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Cell Adhesion Mechanisms and Elasto-Viscoplastic Mechanics of Tumours

Summary: Cell Adhesion Mechanisms and Elasto-Viscoplastic
Mechanics of Tumours
D. Ambrosi, L. Preziosi
Dipartimento di Matematica, Politecnico di Torino
Corso Duca degli Abruzzi 24, I-10129, Torino, Italy,
davide.ambrosi@polito.it - luigi.preziosi@polito.it
March 27, 2008
Tumour cells usually live in a environment formed by other host cells, extra-cellular ma-
trix and extra-cellular liquid. Cells duplicate, reorganise and deform while binding each other
thanks to adhesion molecules exerting forces of measurable strength. In this paper it is illus-
trated a macroscopic mechanical model of solid tumour which takes such adhesion mechanisms
into account. The extracellular matrix is treated as an elastic compressible material, while,
in order to define the relationship between stress and strain for the cellular constituents, the
deformation gradient is decomposed in a multiplicative way distinguishing the contribution
due to growth, to plastic rearrangement and to elastic deformation. On the basis of experi-
mental results at a cellular level, it is proposed that at a macroscopic level there exists a yield
condition separating the elastic and viscoplastic regimes. Previously proposed models are ob-
tained as limit cases, e.g. fluid-like models are obtained in the limit of fast cell reorganisation
and negligible yield stress. A numerical test case shows that the model is able to account for


Source: Ambrosi, Davide - Dipartimento di Matematica, Politecnico di Torino


Collections: Mathematics