Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models
Urszula Ledzewicz - Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, IL 62026, 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  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.
Received: August 2008; Revised: April 2009; Published: July 2009.
2011 Impact Factor.921