A viscoelastic model of capillary growth
主 题: A viscoelastic model of capillary growth
报告人: 郑晓明 教授 (美国中央密歇根大学)
时 间: 2017-04-07 14:00-15:00
地 点: 理科1号楼1479
Abstract：We derive a novel one-dimensional viscoelastic model of blood vessel capillary growth under nonlinear friction with surroundings, analyze its solution properties, and simulate various growth patterns in angiogenesis. The mathematical model treats the cell density as the growth pressure eliciting viscoelastic response of cells, thus extension or regression of the capillary. Nonlinear analysis provides some conditions to guarantee the global existence of biologically meaningful solutions, while linear analysis and numerical simulations predict the global biological solutions exist as long as the cell density change is sufficiently slow in time. Examples with blow-ups are captured by numerical approximations and the global solutions are recovered by slow growth processes. Numerical simulations demonstrate this model can reproduce angiogenesis experiments under several biological conditions including blood vessel extension without proliferation and blood vessel regression. This work is a collaboration with Chunjing Xie at Department of Mathematics and Institute of Natural Sciences of Shanghai Jiaotong University.
