Asclepius's son Machaon did not accompany him to the Mysteries. In fact, Machaon is generally portrayed as fully human, a skilled surgeon who accompanied the Greek troops to Troy when they fought the Trojan War. He isn't really a mythical character in the sense of having anything truly magical about him.

Machaon's healing skills were much in demand on the battlefield, but he was also a skillful soldier. According to tradition he was killed in the tenth and final year of the war. His death is not mentioned in Homer's Iliad, which concludes before the war is over. Homer does mention, however, that at one point Machaon was wounded by the Trojan prince Paris and was unable to fight for a while as a result.