# Modern Techniques for Flavonoid Extraction--To Optimize or Not to Optimize?
## 5 Statistical and Mathematical Modeling Techniques for Optimization Flavonoid Extraction Parameters
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Extraction Method** & **Flavonoids Source** & **Design of Experiment and Modeling Method** & **Optimal Process Conditions** & **Flavonoids Extraction Yield** \\ \hline \multirow{4}{*}{PLE} & roots of _Scutellaria_ & Circumscribed central composite (CCC) design and RSM & temperature, pressure, static & \\  & _pimattifida_([PERSON], 2017) & Circumscribed central composite (CCC) design and RSM & time, dynamic time, and the & \\  & & and RSM & time, dynamic time, and & \\  & & and RSM & time, dynamic time, and & \\  & & & & \\ \hline PLE & goji berry fruits ([PERSON], 2017) & Factorial experimental design and RSM & time, dynamic time, and & \\  & & & & \\ \hline UAPLE & Passion fruit ([PERSON], 2017) & Single-factor experiments and RSM & time, dynamic time, and the & \\  & & & & \\ \hline \multirow{4}{*}{SFE-CO2} & Xinjiang juibbe (_Ziziphus juibbe Mill._) & Box-Behnken design and RSM & temperature of 52.52 \({}^{\circ}\)C, a pressure of 27.12 MPa, a time of 113.42 min, and a cosolvent flow rate of 0.44 mL/mi & \\  & leaves ([PERSON], 2017) & Randomized design full factorial and RSM & time, dynamic time of 270 min and & \\  & & & & \\ \hline \multirow{4}{*}{SFE-CO2} & _Odontonema strictium_ & Randomized design full factorial and RSM & time of 200 min and & \\  & leave ([PERSON], 2017) & Randomized design full factorial and RSM & time of 200 bars, & \\  & & & & \\ \hline \multirow{4}{*}{SFE-CO2} & _Maydis stigma_([PERSON], 2017) & Box-Behnken design and RSM & time, dynamic time, and a cosolvent amount of 2.488 & \\  & & & & mL/g and an extraction time & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline UAESFE & _Iberis amara_([PERSON], 2017) & Single-factor experiments and RSM & time, dynamic time, and & \\  & & & & \\ \hline \multirow{4}{*}{SFE-CO2} & _Lipia organoids_ K. and _Lippiia gravelens_ & Fractional factorial screening design and RSM & time, dynamic time, and & \\  & K. ([PERSON], 2017) & and RSM & time, dynamic time, and & \\ \hline \multirow{4}{*}{SFE-CO2} & _Leptocarpha rivularis_ & Box-Behnken design and RSM & time, dynamic time, and & \\  & leaves ([PERSON], 2017) & Box-Behnken design and RSM & time, dynamic time, and & \\  & & & & \\ \hline \multirow{4}{*}{SFE-CO2} & _Leptocarpha rivularis_ & Box-Behnken design and RSM & time, dynamic time, and & \\  & leaves ([PERSON], 2017) & and RSM & time, dynamic time, and & \\  & & & & \\ \hline \multirow{4}{*}{SFE-CO2} & _Leptocarpha rivularis_ & Box-Behnken design and RSM & time, dynamic time, and & \\  & & & & \\ \cline{1-1}  & leaves ([PERSON], 2017) & and RSM & time, dynamic time, and & \\ \hline \multirow{4}{*}{SFE-CO2} & & Central composite & RSM-DF were 3.34 mL/min, & \\  & & rotatable design using & 166.94 bar, 51.97 \({}^{\circ}\)C, 67.47 min, & \\ \cline{1-1}  & & RSM coupled with & for RSM-GA were 3.23 & \\ \cline{1-1}  & & desirability function (DF) & mL/min, 172.79 bar, 52.37 \({}^{\circ}\)C, & \\ \cline{1-1}  & & and genetic algorithm & 68.53 min, while that for & \\ \cline{1-1}  & & & & ANN-GA were 3.30 mL/min, & \\ \cline{1-1}  & & & & \\ \cline{1-1}  & & & & 174.07 bar, & \\ \hline \multirow{4}{*}{EA-SFE} & _Medicago sativa_ & The response surface methodology (RSM) & the temperature of 68 \({}^{\circ}\)C, the & \\ \cline{1-1}  & leaves ([PERSON], 2017) & based on & pressure of 205 bar and 15.5\% & \\ \cline{1-1}  & & Box-Behnken design & of the co-solvent addition & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._Furthermore, understanding complicated mass transfer, diffusion, and thermodynamic characteristics impacting the extraction requires the use of kinetic modeling [11]. The literature shows that the solid-liquid extraction procedures for the extraction of bioactive compounds from plant materials can be described using various mathematical models. The models used include [PERSON], [PERSON], [PERSON], the second-order model, diffusion model, logarithmic model and [PERSON]'s empirical equation [11] (Table 5).