Piecewise straight line approximation of curve existing in slightly curved mesiobuccal root canal of mandibular first molar: a radiographic investigation / Aproximación a segmentos de línea recta en la curva existente del canal radicular mesiobucal ligeramente curvado del primer molar inferior: una investigación radiográfica

The aim of this study was to radiographically investigate the curve existing in slightly curved mesiobuccal canal of mandibular first molar by applying Piecewise straight line approximation. Extracted human mandibular molars were radiographed and one hundred radiographs were selected whose mesiobuccal canal showed slight curvature (10-20°) according to Schneider's method. The curves were traced and analyzed using Piecewise straight line method. Each curve was considered as a unit consisting of six different pieces of straight lines joining at seven specific points and the angle of curvature at these points was determined using the slope formula. All curves analyzed in this study had varying degrees of curvatures at different points on the curve. Maximum curvature (0.40°) was recorded at the middle third of the root canal. Within the limitation of the study, significant curvature occurs through out the curve existing in the mesiobuccal canal of mandibular first molar and the middle third of the curve showing greater degree of curvature. There is a possibility of greater curvature occurring in the coronal third of the curve. Though three dimensional studies would be more appropriate, Piecewise straight line approximation may be a better method than existing methods to simulate canal geometry.

El objetivo de este estudio fue investigar radiográficamente la curva existente en el canal radicular mesiobucal ligeramente curvado del primer molar inferior mediante la aplicación de aproximaciones a segmentos de línea recta. Se utilizaron molares inferiores humanos extraídos que fueron radiografiados. Fueron seleccionadas, según el método de Schneider, 100 radiografías cuyo canal mesiobucal mostró una ligera curvatura (10-20°). Las curvas fueron delineadas y analizadas mediante el método de aproximación a segmentos de línea recta. Cada curva se consideró como una unidad que consta de seis diferentes segmentos de línea recta que unen a siete puntos específicos y el ángulo de curvatura en estos puntos se determinó utilizando la fórmula de la pendiente. Todas las curvas analizadas en este estudio tenían diversos grados de curvaturas en diferentes puntos de la curva. La curvatura máxima (0,40°) se registró en el tercio medio del canal radicular. Dentro de la limitación del estudio, una curvatura significativa se produce a través de la curva existente en el canal mesiobucal del primer molar inferior y el tercio medio de la curva que muestra un mayor grado de curvatura. Existe la posibilidad que ocurra una mayor curvatura en el tercio coronal de la curva. Aunque un estudio tridimensional sería más apropiado, la aproximación a segmentos de línea recta puede ser un mejor método que los existentes para simular la geometría del canal.

An evaluation of canal curvature at the apical one third in type II mesial canals of mandibular molars

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.