Experimental versus numerical data for breast cancer progression

Nonlinear Analysis: Real World Applications

Volumn 13, Issue 1, 2012, Pages 78-84

  Jorcyk, C L ^a   Kolev, M ^b   Tawara, K ^a   Zubik Kowal, Barbara ^a  

^a BOISE STATE UNIVERSITY   (United States)

^b UNIVERSITY OF WARMIA AND MAZURY IN OLSZTYN   (Poland)

Author keywords

Animal model; Cell lines; Integro differential equations; Mammary; Numerical simulations; Tumor progression

Indexed keywords

ADENOCARCINOMA CELLS; ANIMAL MODEL; BALB/C MICE; BREAST CANCER; CANCER CELLS; CELL LINES; IN-VIVO; MAMMARY; MAMMARY GLAND; MODEL EQUATIONS; MOUSE MODELS; NUMERICAL DATA; NUMERICAL EXPERIMENTS; TUMOR PROGRESSIONS; UNKNOWN PARAMETERS;

CELL CULTURE; DIFFERENTIAL EQUATIONS; DISEASES; INTEGRODIFFERENTIAL EQUATIONS; MAMMALS; TUMORS;

MATHEMATICAL MODELS;

EID: 80052817416     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2011.07.014     Document Type: Article

References (29)

1. A. Jemal, R. Siegel, E. Ward, Y. Hao, J. Xu, and M.J. Thun Cancer statistics Cancer J. Clin. 59 2009 225 249
2. R.E. Coleman, and R.D. Rubens The clinical course of bone metastases from breast cancer Br. J. Cancer 55 1987 61 66 (Pubitemid 17234155)
3. E.F. Solomayer, I.J. Diel, G.C. Meyberg, C. Gollan, and G. Bastert Metastatic breast cancer: clinical course, prognosis and therapy related to the first site of metastasis Breast Cancer Res. Treat. 59 2000 271 278 (Pubitemid 30243049)
4. I.S. Kim, and S.H. Baek Mouse models for breast cancer metastasis Biochem. Biophys. Res. Commun. 394 2010 443 447
5. A. Fantozzi, and G. Christofori Mouse models of breast cancer metastasis Breast Cancer Res. 8 2006 212
6. M. Lelekakis, J.M. Moseley, and T.J. Martin A novel orthotopic model of breast cancer metastasis to bone Clin. Exp. Metastasis 17 1999 163 170 (Pubitemid 29335443)
7. E.K. Sloan, K.L. Stanley, and R.L. Anderson Caveolin-1 inhibits breast cancer growth and metastasis Oncogene 23 2004 7893 7897 (Pubitemid 39457039)
8. A.F. Hurlstone, G. Reid, and J.R. Reeves Analysis of the CAVEOLIN-1 gene at human chromosome 7q31.1 in primary tumours and tumour-derived cell lines Oncogene 18 1999 1881 1890 (Pubitemid 29145855)
9. N. Bellomo Modelling Complex Living Systems 2008 Birkhuser Boston
10. A. Bellouquid, and M. Delitala Modelling Complex Biological SystemsA Kinetic Theory Approach 2006 Birkhuser Boston
11. N. Bellomo, N.K. Li, and P.K. Maini On the foundations of cancer modelling: selected topics, speculations, and perspectives Math. Models Methods Appl. Sci. 18 2008 593 646 (Pubitemid 351730142)
12. N. Bellomo, and B. Carbonaro Toward a mathematical theory of living systems focusing on developmental biology and evolution: a review and perspectives Phys. Life Rev. 8 2011 1 18
13. N. Bellomo, and G. Forni Complex multicellular systems and immune competition: new paradigms looking for a mathematical theory Curr. Top. Dev. Biol. 81 2008 485 502
14. S. De Lillo, M.C. Salvatori, and N. Bellomo Mathematical tools of the kinetic theory of active particles with some reasoning on the modelling progression and heterogeneity Math. Comput. Modelling 45 2007 564 578 (Pubitemid 44820793)
15. M. Kolev A mathematical model of cellular immune response to leukemia Math. Comput. Modelling 41 2005 1071 1081 (Pubitemid 41444864)
16. N. Bellomo, and M. Delitala From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells Phys. Life Rev. 5 2008 183 206
17. N. Bellomo, C. Bianca, and M. Delitala Complexity analysis and mathematical tools towards the modelling of living systems Phys. Life Rev. 6 2009 144 175
18. L. Arlotti, N. Bellomo, and K. Latrach From the Jger and segel model to kinetic population dynamics: nonlinear evolution problems and applications Math. Comput. Modelling 30 1999 15 40 (Pubitemid 29351074)
19. M.L. Bertotti, and M. Delitala Conservation laws and asymptotic behavior of a model of social dynamics Nonlinear Anal. RWA 9 2008 183 196 (Pubitemid 47562894)
20. M. Lo Schiavo The modelling of political dynamics by generalized kinetic (Boltzmann) models Math. Comput. Modelling 37 2003 261 281 (Pubitemid 36257625)
21. N. Bellomo, and B. Carbonaro On the complexity of multiple interactions with additional reasoning about Kate, Jules and Jim Math. Comput. Modelling 47 2008 168 177 (Pubitemid 47615413)
22. M. Delitala, and A. Tosin Mathematical modelling of vehicular traffic: a discrete kinetic theory approach Math. Models Methods Appl. Sci. 17 2007 901 932
23. Z. Jackiewicz, C.L. Jorcyk, M. Kolev, and B. Zubik-Kowal Correlation between animal and mathematical models for prostate cancer progression Comput. Math. Methods Med. 10 2009 241 252
24. K. Drucis, M. Kolev, W. Majda, and B. Zubik-Kowal Nonlinear modeling with mammographic evidence of carcinoma Nonlinear Anal. RWA 11 2010 4326 4334
25. A. Calvo, N. Xiao, J. Kang, C.J.M. Best, I. Leiva, M.R. Emmert-Buck, C. Jorcyk, and J.E. Green Alterations in gene expression profiles during prostate cancer progression: functional correletions to tumorigenicity and down-regulation of selenoprotein-P in mouse and human tumors Cancer Res. 62 2002 5325 5335 (Pubitemid 35024609)
26. L. Arlotti, A. Gamba, and M. Lachowicz A kinetic model of tumour/immune system cellular interactions J. Theor. Med. 4 2002 39 50 (Pubitemid 34506360)
27. L. Arlotti, N. Bellomo, and E. De Angelis Generalized kinetic (Boltzmann) models: mathematical structures and applications Math. Models Methods Appl. Sci. 12 2002 567 591
28. L. Arlotti, N. Bellomo, E. De Angelis, and M. Lachowicz Generalized Kinetic Models in Applied Sciences 2003 World Sci. New Jersey
29. L. Shampine, and M.W. Reichelt The Matlab ODE suite SIAM J. Sci. Comput. 18 1997 1 22 (Pubitemid 127643992)