Former vice president Richard B. Cheney was reportedly “doing exceedingly well” after a heart transplant Saturday that ended a 20-month period of waiting during which he was kept alive with an artificial heart.

Cheney, 71, had the operation at Inova Fairfax Hospital in Northern Virginia, where surgeons had implanted a battery-powered “left-ventricular assist device” (LVAD) in 2010.

“He’s doing terrific,” said Jonathan Reiner, Cheney’s longtime cardiologist at George Washington University Hospital, which does not have a transplant program. Reiner said he saw the former vice president Sunday morning and “he joked with me. He was doing exceedingly well.”

Reiner said it was hard to say how long Cheney would stay in the hospital. Neither he nor Cheney’s family have provided specifics about the procedure or the donor.

The transplantation is the latest chapter in the semi-public chronicling of Cheney’s life with coronary heart disease, the leading cause of death in the United States for more than half a century. Much of his story — he had his first heart attack in 1978 at the age of 37 — has traced the leading edge of cardiac care.

Cheney’s chance of surviving for years with a good quality of life is high, although his predicted longevity depends on how one looks at his medical history.

For example, according to data compiled by the Texas-based International Society for Heart & Lung Transplantation, about 60 percent of people age 70 and over at the time of their heart transplant live at least six years. About 80 percent of people getting transplants because of heart damage caused by coronary disease survive that long. About 70 percent of people who have the kind of mechanical device Cheney did — a continuous-flow LVAD — survive at least six years after they get a new heart. (The data describe the experience of people who got surgery from 2002 to 2009).

“He’s not too old to benefit from it,” Reiner said of Cheney’s most recent procedure.

The use of an implanted heart pump as a “bridge to transplantation” is a rapidly growing strategy. Today, more Americans get the devices each year than get heart transplants.

“Ventricular-assist devices have really revolutionized the field of heart transplantation,” said David A. Bull, 52, who is chief of cardiothoracic surgery at the University of Utah.

“The wait-list mortality has been dramatically reduced, probably into the single digits, mostly because of the newer generation of better VADs,” said Ranjit John, a heart surgeon at the University of Minnesota, in Minneapolis.

About 3,000 VADs are put into Americans each year. About 2,500 heart transplants are performed annually in North America — roughly the same as in 1994.

In 2011, there were 20 heart transplants performed at Inova Fairfax, according to hospital spokesman Tony Raker. Inova’s heart transplant program was established in 1986, and surgeons performed the area’s first heart transplant that year.

In recent years, the number of transplants has actually been falling. Vehicle air bags and the use of helmets by bicyclists and skiers have reduced the number of young healthy men with fatal head injuries — a common source of donor hearts. From 1992 to 2010, the age of donors rose slightly (from 31 to 34) and the percentage who are male fell slightly (from 81 percent to 77 percent).

That Cheney lived to get a heart transplant may be thanks to the device he got in 2010. Today, more than one-third of people receiving transplants have a similar mechanical device in their chests, and that number is rising.

“We try to get to the patients before they get very, very sick,” Bull said. “In the early days the tendency was to wait until the very last minute.” Putting the devices in earlier allows patients to get into better physical condition for surgery and to stay out of the hospital while waiting.

John, the Minneapolis surgeon, said he knows of three or four patients — including a woman in her 30s who suffered a rare cardiomyopathy after delivering her baby — who have opted to take themselves off transplant lists for the time being. “Having this device gives them the option to go back to work and live fairly active lives at home,” he said.

The device Cheney had was a HeartMate II, which sells for about $80,000, according to a spokeswoman for Thoratec, the California company that makes them. The pump, which is sewn onto the heart, is powered by a wire the size of a computer cable that goes through the skin of the upper abdomen. The current model has an expected mechanical life of at least seven years. Patients must take anticoagulant drugs; stroke, bleeding and infection are the chief hazards.

The cost of using ventricular-assist devices for end-stage heart failure has gone down in recent years but still falls far outside what is conventionally considered a worthwhile investment in medicine.

A study published last November found that treatment similar to what Cheney received costs $167,208 for every year of life saved. Treatments that “buy” a year of life for $50,000 or less are considered cost-effective, and those costing $50,000 to $100,000 are generally considered acceptable. (A European study in 2011 found the device much less of a bargain, at a cost of $414,275 for year of life saved).

Who gets a donor heart when one comes available depends on many variables, including body size and blood type. The most important one, however, is a person’s clinical condition and immediate availability for surgery.

There are strict guidelines for placing someone in the most urgent category and the decision is made by a team of many specialists. Moving someone to the top of the list who shouldn’t be there would be hard to do and would open a hospital to major sanctions. Both Bull and John said they are confident Cheney got no special breaks.