About a month ago, Judith Hansen popped awake in the predawn hours, thinking about her father’s brain.

Her father, Morrie Markoff, was an unusual man. At 110, he was thought to be the oldest in the United States. His brain was unusual, too, even after he recovered from a stroke at 99.

Although he left school after the eighth grade to work, Mr. Markoff became a successful businessman. Later in life, his curiosity and creativity led him to the arts, including photography and sculpture fashioned from scrap metal.

He was a healthy centenarian when he exhibited his work at a gallery in Los Angeles, where he lived. At 103, he published a memoir called “Keep Breathing.” He blogged regularly, pored over The Los Angeles Times daily, discussed articles in Scientific American and followed the national news on CNN and “60 Minutes.”

Now he was nearing death, enrolled in home hospice care. “In the middle of the night, I thought, ‘Dad’s brain is so great,’” said Ms. Hansen, 82, a retired librarian in Seattle. “I went online and looked up ‘brain donation.’”

Her search led to a National Institutes of Health web page explaining that its NeuroBioBank, established in 2013, collected post-mortem human brain tissue to advance neurological research.

Through the site, Ms. Hansen contacted the nonprofit Brain Donor Project. It promotes and simplifies donations through a network of university brain banks, which distribute preserved tissue to research teams.

Tish Hevel, the founder of the project, responded quickly, putting Ms. Hansen and her brother in touch with the brain bank at the University of California, Los Angeles. Brain donors may have neurological and other diseases, or they may possess healthy brains, like Mr. Markoff’s.

“We’re going to learn so much from him,” Ms. Hevel said. “What is it about these superagers that allows them to function at such a high level for so long?”

Many older Americans have checked the box on their drivers’ licenses to allow organ donation for transplants; some have also looked into or arranged whole-body donations to medical schools. Fewer know about brain donation, Ms. Hevel said.

The campaign to encourage it began about a decade ago, when “new techniques came on the scene that allow amazing quantitative analysis” of brain cells, said Dr. Walter Koroshetz, the director of the National Institute of Neurological Disorders and Stroke, which administers the NeuroBioBank. Researchers use its material to study an array of brain diseases and psychiatric disorders.

But “these new techniques require the brains to be taken quickly and then frozen,” because “brain tissue starts to deteriorate in a matter of hours,” Dr. Koroshetz said.

Before the NeuroBioBank was established, some universities were already collecting donated brains, but the process “was scattered around the country,” he said. “Access to tissue was not centralized.”

Ms. Hevel encountered such obstacles when her own father was dying of Lewy body dementia in 2015. “It was a terribly complicated process at the time,” she said. The Brain Donor Project now works to inform the public of the importance of brain donation and the best way to arrange it.

Though some neurological research relies on scans and computer simulations, there’s no substitute for human tissue, Dr. Koroshetz said: “It‘s like the difference between looking at a cartoon and a Rembrandt.”

Now, each of the six university brain banks affiliated with the NeuroBioBank averages 100 donations annually, enabling research on topics from Parkinson’s disease and schizophrenia to the effects of military blasts. The Brain Donor Project, working with N.I.H., has registered 23,000 donors since its inception in 2016. “There’s a need for more,” Dr. Koroshetz said.

Brain donation remains a sensitive topic, he acknowledged: “For some families, it’s very uncomfortable to talk about,” and some religious and ethnic groups find it objectionable. When he led research on Huntington’s disease decades ago and raised the issue with patients, “it would take years of people asking questions before they’d feel comfortable signing a form.”

How does it work? The Brain Donor Project connects would-be donors with N.I.H.- affiliated university brain banks. “Don’t try to pick a brain bank on your own,” Ms. Hevel said. They have different requirements and protocols, and the project will connect a donor with the appropriate one.

The donor signs the necessary paperwork, or a relative or medical team member may sign on the donor’s behalf. The family or medical staff must alert the bank immediately after the donor dies.

At the funeral home or morgue where the body is being kept, a “recovery specialist,” often a pathologist or medical examiner, removes the brain from the back of the skull to avoid disfigurement (thus, the deceased can still have an open-casket funeral) and delivers it to a brain bank for freezing and distribution to research labs.

“I’ve heard from so many families that even in the face of great loss, there’s a sense of solace and comfort, knowing something positive can come from it,” Ms. Hevel said.

There is no cost to families, who can opt to receive a neuropathology report a few months later. It may prove useful in alerting relatives to potential disorders or abnormalities.

There are other ways to regard one’s body as a legacy, of course. Under the Uniform Anatomical Gift Act, almost any adult can become an organ donor when getting or renewing a driver’s license, or by signing up at an online state registry. (Agreeing to donate organs for transplantation doesn’t include brain donation for neuroscience research.)

More than 100,000 Americans are on waiting lists for transplants, the greatest number hoping for a kidney.

It’s “a different world” when people want to donate their bodies to medical schools to help educate health care professionals, said Sheldon Kurtz, who teaches law at the University of Iowa and helped draft the current legislation on organ donation.

In that case, donors must contact schools directly, and they can be picky about which bodies they will accept and under what terms. Some will not work with out-of-state donors, for instance, or accept “next-of-kin donations” arranged by families if the donor has not personally signed the paperwork.

It’s sometimes possible to donate both a brain and a whole body. “There’s no set legislation for these arrangements,” Mr. Kurtz said. “It’s really a contract between the donor and the institution.”

In 2021, Joy Balta, the chair of the American Association for Anatomy’s body donation committee, and his colleagues surveyed 72 medical schools that annually received more than 26,000 whole-body donations. About 70 percent of respondents reported receiving enough donations for research; a few had more than they needed.

But their needs are increasing, Dr. Balta said in an interview. Improved preservation techniques mean that human cadavers are now used not only to teach anatomy, their traditional purpose, but also to help train surgeons and other clinicians.

For Mr. Markoff, the 110-year-old man, however, his children saw his brain, more than his body, as a gift that could benefit others.

“There’s a secret sitting there,” Dr. Koroshetz agreed. “In the very elderly, it’s rare that a brain doesn’t have neurological pathology, but 38 percent of them have no cognitive difficulty. The circuits are still working, even when the pathology is severe. What is causing that resilience?”

Mr. Markoff died at home on June 3, just two days after his daughter’s predawn revelation. Because the Brain Donor Project had immediately connected Ms. Hansen with U.C.L.A., “they had his precious brain stored properly within four hours” of his death, Ms. Hevel said.

That has proved a consolation.

“We felt so happy that Dad could be useful,” Ms. Hansen said. “Isn’t that what we all want? To have purpose?”