A catheter apparatus, comprising: an elongated shaft having a proximal portion and a distal portion , wherein the distal portion of the shaft is configured for intravascular delivery to a renal artery (RA) of a human patient; a pre-shaped section of the distal portion of the elongated shaft , wherein the pre-shaped section comprises a self-expanding helical structure, wherein the elongated shaft and the pre-shaped section comprise a central lumen configured to receive a control member; and a plurality of energy delivery elements carried by the pre-shaped section , wherein the pre-shaped section is transformable between- a low-profile configuration wherein the control member is positioned in the central lumen, and an expanded configuration wherein the control member is at least partially retracted from the pre-shaped section and the pre-shaped section is helically shaped to position the energy delivery elements in stable contact with a wall of the renal artery (RA), wherein the helical structure includes a solid structural element selected from the group consisting of a coiled cable or a braided cable, the catheter apparatus further comprising a guide wire configured to deliver the pre-shaped section to the renal artery (RA) of the patient, wherein the guide wire comprises the control member, and wherein, in the expanded configuration, the guide wire is at least partially withdrawn or removed from the central lumen of the pre-shaped section , wherein the guide wire has a variable stiffness or flexibility along its length so as to provide increased flexibility in the proximal to distal direction. an elongated shaft having a proximal portion and a distal portion , wherein the distal portion of the shaft is configured for intravascular delivery to a renal artery (RA) of a human patient; a pre-shaped section of the distal portion of the elongated shaft , wherein the pre-shaped section comprises a self-expanding helical structure, wherein the elongated shaft and the pre-shaped section comprise a central lumen configured to receive a control member; and a plurality of energy delivery elements carried by the pre-shaped section , wherein the pre-shaped section is transformable between- a low-profile configuration wherein the control member is positioned in the central lumen, and an expanded configuration wherein the control member is at least partially retracted from the pre-shaped section and the pre-shaped section is helically shaped to position the energy delivery elements in stable contact with a wall of the renal artery (RA), wherein the helical structure includes a solid structural element selected from the group consisting of a coiled cable or a braided cable, the catheter apparatus further comprising a guide wire configured to deliver the pre-shaped section to the renal artery (RA) of the patient, wherein the guide wire comprises the control member, and wherein, in the expanded configuration, the guide wire is at least partially withdrawn or removed from the central lumen of the pre-shaped section , wherein the guide wire has a variable stiffness or flexibility along its length so as to provide increased flexibility in the proximal to distal direction. <EOS>