Numerical dosimetry is a mandatory step in the designing process of any new EM device that operates in presence of living beings. One of its objectives is to ensure that a maximum Specific Absorption Rate (SAR) never exceeds the recommended values. In addition, including human models in simulations is necessary to evaluate the impact of human presence on the performance of the new EM device under design; hence, the device can be optimized accordingly. This article presents a numerical scheme for computing the SAR in multi-scale scenarios involving complex media (ex. human tissues). Cartesian sub-gridding is used to increase the resolution in certain regions in the computational domain. An experiment of SAR computation in a human head illuminated by a plane wave is presented. Sub-gridding is used to finely mesh the eye region as it contains sensitive tissues. Note that the sub-gridding interface crosses several heterogeneous tissues in the human head without affecting the accuracy of the simulations. Comparisons with uniform meshing are presented to show the CPU time and memory gain and the validity of the proposed approach