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Computational and Mathematical Methods in Medicine
Volume 8, Issue 1, Pages 51-69
Original Article

A Single Cell-Based Model of the Ductal Tumour Microarchitecture

1Division of Mathematics, University of Dundee, Dundee DD1 4HN, Scotland, UK
2Department of Mathematics, Washington State University, Pullman, WA 99164, USA

Received 21 August 2006; Revised 11 February 2007; Accepted 16 February 2007

Copyright © 2007 Hindawi Publishing Corporation. 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.


The preinvasive intraductal tumours, such as the breast or prostate carcinomas, develop in many different architectural forms. There are, however, no experimental models explaining why cancer cells grow in these various configurations. We use a mathematical model to compare different proliferative conditions that can lead to such distinct microarchitectures. In order to simulate different scenarios of tumour growth, we employed a single cell-based technique that allows us to model development of the whole tumour tissue by focusing on biomechanical processes of individual cells and on communication between cells and their microenvironment. Formation of four specific intraductal tumour patterns, micropapillary, cribriform, tufting and solid, are presented in this paper together with a discussion on gradual dedifferentiation of ductal epithelial cells that gives rise to these distinct carcinomas. We introduce two versions of our cell-based model to show that the obtained results do not depend on a particularly chosen cell structure.