Tumor growth instability and the onset of invasion

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

Volumn 72, Issue 4, 2005, Pages

  Castro, Mario ^a   Molina París, Carmen ^b,c   Deisboeck, Thomas S ^d  

^a UNIVERSIDAD PONTIFICIA COMILLAS   (Spain)

^b UNIVERSITY OF LEEDS   (United Kingdom)

^c UNIVERSIDAD SAN PABLO CEU   (Spain)

^d MASSACHUSETTS GENERAL HOSPITAL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMOTHERAPY; MATHEMATICAL MODELS; NUMERICAL METHODS;

CHEMOTAXIS; HOMOTYPE CHEMOTAXIS; TUMOR GROWTH;

TUMORS;

ANIMAL; BIOLOGICAL MODEL; BYSTANDER EFFECT; CELL PROLIFERATION; CHEMOTAXIS; COMPUTER SIMULATION; DISEASE COURSE; HUMAN; MULTICELLULAR SPHEROID; NEOPLASM; PARACRINE SIGNALING; PATHOLOGY; PATHOPHYSIOLOGY; TUMOR INVASION;

ANIMALS; BYSTANDER EFFECT; CELL PROLIFERATION; CHEMOTAXIS; COMPUTER SIMULATION; DISEASE PROGRESSION; HUMANS; MODELS, BIOLOGICAL; NEOPLASM INVASIVENESS; NEOPLASMS; PARACRINE COMMUNICATION; SPHEROIDS, CELLULAR;

EID: 33244462445     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.72.041907     Document Type: Article

References (55)

1. C. Betsholtz, B. Westermark, B. Ek, and C. H. Heldin, Cell CELLB5 0092-8674 39, 447-57 (1984).
2. J. Laterra, E. Rosen, M. Nam, S. Ranganathan, K. Fielding, and P. Johnston, Biochem. Biophys. Res. Commun. BBRCA9 0006-291X 10.1006/bbrc.1997.6853 235, 743 (1997).
3. M. R. Chicoine, C. L. Madsen, and D. L. Silbergeld, Neurosurgery 0148-396X 36, 1165 (1995).
4. M. J. Plank, B. D. Sleeman, and P. F. Jones, Theor Med. 0167-9902 4, 251 (2002)
5. M. J. Plank and B. D. Sleeman, Bull. Math. Biol. BMTBAP 0092-8240 10.1016/j.bulm.2004.04.001 66, 1785 (2004).
6. S. Koochekpour, M. Jeffers, S. Rulong, G. Taylor, E. Klineberg, E. A. Hudson, J. H. Resau, and G. F. Vande Woude, Cancer Res. CNREA8 0008-5472 57, 5391 (1997)
7. A. J. Ekstrand, C. D. James, W. K. Cavenee, B. Seliger, R. F. Pettersson, and V. P. Collins, Cancer Res. CNREA8 0008-5472 51, 2164 (1991).
8. A. Wells, Adv. Cancer Res. 0065-230X 78, 31 (2000).
9. L. M. Sander and T. S. Deisboeck, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.66.051901 66, 051901 (2002).
10. T. S. Deisboeck, M. E. Berens, A. R. Kansal, S. Torquato, A. O. Stemmer-Rachamimov, and E. A. Chiocca, Cell Prolif 0960-7722 10.1046/j.1365-2184.2001.00202.x 34, 115 (2001).
11. R. B. Vernon and E. H. Sage, Microvasc. Res. MIVRA6 0026-2862 57, 118-133 (1999).
12. H. M. Byrne and M. A. J. Chaplain, Eur. J. Appl. Math. 0956-7925 8, 639 (1998).
13. T. L. Jackson, S. R. Lubkin, and J. D. Murray, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s002850050195 39, 353 (1999).
14. L. Derbel, Math. Models Meth. Appl. Sci. MMMSEU 0218-2025 10.1142/S0218202504003738 14, 1657 (2004)
15. E. De Angelis and P. E. Jabin, Math. Models Meth. Appl. Sci. MMMSEU 0218-2025, 13, 187 (2003).
16. H. Greenspan, J. Theor. Biol. JTBIAP 0022-5193 56, 229 (1976).
17. J. P. Ward and J. R. King, IMA J. Math. Appl. Med. Biol. 0265-0746 10.1111/j.1600-0838.2003.00333.x 14, 39 (1997).
18. M. J. Holmes and B. D. Sleeman, J. Theor. Biol. JTBIAP 0022-5193 202, 45 (2000).
19. T. Alarcon, H. Byrne, and P. Maini, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2004.04.016 229, 395 (2004).
20. D. S. Jones and B. D. Sleeman, Differential Equations and Mathematical Biology (CRC Press, London, 2003), and references therein.
21. H. Levine, S. Pamuk, B. Sleeman, and M. Nilsen-Hamilton, Bull. Math. Biol. BMTBAP 0092-8240 10.1006/bulm.2001.0240 63, 801 (2001).
22. H. Levine, S. Pamuk, B. Sleeman, and M. Nilsen-Hamilton, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s002850000037 42, 195 (2001).
23. N. Bellomo, E. De Angelis, and L. Preziosi, Theor Med. 0167-9902 5, 111 (2003).
24. N. Bellomo, A. Bellouquid, and M. Delitala, Math. Models Meth. Appl. Sci. MMMSEU 0218-2025 10.1142/S0218202504003799 14, 1683 (2004).
25. Z. Bajzer and S. Vuk-Pavlovic, BioSystems BSYMBO 0303-2647 80, 1 (2005).
26. S. Habib, C. Molina-Parĺs, and T. S. Deisboeck, Physica A PHYADX 0378-4371 10.1016/S0378-4371(03)00391-1 327, 501 (2003).
27. E. F. Keller, and L. A. Segel, J. Theor. Biol. JTBIAP 0022-5193 30, 225 (1971)
28. E. F. Keller, and L. A. Segel, J. Theor. Biol. JTBIAP 0022-5193 30, 235 (1971).
29. J. A. Sherratt, Bull. Math. Biol. BMTBAP 0092-8240 10.1016/S0092-8240(05) 80208-3 56, 129-146 (1994)
30. K. J. Painter, P. K. Maini and H. G. Othmer, J. Math. Biol. JMBLAJ 0303-6812 10.1007/s002850000035 41, 285 (2000).
31. A. J. Ekstrand, C. D. James, W. K. Cavenee, B. Seliger, R. F. Pettersson, and V. P. Collins, Cancer Res. CNREA8 0008-5472 51, 2164 (1991).
32. J. Folkman and M. Hochberg, J. Exp. Med. JEMEAV 0022-1007 10.1084/jem.138.4.745 138, 745 (1973).
33. C. K. N. Li, Cancer 0008-543X 50, 2066 (1982).
34. J. P. Freyer, Cancer Res. CNREA8 0008-5472 48, 2432 (1988).
35. J. P. Freyer and R. M. Sutherland, Cancer Res. CNREA8 0008-5472 46, 3504 (1986).
36. H. M. Byrne and M. Chaplain, Math. Biosci. MABIAR 0025-5564 10.1016/0025-5564(96)00023-5 135, 187 (1996).
37. J. Xin, SIAM Rev. SIREAD 0036-1445 10.1137/S0036144599364296 42, 161 (2000).
38. R. A. Fisher, Ann. Eugenics VII 355, (1936)
39. A. Kolmogorov, I. Petrosvky and N. Piscounov, Moscow Univ. Bull. Math. A 1, 1 (1937).
40. See A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambdridge, 1995). and references therein.
41. J. Müller and W. van Saarloos, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.061111 65, 061111 (2002).
42. M. R. Chicoine and D. L. Silbergeld, Neurosurgery 0148-396X 82, 615 (1995)
43. R. K. Jain, Cancer Res. CNREA8 0008-5472 47, 3039 (1987).
44. A. H. Nayfeh, Introduction to Perturbation Techniques (Wiley, Mew York, 1981).
45. P. C. Fife, Dynamics of Internal Layers and Diffusive Interfaces, (SIAM, Philadelphia, PA, 1988).
46. R. F. Almgren, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/ S0036139997330027 59, 2086 (1999).
47. J. S. Langer, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.52.1 52, 1 (1980).
48. A. Karma and W.-J. Rappel, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.60.3614 60, 3614 (1999).
49. P. G. Saffman and G. I. Taylor, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 245, 312 (1958)
50. D. Bensimon, L. Kadano, S. Liang, B. I. Shraiman, and C. Tang, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.58.977 58, 977 (1986).
51. P. Grindrod, The Theory and Applications of Reaction-Diffusion Equations: Patterns and Waves (Oxford University Press, New York, 1996).
52. F. Brightman and D. Fell, FEBS Lett. FEBLAL 0014-5793 10.1016/S0014-5793(00)02037-8 482, 169 (2000)
53. B. Schoeberl, C. Eichler-Jonsson, E. D. Gilles, and G. Muller, Nat. Biotechnol. NABIF9 1087-0156 10.1038/nbt0402-370 20, 370 (2002).
54. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering (Perseu, New York, 1994).
55. J. Valenciano and M. A. J. Chaplain, Math. Models Meth. Appl. Sci. MMMSEU 0218-2025 10.1142/S0218202504003155 14, 165 (2004).