Woven structures and associated systems for weaving such structures are disclosed. Some disclosed innovations pertain to braided structures, such as braided wire structures, with axially asymmetric woven structures (or “directional meshes”) being examples. Other innovations disclosed herein pertain to methods of manufacturing woven structures, with automated methods of braiding directional meshes being examples. Some directional mesh embodiments can be configured and used as energizable electrodes for electrosurgical therapies, for example, bipolar vaporization therapies.