Functional optimality of the sulcus pattern of the human brain

TL;DR

This paper models the human brain's neural network to show that sulcus patterns enhance information transmission rates, suggesting evolutionary optimization of brain structure for efficient communication.

Contribution

It introduces a mathematical model linking sulcus patterns to maximized information transmission, supported by numerical experiments on spherical domains with slits.

Findings

Sulcus patterns increase transmission rates in the brain model.

Preferred transmission modes correspond to Steklov eigenfunctions.

Numerical experiments confirm sulci improve information flow.

Abstract

We develop a mathematical model of information transmission across the biological neural network of the human brain. The overall function of the brain consists of the emergent processes resulting from the spread of information through the neural network. The capacity of the brain is therefore related to the rate at which it can transmit information through the neural network. The particular transmission model under consideration allows for information to be transmitted along multiple paths between points of the cortex. The resulting transmission rates are governed by potential theory. According to this theory, the brain has preferred and quantized transmission modes that correspond to eigenfunctions of the classical Steklov eigenvalue problem, with the reciprocal eigenvalues quantifying the corresponding transmission rates. We take the model as a basis for testing the hypothesis that the sulcus pattern of the human brain has evolved to maximize the rate of transmission of information between points in the cerebral cortex. We show that the introduction of sulci, or cuts, in an otherwise smooth domain indeed increases the overall transmission rate. We demonstrate this result by means of numerical experiments concerned with a spherical domain with a varying number of slits on its surface.