A catheter includes a flexible shaft having a length sufficient to access a patients renal artery. A treatment element at the distal end of the shaft is dimensioned for deployment within the renal artery. The treatment element comprises a radially expandable structure configured to maintain positioning within the renal artery. A multiplicity of electrodes are spaced apart on the treatment element and configured for switchable activation and deactivation in a predetermined sequence to generate overlapping zones of heating directed at perivascular nerves of the renal artery. The overlapping heating zones comprise a distal zone associated with relatively high current densities at a distance from the treatment element sufficient to ablate the perivascular renal nerves and a proximal zone associated with current densities lower than those of the distal zone and insufficient to cause thermal injury to tissue of the renal artery adjacent the treatment element.
