# Curve of Spee and Second Mandibular Premolar Agenesis--Present Knowledge and Future Perspectives
## 1 Introduction  
The Curve of Spee (COS) is a naturally occurring concave mandibular and convex maxillary line (i.e., compensating curve), and should in continuation be directly related to the anterior border of the jaw condyle. It was first described by [PERSON] in 1890 [1]. Today, the COS is an important reference plane for occlusion in the field of Orthodontics; it is defined clinically as a sagittal occlusal line between the incisal edges of permanent mandibular incisors and the buccal cusp tips of the molar teeth [2]. With permanent incisor and mandibular first molar eruption, the COS develops and deepens when the second mandibular molar erupts [3]. Despite the relation to tooth eruption, underlying mechanisms of the curve's formation and maintenance remain unknown. With the six keys of occlusion, [PERSON] [4] stated in 1972 that the presence of a deep COS is associated with post orthodontic treatment relapse, concluding a flat plane as treatment goal in the field of Orthodontics. The functional significance of the COS consecutively considers importance for maintenance of maximum tooth contacts during mastication [5], and further initiates a protrusive contact of the incisors without tooth interferences in the posterior section [6]. Taken together, a physiological COS is required for an efficient masticatory system [7]. Its proper management is critical for the construction of stable complete dentures, both in Dentistry andOrthodontics [3; 4; 8]. In complete denture prosthodontics, establishing a COS in harmony with the condylar guidance, incisal guidance, plane of occlusion, and prosthetic tooth cusp height is essential for developing a bilaterally balanced articulation, believed to maintain optimal denture stability [3]. It might also play a role in the success of implant-supported restorations [3; 9]. Especially in the field of Orthodontics, the COS is an important diagnostic tool for treatment planning. Since [PERSON] proposed the flattening of the occlusal plane as a treatment goal, COS levelling is an everyday practice in orthodontic offices. Few studies suggested that levelling the COS leads to a prolonged dental arch, indicating a relationship between arch length and amount of levelling [10; 11]. Otherwise, [PERSON] et al. [11] disagreed, considering the lower incisors as an independent segment, which can be intruded for COS levelling without prolonging the dental arch. More recently, [PERSON] et al. [12] showed that levelling one millimetre of the COS increases mandibular arch length by 0.8 mm. In any case, depth measurement of the COS is a key part of space analysis, needed for every single planning of orthodontic patients [13]. As part of the masticatory system, the COS is likely to change individually with age or due to pathophysiological situations [7; 13]. The most prevalent craniofacial malformation in humans is tooth agenesis [14]. Except the third molars, mandibular second premolars and maxillary lateral incisors are most likely to be missing [15]. The prevalence of a missing lower second premolar is about 3% [16; 17]. For the second mandibular premolar, a unilateral agenesis was reported to occur more often [17]. Without a normal root resorption, the deciduous teeth may stay up to 40 or 50 years [18]. Hypodontia patients present dentofacial changes, such as a smaller lower anterior face hight [19] and angle-class III tendency [20]. Taking this into consideration, it can be hypothesised that the presence of a persisting primary second mandibular molar (ppM2), due to the agenesis of the second mandibular premolar, has an influence on the COS depth as well. The understanding of the COS and its consequences for patients' orthodontic therapy is very important and may lead to individualized treatment planning. The aim of the study was to compare the depth of the COS between patients with a ppM2 due to an agenesis of the second mandibular premolar and patients with no agenesis. Further, a potential association between COS depth and age, gender, and angle-classification should be disclosed.