Chair and Professor of Applied Computational Mathematics & Statistics
University of Notre Dame
Bei Hu of Mathematics is studying mathematical models from mathematical biology. Examples among them include tumor growth, plaque formation, and others.
Tumor growth: Tumor growth models are 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 tumor's shape changes over time.
Plaque formation: A simplified model of plaque growth involving LDL and HDL cholesterols, macrophages and foam cells, which satisfy a coupled system of PDEs with a free boundary, the interface between the plaque and the blood flow. Atherosclerosis is a leading cause of death worldwide; it originates from a plaque that builds up in the artery. A variety of properties are investigated.