Brain scientist models neural networks on forest fire patterns

By Joel Lanceta

University researchers, led by Dr. Jack Cowan, using the patterns of forest fires to better understand how the brain functions, have conceived a new model of simulated neural behavior in which neurons around the visual cortex of the brain experience clustered bursts of activity, rather than in a spiral or a wave form.

According to Cowan, a professor in mathematics, in neurology, and on the Committee on Computational Neuroscience at Chicago, the finding adds confusion to a growing argument in his field.

“A big debate has been going on for at least a decade now about how to interpret the firing patterns in the cortex,” Cowan said. “This adds a new wrinkle to that debate.”

Makoto Fukushima, a psychology graduate student with a master’s degree in physics has been helping Cowan’s research for about a year.

“I do not try to equate the real forest fire to the brain, but the forest fire model is one of the simplest models analogous to the neural network model,” Fukushima said of the study. “Because of the abstract nature of the model, we can apply the same mathematical architecture for the forest fire to understand a completely different phenomenon: behavior of the brain. This is one of the fascinating things that we can do with mathematical models.”

Cowan’s research was inspired by complexity theory, a statistical relationship between phenomena as varied as forest fires, earthquakes, traffic-flow patterns, the size of cities and, in this case, brain-wave fluctuations.

Another inspiration, however, for Cowan came from the late Danish theoretical physicist Per Bak, whose work employed a forest fire analogy. The experiment compared burning trees to firing neurons in the brain, where verdant trees awaiting the fire corresponded to neurons preparing to produce a pulse, and burnt trees corresponded to neurons recovering from firing a pulse.

“Because of its simplicity, this research may allow us to find out the minimum architecture required to produce complex spatio-temporal patterns in the network,” Fukushima said. “Then, once it is found out, we may be able to interpret the firing pattern in the brain in terms of the architecture of the network underlying it.”

Cowan began his studies 30 years ago developing a basic theory of how large-scale brain activity works. A few years later, he introduced a three-state neural model for the brain’s inner workings. The model illustrated how neurons exist in one of three states: building up to a pulse, producing a pulse, and the aftermath of a pulse.

Bak’s forest fire analogy struck Cowan as similar to his research.

“It’s clear that this forest fire model is a version of the three-state model,” Cowan said. “Right away it triggered my interest.”

Students who helped Cowan’s research are thrilled by the initial findings and its potential for further research.

“There currently is something of a debate about the role of synchronous behavior in neural dynamics,” said Michael Buice, a physics graduate student involved in the research. “These discussions impact the understanding of diseases such as Parkinson’s and epilepsy.”

Tanya Baker, also a Physics graduate student involved in Cowan’s research, emphasized, however, that the study is still far from completion. The modeling of neurons is only one aspect of brain activity on which the reasearch team is focusing.

“As with other students in the research group, we are working on a number of problems,” Baker said. “Mainly our work has been to understand the population activity of the visual cortex and how it might encode and process information. We have been working extensively with a spherical model for orientation and spatial frequency tuning that was developed by Paul Bressloff and Jack Cowan.”

“This study is to try to understand better the vast literature on the subject, to understand how the forest fire analogy really maps onto a network of neurons, and to understand the phase plane of parameters that leads to very different population activity. This is all work in progress,” she said.

Cowan presented the initial findings of the study on February 14 at the annual meeting of the American Association for the Advancement of Science in Denver.