Hybrid Simulation of Heterogeneous Cell Populations

The modeling of heterogeneous dynamic cell populations based on population balance equations is an important tool to describe the interaction between intracellular dynamics and population dynamics. However, the numerical simulation of such models remains challenging for models with high-dimensional intracellular dynamics, when these dynamics influence the growth rate of the cells. To cope with this challenge, we propose a hybrid simulation scheme based on the method of partial characteristics. We show that important features of the population density function, such as its moments or marginals, can be approximated by this scheme in a statistically converging way. In a case study with a population of differentiating cells, we illustrate how to obtain the growth dynamics of the individual subpopulations and deduce the extent of cell differentiation under a time-varying stimulus.