Application of Hybrid Models to Blood Cell Production in the Bone Marrow
N. Bessonov; F. Crauste; S. Fischer; P. Kurbatova; V. Volpert
Mathematical Modelling of Natural Phenomena (2011)
- Volume: 6, Issue: 7, page 2-12
- ISSN: 0973-5348
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top- A. R.A. Anderson.A hybrid multiscale model of solid tumour growth and invasion: Evolution and the microenvironment. in Single-Cell-Based Models in Biology and Medicine (Ed. A.R.A. Anderson, M.A.J. Chaplain and K.A. Rejniak), Series Mathematics and Biosciences in Interaction, Springer, Birkhauser Basel, 2007, 3–28.
- A.R.A. Anderson, M. Chaplain, K.A. Rejniak. Single cell based models in biology and medicine, Mathematics and Biosciences in Interaction. Springer, Birkhauser Basel, 2007.
- A. R. A. Anderson, K.A. Rejniak, P. Gerlee, V. Quaranta. Modelling of cancer growth, evolution and invasion: bridging scales and models. Math. Model. Nat. Phenom., 2(3) (2007), 1–29.
- J. Bélair, M.C. Mackey, J.M. Mahaffy. Age-structured and two delay models for erythropoiesis. Math. Biosci., 128 (1995), 317–346.
- N. Bessonov, L. Pujo-Menjouet, V. Volpert. Cell modelling of hematopoiesis. Math. Model. Nat. Phenom., 1 (2006), No. 2, 81–103.
- N. Bessonov, I. Demin, L. Pujo-Menjouet, V. Volpert. A multi-agent model describing self-renewal or differentiation effect of blood cell population. Mathematical and Computer Modelling, 49 (2009), 2116–2127.
- N. Bessonov, P. Kurbatova, V. Volpert. Particle dynamics modelling of cell populations. Prooceedings of the conference JANO, Mohamadia 2008, Math. Model. Nat. Phenom., 5 (2010), No. 7, 42–47.
- N. Bessonov, P. Kurbatova, V. Volpert. Dynamics of growing cell populations. CRM, preprint num. 931 for Mathematical Biology, February 2010.
- J.A. Chasis, N. Mohandas. Erythroblastic islands: niches for erythropoiesis. Blood, 112 (2008), pp. 470-478.
- F. Crauste, I. Demin, O. Gandrillon, V. Volpert. Mathematical study of feedback control roles and relevance in stress erythropoiesis. J. Theo. Biol., 263 (2010), 303–316.
- 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. Biol., 250 (2008), 322–338.
- I. Demin, F. Crauste, O. Gandrillon, V. Volpert. A multi-scale model of erythropoiesis, J. Biol. Dyn. 4 (2010), pp. 59–70.
- D. Drasdo.Center-based single-cell models: An approach to multi-cellular organization based on a conceptual analogy to colloidal particles. In: Single-Cell-Based Models in Biology and Medicine (Ed. A.R.A. Anderson, M.A.J. Chaplain and K.A. Rejniak), Series Mathematics and Biosciences in Interaction, Springer, Birkhauser Basel, 2007, 171-196.
- O. Gandrillon, U. Schmidt, H. Beug, J. Samarut. TGF-beta cooperates with TGF-alpha to induce the self-renewal of normal erythrocytic progenitors: evidence for an autocrine mechanism. EMBO J., 18 (1999), 2764–2781.
- M. Karttunen, I. Vattulainen, A.Lukkarinen. A novel methods in soft matter simulations, Springer, Berlin, 2004.
- M.J. Koury, M.C. Bondurant. Erythropoietin retards DNA breakdown and prevents programmed death in erythroid progenitor cells, Science, 248 (1990), 378–381.
- 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.