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All issues Volume 10 / No 1 (2015) Math. Model. Nat. Phenom., 10 1 (2015) 48-63 References
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Issue
Math. Model. Nat. Phenom.
Volume 10, Number 1, 2015
Hybrid models
Page(s) 48 - 63
DOI https://doi.org/10.1051/mmnp/201510103
Published online 13 February 2015
  1. A.S. Ackleh, K. Deng, K. Ito, J. Thibodeaux. A structured erythropoiesis model with nonlinear cell maturation velocity and hormone decay rate. Math. Bios. 204, (2006), 21–48. [Google Scholar]
  2. E. Afenya, S. Mundle. Hematologic disorders and bone marrow-peripheral blood dynamics. Math. Model. Nat. Phenom., 5 (2010), no. 3, 15–27. [CrossRef] [EDP Sciences] [Google Scholar]
  3. R. Apostu, M.C. Mackey. Understanding cyclical thrombocytopenia: A mathematical modeling approach. J. Theor. Biol., 251 (2008), 297–316. [CrossRef] [PubMed] [Google Scholar]
  4. S. Balea, A. Halanay, D. Jardan, M. Neamtu. Stability analysis of a feedback model for the action of the immune system in leukemia. Math. Model. Nat. Phenom., 9 (2014), no. 1, 108–132. [CrossRef] [EDP Sciences] [Google Scholar]
  5. S. Bernard, J. Bélair, M.C. Mackey. Oscillations in cyclical neutropenia: New evidence based on mathematical modeling. J. Theor. Biol., 223, (2003), 283–298. [CrossRef] [PubMed] [Google Scholar]
  6. N. Bessonov, L. Pujo-Menjouet, V. Volpert. Cell modelling of hematopoiesis. Math. Model. Nat. Phenom., 1 (2006), no. 2, 81–103. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  7. N. Bessonov, P. Kurbatova, V. Volpert. Particle dynamics modelling of cell populations. Proc. Conf. JANO, Mohhamadia, 2008. Math. Model. Nat. Phenom., 5 (2010), 7, 42–47. [Google Scholar]
  8. N. Bessonov, F. Crauste, I. Demin, V. Volpert. Dynamics of erythroid progenitors and erythroleukemia. Math. Model. Nat. Phenom., 4 (2009), no. 3, 210–232. [CrossRef] [EDP Sciences] [Google Scholar]
  9. N. Bessonov, F. Crauste, S. Fischer, P. Kurbatova, V. Volpert. Application of hybrid models to blood cell production in the bone marrow. Math. Model. Nat. Phenom., 6 (2011), no. 7, 2–12. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  10. N. Bessonov, I. Demin, P. Kurbatova, L. Pujo-Menjouet, V. Volpert. Multi-agent systems and blood cell formation. In: Multi-Agent Systems - Modeling, Interactions, Simulations and Case Studies, F. Alkhateeb, E. Al Maghayreh, I. A. Doush, Editors, (2011), 395–424. [Google Scholar]
  11. N. Bessonov, N. Eymard, P. Kurbatova, V. Volpert. Mathematical modeling of erythropoiesis in vivo with multiple erythroblastic islands. Applied Mathematics Letters, 25 (2012), 1217–1221. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Bouilloux, G. Juban, N. Cohet, D. Buet, B. Guyot, W. Vainchenker, F. Louache, F. Morle. EKLF restricts megakaryocytic differentiation at the benefit of erythrocytic differentiation. Blood, 1 112 (3) (2008), 576-84. [Google Scholar]
  13. A.B. Cantor, S.H. Orkin. Transcriptional regulation of erythropoiesis: an affair involving multiple partners. Oncogene 21 (2002), 3368–3376. [CrossRef] [PubMed] [Google Scholar]
  14. J.A. Chasis, N. Mohandas. Erythroblastic islands: niches for erythropoiesis. Blood, 112 (2008). [Google Scholar]
  15. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis – I. Periodic chronic myelogenous leukemia. J. Theor. Biol., 237, (2005), 117–132. [CrossRef] [PubMed] [Google Scholar]
  16. C. Colijn, M.C. Mackey. A mathematical model of hematopoiesis – II. Cyclical neutropenia. J. Theor. Biol., 237 (2005), 133–146. [CrossRef] [PubMed] [Google Scholar]
  17. F. Crauste, I. Demin, O. Gandrillon, V. Volpert. Mathematical study of feedback control roles and relevance in stress erythropoiesis. J. Theor. Biology, 263 (2010), 303–316. [Google Scholar]
  18. F. Crauste, L. Pujo-Menjouet, S. Génieys, C. Molina, O. Gandrillon. Adding Self-Renewal in Committed Erythroid Progenitors Improves the Biological Relevance of a Mathematical Model of Erythropoiesis, J. Theor. Biology, 250 (2008), 322–338. [Google Scholar]
  19. S. Dazy, F. Damiola, N. Parisey, H. Beug, O. Gandrillon. The MEK-1/ERKs signaling pathway is differentially involved in the self-renewal of early and late avian erythroid progenitor cells. Oncogene, 22 (2003), 9205–9216. [CrossRef] [PubMed] [Google Scholar]
  20. I. Demin, F. Crauste, O. Gandrillon, V. Volpert. A multi-scale model of erythropoiesis. Journal of Biological Dynamics, 4 (2010), 59–70. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  21. C. Duff, K. Smith-Miles, L. Lopes, T. Tian. Mathematical modelling of stem cell differentiation: the PU.1-GATA-1 interaction. J. Math. Biol., 64 (2012), 449–468. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  22. J. Eller, I. Gyori, M. Zollei, F. Krizsa. Modelling Thrombopoiesis Regulation - I Model description and simulation results. Comput. Math. Appli, 14 (1987), 841–848. [CrossRef] [Google Scholar]
  23. N. Eymard, N. Bessonov, O. Gandrillon, M.J. Koury, V. Volpert, The role of spatial organisation of cells in erythropoiesis. Journal of Mathematical Biology (2014). [Google Scholar]
  24. S. Fischer, P. Kurbatova, N. Bessonov, O. Gandrillon, V. Volpert, F. Crauste. Modelling erythroblastic islands : using a hybrid model to assess the function of central macrophage. Journal of Theoretical Biology, 298 (2012), 92–106. [Google Scholar]
  25. P. Frontelo, D. Manwani, M. Galdass, H. Karsunky, F. Lohmann, P.G. Gallagher, J.J. Bieker. Novel role for EKLF in megakaryocyte lineage commitment. Blood, 110 (12) (2007), 3871–3880. [CrossRef] [PubMed] [Google Scholar]
  26. A. Golubev. Random discrete competing events vs. dynamic bistable switches in cell proliferation in differentiation. J. Theor. Biol., 267(3) (2010), 341–354. [CrossRef] [PubMed] [Google Scholar]
  27. A. Halanay. Periodic solutions in a mathematical model for the treatment of chronic myelogenous leukemia. Math. Model. Nat. Phenom., 7 (2012), no. 1, 235–244. [CrossRef] [EDP Sciences] [Google Scholar]
  28. A. Halanay, D. Candea, I. R. Radulescu. Existence and stability of limit cycles in a two-delays model of hematopoiesis including asymmetric division. Math. Model. Nat. Phenom., 9 (2014), no. 1, 58–78. [CrossRef] [EDP Sciences] [MathSciNet] [PubMed] [Google Scholar]
  29. M. J. Koury, M.C. Bondurant. Erythropoietin retards DNA breakdown and prevents programmed death in erythroid progenitor cells. Science, 248 (1990), 378–381. [CrossRef] [PubMed] [Google Scholar]
  30. P. Kurbatova, S. Bernard, N. Bessonov, F. Crauste, I. Demin, C. Dumontet, S. Fischer, V. Volpert. Hybrid Model of Erythropoiesis and Leukemia Treatment with Cytosine Arabinoside. 2011, SIAM J. Appl. Math, Volume 71, Issue 6, (2011) 2246–2268. [Google Scholar]
  31. P. Kurbatova, N. Eymard, V. Volpert. Hybrid model of erythropoiesis. Acta Biotheoretica, Volume 61, Issue 3 (2013), 305-315. [Google Scholar]
  32. F. Lohmann, J. J. Bieker. The EKLF gene is induced in response to Bmp4/Smad signaling and Gata factor activity during erythropoiesis Blood Cells, Molecules, and Diseases 38 (2007) 120 –191 [CrossRef] [Google Scholar]
  33. M.C. Mackey. Unified hypothesis of the origin of aplastic anaemia and periodic hematopoïesis. Blood 51, (1978), 941–956. [PubMed] [Google Scholar]
  34. M.C Mackey. Dynamic hematological disorders of stem cell origin. In: G. Vassileva-Popova and E. V. Jensen, Editors. Biophysical and Biochemical Information Transfer in Recognition, Plenum Press, New York, (1979), 373–409. [Google Scholar]
  35. M.C. Mackey, R. Rudnicki. A new criterion for the global stability of simultaneous cell replication and maturation processes. J. Math. Biol., 38 (1999), 195–219. [CrossRef] [Google Scholar]
  36. J.M. Mahaffy, J. Belair, M.C. Mackey. Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis. J. Theor. Biol., 190, (1998) 135–146. [CrossRef] [PubMed] [Google Scholar]
  37. R. De Maria, U. Testa, L. Luchetti, A. Zeuner, G. Stassi, E. Pelosi, R. Riccioni, N. Felli, P. Samoggia, C. Peschle. Apoptotic Role of Fas/Fas Ligand System in the Regulation of Erythropoiesis. Blood, 93 (1999), 796–803. [PubMed] [Google Scholar]
  38. J.M. Osborne, A. Walter, S.K. Kershaw, G.R. Mirams, A.G. Fletcher, P. Pathmanathan, D. Gavaghan, O.E. Jensen, P.K. Maini, H.M. Byrne. A hybrid approach to multi-scale modelling of cancer. Phil. Trans. R. Soc. A, 368 (2010), 5013–5028. [Google Scholar]
  39. H. Ozbay, C. Bonnet, H. Benjelloun, J. Clairambault. Stability analysis of cell dynamics in leukemia. Math. Model. Nat. Phenom., 7 (2012), no. 1, 203–234. [Google Scholar]
  40. A.A. Patel, E.T. Gawlinsky, S.K. Lemieux, R.A. Gatenby. A Cellular Automaton Model of Early Tumor Growth and Invasion: The Effects of Native Tissue Vascularity and Increased Anaerobic Tumor Metabolism. J. Theor. Biol., 213 (2001), 315–331. [CrossRef] [PubMed] [Google Scholar]
  41. I. Roeder. Quantitative stem cell biology: computational studies in the hematopoietic system. Curr. Opin. Hematol., 13 (2006), 222–228. [CrossRef] [PubMed] [Google Scholar]
  42. C. Rubiolo, D. Piazzolla, K. Meissl, H. Beug, J.C. Huber, A. Kolbus, M. Baccarini. A balance between Raf-1 and Fas expression sets the pace of erythroid differentiation. Blood, 108 (2006), 152–159. [CrossRef] [PubMed] [Google Scholar]
  43. M. Santillan, J.M. Mahaffy, J. Belair, M.C. Mackey. Regulation of platelet production: The normal response to perturbation and cyclical platelet disease. J. Theor. Biol., 206 (2000), 585–603. [Google Scholar]
  44. J. Starck, M. Weiss-Gayet, C. Gonnet, B. Guyot, J.M. Vicat, F. Morlé. Inducible Fli-1 gene deletion in adult mice modifies several myeloid lineage commitment decisions and accelerates proliferation arrest and terminal erythrocytic differentiation. Blood. 116(23) (2010), 4795–805. [CrossRef] [PubMed] [Google Scholar]
  45. T. Stiehl, A. Marciniak-Czochra. Mathematical modeling of leukemogenesis and cancer stem cell dynamics. Math. Model. Nat. Phenom., 7 (2012), no. 1, 166–202. [Google Scholar]
  46. V. Volpert. Elliptic partial differential equations. Volume 2. Reaction-diffusion equations. Birkhäuser, 2014. [Google Scholar]
  47. H.E. Wichmann, M.D. Gerhardts, H. SPechtmeyer, R. Gross. A mathematical model of thrombopoiesis in rats. Cell Tissue Kinet., 12 (1979), 551–567. [PubMed] [Google Scholar]
  48. H.E. Wichmann, M. Loeffler. Mathematical Modeling of Cell Proliferation. Boca Raton, FL, CRC, 1985. [Google Scholar]
  49. H. Wulff, H.E. Wichmann, M. Loeffler, K. Pantel. A mathematical model of erythropoiesis in mice and rats. Part 3. Suppressed erythropoiesis. Cell Tissue Kinet., 22 (1989), 51–61. [PubMed] [Google Scholar]
  50. H.E. Wichmann, M. Loeffler, K. Pantel, H. Wulff. A mathematical model of erythropoiesis in mice and rats. Part 2. Stimulated erythropoiesis. Cell Tissue Kinet., 22 (1989), 31–49. [PubMed] [Google Scholar]
  51. M. Yamamoto, S. Takahashi, K. Onodera, Y. Muraosa, J. D. Engel. Upstream and downstream of erythroid transcription factor GATA-1. Genes Cells. 2 (1997), 107–115. [CrossRef] [PubMed] [Google Scholar]

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