LCH-control pairs were investigated. In one ROI located in the supracortical area above the left mandibular angle, FD values of LCH cases (1.273 ± 112.8) were significantly lower than controls (1.308 ± 85.3; P < .05). Lower FD values were also calculated for some of the remaining ROIs, but there was no significant difference between groups (P > .05).

CONCLUSIONS

Regarding our results, FA was not a useful parameter to discern radiographical trabecular changes between LCH cases and controls. Multicenter studies with larger populations are needed to investigate the potential of FA in the identification of this rare disease.

Fractal Dimension as a Tool for Assessment of Dental Implant Stability—A Scoping Review

A lot of modalities for assessing implant stability are available for clinicians, but they fail to assess trabecular changes as they are solely dependent on the operator’s skills. The use of Fractal Dimension (FD) has evolved to be used as a measure for trabecular changes depicting implant stability before and after implant placement. The objective of this systematic review was to qualitatively analyse the available scientific literature describing the use of FD as a tool to measure implant stability on the basis of trabecular changes. An electronic search in PubMed, Web of Science and Scopus was carried out using relevant keywords, such as: fractal dimension; fractal analysis; dental implants; implant stability; osseointegration, etc. Studies reporting the use of FD as a tool to measure implant stability were included and subjected to qualitative analysis using ROBINS-I and Cochrane risk of bias assessment criteria. Fourteen studies were included in this review. Results showed that FD was found to be used solely as a measure of implant stability in seven studies, out of which six studies showed an increment in FD values. The majority of studies concluded with a statistical correlation between FD and respective other assessment methods used. FD may not serve as a sole indicator of implant stability; however, it can be used as an adjunct to conventional methods along with additional fractal factors.

Peri-implant bone microstructural analysis and comparison of resonance frequency analysis before prosthetic placement: a retrospective study

Objectives

Fractal analysis is a mathematical method used for the calculation of bone trabeculation and lacunarity. This study aims to evaluate the relationship between resonance frequency analysis (RFA) and fractal dimension (FD) of peri-implant bone to determine the preload stability of implants.

Materials and methods

In this study, the results of the fractal analysis calculated from the resonance frequency analysis results taken in the 3rd month of the patients who underwent 2-stage implant by the same doctor and the radiographs taken in the same session were evaluated. A hundred implants in 20 patients were applied in this study. The implant stability quotient (ISQ) values of the implants and fractal dimension values of the peri-implant bone were calculated.

Results

The findings showed that the ISQ1 (p = 0.008), ISQ2 (p = 0.038), ROI2 (p = 0.013), and ROI3 (p < 0.001) values were statistically significantly higher in men than women. The ISQ1 (p = 0.003), ISQ2 (p = 0.013), ROI1 (p = 0.011), and ROI3 (p < 0.001) of the mandible were statistically higher than the maxilla. The fractal dimension cut-off value to assess prosthetic loading was found 1.198.

Conclusion

Fractal analysis is a non-invasive method that can be used in conjunction with clinical examination in the prosthetic loading decision of implants. It is a valuable parameter that can be used without the need for an extra device when it is necessary to reduce the clinical study time.

Clinical relevance

Calculating the fractal dimension of the peri-implant bone is a practical, economical, and applicable method for clinicians. FD calculated from panoramic radiographs used for diagnosis in routine treatments in clinics where access to the necessary devices for ISQ measurement is not available will contribute to clinical practice.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00784-022-04464-3.

Evaluation of change in trabecular bone structure surrounding dental implants by fractal dimension analysis and comparison with radiomorphometric indicators: a retrospective study

Background

The trabecular bone surrounding dental implant show some structural changes during healing period. The purpose of this study is to observe the change in trabecular bone with fractal dimensional analysis from baseline to 3rd month of implant placement. It was also aimed to determine the correlation of fractal dimension (FD) change with morphometric indices, mandibular cortical index (MCI) and mandibular cortical width (MCW).

Methods

Digital panoramic radiographs taken from 14 patients were evaluated in this study. A total of 30 implants which were placed on mandibular premolar or molar region were included. MCI and MCW assessments were made on baseline radiograph and FD were analyzed on baseline and 3rd month radiograph. FD change by time was recorded separately for every ROI. A paired sample t-test was used to evaluate the change between FD-baseline and FD-3rdmonth values. One-way ANOVA was used to determine the relationship between FD change and MCI. FD change and MCW measurements correlation was calculated by Pearson correlation analysis.

Results

FD value increased in 75 of 90 implant-adjacent regions evaluated in the 3rd month and it was observed that the FD values were statistically significantly increased in the mesial, distal and apical regions at the 3rd month measurements. There was no statistically significant relationship between mean FD change and MCI, and there was no correlation between mean FD change and MCW value.

Discussion

There are many studies evaluating the resorptive changes in bone. However, there are few studies investigating whether there is a correlation between pre- and post-operative trabecular pattern with MCI and MCW. The results of this study indicate that the implants have an improving effect on bone trabeculation in the region where they are placed.

Evaluation of the effects of prolotherapy on condyles in temporomandibular joint hypermobility using fractal dimension analysis

Objectives

Prolotherapy is a method that has gained popularity in recent years and has been reported to have positive short-term and long-term clinical results in maxillofacial surgery, especially temporomandibular joint (TMJ) hypermobility. This study aimed to evaluate the changes in the trabecular structure of mandibular condyles in patients who underwent prolotherapy due to TMJ hypermobility using the fractal analysis method.

Materials and Methods

Forty-five patients who received dextrose prolotherapy at a concentration of 20% and fifteen control patients were included in the study. All patients had panoramic radiographs just before (T0) and six months after treatment (T1). The patients who received treatment were divided into three groups according to the number of prolotherapy injections. The regions of interest were selected from bone areas close to the articular surfaces of the condyles. The fractal dimension (FD) values were calculated.

Results

The main effect of time on the FD value was significant [F (1, 56)=86.176, P<0.001]. This effect was qualified by a significant time×group interaction effect [F (3, 56)=9.023, P<0.001]. The decreases in FD values in all treatment groups between T0 and T1 times were significant (P=0.004). However, changes in FD values were not significant in the control group (P=0.728).

Conclusion

Dextrose prolotherapy without the effect of the number of injections caused a decrease in FD values in the mandibular condyles over time.

Comparison of cone-beam computed tomography and digital panoramic radiography for detecting peri-implant alveolar bone changes using trabecular micro-structure analysis

Objectives

We compared changes in fractal dimension (FD) and grayscale value (GSV) of peri-implant alveolar bone on digital panoramic radiography (DPR) and cone-beam computed tomography (CBCT) immediately after implant surgery and 12 months postoperative.

Materials and Methods

In this retrospective study, 16 patients who received posterior mandibular area dental implants with CBCT scans taken about 2 weeks after implantation and one year after implantation were analyzed. A region of interest was selected for each patient. FDs and GSVs were evaluated immediately after implant surgery and at 12-month follow-up to examine the functional loading of the implants.

Results

There were no significant differences between DPR and CBCT measurements of FD values (P>0.05). No significant differences were observed between FD values and GSVs calculated after implant surgery and at the 12-month follow-up (P>0.05). GSVs were not correlated with FD values (P>0.05).

Conclusion

The DPR and reconstructed panoramic CBCT images exhibit similar image quality for the assessment of FD. There were no changes in FD values or GSVs of the peri-implant trabecular bone structure at the 12-month postoperative evaluation of the functional loading of the implant in comparison to values immediately after implantation. GSVs representing bone mass do not align with FD values that predict bone microstructural parameters. Therefore, GSVs and FDs should be considered different parameters for assessing bone quality.

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.

Effect of Platelet Concentrates on Marginal Bone Loss of Immediate Implant Procedures: A Systematic Review and Meta-Analysis

BACKGROUND

To evaluate marginal bone loss (MBL) in immediate implant procedures (IIP) placed in conjunction with platelet concentrates (PCs) compared to IIP without PCs.

METHODS

A search was performed in four databases. Clinical trials evaluating MBL of IIP placed with and without PCs were included. The random effects model was conducted for meta-analysis.

RESULTS

Eight clinical trials that evaluated MBL in millimeters were included. A total of 148 patients and 232 immediate implants were evaluated. The meta-analysis showed a statistically significant reduction on MBL of IIP placed with PCs when compared to the non-PCs group at 6 months (p < 0.00001) and 12 months (p < 0.00001) follow-ups. No statistically significant differences were observed on MBL of IIP when compared PCs + bone graft group vs. only bone grafting at 6 months (p = 0.51), and a significant higher MBL of IIP placed with PCs + bone graft when compared to only bone grafting at 12 months was found (p = 0.03).

CONCLUSIONS

MBL of IIP at 6 and 12 months follow-ups is lower when PCs are applied in comparison to not placing PCs, which may lead to more predictable implant treatments in the medium term. However, MBL seems not to diminish when PCs + bone graft are applied when compared to only bone grafting.

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.

Evaluation of trabecular bone healing using fractal dimension analysis after augmentation of alveolar crests with autogenous bone grafts: a preliminary study

OBJECTIVE

The aim of this study is to evaluate bone remodeling after alveolar crest augmentation with autogenous bone grafts.

METHODS

50 patients who were applied augmentation due to alveolar deficiency were included in this study. Fractal dimensions were measured on the radiographs in the preoperative, postoperative, follow-up periods. The ROI was selected specific to each patient, but repeated in a standardized manner on subsequent radiographs.

RESULTS

A total of 50 patients were included in the study; There were 31 females and 19 males. Implants were placed in all patients without any complications. The mean fractal dimensions on the graft recipient side were statistically higher in the postoperative 5th month compared to the postoperative 1st week (p = 0.002). The mean fractal dimensions on the donor side were statistically higher in the preoperative and postoperative 5th month compared to the postoperative 1st week (p < 0.001).

CONCLUSION

Any clinical imaging method cannot fully reflect the histological microstructures of the bone. Evaluating the fractal analysis together with the clinical results can demonstrate adequate bone healing and quality prior to implant placement. Fractal analysis is a non-invasive, reproducible, method but further, prospective, randomized, controlled clinical studies are needed to estimate bone quality prior to implant placement.

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.

Validity of fractal analysis of implants in individuals with healthy and diseased peri-implant mucosa

OBJECTIVE

The purpose of this study was to determine whether fractal analysis could discriminate the peri-implant trabecular bone between individuals with healthy peri-implant mucosa and peri-implant disease using digital periapical radiographs.

MATERIAL AND METHODS

The electronic health records of patients with a dental implant were reviewed to determine their eligibility. One hundred four patients (aged 27-89 years) were included and divided into three groups. Group 1) Individuals with healthy peri-implant mucosa; Group 2) Individuals with peri-implant mucositis; or Group 3) Individuals with peri-implantitis. The following clinical measurements for each dental implant were extracted: probing depth (PD), clinical attachment level (CAL), and the presence or absence of bleeding on probing (BOP). Digital periapical images of the implant were used to calculate the fractal dimension (FD) for each implant at two regions of interest (ROI). Summary statistics were calculated for mean PD, mean CAL, mean percent BOP, and mean FD by group. Differences among groups were tested using one-way analysis of variance (ANOVA). Spearman nonparametric correlations were tabulated for mean PD, mean CAL, mean percent BOP, and mean FD.

RESULTS

The only measure that did not demonstrate significant differences among groups was FD (p = .559) with all other measures demonstrating a significant difference (p < .001).

CONCLUSIONS

Based on this study, FD of the peri-implant bone calculated from a periapical radiograph does not appear to be a valid method to distinguish between healthy and diseased implants, while clinical measures of PD, CAL, and BOP are useful for the diagnosis of peri-implant health, peri-implant mucositis, and peri-implantitis.

A universal mathematical model applied to the congenital ventral penile curvature

INTRODUCTION

The macroscopic dynamic of fetal penis development presents a pattern resembling the unfolding of a spiral, so congenital ventral penile curvature could indicate that this natural sequence has been interrupted. Our aim in this article is to offer a mathematical model of congenital ventral curvature of the penis.

MATERIALS AND METHODS

Five individuals who presented with congenital ventral penile curvature and three who presented with acquired penile ventral curvature due to Peyronie's disease were evaluated. The penises were photographed during an induced erection test and the penile curvature patterns were compared with an equiangular spiral. When an association was found, a potential relationship to the golden spiral-a type of equiangular spiral-was also assessed. The mathematical spiral relationships were analyzed using Wolfram CDF Player® (Logarithmic Spiral) and PhiMatrix® software. The Wolfram software generated logarithmic spirals equivalent to the penile curvature with appropriate mathematical values. The PhiMatrix software, which builds any golden spirals from golden rectangles, was used to check whether the spiral was golden as well as equiangular.

RESULTS

An equiangular spiral that was also golden was found in all cases of congenital ventral penile curvature. In contrast, none of the acquired penile ventral curvature cases showed a specific pattern.

CONCLUSION

Congenital ventral penile curvature has the mathematical pattern of a golden spiral. Our results offer a mathematical algorithm for potential use in surgical reconstruction procedures, regenerative medicine, tissue engineering, robotics, and body-machine interfaces.

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.

Correlating Radiographic Fractal Analysis at Implant Recipient Sites with Primary Implant Stability: An In Vivo Preliminary Study

Objectives

The aim of this study was to demonstrate a possible correlation between radiographic trabecular bone quantified with fractal dimensions analysis and values of primary implant stability deliberated using the Osstell^® monitor (Integration Diagnostics AB, Goteborgsvagen, Sweden) with the density of bone specimens harvested from the implant recipient sites and calculated using the mass and volume of the bone bloc specimens.

Material and methods

Fifty implants of the same brand, diameter, and length were inserted with the same surgical procedures; 25 implants in the molar premolar region of the maxilla and 25 implants in the mandibular posterior region of only healthy male patients between 20 and 50 years of age. Prior to the placement of the implants, biopsies were taken from the selected site for density calculation using a calibrated trephine. Two photostimulable phosphor digital periapical radiographs were obtained for each patient and two regions of interest were selected for a fractal dimension analysis: one site before implantation and the same site immediately postoperatively adjacent to the implant.

Results

There were correlations between the fractal dimensions and implant stability quotient as well as between fractal dimensions and bone density. No significant difference was found between the fractal dimensions of pre- and postoperative periapical radiographs for the same region of interest and between implant stability quotient values of the maxillae and mandible sites.

Conclusion

All executed analyses were helpful in assessing the bone density in the recipient site of implant placement using fractal dimensions, offering complementary information about predictable bone density assessed on a periapical radiograph.

Image-based Bone Density Classification Using Fractal Dimensions and Histological Analysis of Implant Recipient Site

Background:

Success of dental implants is affected by the quality and density of the alveolar bone. These parameters are essential for implant stability and influence its load-bearing capacity. Their assessment is usually based on preoperative radiographs used as a tool prior to implant procedures.

Objective:

The aim of the study was to compare the bone density of surgically harvested bone specimens at implant recipient sites in the maxillary and mandibular posterior region using histological analysis to the radiographic bone density using fractal dimension for reliability and determining an image based classification of bone density prior surgery.

Methods:

Fifty implants were placed in the posterior region of male patients, (twenty five implants in the maxilla and twenty five in the mandible). The edentulous regions were presurgically assessed using Photo Stimulable Phosphor Plate (PSP) intra-oral radiographs and the fractal dimension box counting of region of interest was calculated at the implant recipient site. During surgery, bone core specimens were trephined, and bone densities and minerals parameters were evaluated based on histological analysis using SEM (Scanning Electron Microscopy), and atomic absorption spectrometry.

Results:

Fractal dimensions (FD) values for the same region of interest (ROI) selected on the radiographs of bone blocks and edentulous sites were different but showed a proportional variation in molar and premolar region of the maxilla and mandible. Bone density results, calculated by the ratio of bone mass (BM) to the bone volume (BV) of the bone core specimen (D=M/V), increased in the mandibular bone blocks, and decreased in the maxilla specimens. Moreover, fractal dimension values of preoperative radiographs at implant recipient sites and bone density of trephined showed a statistically similar distribution. However, no significant difference was shown in the percentage of minerals contents and mass of calcium phosphate of each bone specimen between maxilla and mandible based on scanning electron microscopy analysis. Four types of bone densities were classified according to the distribution of FD values based on preoperative radiographs and on the densities of bone cores calculations.

Conclusion:

Radiographic estimation of bone quality calculated with fractal dimension could be a useful, non-invasive tool when using preoperative intra-oral radiographs to predict bone density at implant recipient sites with caution and limits concerning the kind of digital radiographs and size of region of interest, especially when these results were based with bone specimens harvested from implant site as an absolute reference.

Image-based analysis of trabecular bone in osteoporotic rabbits: correlation of morphological features and bone mineral density profile

OBJECTIVE

To analyse a set of morphological features from digital radiographs (RX) and bone mineral density (BMD) values estimated from quantitative computerized tomography scans (QCT scans) of the knee joint of an osteoporotic rabbits, and to determine the relationship and correlation of these variables to be considered as an alternative diagnosis method.

METHODS

The knee joint of rabbits (N = 9 ovariectomized and injected with of methylprednisolone sodium succinate (OVX + MPSS) and 3 sham operated healthy controls) were subjected to radiographic examination before the beginning of the study and after 6 weeks; after sacrifice, they were immediately scanned with a 64-channel CT. A set of morphological features was extracted from RX images and then subjected to Principal Component Analysis (PCA); BMD-values were calculated at different depths from the articular surface of the femur and the tibia. The selected morphological variables and the BMD values were correlated in order to determine useful information in medical diagnostics.

RESULTS

Ten morphological variables explained 80.39% of the total variability, but only some of them demonstrated significant differences between baseline and OVX + SSMP states and between OVX + SSMP and control. Spearman analysis showed higher positive and negative correlation of these parameters among them (r = 0.67, 0.81, 0.83 and 1); and a moderate correlation with the BMD values (r = 0.50, 0.52, 0.52 and 0.55) during the progression of osteoporosis (OP).

CONCLUSION

The Spearman's rank test supported the overall significant correlation between both, the morphological features and BMD values, making them as a reliable alternative option to the diagnosis of osteoporosis.

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.

A Comparison between the Implant Stability Quotient and the Fractal Dimension of Alveolar Bone at the Implant Site

Objectives

Fractal analysis of the radiographic pattern of bone has been used to evaluate its quantitative properties. However, the relation between initial implant stability and quality of bone remains unclear. The objective of this study was to evaluate RFA values in relation to the fractal dimension of bone where the implant was inserted.

Material and Methods

A total of 50 two-stage dental implants were placed in the maxilla and mandible of 32 patients. After implant placement, an implant stability quotient (ISQ) was measured in two perpendicular planes. On intraoral digital periapical radiographs, three 35x35 pixels' regions of interest (ROIs) were chosen covering the bone adjacent to the neck (ROI 1), middle (ROI 2), and apical (ROI 3) part of the implant, respectively. For every ROI, a fractal dimension (FD) was calculated. A linear correlation, as well as a logistic regression analysis, was used to identify a possible relation between the ISQ and FD values for every ROI in the maxilla and mandible.

Results

The ISQ and FD values were found to be correlated at ROI 1 for the maxilla. There was no linear correlation between ISQ and FD values in any of the three ROIs in the mandible. However, logistic regression analysis showed that in ROI 1 and ROI 3 the values of FD and ISQ are statistically important and may be used to express the difference between maxilla and mandible.

Conclusion

The fractal dimension of alveolar bone measured from intraoral digital radiographs alone may be an insufficient parameter to determine initial implant stability.

Computer-based automatic classification of trabecular bone pattern can assist radiographic bone quality assessment at dental implant site

OBJECTIVE:

To develop and validate an automated classification method that determines the trabecular bone pattern at implant site based on three-dimensional bone morphometric parameters derived from CBCT images.

METHODS:

25 human cadaver mandibles were scanned using CBCT clinical scanning protocol. Volumes-of-interest comprising only the trabecular bone of the posterior regions were selected and segmented for three-dimensional morphometric parameters calculation. Three experts rated all bone regions into one of the three trabecular pattern classes (sparse, intermediate and dense) to generate a reference classification. Morphometric parameters were used to automatically classify the trabecular pattern with linear discriminant analysis statistical model. The discriminatory power of each morphometric parameter for automatic classification was indicated and the accuracy compared to the reference classification. Repeated-measures analysis of variances were used to statistically compare morphometric indices between the three classes. Finally, the outcome of the automatic classification was evaluated against a subjective classification performed independently by four different observers.

RESULTS:

The overall correct classification was 83% for quantity-, 86% for structure-related parameters and 84% for the parameters combined. Cross-validation showed a 79% model prediction accuracy. Bone volume fraction (BV/TV) had the most discriminatory power in the automatic classification. Trabecular bone patterns could be distinguished based on most morphometric parameters, except for trabecular thickness (Tb.Th) and degree of anisotropy (DA). The interobserver agreement between the subjective observers was fair (0.25), while the test-retest agreement was moderate (0.46). In comparison with the reference standard, the overall agreement was moderate (0.44).

CONCLUSION:

Automatic classification performed better than subjective classification with a prediction model comprising structure- and quantity-related morphometric parameters.

ADVANCES IN KNOWLEDGE:

Computer-aided trabecular bone pattern assessment based on morphometric parameters could assist objectivity in clinical bone quality classification.

Trabecular structure designation using fractal analysis technique on panoramic radiographs of patients with bisphosphonate intake: a preliminary study

OBJECTIVE

This study was performed to evaluate the trabecular pattern of patients with cancer taking bisphosphonates on panoramic images using fractal dimension (FD) analysis by comparison with healthy subjects and to assess whether any difference exists between regions.

METHODS

FD analysis was conducted using ImageJ 1.3 software (National Institutes of Health, Bethesda, MD, USA) with the box-counting method on panoramic radiographs of 33 patients taking bisphosphonates (13 males and 20 females) and 33 healthy sex- and age-matched individuals.

RESULTS

FD values were higher (1.39 ± 0.14) in the study group than control group (1.38 ± 0.07) (p ≤ 0.05). No difference was detected in the FD values among the tested regions. The mean FD values in the control and study groups were as follows: region 1, 1.49 and 1.41 (p = 0.54); region 2, 1.36 and 1.37 (p = 0.84); region 3, 1.35 and 1.42 (p = 0.11); and region 4, 1.39 and 1.39 (p = 0.90), respectively. Female patients showed significantly lower values above the mandibular canal on the distal side of the second premolar and anterior to the mental foramen than did male patients (p ≤ 0.05). Age was unrelated to the FD in the study group (p ≥ 0.05).

CONCLUSIONS

The FD values of the patients with cancer taking bisphosphonates were higher than those of the controls. FD analysis showed the potential for examining bone structure in panoramic radiographs. Studies with a larger sample size are necessary to confirm these results.

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.

Fractal analysis of subchondral bone changes of the hand in rheumatoid arthritis

Rheumatoid arthritis (RA) is a chronic and systemic inflammatory disorder. Conventional radiography, a widely available and cost-effective examination method, remains the standard of reference for the detection and quantification of joint involvement in RA. Fractal dimension (FD) of the trabecular bone structure has been proven to correlate with the bone's physical properties. The present study was designed to use fractal analysis to validate radiograph changes in the hand of RA patients.This study retrospectively evaluated the hand radiographs of 108 subjects. Fifty-four patients were suffering from RA, of which 18 were men and 36 were women. Their ages ranged from 25 to 90 years. The hand radiographs of 54 healthy patients, 18 men and 36 women (age range 23-88 years), were used as the control group. Bone structure value (BSV) is a critical parameter for the assessment and analysis of bone microarchitecture. The BSVs were calculated over the fractal dimension using the Brownian motion.The BSV calculated for ROI showed a significant difference in ROI5 (0.210 ± 0.045), ROI6 (0.186 ± 0.066), and ROI11 (0.201 ± 0.056) in patients with RA, in comparison to the CG (P < 0.05). A significant correlation was observed between anti-CCP and ROI4, ROI5, ROI6, ROI9, and ROI12 in seropositive RA patients (post hoc test (Bonferroni) P <0.001).This study demonstrates that the bone textural image analysis technique can be used to quantify the radiographic changes in RA hands, based on comparisons of FDs.

Fractal properties of the trabecular pattern of the mandible in chronic renal failure

OBJECTIVES

The purpose of this study was to evaluate fractal analysis as a tool to quantitatively determine the mandibular trabecular bone changes in patients with chronic renal failure (CRF).

METHODS

In the present study, fractal analysis was performed using ImageJ (National Institutes of Health, Bethesda, MD) program with box-counting method over panoramic radiographs of 25 patients (14 females and 11 males) with CRF and 26 healthy individuals (14 females and 12 males) as a control group. The fractal dimension (FD) values of the patients and healthy individuals were compared. In addition, average biochemical parameters [parathyroid hormone (PTH), calcium (Ca), phosphorus (P), product of Ca and P levels (CaxP), alkaline phosphatase (ALP), vitamin D] of the patients with CRF, as measured during the 3 months before the panoramic radiographs, were compared with FD values.

RESULTS

According to the results, FD values of the patients with CRF were found to be statistically lower than the control group (p < 0.05). The average PTH levels of the patients with CRF were 416.16 ± 310.3 pg ml(-1); average Ca levels were 8.94 ± 1.2 mg dl(-1); average P levels were 5.76 ± 1.7 mg dl(-1); average CaxP values were 51.12 ± 15.03; average ALP levels were 83.44 ± 36.8 U l(-1); and the average vitamin D values were 19.43 ± 9.7 ng ml(-1). In addition, there was no significant correlation between FD values and the biochemical parameters of the patients, and there was no correlation between age, gender and FD.

CONCLUSIONS

The FD values of the patients with CRF were lower than those of the controls. This finding suggests that FD analysis might be a promising simple and cost-effective tool for evaluating trabecular bone structure.

Intraoral radiographs texture analysis for dental implant planning

BACKGROUND AND OBJECTIVES

Computer vision extracts features or attributes from images improving diagnosis accuracy and aiding in clinical decisions. This study aims to investigate the feasibility of using texture analysis of periapical radiograph images as a tool for dental implant treatment planning.

METHODS

Periapical radiograph images of 127 jawbone sites were obtained before and after implant placement. From the superimposition of the pre- and post-implant images, four regions of interest (ROI) were delineated on the pre-implant images for each implant site: mesial, distal and apical peri-implant areas and a central area. Each ROI was analysed using Matlab® software and seven image attributes were extracted: mean grey level (MGL), standard deviation of grey levels (SDGL), coefficient of variation (CV), entropy (En), contrast, correlation (Cor) and angular second moment (ASM). Images were grouped by bone types-Lekholm and Zarb classification (1,2,3,4). Peak insertion torque (PIT) and resonance frequency analysis (RFA) were recorded during implant placement. Differences among groups were tested for each image attribute. Agreement between measurements of the peri-implant ROIs and overall ROI (peri-implant + central area) was tested, as well as the association between primary stability measures (PIT and RFA) and texture attributes.

RESULTS

Differences among bone type groups were found for MGL (p = 0.035), SDGL (p = 0.024), CV (p < 0.001) and En (p < 0.001). The apical ROI showed a significant difference from the other regions for all attributes, except Cor. Concordance correlation coefficients were all almost perfect (ρ > 0.93), except for ASM (ρ = 0.62). Texture attributes were significantly associated with the implant stability measures.

CONCLUSION

Texture analysis of periapical radiographs may be a reliable non-invasive quantitative method for the assessment of jawbone and prediction of implant stability, with potential clinical applications.