## 1 Introduction  
The development of skeletal anchorage has gradually expanded the scope of non-surgical orthodontic treatment. Biomechanics using skeletal anchorages can create various lines of action by adjusting the placement site of temporary anchorage devices and the application point of force. Doing this enables precise tooth movement while minimizing undesirable tooth movement. However, it is difficult to achieve teeth movement beyond the anatomical limits, and excessive teeth movement can increase the risk of side effects such as root resorption [1]. Therefore, it is still crucial to know the anatomical limits of tooth movement to achieve a treatment goal.  
Unlike the U-shaped mandibular dental arch, the mandibular basal bone has a V-shape with its width increasing posteriorly. Therefore, the posterior mandibular roots become closer to the mandibular lingual cortical bone in the posterior region [2; 3; 4]. Despite the proximity of the posterior mandibular roots to the lingual cortical bone, the anatomical limit of posterior movement was thought to be the mandibular ramus [5; 6]. This is because the interference between the roots and lingual cortical bone cannot be confirmed in a two-dimensional image. However, recent studies using three-dimensional computed tomography showed that posterior movement of mandibular teeth was limited by the lingual cortical bone, not the mandibular ramus [2].  
The lingual cortical bone of the posterior mandible contains a mylohyoid line to which the mylohyoid is attached and a fossa for the submandibular gland in the posterior part. The shape of the alveolar bone, the mylohyoid line, and the submandibular fossa differ between individuals. Unfortunately, some may have insufficient space for tooth movement [7; 8; 9; 10]. Additionally, the intrusion force applied on the buccal side can cause the mandibular molar roots to move lingually. When the mandibular molar roots and the lingual cortical bone are in contact, distal or intrusive movement of the mandibular posterior teeth may be even more difficult. Information on the buccolingual distance between the mandibular molar roots and lingual cortical bone is currently limited. Most previous studies on the relationship between the mandibular molar roots and lingual cortical bone focused on the limits of the posterior movement of the posterior teeth and measured the anteroposterior distance between the roots of the second mandibular molar and lingual cortical bone [2; 11; 12; 13].  
The shape of the jaw, thickness of the cortical bone, and buccolingual inclination of the teeth differ according to the vertical facial patterns [14; 15; 16; 17; 18]. As those with a hyperdivergent facial type have a narrow buccolingual width of the mandible and no differences in the buccolingual inclination of the posterior mandibular teeth, we hypothesized that the proximity of the mandibular molar roots and lingual cortical bone would differ according to the vertical facial pattern.  
Therefore, we compared the distance and contact ratio between the mandibular molar roots and lingual cortical bone in young adults with various vertical facial patterns using cone-beam computed tomography (CBCT). Additionally, the relationship between variables and root-lingual cortical bone contact was evaluated.