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

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

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.
Citation: V. Lanza, D. Ambrosi, L. Preziosi. Exogenous control of vascular network formation in vitro: a mathematical model. Networks and Heterogeneous Media, 2006, 1 (4) : 621-637. doi: 10.3934/nhm.2006.1.621
[1]

M.A.J Chaplain, G. Lolas. Mathematical modelling of cancer invasion of tissue: dynamic heterogeneity. Networks and Heterogeneous Media, 2006, 1 (3) : 399-439. doi: 10.3934/nhm.2006.1.399

[2]

Julien Barré, Pierre Degond, Diane Peurichard, Ewelina Zatorska. Modelling pattern formation through differential repulsion. Networks and Heterogeneous Media, 2020, 15 (3) : 307-352. doi: 10.3934/nhm.2020021

[3]

Christos V. Nikolopoulos. Mathematical modelling of a mushy region formation during sulphation of calcium carbonate. Networks and Heterogeneous Media, 2014, 9 (4) : 635-654. doi: 10.3934/nhm.2014.9.635

[4]

Julien Cividini. Pattern formation in 2D traffic flows. Discrete and Continuous Dynamical Systems - S, 2014, 7 (3) : 395-409. doi: 10.3934/dcdss.2014.7.395

[5]

Yuan Lou, Wei-Ming Ni, Shoji Yotsutani. Pattern formation in a cross-diffusion system. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1589-1607. doi: 10.3934/dcds.2015.35.1589

[6]

Peter Rashkov. Remarks on pattern formation in a model for hair follicle spacing. Discrete and Continuous Dynamical Systems - B, 2015, 20 (5) : 1555-1572. doi: 10.3934/dcdsb.2015.20.1555

[7]

Tian Ma, Shouhong Wang. Dynamic transition and pattern formation for chemotactic systems. Discrete and Continuous Dynamical Systems - B, 2014, 19 (9) : 2809-2835. doi: 10.3934/dcdsb.2014.19.2809

[8]

Taylan Sengul, Shouhong Wang. Pattern formation and dynamic transition for magnetohydrodynamic convection. Communications on Pure and Applied Analysis, 2014, 13 (6) : 2609-2639. doi: 10.3934/cpaa.2014.13.2609

[9]

Rui Peng, Fengqi Yi. On spatiotemporal pattern formation in a diffusive bimolecular model. Discrete and Continuous Dynamical Systems - B, 2011, 15 (1) : 217-230. doi: 10.3934/dcdsb.2011.15.217

[10]

Maxime Breden, Christian Kuehn, Cinzia Soresina. On the influence of cross-diffusion in pattern formation. Journal of Computational Dynamics, 2021, 8 (2) : 213-240. doi: 10.3934/jcd.2021010

[11]

Yansu Ji, Jianwei Shen, Xiaochen Mao. Pattern formation of Brusselator in the reaction-diffusion system. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022103

[12]

Juan Pablo Aparicio, Carlos Castillo-Chávez. Mathematical modelling of tuberculosis epidemics. Mathematical Biosciences & Engineering, 2009, 6 (2) : 209-237. doi: 10.3934/mbe.2009.6.209

[13]

Aniello Buonocore, Antonio Di Crescenzo, Alan Hastings. Preface for the special issue of Mathematical Biosciences and Engineering, BIOCOMP 2012. Mathematical Biosciences & Engineering, 2014, 11 (2) : i-ii. doi: 10.3934/mbe.2014.11.2i

[14]

Pierre Degond, Marcello Delitala. Modelling and simulation of vehicular traffic jam formation. Kinetic and Related Models, 2008, 1 (2) : 279-293. doi: 10.3934/krm.2008.1.279

[15]

Geoffrey Beck, Sebastien Imperiale, Patrick Joly. Mathematical modelling of multi conductor cables. Discrete and Continuous Dynamical Systems - S, 2015, 8 (3) : 521-546. doi: 10.3934/dcdss.2015.8.521

[16]

Nirav Dalal, David Greenhalgh, Xuerong Mao. Mathematical modelling of internal HIV dynamics. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 305-321. doi: 10.3934/dcdsb.2009.12.305

[17]

Oliver Penrose, John W. Cahn. On the mathematical modelling of cellular (discontinuous) precipitation. Discrete and Continuous Dynamical Systems, 2017, 37 (2) : 963-982. doi: 10.3934/dcds.2017040

[18]

Martin Baurmann, Wolfgang Ebenhöh, Ulrike Feudel. Turing instabilities and pattern formation in a benthic nutrient-microorganism system. Mathematical Biosciences & Engineering, 2004, 1 (1) : 111-130. doi: 10.3934/mbe.2004.1.111

[19]

Ping Liu, Junping Shi, Zhi-An Wang. Pattern formation of the attraction-repulsion Keller-Segel system. Discrete and Continuous Dynamical Systems - B, 2013, 18 (10) : 2597-2625. doi: 10.3934/dcdsb.2013.18.2597

[20]

Shanshan Chen, Junping Shi, Guohong Zhang. Spatial pattern formation in activator-inhibitor models with nonlocal dispersal. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 1843-1866. doi: 10.3934/dcdsb.2020042

2021 Impact Factor: 1.41

Metrics

  • PDF downloads (49)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]