## 3 Results  
The range of motion (ROM) of the L3-L4 lumbar model was obtained for all models when moved in flexion, extension, axial rotation, and lateral bending (Table 3). The distance between facet joints (FJ gap) was calculated as a percentage change from the intact model. The results from models c and d show that aggressive PTED reduced the stability of the spine and narrowed the FJ gap in the medial/lateral (ML) direction during flexion (maximum 6.7 degrees and 90.5%), extension (maximum 2.1 degrees and 38.6%), and axial rotation (maximum 4.2 degrees and 90.1%). Aggressive PTED also affected the stability and reduced the FJ gap in the anterior/posterior (AP) direction during lateral bending (maximum 2.0 degrees and 44.2%). Conservative PTED (model b) had a lesser effect on the range of motion and spacing between facet joints. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Body Position** & \multicolumn{4}{c}{**Flexion**} \\ \hline \multicolumn{5}{c}{**ROM about the**} \\ \hline \hline  & **x-Axis (Degree), ML** & **y-Axis (Degree), AP** & **z-Axis (Degree)** & **FJ Gap \({}^{*}\)** \\  & **Direction [\% *]** & **Direction [\% *]** & **Direction [\% *]** & **Direction [\% *]** & **FJ Gap \({}^{*}\)** \\ \hline model a (intact) & \(-0.7\) & \(3.6\) & \(0.0\) & \(-\) \\  & [undefined] & \([-21.7\%]\) & \([0\%]\) & \(-\) \\ model b (conservative) & \(-6.7\) & \(5.1\) & \(0.0\) & \(-11.5\%\) \\  & [undefined] & \([10.9\%]\) & \([0\%]\) & \(-90.5\%\) \\ model c (aggressive) & \(-6.7\) & \(5.1\) & \(0.0\) & \(-90.5\%\) \\  & [undefined] & \([10.9\%]\) & \([0\%]\) & \(-90.5\%\) \\ model d (aggressive & \(1.1\) & \(3.4\) & \(0.2\) & \(-89.4\%\) \\  & [undefined] & \([-26.1\%]\) & [undefined] & \(-89.4\%\) \\  & \(-4.5\) & \(4.6\) & \(0.3\) & \(-40.5\%\) \\ model e (FU) & [undefined] & \([0\%]\) & [undefined] & \(-40.5\%\) \\  & \(-0.7\) & \(3.6\) & \(0.0\) & \(-73.1\%\) \\  & [undefined] & \([-21.7\%]\) & \([0\%]\) & \(-73.1\%\) \\ \hline \hline
**Body Position** & \multicolumn{4}{c}{**Extension**} \\ \hline \hline  & **x-Axis (Degree), ML** & **y-Axis (Degree), AP** & **z-Axis (Degree)** & **FJ Gap \({}^{*}\)** \\  & **Direction [\% *]** & **Direction [\% *]** & **Direction [\% *]** & **Direction [\% *]** & **Direction [\% *]** \\ \hline model a (intact) & \(0.0\) & \(-2.4\) & \(0.0\) & \(-\) \\ model b (conservative) & \(-0.5\) & \(-1.3\) & \(0.0\) & \(-13.1\%\) \\  & [undefined] & \([45.8\%]\) & \([0\%]\) & \(-13.1\%\) \\ model c (aggressive) & \(-2.1\) & \(-2.1\) & \(0.0\) & \(-38.6\%\) \\ model d (aggressive) & \(-2.1\) & \(-2.0\) & \(0.0\) & \(-37.8\%\) \\ with annular repair) & [undefined] & \([16.7\%]\) & \([0\%]\) & \(-37.8\%\) \\  & 0.9 & \(-1.4\) & \(0.2\) & \(-48.0\%\) \\  & [undefined] & \([41.7\%]\) & [undefined] & \(-48.0\%\) \\  & \(-1.5\) & \(-1.8\) & \(0.3\) & \(-50.5\%\) \\  & [undefined] & \([25\%]\) & [undefined] & \(-50.5\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: ROM and FJ gap in each model when moved through different motions. Figure 3: Method to determining the ROM (\(\theta\) represents the ROM). Following PU augmentation after aggressive PTED (models d and e), the spine was more stable in the ML and AP directions than in models c and d, with the results being close to the intact model. However, augmenting the nucleus with hydrogel did not have the same effect, and there was little difference from the PTED-only models. Figure 4 shows the change in height of the intervertebral disc as a percentage of the intact model (model a, INT) at the anterior (A), lateral medial (M), and posterior (P) regions of the disc. Both conservative and aggressive PTED reduced the disc height on the lateral medial side of the disc in all motions. In flexion, PU augmentation increased the disc height on the anterior and lateral medial side (increased 27.7% and 97.4% as compared to INT), but this result was not replicated with the hydrogel, which caused an almost fivefold reduction in disc height from the intact model.