It's been half a month since Bobbi Kristina Brown was found unconscious in her own bathtub. Just this week, Bobbi, who remains in critical condition, underwent a routine tracheotomy. While the procedure was successful, a source close to the family told People that the surgery was "normal" and that her situation had not otherwise changed.

Doctors frequently perform tracheotomies on patients to limit the risk of infection. According to the source, the tracheotomy is just "a different place for the tube to go," adding, "everything else remains the same. It's a waiting game. The family is hoping and waiting."

While tracheotomies are common surgical procedures, side effects can be severe. A separate family source also told People, "There's a medical reason behind [the tracheotomy], but it's making things clear to everyone how serious this is. Even if she wakes up, there's a possibility that this could do some damage to her vocal chords, I hear."

"This is happening because there are no other options," the source explained. "If there was another way, Bobby [Brown, Bobbi's father] would do it."

Despite the procedure, Bobbi's situation has remained otherwise unchanged for the past week. Bobbi's father, Bobby Brown, and her grandmother, Cissy Houston, continue to sit by the young woman's side. Earlier in the week, a source revealed to E! News that steps were being taken to pull Bobbi out of a medically induced coma.

Medical reports have been grim, but the family continues to be hopeful. We're hoping, too.