Deep brain stimulation (DBS) is an increasingly used clinical treatment for various neurological disorders, particularly movement disorders such as Parkinson's disease. However, the mechanism by which these high frequency electrical pulses act on neuronal activity is unclear. Once the stimulating electrode is placed in situ, an electrode–brain interface (EBI) is created. To compensate for the lack of studies on the effects of this generic depth EBI on therapeutic DBS, we constructed a three-dimensional computational model of the EBI using the finite element method, in which the structural details and biophysical properties of the EBI are preserved. Our investigations focus on the peri-electrode space as a significant element of the EBI, and its physiological and pathological modulation, in particular by brain pulsation and giant cell formation. We also consider the difference between the current fields induced by different configurations of the quadripolar electrode contacts. These results quantitatively demonstrated that the peri-electrode space is a significant element of the EBI and its biophysical properties are modulated by brain pulsation and giant cell formation, as well as by the choice of electrode contact configuration. This study leads to a fuller understanding of the EBI and its effects on the crossing electric currents, and will ultimately lead to optimisation of the therapeutic effects of DBS.