Dr. Grogan, or sometimes called "Doc Grog" for his love of alchohol, was a doctor on the island of Tortuga in the 1740s.
Grogan was once a surgeon in the British Royal Navy. For he was so full of grog and not doing his Naval justise, he accidentally severed the leg of a Naval Officer. He was either sentenced to hang from the yardarms or take chances with the sharks. Grogan chose the second. On the verge of drowning, he was rescued by the Black Pearl. Grogan since had a dept to Jack Sparrow, but not offering Sparrow's offer to join his crew, for Grogan got sea sick on long voyages.
Jack Sparrow took Grogan to Tortuga from his ship. Grogan chose the employment of the island's doctor. From there, Grogan took on an apprentice, a self-taught sergeon named Le Cerdo. Cerdo doesn't help at all with Grogan's rent and bill. Grogan found out a way to get Jack Sparrow a doctor. Grogan brewed a potion that knocked Le Cerdo out and haved him shanghaied on the Black Pearl. Grogan still works as the Tortuga doctor. Grogan's apothecary is across from the notable Tortugan tavern, the Faithful Bride.