A technology the institute adopted just months ago was a game changer for Crosslin, whose lungs were fused so tightly to his chest cavity that doctors needed extra time to delicately remove them.

The call came in the middle of the night. Sondos Shalabi was whispering. There was panic in her voice. “Help please,” she whispered to her father-in-law. “You have to save us.” Organisers ...