The DBS electrodes (model 3389, Medtronic) will be stereotactically implanted bilaterally in the PPN, according to the technique usually used for STN-DBS, and connected to the subcutaneously implanted stimulator (Kinetra, Medtronic). After the surgery, the study will comprise two phases: a 6-month phase dedicated to optimisation of the stimulation parameters (including systematic evaluation of defined parameters); followed by a phase of evaluation, that will compare, in a double-blind setting, 4 conditions (right unilateral, left unilateral, bilateral and off stimulation). Efficacy of PPN-DBS will be evaluated by clinical rating scales quantifying motor disturbance, cognitive function and quality of life, and by the means of computer-based measure of gait and balance (system Gaitrite and Vicon).