  Survival of living tumor cells underlies many influences such as nutrient
saturation, oxygen level, drug concentrations or mechanical forces.
Data-supported mathematical modeling can be a powerful tool to get a better
understanding of cell behavior in different settings. However, under
consideration of numerous environmental factors mathematical modeling can get
challenging. We present an approach to model the separate influences of each
environmental quantity on the cells in a collective manner by introducing the
"environmental stress level". It is an immeasurable auxiliary variable, which
quantifies to what extent viable cells would get in a stressed state, if
exposed to certain conditions. A high stress level can inhibit cell growth,
promote cell death and influence cell movement. As a proof of concept, we
compare two systems of ordinary differential equations, which model tumor cell
dynamics under various nutrient saturations respectively with and without
considering an environmental stress level. Particle-based Bayesian inversion
methods are used to quantify uncertainties and calibrate unknown model
parameters with time resolved measurements of in vitro populations of liver
cancer cells. The calibration results of both models are compared and the
quality of fit is quantified. While predictions of both models show good
agreement with the data, there is indication that the model considering the
stress level yields a better fitting. The proposed modeling approach offers a
flexible and extendable framework for considering systems with additional
environmental factors affecting the cell dynamics.
