Development of a macro-scale model from a meso-scale model for cell culture population dynamics

Figures & data

Figure 1. N × N grid representing the flask, each mesh referred to as ‘locus’.

Figure 2. Approximate model of the q(t) as a function of total population p(t).

Figure 3. Meso-scale simulation results showing average toxicity $\xi \left(t\right)$, its approximate lower bound ${\xi }_{min}\left(t\right)$ and upper bound ${\xi }_{max}\left(t\right)$.

Figure 4. Energy histogram of the cells and the uniform distribution approximation.

Figure 5. (a) Fraction of cells $\left(d{\mathrm{\Delta }}_{div}\right)$ that will undergo mitotic division within the next dt for $\alpha >{\dot{\epsilon }}_{rem}\left(t\right)$; (b) Fraction of cells $\left(d{\mathrm{\Delta }}_{die}\right)$ that will die within the next dt for $\alpha <{\dot{\epsilon }}_{rem}\left(t\right)$.

Figure 6. Time profile of (a) the population size $p\left(t\right)$, (b) the total toxicity $\zeta \left(t\right)$, (c) the upper boundary of energy distribution ${\eta }_H\left(t\right)$ and (d) the lower boundary of energy distribution ${\eta }_L\left(t\right)$. These results are obtained for an initial population occupying 40% of the flask. (Meso-scale: ––, macro-scale approximation: –•–).

Figure 7. The performance criteria which evaluate how well the macro-scale model results (with $\alpha =1$) resemble the meso-scale model results: (a) $\mathrm{\%}{\in }_{RMS}$, (b) $\mathrm{\%}{\in }_{pmax}$ c) $\mathrm{\%}{\in }_{td}$ and d)$\mathrm{\%}{\in }_{te}$ as a function of initial occupation percentage of the flask.

Figure 8. (a) Quiescent population size $q$ versus $p$, (b) active population size ($p-q$) versus $p$, where all are expressed as percentage of the flask. (Meso-scale: ––, macro-scale approximation: –•–).

Figure 9. Energy histograms at the (a) 1st, (b) 25th, (c) 45th, (d) 65th, (e) 85th and (f) 105th time steps for an initial population occupying 10% of the flask.

Figure 10. Time profile of p(t) according to the meso-scale and macro-scale model for initial populations (a) 60% (b) 30% and (c) 6% of the flask. (Meso-scale: ––, macro-scale approximation: –•–).