Halliday & Matthiessen (2014: 341, 343):
Every process has associated with it one participant that is the key figure in that process; this is the one through which the process is actualised, and without which there would be no process at all. Let us call this element the Medium, since it is the entity through the medium of which the process comes into existence. … in a material process the Medium is equivalent to the Actor in an intransitive clause and Goal in a transitive clause. …
Thus the Medium is the nodal participant throughout the system. It is not the doer, nor the causer, but the one that is critically involved, in some way or other according to the particular nature of the process.