Plenary Lecture

On Dynamical Systems Describing Tumor Growth under Novel Therapies

Professor Urszula Ledzewicz
Department of Mathematics and Statistics,
Southern Illinois University Edwardsville,
Edwardsville, Illinois, USA

E-mail: uledzew@siue.edu

Co-Author

Professor Heinz Schattler
Department of Electrical and Systems Engineering,
Washington University,
St. Louis, Missouri, USA
 

Abstract: In this talk dynamical systems arising in biomedicine describing various treatments of cancer will be discussed. Mathematical models for cancer treatments have a long history, but with the development of medicine new challenges in modeling and the analysis of these models are appearing. Here novel cancer treatments and the mathematical models that describe their dynamics as systems of nonlinear ordinary differential equations will be presented. The focus primarily will be on mathematical models for tumor anti-angiogenesis. The importance of this novel treatment is that by targeting the cells of the vascularization of the tumor rather then the tumor itself, it is not prone to drug resistance and as such has been a topic of active research both in medicine and mathematical biology. In the talk a class of mathematical models for anti-angiogenesis will be analyzed. The nonlinear dynamics in these models illustrates the growth of the primary tumor volume and its corresponding vasculature as well as the effect of the control functions representing anti-angiogenic treatment on this growth. Following the analysis of this system with constant doses of the drug, the optimal control problem of how to schedule an a priori given amount of angiogenic inhibitors so as to minimize the primary tumor volume will be considered. Examples of optimal protocols resulting from the analysis will be given. Then, following medical research on so-called combination therapies, the model will be augmented to include the effect of traditional chemotherapy on the system. Due to the multi-control aspect, even with simplified dynamical equations, this becomes a challenging problem mathematically and some initial results about the structure of optimal controls will be presented.

Brief Biography of the Speaker:
Urszula Ledzewicz received her Ph. D in 1984 from the University of Lodz, Poland. Since 1986 she has been holding academic positions in the United States, first as a visiting faculty at Louisiana State University, Baton Rouge, and then at Southern Illinois University, as a tenured faculty in the rank of the Full Professor since 1995.

Her research area is primarily control theory and optimization, but in more recent years she became interested in applications of the methods of optimal control and systems theory to biomedicine. Currently her main direction of research includes analysis of systems describing dynamics of cancer growth under various treatments like chemotherapy or anti-angiogenesis.

She is a member of five editorial boards including Discrete and Continuous Dynamical Systems, Series B, and Mathematical Biosciences and Engineering and author or co-author of close to 100 publications in refereed journals and proceedings of international conferences. She was invited to present lectures at various mathematical and engineering oriented conferences as well as was a member of the organizing committees or co-organized sessions or mini-symposia at several of them like IEEE Conferences on Decision and Control (CDC), Mathematical Theory of Network and Systems (MTNS) or World Congress of Nonlinear Analysts (WCNA). For her research she was awarded several grants from the National Science Foundation, NATO and her university.