• Imaging Science in Dentistry
• /
• 제36권4호
• /
• pp.183-188
• /
• 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
• /
• 제42권4호
• /
• pp.231-235
• /
• 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
• /
• 제40권3호
• /
• pp.123-129
• /
• 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.

• 콘크리트학회논문집
• /
• 제13권2호
• /
• pp.146-152
• /
• 2001

프랙탈 기하는 재료의 파괴거동과 같은 자연계에 존재하는 불규칙한 현상을 비정수의 프랙탈 차원으로 정량화할 수 있다. 이런. 프랙탈 차원에 기초하면 프랙탈 도형은 도형의 일부를 확대하면 전체와 같아지는 자기상사성 특성을 지닌다. 프랙탈적 해석방법을 시멘트 복합체의 파괴시의 균열성장거동에 적용하여 복합체의 미세구조와 파괴거동과의 관계를 알아볼 수 있다. 본 연구의 목적은 시멘트 복합체의 파괴시 소산되는 에너지와 균열의 프랙탈 차원과의 관계를 알아보는데 있다. 시멘트 복합체의 파괴실험을 실시하여 파괴에너지를 측정한 후, 파괴시 형성된 균열형상의 프랙탈 차원을 박스계수법을 통해 산정하고 그 관계를 알아보았다. 실험결과 프랙탈 차원과 파괴에너지의 관계는 비례관계를 나타냈으며 파괴에너지에 대한 프랙탈 차원의 정량적 평가가 가능하다고 사료된다.

• 한국해양학회지
• /
• 제29권3호
• /
• pp.228-238
• /
• 1994

제4기 동안에 일어난 해수면 변화는 지역적 그리고 나아가 전 지구 기후변화에 좋 은 지시자가 되고 있다. 세계 해수면은 제 4기 동안 매우 불규칙하게 변해왔는데 여기 에 대한 정밀한 수학적 접근은 어려운 실정이었다. 이 연구에서 처음으로 세계 해수면 변동자료에 확율 프랙탈을 적용하여 제4기 해수면 변동을 재구성 하였다. 미국 대서양 연안에 위치한 허드슨만과 델라웨어 해안의 홀로세 해수면 변화에 대한 프랙탈 차원을 상자 계산 방법으로 측정한 결과, 허드슨만 해수면 분노는 프랙탈 차원이 1,358이고 델라웨어 해수면 변화는 1,346이다. 프랙탈 내삽함수의 역산 방법 (IFIF)의 유효성이 허드슨만과 델라웨어 해수면의 내삽에 의해서 검증되었고, IFIF에 의해서 두지역에서 의 합리적인 해수면들이 복원되었다. 델라웨어 해수면 자료는 허드슨 해수면 자료보다 IFIF의 내삽에 대해 통계적 오차가 적게 나타나는데, 이는 델라웨어 해수면 자료가 허 드슨 자료보다 더 신빙성이 높다는 것을 의미한다. IFIF는 한국 해안의 해수면을 추정 하는 데도 이용되었는데, 한국 해안의 해수면 자료는 허드슨만이나 델라웨어 지역보다 자료가 충분치 못하다. 따라서 IFIF 의 적용 통계 오차가 적은 텔라웨어 해수면 자료 에서 구한 프랙탈 차원을 사용하여 한국 해안에 대한 IFIF의 수직 비율 인자를 계산하 였다.함수(FIF)를 한국 해안과 미국 대서양 연안의 고해수면의 재구성에 적용한 결과,한국의 고해수면은 미국의 고해수면과 다른 변화를 보였다.8000년 전부터 현재까지 두지역의 해수면은 비교해 보면 한국 해수면이 미국 해수면 보다 훨씬 높았다.