December  2011, 4(6): 1465-1498. doi: 10.3934/dcdss.2011.4.1465

An enzyme kinetics model of tumor dormancy, regulation of secondary metastases

1. 

Department of Mathematics & Statistics, University of Michigan, Dearborn, MI 48128, United States

2. 

Iowa State University, Department of Mathematics, 482 Carver Hall Ames, IA 50011

Received  March 2009 Revised  November 2009 Published  December 2010

In this paper we study 1 dimensional (1D) and 2D extended version of a two compartment model for tumor dormancy suggested by Boushaba et al. [3]. The model is based on the idea that the vascularization of a secondary tumor can be suppressed by inhibitor originating from a larger primary tumor. It has been observed emergence of a polypoid melanoma at a site remote from a primary polypoid melanoma after excision of the latter. The authors observed no recurrence of the melanoma at the primary site, but did observe secondary tumors at secondary sites five to seven centimeters from the primary site within a period of one month after the excision of the primary site. 1D and 2D simulations show that when the tumors are sufficiently remote, the primary tumor will not influence the secondary tumors while, if they are too close together, the primary tumor can effectively prevent the growth of the secondary tumors, even after it is removed. The sensitivity analysis was carried out for the 1D model. It has been long observed that surgery should be followed by other treatment options such as chemotherapy. 2D simulation suggests a possible treatment options with different dosage schedule after a surgery in order to achieve better clinical outcome.
Citation: Yangjin Kim, Khalid Boushaba. An enzyme kinetics model of tumor dormancy, regulation of secondary metastases. Discrete & Continuous Dynamical Systems - S, 2011, 4 (6) : 1465-1498. doi: 10.3934/dcdss.2011.4.1465
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show all references

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[9]

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[11]

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[12]

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[13]

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[14]

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[17]

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[18]

V. De Giorgi, D. Massai, G. Gerlini, F. Mannone, E. Quercioli and P. Carli, Immediate local and regional recurrence after the excision of a polypoid melanoma: tumor dormancy or tumor activation?,, Derm. Surgery, 29 (2003), 664. doi: 10.1046/j.1524-4725.2003.29163.x. Google Scholar

[19]

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[20]

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[21]

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[22]

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[23]

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