An Ontario couple faces an unspeakable dilemma: their ailing twin girls both need new livers to live, but the father can only save one.

Michael Wagner found out this week that he is a match to give part of his liver to one of his three-year-old daughters, who both suffer from Alagille syndrome -- a genetic disorder that affects the liver, heart and other organs.

A team of doctors at Toronto General Hospital will decide which of the girls, named Binh and Phuoc, will receive the transplant, said Johanne Wagner, Michael's wife and the girls' mother.

"We told them we didn't want to be burdened with the decision making," she said from Kingston, the family's hometown.

Johanne Wagner said doctors are expected to perform the surgery in about two weeks. In the meantime, the family is going public with their story in the hopes of finding a donor for the other daughter.

The main problem the girls are facing is the function of their livers, which are slowly dying, Wagner said. They have fewer bile ducts than normal, which means less bile gets into the liver that causes problems with fat digestion and vitamin absorption.

The twin girls were 18 months old when the Wagners adopted them from Vietnam. They are the youngest of the couple's nine children -- they had five of their own before deciding to adopt.

They knew early on that the girls had liver problems, but didn't know the extent, said Johanne Wagner.

"When we saw them at the orphanage we were shocked, really," she said.

"They were 9 pounds at 18 months. So we left the orphanage that day and went to buy two little containers with dragonflies on them and that's what we were going to lay their ashes in if they didn't make it."

The mother said the girls continue to play and enjoy life as little, curious girls, even if they are developmentally delayed because of their poor health.

But she said they are becoming aware that they aren't like other kids their age. They know that other girls don't have feeding tubes sticking out of their little bellies.

Itchiness is another problem the girls have from the disease, Wagner said.

"There's blood in the bed in the morning from scratching. There's no way they can concentrate. It rules their life."

A new liver doesn't guarantee a long, healthy life, Johanne Wagner said, but the girls' livers will fail them at some point and if the family doesn't find a donor for their other daughter, she will die.

Despite this, the family remains positive.

"We look back and we have no regrets," Johanne Wagner said.

"We would travel this path all over again. They have taught us openness, they have taught our children sharing and openness. It's been nothing but a wonderful mess."