• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.461-477
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• 2016

This work considers a particular type of swept surface named canal surfaces in Euclidean 3-space. For such a kind of surfaces, some interesting and important relations about the Gaussian curvature, the mean curvature and the second Gaussian curvature are found. Based on these relations, some canal surfaces are characterized.

• Restorative Dentistry and Endodontics
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• v.28 no.1
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• pp.41-49
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• 2003

There are increasing usage of Nickel-Titanium rotary files in modern clinical endodontic treatment because it is effective and faster than hand filing due to reduced step. This study was conducted to evaluate the effect of canal preparations using 3 different rotary Nickel-Titanium files that has different cross sectional shape and taper on the maintenance of canal curvature. Simulated resin block were instrumented with Profile(Dentsply, USA), GT rotary files(Dentsply, USA), Hero 642(Micro-Mega France), and Pro-Taper(Dentsply, USA). The image of Pre-instrumentation and Post-instrumentation were acquired using digital camera and overspreaded in the computer. Then the total differences of canal diameter, deviation at the outer portion of curvature, deviation at the inner portion of curvature, movement of center of the canal and the centering ratio at the pre-determined level from the apex were measured. Results were statistically analyzed by means of ANOVA, followed by Scheffe test at a significance level of 0.05. The results were as follows； 1. Deviation at the outer portion of curvature, deviation at the inner portion of curvature were showed largest in Pro-Taper so also did in the total differences of canal diameter(p＜0.05). 2. All the groups showed movements of center Profile combined with GT rotary files and Hero 642 has no difference but Pro-Taper showed the most deviation(p＜0.05). 3. At the 1, 2, 3mm level from the apex movements of center directed toward the outer portion of curvature, but in 4, 5 mm level directed toward the inner portion of curvature(p＜0.05). As a results of this study, it could be concluded that combined use of other Nickel-Titanium rotary files is strongly recommended when use Pro-Taper file because it could be remove too much canal structure and also made more deviation of canal curvature than others.

• Restorative Dentistry and Endodontics
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• v.24 no.4
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• pp.623-627
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• 1999

During canal instrumentation of a curved canal, restoring force of endodontic instrument remove more dentin from the inner wall of the curvature. This effect tends to straighten the canal and thus may significantly shorten the working length. This study was to determine the mean reduction in working length after instrumentation according to the curvature. The curvature of mandibular mesial root was determined before instrumentation. 30 canals were divided into 3 groups each 10 on the basis of degree of curvature. Experimental groups as follows. In group 1, canals having curvature from 15 to 20 degrees: in group 2, canals having curvature from 20 to 30degrees; in group 3, canals having curvature above 30 degrees. Experimental teeth in all groups were accessed, and their actual working length determined by passing a size 15 K-file(IAF) just through the minor apical foramen. The canals were sequentially enlarged to size 35 with ProFile .06 series. The change of working length was calculated by measuring the tip of IAF beyond apical foramen by using stereomicroscope. The change of canal curvature following instrumentation were measured using the Schneider technique. The results were as follows. 1. The greatest changes of curvature and working length were observed in the group 3 canals(P<0.05), next were group 2 canals and group 1 canals(P>0.05). 2. Group 1 canals showed a mean reduction in 1.61 degrees and length of 0.12m respectively(P>0.05). 3. Group 2 canals showed a mean reduction in 3.42 degrees(P<0.05) and length of 0.25mm(P>0.05) respectively. 4. Group 3 canals showed a mean reduction in 7.23 degrees(<0.05) and length of 0.64mm respectively(P<0.05).

• Proceedings of the KACD Conference
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• 2003.11a
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• pp.595-595
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• 2003

I. Objectives This study was done to evaluate which type of Ni-Ti instrument be able to perform canal shape well in the simulated canal with abrupt curvature near it's apex. II. Materials and Methods A total of 96 simulated root canals were made in epoxy resin(EPOXICURETM, BUEHLER, USA), ＃15 finger spreader (MANI, Japan) were used as root canal templates. The simulated root canal were made with radius of curvature of 1.5 mm, 3.0 mm, 4.0 mm, 6.0 mm respectively, and angle of curvature of all simulate camals was 90 degree.(omitted)

• Restorative Dentistry and Endodontics
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• v.22 no.1
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• pp.220-227
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• 1997

The purpose of our study is to evaluate the ability of nickel-titanium(NiTi) files in maintaining the original curvature of a curved root canal during canal preparation. Curved canals on translucent resin blocks were prepared with NiTi and stainless steel files, and they were placed at the platform which can reproduce the same position. The unprepared and prepared canal forms were accurately compared by double exposure technique of photography. By finite element methods we also analyzed stress distributions of NiTi and stainless steel files in a curved canal. The results were as follows : 1. NiTi files were excellent in maintaining the original curvature of a curved canal than stainless steel files after canal preparation. 2. The results of canal preparation with these files were well verified by the analysis of stress distributions using finite element methods.

• Imaging Science in Dentistry
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• v.45 no.4
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• pp.221-226
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• 2015

Purpose: This study evaluated the prevalence of distolingual roots in mandibular molars among Koreans, the root canal system associated with distolingual roots, and the concurrent appearance of a distolingual root in the mandibular first molar and a C-shaped canal in the mandibular second molar. Materials and Methods: Cone-beam computed tomographic images of 264 patients were screened and examined. Axial sections of 1056 mandibular molars were evaluated to determine the number of roots. The interorifice distances from the distolingual canal to the distobuccal canal were also estimated. Using an image analysis program, the root canal curvature was calculated. Pearson's chi-square test, the paired t-test, one-way analysis of variance, and post-hoc analysis were performed. Results: Distolingual roots were observed in 26.1% of the subjects. In cases where a distolingual root was observed in the mandibular molar, a significant difference was observed in the root canal curvature between the buccolingual and mesiodistal orientations. The maximum root canal curvature was most commonly observed in the mesiodistal orientation in the coronal portion, but in the apical portion, maximum root canal curvature was most often observed in the buccolingual orientation. Conclusion: The canal curvature of distolingual roots was found to be very complex, with a different direction in each portion. No correlation was found between the presence of a distolingual root in the mandibular first molar and the presence of a C-shaped canal in the mandibular second molar.

• The Journal of the Korean dental association
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• v.47 no.7
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• pp.435-443
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• 2009

The purpose of this study was to compare the centering ratio and reduction of canal curvature according to the preparation sizes of #30, #40 and #50 using three rotary NiTi instruments which have different shaft tapers. Seventy-two simulated root canals in clear resin blocks (Endo Training Bloc; Dentsply Maillefer, Ballaigues, Switzerland) were divided as following 3 groups according to the file system; the 24 canal blocks prepared with each of ProTaper Universal system (Group P), LightSpeed eXtra system (Group L), and K3 (Group K). The pre- and post-instrumented root canals were scanned and superimposed to evaluate and calculate the centering ratio and reduction of canal curvature. Mean scores of each group were statistically analyzed using one-way ANOV A and Duncan's multiple range test for post-hoc comparison. The results were as followings: 1. Group L showed better centering ratio, followed by K and P. And all experimental groups generally showed increasing tendency of centering ratio as the apical size was increasing from #30 to #50, except at 1 mm level of group P where showed reducing tendency of centering ratio. The smaller the ratio, the better the instrument remained centered in the canal. 2. Group P showed more decrease of canal curvature at all apical shaping size (p < 0.05). Under the conditions of this study, the shaft design could affect the quality of canal shaping and the smooth taperless flexible (LightSpeed) shaft design was capable of preparing canals with good morphological characteristics in curved canals.

• Restorative Dentistry and Endodontics
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• v.37 no.2
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• pp.104-109
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• 2012

Objectives: The purpose of this study was to evaluate the buccolingual curvature at the apical one third in type II mesial canals of mandibular molars using the radius and angle of curvature. Materials and Methods: Total 100 mandibular molars were selected. Following an endodontic access in the teeth, their distal roots were removed. #15 H- or K-files (Dentsply Maillefer) were inserted into the mesiobuccal and mesiolingual canals of the teeth. Radiographs of the teeth were taken for the proximal view. Among them, type II canals were selected and divided into two subgroups, IIa and IIb. In type IIa, two separate canals merged into one canal before reaching the apex and in type IIb, two separate canals merged into one canal within the apical foramen. The radius and angle of curvature of specimens were examined. Results: In type II, mean radius of curvature in mesiolingual and mesiobuccal canals were 2.82 mm and 3.58 mm, respectively. The radius of the curvature of mesiolingual canals were significantly smaller than that of mesiobuccal canals in type II, and especially in type IIa. However, there were no statistically significant differences in radius of curvature between mesiobuccal and mesiolingual canals in type IIb and there were no significant differences in angle of curvature between type IIa and IIb. Conclusion: In this study, type II mesial canals of mandibular molars showed severe curvature in the proximal view. Especially, mesiolingual canals of type IIa had more abrupt curvature than mesiobuccal canals at the apical one third.

• Restorative Dentistry and Endodontics
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• v.22 no.1
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• pp.291-304
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• 1997

The purposes of this study were to evaluate the changes in root canal configuration with canal instrumentation using different file types and techniques and to investigate most appropriate instrumentation technique in maintaining the original canal configuration with different file types. Fifty curved mesiobuccal or distobuccal canals of extracted human maxillary molar teeth were instrumented using a step-back technique with stainless steel K-files or nickel-titanium K-files, a crown-down pressureless technique with stainless steel K-files or nickel-titanium K-files and nickel-titanium engine-driven files. Radiographs were taken before and after instrumentation using a specially designed device that allowed for the pre-and postinstrumentation canals to be taken with the same X-ray angulation. Magnified X-ray images on a magnifier screen were traced and post instrumentation canal images were compared with the preinstrumentation ones. Changes in canal curvature and the incidence of procedural accidents were analyzed. The results were as follows : Crown-down pressureless technique with nickel-titanium K-files and nickel-titanium engine-driven filing produced no significant changes in canal curvature (p>0.05), while the step-back technique with stainless steel K-files or nickel-titanium K-files (p<0.01) and the crown-down pressureless technique with stainless steel K-files (p<0.05) produced significant changes. With nickel-titanium K-file, crown-down pressureless technique produced significantly less changes in canal curvature than step-back technique (p<0.05), while there was no significant difference between techniques with stainless steel K-files (p>0.05). File types exerted no significant influences in the changes of canal curvature both in the step-back technique and crown-down pressureless technique (0>0.05). Regardless of the file types used, step-back technique produced more procedural accidents such as ledge or elbow formation, apical zipping and apical transportation than the crowndown pressureless technique and nickel-titanium engine-driven filing. Both with stainless steel K-files and with nickel-titanium K-files, the incidence of apical extrusion of canal debris was higher in step-back technique than in crown-down pressureless technique.

• Restorative Dentistry and Endodontics
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• v.22 no.1
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• pp.388-395
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• 1997

Maintaining the original canal path during instrumentation is a challenge in narrow curved canals. This study compared the maintenance of the original canal path of curved root canals during instrumentation with two kinds of stainless steel K-files(Brassler USA & Mani Japan), K-flexofiles(Maillefer Swiss) and Ni-Ti files(Brassler USA, Savannah, GA) using circumferential filing technique to # 40 MAF on 60 extracted human molars. Buccal and mesial canals with minimal initial curvature of 20 degrees were used. The maximal initial curvature was 41.5 degrees. Sixty curved canals divided into four groups according to file type(Group 1 : Ni-Ti file, Group 2 : K-flexofile, Group 3: K-file(Brassler), Group 4 : K-file(Mani)). Radiographs of canals were obtained before and after canal shaping. And postoperative radiographs were compared with preoperative radiographs using superimposition method. Data analysis was performed using Covariance analysis and paired-comparison test. The results observed were as follow ; 1. The angle of curvature was better maintained with Ni-Ti file than with stainless steel files. (p<0.01) 2. There was no significant difference in maintaining canal curvature between K-flexofile, Brassler$^{(R)}$ K-file and Mani$^{(R)}$ K-file, although there was some differences in mean values of postoperative canal curvature. 3. Paired-comparison t test revealed significant differences within each of the three stainless steel file types when comparing the mean differences before and after instrumentation, but no significant differences were observed within Ni-Ti file group.