Cell adhesion mechanisms and stress relaxation in the mechanics of tumours
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Tumour cells usually live in an environment formed by other host cells, extra-cellular matrix and extra-cellular liquid. Cells duplicate, reorganise and deform while binding each other due to adhesion molecules exerting forces of measurable strength. In this paper, a macroscopic mechanical model of solid tumour is investigated 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 cell rearrangement and to elastic deformation. On the basis of experimental results at a cellular level, it is proposed that at a macroscopic level there exists a yield condition separating the elastic and dissipative regimes. Previously proposed models are obtained 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 several complex interactions: how tumour growth can be influenced by stress, how and where it can generate cell reorganisation to release the stress level, how it can lead to capsule formation and compression of the surrounding tissue.
KeywordsStress Relaxation Deformation Gradient Math Biol Multicellular Spheroid Solid Tumour Growth
- Canetta E, Duperray A, Leyrat A, Verdier C (2005) Measuring cell viscoelastic properties using a force-spectrometer: Influence of the protein–cytoplasm interactions. Biorheology 42: 298–303Google Scholar
- Gibson RF (1994) Principles of Composite Material Mechanics. McGraw-Hill, NY, USAGoogle Scholar
- Malvern LE (1969) Introduction of the Mechanics of a Continuous Medium. Prentice Hall Inc., Englewood CliffsGoogle Scholar
- Netti PA, Jain RK (2003) Interstitial transport in solid tumours. In: Preziosi L (eds) Cancer Modelling and Simulation. CRC Press, Chapman Hall, Boca RatonGoogle Scholar