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Complex thoughts are enabled by fractal networks

Complex thoughts are enabled by fractal networks

Fractals are forms that seem similar at different sizes in the area of geometry. Shapes and patterns within a fractal are repeated in an infinite cascade, such as spirals made up of smaller spirals that are made up of even smaller spirals, and so on.

Previous research has shown how the brain uses fractal networks for better connectivity. A new study from Dartmouth College has discovered a novel approach to examine brain networks by employing the mathematical concept of fractals to express communication patterns between various brain areas as individuals listened to a short tale. Their results show that patterns of brain interactions are mirrored simultaneously at different scales.

“To generate our thoughts, our brains create this amazing lightning storm of connection patterns,” said senior author Jeremy R. Manning, an assistant professor of psychological and brain sciences, and director of the Contextual Dynamics Lab at Dartmouth.“The patterns look beautiful, but they are also incredibly complicated. Our mathematical framework lets us quantify how those patterns relate at different scales, and how they change over time.”

The elucidation of the neural code, i.e. the mapping between (a) mental states or cognitive representations and (b) neuronal activity patterns, is a key objective in cognitive neuroscience. One way to put neural code models to the test is to see how well they “translate” neural activity patterns into known (or speculated) mental states or cognitive representations.

When people think about complicated things, their networks appear to spontaneously arrange into fractal-like patterns. When such thoughts are interrupted, the fractal patterns jumble and lose their integrity.

The researchers created a mathematical framework for detecting commonalities in network interactions at various sizes or “orders.” The scientists referred to this as a “zero-order” pattern when brain areas did not display any regular patterns of interaction.

A “first-order” pattern occurs when individual pairs of brain regions interact. “Second-order” patterns are comparable patterns of interactions in distinct sets of brain regions at various sizes. When interaction patterns become fractal—“first-order” or higher—the order specifies how many times the patterns are reproduced at different sizes. According to the findings, when participants listened to an audio recording of a 10-minute tale, their brain networks spontaneously formed into fourth-order network patterns.

Each color corresponds to one order of inter-subject functional correlations. To calculate the dynamic correlations, eigenvector centrality has been used to project the high-dimensional patterns of dynamic correlations onto a lower-dimensional space at each previous order, which allows us to map the brain regions at each order by retaining the features of the original space. The inflated brain plots display the locations of the endpoints of the 10 strongest (absolute value) correlations at each order, thresholded at 0.999, and projected onto the cortical surface91. The lists of terms on the right display the top five Neurosynth terms38 decoded from the corresponding brain maps for each order. Each row displays data from a different experimental condition.

This structure, however, was shattered when individuals listened to edited copies of the tape. People’s brain networks exhibited only second-order patterns when the story’s paragraphs were randomly mixed, maintaining some but not all of the story’s meaning. All except the lowest level (zero-order) patterns were broken when every word in the tale was jumbled.

“Since the disruptions in those fractal patterns seemed directly linked with how well people could make sense of the story, this finding may provide clues about how our brain structures work together to understand what is happening in the narrative.”

The results reveal that first- and second-order correlations were most significantly related with auditory and speech processing regions for all of the narrative listening conditions (intact, paragraph, and word; top three rows). Third-order correlations during intact narrative listening showed integration with visual regions, whereas fourth-order correlations reflected integration with areas linked with high-level cognition and cognitive control.

The researchers believe that when these networks organize at many dimensions, it may reveal how the brain transforms raw sensory input into sophisticated thought—from raw noises to speech, imagery, and full-on comprehension.

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The fractal network patterns were remarkably comparable across people: patterns from one group could properly predict what section of the tale another group was listening to.

The computational framework developed by the researchers may be extended to fields other than neurology, and the team has already begun to use an equivalent technique to investigate connections in stock prices and animal migratory patterns.

High-level cognition during story listening is reflected in high-order dynamic correlations in neural activity patterns, by Lucy L. W. Owen, Thomas H. Chang & Jeremy R. Manning

Published: September 2021

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