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Background  Before extracting impacted lower third molars, dentists must first identify the spatial relationship between the inferior alveolar nerve (IAN) and an impacted lower third molar to prevent nerve injury from the extraction. Nevertheless, the current method for describing the spatial relationship between the IAN and an impacted lower third molar is deficient. Therefore, the objectives of this study were to: (1) evaluate the relative position between impacted lower third molars and the IAN; and (2) investigate the relative position between impacted lower third molars and the IAN by using a cylindrical coordinate system.    Methods  From the radiology department’s database, we selected computed tomography images of 137 lower third molars (from 75 patients) requiring removal and applied a Cartesian coordinate system by using Mimics, a medical imaging software application, to measure the distribution between impacted mandibular third molars and the IAN. In addition, the orientation of the lower third molar to the IAN was also measured, but by using a cylindrical coordinate system with the IAN as the origin.    Results  According to the Cartesian coordinate system, most of the IAN runs through the inferior side of the third molar (78.6 %), followed by the lingual side (11.8 %), and the buccal side (8.9 %); only 0.7 % is positioned between the roots. Unlike the Cartesian coordinate system, the cylindrical coordinate system clearly identified the relative position,  r  and  θ , between the IAN and lower third molar.    Conclusions  Using the cylindrical coordinate system to present the relationship between the IAN and lower third molar as ( r ,  θ ) might provide clinical practitioners with a more explicit and objective description of the relative position of both sites. However, comprehensive research and cautious application of this system remain necessary.

New quantitative classification of the anatomical relationship between impacted third molars and the inferior alveolar nerve