# In Silico Modeling Study of Curcumin Diffusion and Cellular Growth
## 3 Results and Discussion  
### Fibroblast Culture Growth Model  
The fibroblast proliferation simulation resulted in a doubling time of 27.1 h (Figure 5) found within the expected time range of 24-32 h. This initial doubling time can be altered  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Concentration (\(\upmu\)M)**} & \multicolumn{2}{c}{**Cell Type**} \\ \cline{2-3}  & **Left Interior** & **Right Interior** \\ \hline
0 (control) & p1 & p1 \\
0.25 & p1 & p1 \\
0.5 & p1 & p2 \\
1 & p2 & p2 \\
5 & p3 & p2 \\
10 & p1 & p1 \\
20 & p3 & p3 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Combination of probabilities defined for the left and right interior cell types for each curcumin concentration.  
Figure 4: Dose-dependent effect of curcumin on the model’s parameters, an approximation to a linear equation with \(R^{2}=0.9713\).  
depending on the experimental conditions and cell line depicted, as studies report varying times [56; 57; 58]. To obtain this period, the original model parameters were multiplied by a factor of 2/3. In addition, the cdc20 concentration was lowered to 4 uM to avoid a strong inhibitory effect in response to parameter manipulation.  
Figure 6a shows the initial cell arrangement, randomly generated by the software. The simulated scratch wound is visible. Green and blue were used to represent the G2-M transition for cycB > 2.6 uM and cycB > 2.9 uM, respectively. Every other phase of the cell cycle (cycB < 2.6 uM) is also represented by green, since the generated images can only show the change in a single variable (in this case, cycB). Note that only the innermost cells are colored, since only the two cell types closest to the wound are affected by the cell cycle and will therefore proliferate. Figure 6b shows the cell arrangement after 12 h, where some of the innermost cells invaded the scratch wound and simulated cell migration to the wound site. The 447 seeded cells achieved an initial confluence of 34.28%.  
Figure 5: Simulated fibroblast cell cycle protein oscillatory behavior. Cell division occurs at approximately 27 h. Markers show the cycB threshold for G2–M transition.  
Figure 6: Initial cell arrangement for 447 cells. The threshold of cell division is shown. (**a**) Cell arrangement at \(t\) = 1 h, scratch line is visible. (**b**) Cell arrangement at \(t\) = 12 h, some of the innermost cells have migrated to the wound. Seeded cells achieved an initial confluence of 34.28%. Images were generated with a time step of 1.  
After 12 h, the cell migration phase was complete, following the same behavior exhibited in [14], where cell migration occurred prior to cell proliferation in the first 24 h. The authors of [14] observed that cellular migration was dictated by the orientation of the cells, as those perpendicular to the wound were the first to migrate, followed by those parallel to it. This behavior was not recreated in the present model, since fibroblast shape was simplified to a circle. Instead, the proximity of the cell to the wound area is what determined the migration. Moreover, fibroblasts began to form a bridge in the wound [14]. Single-cell migration was modeled in the present model; however, the strength of the interactions between cells obliged them to cluster, forming structures similar to the cell bridges.  
Entering the proliferation phase, when cycB > 2.9 uM, cell division conditions were met, and each cell's probability to divide was evaluated according to the selected curcumin concentration and cell type (as shown in Table 2). After 27.85 h, every internal cell had divided, reaching a final population of 557 cells, as shown in Figure 7. The final confluence was 42.82%. Due to the probabilistic conditions, the internal cell population gradually entered mitosis, doubling from 110 to 220 cells. Figure 7 shows this behavior. This exponential growth occurs in diverse fibroblast cell lines, as demonstrated in various studies [58; 59; 60]. The results from this simulation were used as the control group.