Surgeons were “cautiously optimistic” yesterday about the recovery chances of US congresswoman Gabrielle Giffords, who was shot in the head at an Arizona political event by a would-be assassin.

Part of her skull had been removed to allow her brain to relax, but Ms Giffords, 40, had shown she was “able to communicate” by following simple commands, doctors at the University of Arizona Medical Centre said.

Chief of neurosurgery Michael Lemole, who operated on Ms Giffords, said that although the commands she followed are seen as simple, they actually show “a very high level of functioning in the brain.”

Although Ms Giffords remained in a critical condition, Mr Lemole said recovery hopes were high because the bullet did not cross from one side of her brain to the other, instead passing the length of the left side.

“When we talk about gunshot wounds to the head, the things that are most concerning to us are if the bullet crosses from one hemisphere to the other — one side to the other,” he said.

“I’m happy to say those were not the case in this instance. And because of that, Congresswoman Giffords is able to communicate with us this morning through following simple commands. We’re very encouraged by that.”

Doctors were clear, however, that Ms Giffords’s condition was still critical.

“Brain swelling at any time can take a turn for the worse. But I am cautiously optimistic,” said Mr Lemole.

Peter Rhee, the director of the medical centre, said the fact the bullet broke through Mr Giffords’s skull, had “done our work for us” to remove bone and take the pressure off her brain from swelling.

“This wasn’t a grazing wound to the brain. This wound travelled the length of the brain on the left side,” he explained.

“We typically will protect the brain with an artificial layer and close the scalp over it. We put it back when the brain is relaxed sufficiently. It may take several months but every case is individual.”

Ms Giffords was being kept induced in a medical coma so that “she is not suffering in bed from being operated on and being on a ventilator,” said Mr Rhee.

But the coma will be eased to determine her level of brain function.

“It puts you to sleep like anaesthetic does and you can turn it off and within minutes we can examine how it is,” he said.

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