• Imaging Science in Dentistry
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• v.36 no.4
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• pp.183-188
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• 2006

Purpose: The purpose of this research was to study bone changes after bilateral sagittal split osteotomy through fractal analysis and measurement of mandibular cortical thickness. Materials and Methods: This study included twenty-two prognathic patients who underwent bilateral sagittal split osteotomy. Panoramic radiographs of these patients were taken immediately before operation and at 1 month, 6 months, and 12 months postoperatively. The fractal dimension was measured by the box-counting method in the region of interest centered on both the basal and interdental bones between the first and second mandibular molars. Measurements of mandibular cortical thickness were taken both in the area between the first and second mandibular molars and at the osteotomy site. Changes of fractal dimension and cortical thickness over four stages were statistically analyzed. Results: The fractal dimension of the mandibular basal bone before surgery and after 1 month, 6 months and 12 months were $1.4099{\pm}0.0657,\;1.382{\pm}0.0595,\;1.2995{\pm}0.0949,\;and\;1.4166{\pm}0.0676$, respectively (Repeated-measures ANOVA, P<0.001). However, no statistically significant differences were noted in interdental fractal dimensions among the four stages. Mandibular cortical thickness between the first and second mandibular molars before operation and after 1 month, 6 months and 12 months was $3.74{\pm}0.48mm,\;3.63{\pm}0.47mm,\;3.41{\pm}0.61mm\;and\;3.55{\pm}0.66mm$ (P<0.01), respectively. Mandibular cortical thickness at the osteotomy site at each of the four stages was $3.22{\pm}0.44mm,\;2.87{\pm}0.59mm,\;2.37{\pm}0.61mm\;and\;2.64{\pm}0.62mm$, respectively (P<0.001). Conclusion: This study suggests that the mandibular tissue continued decreasing for 6 months postoperatively and then increased over the subsequent 6 months.

• Imaging Science in Dentistry
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• v.42 no.4
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• pp.231-235
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• 2012

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 ($51{\times}51$ 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.

• Imaging Science in Dentistry
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• v.40 no.3
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• pp.123-129
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• 2010

Purpose : To evaluate the effect of surgical treatment of ligature-induced peri-implantitis in dogs using fractal analysis. Also, the capabilities of fractal analysis as bone analysis techniques were compared with those of histomorphometric analysis. Materials and Methods : A total of 24 implants were inserted in 6 dogs. After a 3-months, experimental periimplantitis characterized by a bone loss of about 3 mm was established by inducing with wires. Surgical treatment involving flap procedure, debridement of implants surface with chlorhexidine and saline (group 1), guided bone regeneration (GBR) with absorbable collagen membrane and mineralized bone graft (group 2), and $CO_2$ laser application with GBR (group 3) were performed. After animals were sacrificed in 8 and 16 weeks respectively, bone sections including implants were made. Fractal dimensions were calculated by box-counting method on the skeletonized images, made from each region of interest, including five screws at medial and distal aspects of implant, were selected. Results : Statistically significant differences in the fractal dimensions between the group 1($0.9340{\pm}0.0126$) and group 3($0.9783{\pm}0.0118$) at 16 weeks were found (P<0.05). The fractal dimension was statistically significant different between 8($0.9395{\pm}0.0283$) and 16 weeks in group 3 (P<0.05). These results were similar with the result of the evaluation of new bone formation in histomorphometric analysis. Conclusions : Treatment of experimental peri-implantitis by using $CO_2$ laser with GBR is more useful than other treatments in the formation of new bone and also the tendency of fractal dimension to increase relative to healing time may be a useful means of evaluating.

• Journal of the Korea Concrete Institute
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• v.13 no.2
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• pp.146-152
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• 2001

The fractal geometry is a non-Euclidean geometry which discribes the naturally irregular or fragmented shaps, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cemposite composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is appearent.ent.

• 한국해양학회지
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• v.29 no.3
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• pp.228-238
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• 1994

The change of sea-level is a good indicator of the change of climate during the Quaternary period. The sea-levels in the world have been changing very irregularly during that time. The pattern of the Quaternary sea-level change was assumed to be a stochastic fractal in this study. We measured fractal dimensions of the Holocene sea-levels of the Hudson river estuary and the Delaware coast. A box counting method gave almost the same values. i.e., D=1.358 for the Hudson sea-level changes and D+1.346 for the Delaware sea-level changes. the ability of the inverse method of fractal interposea-levels. IFIF reproduction the realistic sea-levels for the both of them. The delaware sea-level data made less statistical errors for the interpolation of IFIF than the Hudson and the Delaware sea-levels. IFIF reproduction the realistic sea-levels for the both of them. The Delaware sea-level data made less statistical errors for the interpolation of IFIF than the Hudson sea-level data. This suggests that the Delaware sea-level data are more reliable than the Hudson sea-level data was calculated from the fractal dimension of the Delaware sea-level data. Fractal interpolation functions (FIF) was used to reconstruct the peleosea-levels of the Korean coasts and the Atlantic Ocean coasts of the United States. The Korean Peleosea-level change generacted by FIF is different from the peleosea-level change of the eastern U.S.. The Korean peleosea-levels are much higher than the eastern U.S. Paleosea-levels, comparing to each other from the present to 8,000 BP.