Bobbi Kristina Brown Bobbi Kristina Brown

Bobbi Kristina Brown underwent a tracheotomy this week, as family members continue to hope for her recovery, Peoplereports.

The procedure is intended for patients who may need to have a ventilator long-term. It allows for another type of breathing tube to be inserted because leaving the original tube in long-term can become infected. A tracheotomy can eventually be removed if the patient no longer needs ventilator support, and the hole left from the procedure can heal with time.

Brown family lawyer: Bobbi Kristina will not be taken off life support

"She is still critical," a family source told the magazine. "We don't know what the outcome will be. No one is giving up on this kid."

Brown has been hospitalized since Jan. 31, when she was found unresponsive in a bathtub in her home.