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Computational and Mathematical Methods in Medicine
Volume 2013, Article ID 802512, 8 pages
Research Article

In Vivo Imaging-Based Mathematical Modeling Techniques That Enhance the Understanding of Oncogene Addiction in relation to Tumor Growth

1Department of Electrical Engineering, Stanford University School of Medicine, Stanford, CA 94305, USA
2Department of Radiology, Stanford University School of Medicine, Stanford, CA 94305, USA
3Department of Medicine, Stanford University School of Medicine, Stanford, CA 94305, USA

Received 21 December 2012; Accepted 15 February 2013

Academic Editor: Kumar Durai

Copyright © 2013 Chinyere Nwabugwu 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.


The dependence on the overexpression of a single oncogene constitutes an exploitable weakness for molecular targeted therapy. These drugs can produce dramatic tumor regression by targeting the driving oncogene, but relapse often follows. Understanding the complex interactions of the tumor’s multifaceted response to oncogene inactivation is key to tumor regression. It has become clear that a collection of cellular responses lead to regression and that immune-mediated steps are vital to preventing relapse. Our integrative mathematical model includes a variety of cellular response mechanisms of tumors to oncogene inactivation. It allows for correct predictions of the time course of events following oncogene inactivation and their impact on tumor burden. A number of aspects of our mathematical model have proven to be necessary for recapitulating our experimental results. These include a number of heterogeneous tumor cell states since cells following different cellular programs have vastly different fates. Stochastic transitions between these states are necessary to capture the effect of escape from oncogene addiction (i.e., resistance). Finally, delay differential equations were used to accurately model the tumor growth kinetics that we have observed. We use this to model oncogene addiction in MYC-induced lymphoma, osteosarcoma, and hepatocellular carcinoma.