Macroscopic thermal profile of heterogeneous cancerous breasts. A three-dimensional multiscale analysis. (November 2019) - Marchena-Menéndez, J.; Ramírez-Torres, A.; Penta, R.; Rodríguez-Ramos, R.; Merodio, J.
Abstract: The present work focuses on a multiscale analysis of temperature maps for cancerous breasts. A three-dimensional model is proposed based on a system of bioheat transfer equations for the healthy and cancerous breast regions, which are characterized by different microstructure and thermophysical properties. The geometrical model of the cancerous breast is identified by the presence of muscle, glandular and fat tissues, as well as the heterogeneous tumorous tissue. The latter is assumed to be a two-phase periodic composite with spherical inclusions. A cubic lattice distribution is chosen, wherein the constituents exhibit isotropic thermal conductivity behavior. The tissue effective thermal conductivities are computed by means of the asymptotic homogenization approach, i.e. by solving relevant periodic problems on the cell which is representative of the malignant tissue microstructure. These are then exploited to solve the macroscale homogenized model by finite elements. The obtained results, in terms of temperature maps, are successfully compared with relevant experiments and could pave the way towards the development of a robust multiscale mathematical framework featuring microstructural information which can be useful in cancer diagnosis. This approach could provide qualitative and quantitative hints that can be used to improve tumor detection based on temperature maps of the breast tissue.