  Histopathological evidence supports the idea that the emergence of phenotypic
heterogeneity and resistance to cytotoxic drugs can be considered as a process
of adaptation, or evolution, in tumor cell populations. In this framework, can
we explain intra-tumor heterogeneity in terms of cell adaptation to local
conditions? How do anti-cancer therapies affect the outcome of cell competition
for nutrients within solid tumors? Can we overcome the emergence of resistance
and favor the eradication of cancer cells by using combination therapies?
Bearing these questions in mind, we develop a model describing cell dynamics
inside a tumor spheroid under the effects of cytotoxic and cytostatic drugs.
Cancer cells are assumed to be structured as a population by two real variables
standing for space position and the expression level of a cytotoxic resistant
phenotype. The model takes explicitly into account the dynamics of resources
and anti-cancer drugs as well as their interactions with the cell population
under treatment. We analyze the effects of space structure and combination
therapies on phenotypic heterogeneity and chemotherapeutic resistance.
Furthermore, we study the efficacy of combined therapy protocols based on
constant infusion and/or bang-bang delivery of cytotoxic and cytostatic drugs.
