Hybrid  models of cell and tissue dynamics in tumor growth

Yangjin Kim; Hans G.  Othmer

doi:10.3934/mbe.2015.12.1141

Article Contents

2015, Volume 12, Issue 6: 1141-1156. Doi: 10.3934/mbe.2015.12.1141 open access

This issue Previous Article Application of ecological and mathematical theory to cancer: New challenges Next Article A data-motivated density-dependent diffusion model of in vitro glioblastoma growth

Hybrid models of cell and tissue dynamics in tumor growth

Yangjin Kim^1, and
Hans G. Othmer^2,

1.
Department of Mathematics, Konkuk University, Seoul
2.
School of Mathematics, University of Minnesota, Minneapolis, MN 55445

Received: October 2014

Revised: March 2015

Published: July 2015

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Abstract

Hybrid models of tumor growth, in which some regions are described at the cell level and others at the continuum level, provide a flexible description that allows alterations of cell-level properties and detailed descriptions of the interaction with the tumor environment, yet retain the computational advantages of continuum models where appropriate. We review aspects of the general approach and discuss applications to breast cancer and glioblastoma.

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Mathematics Subject Classification: Primary: 92C45, 92C50; Secondary: 92B05.

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