## 3 Results  
### Method Validation  
The method was successfully validated in the ranges of 0.1-100 mg/L for the keto-acids (KBA and AKBA), 1-100 mg/L for the A-BA and B-BA. Finally, the acetyl boswellic acids A-ABA and A-BBA curves were validated in the range 5-100 mg/L. Table 1 reports the results of the validation process, while Figures S1-S3 in the Supplementary Materials report, respectively, an example of a chromatogram for a sample, a calibration standard mix and a blank sample. All the R\({}^{2}\) of the calibration lines exceed the 0.995 value, in particular the values for KBA, AKBA, A-BA and B-BA were higher than 0.999. The parameter of relative standard deviation of the calibration lines, expressed as RSD % of the slopes, shows low values and consequently highlights a good signal stability and repeatability for the three calibration line replicates.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameter** & **KBA** & **AKBA** & **A-BA** & **B-BA** & **A-ABA** & **A-BBA** \\ \hline Rt (minutes) & 12.3 & 16.1 & 19.8 & 20.3 & 24.1 & 24.9 \\ \hline Range (mg/L) & 0.1–100 & 0.1–100 & 1–100 & 1–100 & 5–100 & 5–100 \\ \hline R2 (\(n=3\)) & 0.999 & 0.999 & 0.999 & 0.999 & 0.998 & 0.997 \\  & 0.999 & 0.999 & 0.999 & 0.999 & 0.998 & 0.997 \\ \hline RSD \% of slopes (\(n=3\)) & 1.76 & \(-\)0.25 & \(-\)0.72 & \(-\)0.45 & 0.51 & \(-\)0.74 \\  & \(-\)0.69 & 1.04 & 0.84 & 2.93 & \(-\)0.43 & 0.56 \\  & \(-\)1.07 & \(-\)0.79 & \(-\)0.11 & \(-\)2.48 & \(-\)0.08 & 0.18 \\ \hline  & 8.6 & 0.2 & 1.52 & 11 & \(-\)23.0 & \(-\)12.2 \\  & 5 mg/L & 2.1 & 4.3 & 5.65 & 8.6 & \(-\)23.4 & \(-\)11.2 \\  & 3.6 & \(-\)2.5 & 3.05 & \(-\)15.0 & \(-\)23.5 & \(-\)11.7 \\  & 0.3 & 0.9 & \(-\)10.5 & 6.0 & 11.8 & 4.5 \\ Acc. BIAS \% (\(n=3\)) & 20 mg/L & 2.1 & 4.4 & 5.59 & 5.5 & 26.8 & 7.7 \\  & \(-\)0.6 & \(-\)2.1 & 0.3 & \(-\)5.3 & 21.9 & 6.0 \\  & \(-\)3.6 & 0.01 & \(-\)0.9 & 0.2 & 8.7 & 0.3 \\  & 100 mg/L & \(-\)2.5 & 1.0 & 0.9 & 3.2 & 10.4 & 1.4 \\  & \(-\)1.2 & \(-\)0.8 & 0.1 & \(-\)2.74 & 9.7 & 1.3 \\ \hline RSD \% & 5 mg/L & 6.3 & 3.4 & 2.4 & 14.5 & 2.4 & 2.4 \\ (\(n=3\)) & 20 mg/L & 2.3 & 3.3 & 8.3 & 6.5 & 8.3 & 8.3 \\  & 100 mg/L & 1,6 & 0.9 & 0.9 & 3 & 0.9 & 0.0 \\ \hline LOD (ppm) & 0.19 & 0.45 & 0.47 & 0.97 & 4.6 & 3.59 \\ LOQ (ppm) & 0.62 & 1.50 & 1.58 & 3.25 & 15.2 & 11.95 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Validation data for the boswellic acid quantitative method. The columns report the different molecules studied: KBA, AKBA, A-BA, B-BA, A-ABA and A-BBA. Each row shows the validation parameter. Rt: retention time; R2: linearity coefficient; RSD % of slopes: relative standard deviation of the slopes; Acc. BIAS %: quantitation error expressed as % on three different measurements; RSD %: precision expressed as relative standard deviation of three different measurements; LOD: limit of quantitation; and LOD: limit of detection.  
The parameter for accuracy, Acc. BIAS %, shows good values for all the concentrations studied in all the replicates as well as the RSD % describing method precision. LOD and LOQ, as calculated from the residuals of the calibration curves and their slopes, show the lowest concentrations of the boswellic acids that the method can detect and quantify with the minimal error.