School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia and Center for Integrative Brain Function, University of Sydney, Sydney, New South Wales 2006, Australia.
Phys Rev E. 2019 Jan;99(1-1):012421. doi: 10.1103/PhysRevE.99.012421.
Brain connectivity and structure-function relationships are analyzed from a physical perspective in place of common graph-theoretic and statistical approaches that overwhelmingly ignore the brain's physical structure and geometry. Field theory is used to define connectivity tensors in terms of bare and dressed propagators, and discretized representations are implemented that respect the physical nature and dimensionality of the quantities involved, retain the correct continuum limit, and enable diagrammatic analysis. Eigenfunction analysis is used to simultaneously characterize and probe patterns of brain connectivity and activity, in place of statistical or phenomenological patterns. Physically based measures that characterize the connectivity are then developed in coordinate and spectral domains; some of which generalize or rectify graph-theoretic measures to implement correct dimensionality and continuum limits, and some replace graph-theoretic quantities. Traditional graph-based measures are shown to be highly prone to artifacts introduced by discretization and threshold, often because essential physical constraints have not been imposed, dimensionality has not been included, and/or distinctions between scalar, vector, and tensor quantities have not been considered. The results can replace them in ways that converge correctly and measure properties of brain structure, rather than of its discretization, and thus potentially enable physical interpretation of the many phenomenological results in the literature. Geometric effects are shown to dominate in determining many brain properties and care must be taken not to interpret geometric differences as differences in intrinsic neural connectivity. The results demonstrate the need to use systematic physical methods to analyze the brain and the potential of such methods to obtain new insights from data, make new predictions for experimental test, and go beyond phenomenological classification to dynamics and mechanisms.
从物理角度分析大脑连接和结构-功能关系，取代了普遍忽略大脑物理结构和几何形状的常见图论和统计方法。用场论定义连接张量，用裸露和 dressed 传播子来表示，并实现离散化表示，这些表示尊重所涉及的物理性质和维度，保留正确的连续极限，并能够进行图表分析。本研究采用特征函数分析来同时描述和探测大脑连接和活动模式，而不是采用统计或唯象模式。然后在坐标和谱域中开发了描述连接的物理基础度量；其中一些将图论度量推广或修正为实施正确的维度和连续极限，而另一些则取代图论量。研究表明，传统的基于图的度量很容易受到离散化和阈值引入的伪影的影响，这主要是因为没有施加基本的物理约束，没有包含维度，并且/或者没有考虑标量、向量和张量量之间的区别。本研究的结果可以以正确收敛的方式替代它们，衡量大脑结构的性质，而不是其离散化的性质，从而有可能为文献中的许多唯象结果提供物理解释。研究表明，几何效应在决定许多大脑性质方面起着主导作用，因此必须注意不要将几何差异解释为内在神经连接的差异。研究结果表明，需要使用系统的物理方法来分析大脑，以及这些方法从数据中获得新见解、为实验测试做出新预测以及超越唯象分类到动力学和机制的潜力。
