A tracheotomy to put a breathing tube in the throat of an infant can be a risky procedure, says Dr Court Cutting, a leading plastic surgeon at New York University Medical Center; it runs the danger of cutting the superior thyroid artery, which can cause blood to spurt out as fast as it can be sucked up. The surgeon probably won’t make that mistake again, but it can be tough luck for the baby.

Talking with a pilot friend one day, Cutting realised that the way we teach surgeons is like training pilots by sending them up in loaded 747s—loaded mostly with poor people, since the affluent seek out experienced doctors as private patients. But pilots learn to fly on simulators. Why can’t surgeons practise on machines, instead of bodies?

They already do, but existing devices all have shortcomings. Cutting himself has developed a videogame-based system for teaching cleft-lip and -palate repair, and there are programs for cardiac surgeons to practice threading catheters up the femoral artery to the heart. But those are based on generic anatomical models. Cutting wanted the ability to rehearse an operation on a virtual model of a real patient’s actual anatomy, based on CT or MRI scans. And he wanted to be able to do it in real time, interactively, on a model incorporating skin, muscle, nerves, organs, bones—and blood.

How hard can that be? Well, equations exist to calculate how tissues will stretch or tear when a surgeon manipulates them, and how they will respond when they’re sutured up again. But on existing desktop computers they can take days to solve, says Joseph Teran, a UCLA mathematician who organised a conference on “virtual surgery” at the university in January.

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