# Modern Techniques for Flavonoid Extraction--To Optimize or Not to Optimize?
## 6 Conclusions  
There is a growing interest in the extraction of bioactive molecules, namely flavonoids from plant materials. It is also noted that the mentioned modern extraction methods (microwave-assisted extraction, ultrasound-assisted extraction, pressurized liquids-assisted extraction, and supercritical fluids extraction) ensure higher extraction yields with lower energy and solvent consumption compared to the classic extraction method. However, due to the different sources of bioactive molecules, it is necessary to specifically define the optimal process conditions for \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Extraction Method** & **Flavonoids Source** & **Kinetic Model** & **Model Performance** \\ \hline \multirow{4}{*}{UAE [67]} & \multirow{2}{*}{Peanut (_Anchis_ _hypogaea_ L.)} & \multirow{2}{*}{Phenomenological model and [PERSON]’s model} & the mean absolute errors (MPE) for phenomenological model in range 0.158–0.809\% and for [PERSON]’s model in range 0.675 to 1.817\% \\ \hline \multirow{4}{*}{MEA [219]} & \multirow{2}{*}{_Terminalia bellerica_} & \multirow{2}{*}{Second-order kinetic model} & The average absolute relative deviation (AARD) and the relative standard deviation between the experimental data and those predicted by second-order kinetics are 0.38\% and 0.62\%, respectively. \\ \hline MAE [91] & _Helichrysum arenarium_ & First-order kinetic model & \(R^{2}\) > 0.98 \\ \hline \multirow{4}{*}{UAE [203]} & \multirow{2}{*}{Lentils (_Lens_ _culinaris_ L.)} & Parabolic diffusion & RMS and SEE diminished and \(R^{2}\) increased in the following order: hyperbolic model \\  & & Power law & \(\rightarrow\) parabolic model \(\rightarrow\) [PERSON]’s equation \\  & & [PERSON]’s model & \(\rightarrow\) power-law model. \\ \hline \multirow{4}{*}{Conventional extraction [204]} & \multirow{2}{*}{Linden (_Tilia cordata_ M.) flowers} & Unsteady-state diffusion & \(R^{2}\) increased in the following order Film theory -? Empirical equation of \\  & & Film theory & \(\rightarrow\) Ponomaryov -? Unsteady diffusion \\  & & Ponomaryov & through plant material \\ \hline \multirow{4}{*}{Conventional extraction (infusion) [202]} & \multirow{4}{*}{Roots of _Carlina aculis_} & change in the concentration of \\  & & volume over time & \\  & & change in the concentration of \\  & & the target substance in \\  & & intercellular space over time \\  & & material balance equation & \\ \hline \multirow{2}{*}{PLE [29]} & \multirow{2}{*}{Cocoa shell} & [PERSON]’s model & \(R^{2}\) were high in all experimental data set \\  & & & (0.9335–0.9930) \\ \hline \multirow{2}{*}{UAPLE [196]} & \multirow{2}{*}{Passionfruit} & Spline model & \multirow{2}{*}{Spline model} \\  & & two-site desorption model & \\ \hline \multirow{2}{*}{UAE-SC CO\({}_{2}\)[136]} & \multirow{2}{*}{_Scutellaria barbata_} & Second-order kinetic model & \(R^{2}\) = 0.98 at all analyzed temperatures (\(T\) = 33, 39, 45, 52 \({}^{\circ}\)C) \\ \hline \multirow{2}{*}{SFE-CO\({}_{2}\)[220]} & \multirow{2}{*}{Brazilian orchid tree (_Baulinia foffica_)} & Empirical model dividing & \(R^{2}\) > 0.960\(\circ\)for analyzed \\  & & extraction process into & extraction conditions \\ \hline \multirow{2}{*}{SFE-CO\({}_{2}\)[139]} & \multirow{2}{*}{_Capsicum_ _annuum_ pepper} & Logistic and spline model & \(R^{2}\) > 0.99 for both models for all analyzed \\  & & & extraction conditions \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Application of kinetic modeling in flavonoids extraction. the selected plant material. Therefore, it is necessary to use mathematical tools to optimize the extraction process and to analyze the extraction dynamics. Conceptualization, A.J.T., D.S. and A.S.; writing--original draft preparation, A.J.T. ; writing--review and editing, A.J.T., D.S. and A.S.; visualization, A.S.; funding acquisition, D.S. All authors have read and agreed to the published version of the manuscript. This work has been supported by Croatian Science Foundation project \"Biflavonoids role in plants: _Ginkgo biloba_ L. as a model system\" under the project no.