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Video abstract for the article 'A multiphase model for three-dimensional tumor growth' by G Sciumè, S Shelton, W G Gray, C T Miller, F Hussain, M Ferrari, P Decuzzi and B A Schrefler (G Sciumè et al 2013 New J. Phys. 15 015005). Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/15/1/015005/article. Part of Focus on the Physics of Cancer GENERAL SCIENTIFIC SUMMARY Introduction and background. Multiphase porous media mechanics is here applied to model tumor growth. The governing equations obtained via the thermodynamically constrained averaging theory (TCAT) are solved numerically by means of the finite element method. The multiphase system consists of four phases: the extracellular matrix (ECM), the tumor cells (TC), which may include a necrotic portion depending on the environmental conditions and pressure; the healthy cells (HC); and the interstitial fluid (IF) with the dissolved chemical species (see the figure). Main results. The computational model is applied to solve three cases of biological relevance. In the first case, the growth of a multicellular tumor spheroid (MTS) in vitro is modeled, providing good agreement between the numerical and the experimental results. As observed experimentally, when the spheroid reaches a certain size a necrotic area appears in the center surrounded by a shell of viable tumor cells whose thickness is regulated by the diffusion of oxygen and nutrients. In the second case, the MTS is confined within the healthy tissue which induces less favorable nutrient diffusion reducing substantially the tumor growth rate. In the third case, tumor cells growing along microvessels (the so called 'tumor cord') are modeled in a 3D geometry and it is shown that the malignant cells migrate within adjacent vessels in search of new sources for nutrients and oxygen. Wider implications. The modular architecture of the model allows us to incorporate additional components, such as multiple nutrients, cell secreted biochemical species, as well as drug molecules, and new phases, such as the vascular compartments, with the objective of predicting accurately the outcome of different, patient-specific therapeutic interventions.