Mathematical Sequence Reinforces fMRI Data

By combining advanced mathematical techniques more typically used by spies rather than scientists with the power and versatility of functional magnetic resonance imaging (fMRI), a US neurologist has developed a new approach for examining the inner workings of the brain.

A hidden pattern is encoded in the seemingly random order of things presented to a human subject, which the brain reveals when observed with fMRI. The research is published in the April 2011 issue of the journal NeuroImage. Geoffrey K. Aguirre, MD, assistant professor of neurology at the University of Pennsylvania School of Medicine (Philadelphia, PA, USA) noted, "the same math that could break into your car can be used to crack the brain's codes.”

It is called a de Bruijn sequence, which is a set or "alphabet” of things (letters, pictures, sounds) in a cyclic order such that every possible "word” or combination of things occurs only once. De Bruijn sequences are what mathematicians call "pseudo-random” because they seem to be a confused hodgepodge but actually contain an underlying structure. To break into a car protected by an electronic lock with a five-digit numerical keycode, for instance, a thief could try every possible combination. However, such a brute-force technique is time-consuming because it involves a great amount of repetition. However, a de Bruijn sequence uses "every possible combination squeezed together,” explained Dr. Aguirre. The overlapping combinations encode a pattern scientists can observe in brain activity using fMRI, revealing how nerve cells work to represent the world.

This new application measures how the order of things alters brain responses. Does one see a photo of his/her brother differently when it follows a picture of his/her sister? Dr. Aguirre remarked, "Many neuroscience experiments use the context and order of sights, sounds, words, and feelings to reveal how the nervous system is organized.”
Earlier research had presented information to study participants in more or less completely random order. This can be inefficient and inaccurate, making it hard to differentiate significant patterns and correlations between stimuli and neural responses. "We use the de Bruijn sequence to design the experiment,” Dr. Aguirre said. "It tells us how to present things to the subject. By presenting a series of faces in different combinations and orders, as dictated by the de Bruijn sequence, it's possible to measure the brain response to each face individually.”

Dr. Aguirre's new algorithm for creating de Bruijn sequences also helps correct an important limitation of fMRI, which works by measuring changes in brain blood flow. "It takes a little while for the blood flow changes to catch up with the brain response,” Dr. Aguirre noted. "By creating these sequences in a special way that accounts for the slower blood flow response, experiments are many times more powerful than before.”

Dr. Aguirre's novel mixture of advanced mathematics with the latest neuroimaging techniques has the potential to both create new avenues of research and improve current research designs in the study of the brain. The next step is to apply the new algorithm to actual fMRI studies in one of Dr. Aguirre's major research areas, visual perception, and representation in the brain.

"The amazing thing is the person in the experiment just sees random pictures,” Dr. Aguirre concluded. "But in fact, we're hiding in this seemingly random sequence a signal that's invisible to the person but can be decoded by the MRI scanner. We can measure the nerve cells' response to that hidden pattern and then use that to understand how the brain is representing information.”

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