A system forms a cardiac conduction block at a location in a heart of a patient without substantially ablating cardiac tissue. The system includes a delivery system coupled to a source of material that is substantially non-ablative with respect to cardiac tissue. The delivery system delivers the material to the location, and the material at the location forms a conduction block without ablating the cardiac cells there. The material may include living cells, such as for example skeletal myocytes, and/or may include a non-living matter such as biopolymers such as a fibrin glue agent, or collagen agents. An expandable member with needle assembly is used to deliver the material so as to form a non-ablative circumferential conduction block at a location where a pulmonary vein extends from an atrium.