Mathematical modeling of cell growth in a 3D scaffold and validation of static and dynamic cultures

Tissue engineering, an immensely important field in contemporary clinical practices, aims at the repair or replacement of damaged tissues. The mathematical model proposed herein shows the distribution and growth of cells in their characteristic time in a 3D scaffold model. This study contributes to the progress of simulation techniques in static and dynamic cultures of bone tissue. Brinkman, nutrient transport, and cell growth equations are brought together to quantify the growth behavior of cells. However, when a static culture is being studied, the Brinkman equation is eliminated. The model was validated by experimental cell culture using 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide assay and scanning electron microscopy. Then, static and dynamic cultures were compared to assess the cell density and cell distribution in the scaffold. Cell counting after 21 days of cell culture showed that the number of cells increased 42-fold in static and 53.5-fold in dynamic cultures, which was in good agreement with our model estimations (37-fold increase in the number of cells in static and 49-fold increase in dynamic cultures). In conclusion, our mathematical model could predict cell distribution and growth in the scaffold.