## 2 Materials and Methods
### Validation of the HPLC Analytical Procedure  
Generally, to apply the developed method for the simultaneous quantitative analysis and standardization of TKM formulations, the method must be validated. In this study, we validated the analytical procedure in accordance with the following strict parameters: limit of detection (LOD), limit of quantification (LOQ), and accuracy, and precision according to the International Conference on Harmonisation (ICH) guidelines [22].  
In short, the linearity of these parameters was confirmed by the value of the coefficient determination (\(r^{2}\)) of the calibration curve, drawn at different concentration ranges of each marker  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Compound** & \
\begin{tabular}{c} **Linear Range** \\ **(\(\upmu\)g/mL)** \\ \end{tabular} &
\begin{tabular}{c} **Regression Equation \({}^{\text{a}}\)** \\ _y=ax+b_ \\ \end{tabular} & \(r^{2}\) & **LOD (\(\upmu\)g/mL)** & **LOQ (\(\upmu\)g/mL)** \\ \hline LIQA & 1.56–100.00 & \(y=14516.82x+1576.68\) & 0.99999 & 0.04 & 0.13 \\ LIQ & 0.78–50.00 & \(y=20297.12x+832.37\) & 0.99999 & 0.07 & 0.20 \\ NOD & 1.56–100.00 & \(y=32616.18x-1073.11\) & 0.99998 & 0.33 & 1.01 \\ NAR & 1.56–100.00 & \(y=20454.28x+2443.73\) & 0.99999 & 0.08 & 0.25 \\ NARG & 2.34–150.00 & \(y=16308.76x+4074.11\) & 0.99996 & 0.37 & 1.11 \\ HES & 2.34–150.00 & \(y=17321.00x+3459.89\) & 0.99999 & 0.22 & 0.65 \\ NON & 0.78–50.00 & \(y=26805.64x+1579.48\) & 0.99999 & 0.05 & 0.15 \\ PON & 3.13–200.00 & \(y=13843.50x+4372.92\) & 0.99999 & 0.21 & 0.65 \\ API & 0.31–20.00 & \(y=39730.97x+466.23\) & 0.99999 & 0.02 & 0.05 \\ GLY & 1.56–100.00 & \(y=9792.06x+907.65\) & 0.99999 & 0.08 & 0.26 \\ HON & 0.31–20.00 & \(y=18705.23x+920.39\) & 0.99999 & 0.02 & 0.05 \\ DEC & 0.78–50.00 & \(y=34364.13x-379.84\) & 0.99998 & 0.15 & 0.47 \\ DECA & 0.78–50.00 & \(y=22150.45x-68.44\) & 0.99999 & 0.15 & 0.47 \\ PRAA & 0.31–20.00 & \(y=17562.36x+2511.48\) & 0.99999 & 0.01 & 0.04 \\ \hline \hline \end{tabular}  
* _y:_ peak area (mAU) of compounds; _x_: concentration (\(\upmu\)g/mL) of compounds.  
\end{table}
Table 1: Linear range, regression equation, \(r^{2}\), limit of detection (LODs), and limit of quantification (LOQs) for marker compounds using high-performance liquid chromatography–photodiode array detection (HPLC-PDA) (\(n=3\)).  
compound. LOD and LOQ concentrations were set using equations where \(\sigma\) is the standard deviation of the \(y\)-intercept and \(S\) is the slope of the calibration curve.  
\[\text{LOD}=3.3\times\frac{\sigma}{S}\]  
The accuracy was evaluated based on the recovery test of the standard addition method, using the equation:  
\[\text{Recovery}\;(\%)=\frac{(\text{found concentration}-\text{original concentration})}{\text{spiked concentration}}\times 100\]  
where precision was verified by intraday and interday precision and repeatability measurements. Intraday and interday precisions were measured five times in a single day and on three consecutive days at different concentrations (low, medium, and high) using the standard solution. The relative standard deviation (RSD) of the recorded series of repeatability was also measured six times using the equation:  
\[\text{RSD}\;(\%)=\frac{\text{standard deviation}\;(\text{SD})}{\text{mean}} \times 100\]  
The system suitability of the assay was evaluated using the parameters such as capacity factor (\(k^{\prime}\)), selectivity factor (\(\alpha\)), resolution (\(R\)s), number of theoretical plates (\(N\)), and tailing factor (\(Tf\)).