Philip Drinker and Louis Agassiz Shaw were working in industrial hygiene at Harvard, not medicine, when they put the thing together: a sheet-metal box, a rubber collar at the neck, and two vacuum-cleaner blowers to pull the pressure down and let it back up again. They'd tested it on cats first. Then in 1928 it went to Boston Children's and an eight-year-old girl paralysed by polio breathed inside it.
Vacuum-cleaner blowers. Wendell, that's the same instinct that built half the early spaceflight hardware — grab the motor that already works and point it at the new problem. And testing on the cats first before anyone put a child in it says a lot about how carefully they were thinking.
The clever bit is that it doesn't push air in at all. It pulls the box pressure down, so the chest expands and air walks in through the nose on its own — the same way your lungs normally work, just done from the outside. Which means the throat and vocal cords are left alone. For a child with polio whose diaphragm had stopped, that was the whole difference.