An embolic element comprises a filament composed of a shape memory material having an unexpanded coil configuration and an expanded random matrix configuration. The embolic element may be delivered to a blood vessel treatment site in its coiled configuration over a delivery wire through a guide catheter. Usually, the coiled embolic element will be disposed over a helical section of the delivery wire prior to release. In that way, proper positioning of the embolic element may be confirmed prior to release. The embolic element is then expanded to its enlarged configuration by heating or otherwise exposing to a temperature over the transition temperature of the shape memory material.