Mathematical formulas versus the brain’s mysteries: a new perspective on autism and aging

A new study by an international team of scientists shows that rigorous mathematical methods can help better understand how brain function changes with age and in autism spectrum disorder. The work was carried out by experts in mathematics and neuroscience and published in the journal Patterns.

Modern brain imaging techniques make it possible to observe how different brain regions interact with one another even at rest. However, such data are extremely complex: hundreds of brain areas form an intricate network of connections, and it is not always clear which of them are truly important. In the new study, the researchers applied a mathematical approach that analyzes not individual connections, but the overall structure and stability of the entire system.

Instead of setting arbitrary thresholds for “strong” and “weak” connections in advance, the scientists tracked which elements of the brain network persist across different levels of interaction and which disappear quickly. This made it possible to determine which brain regions play a key role in the overall organization of brain function. To achieve this, the researchers introduced a new metric that reflects how stably a particular brain region is integrated into the activity of the whole network.

An analysis of data from more than a thousand individuals showed that brain networks in young adults are generally more complex and stable than those in older people. In autism, the picture is different: connections between brain regions appear less organized, and the overall structure is more variable. At the same time, these changes do not affect the entire brain uniformly. With aging, regions associated with movement and attention show the most pronounced changes, whereas in autism the differences are most evident in areas responsible for social interaction, cognition, and information processing.

The researchers identified dozens of specific brain regions where the structure of connections differs in autism, as well as more than a hundred regions that are sensitive to age-related changes. Many of these areas have previously been linked to memory, speech, movement, and social behavior.

The authors emphasize that the value of this approach lies not only in detecting differences, but also in the ability to pinpoint exactly where they arise. In the future, this could contribute to more precise diagnostics and to the development of new therapeutic strategies.