We present a high performance computing methodology for the simulation of electromagnetic wave propagation in biological tissues and its application to the numerical evaluation of radio frequency absorption in head tissues as they are exposed to radiation from a cellular phone. For this purpose, the system of time-domain Maxwell equations is discretized in space by a discontinuous Galerkin method which is formulated on a tetrahedral mesh and which relies on a high order interpolation of the electromagnetic field components within a mesh element. The semi-discretized equations are then time integrated by a second order leap-frog scheme. The resulting numerical methodology is adapted to modern parallel computing systems with multiple GPU acceleration cards by adopting a hybrid strategy that combines a coarse grain SPMD programming model for inter-GPU parallelization and a fine grain SIMD programming model for intra-GPU parallelization. The performance improvement thanks to multiple-GPU acceleration is demonstrated through large-scale simulations that are performed on a cluster of GPUs using realistic heterogeneous models of head tissues built from medical images.