M5 mesoscopic and macroscopic models for mesenchymal motion

Journal of Mathematical Biology

Volumn 53, Issue 4, 2006, Pages 585-616

  Hillen, Thomas ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FIBRILLAR COLLAGEN;

ALGORITHM; ANIMAL; ARTICLE; BIOLOGICAL MODEL; CANCER INVASION; CELL ADHESION; CELL MOTION; CYTOLOGY; EXTRACELLULAR FLUID; EXTRACELLULAR MATRIX; HUMAN; KINETICS; NEOPLASM; PATHOLOGY; PATHOPHYSIOLOGY; PHYSIOLOGY;

ALGORITHMS; ANIMALS; CELL ADHESION; CELL MOVEMENT; EXTRACELLULAR FLUID; EXTRACELLULAR MATRIX; FIBRILLAR COLLAGENS; HUMANS; KINETICS; MODELS, BIOLOGICAL; NEOPLASM INVASIVENESS; NEOPLASMS;

EID: 33748295649     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-006-0017-y     Document Type: Article

References (25)

1. Alt, W.: Singular perturbation of differential integral equations describing biased random walks. J. Reine Angew. Math. 322, 15-41 (1981)
2. Barocas, V.H., Tranquillo, R.T.: An anisotropic biphasic theory of tissue-equivalent mechanics: The interplay among cell traction, fibrillar network deformation, fibril alignment and cell contact guidance. J. Biomech. Eng. 119, 137-145 (1997)
3. Berenschot, G.: Vizualization of Diffusion Tensor Imaging. Eindhoven University of Technology, Master Thesis (2003)
4. Chalub, F.A.C.C., Markovich, P.A., Perthame, B., Schmeiser, C.: Kinetic models for chemotaxis and their drift-diffusion limits. Monatsh. Math. 123-141 (2004)
5. Dallon, J.C., Sherratt J.A.: A mathematical model for spatially varying extracellular matrix alignment. SIAM J. Appl. Math. 61, 506-527 (2000)
6. Dallon, J.C., Sherratt, J.A., Maini, P.K.: Modelling the effects of transforming growth factor-β on extracellular alignment in dermal wound repair. Wound Rep. Reg. 9, 278-286 (2001)
7. Dickinson, R.: A generalized transport model for biased cell migration in an anisotropic environment. J. Math. Biol. 40, 97-135 (2000)
8. Dickinson, R.B.: A model for cell migration by contact guidance. In: Alt, W., Deutsch, A., Dunn, G. (eds) Dynamics of Cell and Tissue Motion, pp. 149-158, Birkhauser, Basel, (1997)
9. Dolak, Y., Schmeiser, C.: Kinetic models for chemotaxis: Hydrodynamic limits and spatio-temporal mechanics. J. Math. Biol. 51, 595-615 (2005)
10. Friedl, P., Bröcker, E.B.: The biology of cell locomotion within three dimensional extracellular matrix. Cell Motility Life Sci. 57, 41-64 (2000)
11. Friedl, P., Wolf, K.: Tumour-cell invasion and migration: diversity and escape mechanisms. Nat. Rev. 3, 362-374 (2003)
12. 2-closure of transport equations: the Cattaneo closure. Discrete Cont. Dyn. Syst. B 4(4), 961-982 (2004)
13. 2-closure of transport equations: the general case. Discrete Cont. Dyn. Syst. B 5(2), 299-318 (2005)
14. Hillen, T., Othmer, H.G.: The diffusion limit of transport equations derived from velocity jump processes. SIAM J. Appl. Math. 61(3), 751-775 (2000)
15. Hwang, H.J., Kang, K., Stevens, A.: Global solutions of nonlinear transport equations for chemosensitive movement. SIAM J. Math. Anal. 36, 1177-1199 (2005)
16. Levermore, C.D.: Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83, 1021-1065 (1996)
17. Mori, S., Crain, B.J., Chacko, V.P., Zijl, P.C.M.: Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann. Neurol. 45, 265-269 (1999)
18. Othmer, H.G., Dunbar, S.R., Alt, W.: Models of dispersal in biological systems. J. Math. Biol. 26, 263-298 (1988)
19. Othmer, H.G., Hillen, T.: The diffusion limit of transport equations II: Chemotaxis equations. SIAM J. Appl. Math. 62(4), 1122-1250 (2001)
20. Robinson, J.C.: Infinite-Dimensional Dynamical Systems. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2001)
21. Stevens, A.: The derivation of chemotaxis-equations as limit dynamics of moderately interacting stochastic many particle systems. SIAM J. Appl. Math. 61(1), 183-212 (2000)
22. Tranquillo, R.T., Barocas, V.H.: A continuum model for the role of fibroblast contact guidance in wound contraction. In: Alt, W., Deutsch, A., Dunn, G. (eds) Dynamics of Cell and Tissue Motion, pp. 159-164, Birkhauser, Basel (1997)
23. Wang, Z., Hillen, T., Li, M.: Global existence and travling waves to models for mesenchymal motion in one dimension, (in preparation) 2006
24. Wolf, K., Mazo, I., Leung, H., Engelke, K., von Andria, U., Deryngina, E. I., Strongin, A.Y., Bröcker, E.B., Friedl, P.: Compensation mechanism in tumor cell migration: mesenchymal-amoeboid transition after blocking of pericellular proteolysis. J. Cell Biol. 160, 267-277 (2003)
25. Yurchenco, P.D., Birk, D.E., Mechan, R. P.: Extracellular Matrix Assembly. Academic Press, San Diego (1994)