Modelling the motion of a cell population in the extracellular matrix

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.

[1]  P. Friedl,et al.  The biology of cell locomotion within three-dimensional extracellular matrix , 2000, Cellular and Molecular Life Sciences CMLS.

[2]  C. D. Levermore,et al.  Moment closure hierarchies for kinetic theories , 1996 .

[3]  Robert B. Lowrie,et al.  A comparison of implicit time integration methods for nonlinear relaxation and diffusion , 2004 .

[4]  Randall J. LeVeque,et al.  A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions , 2002, SIAM J. Sci. Comput..

[5]  Peter Friedl,et al.  Compensation mechanism in tumor cell migration , 2003, The Journal of cell biology.

[6]  P. Friedl Prespecification and plasticity: shifting mechanisms of cell migration. , 2004, Current opinion in cell biology.

[7]  R T Tranquillo,et al.  An anisotropic biphasic theory of tissue-equivalent mechanics: the interplay among cell traction, fibrillar network deformation, fibril alignment, and cell contact guidance. , 1997, Journal of biomechanical engineering.

[8]  Hans G. Othmer,et al.  The Diffusion Limit of Transport Equations Derived from Velocity-Jump Processes , 2000, SIAM J. Appl. Math..

[9]  R. Dickinson,et al.  A generalized transport model for biased cell migration in an anisotropic environment , 2000, Journal of mathematical biology.

[10]  Luigi Preziosi,et al.  A review of vasculogenesis models , 2005 .

[11]  P. Friedl,et al.  Tumour-cell invasion and migration: diversity and escape mechanisms , 2003, Nature Reviews Cancer.

[12]  J. Murray,et al.  A mechanical model for the formation of vascular networks in vitro , 1996, Acta biotheoretica.

[13]  Jacques Ohayon,et al.  Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields. , 2004, Journal of theoretical biology.

[14]  L. Preziosi,et al.  Modeling the early stages of vascular network assembly , 2003, The EMBO journal.

[15]  Raphael Aronson,et al.  Theory and application of the Boltzmann equation , 1976 .

[16]  T. Hillen M5 mesoscopic and macroscopic models for mesenchymal motion , 2006, Journal of mathematical biology.

[17]  Richard B. Dickinson,et al.  A Model for Cell Migration by Contact Guidance , 1997 .

[18]  L. Preziosi,et al.  Mechanics and Chemotaxis in the Morphogenesis of Vascular Networks , 2006, Bulletin of mathematical biology.