Estimation of three-dimensional long axes of the maxillary and mandibular first molars with regression analysis

Abstract

The purpose of this study was to determine the long axes of molars with multiple roots through ordinary least squares regression (LSR) and to compare them with the axes defined by principal component analysis (PCA). Three-dimensional radiological images of 20 dry skulls were obtained by cone-beam computed tomography (CBCT). Data from maxillary and mandibular first molars were extracted from the CBCT DICOM data with a three-dimensional image visualization system. The obtained data were reconstructed, converted to STL files, and three-dimensional coordinate values were extracted. The long axes were estimated by an algorithm to synchronize the LSR line with the horizontal axis which was translated to the vertical axis. The axes of the molars defined by LSR were compared with the axes of the molars defined by PCA. The coordinate point number of each molar was 5400-5800. The algorithm for determining the tooth axes in this study consisted of four stages containing three steps each. The distance between the two axes calculated by the two methods (LSR and PCA) on the horizontal plane through the origin was less than 10 −12 mm and the deviations between them were less than 0.003°. The long axes of the molars estimated by LSR agree almost exactly with the axes estimated by PCA, and the accuracy is sufficient for clinical usage; however, the distance between them would shorten with a more severe convergence condition of the α value at each stage of this LSR system.

Three-dimensional location and distribution of the center of resistance in the maxillary first molar applied to occlusal force

“…This proves that the CRes was included in the area without accuracy, as the CRes was determined to be found by our algorithm and process as near the center of gravity. The reproducible point was determined without a relationship to the form, due to objectively estimating the axis of the first molar 14,23,24) . The CRes may be determined if the axis is estimated in molars with a moderate breakdown crown, such as in attrition and dental caries.…”

“…USA) was used for three-dimensional computer added design and finite element method. The tooth axis of the maxillary right first molar was estimated from its stereolithography data 14) , and the model moved vertically and matched it to the Z-axis. The center of gravity of the molar model was set as the origin; the X-axis and Y-axis were set in the mesiodistal and buccolingual directions, respectively, on a plane perpendicular to the Z-axis passing through the origin (Fig.…”

Automatic simulated dental implants method with implant parameter estimation based on CBCT images

“…We can also regard it as a disguised problem of determining the long axis of teeth to reduce operators' experience and improve the design efficiency and quality of surgical guide blind holes. In 2019, Terada et al . (2020) determined the long axis of multiple molars by the ordinary least squares regression method and compared it with the long axis determined by principal component analysis.…”

Emergence angle: Comprehensive analysis and machine learning prediction for clinical application

“…The long axis is defined as a theoretical line that passes through the center of any body (GPT 9). In the analog method, the long axis is created as a line connecting the midpoints of both the crown and root [22,23]. To create the tooth axis using the software, a digital disc caliper with a sufficient radius (GOM Inspect Pro 2020) was used to visualize and determine the outermost points of the tooth.…”