Macrophage-tumour interactions: In vivo dynamics

Discrete and Continuous Dynamical Systems - Series B

Volumn 4, Issue 1, 2004, Pages 81-98

  Byrne, H M ^a   Cox, S M ^a   Kelly, C E ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Bifurcation theory; Cancer therapy; Normal form; Weakly nonlinear analysis

Indexed keywords

EID: 1042291034     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2004.4.81     Document Type: Conference Paper

References (30)

1. A.R.A. Anderson and M.A.J. Chaplain, CONTINUOUS AND DISCRETE MATHEMATICAL MODELS OF TUMOUR-INDUCED ANGIOGENESIS, Bull. Math. Biol., 60 (1998), 857-899.
2. C.J.W. Breward, H.M. Byrne and C.E. Lewis, MODELLING THE INTERACTIONS BETWEEN TUMOUR CELLS AND A BLOOD VESSEL IN A MICROENVIRONMENT WITHIN A VASCULAR TUMOUR, Eur. J. Appl. Math., 12 (2001), 529-556.
3. C.J.W. Breward, H.M. Byrne and C.E. Lewis, THE ROLE OF CELL-CELL INTERACTIONS IN A TWO-PHASE OF SOLID TUMOR GROWTH, J. Math. Biol., 45 (2002), 125-152.
4. C.J.W. Breward, H.M. Byrne and C.E. Lewis, A MULTIPHASE MODEL DESCRIBING VASCULAR TUMOUR GROWTH. Bull. Math. Biol., 65 (2003), 609-640.
5. H.M. Byrne and M.R. Owen, Use of mathematical models to predict and predict macrophage activity in diseased tissues. In: "The Macrophage" (second edition), B. Burke and C.E. Lewis (editors), Oxford University Press, 2002.
6. L.A. DiPietro, WOUND HEALING: THE ROLE OF THE MACROPHAGE AND OTHER IMMUNE CELLS, Shock, 4 (1995), 233-240.
7. K.D. Elgert, D.G. Alleva and D.W. Mullins, TUMOUR-INDUCED IMMUNE DYSFUNCTION: THE MACROPHAGE CONNECTION, J. Leuk. Biol., 64 (1998), 275-290.
8. C.F. Gerald and P.O. Wheatley, "Applied Numerical Analysis," Addison-Wesley, 1992.
9. H.P. Greenspan, MODELS FOR THE GROWTH OF A SOLID TUMOUR BY DIFFUSION, Stud. Appl. Math., 52 (1972) 317-340.
10. L. Griffith, K. Binley, S. Iqball, O. Kin, P. Maxwell, P. Ratcliffe, C. Lewis, A. Harris, S. Kingsman and S. Naylor, THE MACROPHAGE - A NOVEL SYSTEM TO DELIVER GENE THERAPY TO PATHOLOGICAL HYPOXIA, Gene Ther., 7 (2000), 255-262.
11. A.P. Hollander. K.P. Corke, A.J. Freemont and C.E. Lewis, EXPRESSION OF HYPOXIA-INDUCIBLE FACTOR-1 [ALPHA] BY MACROPHAGES IN RHEUMATOID SYNOVIUM: IMPLICATIONS FOR TARGETING OF THERAPEUTIC GENES TO THE INFLAMED JOINT, Arthritis and Rheumatism, 44 (2001), 1510-1544.
12. T.L. Jackson and H.M. Byrne, A MATHEMATICAL MODEL TO STUDY THE EFFECTS OF DRUG RESISTANCE AND VASCULATURE ON THE RESPONSE OF SOLID TUMOURS TO CHEMOTHERAPY, Math. Biosci., 164 (2000), 17-38.
13. C.E. Kelly, MATHEMATICAL MODELLING OF MACROPHAGE-MEDIATED THERAPY IN CANCER, PhD thesis, University of Nottingham, 2002.
14. C.E. Kelly, R.D. Leek, H.M. Byrne, S.M. Cox, A.L. Harris and C.E. Lewis, MODELLING MACROPHAGE INFILTRATION INTO AVASCULAR TUMOURS, J. Theor. Med., 4 (2002), 21-38.
15. R.D. Leek, C.E. Lewis, R. Whitehouse, M. Greenall, J. Clarke and A.L. Harris, ASSOCIATION OF MACROPHAGE INFILTRATION WITH ANGIOGENESIS AND PROGNOSIS IN INVASIVE BREAST CARCINOMA, Cancer Res., 56 (1996), 4625-4629.
16. R.D. Leek, C.E. Lewis and A.L. Harris, THE ROLE OF MACROPHAGES IN TUMOUR ANGIOGENESIS, J. Pathol., 182 (1997), 81-99.
17. R.D. Leek, R.J. Landers, A.L. Harris and C.E. Lewis, MACROPHAGE INFILTRATION IS ASSOCIATED WITH VEGF AND EGFR EXPRESSION IN BREAST CANCER, J. Pathol., 190 (2000), 430-436.
18. C.E. Lewis and J.O'D. McGee, "The Macrophage," Oxford University Press, 1992.
19. J.S. Lewis, J.A. Lee, J.C.E. Underwood, A.L. Harris and C.E. Lewis, MACROPHAGE RESPONSES TO HYPOXIA: RELEVANCE TO DISEASE MECHANISMS, J. Leukoc. Biol., 66 (1999), 889-900.
20. A. Mantovani, W.J. Ming, C. Balotta, B. Abdeljalil and B. Bottazzi, ORIGIN AND REGULATION OF TUMOUR-ASSOCIATED MACROPHAGES: THE ROLE OF TUMOUR-DERIVED CHEMOTACTIC FACTOR, Biochim Biophys Acta, 865 (1986) 59-67.
21. C. Panetta and J.A. Adam, A MATHEMATICAL MODEL OF CYCLE-SPECIFIC CHEMOTHERAPY, Math. Comput. Modell., 22 (1995), 67-82.
22. J.C. Panetta, A MATHEMATICAL MODEL OF BREAST AND OVARIAN CANCER TREATED WITH PACLITAXEL, Math. Biosci., 146 (1997), 89-113.
23. C. O'Sullivan and C.E. Lewis, TUMOUR-ASSOCIATED LEUCOCYTES: FRIENDS OR FOES IN BREAST CARCINOMA, J. Pathol., 172 (1994), 229-235.
24. M.R. Owen, H.M. Byrne and C.E. Lewis, MATHEMATICAL MODELLING OF THE USE OF MACROPHAGES AS VEHICLES FOR DRUG-DELIVERY TO HYPOXIC TUMOUR SITES, J. theor. Biol. (in press 2003).
25. M.R. Owen and J.A. Sherratt, PATTERN FORMATION AND SPATIOTEMPORAL IRREGULARITY IN A MODEL FOR MACROPHAGE-TUMOUR INTERACTIONS, J. theor. Biol., 189 (1997), 63-80.
26. M.R. Owen and J.A. Sherratt, MODELLING THE MACROPHAGE INVASION OF TUMOURS: EFFECTS ON GROWTH AND COMPOSITION, IMA J. Math. Appl. Med. Biol., 15 (1998), 165-185.
27. M.R. Owen and J.A. Sherratt, MATHEMATICAL MODELLING OF MACROPHAGE DYNAMICS IN TUMOURS, Math. Mod. Meth. Appl. Sci., 4 (1999), 513-530.
28. D.R. Senger, C.A. Peruzzi, J. Feder and H.F. Dvorak, A HIGHLY CONSERVED VASCULAR PERMEABILITY FACTOR SECRETED BY A VARIETY OF HUMAN AND RODENT TUMOUR CELL LINES, Cancer Res., 46 (1986), 5629-5632.
29. C. Sunderkotter, K. Steinbrink, M. Goebeler, R. Bhardwaj and. C Sorg, MACROPHAGES AND ANGIOGENESIS, J. Leuk. Biol., 55 (1994), 410-422.
30. J.P. Ward and J.R. King, MATHEMATICAL MODELLING OF AVASCULAR TUMOUR GROWTH, IMA J. Math. Appl. Med. Biol., 14 (1997), 39-69.