Yet that is no guarantee that the ex-cop, or many others like him, will qualify for a substantial share of the $2.78 billion Congress has set to compensate people who fell ill after being exposed to ground zero toxins.
Like thousands of other rescue and recovery workers, Volpe suffers from an ailment that is not expressly covered by the law.
Only a few diseases were singled out by name in the act, including asthma, certain types of lung disease and a handful of other respiratory ailments. They were included because research has suggested there is a link between those illnesses and the tons of caustic dust that blanketed lower Manhattan after the twin towers collapsed.
Federal administrators still have to decide whether to cover other conditions, like cancer, where there is less hard evidence of a tie to ground zero toxins.
Volpe's problem, a kidney disease called IgA nephropathy, is among those that haven't yet been linked to the dust.
"I'm hoping that when they set up the parameters ... my most serious illness is going to be included," said Volpe, who also suffers from mild respiratory problems.
"I got diagnosed at 34 years old. I was as healthy as I have ever been. To me, it's not a coincidence," he said of his exposure to the ash and dust and the sudden onset of his symptoms.
Volpe's old partner in the detective bureau, John Walcott, is in a similar situation. He was diagnosed in 2003 with acute myelogenous leukemia.
There has been tremendous pressure from first responders to add at least some types of cancer to the list of conditions presumed to be caused by trade center dust. Some of the police officers, firefighters and construction workers who campaigned hardest for the law suffer from some form of cancer.
Yet, scientists say that so far they have been unable to link cancer to the dust, and although theories abound ways the soot might have triggered the disease in some people, there might not be solid evidence one way or another for many years.
To Walcott, an omission of cancer from the program would be inconceivable.
"They have to add it," Walcott said. "If they don't, they're going to have another 5,000 lawsuits on their hands. Everybody I talk to says, 'Don't worry about it. It will be covered."' The task of deciding who qualifies for compensation, and who doesn't, will eventually fall the program's special master, who has yet to be appointed. U.S. Sen. Charles Schumer has already suggested the job should go to Kenneth Feinberg, the lawyer who oversaw the original compensation fund for 9/11 victims.
This administrator will have discretion over the cash payments that are to be distributed to people sickened by the dust, but will probably be guided by rules created over the next few months by the Justice Department and Department of Health and Human Services.
More than 55,000 people who either worked at the trade center site or were exposed to the dust in Lower Manhattan are enrolled in a medical monitoring program. Of those, about 17,000 received some type of medical treatment within the past year, according to the National Institute for Occupational Safety and Health. The people getting care have blamed hundreds of different ailments on trade center toxins, from heart attacks, to skin cancer, to chronic cough.
A separate administrator overseeing a companion $1.5 billion health program for responders will also have the power to put additional diseases on the list of ailments for which the government shoulders treatment costs.
Doctors say deciding which diseases are linked to ground zero and which occurred naturally could be tough.
Tens of thousands of people were involved in the trade center cleanup. Many are now middle-aged, when illnesses of all types become more common.
"It's hard to say 'No' to someone who has cancer and who is struggling. It is very, very difficult," said Dr. James Melius, an occupational health expert who administers the New York State Laborers' Health and Safety Fund and chairs a committee for two existing World Trade Center health programs.
"People are going to have a hard time understanding why their condition isn't covered, especially when you tell them about how uncertain you are," Melius said.
On the other hand, if program administrators balk at paying claims until all the scientific evidence is in, "it could be 20 to 30 years."
The federal law requires the government to review the latest medical evidence on cancer and report back within 180 days as to whether some forms of the illness should be added to the program.
Volpe's condition is another one that could be challenging for the program.
It is common, affecting millions of people worldwide. Doctors say it often simmers unnoticed in a person's body for years until symptoms show up when the patient is in his late 30s. Scientists aren't sure about the cause.
Volpe said when he was first diagnosed, he didn't connect the illness to 9/11 either, but became suspicious after Walcott and other colleagues fell ill.
"I sat down with my doctor and I asked him, 'Do you think it's possible there's a connection?"' Volpe said the doctor told him he couldn't be sure, but had never seen someone his age who had lost so much kidney function so quickly.
"He believes it in his heart. The thing is, he can't prove it." Volpe said.
The kidney condition also wasn't covered by a multimillion-dollar legal settlement worked out last year between 9/11 responders and the special insurance fund representing New York City.
That omission, and other concerns, led him to reject the deal.
Walcott said 'no' to the settlement, too. They were among only a few dozen to do so, out of around 10,000 plaintiffs.
The lawyer the two detectives have hired to handle their compensation fund claims, Noah Kushlefsky of the firm Kreindler & Kreindler, said he believed his clients had a better shot under the federal program.
"This is not litigation," he said, noting that there will be no lawyer standing up on the other side to argue that an illness isn't related to ground zero.
"There has to be a general philosophy of inclusion, within reason."