WASHINGTON — Gulf War illness, the series of symptoms ranging from headaches to memory loss to chronic fatigue that plagues one of four veterans of the 1991 Persian Gulf war, is due to damage to the autonomic nervous system, a study released Monday shows.

“This is the linchpin,” said the study’s lead author, Robert Haley, chief of epidemiology at the University of Texas Southwestern Medical Center in Dallas.

“The disease itself is so difficult to express and to understand,” Haley said, explaining that veterans described simply that they “don’t feel well” or “can’t function,” without being able to further explain a disease that affects the automatic functions of their bodies, such as heat regulation, sleep or even their heartbeats.

“Docs don’t know what the disease is, so they can’t help,” Haley said. “But if you can figure out what the disease is, the other problems will fall in line.”

Researchers spent 15 years researching a hypothesis, and then “we planned the ultimate study that proved that hypothesis,” Haley said.

Along with Steven Vernino, chief of the neuromuscular division at Southwestern, Haley sent 97 veterans through 25 tests, including brain imaging, in seven days. The group had been drawn from a sample of 8,000 Gulf War veterans. The study was published Monday in Archives of Neurology.

“Veterans have high faith in Dr. Haley’s dedicated and informative research,” said Paul Sullivan of Veterans for Common Sense and a Gulf War veteran. “This finding is important because for the first time physicians who care for Gulf War veterans now have a medical explanation for many of the unusual symptoms.”

The team conducted several studies, and then built a theory based on the results of that work.

The doctors had funding from Congress until 2010, when they were dropped by the Department of Veterans Affairs after being accused of wasting millions of dollars in research money. That came directly after a 2009 study from Haley showed that neurotoxins such as anti-nerve agent pills, insect repellent and the nerve agent sarin caused neurological changes to the brain, and that the changes seem to correlate with different symptoms.

After they lost funding, Haley and the other researchers continued their work on their own time.

“This is the most important study of all,” Haley said. “The veterans want to know what’s wrong with them. Now, for the first time, all the doctors in the country can say, ‘Oh, maybe these are autonomic symptoms.’ If you’re not thinking autonomic, the symptoms can sound kind of flaky.”

Music is known to “soothe the savage beast” but it also can improve cognitive function and motor coordination in those with a brain injury or disease, say music therapy advocates.

Now patients at the National Intrepid Center of Excellence and Walter Reed National Military Medical Center in Bethesda, Md., will have a chance to see whether learning or playing an instrument can improve their brain power.

Officials with the Intrepid Center, or NICoE, announced Nov. 16 they will expand the facility’s therapeutic arts program to include music.

The therapy will be offered as part of Operation Homecoming, an initiative co-sponsored by the National Endowment for the Arts that explores the healing power of the arts, including writing, drawing and painting.

“Neurologic music therapy, which is science-based music training, helps people regain speech, movement and other neurological function lost to disease,” NEA Chairman Rocco Landesman said.

Music therapy will be available to the roughly 240 patients seen at the NICoE each year as well as Walter Reed outpatients who have a traumatic brain injury, post-traumatic stress disorder, Alzheimer’s, Parkinson’s or other neurologic conditions.

The program will be evaluated clinically to determine whether it should be expanded to other military treatment facilities and brain injury centers nationwide, according to Rear Adm. Alton Stocks, Walter Reed’s commander.

“Our role at the NICoE isn’t to treat thousands of patients who have TBI or PTS right now but to do the research and education on what works. We expect it will have much more far-reaching effects,” Stocks said.

Operation Homecoming was first established in 2004 by the NEA to help troops and families write about their experiences in Afghanistan, Iraq and at home. Of the program’s roughly $200,000-a-year budget, about $70,000 will go to music instruction and therapy research through 2015, officials said.