Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012
Cancer modeling
Page(s) 166 - 202
DOI https://doi.org/10.1051/mmnp/20127199
Published online 25 January 2012
  1. J. Ablain, H. de The. Revisiting the differentiation paradigm in acute promyelocytic leukemia. Blood, 117 (2008), No. 22, 5795–5802. [CrossRef] [Google Scholar]
  2. M. Adimy, F. Crauste. Modeling and asymptotic stability of a growth factor- dependent stem cell dynamics model with distributed delay. Discrete Contin. Dyn. Syst. Ser. B, 8 (2007), No. 1, 19–38. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Adimy, F. Crauste, S. Ruan. A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math., 65 (2005), No. 4, 1328–1352. [CrossRef] [MathSciNet] [Google Scholar]
  4. M. Adimy, F. Crauste, S. Ruan. Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull. Math. Biol., 68 (2006), No. 8, 2321–2351. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  5. M. Aglietta, W. Piacibello, F. Sanavio, A. Stacchini, F. Apra, M. Schena, C. Mossetti, F. Carnino, F. Caligaris-Cappio, F. Gavosto. Kinetics of human hemopoietic cells after in vivo administration of granulocyte-macrophage colony-stimulating factor. J. Clin. Invest., 83 (1989), No. 2, 551–557. [CrossRef] [PubMed] [Google Scholar]
  6. T. Alarcon, P. Getto, A. Marciniak-Czochra, MdM. Vivanco. A model for stem cell population dynamics with regulated maturation delay. Discr. Cont. Dyn. Systems B (2011), to appear. [Google Scholar]
  7. L. Andrey. Chaos in cancer. Med. Hypotheses, 28 (1989), No. 3, 143–144. [CrossRef] [PubMed] [Google Scholar]
  8. O. Arino, M. Kimmel. Stability analysis of models of cell production systems. Math. Modelling, 7 (1986), No. 9-12, 1269–1300. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Baum, MA. Chaplain, AR. Anderson, M. Douek, JS. Vaidya. Does breast cancer exist in a state of chaos ? Eur. J. Cancer, 35 (1999), No. 6, 886–891. [CrossRef] [PubMed] [Google Scholar]
  10. R. Bejar, R. Levine, and B. L. Ebert. Unraveling the molecular pathophysiology of myelodysplastic syndromes. J. Clin. Oncol., 29 (2011), No. 5, 504–514. [CrossRef] [PubMed] [Google Scholar]
  11. J. Belair, MC. Mackey, J. M. Mahaffy. Age-structured and two-delay models for erythropoiesis. Math. Biosci., 128 (1995), No. 1-2, 317–346. [CrossRef] [PubMed] [Google Scholar]
  12. C. Bellan, L. Stefano, dF. Giulia, E. A. Rogena, L. Lorenzo. Burkitt lymphoma versus diffuse large B-cell lymphoma : a practical approach. Hematol. Oncol., 28 (2010), No. 2, 53–56. [PubMed] [Google Scholar]
  13. MT. Bocker, I. Hellwig, A. Breiling, V. Eckstein, A. D. Ho, F. Lyko. Genome-wide promoter DNA methylation dynamics of human hematopoietic progenitor cells during differentiation and aging. Blood, 117 (2011), No. 19 : e182–e189. [CrossRef] [PubMed] [Google Scholar]
  14. V. Bogner, L. Keil, KG. Kanz, C. Kirchhoff, B. A. Leidel, W. Mutschler, P. Biberthaler. Very early posttraumatic serum alterations are signiïňĄcantly associated to initial massive RBC substitution, injury severity, multiple organ failure and adverse clinical outcome in multiple injured patients. Eur. J. Med. Res., 14 (2009), No. 7, 284–291. [CrossRef] [PubMed] [Google Scholar]
  15. 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. [CrossRef] [PubMed] [Google Scholar]
  16. J. Bryan, E. Jabbour, H. Prescott, G. Garcia-Manero, J. P. Issa, H. Kantarjian. Current and future management options for myelodysplastic syndromes. Drugs, 70 (2010), No. 11, 1381– 1394. [CrossRef] [PubMed] [Google Scholar]
  17. EC. Buss, A. D. Ho. Leukemia stem cells. Int. J. Cancer., 129 (2011), No. 10, 2328–2336. [CrossRef] [PubMed] [Google Scholar]
  18. SY. Chen, YC. Huang, SP Liu, FJ Tsai, WC Shyu, SZ Lin. An overview of concepts for cancer stem cells. Cell Transplant., 20 (2011), No. 1, 113–120. [CrossRef] [PubMed] [Google Scholar]
  19. BD. Cheson. Standard and low-dose chemotherapy for the treatment of myelodysplastic syndromes. Leuk. Res., Suppl. 1 (1998), S17–S21. [CrossRef] [Google Scholar]
  20. H. Clevers. The cancer stem cell : premises, promises and challenges. Nat Med., 17 (2011), No. 3, 313–319. [CrossRef] [PubMed] [Google Scholar]
  21. D.S. Coffey. Self-organization, complexity and chaos : the new biology for medicine. Nat. Med., 4 (1998), No. 8, 882–885. [CrossRef] [PubMed] [Google Scholar]
  22. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis –I. periodic chronic myelogenous leukemia. J. Theor. Biol., 237 (2005), No. 2, 117–132. [CrossRef] [PubMed] [Google Scholar]
  23. D. Dingli, JM. Pacheco. Stochastic dynamics and the evolution of mutations in stem cells. BMC Biol., 9 :41 (2011). [Google Scholar]
  24. M. Doumic-Jauffret, PS. Kim, B. Perthame. Stability analysis of a simplied yet complete model for chronic myelogenous leukemia. Bull. Math. Biol., 72 (2010), No. 7, 1732–1759. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  25. M. Doumic-Jauffret, A. Marciniak-Czochra, B. Perthame, JP. Zubelli. A Structured Population Model of Cell Differentiation. SIAM J. Appl. Math., 71 (2011), 1918–1940. [CrossRef] [Google Scholar]
  26. P. Fenaux, GJ. Mufti, E. Hellstrom-Lindberg, V. Santini, C. Finelli, A. Giagounidis, R. Schoch, N. Gattermann, G. Sanz, A. List, SD. Gore, JF. Seymour, JM. Bennett, J. Byrd, J. Backstrom, L. Zimmerman, D. McKenzie, C. Beach, LR. Silverman; International Vidaza High-Risk MDS Survival Study Group. Efficacy of azacitidine compared with that of conventional care regimens in the treatment of higher-risk myelodysplastic syndromes : a randomised, open-label, phase III study. Lancet Oncol., 10 (2009), No. 3, 223–232. [CrossRef] [PubMed] [Google Scholar]
  27. C. Foley, S. Bernard, MC. Mackey. Cost-effective G-CSF therapy strategies for cyclical neutropenia : Mathematical modelling based hypotheses. J. Theor. Biol., 238 (2006), No. 4, 754–763. [CrossRef] [PubMed] [Google Scholar]
  28. W. Fried. Erythropoietin and erythropoiesis. Exp. Hematol., 37 (2009), No. 9, 1007–1015. [CrossRef] [PubMed] [Google Scholar]
  29. FR. Gantmacher. The theory of matrices 2. Chelsea Publishing, New York, 1964. [Google Scholar]
  30. P. Getto, A. Marciniak-Czochra, Y. Nakata, MdM. Vivanco. Global dynamics of two compartment models for cell production systems with regulatory mechanisms. (2011), submitted. [Google Scholar]
  31. J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer, New York, 2002. [Google Scholar]
  32. H. Haeno, RL. Levine, DG. Gilliland, F. Michor. A progenitor cell origin of myeloid malignancies. PNAS, 106 (2009), No. 39, 16616–16621. [CrossRef] [PubMed] [Google Scholar]
  33. KJ. Hope, L. Jin, JE. Dick. Acute myeloid leukemia originates from a hierarchy of leukemic stem cell classes that differ in self-renewal capacity. Nat. Immun., 5 (2004), No. 7, 738–743. [CrossRef] [Google Scholar]
  34. JH. Jandl (ed), Textbook of Hematology, Little Brown, Boston, MA, 1996. [Google Scholar]
  35. S. Janz, M. Potter, CS. Rabkin. Lymphoma- and leukemia-associated chromosomal translocations in healthy individuals. Genes Chromosomes Cancer, 36 (2003), No. 3, 211–223. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  36. H. Kantarjian, Y. Oki, G. Garcia-Manero, X. Huang, S. OBrien, J. Cortes, S. Faderl, C. Bueso-Ramos, F. Ravandi, Z. Estrov, A. Ferrajoli, W. Wierda, J. Shan, J. Davis, F. Giles, HI. Saba, JP. Issa. Results of a randomized study of 3 schedules of low- dose decitabine in higher-risk myelodysplastic syndrome and chronic myelomonocytic leukemia. Blood, 109 (2007), No. 1, 52–57. [CrossRef] [PubMed] [Google Scholar]
  37. S. Knipp, B. Hildebrand, A. Kündgen, A. Giagounidis, G. Kobbe, R. Haas, C. Aul, N. Gat- termann, U. Germing. Intensive chemotherapy is not recommended for patients aged > 60 years who have myelodysplastic syndromes or acute myeloid leukemia with high-risk karyotypes. Cancer, 110 (2007), No. 2, 345–352. [CrossRef] [PubMed] [Google Scholar]
  38. N. Korde, SY. Kristinsson, O. Landgren. Monoclonal gammopathy of undetermined signiïňĄcance (MGUS) and smoldering multiple myeloma (Smm) : novel biological insights and development of early treatment strategies. Blood, 117 (2011), No. 21, 5573–5581. [CrossRef] [PubMed] [Google Scholar]
  39. A. Lander, K. Gokoffski, F. Wan, Q. Nie, A. Calof. Cell lineages and the logic of proliferative control. PLoS biology, 7 (2009), No. 1, 84–100. [CrossRef] [Google Scholar]
  40. SS. Lange, K. Takata, RD. Wood. DNA polymerases and cancer. Nat. Rev. Cancer, 11 (2011), No. 2, 96–110. [CrossRef] [PubMed] [Google Scholar]
  41. PM. Lansdorp. Stem cell biology for the transfusionist. Vox Sang., 74 Suppl. 2 (1998), 91–94. [CrossRef] [PubMed] [Google Scholar]
  42. JE. Layton, H. Hockman, WP. Sheridan, G. Morstyn. Evidence for a novel in vivo control mechanism of granulopoiesis : mature cell-related control of a regulatory growth factor. Blood, 74 (1989), No. 4, 1303–1307. [PubMed] [Google Scholar]
  43. W. Lo, C. Chou, K. Gokoffski, F. Wan, A. Lander, A. Calof, Q. Nie. Feedback regulation in multistage cell lineages. Math. Biosci. Eng., 6 (2009), No. 1, 59–82. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  44. MC. Mackey. Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood, 51 (1978), No. 5, 941–956. [PubMed] [Google Scholar]
  45. MC. Mackey, L. Glass, Oscillation and chaos in physiological control systems. Science, 197 (1977), No. 4300, 287–289. [CrossRef] [PubMed] [Google Scholar]
  46. A. Marciniak-Czochra, T.Stiehl. Mathematical models of hematopoietic reconstitution after stem cell transplantation. In HG. Bock, T. Carraro, W. Jäger, S. Koerkel, R. Rannacher, JP. Schloeder (eds), Model Based Parameter Estimation : Theory and Applications. Springer, Heidelberg, 2011. [Google Scholar]
  47. A. Marciniak-Czochra, T. Stiehl, W. Jäger, AD. Ho, W. Wagner. Modeling of asymmetric cell division in hematopoietic stem cells – regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev., 18 (2009), No. 3, 377–385. [CrossRef] [PubMed] [Google Scholar]
  48. A. Marciniak-Czochra, T. Stiehl, W. Wagner. Modeling of replicative senescence in hematopoietic development. Aging (Albany NY), 1 (2009), No. 8, 723–732. [CrossRef] [PubMed] [Google Scholar]
  49. D. Metcalf. Hematopoietic cytokines. Blood, 111 (2008), No. 2, 485–491. [CrossRef] [PubMed] [Google Scholar]
  50. F. Michor, TP. Hughes, Y. Iwasa, S. Branford, NP. Shah, CL. Sawyers, MA. Nowak. Dynamics of chronic myeloid leukaemia. Nature, 435 (2005), No. 7046, 1267–1270. [CrossRef] [PubMed] [Google Scholar]
  51. KA. Moore, IR. Lemischka. Stem cells and their niches. Science, 311 (2006), No. 5769, 1880–1805. [CrossRef] [PubMed] [Google Scholar]
  52. D. Morgan, A. Murray, T. Hunt, P. Nurse. In : Alberts Molecular Biology of the Cell, 4th Edition, Garland Science, New York, 2002. [Google Scholar]
  53. I. Munk Pedersen, J. Reed. Microenvironmental interactions and survival of CLL B-cells. Leuk. Lymphoma, 45 (2004), No. 12, 2365–2372. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  54. Y. Nakata, P. Getto, A. Marciniak-Czochra, T. Alarcon. Stability analysis of multi-compartment models for cell production systems. J. Biol. Dyn., (2011), doi : 10.1080/17513758.2011.558214. [PubMed] [Google Scholar]
  55. L. Pujo-Menjouet, S. Bernard, MC. Mackey. Long period oscillations in a G0 model of hematopoietic stem cells. SIAM J. Appl. Dyn. Syst, 4 (2005), No. 2, 312–332. [CrossRef] [Google Scholar]
  56. T. Reya, SJ. Morrison, MF. Clarke, IL. Weissman. Stem cells, cancer, and cancer stem cells. Nature, 414 (2001), No. 6859, 105–111. [CrossRef] [PubMed] [Google Scholar]
  57. I. Roeder, M. Herberg, M. Horn. An age-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. Bull. Math. Biol., 71 (2009), No. 3, 602–626. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  58. I. Roeder, M. Horn, I. Glauche, A. Hochhaus, MC. Mueller, M. Loeffler. Dynamic modeling of imatinib-treated chronic myeloid leukemia : functional insights and clinical implications. Nat. Med., 12 (2006), No. 10, 1181–1184. [CrossRef] [PubMed] [Google Scholar]
  59. I. Roeder, M. Loeffler. A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp. Hematol., 30 (2002), 853–861. [CrossRef] [PubMed] [Google Scholar]
  60. R. Rudnicki. Chaoticity of the blood cell production system. Chaos, doi : 10.1063/1.3258364, 2009. [Google Scholar]
  61. F. Schueler, C. Hirt, G. Doelken. Chromosomal translocation t (14 ;18) in healthy individuals. Semin. Cancer. Biol., 13 (2003), 3, 203–209. [CrossRef] [PubMed] [Google Scholar]
  62. K. Shinjo, A. Takeshita, K. Ohnishi, R. Ohno. Granulocyte colony-stimulating factor receptor at various stages of normal and leukemic hematopoietic cells. Leuk. Lymphoma, 25 (1997), No. 1-2, 37–46. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  63. S. Soltanian, MM. Matin. Cancer stem cells and cancer therapy. Tumour Biol., 32 (2011), No. 3, 425–440. [CrossRef] [PubMed] [Google Scholar]
  64. T. Stiehl, A. Marciniak-Czochra. Characterization of stem cells using mathematical models of multistage cell lineages. Mathematical and Computer Modelling, 53 (2011), No. 7-8, 1505–1517. [CrossRef] [Google Scholar]
  65. JE. Till, L. Siminovitch, EA. McCulloch. Stochastic Model of Stem Cell Proliferation Based on Growth of Spleen Colony-Forming Cells. PNAS, 51 (1964), 29–49. [CrossRef] [Google Scholar]
  66. C. Tomasetti, D. Levy. Role of symmetric and asymmetric division of stem cells in developing drug resistance. PNAS., 107 (2010), No. 39. 16766-16771. [CrossRef] [Google Scholar]
  67. M. Tormo, I. Marugan, M. Calabuig. Myelodysplastic syndromes : an update on molecular pathology. Clin. Transl. Oncol., 12 (2010), No. 10, 652–661. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.