人类大脑沟模式的功能优化。

IF 0.8 4区 数学 Q4 BIOLOGY
S Heyden, M Ortiz
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引用次数: 4

摘要

我们开发了一个通过人类大脑的生物神经网络传递信息的数学模型。大脑的整体功能由信息通过神经网络传播而产生的突发过程组成。因此,大脑的容量与它通过神经网络传递信息的速度有关。正在考虑的特定传输模型允许信息沿着皮质点之间的多条路径传输。由此产生的传输速率由电位理论控制。根据这一理论,大脑具有与经典Steklov特征值问题的特征函数相对应的首选和量化的传输模式,其倒数特征值量化了相应的传输速率。我们将该模型作为检验假设的基础,即人类大脑的沟模式已经进化到最大化大脑皮层中点之间的信息传输速率。我们表明,在平滑域中引入沟槽或切割确实增加了总体传输速率。我们通过数值实验证明了这一结果,该数值实验涉及球面上有不同数量的狭缝。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Functional optimality of the sulcus pattern of the human brain.

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.

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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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