Anatomical variations of trabecular bone structure in intraoral radiographs using fractal and particles count analyses

Evaluation of trabecular bone in individuals with periodontitis using fractal analysis: An observational cross-sectional study

Background

It is very difficult to objectively evaluate the negative changes in bone structure due to periodontitis. The present study was aimed to evaluate the trabecular bone structure between healthy individuals and periodontitis patients by fractal analysis (FA) on digital panoramic radiographs.

Material and Methods

The study included 50 periodontally healthy individuals (control group), 50 individuals with Stage 1 periodontitis (S1-P group), 50 individuals with Stage 2 periodontitis (S2-P), and 50 individuals with Stage 3 periodontitis (S3-P), a total of 200 individuals were included. The fractal dimension (FD) value of the trabecular bone in the interdental space between mandibular first molar and second premolar tooth roots was evaluated using Image J program. The mean FD values of the two regions were calculated by box counting method.

Results

There was a statistically significant difference between the groups in terms of all periodontal parameter values (p<0.05). The mean FD values of individuals diagnosed with periodontitis were 1.36±0.08 in the S1-P group, 1.35±0.07 in the S2-P group, 1.28±0.15 in the S3-P group, and 1.44±0.06 in the control group. When the FD values between the groups were examined, it was seen that there was a statistically significant difference between the control and individuals with periodontitis, and the mean FD values were significantly higher in the healthy group (p<0.05). The best receiver operator curve was identified for periodontitis at the ≤1.409 cut-off FD value (area under the curve: 0.828; 95% CI: 0.758-0.899); p=0.000, p<0.001).

Conclusions

FD evaluation can give an objective result about the effect of periodontitis on alveolar bone. The FD values of trabecular bone are different in healthy individuals and individuals with different stages of periodontitis. The findings suggested that a negative correlation between the periodontal data with the sites in which FD was measured and as the periodontitis stage progresses, FD decreases. Key words:Diagnosis, Periodontal Diseases, Radiographic Evaluation.

Evaluation of the effect of sickle cell disease on the mandibular bone of children and adolescents by image texture and radiomorphometric analysis

OBJECTIVES

Sickle cell disease (SCD) can cause osteoporotic changes in the jaw bones. In this study, it was aimed to evaluate possible bone changes using fractal analysis (FA) and morphometric analyses in dental panoramic radiographs of children and adolescents diagnosed with both homozygous and heterozygous forms of SCD.

METHODS

Sixty-five individuals (33 SCD, 32 controls) aged 6-17 years were included in the study. Four separate areas of interest (ROI) were selected for the right and left sides of all panoramic radiographs, and the FA value of the ROIs was calculated. Mandibular cortical width (MCW), panoramic mandibular index (PMI) and mandibular cortical index (MCI) and were evaluated. Data were statistically analyzed and p < 0.05 was accepted for statistical significance.

RESULTS

Fractal values of right and left ROI1 (the center of the mandibular angle.) and ROI4 (the cortical bone), and right ROI2 (the middle of the mandibular ramus) were statistically lower in the case group (p < 0.05). Right ROI2 and ROI4 fractal values of individuals in the case group were lower than those on the left side (p < 0.05). While MCI categories did not differ from the case-control group (p > 0.05), PMI and MCW values were lower in the case group (p < 0.05). All evaluated parameters did not differ according to age and gender (p > 0.05).

CONCLUSION

The results of this study showed that SCD affects the mandible. FA, MCW and PMI parameters can be used to detect early osteoporotic changes in the disease.

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.

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.

Evaluation of mandibular trabecular bone by fractal analysis on panoramic radiograph in paediatric patients with sleep bruxism

OBJECTIVE

To evaluate the trabecular bone density in the mandible of paediatric patients diagnosed with sleep bruxism (SB) using the fractal analysis method on panoramic radiographs.

METHODS

A total of 37 patients whose anamnesis and clinical signs were compatible with SB were diagnosed with SB using BiteStrip^® . Three areas were identified on the panoramic radiographs of the patients: the geometric center of the condyle, the angulus region under the mandibular canal, and the distal region of the mental foramen. Regions of interest (ROIs) of 60 × 60 pixels were selected in these three locations, and fractal dimensions (FDs) were calculated. Results were compared with the control group.

RESULTS

There was no statistically significant difference between the right and left FD values, and male and female FD values in all regions and both groups (p > .05). In the angulus (p = .03) and condyle (p = .03) regions, the SB group had a significantly higher FD value than the control group. There was no statistically significant difference between the SB and control groups in the corpus region (p = .98). A moderate negative correlation arose between age and condyle FD values among controls (r = -0.38, p = .02).

CONCLUSION

Fractal dimension values evaluating trabeculation of the mandibular bone are affected by SB in the angulus and condyle regions.

Is there an association between proton pump inhibitors and radiomorphometric parameters of the mandible? A preliminary study

OBJECTIVES

This study aimed to analyze the association between the use of proton pump inhibitors (PPIs) and radiomorphometric parameters of trabecular and cortical bone of the mandible.

METHODS

A total of 64 patients (37 females and 27 males) using PPIs (PPI group) and 64 age- and gender-matched healthy individuals (control group) were included in this study. The analyzed radiomorphometric parameters were fractal dimension (FD), mandibular cortical width (MCW), and mandibular cortical index (MCI).

RESULTS

There were no significant differences in the mean FDs of selected regions and MCW between the two groups (p > 0.05). The mean MCW was 1.95 mm in the PPI group and 2 mm in the control group. The MCI C3 category, which represents the most porous state of the mandibular cortex, was 2.5 times more frequent in the PPI group (p = 0.002). PPI use duration did not correlate with FD or MCW. No significant differences were observed in FD, MCW, and MCI distribution according to PPI type (p > 0.05).

CONCLUSIONS

Although not all radiomorphometric parameters indicated osteoporotic effects of PPI use, the mandibular cortex of PPI users is prone to erosive defects.

Fractal analysis and periapical index evaluation of multivisit nonsurgical endodontic retreatment: A retrospective study

OBJECTIVE

This retrospective study compared changes in periapical trabecular patterns using fractal analysis and the periapical index (PAI) on the periapical radiographs of patients who underwent multivisit nonsurgical endodontic retreatment of persistent periapical disease.

STUDY DESIGN

In total, 50 participants were included in the study. For each patient, baseline periapical radiographs were acquired just before retreatment and postoperative radiographs were acquired 1 year later. The region of interest, located in the abnormal tissue around the root apex, was selected from each of the paired radiographs and the fractal dimension (FD) was calculated. Periapical status was classified using the PAI as "healed" (PAI <3) or "unhealed" (PAI ≥3).

RESULTS

According to the PAI scores, retreatment after 1 year had a healing rate of 70%. In healed cases, the FD values increased significantly (P < .001), whereas FD decreased significantly in unhealed cases (P = .021). Change in FD was significantly different between healed and unhealed cases (P < .001). However, change in FD did not have a significant correlation with PAI in either healed or unhealed cases (P > .05). There was no significant effect of sex on the change in FD values in either healed or unhealed cases (P ≥ .690).

CONCLUSIONS

The significant differences in FD suggest that this parameter may be useful in detecting increased trabeculation and estimating retreatment prognosis.

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.

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.

Impact of radiotherapy on mandibular bone: A retrospective study of digital panoramic radiographs

Purpose

The purpose of this study was to investigate the impact of radiotherapy on mandibular bone tissue in head and neck cancer patients through an analysis of pixel intensity and fractal dimension values on digital panoramic radiographs.

Materials and Methods

Thirty patients with radiographic records from before and after 3-dimensional (3D) conformational radiotherapy were selected. A single examiner carried out digital analyses of pixel intensity values and fractal dimensions, with the areas of interest unilaterally located in the right angle medullary region of the mandible below the mandibular canal and posterior to the molar region.

Results

Statistically significant decreases were observed in the mean pixel intensity (P=0.0368) and fractal dimension (P=0.0495) values after radiotherapy.

Conclusion

The results suggest that 3D conformational radiotherapy for head and neck cancer negatively affected the trabecular microarchitecture and mandibular bone mass.

Evaluation of the mandibular trabecular bone in patients with bruxism using fractal analysis

OBJECTIVE

The aims of this study were (1) to investigate the effect of bruxism on the fractal dimension (FD) of the mandibular trabecular bone through digital panoramic radiographs, and (2) to evaluate the effectiveness of fractal analysis as a diagnostic test for bruxism.

METHODS

One hundred and six bruxer and 106 non-bruxer patients were included in the study. Three bilateral regions of interest (ROI) were selected: ROI-1, the mandibular condyle; ROI-2, the mandibular angle; ROI-3, the-area between the apical regions of the mandibular second premolar and the first molar teeth. FD values for the bruxer and non-bruxer groups were compared for each ROI.

RESULTS

Only the FD measurements for the right mandibular condyle (ROI-1) showed a statistically significant difference (p = 0.041) between the bruxer and non-bruxer individuals. FD values measured in the bruxers (1.40 ± 0.09) were lower than in the non-bruxers (1.42 ± 0.08).

CONCLUSION

Fractal analysis may be a useful method for discerning trabecular differences in the condylar areas of bruxer individuals. In future studies, the unilateral mastication habits, the characteristics of dental wear, and the occlusal bite forces of individuals should be documented.

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.

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.

Method for Automated Selection of the Trabecular Area in Digital Periapical Radiographic Images Using Morphological Operations

Objectives

The aim of this study is to propose a method that automatically select the trabecular bone area in digital periapical radiographic images using a sequence of morphological operations.

Methods

The study involved 50 digital periapical radiographic images of women aged from 36 to 58 years old. The proposed method consists of three stages: teeth detection, trabecular identification, and validation. A series of morphological operations—top-hat and bottom-hat filtering, automatic thresholding, closing, labeling, global thresholding, and image subtraction—are performed to automatically obtain the trabecular bone area in images. For validation, the results of the proposed method were compared with those of two dentists pixel by pixel. Three parameters were used in the validation: trabecular area, percentage of agreed area, and percentage of disagreed area.

Results

The proposed method obtains the trabecular bone area in a polygon. The obtained trabecular bone area is usually larger than that of previous studies, but is usually smaller than the dentists'. On average over all images, the trabecular area produced by the proposed method is 5.83% smaller than that identified by dentists. Furthermore, the average percentage of agreed area and the average percentage of disagreed area of the proposed method against the dentists' results were 75.22% and 8.75%, respectively.

Conclusions

The shape of the trabecular bone area produced by the proposed method is similar and closer to that identified by dentists. The method, which consists of only simple morphological operations on digital periapical radiographic images, can be considered for selecting the trabecular bone area automatically.

Comparison between fractal analysis and radiopacity evaluation as a tool for studying repair of an osseous defect in an animal model using biomaterials

OBJECTIVES

To evaluate bone repair of an osseous defect in a rat animal model through fractal analysis and radiopacity analysis in radiographic images.

METHODS

120 rats were subjected to extraction of their first molar and divided into four groups (n = 6/group) according to the material used for bone grafting: mineralized bovine bone, demineralized bovine bone (DBB), blood clot (BC - control) or Bio-Oss^® (BO). The animals were sacrificed after 1, 7, 14, 21 and 49 days and subjected to radiographic evaluation. For fractal analysis (FA), a square regionof interest of 30 × 30 pixels was used, and radiopacity was measured as the mean gray scale (MGS) value for three points of 5 × 5 pixels in the apical, medial and coronal regions of the defect. Histomorphometric evaluation was realized as the gold standard for bone neo-formation and maturation of the new osseous matrix.

RESULTS

Histomorphometric evaluation suggested that DBB showed faster mineralized deposition and resulted in more mature bone at the final time point of evaluation. Mineralized bovine bone and Bio-Oss presented similar results. The mineralized groups did not show significant differences in bone maturation. The radiopacity analysis revealed a significant difference (p < 0.05) between the DBB and blood clot groups at the final time point. FA did not show any significant differences at the final time point.

CONCLUSIONS

Mean gray scale seemed to be more effective for the quantification of bone repair than FA in the demineralized group in this animal model. Results for the mineralized groups did not reveal a significant difference, leading to the conclusion that both methods are effective.

Fractal Analysis May Improve the Preoperative Identification of Atypical Meningiomas

Background

There is no objective and readily accessible method for the preoperative determination of atypical characteristics of a meningioma grade.

Objective

To evaluate the feasibility of using fractal analysis as an adjunctive tool to conventional radiological techniques in visualizing histopathological features of meningiomas.

Methods

A group of 27 patients diagnosed with atypical (WHO grade II) meningioma and a second group of 27 patients with benign (WHO grade I) meningioma were enrolled in the study. Preoperative brain magnetic resonance (MR) studies (T1-wieghted, post-gadolinium) were processed and analyzed to determine the average fractal dimension (FDa) and maximum fractal dimension (FDm) of the contrast-enhancing region of the tumor using box-count method. FDa and FDm as well as particular radiological features were included in the logistic regression model as possible predictors of malignancy.

Results

The cohort consisted of 34 women and 20 men, mean age of 62 ± 15 yr. Fractal analysis showed good interobserver reproducibility (Kappa >0.70). Both FDa and FDm were significantly higher in the atypical compared to the benign meningioma group (P < .0001). Multivariate logistic regression model reached statistical significance with P = .0001 and AUC = 0.87. The FDm, which was greater than 1.31 (odds ratio [OR], 12.30; P = .039), and nonskull base localization (OR, .052; P = .015) were confirmed to be statistically significant predictors of the atypical phenotype.

Conclusion

Fractal analysis of preoperative MR images appears to be a feasible adjunctive diagnostic tool in identifying meningiomas with potentially aggressive clinical behavior.

Recent advances in managing/understanding meningioma

Meningiomas are the most common adult primary intracranial tumor. Despite their higher incidence, there have not—until recently—been as many advances in understanding and managing meningiomas. Thus far, two broad classes of meningiomas have emerged on the basis of their mutational profile: those driven by neurofibromatosis 2 (NF2) inactivation and those with non-NF2 driver gene alterations, such as mammalian target of rapamycin and Hedgehog, Wingless/b-catenin, Notch, transforming growth factor-b receptor, mitogen-activated protein kinase, and phospholipase C pathway alterations. In addition to improvements in molecular diagnostics, advances in imaging are being studied to better predict tumor behavior, stratify risk, and potentially monitor for disease response. Management consists primarily of surgery and radiation therapy and there has been limited success from medical therapies, although novel targeted agents are now in clinical trials. Advances in imaging and understanding of the genetic makeup of meningiomas demonstrate the huge potential in revolutionizing the classification, diagnosis, management, and prognosis of meningiomas..

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.

Distributional Variations in the Quantitative Cortical and Trabecular Bone Radiographic Measurements of Mandible, between Male and Female Populations of Korea, and its Utilization

It is important to investigate the irregularities in aging-associated changes in bone, between men and women for bone strength and osteoporosis. The purpose of this study was to characterize the changes and associations of mandibular cortical and trabecular bone measures of men and women based on age and to the evaluation of cortical shape categories, in a large Korean population. Panoramic radiographs of 1047 subjects (603 women and 444 men) aged between 15 to 90 years were used. Mandibular cortical width (MCW), mandibular cortical index (MCI), and fractal dimensions (FD) of the molar, premolar, and anterior regions of the mandibular trabecular bone were measured. Study subjects were grouped into six 10-years age groups. A local linear regression smoothing with bootstrap resampling for robust fitting of data was used to estimate the relationship between radiographic mandibular variables and age groups as well as genders. The mean age of women (49.56 ± 19.5 years) was significantly higher than that of men (45.57 ± 19.6 years). The MCW of men and women (3.17mm and 2.91mm, respectively, p < 0.0001) was strongly associated with age and MCI. Indeed, trabecular measures also correlated with age in men (r > −0.140, p = 0.003), though not as strongly as in women (r > −0.210, p < 0.0001). In men aged over 55 years, only MCW was significantly associated (r = −0.412, p < 0.0001). Furthermore, by comparison of mandibular variables from different age groups and MCI categories, the results suggest that MCW was detected to be strongly associated in both men and women for the detection of bone strength and osteoporosis. The FD measures revealed relatively higher association with age among women than men, but not as strong as MCW.

Correlation of fractal dimension with histomorphometry in maxillary sinus lifting using autogenous bone graft

The aim of this study was to determine the pattern of bone remodeling after maxillary sinus lifting in humans by means of fractal dimension (FD) and histomorphometric analysis. Therefore, the correlation between FD and the histomorphometric findings was evaluated. Sixteen patients with posterior edentulous maxilla were enrolled in this study. Maxillary sinus lifting was performed using autogenous bone grafted from the mandibular retromolar area. Three direct digital panoramic radiographs were obtained: before surgery (Group 1), immediately postoperatively (Group 2) and after 6 months of healing (Group 3) for FD analysis. Biopsies were taken after 6 months, processed and submitted to histological and histomorphometric analysis. Data were analyzed by Shapiro-Wilk test and ANOVA test followed by a Tukey test (a = 0.05). The bone volume fraction of newly trabecular bone (TB) and medullary area (MA) was measured as 62.75% ± 17.16% and 37.25 ± 17.16%, respectively. Significant difference in FD analysis was measured between Group 1 and Group 3. No significant difference was found in the correlation between FD and histomorphometric analysis for TB and MA (p = 0.84). In conclusion, all performed analyses were effective in assessing the bone-remodeling pattern in the maxillary sinus, offering complementary information about healing and predictable outcomes. There were no correlations between FD and histomorphometric analysis.

Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation

Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.

Applying fractal dimension and image analysis to quantify fibrotic collagen deposition and organization in the normal and hypertensive heart

Hearts of mice with reduction of function mutation in STAT3 (SA/SA) develop fibrotic collagen foci and reduced systolic function with hypertension. This model was used to determine if fractal dimension and image analysis can provide a quantitative description of myocardial fibrosis using routinely prepared trichome-stained material. Collagen was characterized by relative density [integrated optical density/area (IOD/A)] and fractal dimension (D), an index of complexity. IOD/A of collagen in wild type mice increased with hypertension while D decreased, suggesting tighter collagen packing that could eventually stiffen the myocardium as in diastolic heart failure. Reduced STAT3 function caused modest collagen fibrosis with increased IOD/A and D, indicating more tightly packed, but more disorganized collagen than normotensive and hypertensive controls. Hypertension in SA/SA mice resulted in large regions where myocytes were lost and replaced by fibrotic collagen characterized by decreased density and increased disorder. This indicates that collagen associated with reparative fibrosis in SA/SA hearts experiencing hypertension was highly disorganized and more space filling. Loss of myocytes and their replacement by disordered collagen fibers may further weaken the myocardium leading to systolic heart failure. Our findings highlight the utility of image analysis in revealing importance of a cellular protein for normal and reparative extracellular matrix deposition.

The three-dimensional microstructure of trabecular bone: Analysis of site-specific variation in the human jaw bone

Purpose

This study was performed to analyze human maxillary and mandibular trabecular bone using the data acquired from micro-computed tomography (micro-CT), and to characterize the site-specific microstructures of trabeculae.

Materials and Methods

Sixty-nine cylindrical bone specimens were prepared from the mandible and maxilla. They were divided into 5 groups by region: the anterior maxilla, posterior maxilla, anterior mandible, posterior mandible, and mandibular condyle. After the specimens were scanned using a micro-CT system, three-dimensional microstructural parameters such as the percent bone volume, bone specific surface, trabecular thickness, trabecular separation, trabecular number, structure model index, and degrees of anisotropy were analyzed.

Results

Among the regions other than the condylar area, the anterior mandibular region showed the highest trabecular thickness and the lowest value for the bone specific surface. On the other hand, the posterior maxilla region showed the lowest trabecular thickness and the highest value for the bone specific surface. The degree of anisotropy was lowest at the anterior mandible. The condyle showed thinner trabeculae with a more anisotropic arrangement than the other mandibular regions.

Conclusion

There were microstructural differences between the regions of the maxilla and mandible. These results suggested that different mechanisms of external force might exist at each site.

Quantification of left ventricular trabeculae using fractal analysis

BACKGROUND

Left ventricular noncompaction (LVNC) is a myocardial disorder characterized by excessive left ventricular (LV) trabeculae. Current methods for quantification of LV trabeculae have limitations. The aim of this study is to describe a novel technique for quantifying LV trabeculation using cardiovascular magnetic resonance (CMR) and fractal geometry. Observing that trabeculae appear complex and irregular, we hypothesize that measuring the fractal dimension (FD) of the endocardial border provides a quantitative parameter that can be used to distinguish normal from abnormal trabecular patterns.

METHODS

Fractal analysis is a method of quantifying complex geometric patterns in biological structures. The resulting FD is a unitless measure index of how completely the object fills space. FD increases with increased structural complexity. LV FD was measured using a box-counting method on CMR short-axis cine stacks. Three groups were studied: LVNC (defined by Jenni criteria), n=30(age 41±13; men, 16); healthy whites, n=75(age, 46±16; men, 36); healthy blacks, n=30(age, 40±11; men, 15).

RESULTS

In healthy volunteers FD varied in a characteristic pattern from base to apex along the LV. This pattern was altered in LVNC where apical FD were abnormally elevated. In healthy volunteers, blacks had higher FD than whites in the apical third of the LV (maximal apical FD: 1.253±0.005 vs. 1.235±0.004, p<0.01) (mean±s.e.m.). Comparing LVNC with healthy volunteers, maximal apical FD was higher in LVNC (1.392±0.010, p<0.00001). The fractal method was more accurate and reproducible (ICC, 0.97 and 0.96 for intra and inter-observer readings) than two other CMR criteria for LVNC (Petersen and Jacquier).

CONCLUSIONS

FD is higher in LVNC patients compared to healthy volunteers and is higher in healthy blacks than in whites. Fractal analysis provides a quantitative measure of trabeculation and has high reproducibility and accuracy for LVNC diagnosis when compared to current CMR criteria.

Prediction of age-related osteoporosis using fractal analysis on panoramic radiographs

PURPOSE

This study was performed to evaluate the trabecular pattern on panoramic radiographs to predict age-related osteoporosis in postmenopausal women.

MATERIALS AND METHODS

Thirty-one postmenopausal osteoporotic women and 25 postmenopausal healthy women between the ages of 50 and 88 were enrolled in this study. The bone mineral density (BMD) of the lumbar vertebrae and femur were calculated using dual-energy X-ray absorptiometry (DXA), and panoramic radiographs were obtained. Fractal dimension (FD) was measured using the box counting method from 560 regions of interest (51×51 pixels) in 6 sites on the panoramic radiographs. The relationships between age and BMD and between FD and BMD were assessed, and the intraobserver agreement was determined.

RESULTS

There was a significant difference in the FD values between the osteoporotic and normal groups (p<0.05). There was a significant difference in the FD values at three sites in the jaws (p<0.05). Age was significantly correlated with the BMD measurements, with an odds ratio of 1.25. However, the FD values were not significantly correlated with the BMD measurements, with an odds ratio of 0.000. The intraobserver agreement showed relatively higher correlation coefficients at the upper premolar, lower premolar, and lower anterior regions than the other sites.

CONCLUSION

Age was an important risk factor for predicting the presence of osteoporosis in postmenopausal women. The lower premolar region was the most appropriate site for evaluating the FD value on panoramic radiographs. However, further investigation might be needed to predict osteoporosis using an FD value on panoramic radiographs.