Efficient coarse simulation of a growing avascular tumor

Kavousanakis, ME; Liu, P; Boudouvis, AG; Lowengrub, J; Kevrekidis, IG

dc.contributor.author	Kavousanakis, ME	en
dc.contributor.author	Liu, P	en
dc.contributor.author	Boudouvis, AG	en
dc.contributor.author	Lowengrub, J	en
dc.contributor.author	Kevrekidis, IG	en
dc.date.accessioned	2014-03-01T02:08:43Z
dc.date.available	2014-03-01T02:08:43Z
dc.date.issued	2012	en
dc.identifier.issn	15393755	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/29721
dc.subject.other	Cancer cells	en
dc.subject.other	Cell-cell interaction	en
dc.subject.other	Computational approach	en
dc.subject.other	Computational demands	en
dc.subject.other	Computational savings	en
dc.subject.other	Continuum model	en
dc.subject.other	Discrete stochastic models	en
dc.subject.other	Early stage tumors	en
dc.subject.other	Equation-Free	en
dc.subject.other	Execution time	en
dc.subject.other	Individual cells	en
dc.subject.other	Individual-based	en
dc.subject.other	Integration scheme	en
dc.subject.other	Long time behavior	en
dc.subject.other	Macroscopic equation	en
dc.subject.other	Microscopic models	en
dc.subject.other	Predictive power	en
dc.subject.other	Projection schemes	en
dc.subject.other	Proof of principles	en
dc.subject.other	Radial symmetrys	en
dc.subject.other	Short time intervals	en
dc.subject.other	Signaling process	en
dc.subject.other	Time-scales	en
dc.subject.other	Tumor progressions	en
dc.subject.other	Upscaling	en
dc.subject.other	Cell culture	en
dc.subject.other	Cell proliferation	en
dc.subject.other	Cells	en
dc.subject.other	Cellular automata	en
dc.subject.other	Continuum mechanics	en
dc.subject.other	Integration	en
dc.subject.other	Tumors	en
dc.subject.other	Computer simulation	en
dc.title	Efficient coarse simulation of a growing avascular tumor	en
heal.type	journalArticle	en
heal.identifier.primary	10.1103/PhysRevE.85.031912	en
heal.identifier.secondary	http://dx.doi.org/10.1103/PhysRevE.85.031912	en
heal.identifier.secondary	031912	en
heal.publicationDate	2012	en
heal.abstract	The subject of this work is the development and implementation of algorithms which accelerate the simulation of early stage tumor growth models. Among the different computational approaches used for the simulation of tumor progression, discrete stochastic models (e.g., cellular automata) have been widely used to describe processes occurring at the cell and subcell scales (e.g., cell-cell interactions and signaling processes). To describe macroscopic characteristics (e.g., morphology) of growing tumors, large numbers of interacting cells must be simulated. However, the high computational demands of stochastic models make the simulation of large-scale systems impractical. Alternatively, continuum models, which can describe behavior at the tumor scale, often rely on phenomenological assumptions in place of rigorous upscaling of microscopic models. This limits their predictive power. In this work, we circumvent the derivation of closed macroscopic equations for the growing cancer cell populations; instead, we construct, based on the so-called ""equation-free"" framework, a computational superstructure, which wraps around the individual-based cell-level simulator and accelerates the computations required for the study of the long-time behavior of systems involving many interacting cells. The microscopic model, e.g., a cellular automaton, which simulates the evolution of cancer cell populations, is executed for relatively short time intervals, at the end of which coarse-scale information is obtained. These coarse variables evolve on slower time scales than each individual cell in the population, enabling the application of forward projection schemes, which extrapolate their values at later times. This technique is referred to as coarse projective integration. Increasing the ratio of projection times to microscopic simulator execution times enhances the computational savings. Crucial accuracy issues arising for growing tumors with radial symmetry are addressed by applying the coarse projective integration scheme in a cotraveling (cogrowing) frame. As a proof of principle, we demonstrate that the application of this scheme yields highly accurate solutions, while preserving the computational savings of coarse projective integration. © 2012 American Physical Society.	en
heal.journalName	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics	en
dc.identifier.doi	10.1103/PhysRevE.85.031912	en
dc.identifier.volume	85	en
dc.identifier.issue	3	en