Speaker: Konstantina Trivisa (University of Maryland)
Title: On mechanical models for tumor growth: modeling, analysis and simulations
Date: Friday, November 4, 2016
Time: 4:00 p.m.
Place: University of Ottawa, KED B005
ABSTRACT: Tumor growth modeling is the investigation of the complex dynamics of cancer progression using a mathematical formulation. Internal dynamics of tumor cells, their interactions with each other and with their surrounding tissue, transfer of chemical substances and many phenomena are typically encoded in mathematical models. This mathematical formulation relies on biological and clinical observations. At the same time, it is currently clear that mathematics could make a huge contribution to many areas of experimental cancer investigation since there is now a wealth of experimental data which requires systematic analysis.
In this research project we investigate the evolution of tumor growth relying on a non-linear model of partial differential equations which incorporates mechanical laws for tissue compression combined with rules for nutrients availability and drug application. Rigorous analysis and simulations are presented which show the role of nutrient and drug application in the evolution of cancerous cells. We construct an explicit convergent numerical scheme to approximate solutions of the nonlinear system by employing compactness methods in the spirit of P.L. Lions.
Extensive numerical tests show that solutions exhibit a necrotic core when the nutrient level falls below a critical level in accordance with medical observations. The talk will present results obtained in collaboration with D. Donatelli and F. Weber.
Short bio: Prof. Trivisa is an applied mathematician holding a joint position at the Department of Mathematics and the Institute for Physical Science and Technology at the University of Maryland. Her research lies on the interface between nonlinear partial differential equations and continuum physics and focuses on applications in fluid dynamics, multiphase flows, continuum mechanics, materials science and math biology. She has been recognized by a series of awards including an Alfred P. Sloan Research Fellowship, The Faculty Early Career Award, The Presidential Early Career Award for Scientists and Engineers (PECASE) as well as a Simons Foundation Fellowship. She was also selected as ADVANCE Professor and Leadership Fellow at the University of Maryland for her work on issues of diversity and inclusion. Prof. Trivisa is a director of the Applied Mathematics & Statistics, and Scientific Computation Program (AMSC), which is the largest interdisciplinary program in the country and is ranked among the top 10 applied math programs in the US. She is currently serving as Associate Director of the Institute for Physical Science and Technology (IPST), an internationally recognized center for interdisciplinary research in emerging areas at the boundaries between physical, mathematical and life sciences, and engineering.