## 3 Results and Discussion
### Kinetics
#### 3.5.3 Kinetics of Phenolic Compound from Apple Released in the Gastric and Intestinal Digestion  
Table 3 shows the results of the kinetic of released phenolic compounds in gastric digestion. According to the \(c_{\infty}\) predicted with the model of the first-order, the amounts of released phenolic subgroups can reach 4.3 to 120.4 mg kg\({}^{-1}\) after the gastric digestion of peel, or 5.7 to 33.8 mg kg\({}^{-1}\) after the gastric digestion of flesh depending on the subgroup. The \(c_{\infty}\) predicted with the second-order model gave similar amounts, reaching 4.3 to 125.1 mg kg\({}^{-1}\) after the gastric digestion of the peel or 5.8 to 33.6 mg kg\({}^{-1}\) after the gastric digestion of flesh, again depending on the subgroup. The total released phenolics is predicted to be 236.5 mg kg\({}^{-1}\) (peel) and 57.7 mg kg\({}^{-1}\) (flesh) according to the first-order, or 240.4 mg kg\({}^{-1}\) (peel) and 57.6 mg kg\({}^{-1}\) (flesh) according to the second-order equation.  
In the intestinal digestion (Table 3), the amount of released phenolic subgroups (\(c_{\infty}\)) predicted with the model of the first-order reached 14.5 to 135.4 mg kg\({}^{-1}\) (peel) or 8.8 to 14 mg kg\({}^{-1}\) (flesh) depending on the subgroup, and the amounts of total phenolics 163.8 mg kg\({}^{-1}\) (peel) and 22.7 mg kg\({}^{-1}\) (flesh). Again, the \(c_{\infty}\) predicted by the second-order model gave similar amounts of released compounds for phenolic subgroups reaching 14.7 to 141.7 mg kg\({}^{-1}\) (peel) or 8.7 to 14.2 mg kg\({}^{-1}\) (flesh), and for total phenolics 160.7 mg kg\({}^{-1}\) (peel) and 22.2 mg kg\({}^{-1}\) (flesh).  
The amounts released in gastric and intestinal digestion at the endpoint, as predicted with kinetic models, correspond well to experimentally determined amounts (\(c_{\rm exp}\)). This can be seen from the correlation between \(c_{\infty}\) and \(c_{\rm exp}\) (r\({}^{2}\) 0.9973 and 0.9946 for first- and second-order models, respectively) (Figure 2). It can be suggested that the models and their parameters describe gastric and intestinal digestion well. To compare the first- and second  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & \multicolumn{3}{c}{**First Order**} & \multicolumn{3}{c}{**Second Order**} & \\  & \(k\) (min\({}^{-1}\)) & \(t_{\rm tr2}\) (min) & \(c_{\infty}\) & \(k\) & \(t_{\rm tr2}\) & \(c_{\infty}\) & \(c_{\infty}\) & **C\({}_{\rm exp}\)** \\  & & & (mg kg\({}^{-1}\)) & (mg kg\({}^{-1}\)) & (mg kg\({}^{-1}\)) & (mg kg\({}^{-1}\)) & & **(mg kg\({}^{-1}\))** & **(mg kg\({}^{-1}\))**order models, it can be seen that somewhat lower standard errors (Table 3) and higher correlation with experimental results (Figure 2) were obtained for the values predicted by the model of the first-order kinetic.  
Table 3 shows the half-life (\(t_{1/2}\)) of phenolic compounds. According to \(t_{1/2}\) of the first-order model, half of the phenolic compounds can be released in gastric digestion in a short time period ranging from 1.6 to 3.5 min (peel) or 2.2 to 2.5 min (flesh), depending on the phenolic subgroup. Similar \(t_{1/2}\) were obtained with the second-order model. Half of the phenolics can be released in gastric digestion in 0.65 to 2.48 min (peel) or 0.08 to 0.47 min (flesh). It can be suggested that the release of phenolic compounds in gastric digestion takes place in the first several minutes of the digestion.  
In the intestinal digestion, half of the release/decrease of phenolic compound happened from 1.7 to 20.9 min (peel) or from 0.8 to 7.3 min (flesh) according to first-order model, and from 1.25 to 32.27 min (peel) or from 0.55 to 4.42 min (flesh) according to second-order model (Table 3). A longer half-life or longer release period was shown for flavonoids from the peel (20.9 or 32.3 min, for the first- and second-order models, respectively). It can be suggested that changes to the phenolic compounds in intestinal digestion take place in the first several minutes, but the exceptions are flavonoids, whose release might happen over a longer period.