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Computational and Mathematical Methods in Medicine
Volume 2012 (2012), Article ID 109019, 11 pages
http://dx.doi.org/10.1155/2012/109019
Research Article

A Novel Method for Simulating the Extracellular Matrix in Models of Tumour Growth

1Institute of Medical Engineering, University of Lübeck, 23562 Lübeck, Germany
2Centre of Excellence for Technology and Engineering in Medicine (TANDEM), University of Lübeck, 23562 Lübeck, Germany
3Graduate School for Computing in Medicine and Life Sciences, University of Lübeck, 23562 Lübeck, Germany

Received 17 April 2012; Revised 1 June 2012; Accepted 11 June 2012

Academic Editor: Quan Long

Copyright © 2012 Alina Toma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A novel hybrid continuum-discrete model to simulate tumour growth on a cellular scale is proposed. The lattice-based spatiotemporal model consists of reaction-diffusion equations that describe interactions between cancer cells and their microenvironment. The fundamental ingredients that are typically considered are the nutrient concentration, the extracellular matrix (ECM), and matrix degrading enzymes (MDEs). The in vivo processes are very complex and occur on different levels. This in turn leads to huge computational costs. The main contribution of the present work is therefore to describe the processes on the basis of simplified mathematical approaches, which, at the same time, depict realistic results to understand the biological processes. In this work, we discuss if we have to simulate the MDE or if the degraded matrix can be estimated directly with respect to the cancer cell distribution. Additionally, we compare the results for modelling tumour growth using the common and our simplified approach, thereby demonstrating the advantages of the proposed method. Therefore, we introduce variations of the positioning of the nutrient delivering blood vessels and use different initializations of the ECM. We conclude that the novel method, which does not explicitly model the matrix degrading enzymes, provides means for a straightforward and fast implementation for modelling tumour growth.