SAN FRANCISCO >>  When a Sacramento woman donated a kidney to a stranger, she set off a series of organ swaps that resulted in five more sick people getting new kidneys at a San Francisco hospital.

Surgeons performed three of the transplants Thursday and are expected to carry out the final three Friday.

“I thought I was going to help this one person who I don’t know,” Zully Broussard said. “But the fact that so many people can have a life extension, that’s pretty big.”

Domino-like kidney swaps are still relatively new, but the option is becoming increasingly common when a donor’s kidney is incompatible with a relative or friend who needs one.

Instead of waiting for a stranger to donate or doctors to harvest a kidney from a deceased body, recipients and donors can sign up for a service that connects them with people in the same situation who appear to match.

Say a woman wants to donate a kidney to her brother, but the two don’t match. Somewhere, another pair includes a donor whose kidney is compatible with the brother in need. The software compares the genetic characteristics of all involved to find these matches and sets up swaps between multiple donors and recipients.

This week’s surgeries at the California Pacific Medical Center represent the largest kidney donation chain in its transplant center’s 44-year history, with a dozen patients and donors, hospital spokesman Dean Fryer said. The patients are between 24 to 70 years old, and most of them are from the San Francisco Bay Area.

In this case, the challenge of finding matches was solved by MatchGrid, a software program developed by 59-year-old David Jacobs, himself a kidney recipient whose brother died of kidney failure.

Jacobs, of San Francisco, said he understands firsthand the despair of waiting for a deceased donor.

“Some of these people might have waited forever and never got the kidney,” he said. “But because of the magic of this technology and the one altruistic donor, she was able to save six lives in 24 hours.”

Fewer than 17,000 kidney transplants are performed in the U.S. each year, and between 5,000 and 6,000 are from living donors, considered the optimal kind.

Kidney swaps are considered one of the best bets at increasing live-donor transplants, and they are becoming more common as transplant centers form alliances to share willing patient-donor pairs. The United Network for Organ Sharing has a national pilot program underway.

In 2001, Johns Hopkins Hospital in Baltimore, Maryland, performed a transplant chain that started as a two-way kidney exchange and grew to 30 pairs.

Jacobs’ kidneys failed in early 2000 from a genetic disease. In late 2003, a living, unrelated donor provided an organ for a transplant.

A new chance at life got him thinking.

“I talked to my doctor about kidney-paired donation. He was excited about the idea but didn’t know how to do it,” he recalled. “I was a tech person. I’ve been in technology my whole professional career. I thought of it as an enterprise software problem I could solve.”

He said the two months he imagined it would take to develop the software stretched into six years. But MatchGrid is catching on, growing to 24 hospitals next year. Other programs do similar work elsewhere.

The National Kidney Foundation says more than 100,000 people in the United States are waiting for kidneys, and 12 people die a day waiting.

Broussard said her son died of cancer 13 years ago and her husband passed away 14 months ago, also from cancer.

Asked why she volunteered to donate a kidney to the man, the 55-year-old said: “I know what it feels like to want an extra day.”

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AP Medical Writer Lauran Neergaard contributed to this report.