RESUMEN
The present work focuses on the integration of analytical and numerical strategies to investigate the thermal distribution of cancerous breasts. Coupled stationary bioheat transfer equations are considered for the glandular and heterogeneous tumor regions, which are characterized by different thermophysical properties. The cross-section of the cancerous breast is identified by a homogeneous glandular tissue that surrounds the heterogeneous tumor tissue, which is assumed to be a two-phase periodic composite with non-overlapping circular inclusions and a square lattice distribution, wherein the constituents exhibit isotropic thermal conductivity behavior. Asymptotic periodic homogenization method is used to find the effective properties in the heterogeneous region. The tissue effective thermal conductivities are computed analytically and then used in the homogenized model, which is solved numerically. Results are compared with appropriate experimental data reported in the literature. In particular, the tissue scale temperature profile agrees with experimental observations. Moreover, as a novelty result we find that the tumor volume fraction in the heterogeneous zone influences the breast surface temperature.
Asunto(s)
Neoplasias de la Mama/patología , Modelos Biológicos , Temperatura , Femenino , Humanos , Carga TumoralRESUMEN
In this manuscript, the equilibrium problem for a flexoelectric one-dimensional composite material is studied. The two-scales asymptotic homogenization method is used to derive the homogenized formulation of this problem. The manuscript offers a step-by-step methodology to derive effective coefficients and to solve local problems. As an illustrative example, results reported in the literature for piezoelectric composites are obtained as a particular case of the formulation derived here. Finally, three flexoelectric/piezoelectric composites are studied to illustrate the influence of the flexoelectric property on the effective coefficients and the global behavior of the structure.