Résumé
This work has been motivated by the study of solid tumor growth and morespecifically by the examination of the most frequent pediatric primary bonetumors (osteosarcoma), which are characterised in their early stage by the for-mation of non-mineralised bone tissue, called osteoid [1]. As the tumor evolvesin time, mineralisation of this growing tissue can take place. The purpose ofthis work thus is to investigate the advection-diffusion of soluble factor suchas calcium and phosphate [2] in the context of tumor mineralisation, how thismineralisation of bone tissue may become a barrier to treatment in the contextof drug transport [3] but also how proteins and growth factors can play a role intumor growth [4]. For this purpose, the method of asymptotic homogenizationis used so as to derive the macroscopic models for describing solute transportin poroelastic media, with an advective-diffusive regime in the fluid-saturatedpores and diffusion in the solid phase, by starting from the description on thepore scale. The fluid/solid equations lead to Biot's model of poroelasticity.Then, homogenization of the transport equations leads to three macroscopicmodels that relate to three orders of magnitude of the diffusivity ratio: a modelin which the solid diffusion only in uences the accumulation term; ii) a modelwith memory effects; iii) a model without solid diffusion. Initially expressed bymeans of orders of magnitude of the diffusivity ratio, the domains of validityof each of these three models can be expressed in terms of relative orders ofmagnitude of two characteristic times. The three models contain a solute-solidinteraction term, due to the advection regime and they are coupled to the poroe-laticity model via the advection term.