Hybrid analytical models to estimate non-equilibrium temperatures in live-tissues based on appropriate initial thermal-field and non-invasive therapeutic heating

Abstract

This study develops an exact analysis of various bio-heat models, namely, classical, single-phase-lag, and dual-phase-lag models, for heat transfer in a single layer of living tissue. A new hybrid scheme coupled with the separation of variables and finite Fourier transform method has been employed for the closed-form solution. The skin surface of living tissues is heated by constant or unique oscillating heat sources to facilitate non-invasive therapeutic treatment. The existing literature survey highlights that most of the research works were associated with a constant initial temperature of tissues, whereas the present work reveals an implementation of a variable initial temperature to justify the prediction of thermal flow in living tissues before the therapy process to be initiated. Two unique oscillating (time-dependent) heat sources at the skin surface are implemented for the comparative aspect to find out an effective therapeutic condition. The results conclude that a sinusoidal heat source is a better option for the longer duration of the therapeutic heating to reach the thermal equilibrium, while a cosine heat source is more applicable for the short time span of treatment with a range of time-lags in the dual-phase-lag bioheat model. Finally, for the accuracy aspect of the model, the present work was validated with the published work by considering a design case. For the accurately analytical establishment, the present work can predict an actual thermal response which may help to decide a proper treatment protocol for thermal therapies.