Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models

Pages: 415 - 438, Volume 12, Issue 2, September 2009

doi:10.3934/dcdsb.2009.12.415       Abstract        Full Text (413.4K)       Related Articles

Urszula Ledzewicz - Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, United States (email)
James Munden - Dept. of Mathematics and Computer Science, St. Louis University, St. Louis, MO 63103, United States (email)
Heinz Schättler - Dept. of Electrical and Systems Engineering, Washington University, St. Louis, Missouri, 63130-4899, United States (email)

Abstract: The problem of scheduling a given amount of angiogenic inhibitors is considered as an optimal control problem with the objective of maximizing the achievable tumor reduction. For a dynamical model for the evolution of the carrying capacity of the vasculature formulated in [15] optimal controls are computed for both a Gompertzian and logistic model of tumor growth. While optimal controls for the Gompertzian model typically contain a segment along which the control is singular, for the logistic model optimal controls are bang-bang with at most two switchings.

Keywords:  optimal control, cancer treatment, anti-angiogenesis, maximum principle, regular synthesis, singular control.
Mathematics Subject Classification:  Primary: 49J15; Secondary: 93C50.

Received: August 2008;      Revised: April 2009;      Published: July 2009.