  Analysis of invasion front has been widely used to decipher biological
properties, as well as the growth dynamics of the corresponding populations.
Likewise, the invasion front of tumors has been investigated, from which
insights into the biological mechanisms of tumor growth have been gained. We
develop a model to study how tumors' invasion front depends on the relevant
properties of a cellular environment. To do so, we develop a model based on a
nonlinear reaction-diffusion equation, the Fisher-Kolmogorov-Petrovsky-Piskunov
(FKPP) equation, to model tumor growth. Our study aims to understand how
heterogeneity in the cellular environment's stiffness, as well as spatial
correlations in its morphology, the existence of both of which has been
demonstrated by experiments, affects the properties of tumor invasion front. It
is demonstrated that three important factors affect the properties of the
front, namely, the spatial distribution of the local diffusion coefficients,
the spatial correlations between them, and the ratio of the cells' duplication
rate and their average diffusion coefficient. Analyzing the scaling properties
of tumor invasion front computed by solving the governing equation, we show
that, contrary to several previous claims, the invasion front of tumors and
cancerous cell colonies cannot be described by the well-known models of kinetic
growth, such as the Kardar-Parisi-Zhang equation.
