Now Dr Michael Belford, of Baylor College of Medicine in Houston, Texas, has developed a new technique to remove the baby and womb so that any spinal defect can be fixed before amniotic fluid eats away further at the gap in the spinal nerve tissue.
Although the womb is still attached to the mother, once outside her body doctors can drain it, light it up and operate through tiny incisions.
One of the first operations was performed last month on hairdresser Lexi Royer, 28, who was initially offered an abortion, but chose instead to take part in the experimental surgery when her baby was 24 weeks old.
"We were looking at brain damage, feeding tubes, a breathing tube, a wheelchair, just a bad quality of life," Royer told the New York Times.
"It's not done, by any means, but I definitely feel it's the right thing for us. Seeing the ultrasound and how good he's doing, moving his ankles and feet, it's such a happy moment. I can't imagine going on further in the pregnancy not knowing every day what damage is being done. It's such a relief to move forward."
During the three-hour operation at Texas Children's Hospital in Houston, Belfort opened Royer's abdomen but instead of cutting into the uterus, removed the whole womb.
He then made two slits in the womb, one for a fetoscope - a tiny camera designed to light up and film inside - and another for surgical tools.
Doctors pumped in carbon dioxide to keep the uterus buoyant, giving them room to work and allowing them to see the spine more easily.
After injecting the fetus with anaesthetic, the team moved skin over the exposed spinal cord and stitched it in place. Doctors then refilled the womb with saltwater and placed it back into Royer.
To develop the procedure Belfort and a colleague spent two years practising on sheep and a rubber ball with a doll inside, wrapped in chicken skin to mimic the defect in spina bifida.
The team is now reporting on its work in the journal Obstetrics & Gynecology following 28 successful operations in which no fetuses have died, and only a few have needed shunts to drain fluid from the brain. Some of the mothers have also not even needed caesarean sections.
Belfort is now helping to train colleagues at Stanford University. However, some doctors have warned that pumping the womb with carbon dioxide during the procedure could damage the baby and cause neurological problems in later life.
Dr Katie Morris, Senior Clinical Lecturer and Consultant in Maternal Fetal Medicine, University of Birmingham, said women in Britain would still be sent for in-utero surgery until there was more evidence to show the new operation was as safe.
"All of these techniques are exciting and novel in that they give an option for in-utero therapy, but as the number of cases is small this is not something that will become widely available. At present, if women come to our fetal medicine centre and request fetal surgery we refer to Belgium for open surgery as there are longer-term outcomes available," she said.
Royer's baby is due in January.