Free Access
Math. Model. Nat. Phenom.
Volume 11, Number 1, 2016
Reviews in mathematical modelling
Page(s) 37 - 48
Published online 03 December 2015
  1. K. Aihara, H. Suzuki. Theory of hybrid dynamical systems and its applications to biological and medical systems. Phil. Trans. R. Soc. A (2010), 368, 4893–4914. [CrossRef] [Google Scholar]
  2. P.J. Antsaklis. Special issue on hybrid system: theory and applications. A brief introduction to the theory and applications of hybrid systems. Proceedings of the IEEE (2000), 88(7), 879–887. [CrossRef] [Google Scholar]
  3. S. Bernard. How to build a multiscale model in biology. Acta biotheor. (2013), 61, 291–303. [CrossRef] [PubMed] [Google Scholar]
  4. N. Bessonov, F. Crauste, S. Fischer, P. Kurbatova, V. Volpert. Application of hybrid models to blood cell production in the bone marrow. Math. Mod. Nat. Phenom. (2011), 6(7), 2–12. [Google Scholar]
  5. B.S. Brooks, S.L. Waters. Mathematical challenges in integrative physiology. J.Math. Biol. (2008), 56, 893–896. [CrossRef] [MathSciNet] [Google Scholar]
  6. H. Byrne and D. Drasdo. Individual-based and continuum models of growing cell populations: a comparison. J. Math. Biol. (2009), 58, 657–687. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  7. C. Cattani, A. Ciancio. Separable transition density in the hybrid model for tumor-immune system competition. Comp. Math. Meth. Med. (2012), 610124. [Google Scholar]
  8. A. Colombi, M. Scianna, L. Preziosi. A measure-theoretic model for collective cell migration and aggregation. Math. Mod. Nat. Phenom. (2015), 10(1), 4. [CrossRef] [EDP Sciences] [Google Scholar]
  9. P.V. Coveney, P.W. Fowler. Modelling biological complexity: a physical scientist’s perspective. J. R. Soc. Interface (2005), 2, 267–280. [CrossRef] [PubMed] [Google Scholar]
  10. T.S. Deisboeck, Z. Wang, P. Macklin, V. Cristini. Multiscale cancer modeling. Annu. Rev. Biomed. Eng. (2011), 13, 127-155. [CrossRef] [PubMed] [Google Scholar]
  11. S. Fischer, P. Kurbatova, N. Bessonov, O. Gandrillon, V. Volpert, F. Crauste. Modeling erythroblastic islands: Using a hybrid model to assess the function of central macrophage. J. theor. Biol. (2012), 298, 92–106. [Google Scholar]
  12. J. Fisher, N. Piterman. The executable pathway to biological networks. Briefings in functional genomics (2010), 9(1), 79–92. [CrossRef] [PubMed] [Google Scholar]
  13. V. Galpin, J. Hillston, L. Bortolussi. HYPE applied to the modelling of hybrid biological systems. Electronic Notes in Theoretical Computer Science (2008), 218, 33–51. [CrossRef] [Google Scholar]
  14. N. Glade, A. Stéphanou. Le vivant discret et continu: modes de représentation en biologie théorique. Editions Matériologiques, Paris, 2013. [Google Scholar]
  15. P. Guerrero, T. Alarcón. Stochastic multiscale models of cell population dynamics: asymptotic and numerical methods. Math. Mod. Nat. Phenom. (2015), 10(1). [Google Scholar]
  16. T.A.M. Heck, M.M. Vaeyens, H. Van Oosterwyck. Computational models of sprouting angiogenesis and cell migration: towards multiscale mechanochemical models of angiogenesis. Math. Mod. Nat. Phenom. (2015), 10(1). [Google Scholar]
  17. W.P.M.H. Heemels, B. De Schutter, J. Lunze, M. Lazar. Stability analysis and controller synthesis for hybrid dynamical systems. Phil. Trans. R. Soc. A (2010), 368, 4937–4960. [CrossRef] [Google Scholar]
  18. X. Li, L. Qian, M.L. Bittner, E.R. Dougherty. A systems biology approach in therapeutic response study for different dosing regimens - a modeling study of drug effects on tumor growth using hybrid systems. Cancer Informatics (2012), 11, 41–60. [PubMed] [Google Scholar]
  19. D. Machado, R.S. Costa, M. Rocha, E.C. Ferreira, B. Tidor, I. Rocha. Modeling formalisms in systems biology. AMB Express (2011), 1, 45. [Google Scholar]
  20. L. Mailleret, V. Lemesle. A note on semi-discrete modelling in the life sciences. Phil. Trans. R. Soc. A (2009), 367, 4779–4799. [CrossRef] [Google Scholar]
  21. A. Masoudi-Nejad, E. Wang. Cancer modeling and network biology: accelerating toward personalized medicine. Seminars in Cancer Biology (2015), 30, 1-3. [CrossRef] [PubMed] [Google Scholar]
  22. B. Mishra. Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology. J. R. Soc. Interface (2009), 6, 575–597. [CrossRef] [PubMed] [Google Scholar]
  23. T. Nomura. Toward integration of biological and physiological functions at multiple levels. Frontiers in Physiology (2010), 1, 164. [CrossRef] [Google Scholar]
  24. 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 (2010), 368, 5013–5028. [Google Scholar]
  25. G.G. Powathil, K.E. Gordon, L.A. Hill, M.A. Chaplain. Modelling the effects of cell-cycle heterogeneity on the response of a solid tumour to chemotherapy: biological insights from a hybrid multiscale cellular automaton model. J. theor. Biol. (2012), 308, 1–9. [CrossRef] [PubMed] [Google Scholar]
  26. G.G. Powathil, M. Swat, M.A.J. Chaplain. Systems oncology: Towards patient-specific treatment regimes informed by multiscale modelling. Seminars in Cancer Biology (2015), 30, 13–20. [CrossRef] [PubMed] [Google Scholar]
  27. L. Preziosi. Hybrid and multiscale modelling. J. Math. Biol. (2006), 53, 977–978. [CrossRef] [PubMed] [Google Scholar]
  28. Z. Qu, A. Garfinkel, J.N. Weiss, M. Nivala. Multi-scale modeling in biology: How to bridge the gaps beween scales ? Prog. Biophys. Mol. Biol. (2011), 107, 21–31. [CrossRef] [PubMed] [Google Scholar]
  29. K.A. Rejniak, A.R.A. Anderson. Hybrid models if tumor growth. Wiley Interdiscipl. Rev. Syst. Biol. Med. (2011), 3(1), 115–125. [Google Scholar]
  30. S. Sanga, H.B. Frieboes, X. Zheng, R. Gatenby, E.L. Bearer, V. Cristini. Predictive oncology: multidisciplinary, multi-scale in-silico modeling linking phenotype, morphology and growth. Neuroimage (2007), 37(1), S120–S134. [CrossRef] [PubMed] [Google Scholar]
  31. A. Singh, J.P. Hespanha. Stochastic hybrid systems for studying biochemical processes. Phil. Trans. R. Soc. A (2010), 368, 4995–5011. [CrossRef] [Google Scholar]
  32. R. Singhania, R.M. Sramkoski, J.W. Jacobberger, J.J. Tyson. A hybrid model of mammalian cell cycle regulation. PLoS Comput. Biol. (2011), 7(2), e1001077. [CrossRef] [Google Scholar]
  33. A. Stéphanou, S. Le Floc’h, A. Chauvière. A hybrid model to test the importance of mechanical cues driving cell migration in angiogenesis. Math. Mod. Nat. Phenom. (2015), 10(1). [Google Scholar]
  34. A. Stéphanou, V. Volpert. Hybrid modelling in cell biology. Math. Mod. Nat. Phenom. (2015), 10(1), 1-3. [CrossRef] [EDP Sciences] [Google Scholar]
  35. G. Tanaka, Y. Hirata, S.L. Goldenberg, N. Bruchovsky, K. Aihara. Mathematical modelling of prostate cancer growth and its application to hormone therapy. Phil. Trans. R. Soc. A (2010), 368, 5029–5044. [CrossRef] [Google Scholar]
  36. R. Thom. Stabilité structurelle et morphogenèse. Interédition, Paris, 1977. [Google Scholar]
  37. A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert. Modelling of thrombus growth in flow with a DPD-PDE-method. J. theor. Biol. (2013), 337, 30–41. [Google Scholar]
  38. A. Tosenberger, N. Bessonov, V. Volpert. Influence of blood coagulation on clot formation in flow by a hybrid model. Math. Mod. Nat. Phenom. (2015), 10(1), 36. [Google Scholar]
  39. D. Vries, P.J.T. Verheijen, A.J. den Dekker. Hybrid system modeling and identification of cell biology systems: perpective and challenges. Symposium on system identification (2009), 227–232. [Google Scholar]
  40. Z. Wang, J.D. Butner, R. Kerketta, V. Cristini. Simulating cancer growth with multiscale agent-based modeling. Seminars in cancer biology (2015), 30. [Google Scholar]
  41. A.L. Woelke, M.S. Murgueitio, R. Preissner. Theoretical modeling techniques and their impact on tumor immunology. Clinical and Developmental Immunology (2010), 271794. [Google Scholar]
  42. L. Zhang, L.L. Chen, T.S. Deisboeck. Multi-scale, multi-resolution brain cancer modeling. Math. Comput. Simul. (2009), 79(7), 2021–2035. [CrossRef] [PubMed] [Google Scholar]
  43. L. Zhang, Z. Wang, J.A. Sagotsky, T.S. Deisboeck. Multiscale agent-based cancer modeling. J. Math. Biol. (2009), 58, 545–559. [Google Scholar]
  44. E.C.Zeeman. Levels of structure in catastrophe theory illustrated by applications in the social and biological sciences, Proceedings of the International Congress of Mathematicians (Vancouver, 1974) 2:533-546, Canad. Math. Congress, Montreal, 1975. [Google Scholar]

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