06/27/2012 01:14 pm ET Updated Jun 27, 2012

Parents Of Sophie Roberts, Toddler With Liver Cancer, Aim To Raise Funds For Surgery In New York

Two-year-old Sophie Roberts has been battling a rare form of liver cancer for about half of her life. Out of treatment options in the United Kingdom, her parents are now on a mission to raise nearly $360,000 for a potentially life-saving surgery in the United States.

Last year, Sophie was diagnosed with hepatoblastoma, a form of liver cancer that is usually caught before a patient turns 2 years old, according to St. Jude Children's Research Hospital. The incidence rate is about 0.9 in 1 million.

Unfortunately, by the time doctors found Sophie's tumor, the cancer had spread to the young girl's lungs. Months after chemotherapy, Sophie underwent surgery to remove the tumor, which resulted in the loss of 1/4 of her liver, according to the website, Sophie Roberts' Story.

Soon after recovery and more chemotherapy to treat several lung metastases, Sophie's parents, Andrew and Ruth, learned the cancer had returned and that surgery was likely the only treatment option.

But two medical teams in the United Kingdom told the couple they would not perform the operation, believing they would not be able to fully remove the cancer.

That's when the couple reached out to a team of doctors at New York City's Memorial Sloan-Kettering Cancer Center who said they would give it a try.

The family needs to raise the money for the operation by July 13. So far, they've managed to raise a portion of that by remortgaging their home and accepting funds from family and friends, according to Metro UK.

Sophie's parents have also set up a donation page on the fundraising site Just Giving in hopes well-wishers will contribute to their daughter's operation. As of early afternoon on June 27, nearly 3,100 donations had been received, totaling more than $227,000.

Online ventures have proven popular among parents striving to solicit help or support for their children.

Earlier this month, one mother made headlines after asking parents to serve their children ice cream for dinner simply to see them smile.

Diane Roberts' son, Ryan, was born with Down syndrome and a congenital heart defect. When doctors said they could no longer do anything to help the baby boy, one of Diane's friends, Melissa Neidhardt, took to Facebook and asked all parents to join "Ryan's Banana Split Party."

Users sent messages and posted photos of their families eating the delicious treat in Ryan's honor.

Similarly, mother Shasta Kearns Moore took to the fundraising site Kickstarter to sell her children's book, "Dark & Light: A Love Story For Babies... And The People Who Read To Them," and raise money for her 2-year-old son's cerebral palsy treatments.

Visit the Sophie Roberts Facebook Page to learn more about her story.