Parents whose children are struggling with math often view intense tutoring as the best way to help them master crucial skills, but a new study released on Monday suggests that for some kids even that is a lost cause.

According to the research, the size of one key brain structure and the connections between it and other regions can help identify the 8- and 9-year olds who will hardly benefit from one-on-one math instruction.

"We could predict how much a child learned from the tutoring based on measures of brain structure and connectivity," said Vinod Menon, a professor of psychiatry and behavioral sciences at Stanford University School of Medicine, who led the research.

The study, published in the online edition of Proceedings of the National Academy of Sciences, is the first to use brain imaging to look for a connection between brain attributes and the ability to learn arithmetic. But despite its publication in a well-respected journal, the research immediately drew criticism.

Jonathan Moreno, professor of medical ethics at the University of Pennsylvania, fears that some parents and teachers might "give up now" on a math-challenged child. "If it gets into the popular consciousness that it's wise to have your kid's brain checked out" before making decisions about academic options, he said, "that raises huge issues."

Menon and his fellow scientists agree that their research shouldn't lead to hasty conclusions. They are exploring whether any interventions might change the brain in such a way that children who struggle with math can benefit more from tutoring.

Just as learning to juggle increases the amount of gray matter in the area of adult brains that is responsible for spatial attention, said Menon, maybe something could pump up regions relevant to learning arithmetic before a child begins math tutoring.

Until then, he said "it's conceivable" that parents will interpret the new study as saying some kids cannot benefit from math tutoring, "and give up before even trying. How this plays out is far from clear."

The study was conceived as a way to understand why some children benefit more than others from math instruction, said study co-author Lynn Fuchs, professor of special education at Vanderbilt University and an expert on ways to improve reading and math skills in students with learning disabilities.

For the research, the scientists first ran several tests on 24 third-graders to measure their IQ, working memory and reading and math ability. The children also underwent brain imaging. Structural MRI (magnetic resonance imaging) revealed the size and shape of various regions, while functional MRIs revealed connections among them.

Then the children received 22 one-on-one tutoring sessions, spread over eight weeks, for eight to nine hours per week. The tutoring emphasized number knowledge (principles like 5 + 4 = 4 + 5, and that many pairs of numbers add up to, say, 9) and fast-paced mental math ("quick, what is 6 + 9?").

After the tutoring, the children all improved in their arithmetic ability, solving more problems correctly and more quickly. But the amount of improvement varied enormously, from 8 percent to 198 percent.

None of the measures - pre-tutoring IQ score, working memory and math skills - predicted how much a child would improve.

But when the scientists compared each child's improvement with his or her pre-tutoring brain images, two connections jumped out. The volume of gray matter (neurons) in the right hippocampus, one of the twin structures crucial for forming memories, varied by about 10 percent in the children, Stanford's Menon said. The strength of the wiring between the hippocampus and the prefrontal cortex and the basal ganglia varied by about 15 percent. Both predicted how much a child's math skills improved with tutoring, the scientists reported.

The prefrontal cortex, behind the forehead, "is important for cognitive control, which plays a role in the formation of long-term memories," Menon said. The basal ganglia, tucked under the brain's outer surface, "is involved in habit formation and procedural memory," such as how to add numbers.

"Children with a larger right hippocampus and greater connectivity between the hippocampus and these two structures improved their arithmetic problem-solving skills more," said Menon.

These brain features explained 25 percent to 55 percent of the variation in improvement after math tutoring, he said. That, of course, leaves almost half of the difference among children to be explained by other factors.

Among the concerns raised about the study is its size. It enrolled only two dozen children, on a par with many neuroimaging studies but quite small for research that might influence people's behavior, said psychologist Scott Lilienfeld of Emory University.

"This is very, very preliminary evidence that brain measurements might tell you something that psychological measurements don't," said Lilienfeld, co-author with psychiatrist Sally Satel of an upcoming book, "Brainwashed: The Seductive Appeal of Mindless Neuroscience," that critiques some uses of neuroimaging. "It's important to see if the findings hold up in a second sample, and if other labs corroborate this."

Because brain images seem more rigorous than psychological measures, he said, there is a risk that parents and educators will interpret the study as definitive evidence that some children are doomed to be innumerate.

"Caution has to be the watchword here," he said.

Massachusetts is launching a sweeping plan to hold down health care costs. A new law is partly designed to get patients to help drive down prices by shopping for medical care.

So when I had a series of migraines over the summer, I decided this was an opportunity to be an engaged, savvy patient.

First decision: whether to even get the doctor-recommended MRI. It’s a very expensive test, and I thought maybe the headaches would just disappear.

But I followed my doctor's advice, called Newton-Wellesley Hospital and asked for the price of the test. My doctor didn’t know, I got transferred to radiology, I got transferred to billing. Billing said they would call me back. They didn't. I couldn't even get a ballpark estimate.

Now, I have insurance with no deductible, so wherever I went was only going to cost me a $25 copayment. (Apologies to all of you with high-deductible or tiered plans out there.)

When I couldn’t get through to Newton-Wellesley, I tried Mass General, which is what we usually hear is the most expensive and best hospital in the country to go to. They were charging $5,315. That’s for an uninsured patient. For one MRI.

But they couldn’t tell me what my rate was going to be as an insured patient. They said they didn’t have that information. So I hit another wall with another hospital.

Then I tried an independent lab called Shields. It’s a chain that specializes in MRIs and other radiology tests. Shields said it would have charged between $2,000 and $3,600 for this test (the higher cost is for an MRI with an injectable dye to show contrast). But that's not what they would bill my HMO Blue Cross plan for my MRI: $600 for the MRI without the contrast dye, and $1,200 for the MRI with the dye is its negotiated rate with my health plan.

Eventually, I got the test at Newton-Wellesley. I thought the price would be somewhere between Mass General and Shields, and I thought there was some value in following my doctor's recommendation. When I got the bill from Newton-Wellesley I was stunned. It was for $7,468. It turns out this is the price Newton-Wellesley charges someone who is uninsured. If you include the charge for reading the test, the total is almost $8,000, even higher than Mass General. I thought that since Newton-Wellsley knows I’m a Blue Cross member, they’d send me the Blue Cross rate — what Blue Cross was going to pay for the test. They didn't.

Newton-Wellesley also didn’t tell me that I’d had two MRIs while lying there in the cave wearing headphones that are supposed to ease the earthquake rumble effects of the test. I found this out months later when I got the "Explanation of Benefits" (EOB) from my insurance company. I still don’t know why the hospital ran two tests. My doctor says he only ordered one. So the $7,468 doesn’t sound as bad if it’s the price of two tests. This is all incredibly confusing and about as far from the transparent process that is supposed to help us “shop” for care as you can get.

Tips For Price-Conscious Consumers

If you want to try to shop around, here are few things you should know, if you don’t already:

1) Insurance companies negotiate different rates with different hospitals. I’ve had a hard time getting doctors or hospitals to give me the negotiated rate, but Blue Cross will tell me, if I’m willing to wait on hold and have the exact code for the exact procedure I need.

2) Get the code for the test of procedure you need. In some cases there will be several billing codes. For example, my MRI codes were 70551 without the dye, 70552 with the dye. I used those numbers in so many different conversations I don’t think I’ll ever forget them. And in the end, since I had another test I didn’t know about, an MRA, I wasn’t using all the right codes. This process really could drive you crazy.

3) Sometimes your insurance company will send you the EOB that lists the price they actually pay the hospital, but good luck trying to decipher all this paperwork.

4) The physician’s charge is often a separate bill, or rather two bills: what the doc charges and what the insurance company pays. You have to ask a lot of questions

Why the huge disparity between what a hospital charges for an MRI and what a stand-alone clinic such as Shields charges? Newton-Wellesley said that it costs a lot to keep a hospital open 24 hours a day. Hospitals lose a lot of money on some services and make it up other other services. MRIs or other tests are a way to make up for money lost on services such as mental health.

And hospitals say they lose money taking care of patients with Medicare — that’s mostly for the elderly — or Medicaid government insurance mostly for the poor. So private insurance payers like me end up paying more for these tests so that the hospitals can have everything balance in the end.

While Shields lab doesn't have the overhead of a hospital, Tom Shields, the company’s president, says charging more for an MRI to make up for losing money on other services is just a sign that health care finances are really broken. "You’re reimbursing for diagnostic imaging at a very high rate to justify the underpayment for other lines of health care. It’s sort of like justifying the $500 Ace bandage. The logic isn’t there."

I wasn't ever able to find out how much of the charge for an MRI is based on "real" costs - like cost of the machine or the salaries of the technician or doctor.

These real costs vary, but in many cases, not much. We know that hospitals with a strong brand name use that brand to boost their charges. Rick Siegrist, who teaches health care management at the Harvard School of Public Health, says hospitals, much like computer giant Apple, can set their charges as they see fit: "A lot of times, people think they’re just going to look at what their cost is and put a little markup on that and that’s what the charge will be. That’s not the way it’s done, just like it’s not the way it’s done in private industry."

We have the health care industry telling us to shop around, to be smart consumers, to make wise choices, and yet it’s really difficult to do that, because we don’t understand how hospitals set prices, and it can take hours to find a price. The whole pricing system seems very arbitrary. And we’re left trying to make choices based on incomplete or wrong information.

There may be some hope, according to Dr. Gene Lindsey who runs Atrius, the state’s largest physicians group. He said while it's a long way way off, "Atrius Health will, in a very, very focused way, begin the work that’s necessary to try to deliver what the bill asks for in terms of cost transparency.”

Atrius and a few other physicians groups have started putting some price information in the record that doctors can see when they are speaking to a patient. It'll be a tough task to say, "You're going in for an appendectomy and here’s what it’s going to cost," because there are so many variables when you go into a hospital for a procedure. But Atrius is shopping for software that will pull all the information, like my health insurance data, together so that they can say, "OK, you’re an HMO patient, here’s what you’ll pay" or, "You have a high deductible, here’s what you’ll pay."

Two months after I had the tests, I got an Explanation of Benefits from my insurer. Blue Cross paid $1,650 for both. Actually, Blue Cross paid $1,360 for the tests and $290 in physician fees. I never saw a bill for the physician fees. I had to call to get that number. Again, a remarkable lack of transparency.

Then the broader advice is: If you really have to pay attention to price because you have a high-deductible or a tiered coverage plan, then do a lot of deep breathing. Be ready for a long journey that will take some patience.

Oh, and I don’t have a brain tumor or anything serious. My doctor sent me a note. My MRI and MRA showed “white matter with a propensity for migraine.” White matter is just brain tissue, by the way, not little bits of white junk floating around in my brain. I’m fine; I just need to get more sleep.

Kaiser Health News is an editorially independent program of the Henry J. Kaiser Family Foundation, a nonprofit, nonpartisan health policy research and communication organization not affiliated with Kaiser Permanente.

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The latest medical images can provide spectacular pictures, giving doctors and patients enormous amounts of information about a wide range of medical conditions. But doctors may have gotten overly enthusiastic about using them.

A study out Tuesday in the Journal of the American Medical Association found that the number of MRIs quadrupled, CT scans tripled and PET scans went up 57 percent between 1996 and 2010. The researchers tracked up to 2 million members of six large health systems in the U.S.

There is no question that before performing a surgery, for example, a doctor wants to see as much as possible. Magnetic Resonance Imaging (MRI) uses magnets and radio frequency fields to scan the body and help doctors make diagnoses of tumors, torn ligaments or strokes without surgery. A PET, or positron emission tomography, scan can be conducted alone or combined with MRI with radioactive isotopes to show metabolic activity in the body such as cancer.  

The images help; the question is just how much.

 “The increase in use of advanced diagnostic images has almost certainly contributed to both improved patient care procedures and outcomes, but there are remarkably few data to quantify the benefits of imaging,” radiology professor and lead author Dr. Rebecca Smith-Bindman from the University of California, San Francisco, and her colleagues write.

Why does it matter? The biggest reason is cost. Americans now spend an estimated $100 billion a year on medical imaging. For each patient, each procedure can cost between a few hundred and several thousand dollars. Usually doctors order them for the best of reasons, but sometimes it is defensive medicine based on the fear of lawsuits or, even worse, the need to amortize the huge cost of a piece of equipment the practice has purchased. 

Another major downside of increased imaging is the “false positive,” which is the discovery of a growth or other apparent problem that presents no danger but needs to be removed -- with additional cost and anxiety.

The biggest danger with scanning comes from CT, or computed tomography. A CT scan exposes the patient to huge amounts of X-rays. One CT scan of the chest, for example, zaps a patient with the same amount of radiation as 150 old-fashioned X-rays. In their survey of medical records, the authors of the latest study found that 3.9 percent of patients were receiving an exposure or more than 50 millisieverts every year. In comparison, that is about the equivalent of the one-time amount that the Japanese government estimates that the nearby residents of the Fukushima power plant got in the hours before they evacuated.

A recent Institute of Medicine report on risk factors for breast cancer listed chest CT scans high on the list. Last week, an international study found that children who get CT scans have a slightly higher risk of later developing leukemia and brain cancer. While the absolute risk of cancer is still small, the British researchers suggested minimizing radiation exposure as much as possible.

In a separate report released by the UCSF researchers Monday, Smith-Bindman said a woman should ask her doctor these questions before getting a CT scan:

• Is this scan absolutely necessary?
• Is it necessary to do it now?
• Are there alternative tests?
• How can I be sure the test will be done in the safest way possible?
• Will having the scan information change the management of my disease?

For the sake of our pocketbooks and peace of mind, we all might be well advised to ask our doctors the same questions about any medical scan we receive.

Robert Bazell is NBC's chief science and medical correspondent. Follow him on Facebook and on Twitter @RobertBazellNBC

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Hospitals around the country may already have the technology to inexpensively diagnose – or rule out – Alzheimer’s disease, two new studies suggest.

The studies looked at an MRI method that can cheaply and accurately detect changes in the brain that are associated with Alzheimer’s disease. Currently doctors who need an accurate diagnosis must send patients off to a center with a PET scanner. Along with a higher price tag, images from PET scanners require the use of radioactive tracers which carry some risks if a patient is tested repeatedly.

 One of the new studies was published in Alzheimer’s and Dementia, the other in Neurology.

 "This can become a useful way of diagnosing the disease and managing therapy," said study co-author Dr. John Detre, a professor of neurology and radiology at the Perelman School of Medicine at the University of Pennsylvania. "It can also be used an inexpensive and non-invasive way to document a patient’s response to new drugs. You can repeat tests without risk since you don’t have to inject a radioactive substance every time you want a new measurement."

PET scanners look at how the various brain regions use glucose – the fuel that keeps us thinking. Doctors can tell by the pattern of glucose use whether a brain is developing Alzheimer’s because nerve cells use less glucose when they are beginning to fail. The pattern of bright and dull spots on a scan tell doctors whether brain regions typically hit by Alzheimer’s have been damaged.

The new MRI technique looks at blood flow in each brain region. Detre and his colleagues showed that patterns of blood flow in Alzheimer’s patients mirrored those of glucose use, which means that MRI scans can give the same information as more expensive PET scanners.

The new technique may also help drive drug discovery. Pharmaceutical companies developing Alzheimer’s treatments could inexpensively track patients and, because there is little exposure to radiation, follow-ups can be more frequent with less risk to trial participants, Detre said.

The new method requires only a standard MRI machine and computer programs that are already available to medical centers, Detre said. So, if the technique catches on, it could be widely available in a very short time.

There is no cure for Alzheimer’s, no matter how early the disease is diagnosed. But patients can use an early diagnosis to get their lives in order while they are still cognitively intact and also as a chance to sign up for clinical trials.

Early Alzheimer's disclosures to become more common