## 3 Results
### Radiological Evaluation Results  
The radiological evaluation results are summarized in Table 3. On the day of implant placement and GBR, the average BA was 3.7 \(\pm\) 1.1 mm; it increased by 4.3 \(\pm\) 1.4 mm in Group 1, 3.7 \(\pm\) 1.0 mm in Group 2, and 3.6 \(\pm\) 1.0 mm in Group 3. There were no statistically significant differences among the amounts of augmentation in the groups (\(p\) > 0.05). The average HG at 6 months after implant placement was 3.1 \(\pm\) 1.3 mm; it was 3.2 \(\pm\) 1.7 mm in Group 1, 3.1 \(\pm\) 1.2 mm in Group 2, and 3.0 \(\pm\) 1.2 mm in Group 3. There was no statistically significant difference between the newly formed hard tissue masses of the groups (\(p\) > 0.05). The overall average BR was 0.7 \(\pm\) 0.9 mm: Group 1: 1.1 \(\pm\) 0.7 mm; Group 2: 0.6 \(\pm\) 1.0 mm; Group 3: 0.6 \(\pm\) 0.8 mm. The overall HGR (HG/BA) was 82.4 \(\pm\) 22.4%; HGR was 71.0 \(\pm\) 23.1% in Group 1, 84.2 \(\pm\) 21.5% in Group 2, and 84.0 \(\pm\) 22.9% in Group 3. Groups 2 and 3 showed significantly higher hard tissue gain rates than Group 1 (all \(p\) < 0.05). However, there was no statistically significant difference between the hard tissue gain rates of groups 2 and 3 (\(p\) > 0.05) (Figure 3).  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **Group 1** & **Group 2** & **Group 3** & **Total** \\ \hline N of sites & 17 & 72 & 40 & 129 \\ ISQ, Mean \(\pm\) SD & 78.9 \(\pm\) 3.8 & 79.9 \(\pm\) 6.8 & 77.0 \(\pm\) 7.4 & 79.0 \(\pm\) 6.7 \\ Mesh exposure, N & 2 & 3 & 2 & 7 \\ Mesh exposure, (\%) & 11.8 & 4.2 & 5.0 & 5.4 \\ Survival rate of implant (\%) & 100 & 100 & 100 & 100 \\ \hline N, number; SD, standard deviation; ISQ, implant stability quotient; Group 1, only three-dimensional preformed titanium mesh (3-D-PFTM) used; Group 2, 3-D-PFTM + cross-linked collagen membrane used; Group 3, 3-D-PFTM + non-cross-linked collagen membrane used. & \\ \end{tabular}
\end{table}
Table 2: Clinical evaluation of the ISQ value, mesh exposure, and survival rate of implants in the groups.  
\begin{table}
\begin{tabular}{c c c c} \hline  & **Group 1** & **Group 2** & **Group 3** & **Total** \\ \hline BA (mean \(\pm\) SD) & 4.3 \(\pm\) 1.4 & 3.7 \(\pm\) 1.0 & 3.6 \(\pm\) 1.0 & 3.7 \(\pm\) 1.1 \\ \hline \(p\)-value & \multicolumn{3}{c}{0.187} \\ \hline HG (mean \(\pm\) SD) & 3.2 \(\pm\) 1.7 & 3.1 \(\pm\) 1.2 & 3.0 \(\pm\) 1.2 & 3.1 \(\pm\) 1.3 \\ \hline \(p\)-value & \multicolumn{3}{c}{0.960} \\ \hline BR (mean \(\pm\) SD) & 1.1 \(\pm\) 0.7 & 0.6 \(\pm\) 1.0 & 0.6 \(\pm\) 0.8 & 0.7 \(\pm\) 0.9 \\ \hline \multirow{3}{*}{\(p\)-value} & 0.006 \({}^{\star}\) & 0.006 \({}^{\star}\) & 0.007 \({}^{\star}\) \\  & (vs. Group 2) & (vs. Group 1) & (vs. Group 1) \\ \cline{1-1}  & 0.007 \({}^{\star}\) & 0.52 & 0.52 \\ \cline{1-1}  & (vs. Group 3) & (vs. Group 3) & (vs. Group 2) \\ \hline HGR (mean \(\pm\) SD) & \multirow{2}{*}{71.0 \(\pm\) 23.1} & \multirow{2}{*}{84.2 \(\pm\) 21.5} & \multirow{2}{*}{84.0 \(\pm\) 22.9} & \multirow{2}{*}{82.4 \(\pm\) 22.4} \\ (\%) & & & & \\ \hline \multirow{3}{*}{\(p\)-value} & 0.007 \({}^{\star}\) & 0.007 \({}^{\star}\) & 0.013 \({}^{\star}\) \\  & (vs. Group 2) & (vs. Group 1) & (vs. Group 1) \\ \cline{1-1}  & 0.013 \({}^{\star}\) & 0.528 & 0.528 \\ \cline{1-1}  & (vs. Group 3) & (vs. Group 3) & (vs. Group 2) \\ \hline \end{tabular} SD, standard deviation; BA, bone augmentation immediately after surgery; HG, hard tissue gain after 6 months of healing; BR, bone graft resorption (BA-HG); HGR, the percentage of HG compared with BA (HG/BA); Group 1, only three-dimensional preformed titanium mesh (3-D-PFTM); Group 2, 3-D-PFTM + cross-linked collagen membrane used; Group 3, 3-D-PFTM + non-cross-linked collagen membrane used. \({}^{\star}\) Statistically significant difference (\(p\) < 0.05; Kruskal–Wallis test).  
\end{table}
Table 3: Radiological assessment of the BA, HG, BR and HGR of the groups.