They sing their ABCs and play with an energy that is almost exhausting to watch. It's hard to believe that 6-year-olds Ahmed and Mohamed Ibrahim were once conjoined twins, confined to a bed and condemned to die.

A 34-hour surgery saved their lives four years ago. Tuesday, the boys got to meet Eileen and Ray Tye, the couple who run the Braintree-based foundation that gave them another chance.

"I'm so proud to be able to say we helped," said Ray Tye, the liquor magnate-turned-philanthropist who oversees the Ray Tye Medical Aid Foundation.

The boys were born in a small village 500 miles south of Cairo, joined at the tops of their heads, a rare form of conjunction that occurs in just one in 10,000,000 live births. Doctors and charities teamed up to send them to the United States to be separated in 2001, but upon their arrival, U.S. surgeons determined they would require a more serious and much more expensive operation.

After 18 months in the United States, doctors considered canceling the surgery because they did not have the money needed to pay the hospital bills. That's when Tye read about them in the newspaper. He sent a $100,000 check that day.

"They were going to be sent home to die," he said.

The surgery took place a few months later at the North Texas Hospital for Children in Dallas. The skin, bone, and blood vessels that had bound them were carefully separated. For the first time in their lives, Ahmed and Mohamed could see one another.

The twins returned home to Egypt in 2005, and the family moved to Cairo so the twins could receive regular therapy and medical monitoring. Since then, hair has grown over their scars, and they have learned to walk.

While they relish going in different directions, they always seem to return to one another. Accustomed to hundreds of interviews, they hardly notice cameras and will cajole anyone in the room to play and sing with them.

"At some point, they are going to be two perfect young men," said Eileen Tye, who set up the foundation in 2002 as an 80th birthday present for her husband.

The boys returned to the United States this month with their mother and baby brother for three weeks of medical checkups in Dallas. Before they were to fly back to Egypt, they stopped in Boston Tuesday, where they met the Tyes at the Hilton Boston Logan Airport.

"We very rarely get to meet the people we help," Eileen Tye said.

The lanky, bespectacled twins climbed over the couple, peppering them with hugs and kisses, pulling on Eileen's necklace and stealing Ray's cane, as though they had always known one another.

"I love you," Mohamed shrieked, grabbing Ray Tye in a headlock.

"I love you, too," Tye said with a laugh.

In addition to Ahmed and Mohamed, more than 100 people have been helped by the foundation, including a Chinese girl with a rare tumor and an Iraqi boy injured in a nighttime air strike by American warplanes.

In the five years since the foundation was started, the Tyes have doled out about $4 million.

"We do these things quietly," Tye said.

"As fast as the money comes in, we spend it. And, still, there are thousands and thousands of people who don't get the help they need."