Even today, after decades of research, artificial hearts are not well-suited to permanently replacing the human heart. They are most often used as a temporary measure to help patients survive while they wait for heart transplants. It turns out permanently replacing an element of biology as complex as the heart is enormously challenging; one of those challenges, providing a reliable power source, still eludes us.
For example, the modern AbioCor heart relies on wireless charging from an external wearable battery pack that holds a charge for a few hours. An internal, implanted battery can only hold about 30 minutes' worth of charge by itself. If only the heart had an unlimited power source like Tony Stark's arc reactor--or, perhaps, the energy provided by nuclear decay? If you're thinking the human chest doesn't sound like a very safe place to store nuclear material, well, you're right--but scientists still wanted to try it 50 years ago.
The Atlantic writes that, from 1967 to 1977, medical researchers in two government-funded programs attempted to develop a nuclear-powered artificial heart for use in humans. One model hoped to use radioactive decay, the other nuclear fission. Neither was successful--which is why we don't currently have human beings walking around with nuclear-powered hearts--but it's an interesting story because they were just so sure nuclear power was the right way to go.
The reason for seeking a nuclear solution is perfectly sane: there was simply no battery technology at the time that could last in a permanent artificial heart. And that's essentially true four decades later.
The Atlantic quotes this explanation from Shelley McKellar, who wrote a paper about the nuclear heart programs for journal Technology and Culture: "Each proposal declared the radioisotope-powered engine as the only possible energy solution for a completely implantable device...The ideal implantable device meant no external lines or connections from the patient to outside power sources and a ten-year reliability span. By comparison, conventional batteries required recharging multiple times each day from an external source and would need to be explanted from patients every two years."
Amazingly, the programs didn't end because researchers decided that radioactive materials would be really bad for human beings.
The programs ended for a number of reasons; McKellar writes "political and social concerns arising in the context of a heightened sense of risk awareness in the 1970s ultimately played the biggest role in shutting down the atomic heart programs, as strong public support for increased government control of both atomic energy and medical devices overrode scientific assertions that further development could produce a safe and practical atomic heart."
Like the NASA program that began only a few years earlier, it's possible (though probably unlikely) that enough time, research and money poured into the nuclear artificial heart program could have actually produced a working result. A radioactive heart may never have turned out to be safe, but it might have actually delivered a 10-year energy source, which would still beat out anything in use today.