## 4 Discussion
### Correlation of Iteration Time with Real Clinical Time  
By implementing previously outlined methodology (Figure 2) and integrating key parameters from previous literature, the present model was able to establish a correlation between the presented simulated findings and the actual clinical duration required for molar uprighting. A key component of this methodology's formation was the graph presented in Figure 3, which illustrates the relationship between applied force and canine displacement velocity. Such a relationship was established utilizing data compiled from multiple clinical studies [24; 25]. The compiled data revealed that tooth movement velocities vary across studies under the same applied force. This variability arises due to differences in tooth anatomy, PDL properties, bone conditions, and experimental protocols. Despite these variations, the black curve represents an average trend rather than a single dataset and includes a broad range of clinical observations, making it a valuable reference for estimating orthodontic tooth movement under varying conditions. Model 1 simulation was conducted under retraction loads ranging from 10 to 800 cN, incorporating carefully selected material assumptions, property values, model interactions, and boundary conditions to ensure consistency with real clinical conditions. These considerations enhance confidence in the robustness of the current FE approach and its outputs. A key outcome of this process was the introduction of a novel technique that directly translates computational iterations into real clinical time, based on the PDL's biomechanical response and bone remodeling velocity (Figure 7). Bone remodeling is driven by fundamental biological responses to mechanical loading, and these processes are not strictly limited to a specific tooth type [10]. For this reason, authors used data from canine retraction studies as an appropriate reference to aid in estimating treatment timelines in the present molar uprighting model. One key advantage of using canine retraction data for time calibration is that they are derived from controlled clinical studies in which a constant orthod \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Clinical** \\ **Week** \\ \end{tabular} } & \begin{tabular}{c} **Molar** \\ **Uprighting** \\ **Angle (°)** \\ \end{tabular} & \begin{tabular}{c} **Molar** \\ **Vertical** \\ **Extrusion** \\ **(mm)** \\ \end{tabular} & \begin{tabular}{c} **Uprighting** \\ **Moment** \\ **(N\(\cdot\)mm)** \\ \end{tabular} & \
\begin{tabular}{c} **Extrusion** \\ **Force (N)** \\ \end{tabular} &
\begin{tabular}{c} **Second** \\ **Premolar** \\ **Intrusion** \\ **(mm)** \\ \end{tabular} \\ \hline Week 0 & 0.32 & 0.04 & 14.6 & 0.6 & 0.002 \\ Week 2 & 3.9 & 0.49 & 12.6 & 0.52 & 0.009 \\ Week 4 & 8.06 & 0.94 & 9.98 & 0.42 & 0.133 \\ Week 6 & 12.09 & 1.35 & 7.63 & 0.32 & 0.196 \\ Week 8 & 15.89 & 1.68 & 5.6 & 0.24 & 0.262 \\ Week 10 & 19.55 & 1.96 & 3.53 & 0.15 & 0.328 \\ Week 12 & 21.9 & 2.13 & 2.12 & 0.09 & 0.374 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Estimated clinical progression of mandibular second molar uprighting using a conventional uprighting spring based on FE simulation results. resulting in a relatively steady tooth movement velocity. This predictable behavior provides a reliable reference for interpreting displacement in study's simulation. In the FE model, the normal displacement at the PDL-root interface--driven by tooth movement--is transmitted to the PDL--bone interface, as the ligament naturally attempts to restore its original uniform thickness. Importantly, this normal displacement is directly proportional to the local mean stress in the ligament, which serves as the primary mechanical stimulus for bone remodeling. By correlating this stress-driven displacement with the known velocity of canine movement, bone remodeling rates can be estimated and iteration count can be converted into a biologically meaningful clinical timeframe.