Solving the advection-diffusion equations in biological contexts using the cellular Potts model

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

Volumn 72, Issue 4, 2005, Pages

  Dan, Debasis ^a   Mueller, Chris ^a   Chen, Kun ^a   Glazier, James A ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; CELLS; FINITE DIFFERENCE METHOD; FLUID DYNAMICS; PHYSIOLOGY; TISSUE;

ADVECTION-DIFFUSION EQUATIONS; CELLULAR POTTS MODEL (CPM); EXTRA-CELLULAR FLUID; MORPHOGENESIS;

DIFFUSION;

GROWTH PROMOTOR; SCLEROPROTEIN;

ALGORITHM; ANIMAL; BIOLOGICAL MODEL; CELL FUNCTION; CHEMICAL MODEL; CHEMISTRY; COMPUTER SIMULATION; DIFFUSION; EXTRACELLULAR MATRIX; HUMAN; METABOLISM; MORPHOGENESIS; PHYSIOLOGY; TRANSPORT AT THE CELLULAR LEVEL;

ALGORITHMS; ANIMALS; BIOLOGICAL TRANSPORT; CELL PHYSIOLOGICAL PHENOMENA; COMPUTER SIMULATION; DIFFUSION; EXTRACELLULAR MATRIX; EXTRACELLULAR MATRIX PROTEINS; GROWTH SUBSTANCES; HUMANS; MODELS, BIOLOGICAL; MODELS, CHEMICAL; MORPHOGENESIS;

EID: 33244464025     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.041909     Document Type: Article

References (50)

1. C. R. Nugent, W. M. Quarles, and T. H. Solomon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.218301 93, 218301 (2004);
2. J. D. Seymour, J. P. Gage, S. L. Codd, and R. Gerlach, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.198103 93, 198103 (2004);
3. M. Leconte, J. Martin, N. Rakotomalala, and D. Salin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.128302 90, 128302 (2003);
4. B. F. Edwards, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89. 104501 89, 104501 (2002).
5. A. Bancaud, G. Wagner, K. D. Dorfman, and J. L. Viovy Anal. Biochem. ANBCA2 0003-2697 77, 833 (2005).
6. T. Yanagita and K. Kaneko, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.78.4297 78, 4297 (1997).
7. J. M. Keller and M. L. Brusseau, Environ. Sci. Technol. ESTHAG 0013-936X 37, 3141 (2003);
8. T. E. McKone and D. H. Bennett, Environ. Sci. Technol. ESTHAG 0013-936X 37, 3123 (2003).
9. G. J. Gibson, C. A. Gilligan, and A. Kleczkowski, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 10.1098/rspb.1999.0841 266, 1743 (1999);
10. J. T. Truscott and C. A. Gilligan, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.1436273100 100, 9067 (2003).
11. T. E. Faber, Fluid Dynamics for Physicists (Cambridge University Press, Cambridge, England, 1995).
12. P. M. Gresho and R. L. Sani, Incompressible Flow and the Finite Element Method (Wiley, New York, 2000);
13. W. Hundsdorfer and J. G. Verwer, Numerical Solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer Series in Computational Mathematics (Springer, New York, 2003).
14. Y. H. Qian, D. D'Humieres, and P. Lallemand, Europhys. Lett. EULEEJ 0295-5075 17, 479 (1992).
15. E. G. Flekkoy, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.47.4247 47, 4247 (1993).
16. S. P. Dawson, S. Chen, and G. D. Doolean, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.464316 98, 1514 (1993).
17. C. P. Lowe and D. Frenkel, Physica A PHYADX 0378-4371 10.1016/0378-4371(95)00208-O 220, 251 (1995);
18. R. H. Merks, J. Comput. Phys. JCTPAH 0021-9991 183, 563 (2002).
19. J. C. Anthony, J. Fluid Mech. JFLSA7 0022-1120 271, 285 (1994).
20. W. Zeng, G. L. Thomas, S. A. Newman, and J. A. Glazier, Mathematical Modeling and Computing in Biology and Medicine, 5th ESMTB Conference 2002, edited by, V. Capasso, (Societ Editrice Esculapio, Bologna, 2003).
21. A. M. Turing, Philos. Trans. R. Soc. London, Ser. B PTRBAE 0962-8436 237, 266 (1952);
22. A. Taylor, Prog. React. Kinet. PRKNAZ 0079-6743 27, 247 (2002).
23. D. V. Zhelev, A. M. Alteraifi, and D. Chodniewicz, Biophys. J. BIOJAU 0006-3495 87, 688-695 (2004).
24. H. C. Berg and P. M. Tedesco, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 72, 3235 (1975).
25. M. H. Kroll, J. D. Hellums, L. V. McIntire, A. L. Schafer, and J. L. Moake, Blood BLOOAW 0006-4971 88, 1525 (1996).
26. S. Jadhav and K. Konstantopoulos, Am. J. Physiol.: Cell Physiol. AJPHAP 0363-6143 283, C1133 (2002).
27. M. U. Nollert, N. J. Panaro, and L. V. McIntire, Ann. N.Y. Acad. Sci. ANYAA9 0077-8923 665, 94 (1992);
28. P. F. Davies, Physiol. Rev. PHREA7 0031-9333 75, 519 (1995).
29. E. B. Finger, K. D. Puri, R. Alon, M. B. Lawrence, U. H. von Andrian, and T. A. Springer, Nature (London) NATUAS 0028-0836 10.1038/379266a0 379, 266 (1996).
30. A. D. Taylor, S. Neelamegham, J. D. Hellums, C. W. Smith, and S. I. Simon, Biophys. J. BIOJAU 0006-3495 71, 3488 (2004).
31. M. Pavlin, N. Pavselj, and D. Miklavcic, IEEE Trans. Biomed. Eng. IEBEAX 0018-9294 49, 605 (2002).
32. H. G. E. Hentschel, J. A. Glazier, and S. A. Newman, Proc. R. Soc. London, Ser. B PRLBA4 0962-8452 271, 1713 (2004).
33. S. Kikichi, Neural Networks NNETEB 0893-6080 16, 1389 (2003).
34. M. S. Alber, A. Kiskowski, J. A. Glazier, and Y. Jiang, Math. Syst. Theory Biology, Communication, and Finance 134, 1 (2003).
35. F. Graner and J. A. Glazier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.2013 69, 2013 (1992).
36. J. A. Glazier and F. Graner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.47.2128 47, 2128 (1993).
37. W. Zeng, G. L. Thomas, and J. A. Glazier, Physica A PHYADX 0378-4371 341, 482 (2004).
38. M. Zajac, G. L. Jones, and J. A. Glazier, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.2022 85, 2022 (2000).
39. S. Maree, Ph.D. thesis University Utrecht, 2000;
40. A. F. MarAee and P. Hogeweg, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.061535198 98, 3879 (2001).
41. Emma Stott, N. F. Britton, J. A. Glazier, and M. Zajac, Math. Comput. Modell. MCMOEG 0895-7177 10.1016/S0895-7177(99)00156-9 30, 183 (1999).
42. R. M. H. Merks, S. A. Newman, and J. A. Glazier, Lect. Notes Comput. Sci. LNCSD9 0302-9743 3305, 425 (2004).
43. R. Chaturvedi, J. A. Izaguirre, C. Huang, T. Cickovski, P. Virtue, G. Thomas, G. Forgacs, M. Alber, G. Hentschel, S. A. Newman, and J. A. Glazier, Lect. Notes Comput. Sci. LNCSD9 0302-9743 2659, 39 (2003).
44. Y. Jiang, Cellular Pattern Formation, Ph.D. dissertation, University of Notre Dame, 1998.
45. E. M. Purcell, Am. J. Phys. AJPIAS 0002-9505 10.1119/1.10903 45, 3 (1977).
46. J. Braun and M. Sambridge, Nature (London) NATUAS 0028-0836 10.1038/376655a0 376, 655 (1995).
47. M. E. J. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University, New York, 1999).
48. S. Wong, Ph.D. thesis, Notre Dame University, 2004.
49. J. D. Murray, Mathematical Biology, Vol. 1 (Springer-Verlag, Berlin, 2002).
50. E. M. Lifsihtz and L. D. Landau, Fluid Mechanics (Butterworth-Heinemann, Oxford, 1987).