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Computational and Mathematical Methods in Medicine
Volume 7, Issue 2-3, Pages 189-213

Dynamics of Growth and Signaling along Linear and Surface Structures in Very Early Tumors

1Institute of Applied Mathematics, Center for Modeling and Simulations in the Biosciences (BIOMS), University of Heidelberg, Im Neuenheimer Feld 294, Heidelberg 69120, Germany
2Department of Statistics, Rice University, 6100 Main St, MS-138, Houston, TX 77005, USA
3Systems Engineering Group, Silesian University of Technology, Akademicka 16, 44-100, Gliwice, Poland

Received 1 June 2006

Copyright © 2006 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.


There exists evidence that in early stages tumors progress along linear, tubular, or irregular surface structures. This seems to be the case for atypical adenomatous hyperplasia (AAH), a precursor of adenocarcinoma of the lung. We previously published a simplified model, which showed that early structures had a potential towards spontaneous invasive growth following a latency phase. The transition was facilitated by diffusion of a growth factor and nonlinear cell cycle regulation in cancer cells. The mechanism is analogous to that in Turing pattern formation, although the patterns are irregular and unstable. We introduce more biologically justifiable signaling, in which only the free growth factor molecules diffuse. Flexible nonlinearities in the model accommodate several growth patterns of cells as well as internal versus external production of the growth factor. We show that the reaction-diffusion setup results in complicated spike-like solutions. We discuss these results in the light of published data on the AAH.