Abstract:
In this thesis the development of three novel models at two di erent scales are presented for population dynamics in cell cultures. Biological knowledge and empirical observations are used to design an agent-based discrete-time model at meso-scale, which then serves as a simulation environment and provides the necessary insight for lumped-parameter models at macro-scale. After demonstrating on basis of meso-scale simulation results that the ask-wide distribution of the population does not consistently become heterogeneous it is concluded that the population dynamics can also be represented at macro-scale. Two continuous time, di erential equation-based, compact macro-scale models are developed. Both macro-scale models can be parameter-tuned and employed for predicting the evolution of the population size for given uniformly distributed initial populations. The thesis provides a procedure for estimating the parameter values of the macro-scale models via some simple tests to be conducted on the cell culture at hand. How well the macro-scale models can predict the evolution of the population size in comparison to the Meso-scale Model is evaluated on basis of four practically signi cant criteria. Furthermore; the robustness of the macro-scale models with respect to di erent initial energy distributions is evaluated. Finally, a philosophical perspective about modelling dynamic phenomena at di erent scales and how to deal with modelling challenges are presented.
