Journal
JOURNAL OF THEORETICAL BIOLOGY
Volume 426, Issue -, Pages 152-161Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2017.05.031
Keywords
Heterogeneous breast cancer; Thermography; Asymptotic homogenization
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Funding
- INdAM
- DGAPA from UNAM, Mexico
- Ministerio de Ciencia in Spain [DPI2014-58885-R]
- Metodos Fisico-Matematicos para el estudio de nuevos materiales y la propagacion de ondas. Aplicaciones [7515]
- CNPq (INCT-MACC)
- Departamento de Matematicas y Mecanica IIMAS-UNAM
- CNPq [303240/2015-6]
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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. (C) 2017 Elsevier Ltd. All rights reserved.
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