Estimation of heat transfer and temperature rise in partial-body regions during MR procedures: an analytical approach with respect to safety considerations

Abstract In order to assess thermal response to RF exposure during MR procedures at the tissue level, simple analytical solutions to the non-stationary Pennes’ bio-heat equation were obtained using the Green’s function approach. Two thermal models appropriate for partial-body exposure were analyzed: In the first model, the temperature field at the periphery of an idealized volume RF resonator was modeled. The analytical solution reveals that tissue response to RF heating is characterized by an equilibration time and length. Both parameters are inversely related to tissue perfusion and vary for the soft-tissues considered between 0.27–25 min and 1.5–12 mm, respectively. None of the tissues investigated increase in temperature more than 0.5°C for each W/kg of power dissipated. Secondly, a homogeneous tissue solution was derived that predicts the temperature-time course to an MR examination with time-varying specific absorption rates (SAR). Since SAR limits indicated in current MR safety standards relate to running SAR averages computed over an appropriate period of time, an expression was formulated that gives an upper limit for the temperature rise averaged over the same period of time, as a function of both the upper limit of running SAR averages and the duration of the MR examination. The analysis revealed that the partial-body SAR limits indicated in the IEC standard may not guarantee under all circumstances compliance with the basic restrictions concerning temperature rise.