That includes several people who arrived with legs attached by just a little skin, a 3-year-old boy with a head wound and bleeding on the brain, and a little girl riddled with nails. Even a transit system police officer whose heart had stopped and was close to bleeding to death after a shootout with the suspects now appears headed for recovery.

“All I feel is joy,” said Dr. George Velmahos, chief of trauma surgery at Massachusetts General Hospital, referring to his hospital’s 31 blast patients. “Whoever came in alive, stayed alive.”

Three people did die in the blasts, but at the scene, before hospitals even had a chance to try to save them. A Massachusetts Institute of Technology police officer who police say was fatally shot Thursday by the suspects was pronounced dead when he arrived at Massachusetts General.

The only person to reach a hospital alive and then die was one of the suspected bombers — 26-year-old Tamerlan Tsarnaev.

But the remarkable, universal survival one week later of all others injured in the blasts is a testimonial to fast care at the scene, on the way to hospitals, then in emergency and operating rooms. Everyone played a part, from doctors, nurses and paramedics to strangers who took off belts to use as tourniquets and staunched bleeding with their bare hands.

As of Monday, 51 people remained hospitalized, three of them in critical condition and five listed as serious. At least 14 people lost all or part of a limb; three of them lost more than one.

Two children with leg injuries remain hospitalized at Boston Children’s Hospital. A 7-year-old girl is in critical condition and 11-year-old Aaron Hern of Martinez, Calif., is in fair condition.

The surviving bombing suspect, 19-year-old Dzhokhar Tsarnaev, is in serious condition at Beth Israel Deaconess Medical Center with a neck wound.

“Our training, our practicing, went a long way” to minimizing chaos so that hospitals and emergency responders worked effectively to treat the many wounded, said Dr. William Mackey, surgery chief at Tufts Medical Center.

“Trauma care is optimism translated into action,” said Dr. Russell Nauta, chairman of surgery at Mount Auburn Hospital in Cambridge, Mass., where the wounded transit police officer, Richard Donohue, remains in stable but critical condition.

Doctors and emergency responders approach each patient as someone who can be saved regardless of how severe the injuries appear.

And some were very bad.

“The legs came hanging on muscles and skin,” said Velmahos, who did three of the four initial amputations at Massachusetts General in the early hours after the bombing. A fifth patient at the hospital had to have an amputation Thursday. Doctors had judged there was a 5 percent chance the woman’s leg could be saved, so they didn’t amputate right away.

“We restored the blood supply to the leg, but all the muscles and nerves were destroyed,” so the leg had to be removed, he explained.

Of the remaining five patients at the hospital with severe leg injuries, “I’m very confident that they will all keep their legs, and even more, that they will have functional legs,” he said.

Although doctors are optimistic, some patients still have life-threatening wounds. Complications can range from blood clots to infections. A few still have injuries that could require amputation, said Dr. Michael Yaffe, a trauma surgeon at Beth Israel.

“We have to see how these are going to heal” over the next few weeks, he said. “Blood supply is key … The two biggest enemies we will face in the next two weeks are maintaining a good blood supply and preventing infection.”

So far, the progress has been in the right direction.

“Every day they’re a little better,” Yaffe said. “A lot of them have a long road of recovery ahead.”