Methods and apparatus for treatment of patent foramen ovale (PFO) generally involve use of a catheter having at least one closure device at its distal end. In some embodiments, the catheter also includes one or more energy transmission members for delivering energy to the closure device(s) and to the tissue adjacent the PFO to induce closure of the PFO. Closure devices may comprise, for example, a bioresorbable matrix or a non-resorbable matrix. In some embodiments, the closure device contains particles dispersed within the closure device to increase conductance and/or to reduce resistance and/or impedance. An exemplary method involves advancing a catheter to position its distal end into the tunnel of the PFO and fixing the closure device within the tunnel of the patent foramen PFO.