###### Abstract
For example, 2-3 weeks of resorption may require 3 months of bone formation for replacement; however, since the orthodontic movement is directed towards the resorption side, the movement rate is limited by the bone resorption rate. The mechanics of tooth movement due to these forces is of interest to the research and orthodontist communities, most of which rely on finite element methods  
Figure 1: Tooth relevant components under X-ray imaging. (FEMs) for simulation purposes (cf. [3; 11; 12; 19; 26]). A somewhat different approach is provided in [27], in which the authors suggest a simulation of the gingival surface mesh instantaneous deformation in orthodontics by the Mass-Spring mesh model, where the PDL tissue is represented by a triangular mesh of masses linked to its neighbors by springs and dumpers, yielding a set of equations that may be numerically solved. [PERSON] et al. [28] offered a numerical model based on the FEM method derived from CBCT scans coupled with intraoral scanner images. [PERSON] et al. [29] developed constitutive laws for modeling PDLs using FEM based on continuum fiber-reinforced composites theory and defined a transversely isotropic nonlinear strain energy function. Yet, note that these studies focus their attention on the intermediate stress distributions rather than the actual tooth movement, while a holistic model of tooth movement should address the remodeling process, as well. Initial attempts to address the entire OTM process was first made by [PERSON] et al. in 1999 [30]. In their paper [30], the researchers tested the now well-established assumption that deformations of the PDL are the key stimulus for orthodontic tooth movement (a similar work was provided in [31]). Later on, [PERSON] et al. [32] introduced a method that monitors every stage of treatment by means of optical impressions to correlate their FEM analysis with the clinically observed movements (cf. [33; 34]). In 2021 [PERSON] et al. assessed the effect of orthodontic load over the periodontium using the FEM approach [35]. To simulate the remodeling process in each given instant, one is required to re-mesh the alveolar bone model whenever reaching an intermediate equilibrium [3]. This approach is a time-consuming procedure, on top of requiring an enormous number of model nodes. In a more recent study [3], [PERSON] et al. aimed to overcome the time-consuming procedures by applying an image-based voxel level set method on the infinitesimally translated tooth (after remodeling) and used it as their new mesh model for their iterative procedure. Here, a fast scheme is proposed for retrieving orthodontic tooth movement, using a simplified spring model to calculate the intermediate stress distribution and the corresponding tooth movement (translation and rotation). The remodeling process, during which the developed stresses are relaxed, is also taken into consideration. This two-step process is repeated until equilibrium is reached. By employing this approach, a computer-aided design of long-term clinical treatments and their expected stress distributions at each step can be facilitated. Furthermore, relevant research studies that attempted to provide a numerical model for OTM are rarely validated against clinical data [28]; therefore, a brief clinical validation will be provided in this study.