Psychologists and mathematicians put heads together on brain research

By Steven Schultz

Princeton NJ -- Before he even accepted his job at Princeton, neuroscientist Jonathan Cohen set his sights on collaborating with faculty members he believed could help push brain research to a whole new level. One person he had in mind was not a fellow psychologist or even a biologist; it was mathematician Ingrid Daubechies.

Cohen, who came to Princeton in 1998 as the founding director of the Center for the Study of Brain, Mind and Behavior, is a pioneer in the use of a technology called functional magnetic resonance imaging (fMRI), a version of the common medical tool that lets researchers watch the brain in action. The fMRI machine creates three-dimensional movies that show what parts of the brain people use as they think and perform tasks.

This series shows how a technique called wavelet transform, developed by Princeton mathematician Ingrid Daubechies, might improve the interpretation of brain scans taken by scientists at the Center for the Study of Brain, Mind and Behavior. Wavelet transform breaks an image (left) into components (middle) that make it easier to distinguish random noise from meaningful data. The operation can be repeated at increasing levels of coarseness (right). This image is one frame from a three-dimensional movie of a brain performing a task; wavelet transform also can be applied across time, breaking the data into different time scales.


In the last decade, this imaging technology has opened new vistas in neuroscience. It offers researchers an unprecedented opportunity to explore the biological underpinnings of human behaviors such as moral reasoning and decision making. This progress, however, is only a beginning. If scientists could overcome several technological hurdles, the promise would be much greater, said Cohen.

That is where Daubechies comes in. Daubechies and Cohen, along with Wolfgang Richter of chemistry and Sylvain Takerkart of the Center for the Study of Brain, Mind and Behavior, recently received a five-year, $2 million grant from the Human Brain Project of the National Institutes of Health to develop mathematical tools that could greatly improve brain-imaging technology.

Daubechies, a professor of applied and computational mathematics, is known for inventing a mathematical tool called wavelets, which has found widespread use in areas such as the analysis and compression of digital images. As soon as he heard of Daubechies' work, Cohen was convinced that wavelets could be used to improve and analyze brain- imaging data.

"Ingrid and I met before I came, when I was visiting," said Cohen. "She was one of the attractions for me in coming here, and it is really exciting to be able to capitalize on that."

Cohen compared the current state of brain imaging research to the story of a man who is looking for his glasses under a streetlight, not because that is where he lost them but because that is where the light is.

"We're searching where we think there is something to find because that's where we've seen something interesting before," said Cohen. "But how much more are we learning? The purpose of these new techniques is to give us a floodlight to fill the whole street and to be able to look wherever the data points us rather than having to presuppose the answer."

The grant covers two main problems in brain imaging. The first is that fMRI images are extremely "noisy" -- like watching a football game on a bad television. Figuring out where the meaningful data is can be like trying to follow the ball through a complicated play where the ball appears smaller than the snowy blotches. Researchers must average the data from many experiments to amplify the real signal compared to the noise, "but the problem is that subjects are only willing to sit for so long," said Cohen.

Cohen and Daubechies believe that wavelets offer a way to isolate the signal from the noise. Once they've thrown out meaningless data, researchers could analyze the remaining information in ways that are impossible today because they require too much computing power, said Cohen.

The second problem is that, as the fMRI machine scans the brain from the outside, it is often hard to tell where signals originated within the skull and how to break a signal into its contributing brain components. In their initial work, Daubechies and Cohen have become convinced the existing techniques for doing this analysis have fundamental flaws because they were adapted from methods used to analyze audio signals, which are very different from fMRI data. Daubechies and her students are developing new techniques that are based specifically on known characteristics of the brain. They are testing their new methods on simulated fMRI data and hope to apply them to actual brain scans within a year.

"The potential payoff is very interesting, possibly huge," said Daubechies, noting that the development of these new analytical tools could eventually have applications far beyond neuroscience, just as wavelets have proven to be a generally useful technique.

Despite their enthusiasm, the collaborators found that progress was not immediate. It took four months, for example, for the two of them to understand what they meant by the word "independent," which came into play in their discussion of locating and isolating signals from different parts of the brain. The mathematical definition of the word is much different and more precise than the colloquial use of the word, said Daubechies.

"So we spent a year and a half in weekly meetings, and we talked a lot," Daubechies said. "And that, I think, is so important when you are trying to do something interdisciplinary. Both sides have to invest a lot of time in getting to the point where they can talk to each other. I was very, very fortunate that Jonathan wanted to do this."

Now that they have made the investment and there is a prospect of making a real difference in brain research, the collaboration is very rewarding, said Daubechies. "That is the exciting thing for me -- to be able to interact with someone on Jonathan's level and be able to ask continuous questions and get answers and gain insights," she said.

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