Hyperthermia therapy of cancerous tumor sitting in breast via analytical fractional model

Abstract

The heat transfer in bi-layer spherical composite region representing a cancerous tumor embedded in a homogenous muscle tissue (Andra et al., 1999; Yu and Jiang, 2019) is modeled by means of fractional energy equations with additional interface boundary constrictions. This hyperthermia problem was explored before in literature with proper hyperthermia experimental parameters and numerical simulations were later on devised by substituting the integer order energy model with the fractional order one. In order to match the experimental data to the fractional model, the order of fractional derivative was determined after a laborious inverse solution scheme. Here, we obtain exact analytical solutions to the fractional hyperthermia problem which is shown to be controlled by four thermal parameters corresponding to each fractional order derivative. The spatio-temporal distribution of temperature within the tumor-tissue medium is then studied via the closed-form solutions. From the solutions, the anomalous heat diffusion process for early and late exposure times is detected. The best derivative of fractional order is eventually determined by matching the experimental temperature to analytically derived one here. Excellent agreement with the numerically fitted fractional value is observed. The present approach is eventually extended to a more realistic situation in which the perfusion of blood relative to tumor and skin zone is taken into account. The presented analytical expressions are further beneficial to elaborately alternate the optimized operational thermal parameters of desire during a hyperthermia treatment of different kind tumors.