## 3 Results and Discussion
### Effects of Different Parameters on the Extraction Yield and Total Carotenoids Content and Recovery  
The experimental conditions and results of the Box-Behnken design for the extraction conditions for _I. galhana_ by SFE for 120 min are listed in Table 2. The range of extraction yield (Y) was 1.09-12.82% (w/w) and that of total carotenoids content (TCC) was 1.34-19.01 mg/g. In this table, the total carotenoids recovery is also mentioned, which was estimated as the percentage of the total carotenoids extracted in each sample to the total carotenoids extracted in a conventional methanol extraction, which was assumed to be 100% (24.40 \(\pm\)2.24 mg/g) with respect to dry biomass. The recovery of total carotenoids reached 5.50% under pure CO\({}_{2}\) and 77.93% when CO\({}_{2}\) modified with 8% (v/v) ethanol was used. The conditions were at 20 MPa/50 \({}^{\circ}\)C and at 300 MPa/60 \({}^{\circ}\)C, respectively. Letters in the experiment column are the acronyms of the tested variables: Pressure (P) and Temperature (T). Values are represented as a mean standard deviation. It was SD \(\leq\) 5% (n = 3 analytical measurement). All values were calculated per gram of initial biomass. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Terms of the**} & \multicolumn{2}{c}{**Y**} & \multicolumn{2}{c}{**TCC**} & \multicolumn{2}{c}{**TC recovery**} & \multicolumn{2}{c}{**TTC**} & \multicolumn{2}{c}{**TECAC**} & \multicolumn{2}{c}{**FAMEs**} \\ \cline{2-11} \multicolumn{1}{c}{**Model**} & **Estimated** & \(p\)**-value** & **Estimated** & \(p\)**-value** & **Estimated** & \(p\)**-value** & **Estimated** & \(p\)**-value** & **Estimated** & \(p\)**-value** \\ \hline constant & 51.47 & & 35.73 & 146.47 & & -619.40 & & -2.85 & & -17.72 \\ AP & -0.09 & 0.05 \({}^{*}\) & 0.11 & 0.18 & 0.44 & 0.18 & 2.38 & 0  
(Figure 3). In this way, the \"optimal values\" delivered by the software for statistical analysis were 15.15%, 18.14 mg/g, and 74.36% w/w of Y, TCC, and TC recovery, respectively, under 40 MPa, \(\sim\)60 \({}^{\circ}\)C and \(\sim\)8% co-solvent. These experiences, in a certain way corresponded to the extraction conditions used in the experiment where the variables were improved (30 MPa, 60 \({}^{\circ}\)C, and 8.0% co-solvent) obtaining a lower value of 12.82% in extraction yield. However, TCC values and TC recovery of 19.01 mg/g and 77.93% w/w, respectively, were slightly higher than those predicted by the software. In general, the values achieved in this study are better than other reports of specific carotenoids extraction from natural sources. For example, the microalgae _Phaeodactyllun tricornutum_ or _Odontella aurita_[27, 28] gave higher yield than those by brown seaweeds including _Laminaria japonica_, _Eisenia  
Figure 3: Response surface plot showing combined effects of pressure and co-solvent on (**A**) extraction yield (Y), (**B**) total carotenoids content (TCC), and (**C**) recovery (TC recovery) from _I. galbana._ All extractions were done at 60 \({}^{\circ}\)C temperature. bicyclis_, and _Undaria pinnatifida_[27; 29; 30]. [PERSON] et al. [27] reported several methods and solvents to maximize fucoxanthin extraction from _P. tricornutum_, achieving the best yield of 16.51 mg/g under pressurized liquid extraction (PLE) at 10.3 MPa, 100 \({}^{\circ}\)C, 100% ethanol, and static time of 30 min. The content yielded was similar to that by maceration extraction (15.71 mg/g). Likewise, _O. aurita_ is another microalga and a natural producer of fucoxanthin as described by [PERSON] et al. [28]. In their study, besides optimizing culture conditions for improving this carotenoid, they attempted to determine the optimal conditions for fucoxanthin extraction using five conventional solvents. The best yield of fucoxanthin among the five tested solvents was obtained with methanol (16.18 mg/mg), followed by ethanol (15.83 mg/g) and acetone (13.93 mg/g).