Free Access
Math. Model. Nat. Phenom.
Volume 5, Number 3, 2010
Mathematical modeling in the medical sciences
Page(s) 40 - 62
Published online 28 April 2010
  1. R.W. Cho, X. Wang X, M. Diehn, K. Shedden, GY Ghen, G Sherlock, A Gurney, J LewickiMF Clarke. Isolation and molecular characterization of cancer stem cells in MMTV-Wnt-1 murine breast tumors. Stem Cells, 26 (2008), No. 2, 364-71. [CrossRef] [PubMed] [Google Scholar]
  2. J. Demongeot, M. KaufmanR. Thomas. Positive feedback circuits and memory. C. R. Acad. Sci. III. 323 (2000), No. 1, 69-79. [PubMed] [Google Scholar]
  3. D. Dingli, A. TraulsenJ. Pacheco. Stochastics Dynamics of Hematopoietic Tumor Stem Cells. Cell Cycle 6 (2007), No. 4, 461-466. [CrossRef] [PubMed] [Google Scholar]
  4. V.S. Donnenberg, R.J. LandreneauA.D. Donnenberg. Tumorigenic stem and progenitor cells: implications for the therapeutic index of anti-cancer agents. Journal Control Release, 122 (2007), No. 3, 385-91. [CrossRef] [Google Scholar]
  5. H. Enderling, M. A. Chaplain, A.R. Andersona, J. S. Vaidyab. A mathematical model of breast cancer development, local treatment and recurrence. Journal of Theoretical Biology, 246 (2007) No. 2, 245-259. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  6. D. Fang, T. K. Nguyen, K. Leishear, R. Finko, A. N. Kulp, S. Hotz, P. A. Van Belle, X. Xu, D. E. Elder, M. Herlyn. A tumorigenic subpopulation with stem cell properties in melanomas. Cancer Res. 65, (2005), No. 20, 9328-37. [CrossRef] [PubMed] [Google Scholar]
  7. M. FreemanJ.B. Gurdon. Regulatory principles of developmental signaling. Annu. Rev. Cell. Dev. Biol. 18 (2002), 515-39. [CrossRef] [PubMed] [Google Scholar]
  8. R. GangulyI.K. Puri. Mathematical model for the cancer stem cell hypothesis. Cell Prolif. 39 (2006), No. 1, 3-14. [CrossRef] [PubMed] [Google Scholar]
  9. R. GangulyI.K. Puri. Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis. Cell Prolif. 40 (2007), No. 3, 338-54. [CrossRef] [PubMed] [Google Scholar]
  10. R.P. Hill. Identifying cancer stem cells in solid tumors: case not proven. Cancer Res. 66 (2006), No. 4, 1891-5. [CrossRef] [PubMed] [Google Scholar]
  11. M.D. Johnston, C.M. Edwards, W.F. Bodmer, P.K. MainiS.J. Chapman. Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer. Proc. Natl. Acad. Sci. 104 (2007), No. 10, 4008-13. [Google Scholar]
  12. E.A. King-SmithA. Morley. Computer simulation of granulopoiesis: normal and impaired granulopoiesis. Blood. 36 (1970), No. 2, 254-62. [PubMed] [Google Scholar]
  13. B. Laquente, F. ViŰalsJ.R. GermĹ. Metronomic chemotherapy: an antiangiogenic scheduling. Clin. Transl. Oncol. 9 (2007), No. 2, 93-8. [CrossRef] [PubMed] [Google Scholar]
  14. M. Leszczyniecka, T. Roberts, P. Dent, S. Grant, P.B. Fisher. Differentiation therapy of human cancer: basic science and clinical applications. Pharmacol Ther. 90 (2001) No. 2-3, 105-56. [CrossRef] [PubMed] [Google Scholar]
  15. I. MalanchiJ. Huelsken. Cancer Stem cells: never Wnt away from the niche. Current Opinion in Oncology 21 (2008), 41-46. [Google Scholar]
  16. J.A. Marchal, F. RodrŠguez-Serrano, R. Madeddu, H. Boulaiz, A. Martinez-Amat, E. Carrillo, O. Caba, J.C. Prados, C. Velez, C. Melguizo, A. MontellaA. Aranega. Differentiation: an encouraging approach to anticancer therapy. J. Anat. Embryol. 111 (2006), No. 1, 45-64. [Google Scholar]
  17. F. Michor, T.P. Hughes, Y. Iwasa, S. Branford,N. P. Shah, C. L. Sawyers, M. A. Nowack. Dynamics of Chronic Myeloid Leukaemia., Nature 435 (2005) 1267-1270. [CrossRef] [PubMed] [Google Scholar]
  18. J.A. NilssonJ.L. Cleveland. Myc pathways provoking cell suicide and cancer. Oncogene. 22 (2003), No. 56, 9007-21. [CrossRef] [PubMed] [Google Scholar]
  19. A.B. Pardee. Regulatory molecular biology. Cell Cycle. 5 (2006), No. 8, 846-52. [CrossRef] [PubMed] [Google Scholar]
  20. A.B. Pardee. Tumor progression–targets for differential therapy. J. Cell Physiol. 209 (2006), No. 3, 589-91. [CrossRef] [PubMed] [Google Scholar]
  21. I. Roeder, M. Horn, I. Glauche, A. Hochlaus, M. C. MuellerM. Loeffler. Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nature Medicine 12 (2006), 1181-1184. [Google Scholar]
  22. T. Schatton, N.Y. Frank, M.H Frank. Identification and targeting of cancer stem cells. Bioessays 31 (2009) No. 10, 1038-49. [CrossRef] [PubMed] [Google Scholar]
  23. R. Thomas. Laws for the dynamics of regulatory networks. Int. J. Dev. Biol. 42 (1998), No. 3, 479-85. [PubMed] [Google Scholar]
  24. M.J. Tindall. Modelling the cell cycle and cell movement in multicellular tumour spheroids. Bull. Math. Biol. 69 (2007), No. 4, 1147-65. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  25. W. C. Lo, C. S. Chou, K. K. Gokoffski, F. Y. Wan, A.D. Lander, A. L. CalofQ. Nie. Feedback regulation in multistage cell lineages. Math. Biosci. Eng. 6 (2009), No. 1, 59-82. [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.