## 1 Introduction  
Regenerative endodontics is a relatively new treatment aimed at regenerating the pulp-dentine complex after pulp necrosis in immature teeth [1]. Until very recently the standard treatment for such teeth was apexification. However, the latter did not allow further root development or revascularisation of the tooth, which remained with thin and short dentine walls [2]. Regenerative endodontics consists of a new cell-based approach and utilises the stem cells located at the periapical tissues that invade the root canal after over-instrumentation of the apex [3], and the growth factors present in the dentine are able to direct stem cell proliferation, migration and differentiation [4], with the final aim of revitalising and inducing further root development of the necrotic tooth. Regenerative endodontics is considered a successful clinical treatment since most teeth show further root development, healing of periapical lesions and resolution of symptomatology [5]. However, with the exception of occasional studies [6], regeneration of the pulp-dentine complex hasnot been observed in vivo. Thus, the posttreatment development of the root is due to the apposition of cementum-like tissue or osteedentine instead of tubular dentine [7; 8; 9]. Dentine is an organised and mineralised tissue with a tubuli-like structure [10] that is able to endure compressive forces, while cementum and other reparative tissues formed after regenerative endodontics have collagen fibres not packed in an orderly fashion [11] and a higher organic composition [12]. As a result, cementum has poorer mechanical properties than dentine [13]. A computational study showed that the mechanical performance of roots reinforced with cementum after regenerative endodontics have been proven to distribute the mechanical stress disadvantageously and unevenly compared to a root reinforced with dentine [14]. In teeth after regenerative endodontics, cementum barely endures stress, which is mainly concentrated in the dentine part of the root [14]. However, it is unknown whether this disadvantageous distribution of stress is transferred and maintained in the periodontal ligament and alveolar bone, producing high peaks of mechanical stress in specific parts of these tissues (i.e., in the neighbouring areas of the dentine with peak stress), or in contrast, whether the periodontal ligament is able to re-distribute the mechanical stress more evenly due to its unique biomechanical and cellular nature [15]. The performance of the periodontal ligament of teeth after regenerative endodontics has not been studied. Periodonal ligament stem cells are sensitive to mechanical loading and play a critical role in periodontal and osseous remodelling during orthodontic movement by regulating the balance between osteoblastic and osteocl activity [16]. Orthodontic tooth movement is produced by mechanical forces and promoted by the remodelling of the periodontal ligament and alveolar bone. Under appropriate stimulation, on the compression side, the periodontal ligament becomes compressed, resulting in a focal necrosis [17]. These necrotic sites release chemokines that induce the migration of multinucleated cells that resorb the necrotic periodontal ligament as well as the underlying bone and cementum [17], and this process is stopped only when mechanical stimulation ceases. Thus, appropriate orthodontic forces produce minor reversible injury to the tooth-supporting tissues [17]. However, when these forces are inappropriate, such as in the case of excessive force magnitude or adequate magnitude but with high concentration of the stress in specific areas, they lead to a sustained inflammation process that reabsorbs the root [18].