Geodesic
Hybrid Modelling in Biology: a Classification Review
A. Stéphanou1 ; V. Volpert2, 3, 4
1 UJF-Grenoble 1, CNRS, Laboratory TIMC-IMAG/DyCTiM, UMR 5525, 38041 Grenoble, France
2 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
3 INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
4 Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia
Mathematical modelling of natural phenomena, Tome 11 (2016) no. 1, pp. 37-48.

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This paper presents a general review on hybrid modelling which is about to become ubiquitous in biological and medical modelling. Hybrid modelling is classically defined as the coupling of a continuous approach with a discrete one, in order to model a complex phenomenon that cannot be described in a standard homogeneous way mainly due to its inherent multiscale nature. In fact, hybrid modelling can be more than that since any types of coupled formalisms qualify as being hybrid. This review first presents the evolution and current context of this modelling approach. It then proposes a classification of the models through three different types that relate to the nature and level of coupling of the formalisms used.
DOI : 10.1051/mmnp/201611103

A. Stéphanou 1 ; V. Volpert 2, 3, 4

1 UJF-Grenoble 1, CNRS, Laboratory TIMC-IMAG/DyCTiM, UMR 5525, 38041 Grenoble, France
2 Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France
3 INRIA Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France
4 Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia 
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A. Stéphanou; V. Volpert. Hybrid Modelling in Biology: a Classification Review. Mathematical modelling of natural phenomena, Tome 11 (2016) no. 1, pp. 37-48. doi : 10.1051/mmnp/201611103. https://geodesic-test.mathdoc.fr/articles/10.1051/mmnp/201611103/

[1] K. Aihara, H. Suzuki Phil. Trans. R. Soc. A 2010 4893 4914

[2] P.J. Antsaklis Proceedings of the IEEE 2000 879 887

[3] S. Bernard Acta biotheor. 2013 291 303

[4] N. Bessonov, F. Crauste, S. Fischer, P. Kurbatova, V. Volpert Math. Mod. Nat. Phenom. 2011 2 12

[5] B.S. Brooks, S.L. Waters J.Math. Biol. 2008 893 896

[6] H. Byrne, D. Drasdo J. Math. Biol. 2009 657 687

[7] C. Cattani, A. Ciancio. Separable transition density in the hybrid model for tumor-immune system competition. Comp. Math. Meth. Med. (2012), 610124.

[8] A. Colombi, M. Scianna, L. Preziosi Math. Mod. Nat. Phenom. 2015 4

[9] P.V. Coveney, P.W. Fowler J. R. Soc. Interface 2005 267 280

[10] T.S. Deisboeck, Z. Wang, P. Macklin, V. Cristini Annu. Rev. Biomed. Eng. 2011 127 155

[11] S. Fischer, P. Kurbatova, N. Bessonov, O. Gandrillon, V. Volpert, F. Crauste J. theor. Biol. 2012 92 106

[12] J. Fisher, N. Piterman The executable pathway to biological networks Briefings in functional genomics 2010 79 92

[13] V. Galpin, J. Hillston, L. Bortolussi Electronic Notes in Theoretical Computer Science 2008 33 51

[14] N. Glade, A. Stéphanou. Le vivant discret et continu: modes de représentation en biologie théorique. Editions Matériologiques, Paris, 2013.

[15] P. Guerrero, T. Alarcón Math. Mod. Nat. Phenom. 2015

[16] T.A.M. Heck, M.M. Vaeyens, H. Van Oosterwyck Math. Mod. Nat. Phenom. 2015

[17] W.P.M.H. Heemels, B. De Schutter, J. Lunze, M. Lazar Phil. Trans. R. Soc. A 2010 4937 4960

[18] X. Li, L. Qian, M.L. Bittner, E.R. Dougherty Cancer Informatics 2012 41 60

[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.

[20] L. Mailleret, V. Lemesle Phil. Trans. R. Soc. A 2009 4779 4799

[21] A. Masoudi-Nejad, E. Wang Seminars in Cancer Biology 2015 1 3

[22] B. Mishra J. R. Soc. Interface 2009 575 597

[23] T. Nomura Frontiers in Physiology 2010

[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 Phil. Trans. R. Soc. A 2010 5013 5028

[25] G.G. Powathil, K.E. Gordon, L.A. Hill, M.A. Chaplain J. theor. Biol. 2012 1 9

[26] G.G. Powathil, M. Swat, M.A.J. Chaplain Seminars in Cancer Biology 2015 13 20

[27] L. Preziosi 2006 977 978

[28] Z. Qu, A. Garfinkel, J.N. Weiss, M. Nivala Prog. Biophys. Mol. Biol. 2011 21 31

[29] K.A. Rejniak, A.R.A. Anderson Wiley Interdiscipl. Rev. Syst. Biol. Med. 2011 115 125

[30] S. Sanga, H.B. Frieboes, X. Zheng, R. Gatenby, E.L. Bearer, V. Cristini Neuroimage 2007 S120 S134

[31] A. Singh, J.P. Hespanha Phil. Trans. R. Soc. A 2010 4995 5011

[32] R. Singhania, R.M. Sramkoski, J.W. Jacobberger, J.J. Tyson PLoS Comput. Biol. 2011

[33] A. Stéphanou, S. Le Floc’H, A. Chauvière Math. Mod. Nat. Phenom. 2015

[34] A. Stéphanou, V. Volpert Math. Mod. Nat. Phenom. 2015 1 3

[35] G. Tanaka, Y. Hirata, S.L. Goldenberg, N. Bruchovsky, K. Aihara Phil. Trans. R. Soc. A 2010 5029 5044

[36] R. Thom. Stabilité structurelle et morphogenèse. Interédition, Paris, 1977.

[37] A. Tosenberger, F. Ataullakhanov, N. Bessonov, M. Panteleev, A. Tokarev, V. Volpert J. theor. Biol. 2013 30 41

[38] A. Tosenberger, N. Bessonov, V. Volpert Math. Mod. Nat. Phenom. 2015 36

[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.

[40] Z. Wang, J.D. Butner, R. Kerketta, V. Cristini. Simulating cancer growth with multiscale agent-based modeling. Seminars in cancer biology (2015), 30.

[41] A.L. Woelke, M.S. Murgueitio, R. Preissner. Theoretical modeling techniques and their impact on tumor immunology. Clinical and Developmental Immunology (2010), 271794.

[42] L. Zhang, L.L. Chen, T.S. Deisboeck Math. Comput. Simul. 2009 2021 2035

[43] L. Zhang, Z. Wang, J.A. Sagotsky, T.S. Deisboeck Multiscale agent-based cancer modeling J. Math. Biol. 2009 545 559

[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.

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