Story highlights Sarah Murnaghan underwent two lung transplants, her family reveals

Her lungs failed after the first operation; she was put on a bypass machine

She underwent a second transplant 3 days

Family: "We're not out of the woods, but Sarah's health is trending in the right direction"

Sarah Murnaghan, the 10-year-old Pennsylvania girl whose struggle for a life-saving lung transplant became a national issue, actually had to undergo two transplants days apart, her family revealed Friday.

In some of their first comments since the girl went into an operating room on June 12, the family released a statement detailing the necessity of the second transplant -- and explaining that the second set of lungs "were high-risk because they were infected with pneumonia.

"They were Sarah's best and only hope," the statement added, as the girl remained on a ventilator Friday and unable to breathe independently yet.

The original transplant on June 12 at Chilldren's Hospital of Philadelphia reportedly went smoothly but that evening "... an emergency code blue was announced. Sarah's vital signs had begun descending rapidly as her new lungs started to fail," the family's statement said.

The girl underwent surgery immediately and was transitioned to a bypass machine that took over the function of her heart and lungs, the statement continued.

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She remained on the bypass machine -- "... her doctors prepared us for the probability that Sarah would die, either before a second surgery could take place or on the operating table," the family said Friday -- until June 15, when new lungs became available and a second transplant took place.

Although the donated lungs were infected with pneumonia, "Each day since (the second transplant), her lungs have improved on x-ray and have continued to work better and better," the statement continued.

Her family expressed cautious optimism as they wait for the new lungs to work independently.

"This week our family fully expected to celebrate the event we've been waiting 19 months for -- our daughter Sarah's first independent breaths with her new donor lungs," the family said.

Her last two chest tubes were removed Friday as doctors prepare to remove her intubation tube.

"We're not out of the woods, but Sarah's health is trending in the right direction," her family said.

"The important thing to us is that sweet little girl is back with us and is very much alive."

Murnaghan, 10, suffers from cystic fibrosis and has been in and out of hospitals her entire life.

Her family fought to allow children to compete with adults waiting for lungs based on sickness in a case that has sparked a public debate. She received her first new lungs after a six-hour surgery that included resizing lungs from an adult.