Deep brain stimulation (DBS) is a well-established treatment for Parkinson's disease, essential tremor and dystonia. It has also been successfully applied to treat various other neurological and psychiatric conditions including depression and obsessive-compulsive disorder. Numerous computational models, mostly based on the Finite Element Method (FEM) approach have been suggested to investigate the biophysical mechanisms of electromagnetic wave-tissue interaction during DBS. These models, although emphasizing the importance of various electrical and geometrical parameters, mostly have used simplified geometries over a tightly restricted tissue volume in the case of monopolar stimulation. In the present work we show that topological arrangements and geometrical properties of the model have a significant effect on the distribution of voltages in the concerned tissues. The results support reconsidering the current approach for modeling monopolar DBS which uses a restricted cubic area extended a few centimeters around the active electrode to predict the volume of activated tissue. We propose a new technique called multi-resolution FEM modeling, which may improve the accuracy of the prediction of volume of activated tissue and yet be computationally tractable on personal computers.