Hemorrhaging was the loss of blood due to injury.
While performing a surgery on Bareil Antos brain in the infirmary aboard Deep Space 9 in 2371, Doctor Julian Bashir told the Bajoran nurse Jabara to put a pressor field on the damaged artery. But Jabara told Bashir that the arterial disruption is too severe and a pressor field couldn't stop the hemorrhaging. (DS9: "Life Support")