Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012
Cancer modeling
Page(s) 136 - 165
DOI https://doi.org/10.1051/mmnp/20127107
Published online 25 January 2012
  1. S. Ahmed, J.F. Passos, M.J. Birket, T. Beckmann, S. Brings, H. Peters, M.A. Birch-Machin, T. von Zglinicki, G. Saretzki. Telomerase Does Not Counteract Telomere Shortening But Protects Mitochondrial Function Under Oxidative Stress. Journal of Cell Science, 121 (2008), No. 7, 1046–1053. [CrossRef] [PubMed]
  2. O. Arino, M. Kimmel, G.F. Webb. Mathematical Modeling of the Loss of Telomere Sequences. J. theor. Biol., 177 (1995), No. 1, 45–57. [CrossRef] [PubMed]
  3. O. Arino, E. Sánchez, G.F. Webb. Polynomial Growth Dynamics of Telomere Loss in a Heterogeneous Cell Population. Dynamic Control Discrete Impulsive System, 3 (1997), No. 3, 263–282.
  4. P. Armitage, R. Doll. The age distribution of cancer and a multi-stage theory of carcinogenosis. IJE, 33 (2004), No. 6, 1174–1179.
  5. S. Bagheri, M. Nosrati, S. Li, S. Fong, S. Torabian, J. Rangel, D.H. Moore, S. Federman, R.R. LaPosa, F.L. Baehner, R.W. Sagebiel, J.E. Cleaver, C. Haqq, R.J. Debs, E.H. Blackburn, M. Kashani-Sabet. Genes and pathways downstream of telomerase in melanoma metastasis. PNAS, 103 (2006), No. 30, 11306–11311. [CrossRef]
  6. H.T. Banks, K.L. Sutton, W.C. Thompson, G. Bocharov, D. Roose, T. Schenkel, A. Meyerhans. Estimation of Cell Proliferation Dynamics Using CFSE Data. Bulletin of Mathematical Biology, 73 (2011), 1, 116–150. [CrossRef] [MathSciNet] [PubMed]
  7. S. Bernard, L. Pujo-Menjouet, M.C. Mackey. Analysis of Cell Kinetics Using a Cell Division Marker : Mathematical Modeling of Experimental Data. Biophysical Journal, 84 (2003), No. 5, 3414–3424. [CrossRef] [PubMed]
  8. D.S. Bernstein. Matrix Mathematics, Second Edition., Princeton University Press, 2009.
  9. D. Bonnet, J.E. Dick. Human Acute Myeloid Leukemia is Organized as a Hierarchy That Originates From a Primitive Hematopoetic Cell. Nature Medicine, 3 (1997), No. 7, 730–737. [CrossRef] [PubMed]
  10. A. Brú, S. Albertos, J.L. Subiza, J.L. García-Asenjo, I. Brú. The Universal Dynamics of Tumor Growth. Biophysical Journal, 85 (2003), No. 5, 2948–2961. [CrossRef] [PubMed]
  11. E.D. Cohen, Y. Tian, E.E. Morrisey. Wnt signaling : an essential regulator of cardiovascular differentiation, morphogenesis and progenitor self-renewal. Development, 135 (2008), No. 5, 789–798. [CrossRef] [PubMed]
  12. A.T. Collins, P.A. Berry, C. Hyde, M.J. Stower, N.J. Maitland. Prospective Identification of Tumorigenic Prostate Cancer Stem Cells. Cancer Res., 65 (2005), No. 23, 10946–10951. [CrossRef] [PubMed]
  13. P. Dalerba, S.J. Dylla, I.-K. Park, R. Liu, X. Wang, R.W. Cho, T. Hoey, A. Gurney, E.H. Huang, D.M. Simeone, A.A. Shelton, G. Parmiani, C. Castelli, M.F. Clarke. Phenotypic characterization of human colorectal cancer stem cells. PNAS, 104 (2007), No. 24, 10158–10163. [CrossRef]
  14. L.G. de Pillis, A.E. Radunskaya, C.L. Wiseman. A Validated Mathematical Model of Cell-Mediated Immune Response to Tumor Growth. Cancer Res., 65 (2005), No. 17, 7950–7958. [PubMed]
  15. B.M. Deasy, R.J. Jankowski, T.R. Payne, B. Cao, J.P. Goff, J.S. Greenberger, J. Huard. Modeling Stem Cell Population Growth : Incorporating Terms for Proliferative Heterogeneity. Stem Cells, 21 (2003), No. 5, 536 – 545. [CrossRef] [PubMed]
  16. J.E. Dick. Breast cancer stem cells revealed. PNAS, 100 (2003), No. 7, 3547–3549. [CrossRef]
  17. D. Dingli, F. Michor. Successful Therapy Must Eradicate Cancer Stem Cells. Stem Cells, 24 (2006), No. 12, 2603–2610. [CrossRef] [PubMed]
  18. J. Dyson, E. Sánchez, R. Villella-Bressan, G.F. Webb. Stabilization of telomeres in nonlinear models of proliferating cell lines. Journal of Theoretical Biology, 244 (2007), No. 3, 400–408. [CrossRef] [MathSciNet] [PubMed]
  19. J. Dyson, R. Villella-Bressan, G.F. Webb. Asymptotic Behaviour Of Solutions To Abstract Logistic Equations. Mathematical Biosciences, 206 (2007), No. 2, 216–232. [CrossRef] [MathSciNet] [PubMed]
  20. H. Enderling, D. Park, L. Hlatky, P. Hahnfeldt. The Importance of Spatial Distribution of Stemness and Proliferation State in Determining Tumor Radioresponse. Math. Model. Nat. Phenom., 4 (2009), No. 3, 117–133. [CrossRef] [EDP Sciences]
  21. A. Eramo, F. Lotti, G. Sette, E. Pilozzi, M. Biffoni, A. Di Virgilio, C. Conticello, L. Ruco, C. Peschle, R. De Maria. Identification and expansion of the tumorigenic lung cancer stem cell population. Cell Death and Differentiation, 15 (2008), No. 3, 504–514. [CrossRef] [PubMed]
  22. E.R. Fearon, B. Vogelstein. A Genetic Model for Colorectal Tumorigenesis. Cell, 61 (1990), 759–767. [CrossRef] [PubMed]
  23. R.W. Frenck, Jr., E.H Blackburn, K.M. Shannon. The rate of telomere sequence loss in human leukocytes varies with age. PNAS, 95 (1998), No. 10, 5607-5610. [CrossRef]
  24. S.N. Gentry, R. Ashkenazi, T.L. Jackson. A Maturity Structured Mathematical Model of Mutation Acquisition in the Absence of Homeostatic Regulation. Math. Model. Nat. Phenom., 4 (2009), 403–422. [CrossRef] [EDP Sciences]
  25. D. Hanahan, R.A. Weinberg. The Hallmarks of Cancer : The Next Generation. Cell., 144 (2011), No. 5, 646–674. [CrossRef] [PubMed]
  26. K.E. Huffman, S.D. Levene, V.M. Tesmer, J.W. Shay, W.E. Wright. Telomere Shortening Is Proportional to the Size of the G-rich Telomeric 3’-Overhang. The Journal of Biological Chemistry, 275 (2000), No. 26, 19719–19722. [CrossRef] [PubMed]
  27. A. G. Knudson, Two genetic hits (more or less) to cancer. Nat. Rev. Cancer., 1 (2001), 157–162. [CrossRef] [PubMed]
  28. S.H. Lang, F.M. Frame, A.T. Collins. Prostate cancer stem cells. Journal of Pathology, 217 (2009), No. 9, 299–306. [CrossRef] [PubMed]
  29. M.Z. Levy, R.C. Allsopp, A.B. Futcher, C.W. Greider, C.B. Harley. Telomere End-replication Problem and Cell Aging. J. Mol. Biol., 225 (1992), No. 4, 951–960. [CrossRef] [PubMed]
  30. H. Lodish, J. Flygare, S. Chou. From stem cell to erythroblast : Regulation of red cell production at multiple levels by multiple hormones. IUBMB Life, 62 (2010), No. 7, 492–496. [CrossRef] [PubMed]
  31. A. Marciniak-Czochra. Mathematical models of stem cells renewal and differentiation. Oberwolfach Reports, 2 (2009), 3414–3424.
  32. S.J. Morrison, N. Uchida, I.L. Weissman. The biology of hematopoietic stem cells. Annu. Rev. Cell Dev. Biol., 11 (1995), 35–71. [CrossRef] [PubMed]
  33. P. Olofsson. Modeling of the Process of Telomere Shortening : an Overview.
  34. L. Perko. Differential Equations and Dynamical Systems, 3rd edition. Springer, New York, NY, 2001.
  35. F. Roegiers, Y.N. Jan. Asymmetric cell division. Current Opinion in Cell Biology, 16 (2004), No. 2, 195-205. [CrossRef] [PubMed]
  36. G.R. Simon, H. Wagner. Small Cell Lung Cancer*. Chest, 123 (2003), No. 1, 259–271. [CrossRef]
  37. S.K. Singh, I.D. Clarke, M. Terasaki, V.E. Bonn, C. Hawkins, J. Squire, P.B. Dirks. Identification of a Cancer Stem Cell in Human Brain Tumors. Cancer Res., 63 (2003), No. 18, 5821–5828. [PubMed]
  38. P. Skehan, S.J. Friedman. Non-exponential growth by mammalian cells in culture. Cell Tissue Kinet., 17 (1984), No. 4, 335–343. [PubMed]
  39. G.I. Solyanik, N.M. Berezetskaya, R.I. Bulkiewicz, G.I. Kulik. Different growth patterns of a cancer cell population as a function of its starting growth characteristics : analysis by mathematical modelling. Cell Prolif, 28 (1995), No. 5, 263–278. [CrossRef] [PubMed]
  40. G.J. Spangrude, S. Heimfeld, I.L. Weissman. Purification and characterization of mouse hematopoietic stem cells. Science, 244 (1988), No. 4861, 58–62. [CrossRef] [PubMed]
  41. J.F. Speer, V.E. Petrosky, M.W. Retsky, R.H. Wardwell", A Stochastic Numerical Model of Breast Cancer Growth That Simulates Clinical Data. Cancer Res., 44 (1984), No. 9, 4124–4130. [PubMed]
  42. K. Sprouffske, J.W. Pepper, C.C. Maley. Accurate Reconstruction of the Temporal Order of Mutations in Neoplastic Progression. Cancer Prev. Res., 4 (2011), No. 7, 1135–1144. [CrossRef]
  43. S.A. Stewart, W.C. Hahn, B.F. O’Connor, E.N. Banner, A.S. Lundberg, P. Modha, H. Mizuno, M.W. Brooks, M. Fleming, D.B. Zimonjic, N.C. Popescu, R.A. Weinberg. Telomerase contributes to tumorigenesis by a telomere length-independent mechanism. PNAS, 99 (2002), No. 20, 12606–12611. [CrossRef]
  44. M.R. Stratton, P.J. Campbell, P.A. Futreal. The Cancer Genome. Nature, 458 (2009), No. 7239, 156–182. [CrossRef] [PubMed]
  45. L.G. van der Flier, H. Clevers. Stem Cells, Self-Renewal, and Differentiation in the Intestinal Epithelium. Annu. Rev. Physiol., 71 (2009), No. 1, 241–260. [CrossRef] [PubMed]
  46. T. von Zglinicki. Oxidative Stress Shortens Telomeres. Trends in Biochemical Scoences, 27 (2002), No. 7, 339–344. [CrossRef] [PubMed]
  47. G.F. Webb. Logistic Models Of Structured Population Growth. Comp and Maths. with Appls., 12 (1986), No. 4-5A, 527–539. [CrossRef]
  48. G.D. Weinstein, J.L. McCullough, P. Ross. Cell Proliferation in Normal Epidermis. The Journal of Investigative Dermatology, 82 (1984), No. 6, 623–628. [CrossRef] [PubMed]
  49. G.D. Wilson, N.J. McNally, S. Dische, M.I. Saunders, C. Des Rochers, A.A. Lewis, M.H. Bennett. Measurement of cell kinetics in human tumours in vivo using bromodeoxyuridine incorporation and flow cytometry. Br. J. Cancer, 58 (1988), No. 4, 423–431. [CrossRef] [PubMed]
  50. Q.-L. Ying, J. Wray, J. Nichols, L. Batlle-Morera, B. Doble, J. Woodgett, P. Cohen, A. Smith. The ground state of embryonic stem cell self-renewal. Nature, 453 (2008), No. 7194, 519–523. [CrossRef] [PubMed]

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