Numerical analysis of the breast thermal state under an influence of an intratissue malignant neoplasm

Abstract

Purpose The purpose of this study is to develop the mathematical model of the thermal nature of the breast having an intratissue malignant neoplasm. Design/methodology/approach The mathematical model is based on a modified Pennes bioheat equation and defines a five-layer structure with skin, adipose, glandular, muscle tissues and the tumor region. A focused hyperthermic source is represented as spatial heating described by an exponentially decaying Beer–Lambert–Bouguer law combined with a Gaussian distribution. The thermal conductivity of tissues and blood perfusion depend on temperature according to linear laws, reflecting the mechanisms of physiological thermoregulation. Various combinations of tumor position and size under the influence of an external source have been analyzed in terms of temperature field formation and accumulation of the Arrhenius integral, which characterizes damage within the tumor. Findings It has been shown that an increase in source intensity in all cases results in a rise in the high temperature and accelerates the accumulation of the Arrhenius integral, however, it simultaneously increases the risk of damage to surrounding healthy tissues. Variation of the spatial attenuation coefficient responsible for longitudinal localization of the source enhances heating and generally improves the alignment of the temperature maximum with the tumor region. An increase in the parameter of the Gaussian distribution, that defines the spatial extent of the influence, improves tumor coverage but significantly reduces selectivity due to the expansion of the damage zone into healthy tissues. It is established that the most effective damage can be achieved for a superficially located tumor. For each tumor position, regimes were identified that ensure the formation of a necrotic zone within the tumor without damaging healthy tissues. Originality/value Present study for the first time describes the mathematical model of the breast having an intratissue malignant neoplasm. Compared with one-dimensional approaches, the proposed two-dimensional model enables a more detailed analysis by accounting for transverse heat transfer, tumour size and the spatial heterogeneity of thermal damage, which cannot be adequately represented in one-dimensional formulations.