Abstract：
:Several studies suggest that one possible cause of impaired wound healing is failed or insufficient lymphangiogenesis, that is the formation of new lymphatic capillaries. Although many mathematical models have been developed to describe the formation of blood capillaries (angiogenesis), very few have been proposed for the regeneration of the lymphatic network. Lymphangiogenesis is a markedly different process from angiogenesis, occurring at different times and in response to different chemical stimuli. Two main hypotheses have been proposed: (1) lymphatic capillaries sprout from existing interrupted ones at the edge of the wound in analogy to the blood angiogenesis case and (2) lymphatic endothelial cells first pool in the wound region following the lymph flow and then, once sufficiently populated, start to form a network. Here, we present two PDE models describing lymphangiogenesis according to these two different hypotheses. Further, we include the effect of advection due to interstitial flow and lymph flow coming from open capillaries. The variables represent different cell densities and growth factor concentrations, and where possible the parameters are estimated from biological data. The models are then solved numerically and the results are compared with the available biological literature.
journal_name
Bull Math Bioljournal_title
Bulletin of mathematical biologyauthors
Bianchi A,Painter KJ,Sherratt JAdoi
10.1007/s11538-016-0205-xsubject
Has Abstractpub_date
2016-09-01 00:00:00pages
1904-1941issue
9eissn
0092-8240issn
1522-9602pii
10.1007/s11538-016-0205-xjournal_volume
78pub_type
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