(437a) Efficient Coarse Simulation of a Tumor Growth Model

The subject of this work is the development and implementation of algorithms that accelerate the simulation of early stage tumor growth models. Among the different computational approaches used for the simulation of developing tumor systems, stochastic models (e.g. cellular automata) have been widely used in order to illuminate the connection between processes that occur at the cellular level, and the macroscopic characteristics (morphology) of a growing tumor. However, the high computational demands often renders the detailed exploration of such models impractical. Deterministic formulations can also be found in the relevant literature; they are, however, often based on extensive simplifications which may lead to unrealistic predictions.

In this work, we circumvent the derivation of closed ?mesoscopic? equations for the tumor cell populations; instead we construct -based on the so-called Equation-Free framework developed by Kevrekidis and co-workers- a computational superstructure, which wraps around the cellular-level simulator and accelerates the computations required for the study of the system's long-time behavior. We will focus in particular on the application of coarse projective integration. The microscopic model ?i.e. a cellular automaton, which simulates the evolution of tumor cell populations- is executed for relatively short time-intervals, at the end of which coarse information is obtained, e.g. the mean radial distribution of tumor cells. These coarse variables evolve in a relatively smooth manner -as opposed to the evolution of each individual cell of the population- and we can approximate their coarse time derivatives, which in turn are introduced in projection schemes. Given the values of the projected coarse variables, new microscopic states (tumor cell distributions in the host tissue) can be constructed and a new set of relatively short time-bursts of the microscopic simulator is initiated.

Increasing the ratio of projection times to microscopic simulator execution times increases the computational savings. However, in the case of growing tumors with radial symmetry, accuracy issues arise when relatively large projection time steps are taken. We can alleviate this impediment by applying the coarse projective integration scheme in a co-traveling (co-growing) frame. We demonstrate that the application of the modified projection scheme in a co-traveling frame produces results of increased accuracy, while the computational savings are kept at a high level.