## 3 Results and Discussion
### Method Validation
#### 3.4.3 Sensitivity (LOD and LOQ)  
The average slope values and y-intercepts obtained from linear regression analysis from the respective fat-soluble vitamins' standard curves were used to calculate the LOD and LOQ of each vitamin (Table 4). The LOD for vitamin \(\rm D_{2}\), \(\rm D_{3}\), \(\rm E\), and \(\rm K_{1}\) was 30.86 ng/band, 19.44 ng/band, 14.17 ng/band, and 0.86 ng/band, respectively, and the LOQ was 93.52 ng/band, 58.92 ng/band, 42.95 ng/band and 2.61 ng/band, respectively (Table 4). In comparison with previously developed HPTLC methods, with a LOD of 17.54 and 0.19 ng/band and a LOQ of 52.62 and 2.50 ng/band respectively we were able to determine and quantify vitamin \(\rm D_{3}\) and \(\rm K_{1}\) with similar limits [4; 15]. Moreover, the newly developed method can also detect and quantify two other fat-soluble vitamins, \(\rm D_{2}\) and \(\rm E\), with a low LOD and LOQ as seen in Table 4 whereas a previous study was only able to determine and quantify vitamin \(\rm E\) (LOD and LOQ 0.89 and 5.71 ng/band respectively [18]).  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Vitamins**} & \multirow{2}{*}{**R\({}_{\rm F}\)**} & \multirow{2}{*}{**Run**} &
\begin{tabular}{c} **Linearity** \\ **Range** \\ **(ng/band)** \\ \end{tabular} & \multirow{2}{*}{**Regression Equation**} & \multirow{2}{*}{**Correlation**} & \multirow{2}{*}{**Slope** (**Average**)} & \multirow{2}{*}{**y-Intercept** (**SD**)} & \multirow{2}{*}{**LOD**} & \multirow{2}{*}{**LOQ** (**ng**)} \\ \cline{5-10}  & & & & & & & & \\ \hline \multirow{4}{*}{\(\rm D_{2}\)} & \multirow{4}{*}{0.20} & Run 1 & 100–300 & y = \(5\times 10^{-6}\)x \(-6\times 10^{-5}\) & 0.9944 & \multirow{4}{*}{6.53 \(\times 10^{-6}\)} & \multirow{4}{*}{6.11 \(\times 10^{-5}\)} & \multirow{4}{*}{30.86} & \multirow{4}{*}{93.52} \\ \cline{5-10}  & & Run 2 & 100–300 & y = \(8\times 10^{-6}\)x \(-2\times 10^{-5}\) & 0.9928 & & & & \\ \cline{5-10}  & & Run 3 & 100–300 & y = \(7\times 10^{-6}\)x \(-1\times 10^{-4}\) & 0.9969 & & & & \\ \hline \multirow{4}{*}{\(\rm D_{3}\)} & \multirow{4}{*}{0.20} & Run 1 & 100–300 & y = \(8\times 10^{-6}\)x \(+1\times 10^{-4}\) & 0.9977 & \multirow{4}{*}{7.07 \(\times 10^{-6}\)} & \multirow{4}{*}{4.16 \(\times 10^{-5}\)} & \multirow{4}{*}{19.44} & \multirow{*}{58.92} \\ \cline{5-10}  & & Run 2 & 100–300 & y = \(5\times 10^{-6}\)x \(+8\times 10^{-5}\) & 0.9959 & & & & \\ \cline{5-10}  & & Run 3 & 100–300 & y = \(7\times 10^{-6}\)x \(+2\times 10^{-4}\) & 0.9978 & & & & \\ \hline \multirow{4}{*}{\(\rm E\)} & \multirow{4}{*}{0.46} & Run 1 & 100–300 & y = \(3\times 10^{-4}\)x \(+3.5\times 10^{-3}\) & 0.9984 & \multirow{4}{*}{3.07 \(\times 10^{-4}\)} & \multirow{4}{*}{1.32 \(\times 10^{-3}\)} & \multirow{4}{*}{14.17} & \multirow{4}{*}{42.95} \\ \cline{5-10}  & & Run 3 & 100–300 & y = \(3\times 10^{-4}\)x \(+9\times 10^{-4}\) & 0.9929 & & & & \\ \cline{5-10}  & & Run 3 & 100–300 & y = \(3\times 10^{-4}\)x \(+2.7\times 10^{-3}\) & 0.9888 & & & & \\ \hline \multirow{4}{*}{\(\rm K_{1}\)} & \multirow{4}{*}{0.68} & Run 1 & 20–60 & y = \(1.1\times 10^{-3}\)x \(+2.9\times 10^{-2}\) & 0.9931 & \multirow{4}{*}{1.37 \(\times 10^{-3}\)} & \multirow{4}{*}{3.58 \(\times 10^{-4}\)} & \multirow{4}{*}{0.86} & \multirow{4}{*}{2.61} \\ \cline{5-10}  & & Run 2 & 20–60 & y = \(1.6\times 10^{-3}\)x \(+3\times 10^{-3}\) & 0.9978 & & & & \\ \cline{5-10}  & & Run 3 & 20–60 & y = \(1.4\times 10^{-3}\)x \(+3\times 10^{-3}\) & 0.9973 & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Linear regression analysis for the calibration curves of vitamins \(\rm D_{2}\), \(\rm D_{3}\), \(\rm E\), and \(\rm K_{1}\).  
However, no other HPTLC-based study was found that allows for the quantification of vitamin D\({}_{2}\) in complex matrices.