Doctor Phlox kept an osmotic eel on board during his assignment to Enterprise NX-01, and it could often be seen in the starship's sickbay, in a tank of water. During their first mission in April of 2151, it was used to cauterize Captain Archer's leg wound. (ENT: "Broken Bow")
In 2152, following the injury of several crewmembers, Phlox told one officer he would have to wait in line for the eel to cauterize his wound, noting that the creature was "getting quite a workout today". (ENT: "Minefield")
He offered to give it to E'Lis, a medical practitioner at a deuterium mining colony later that year, but she joked she wouldn't know what to feed it. Phlox then explained to E'Lis that the eel's feeding needs were relatively modest, as it only required a nutrient broth every three or four days. He further noted that while it was working, it required its nutrient broth even less, as it usually ingested a little blood while healing an injured artery. (ENT: "Marauders")
Later that year, Phlox told Hoshi Sato that his osmotic eel was ill and that he should remain on board Enterprise until the animal was feeling better. This, however, was an excuse for the fact that Phlox didn't want to visit Earth with Sato that evening. (ENT: "Home")
The fictional use of osmotic eels for medical purposes echoes the real-world application of medicinal leeches.
When it came time to design the osmotic eel, the task fell to Makeup Supervisor Michael Westmore, because the eel was supposed to be alive. He later noted, "They just said, 'You do the leech!'" Westmore produced numerous sketches, from which the producers chose the final, starfish-shaped design. The prop of the creature was then manufactured in the makeup lab, again due to it being supposedly alive. The model was created complete with hairs but required an extra small detail for its on-screen appearance. "We had it all goo'd up; there was stringy goo on the bottom, so when it was picked up those little stringy things would hang down," Westmore explained. Between its appearances in Star Trek: Enterprise, the model was placed into his desk drawer. (Star Trek: The Magazine Volume 2, Issue 7, p. 112)