The twin sister of an Ontario girl who successfully underwent a liver transplant this week is expected to undergo the same surgery in coming weeks, doctors say.

Binh Wagner, whose twin sister Phuoc is recovering at Toronto's SickKids Hospital after receiving part of her father Michael Wagner's liver on Tuesday, is still in need of a suitable organ donor.

Both girls have Alagille syndrome, a disorder that affects internal organs, particularly the liver.

Dr. Gary Levy, director of the living donor liver program at Toronto General Hospital, said that more than 400 potential donors from around the world have come forward in recent weeks. He said many of the offers have come from within Ontario, but that people as far away as New Zealand have submitted their medical histories for review.

"We anticipate in the next little while, seven to 14 days, we will define several individuals who can step forward and be a donor for Binh, the second child," he said at a news conference Thursday morning.

While he declined to provide a specific timeline for when Binh may undergo the procedure, the medical team handling the Wagner case anticipates "it will occur in the next month, maybe earlier."

Twins Binh, left, and Phuoc Wagner have Alagille syndrome, which affects the function of their livers. One of the girls had a transplant this week, while a donor is still being sought for the other. (Wagner family/Canadian Press) Without a liver donation, Binh could eventually die from the disorder. The three-year-old is not in a life-threatening scenario right now, said Dr. Binita Kamath, a hepatologist at SickKids Hospital, who assisted with Phuoc's procedure this week.

Kamath said her medical team chose Phuoc to receive her father's liver donation based on the severity of symptoms she was experiencing and the degree to which the condition was affecting her quality of life. Wagner could not donate to both girls.

The Wagner family, from Kingston, Ont., took part in the process, but the ultimate decision was made by Kamath and her team.

'Courageous souls'

Both Phuoc and her father are recovering separately and are both in stable condition, Levy said. Wagner will likely spend at least a week under supervision at Toronto General Hospital before he can go home. His liver will regenerate to its full size within eight to 12 weeks.

The mother of the girls, Johanne Wagner, said she was overjoyed with the result of the procedure this week and the positive prospects for Binh.

Three-year-old Phuoc after coming out of surgery at SickKids Hospital in Toronto, following a liver transplant. (Wagner family/Facebook)

"I would like to thank the very courageous people who have come forward to volunteer to be live liver donors. That takes a lot of courage," she told reporters.

"I'm hoping once this ordeal is behind us, once Binh has received her precious gift, that many of those courageous souls will leave their names on the list and volunteer to be anonymous donors to all the people who are waiting for an organ."

Those people that have offered to donate a piece of their liver to Binh have the option to possibly be matched with another recipient if they are not chosen, Levy said.

Currently, there are about 1,500 people in need of a liver transplant in Ontario. Levy said that nearly 85 per cent of patients waiting for a donor at Toronto General die before they can undergo the procedure.