Chair and Professor of Applied Computational Mathematics & Statistics
University of Notre Dame
Modeling tumor growth
Bei Hu of Mathematics is studying mathematical models of tumor growth, based on density of cells and concentrations of nutrients and signaling molecules. Tumor growth is usually modeled by dynamical systems, and because of spatial effects due to cell proliferation, it is natural to model the evolution of tumors in terms of partial differential equations.
Tumors grow or die when the amount of nutrients available to them is above or below a certain threshold (equilibrium). There is also an internal pressure governed by either Darcy’s law (solid tumor) or Stoke’s equation (breast cancer and brain tumor). One way to study whether and how the tumor grows is to focus on the steady state solution. An asymptotically stable solution means that the tumor will not grow much, while an unstable solution means that the tumor will likely grow and spread. The study and simulation showed that a larger tumor aggressiveness coefficient will likely cause the steady state tumor to become unstable. The numerical simulation showed how the shape of the tumor actually changes over time.