SHOCK WAVES IN BIOLOGICAL TISSUES UNDER TELEGRAPH EQUATION HEAT CONDUCTION

Electrosurgery aimed at the removal of tumors results in highly transient heat conduction. Simulations of temperature fields, under the assumption that heat in soft tissue organs is governed by a telegraph (damped hyperbolic) equation, are conducted in a two-dimensional setting with finite differencing in space and time. Six trajectories of a heat source motion are simulated: along a two-phase interface, along the latter with an offset, normal to a two-phase interface, on a curved (sine function) path in a single phase, along a circular path in a single phase, and along the latter around inclusion of one type in a matrix of another type. With the surgeon’s hand motion velocity roughly the order of magnitude greater than the velocity of the heat propagation in the tissue, the heat source motion is supersonic, giving rise to the multiscale phenomena—evolving shock waves, Mach wedges, and high-temperature concentrations.