Blackwell was placed in an induced coma after losing his British middleweight title in the bout.
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The bout was stopped on medical advice in the 10th round, in which Blackwell took a pummeling from Eubank. Blackwell had a closed and badly swollen area around his left eye.
Doctors on Sunday said they saw no increase in the swelling, a positive sign for Blackwell, according to the BBC.
Both boxers are from England. Blackwell is from Trowbridge; Eubank is from Hove.
Blackwell amazed onlookers by taking a bloody beating. But English news site The Guardian put it best with this headline: Boxing is a sweet science but Nick Blackwell was too brave for his own good.
“It is our understanding that Nick has a bleed on the brain and is under observation by hospital staff,” British Boxing Board of Control general secretary Robert Smith told the BBC. “We will just have to wait and see what the hospital says.”
Eubank admitted after the fight: “I hit him with some big shots — maybe the referee should have stopped the fight earlier.” He also offered his support to Blackwell via Twitter.
Video from the bout showed Eubank’s father stepping into the ring and advising his son to stop hammering Blackwell’s face. The elder Eubank said his advice might have prevented Blackwell’s death in the ring.
British heavyweight champion Tyson Fury was among those offering wishes for Blackwell’s recovery.
In an update, Smith told the BBC that Blackwell “is resting and being looked after by the experts.”
“It’s a very normal procedure. They put you in a coma to get the swelling to go down,” Smith said. “There’s no timescale. Now it’s just a matter of waiting and seeing.”