Multiple electrode support structures have asymmetric geometries, either axially, or radially, or both. The asymmetric support structures are assembled from spline elements that extend between a distal hub and a proximal base. In one embodiment, the spline elements are circumferentially spaced about the distal hub in a radially asymmetric fashion, creating a greater density of spline elements in one region of the structure than in another region. In the same or another embodiment, the spline elements are preformed in an axially asymmetric fashion along their lengths, creating a different geometry in their distal regions than in their proximal regions.
