April 26, 2001
Vol. 20 No. 15

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    Mathematicians view unstable activity in brain to better understand circuitry of visual cortex

    By Steve Koppes
    News Office

    Scientists are deducing the internal circuitry of the visual brain by mathematically reproducing the geometric hallucinations people see when they ingest mind-altering drugs, view bright, flickering lights or encounter near-death experiences.

    The findings by the University’s Jack Cowan, the University of Utah’s Paul Bressloff and three of their colleagues provide new insights into the complexities of vision, the workings of the brain and even the origins of art.

    “We take it for granted, but seeing is an amazing process,” said Cowan, Professor in Mathematics and Neurology. “In something less than a second, we can see objects and classify them under all kinds of differing illumination from very dim to very bright. We’re just scratching the surface of what’s going on.”
    The mathematical study of vision and the brain recently appeared in the Philosophical Transactions of the Royal Society of London, Series B. Co-authoring the study were Martin Golubitsky, University of Houston; and two of Cowan’s former graduate students, Peter Thomas (Ph.D. ’00), Salk Institute for Biological Studies; and Matthew Wiener (Ph.D. ’94), National Institutes of Health.

    “We’re trying to understand how the intrinsic circuitry of the visual cortex of the brain can generate patterns of activity that underlie hallucinations,” Bressloff said. These geometric hallucinations take the form of checkerboards, honeycombs, tunnels, spirals and cobwebs, a phenomenon originally studied as early as the 1920s and 1930s by the late Heinrich Klüver, a pioneering Chicago neurologist.

    “Because we know how the eyes are wired to the visual cortex, we can calculate what the patterns actually look like there,” said Cowan. “They correspond very closely to the patterns that people report seeing.”

    A technique called “perturbation theory” proved crucial to reproducing the geometric patterns, Bressloff said. Also crucial was an understanding, based on recent advances in brain anatomy and physiology, of the strong short-range connections and weaker long-range connections between neurons in the visual cortex.
    “It is a situation where you have something strong and something else that’s weak, so it perturbs the system,” Bressloff said.

    The mathematics that model the perturbation are, coincidentally, similar to those used in calculating the Zeeman Effect in quantum mechanics, which describes the effects on hydrogen atoms of a weak magnetic field. Bressloff noted, however, that “there are no quantum mechanics involved in the actual working of the brain.”
    Academically trained in physics and electrical engineering, Cowan may be the world’s only university faculty member who holds dual appointments in mathematics and neurology. In 1986, he organized one of the founding workshops of the Santa Fe Institute, a private, not-for-profit research and education center devoted to the study of complexity and complex adaptive systems. He became interested in geometric hallucinations in the late 1970s, when he realized that they might provide clues regarding the brain’s circuitry.

    “Producing hallucinatory images in the brain could be understood in terms of spontaneous pattern formation in the brain,” Cowan said. “The brain makes patterns of activity when it becomes unstable.”

    Such instabilities follow the ingestion of such substances as LSD, psilocybin and cannabis, which act on control networks in the brainstem that secrete noradrenalin, seratonin and dopamine, which in turn control brain states.

    “If there’s any noise–random fluctuations of brain activity–in the brain, it is amplified into a pattern that reflects the architecture of the brain. The brain just takes the noise and shapes it into a pattern,” Cowan said. “In the case of geometric visual hallucinations this is a direct consequence of the pattern of connections in the visual cortex.”

    Some researchers foresee the day that blind people will see again following the implantation of a vision computer chip in the brain. “We’re a long way from that,” Cowan said. “So far, we’ve only described the interactions between edge detectors in the visual brain, but there are all kinds of things going on in the visual cortex. There’s detection of color and movement and depth and texture and surfaces. The circuitry involved in all of that is complicated and needs to be worked out.”

    Cowan, Bressloff and their colleagues are ready to continue the work. “It’s just the beginning of a long program of studying more and more complex hallucination patterns, trying to see how far we can go with deducing the intrinsic circuitry of the cortex,” said Bressloff.

    As for the origins of art, this June, Cowan will participate in a conference on this topic in Montana. Geometric patterns are a common design element in cave paintings and prehistoric rock art. Some experts trace the prehistoric origins of art to hallucinogenic experiences. “A lot of the imagery is clearly related to what people report seeing when they take hallucinogens,” Cowan said.