### 3.1 Microwave-assisted extraction

Extraction experiments were carried out using a modified domestic microwave oven apparatus (DAE WOO, KOG-360, Combi Grill) adapted to a condenser. 100 g of dried *Securidaca longepedunculata* powder was extracted with 1000 mL solvent (acetone 95%) under different MAE conditions. After extraction, the vessels were allowed to cool at room temperature before opening. Microwave power (200, 400, 600, 800, 100 W), extraction time (20 to140 s, with an interval of 20 s) and solid–liquid ratio (0.25 to 2 g/20 mL with an interval of 0.25 g/20 mL) were evaluated for the extraction of xanthone from *S. longepedunculata*. The final extract was evaporated and dissolved in dimethyl sulfoxide before UV–Vis spectrophotometric (Spectroquant® Pharo 100 M) analysis. Three replicates were performed in each extraction.

### 3.2 Quantification of the total xanthones by colorimetric method

Colorimetric method followed by visible spectroscopy technique is one of the common analytical techniques used for the determination of a group of components in a mixture. This method is especially useful for the analysis of natural products which are very complicated mixtures [8]. Thus, this method may provide a solution for the quantification of the xanthones the *S. longepedunculata* extracts. The principle of this analysis was based on the oxidation of xanthones by the sodium acetate [9], which leads to the formation of yellow complex absorbing at 410 nm. 250 μL microwave extract and 75 μL of sodium acetate (5%) were mixed. This mixture was kept at ambient temperature for 30 min in order to gain a maximum of yellow color. The absorbance of the upper phase was read at 400 nm on an UV/Vis spectrophotometer (Spectroquant® Pharo 100 M) using glass cuvettes against blank in the number one test tube. Calibration curve was developed from 0 to 0.08 μL with an interval of 0.02 μL in different test tube with standard solution standard of 2-hydroxy-1,7-diméthoxyxanthone. Total xanthone were expressed as mg 2-hydroxy-1,7-diméthoxyxanthone equivalent per gram of dry weight extract (EDMX/gP).

### 3.3 Empirical kinetic models

in this study, kinetics of microwave-assisted-extraction of xanthones from* S. longepedunculata* roots is performed using first-order and second-order models, it could be known rate of extraction from xanthones.

### 3.4 Hervas et al. model [10]

The kinetics mechanism proposed by Hervas et al*.* was used to study the extraction process under equilibrium conditions, as shown in Eq. (1)

$$\frac{{{\text{d}}C}}{{{\text{d}}t}} = k\left( {C_{0} - C} \right)$$

(1)

where *C* is the concentration of xanthones (µg EDMX/mL) produced at any time *t*, *C*_{0} is the initial concentration of xanthones (µg EDMX/mL) present, and *k* is the effective diffusion coefficient (µL/µg EDMX s).

Integrating Eq. (1) between the initial moment and a given point at time *t* gives Eq. (2) with the boundary conditions as *Ct*|*t* = 0 = 0 and *Ct*|*t* = *t* = *Ct*

$$C\left( t \right) = C_{0} \left( {1 - e^{ - kt} } \right)$$

(2)

### 3.5 Peleg model [11]

The model proposed by Peleg was adapted for the extraction and used in the form:

$$C\left( t \right) = \frac{t}{{K_{1} + K_{2} *t}}$$

(3)

where *C*(*t*) is the concentration of xanthones at time *t* (µg EDMX/g), *t* is the extraction time (s), *K*_{1} is the Peleg rate constant (s g/µg EDMX), and *K*_{2} is the Peleg’s capacity constant (g/µg EDMX).

The Peleg rate constant *K*_{1} relates to the extraction rate (*B*_{0}) at the very beginning (*t* = *t*_{0})

$$B0 = \frac{1}{K1}$$

(4)

The Peleg capacity constant *K*_{2} relates to maximum extraction yield, i.e., equilibrium concentration of xanthones extracted (*ce*) when *t* → ∞. Equation (5) gives the relation between equilibrium concentration and *K*_{2} constant

$$C0 = \frac{1}{{K_{2} }}$$

(5)

Thus, the extraction rate coefficient can be written as in Eq. (6)

$$k = \frac{{K_{2} }}{{K_{1} }}$$

(6)

### 3.6 Gaussian model

The model proposed by Gauss was adapted for the extraction and used in the form:

$$Y = \, a\,\exp \,\left[ { - 0,5\left( {\left( {x - x_{0} } \right)/k} \right)^{2} } \right]$$

(7)

*Y* is the extraction rate, *a* is the maximum value of the extraction rate, *x* is the variable studied in the extraction, *x*_{0} is the variable corresponding to the maximum value of the extraction rate *a*, and *k* is the constant of the extraction rate.

### 3.7 Statistical analysis

All analyses were performed in triplicate. The results are presented as average values with standard error and were analyzed statistically using one-way ANOVA. Statistical significance was accepted at a level of *p* < 0.05 using the statistical program Statgraphics centurion 12.