http://www.ccel.org/ccel/mcgarvey/gospels.vii.iv.html
9 And he spake to his disciples, that a little boat should wait on him because of the crowd, lest they should throng him: 10 for he had healed many; insomuch that as many as plagues pressed upon him that they might touch him. [Literally, they “fell upon him;” such was their eagerness to be healed by touching him.]
Jesus the healer is so pressed upon that the masses “fall upon” him. That’s an image that I hadn’t considered.