Bio-heat regimes in fractal-based models of tumors

Anomalous heat diffusion is investigated for biological tissues displaying a fractal structure and long-term thermal memory, which is modeled via a fractional derivative. For increasing values of the fractional derivation order, the tissue temperature displays three kinds of bio-heat regimes: damped (or sub-diffusive), critical damping and under-damped oscillations. The temperature profiles depend on the fractal dimension of the tissue but notably also on a parameter related to its topology: the spectral dimension. The parametric analysis reveals that these two parameters have antagonistic effects on the pseudo period of the temperature oscillations and their amplitudes. We discuss how our results might impact some treatment protocols.