# Engineering and Clinical Study of Surface Geometry of Clear Aligners at the Nanoscale
## 3 Results and Discussion
### Functional Parameters
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Condition**} & \multirow{2}{*}{\(n\)} & \multirow{2}{*}{**Variable**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**Median**} & \multirow{2}{*}{**Var**} & \multirow{2}{*}{**StD**} & \multirow{2}{*}{**IQR**} & \multicolumn{2}{c}{**S–W Test**} \\  & & & & & & & \(p\) \textless{} 0.05** \\ \hline \multirow{8}{*}{REF} & \multirow{8}{*}{23} & Sk (nm) & 4.29 & 3.66 & 2.67 & 1.63 & 2.69 & 0.043 \\ \cline{3-8}  & & Spk (nm) & 2.29 & 2.07 & 0.95 & 0.97 & 1.28 & 0.017 \\ \cline{2-8}  & & Svk (nm) & 1.45 & 1.22 & 0.54 & 0.74 & 1.02 & 0.012 \\ \cline{2-8}  & & Smrk1 (\%) & 12.30 & 12.60 & 4.84 & 2.20 & 3.09 & 0.660 \\ \cline{2-8}  & & Smrk2 (\%) & 91.30 & 90.70 & 5.00 & 2.25 & 2.58 & 0.474 \\ \cline{2-8}  & & Vmp (nm\({}^{3}\)/nm\({}^{2}\)) & 0.181 & 0.129 & 0.030 & 0.172 & 0.093 & \textless{}0.001 \\ \cline{2-8}  & & Vmc (nm\({}^{3}\)/nm\({}^{2}\)) & 2.190 & 1.880 & 0.714 & 0.845 & 1.454 & 0.032 \\ \cline{2-8}  & & Vvv (nm\({}^{3}\)/nm\({}^{2}\)) & 0.067 & 0.052 & 0.002 & 0.046 & 0.070 & 0.002 \\ \hline \multirow{8}{*}{WORN} & \multirow{8}{*}{61} & Sk (nm) & 3.99 & 3.84 & 1.07 & 1.03 & 1.55 & 0.003 \\ \cline{2-8}  & & Spk (nm) & 1.78 & 1.75 & 0.28 & 0.53 & 0.64 & 0.091 \\ \cline{1-1} \cline{2-8}  & & Svk (nm) & 1.40 & 1.21 & 0.20 & 0.45 & 0.79 & \textless{}0.001 \\ \cline{1-1} \cline{2-8}  & & Smrk1 (\%) & 11.4 & 11.1 & 4.38 & 2.09 & 3.56 & 0.104 \\ \cline{1-1} \cline{2-8}  & & Smrk2 (\%) & 90.6 & 90.6 & 1.76 & 1.326 & 1.77 & 0.616 \\ \cline{1-1} \cline{2-8}  & & Vmp (nm\({}^{3}\)/nm\({}^{2}\)) & 0.104 & 0.107 & 0.002 & 0.044 & 0.063 & 0.003 \\ \cline{1-1} \cline{2-8}  & & Vmc (nm\({}^{3}\)/nm\({}^{2}\)) & 2.02 & 1.94 & 0.269 & 0.519 & 0.784 & 0.005 \\ \cline{1-1} \cline{2-8}  & & Vvv (nm\({}^{3}\)/nm\({}^{2}\)) & 0.067 & 0.057 & 0.001 & 0.026 & 0.047 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptive statistics of the functional parameters of the surface texture determined from the AFC: Spk—mean height of peaks above the core surface, Sk—mean height of the core surface and Svk—mean valley depth below the core roughness, Smrk1—material ratio separating the reduced peaks from the core surface, Smrk2—material ratio separating the reduced valleys from the core surface, Vmp—volume of the peak layer per unit surface, Vmc—volume of the core layer per unit surface and Vvv—volume of the valley void layer per unit surface. The following statistical measures of variability are provided as well: Var—variance, $tD—standard deviation, IQR—inter-quartile range, together with the results of the test of normality using Shapiro–Wilk method with \(\alpha\) = 0.05.  
enzymes. The observation that the remaining functional parameters explaining deeper-lying parts of the surface are found intact agrees well with that, and confirms that the wear is a process of superficial character. It should be noted that the previously studied rms roughness Sq and surface development ratio Sdr values appeared unchanged, which was not counterintuitive because these parameters were associated with the total thickness of the outer layer without dividing it into specific sub-layers (Table 2). Note, however, that single results for Sq and Sdr were found to be less deviated in worn aligners compared with the new aligners, from which the conclusion was drawn that the roughness profiles of worn aligners were becoming more similar to each other. This might have been equivalent to the smoothing of the overall surfaces under study.