# In Silico Modeling Study of Curcumin Diffusion and Cellular Growth
## 3 Results and Discussion
### Integration of Fibroblast Proliferation and Curcumin Diffusion Models  
The six selected concentrations were simulated using the integrated model to visualize the effect of curcumin on wound healing. Table 3 summarizes the effect of curcumin on the cell division period and the final cell population obtained for each dose of curcumin and release model. All simulations had an initial cell population of 447. The lowest cell division period and highest final cell population were obtained at 0.25 uM. For both models, this period was similar to the previously calculated time frame (12.69 h), with a margin of error of 2%. Therefore, a dose-dependent effect of 3.4 was achieved. The administration of low doses of curcumin (0.25, 0.5, 1, and 5 uM) allowed for two cell divisions to occur, resulting in a higher final cell population than the control. Notably, the second cell division was slower than the control's first cell division for these concentrations. Since cell cycle oscillations are not perfectly defined as a sine or cosine wave, the time period for cell division is not exact. As shown in Figure 5, there is a difference between the time that CycB's concentration is low and when it peaks. Thus, a time-delay effect exists between cell divisions. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & & \multicolumn{3}{c}{**Korsmeyer–Peppas Model**} \\ \hline
**Concentration (\(\mu\)M)** & **d1 (h)** & **d2 (h)** & **Final Cell Population (Number of Cells)** \\ \hline
0 (control) & 27.10 & - & 557 \\
0.25 & 12.95 & 28.35 & 777 \\
0.5 & 13.00 & 28.55 & 682 \\
1 & 13.20 & 29.05 & 629 \\
5 & 14.90 & 34.05 & 590 \\
10 & 18.40 & - & 557 \\
20 & - & - & 447 (Same as initial) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time of cell division and final cell population for each curcumin concentration for 447 initial cells, where d1 and d2 are the times of the first and second divisions, respectively. As expected, for a concentration of 10 uM, the only beneficial effect is reducing cell division time. Conversely, the highest concentration of curcumin (20 uM) showed the lowest final cell population, as no cell division occurred. This same dose-dependent effect can be observed for both release models, with minimal variation in cell division time and final cell population. Hence, both curcumin-release models are viable to use for this application. Figure 9 summarizes the effect of curcumin on confluence for both curcumin diffusion models. For the K-P model in Figure 9a, the best benefit, obtained at a concentration of 0.25 uM, represented the highest confluence (59.90%). Similarly, low concentrations (0.5, 1, and 5 uM) show curcumin's beneficial effects, with a higher confluence than the control (52.39, 48.44, and 45.33%, respectively). For a 10 uM concentration, a similar confluence to the control was obtained (42.80%). Higher concentrations show inhibitory and cytotoxic effects: a dose of 20 uM negatively impacted cell division time; thus, the internal cells did not enter mitosis within the 36-hour time frame, resulting in the lowest confluence (34.28%). For [PERSON]'s hyperbolic model in Figure 9b, the same dose-dependent effect was observed, and the confluence results showed only slight variations attributable to randomly defined fibroblast diameters in each simulation in the 15-20 uM range. The most beneficial effect was observed at a concentration of 0.25 uM with a confluence of 59.78%. Low concen  
Figure 9: Results obtained by simulating the integrated model for \(t=36\) h with 447 initial cells and 34.28% initial confluence for the control and each curcumin concentration: (**a**) K-P model, (**b**) [PERSON]’s hyperbolic model. trations (0.5, 1, and 5 \(\upmu\)M) showed a higher confluence than the control (55.04, 47.55, and 46.19%, respectively), whereas a medium concentration (10 \(\upmu\)M) showed no difference from the control (42.83%). The highest concentration (20 \(\upmu\)M) resulted in no cell division and the lowest confluence (34.27%).