Abba Umna, may his memory be blessed, would draw blood and would receive peace from the heavens every day, and for Abaye, every Sabbath eve, and for Rava, on the eve of Yom Kippur. Rava's opinion was weakened concerning Abaye, and Abaye concerning Abba Umna, and they said to him, "You cannot act like him." Abaye sent a pair of Rabbis to examine him, and he performed charity with them [(Taanit 21b). Mamre is Abba Umna, who was a physician.
Mamre is the gematria of Rafael (it should be noted that "Rafa" means "he healed," while "Rafael" is the angel sent by HaShem to heal Abraham) because he advised Abraham to circumcise himself and not to be concerned about danger; therefore, he was a physician (G'n).]
Seder_HaDorot,_Tanaim_and_Amoraim.29:1