Spring ’19 Joint CSC@USC/CommNetS-MHI Seminar Series
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Paul Newton,
University of Southern California
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Abstract
I will first describe current biophysical/mathematical descriptions of a tumor, and show how our view of the tumor influences treatment strategies. Current approaches view the tumor as a micro-ecology made up of a heterogeneous collection of cells competing for resources over a fitness landscape that can be quantified. I will describe our adaptive therapy models based on the replicator dynamical system of three competing species (healthy, chemo-sensitive, chemo-resistant), with a payoff matrix based on a prisoner’s dilemma evolutionary game. I will show how we design time-dependent chemo-schedules that overcome competitive release of resistant cells using knowledge of the phase space trajectories of the nonlinear dynamical system. The goal of the chemo-schedules are to keep the sensitive and resistant cell populations in perpetual competition without completely eliminating either. I will then describe a second model, based on a statistical mechanical formulation of cell states, with growth proportional to a measure of tumor heterogeneity, that provides a framework for how functional coupling of cells determines volumetric growth laws (Gompertzian growth). The work described is joint work with former Ph.D. student Jeffrey West (AME – currently at Moffitt Cancer Center), and current Ph.D. students Yongian Ma (Physics), and Jiyeon Park (Math).
Biosketch
Prof. Newton received his B.S. in Applied Math/Physics at Harvard University and Ph.D. in Applied Mathematics from Brown University. After a post-doctoral fellowship in mathematics at Stanford University, he was Assistant and Associate Professor of Mathematics and The Center for Complex Systems Research at the University of Illinois Champaign-Urbana. He has held visiting appointments at Caltech, Brown, Hokkaido University, The Kavli Institute for Theoretical Physics at U.C. Santa Barbara, and The Scripps Research Institute. Prof. Newton is currently Professor of Applied Math, Engineering (AME), and Medicine in the Viterbi School of Engineering and the Norris Comprehensive Cancer Center at USC. He currently serves as Editor-in-Chief of The Journal of Nonlinear Science and as an Advisor on Texts in Applied Mathematics Series for Springer-Verlag, New York. His research areas focus on nonlinear dynamical systems and biophysics, with particular emphasis on mathematical oncology, evolutionary game theory, and medical forecasting.