A SHORT COURSE IN THE MODELING OF CHEMOTAXIS

List of Figures
1.1 Life Cycle of Dictyostelium Discoideum . . . . . . . . . . . . . . . . . 5
2.1 The experimental configuration . . . . . . . . . . . . . . . . . . . . . 16
4.1 Cartoon of the process of tumor induced angiogenesis. . . . . . . . . 39
4.2 Time evolution of the onset of angiogenesis for the system (4.12)–
(4.15). Evolution of fibronectin decay showing an opening of about 6
microns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3 Time evolution of the endothelial cell movement. Note the bimodality
for each time slice. This figure fails to correctly capture the events on
the time interval [0, 0.05] where the growth factor is changing most
rapidly. The numerical solution breaks down sometime after 0.2 hours
when the two maxima coalesce (the authors do not provide a plot of
this phenomenon). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 This plot shows the evolution of the EC as in 4.3 on the time interval
[0, 0.05]. Bimodality appears almost immediately. . . . . . . . . . . . 49
4.5 Evolution of the growth factor decay showing that growth factor is
gone within 0.025 hours. . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.6 Evolution of the protease showing that the concentration comes to a
near steady state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.7 Cartoon picture of the thick walled, multi-layered artery. . . . . . . . 55
4.8 Lesion with Smooth Muscle Cell Cap . . . . . . . . . . . . . . . . . . 71
iv