Kimberly Bari had her first seizure in 2010 at age 26 and since then has had hundreds. Some rendered her unconscious, others left her confused and terrified. By 2016, her surgery- and drug-resistant condition led her to try something fewer than 2,000 people in the world have attempted: implanting a computer into her brain.

The NeuroPace Responsive Neurostimulation System “literally provides peace of mind I never imagined could exist,” she said. And, according to its makers, it would be impossible without a type of artificial...