You’re a heart transplant patient. You’ve been on the waiting list for months, maybe years. Now, you’re being wheeled out of the operating room, a donated heart beating in your chest.

You’ve finished one journey, but are only just starting on a new one: keeping your body from rejecting your new heart.

Luckily for you, new methods under development could help tell early on when chronic rejection problems—the kind that arise five or 10 years after your transplant—start to loom. And even better, scientists are homing in on a new way to prevent chronic (and maybe short-term) rejection from happening in the first place. …