Spatio-temporal Models of Lymphangiogenesis in Wound Healing

Several studies suggest that one possible cause of impaired wound healingis failed or insufficient lymphangiogenesis, that is the formation of new lymphaticcapillaries. Although many mathematical models have been developed to describe theformation of blood capillaries (angiogenesis), very few have been proposed for theregeneration of the lymphatic network. Lymphangiogenesis is a markedly differentprocess from angiogenesis, occurring at different times and in response to differentchemical stimuli. Two main hypotheses have been proposed: (1) lymphatic capillariessprout from existing interrupted ones at the edge of the wound in analogy to the bloodangiogenesis case and (2) lymphatic endothelial cells first pool in the wound regionfollowing the lymph flow and then, once sufficiently populated, start to form a network.Here, we present two PDE models describing lymphangiogenesis according to thesetwo different hypotheses. Further, we include the effect of advection due to interstitialflow and lymph flow coming from open capillaries. The variables represent differentcell densities and growth factor concentrations, and where possible the parametersare estimated from biological data. The models are then solved numerically and theresults are compared with the available biological literature.