Exogenous control of vascular network formation in vitro: a mathematical model
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Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi, 24, Torino, 10123
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Received:
01 July 2006
Revised:
01 September 2006
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Primary: 92C15, 92C17; Secondary: 92C50.
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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.
Citation: V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model[J]. Networks and Heterogeneous Media, 2006, 1(4): 621-637. doi: 10.3934/nhm.2006.1.621
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Abstract
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.
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