Thomas Hillen
(University of Alberta, Canada)
''Pointwise weak steady states of transport equations for cell movement in network tissue''
(joint work with K. Painter (Heriot-Watt), P. Hinow (Milwaukee) and Z.A. Wang (Vanderbilt))

Some metastatic cancer cells use an interesting mechanism to move through network tissue, such as collagen networks. I will present a transport equation model, which describes the movement of these cells along network fibers and the network degradation due to proteolytic enzymes which are produced by the cells. In numerical implementation we find that the resulting models shows generation of networks which resemble vasculature formation. We believe that pointwise weak steady states are the organizing centres behind these network patterns. I will introduce the notion of pointwise weak steady states and discuss their use to understand network formation.