Classifying general nonlinear force laws in cell-based models via the continuum limit

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 2, 2012, Pages

  Murray, Philip J ^a   Edwards, Carina M ^b   Tindall, Marcus J ^c   Maini, Philip K ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF HEIDELBERG   (Germany)

^c UNIVERSITY OF READING   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIOLOGICAL PHENOMENA; CELL BEHAVIORS; CELL-BASED; CONTINUUM LIMITS; CONTINUUM MODEL; DIFFUSION COEFFICIENTS; DISCRETE MODELS; DISCRETE SIMULATIONS; FORCE LAWS; INDIVIDUAL CELLS; INTERCELL; NONLINEAR DIFFUSION; NONLINEAR FORCE; NUMERICAL SOLUTION; SPATIAL DIMENSION;

CONTINUUM MECHANICS; CYTOLOGY; DIFFUSION;

CELLS;

EID: 84857724328     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.021921     Document Type: Article

References (32)

1. J. von Neumann, in The Theory of Self-reproducing Automata, edited by, A. Burks, (University of Illinois Press, Champaign, 1966).
2. T. Alarcón, H. M. Byrne, and P. K. Maini, J. Theor. Biol. JTBIAP 0022-5193 10.1016/S0022-5193(03)00244-3 225, 257 (2003). (Pubitemid 37324088)
3. A. R. A. Anderson, Math. Med. Biol. 1477-8599 10.1093/imammb/dqi005 22, 163 (2005). (Pubitemid 41511340)
4. A. Deutsch and S. Dormann, Cellular Automaton Modelling of Biological Pattern Formation (Birkhauser, Basel, 2005).
5. W. Düchting and G. Dehl, J. Biomed. Eng. JBIEDR 0141-5425 10.1016/0141-5425(80)90143-0 2, 167 (1980).
6. K. Smallbone, R. A. Gatenby, R. J. Gillies, D. J. Gavaghan, and P. K. Maini, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2006.09.010 244, 703 (2007). (Pubitemid 46148971)
7. M. V. Plikus, J. A. Mayer, D. de La Cruz, R. E. Baker, P. K. Maini, R. Maxson, and C. M. Chuong, Nature (London) NATUAS 0028-0836 10.1038/nature06457 451, 340 (2008).
8. F. Graner and J. A. Glazier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2013 69, 2013 (1992).
9. D. Drasdo and S. Hohme, Phys. Biol. 1478-3967 10.1088/1478-3975/2/3/001 2, 133 (2005). (Pubitemid 41483079)
10. D. Drasdo and M. Loeffler, Nonlinear Anal. Theory, Methods Appl. NOANDD 0362-546X 10.1016/S0362-546X(01)00173-0 47, 245 (2001). (Pubitemid 32707166)
11. J. Galle, M. Loeffler, and D. Drasdo, Biophys. J. BIOJAU 0006-3495 10.1529/biophysj.104.041459 88, 62 (2005). (Pubitemid 40070658)
12. F. Meineke, C. S. Potten, and M. Loeffler, Cell Proliferation 0960-7722 10.1046/j.0960-7722.2001.00216.x 34, 253 (2001). (Pubitemid 32738648)
13. G. Schaller and M. Meyer-Hermann, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2007.03.023 247, 554 (2007). (Pubitemid 46935216)
14. G. Schaller and M. Meyer-Hermann, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.051910 71, 051910 (2005). (Pubitemid 41480973)
15. I. M. M. van Leeuwen, G. R. Mirams, A. Walter, A. Fletcher, P. Murray, J. Osborne, S. Varma, S. J. Young, J. Cooper, B. Doyle, J. M. Pitt-Francis, L. Momtahan, P. Pathmanathan, J. P. Whiteley, S. J. Chapman, D. J. Gavaghan, O. E. Jensen, J. R. King, P. K. Maini, S. L. Waters, and H. M. Byrne, Cell Proliferation 0960-7722 10.1111/j.1365-2184.2009.00627.x 42, 617 (2009).
16. P. J. Murray, C. M. Edwards, M. J. Tindall, and P. K. Maini, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.031912 80, 031912 (2009).
17. P. Pathmanathan, J. Cooper, A. Fletcher, G. Mirams, P. Murray, J. Osborne, J. Pitt-Francis, A. Walter, and S. J. Chapman, Phys. Biol. 1478-3967 10.1088/1478-3975/6/3/036001 6, 036001 (2009).
18. J. Jeon, V. Quaranta, and P. T. Cummings, Biophys. J. BIOJAU 0006-3495 10.1016/j.bpj.2009.10.002 98, 37 (2010).
19. C. R. Sweet, S. Chatterjee, Z. Xu, K. Bisordi, E. D. Rosen, and M. Alber, J. R. Soc., Interface 1742-5689 10.1098/rsif.2011.0180 8, 1760 (2011).
20. R. Erban and H. G. Othmer, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139903433232 65, 361 (2004).
21. M. Alber, N. Chen, P. M. Lushnikov, and S. A. Newman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.168102 99, 168102 (2007). (Pubitemid 47613326)
22. P. M. Lushnikov, N. Chen, and M. Alber, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.061904 78, 061904 (2008).
23. H. M. Byrne and D. Drasdo, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s00285-008-0212-0 58, 657 (2009).
24. J. A. Fozard, H. M. Byrne, O. E. Jensen, and J. R. King, Math. Med. Biol. 1477-8599 10.1093/imammb/dqp015 27, 39 (2009).
25. M. Bodnar and J. J. L. Velazquez, Math. Methods Appl. Sci. MMSCDB 0170-4214 10.1002/mma.638 28, 1757 (2005). (Pubitemid 41360038)
26. M. J. Simpson, K. A. Landman, B. D. Hughes, and A. E. Fernando, Physica A PHYADX 0378-4371 10.1016/j.physa.2009.12.010 389, 1412 (2010).
27. A. E. Fernando, K. A. Landman, and M. J. Simpson, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.011903 81, 011903 (2010).
28. P. E. Rouse, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1699180 21, 1272 (1953).
29. P. J. Murray, A. Walter, A. G. Fletcher, C. M. Edwards, M. J. Tindall, and P. K. Maini, Phys. Biol. 1478-3967 10.1088/1478-3975/8/2/026011 8, 026011 (2011).
30. P. J. Murray, J. W. Kang, G. R. Mirams, S. Y. Shin, H. M. Byrne, P. K. Maini, and K. H. Cho, Biophys. J. BIOJAU 0006-3495 10.1016/j.bpj.2010.05.016 99, 716 (2010).
31. J. D. Murray, in Mathematical Biology, edited by, S. S. Antman, J. E. Marsden, L. Sirovich, and, S. Wiggins, (Springer, Berlin, 1989).
32. K. Mertens, V. Putkaradze, D. Xia, and S. R. J. Brueck, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1999029 98, 034309 (2005). (Pubitemid 41204820)