2007, 2007(Special): 250-259. doi: 10.3934/proc.2007.2007.250

Modeling the motion of a cell population in the extracellular matrix

1. 

Politecnico di Torino, 24 Corso Duca degli A bruzzi, Torion 10129

2. 

University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Received  September 2006 Revised  January 2007 Published  September 2007

The paper aims at describing the motion of cells in fibrous tissues taking into account the interaction with the network fibers and among cells, chemotaxis, and contact guidance from network fibers. Both a kinetic model and its continuum limit are described.
Citation: A. Chauviere, L. Preziosi, T. Hillen. Modeling the motion of a cell population in the extracellular matrix. Conference Publications, 2007, 2007 (Special) : 250-259. doi: 10.3934/proc.2007.2007.250
[1]

Ezio Di Costanzo, Marta Menci, Eleonora Messina, Roberto Natalini, Antonia Vecchio. A hybrid model of collective motion of discrete particles under alignment and continuum chemotaxis. Discrete and Continuous Dynamical Systems - B, 2020, 25 (1) : 443-472. doi: 10.3934/dcdsb.2019189

[2]

Pierre Degond, Sophie Hecht, Nicolas Vauchelet. Incompressible limit of a continuum model of tissue growth for two cell populations. Networks and Heterogeneous Media, 2020, 15 (1) : 57-85. doi: 10.3934/nhm.2020003

[3]

J. C. Dallon, Lynnae C. Despain, Emily J. Evans, Christopher P. Grant. A continuous-time stochastic model of cell motion in the presence of a chemoattractant. Discrete and Continuous Dynamical Systems - B, 2020, 25 (12) : 4839-4852. doi: 10.3934/dcdsb.2020129

[4]

Brock C. Price, Xiangsheng Xu. Global existence theorem for a model governing the motion of two cell populations. Kinetic and Related Models, 2020, 13 (6) : 1175-1191. doi: 10.3934/krm.2020042

[5]

Gonzalo Galiano, Sergey Shmarev, Julian Velasco. Existence and multiplicity of segregated solutions to a cell-growth contact inhibition problem. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1479-1501. doi: 10.3934/dcds.2015.35.1479

[6]

Gabriella Bretti, Ciro D’Apice, Rosanna Manzo, Benedetto Piccoli. A continuum-discrete model for supply chains dynamics. Networks and Heterogeneous Media, 2007, 2 (4) : 661-694. doi: 10.3934/nhm.2007.2.661

[7]

G. Idone, A. Maugeri. Variational inequalities and a transport planning for an elastic and continuum model. Journal of Industrial and Management Optimization, 2005, 1 (1) : 81-86. doi: 10.3934/jimo.2005.1.81

[8]

Phoebus Rosakis. Continuum surface energy from a lattice model. Networks and Heterogeneous Media, 2014, 9 (3) : 453-476. doi: 10.3934/nhm.2014.9.453

[9]

Ali Ashher Zaidi, Bruce Van Brunt, Graeme Charles Wake. A model for asymmetrical cell division. Mathematical Biosciences & Engineering, 2015, 12 (3) : 491-501. doi: 10.3934/mbe.2015.12.491

[10]

Julien Dambrine, Nicolas Meunier, Bertrand Maury, Aude Roudneff-Chupin. A congestion model for cell migration. Communications on Pure and Applied Analysis, 2012, 11 (1) : 243-260. doi: 10.3934/cpaa.2012.11.243

[11]

Antonio DeSimone, Natalie Grunewald, Felix Otto. A new model for contact angle hysteresis. Networks and Heterogeneous Media, 2007, 2 (2) : 211-225. doi: 10.3934/nhm.2007.2.211

[12]

Zhenzhen Zheng, Ching-Shan Chou, Tau-Mu Yi, Qing Nie. Mathematical analysis of steady-state solutions in compartment and continuum models of cell polarization. Mathematical Biosciences & Engineering, 2011, 8 (4) : 1135-1168. doi: 10.3934/mbe.2011.8.1135

[13]

Peicheng Zhu, Lei Yu, Yang Xiang. Weak solutions to an initial-boundary value problem for a continuum equation of motion of grain boundaries. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022139

[14]

Li Xie, Shigui Ruan. On a macrophage and tumor cell chemotaxis system with both paracrine and autocrine loops. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1447-1479. doi: 10.3934/cpaa.2022025

[15]

Keith E. Howard. A size structured model of cell dwarfism. Discrete and Continuous Dynamical Systems - B, 2001, 1 (4) : 471-484. doi: 10.3934/dcdsb.2001.1.471

[16]

Andrey Zvyagin. Attractors for model of polymer solutions motion. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 6305-6325. doi: 10.3934/dcds.2018269

[17]

Pierre Degond, Angelika Manhart, Hui Yu. A continuum model for nematic alignment of self-propelled particles. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1295-1327. doi: 10.3934/dcdsb.2017063

[18]

Xiaoming Wang. On the coupled continuum pipe flow model (CCPF) for flows in karst aquifer. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 489-501. doi: 10.3934/dcdsb.2010.13.489

[19]

Seung-Yeal Ha, Myeongju Kang, Bora Moon. Uniform-in-time continuum limit of the lattice Winfree model and emergent dynamics. Kinetic and Related Models, 2021, 14 (6) : 1003-1033. doi: 10.3934/krm.2021036

[20]

Oanh Chau, R. Oujja, Mohamed Rochdi. A mathematical analysis of a dynamical frictional contact model in thermoviscoelasticity. Discrete and Continuous Dynamical Systems - S, 2008, 1 (1) : 61-70. doi: 10.3934/dcdss.2008.1.61

 Impact Factor: 

Metrics

  • PDF downloads (45)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]