A mathematical model of vascular tumor treatment by chemotherapy

Mathematical and Computer Modelling

Volumn 42, Issue 9-10, 2005, Pages 1089-1112

  Liu, Wenxiang ^a   Freedman, H I ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Growth hypothesis; Hopf bifurcation; Permanence; Stoichiometry; Vascular tumor

Indexed keywords

BIFURCATION (MATHEMATICS); CELLS; CHEMOTHERAPY; GROWTH KINETICS; MATHEMATICAL MODELS; STOICHIOMETRY;

GROWTH HYPOTHESIS; HOPF BIFURCATION; PERMANENCE; VASCULAR TUMOR;

TUMORS;

EID: 28844503182     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2004.09.008     Document Type: Article

References (28)

1. J.L. Bos The ras oncogene family and human carcinogenesis Mut. Res. 195 1998 255 271
2. C. Gambke, A. Hall, and C. Moroni Activation of N ras oncogene in Acute Myelobastic Leukemia Pro. Natl. Acad. Sci. U.S.A. 82 1984 879 882
3. A.S. Levine The biology of human cancer and the development of a rational basis for treatment R.H. Goldfarb Cancer Growth and Progression. Fundamental Aspects of Cancer 1989 Kluwer Academic 1 22
4. A. Neri, D.M. Knowles, A. Greco, F. McCormick, and R. Dalla-Favera Analysis of RAS oncogene mutations in human lympoid malignancies Pro. Natl. Acad. Sci. U.S.A. 85 1998 9268 9272
5. H.C. Pitot Fundamentals of Oncology 1986 Marcel Dekker Boston, MA
6. A. Budde, and I. Grummt p53 represses ribosomal gene transcription Oncogene 19 1998 1119 1124
7. C.A. Cairns, and R.J. White p53 is a general repressor of RNA polymerase III transcription EMBO 17 1998 3112 3123
8. W. Zhai, and L. Comai Repression of RNA polymerase I transcription by the tumor suppressor p53 Mol. Cell. Biol. 20 2000 5930 5938
9. K. Boon, H.N. Caron, R. van Asperen, L. Valentijn, R.-C. Hermus, P. van Sluis, I. Roobeek, I. Weis, P.A. Voute, M. Schwab, and R. Versteeg N-myc enhances the expression of a large set of genes functioning in ribosome biogenesis and proteins synthesis EMBO 20 2001 1383 1393
10. R.J. Donahue, M. Razmara, J.B. Hoek, and R.B. Knudsen Direct influence of the p53 tumor suppressor on mitochondrial biogenesis and function FASEB 15 2001 635 644
11. P.J. Greasley, C. Bonnard, and B. Amati Myc induces the nucleolin and BN51 genes: Possible implications in ribosome biogenesis Nuc. Acids Res. 28 2000 446 453
12. M. Derenzini, D. Trere, A. Pession, M. Govoni, V. Sirri, and P. Chieco Nucleolar size indicates the rapidity of cell proliferation in cancer tissues J. Pathol. 191 2000 181 186
13. R.W. Sterner, and J.J. Elser Ecological Stoichiometry 2002 Princeton University New York
14. J.J. Elser, R.W. Sterner, E. Gorokhova, W.F. Fagan, T.A. Markow, J.B. Cotner, J.F. Harrison, S.E. Hobbie, G.M. Odell, and L.J. Weider Biological stoiciometry from genes to ecosystems Ecology Lett. 3 2000 540 550
15. Y. Kuang, J.D. Nagy, and J.J. Elser Biological stoichiometry of tumor dynamics: Mathematical models and analysis Discrete and Continuous Dynamical Systems-Series B 4 2004 21 240
16. th century: A period analysis Lancet 360 2002 1131 1135
17. R.A. Gatenby, P.K. Maini, and E.T. Gawlinski Analysis of tumor as an inverse problem provides a novel theoretic framework for understanding tumor biology and therapy Appl. Math. Lett. 15 3 2002 339 345
18. W. Liu and H.I. Freedman, Dynimic processes leading to blast cell dominance in chronic myeloctic leukemia, J. Math. Biol., (submitted).
19. H.I. Freedman, and V.S.H. Rao The trade-off between mutual interference and time lags in predator-prey systems Bull. Math. Biol. 45 1983 991 1004
20. J.K. Hale, and P. Waltman Persistence in infinite-dimensional systems SIAM J. Math. Anal. 20 1989 388 396
21. G.J. Butler, H.I. Freedman, and P. Waltman Uniformly persistent systems Proc. Am. Math. Soc. 96 1986 425 430
22. Shukla A nonlinear cell population model of periodic chemotherapy treatment Recent Trends in Ordinary Differential Equations, Series in Applicable Analysis Volume 1 1992 World Scientific Princeton, NJ 569 583
23. J. Mahaffy A test for stability of linear differential equations Quart. Appl. Math. 40 1982 193 202
24. K. Cooke, and P. van den Driessche On the zeros of some transcendental equations Funkcialaj Ekuacioj 29 1986 77 90
25. Q.J.A. Khan, and D. Greenhalgh Hopf bifurcation in epidemic models with a time delay in vaccination IMA J. Math. Appl. Med. Biol. 16 1999 113 142
26. J.E. Marsden, and M. McCracken The Hopf Bifurcation and its Applications 1976 Springer-Verlag
27. S.N. Chow, and J.K. Hale Methods of Bifurcation Theory 1982 Springer-Verlag New York
28. W.A. Coppel Stability and Asympotic Behavior of Differential Equations 1965 D.C. Heath and Company New York