Multi-layered tumor cell cultures with almost periodic nutrient supply

Abstract

Modeling of multi-layered cell cultures (MCC) assume flat geometry in a 3D tumor growth model.Some results available in the time-dependent framework assume a periodic nutrient supply $\Phi (t)$. Our aim is to generalize such considerations. Namely, we show that a stable oscillating tumor growth arises in the long term, whenever the mean value of the almost periodic nutrient supply $\overline{\Phi }$ surpasses certain threshold level, $\overline{\Phi }>\tilde{\sigma }$. Meanwhile, a vanishing tumor is predicted in the complementary case, $\overline{\Phi }\le \tilde{\sigma }$.