  Tissue growth kinetics and interface dynamics depend on the properties of the
tissue environment and cell-cell interactions. In cellular environments,
substrate heterogeneity and geometry arise from a variety factors, such as the
structure of the extracellular matrix and nutrient concentration. We used the
CellSim3D model, a kinetic division simulator, to investigate the growth
kinetics and interface roughness dynamics of epithelial tissue growth on
heterogeneous substrates with varying topologies. The results show that the
presence of quenched disorder has a clear effect on the colony morphology and
the roughness scaling of the interface in the moving interface regime. In a
medium with quenched disorder, the tissue interface has a smaller interface
roughness exponent, $\alpha$, and a larger growth exponent, $\beta$. The
scaling exponents also depend on the topology of the substrate and cannot be
categorized by well-known universality classes.
