SDE-driven modeling of phenotypically heterogeneous tumors: The influence of cancer cell stemness

Abstract

We deduce cell population models describing the evolution of a tumor (possibly interacting with its environment of healthy cells) with the aid of differential equations. Thereby, different subpopulations of cancer cells allow accounting for the tumor heterogeneity. In our settings these include cancer stem cells known to be less sensitive to treatment and differentiated cancer cells having a higher sensitivity towards chemo-and radiotherapy. Our approach relies on stochastic differential equations in order to account for randomness in the system, arising e.g., due to the therapy-induced decreasing number of clonogens, which renders a pure deterministic model arguable. The equations are deduced relying on transition probabilities characterizing innovations of the two cancer cell subpopulations, and similarly extended to also account for the evolution of normal tissue. Several therapy approaches are introduced and compared by way of tumor control probability (TCP) and uncomplicated tumor control probability (UTCP). A PDE approach allows to assess the evolution of tumor and normal tissue with respect to time and to cell population densities which can vary continuously in a given set of states. Analytical approximations of solutions to the obtained PDE system are provided as well.

Models of Functional Heterogeneity and Targeting Strategies for Cancer Stem Cells

“…On the other hand, the stochastic model argues that all tumour cells are biologically homogeneous, and that their behaviours are influenced by intrinsic and extrinsic factors which randomly result in new functional characteristics among cells [6]. Lastly, the plasticity model is founded on the idea that cancer cells are in a constantly evolving state [6]. This dynamic process may increase or decrease the expression of CSC markers on a cell at any given moment.…”