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Upcoming events in Mathematics

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Today 15:00
Fulton G20
Mathematics Seminar
Prof. Alfio Grillo (Politecnico di Torino)
An overview on some recent models of tumour growth: consolidated ideas and new perspectives
abstract

Abstract

The focus of my talk is an overview on some recent models of tumour growth in avascular stage. After mentioning a few biological aspects [1, 2], such as the mass exchange among the constituents of a tumour and the transport of chemical species, I will concentrate on some purely mechanical and geometrical features of tumour growth. More specifically, taking inspiration from [3, 4], I will adopt Differential Geometry to show how the Riemannian curvature arising from the inelastic distortions accompanying growth can be joined together with the concept of material inhomogeneities [5]. Then, I will describe a way of contextualising this geometric framework within a “minimal” chemo-mechanical model of tumour growth [6, 7], in which the evolving structure of a tumour concurs to modulate the diffusion and mass exchange processes necessary for growth to occur [7]. In particular, I will discuss the case in which one or more chemical species undergo anomalous diffusion, and I will compare this situation with the one of standard Fickian diffusion. This last part of the talk summarises some preliminary results of a work in progress done in collaboration with Ariel Ramírez-Torres and Salvatore Di Stefano.

References
[1] Chaplain, M.A.J., Benson, D.L., Maini, P.K., “Nonlinear Diffusion of a Growth Inhibitory Factor in Multicell Spheroids”, Mathematical Biosciences, 121 (1994) 1–13.
[2] Byrne, H., Preziosi, L: “Modelling solid tumour growth using the theory of mixtures”, Math. Med. Biol., 20(4) (2003) 341–366 http://dx.doi.org/10.1093/imammb/20.4.341.
[3] Yavari, A., Goriely, A.: “Weyl geometry and the nonlinear mechanics of distributed point defects”, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 468 (2012) 3902–3922 DOI:10.1098/rspa.2012.0342
[4] Goriely, A.: The mathematics and mechanics of biological growth, Springer, New York, 2016.
[5] Epstein, M.: “Self-driven continuous dislocations and growth”, in: M.G. Steinmann P. (Ed.), Mechanics of Material Forces, in: Advances in Mechanics and Mathematics, vol. 11, Springer, Boston, MA, 2005, pp. 129–139.
[6] Mascheroni, P., Carfagna, M., Grillo, A., Boso, D.P., Schrefler, B.A.: “An avascular tumor growth model based on porous media mechanics and evolving natural states”, 23(4) (2018) 686–712 DOI: 10.1177/1081286517711217
[7] Di Stefano, S., Ramírez-Torres, A., Penta, R., Grillo, A.: “Self-influenced growth through evolving material inhomogeneities”, Int. J. Non-Linear Mechanics, 106 (2018) 174–187 https://doi.org/10.1016/j.ijnonlinmec.2018.08.003.

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Mon 24/02/20 14:00
Fulton G20
Mathematics Seminar
Dr. Roman Schubert (University of Bristol)
(Themes: Open quantum systems)
Mon 16/03/20 14:00
Fulton G20
Mathematics Seminar
Dr. Mike Todd (University of St Andrews)
(Themes: Ergodic theory, Dynamical Systems)
Mon 16/03/20 14:00
Fulton G20
Mathematics Seminar
Dr. Costanza Benassi (Northumbria University)
(Themes: Statistical mechanics)