A catheter and catheter system can use energy tailored for remodeling and/or removal of target material along a body lumen, often of atherosclerotic material of a blood vessel of a patient. An elongate flexible catheter body with a radially expandable structure may have a plurality of electrodes or other electrosurgical energy delivery surfaces to radially engage atherosclerotic material when the structure expands. An atherosclerotic material detector system may measure and/or characterize the atherosclerotic material and its location, optionally using impedance monitoring.