The sixteen year old girl was Jack's first solo procedure patient.
St. Sebastian's Hospital
During her spinal procedure, Jack accidentally ripped her dural sac. After he counted to five, under orders from his father, Jack got rid of his fear, and he sewed her up save her life. Later on, Christian most likely did some tests on her to see how she responded, and he came to the conclusion that she wasn't paralysed. ("The Incident, Part 2")
On the day of the crash, as Kate was sewing Jack's wound up, he told her the story about him cutting her dural sack. ("Pilot, Part 1")
Months later, during Ben's spinal surgery, Jack told Kate to recall the story of the girl when she and Sawyer had gotten to a safe place. When they eventually did, Kate told the story in front of Sawyer, Juliet, Karl and Alex. ("I Do")