I noted to Colkoch previously that Jesus is not the model for distribution or reception of Holy Communion; that belongs to the Rite.  
The Melkites, a Byzantine Rite group found primarily in Syria, use leavened bread and wine to be consecrated.  A relatively large piece of Consecrated Bread is placed into the Chalice and the resulting mixture is placed on the communicant's tongue using a small spoon.  The Maronite Rite and some other Eastern Rites use intinction as, in some relatively few cases, does the Latin Rite.  The image of the Last Supper, then, is not the mode of distribution or reception - else all would also recline around tables and speak Aramaic - but of Jesus being fully present in the Sacred Species and given to us to consume.