Free Access
Issue
Math. Model. Nat. Phenom.
Volume 4, Number 3, 2009
Cancer modelling (Part 2)
Page(s) 117 - 133
DOI https://doi.org/10.1051/mmnp/20094305
Published online 05 June 2009
  1. D. Hanahan, R. Weinberg. The hallmarks of cancer. Cell, 100 (2000), No.1, 57–70.
  2. P. Armitage, R. Doll. The age distribution of cancer and a multi-stage theory of carcinogenesis. Br J Cancer, 8 (1954), No.1, 1–12.
  3. W.C. Black, H.G. Welch. Advances in diagnostic imaging and overestimations of disease prevalence and the benefits of therapy. N Engl J Med, 328 (1993), No.17, 1237–1243.
  4. T. Lapidot, C. Sirard, B. Murdoch, et al. A cell initiating human acute myeloid leukaemia after transplantation into SCID mice. Nature, 367 (1994), No. 6464, 645–648.
  5. D. Bonnet, J.E. Dick. Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat Med, 3 (1997), No. 7, 730–737.
  6. M. Al-Hajj, M.S. Wicha, A. Benito-Hernandez, S.J. Morrison, M.F. Clarke. Prospective identification of tumorigenic breast cancer cells. Proc Natl Acad Sci USA, 100 (2003), No.7, 3983–3988.
  7. J.E. Dick. Breast cancer stem cells revealed. Proc Natl Acad Sci USA, 100 (2003), No.7, 3547–3549.
  8. S.K. Singh, C. Hawkins, I.D. Clarke. Identification of a cancer stem cell in human brain tumors. Cancer Res, 63 (2003), No.18, 5821–5828.
  9. S.K. Singh, I.D. Clarke, M. Terasaki, et al. Identification of human brain tumour initiating cells. Nature, 432 (2004), No.7015, 396–401.
  10. D. Fioriti, M. Mischitelli, F. Di Monaco, et al. Cancer stem cells in prostate adenocarcinoma: a target for new anticancer strategies. J. Cell Physiol., 216 (2008), No.3, 571–575.
  11. N.J. Maitland, T. Colling. Prostate cancer stem cells: a new target for therapy. J. Clin. Oncol., 26 (2008), No.17, 2862–2870.
  12. M. Todaro, M. Perez Alea, A.B. Di Stefano, et al. Colon cancer stem cells dictate tumor growth and resist cell death by production of interleukin-4. Cell stem cell, 1 (2007), No.4, 389–402.
  13. P. Cammareri, Y. Lombardo, M.G. Francipane, et al. Isolation and culture of colon cancer stem cells. Methods Cell Biol., 86 (2008), 311–324. [CrossRef] [PubMed]
  14. S.J. Morrison, J. Kimble. Asymmetric and symmetric stem-cell divisions in development and cancer. Nature, 41 (2006), No. 7097, 1068–1074.
  15. R. Reya, R., S.J. Morrison, M.F. Clarke, I.L. Weissman. Stem cells, cancer, and cancer stem cells. Nature, 414 (2001), No.6859, 105–111.
  16. D. Dingli, F. Michor. Successful therapy must eradicate cancer stem cells. Stem Cells, 24 (2006), No.12, 2603–2610.
  17. R.T. Prehn. The inhibition of tumor growth by tumor mass. Cancer Res, 51 (1991), No.1, 2–4.
  18. J. Folkman. Tumor angiogenesis: therapeutic implications. N Engl J Med, 285 (1971), No.21, 1182–1186.
  19. G.N. Naumov, E. Bender, D. Zurakowski, et al. A model of human tumor dormancy: an angiogenic switch from the nonangiogenic phenotype. J Natl Cancer Inst, 98 (2006), No.5, 316–325.
  20. M.H. Barcellos-Hoff. It takes a tissue to make a tumor: epigenetics, cancer and the microenvironment. Journal of mammary gland biology and neoplasia, 6 (2001), No.2, 213–221.
  21. R. Gatenby, R.J. Gillies. A microenvironmental model of carcinogenesis. Nat Rev Cancer, 8 (2008), No.1, 56–61.
  22. A. Brú, S. Albertos, J.L. Subiza et al. The universal dynamics of tumor growth. Biophys J 85 (2003), No.5, 2948–2961.
  23. J. Galle, M. Hoffmann, G. Aust. From single cells to tissue architecture – a bottom-up approach to modelling the spatio-temporal organization of complex multi-cellular systems. J Math Biol 58 (2009), 261–283.
  24. L. Norton. Conceptual and practical implications of breast tissue geometry: toward a more effective, less toxic therapy. Oncologist, 10 (2005), No. 6, 370–381.
  25. L. Norton, J. Massague. Is cancer a disease of self-seeding? Nat Med, 12 (2006), No.8, 875–878
  26. S. Masunaga, K. Ono, M. Abe. A method for the selective measurement of the radiosensitivity of quiescent cells in solid tumors – combination of immunofluorescence staining to BrdU and micronucleus assay. Radiat Res, 125 (1991), No. 3, 243–247.
  27. G.W. Barendsen, C. Van Bree, N.A.P. Franken. Importance of cell proliferative state and potentially lethal damage repair on radiation effectiveness: implications for combined tumor treatments. Int. J. Oncol., 19 (2001), No. 2, 247–256.
  28. J.J. Kim, I.F. Tannock. Repopulation of cancer cells during therapy: an important cause of treatment failure. Nat Rev Cancer, 5 (2005), No. 7, 516–25.
  29. H. Enderling, A.R.A. Anderson, M.A.J. Chaplain, A.J. Munro, J.S. Vaidya. Mathematical modelling of radiotherapy strategies for early breast cancer. J. Theor. Biol., 241 (2006), No. 1, 158–171.
  30. H. Enderling, M.A.J. Chaplain, A.R.A. Anderson, J.S. Vaidya. A mathematical model of breast cancer development, local treatment and recurrence. J. Theor. Biol., 246 (2007), No. 2, 245–259.
  31. B. Ribba, T. Colin, S. Schnell. A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor. Biol. Med. Model. 3 (2006), No.7.
  32. A. Dawson, T. Hillen. Derivation of the Tumour Control Probability (TCP) from a Cell Cycle Model. Comp. Math. Meth. Med, 7 (2006), 121–142. [CrossRef]
  33. T.L. Jackson, H.M. Byrne. A mathematical model to study the effects of drug resistance and vasculature on the response of solid tumors to chemotherapy. Math Biosci,164 (2000), No. 1, 17–38.
  34. T. Alarcon, M.R. Owen, H.M. Byrne et al. Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy. Comp Math Methods Med, 7(2006), 85–119.
  35. H.M. Byrne, T. Alarcon, M.R. Owen et al. Modelling the response of vascular tumours to chemotherapy: a multiscale approach. Math Mod Meth Appl Sci, 16 (2006), No. 1, 1219–1241.
  36. E.S. Norris, J.R. King, H.M. Byrne. Modelling the response of spatially structured tumours to chemotherapy: drug kinetics. Math Comp Mod, 43 (2006), No. 7-8, 820–837.
  37. A.R.A. Anderson, M.A.J. Chaplain, K.A. Rejniak. Single-Cell-Based Models in Biology and Medicine. Birkhauser, Basel, 2007.
  38. P.K. Maini, D.L.S. McElwain, D.I. Leavesley. Traveling wave model to interpret a wound-healing cell migration assay for human peritoneal mesothelial cells. Tissue Eng., 10 (2004), No.(3-4), 475–482.
  39. B. Ribba, K. Marron, Z. Agur, T. Alarcon, P.K. Maini. A mathematical model of Doxorubicin treatment efficacy for non-Hodgkin's lymphoma: investigation of the current protocol through theoretical modelling results. Bull Math Biol, 67 (2005), No.1, 79–99.
  40. M. Guerrero, X. Allen Li. Analysis of a large number of clinical studies for breast cancer radiotherapy: estimation of radiobiological parameters for treatment planning. Phys Med Biol, 48 (2003), No.20, 3307–3326.
  41. D.J. Brenner, L.R. Hlatky, P.J. Hahnfeldt, E.J. Hall, R.K. Sachs. A convenient extension of the linear-quadratic model to include redistribution and reoxygenation. Int J Radiat Oncol Biol Phys, 32 (1995), No. 2, 379–390.
  42. J.A. Stanley, W.U. Shipley, G.G. Steele. Influence of tumour size on hypoxic fraction and therapeutic sensitivity of Lewis lung tumour. Br J Cancer, 26 (1977), No.1, 105–113.
  43. J. Folkman, M. Hochberg. Self-regulation of growth in three dimensions. J Exp Med 138 (1973) No. 4, 745–753.
  44. J.M. Brown, A.J. Giaccia. The unique physiology of solid tumors: Opportunities (and problems) for cancer therapy. Cancer Res, 58 (1998), 1408 –1416.
  45. S. Masunaga, K. Ono, A. Takahashi, T. Ohnishi, Y. Kinashi, M. Takagaki. Radiobiological characteristics of solid tumours depending on the p53 status of the tumour cells, with emphasis on the response of intratumour quiescent cells. Eur J Cancer, 38 (2002), No. 5, 718–727.
  46. P. Ubezio, D. Cameron. Cell killing and resistance in pre-operative breast cancer chemotherapy. BMC Cancer, 8 (2008).
  47. M. Baumann, M. Krause, R. Hill. Exploring the role of cancer stem cells in radioresistance. Nat Rev Cancer, 8 (2008), No. 7, 545–554. [CrossRef] [PubMed]
  48. M. Baum, J.S. Vaidya. Targeted intra-operative radiotherapy–TARGIT for early breast cancer. Ann N Y Acad Sci, 1138 (2008), 132–135. [CrossRef] [PubMed]
  49. START Trialists' Group. The UK Standardisation of Breast Radiotherapy (START) Trial A of radiotherapy hypofractionation for treatment of early breast cancer: a randomised trial. Lancet Oncol, 9 (2008), No. 4, 331–341.
  50. J. Yarnold, D. Bloomeld, J. LeVay. Prospective randomized trial testing 5.7 Gy and 6.0 Gy fractions of whole breast radiotherapy in women with early breast cancer (FAST) trial. Clin Oncol, 16 (2004), S30.
  51. E.J. Hall. Radiobiology for the Radiologist 5th edn. Lippincott Williams & Wilkins, Philadelphia, 2000.
  52. S.K. Kang, J.B. Park, S.H. Cha. Multipotent, dedifferentiated cancer stem-like cells from brain gliomas. Stem Cells Dev, 15 (2006), No. 3, 423–435.
  53. S.A. Mani, W. Guo, M.J. Liao et al. The epithelial-mesenchymal transition generates cells with properties of stem cells. Cell, 133 (2008), No. 4, 704–715.
  54. C. Guiot, P.G. Degiorgis, P.P. Delsanto et al. Does tumor growth follow a “universal law”? J Theor Biol, 225 (2003), No. 2, 147–151.
  55. A. Wichmann, B. Jaklevic, T.T. Su. Ionizing radiation induces caspase-dependent but Chk2- and p53-independent cell death in Drosophila melanogaster. Proc Natl Acad Sci USA, 103 (2006), No. 26, 9952–9957.

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