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Functional optimality of the sulcus pattern of the human brain

Heyden, S. and Ortiz, M. (2019) Functional optimality of the sulcus pattern of the human brain. Mathematical Medicine and Biology, 36 (2). pp. 207-221. ISSN 1477-8599. doi:10.1093/imammb/dqy007.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Heyden, S.0000-0002-7035-7975
Ortiz, M.0000-0001-5877-4824
Additional Information:© The Author(s) 2018. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model ( Received: 16 January 2018; Revision Received: 08 May 2018; Accepted: 10 May 2018; Published: 28 May 2018. SH gratefully acknowledges support from the Alexander von Humboldt Stiftung through a Research Fellowship for Postdoctoral Researchers.
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Alexander von Humboldt FoundationUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20180604-073442987
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Official Citation:S Heyden, M Ortiz, Functional optimality of the sulcus pattern of the human brain, Mathematical Medicine and Biology: A Journal of the IMA, Volume 36, Issue 2, June 2019, Pages 207–221,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:86769
Deposited By: Tony Diaz
Deposited On:04 Jun 2018 18:18
Last Modified:15 Nov 2021 20:42

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