A more common form of the condition is known as obstructive sleep apnoea, often associated with obesity and being overweight, where the air supply is cut off by the weight of the chest or by narrow nostrils, even though the sleeper is attempting to breathe normally.
Prof William Abraham of Ohio State University, who carried out the research, said: "The Remede system is the first fully implantable device to treat central sleep apnoea in heart failure patients.
"Unlike traditional mask-based therapies - which have been shown to work only in some patients under certain conditions in central sleep apnoea - the Remede system is acceptable to patients and improves their sleep and heart function. Patients using the device tell us they haven't slept so well in years. They have more energy and can do their normal daily activities without falling asleep. They also don't have to fight with a mask."
The device is implanted under the skin like a pacemaker, just below the collar bone, and a wire is threaded into one of the veins near the phrenic nerve.
Prof Abraham said: "The device stimulates the diaphragm via the phrenic nerve, causing the diaphragm to contract. It regularises the patient's breathing pattern throughout the night, rather than waiting until the patient stops breathing to react."
There are around 500,000 people in Britain with heart failure and central sleep apnoea will affect one in three of them. Prof Abraham said the device may work in any patient with central sleep apnoea, which can also affect up to one in five of people with a heart flutter known as atrial fibrillation and some people with neurological disorders.
The study involved 46 people with moderate to severe sleep apnoea who used the device for a year. They were found to have spent less time at night with low blood oxygen levels, which would indicate interrupted breathing.