# Optimized Isolation Procedure for the Extraction of Bioactive Compounds from Spent Coffee Grounds
## 2 Materials and Methods
### Design of the Experiments and Response Surface Methodology (RSM) Optimization  
An RSM approach was employed in order to maximize the extraction yield of caffeine, as well as those of polyphenols (total polyphenol content; TPC) and other compounds with antioxidant activity (evaluated using the DPPH and FRAP assays). Thus, caffeine concentration and TPC, DPPH, and FRAP values were the objectives of the design. The composition of the solvent (\(C\), % \(v/v\) ethanol in water; selected so as to examine solvents with various polarities), the extraction time (\(t\), min; selection was based on preliminary experiments), the extraction temperature (\(T\), \({}^{\circ}\)C; a maximum temperature of 80 \({}^{\circ}\)C was selected, so that the extracted compounds would be stable, and the extraction feasible, as the extraction could not be carried out with ethanol above that temperature), and the ratio of liquid to solid (\(R_{\text{L/S}}\), mL/g; selection was based on preliminary experiments) were examined so as to achieve optimum results. The optimization was based on an experiment with a 20-design point main effects screening design. The process variables were set up in 5 levels, according to the experimental design: \(-2\), \(-1\), \(0\), \(1\), and \(2\). The coded and actual levels are listed in Table 1. The significance of the model (equations) coefficients and the overall model significance (R\({}^{2},p\)) were evaluated at a minimum level of 95% using analysis of variance (ANOVA) and summary-of-fit tests.  
The response variable was estimated using a second-order polynomial model, expressed as follows:  
\[Y_{k} =\beta_{0}+\sum_{i=1}^{2}\beta_{i}X_{i}+\sum_{i=1}^{2}\beta_{ii}X_{i} ^{2}+\sum_{i=1}^{2}\sum_{j=i+1}^{3}\beta_{ij}X_{i}X_{j} \tag{1}\]  
where \(Y_{k}\) represents the predicted response variable, while \(X_{i}\) and \(X_{j}\) represent the independent variables. The values \(\beta_{0}\), \(\beta_{i}\), \(\beta_{ii}\), and \(\beta_{ij}\) stand for the intercept and the regression coefficients associated with the linear, quadratic, and interaction terms of the model, respectively.  
The RSM was used to optimize the extraction yield of caffeine. The purpose was to find the highest peak area and to understand the impact of significant independent variables on the response. The results of the model are represented through 3D surface response graphs, which showed the relationship between the response and the independent variables.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Independent Variables**} & \multirow{2}{*}{**Code Units**} & \multicolumn{6}{c}{**Coded Variable Level**} \\ \cline{3-6}  & & \(-2\) & \(-1\) & \(0\) & \(1\) & \(2\) \\ \hline \(C\) (\%, \(v/v\)) & \(X_{1}\) & \(0\) & \(25\) & \(50\) & \(75\) & \(100\) \\ \(t\) (min) & \(X_{2}\) & \(18\) & \(69\) & \(120\) & \(171\) & \(222\) \\ \(T\) (\({}^{\circ}\)C) & \(X_{3}\) & \(20\) & \(35\) & \(50\) & \(65\) & \(80\) \\ \(R_{\text{L/S}}\) (mL/g) & \(X_{4}\) & \(5\) & \(13\) & \(20\) & \(28\) & \(35\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: The actual and coded levels of the independent variables were used to optimize the process.