Methods, systems, and devices for providing a denervating energy treatment to the tissue of the pulmonary vein utilizing a catheter-based structure having one or more energy delivery surfaces. In some instances energy delivery surfaces are arranged with a circumferential and axial offset relative to one another. A pattern of individual lesions loosely approximating a helix are placed at the pulmonary vein so as to provide a pattern which covers substantially the circumference of the pulmonary vein with an axial offset that distributes the lesions to avoid stenosis. Denervating energy is applied by modulation of the energy delivery surfaces using an energy source integrated with a controller and control algorithm. In some instances feedback is used in a control algorithm for energy modulation. Energy sources are radiofrequency, ultrasound, and cryogenic.
