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December  2006, 1(4): 621-637. doi: 10.3934/nhm.2006.1.621

Exogenous control of vascular network formation in vitro: a mathematical model

V. Lanza 1, , D. Ambrosi 1, and  L. Preziosi 1,

1. 

Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, 10123, Italy, Italy, Italy

Received  July 2006 Revised  September 2006 Published  October 2006

The reconstitution of a proper and functional vascular network is a major issue in tissue engineering and regeneration. The limited success of current technologies may be related to the difficulties to build a vascular tree with correct geometric ratios for nutrient delivery. The present paper develops a mathematical model suggesting how an anisotropic vascular network can be built in vitro by using exogenous chemoattractant and chemorepellent. The formation of the network is strongly related to the nonlinear characteristics of the model.
Keywords: Mathematical Modelling, Tissue Engineering., Pattern Formation, Vascularization.
Mathematics Subject Classification: Primary: 92C15, 92C17; Secondary: 92C5.
Citation: V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks & Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621
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