Events Calendar

Aerospace and Mechanical Engineering Seminar Series

Speaker: Paul Newton, Professor of Applied Mathematics in Department of Aerospace & Mechanical Engineering at University of Southern California, Los Angeles, CA

Talk Title: Random Walks, Markov Chains, and Cancer Progression Models from Longitudinal and Autopsy Data

Series: Aerospace and Mechanical Engineering Seminar Series

Abstract: We will describe models of metastatic cancer progression using Markov chain modeling on a directed graph of nodes that are the various anatomical sites where metastatic tumors can form for a given type of primary cancer. We use metastatic tumor distributions gathered from historical autopsy data, as well as current longitudinal data sets to estimate the transition probabilities (stochastic parameters) from site to site. This creates a systemic network diagram from which we can calculate reduced two-step diagrams using the fact that the systems converge to their steady-state distribution after roughly two steps. The diagrams are used to categorize metastatic sites as `sponges' or `spreaders', as well as to run hypothetical therapeutic scenarios based on Monte Carlo simulations of progression with mean first-passage times as a surrogate timescale measure. A useful metric which we describe is the notion of metastatic entropy and how is correlates with graph conductance dictating Markov convergence rates, mixing times, and complexity. If time permits, we will describe a more fine-scale cell based model which is driven by a stochastic Moran process acting on a heterogeneous population of cells trafficking across the directed graph to various sites, governed by a fitness landscape, with simple point-mutations, interacting via the prisoner’s dilemma paradigm in which the cancer cells are the `defectors’ and the healthy cells are the `cooperators'.

Biography: Paul Newton received his B.S. in Applied Math/Physics at Harvard University and his Ph.D. in Applied Mathematics from Brown University. After a post-doctoral fellowship 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. He is currently Professor of Applied Math, Engineering, and Medicine in the Viterbi School of Engineering and the Norris Comprehensive Cancer Center at the University of Southern California. He serves as Managing Editor of The Journal of Nonlinear Science, Advisor on Texts in Applied Mathematics Series, Springer-Verlag, New York, and is on The Center Advisory Committee for The Physical Sciences Oncology Center at The Scripps Research Institute in La Jolla, CA where he serves as Project Leader, Mathematical Modeling: Physics and Mathematics of Cancer Metastasis.

Host: Professor Paul Ronney

Location: Seaver Science Library (SSL) - 150

Audiences: Everyone Is Invited

Contact: Valerie Childress