Abstract We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields — and predictions of the model — stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature — such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface — demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

Gerald K Cooray

Vernon Cooray

Karl Friston

Journal of Computational Neuroscience

计算神经科学杂志为适合神经科学计算和实验工作之间接口的论文提供了一个论坛。 《计算神经科学杂志》发表完整的原创论文、快速通讯和评论文章，描述与大脑和神经系统计算相关的理论和实验工作。特别鼓励结合理论和实验工作的论文。主要的理论论文应该处理与生物神经系统明显相关的问题。实验论文应该对神经系统的计算功能有影响，并且可以使用包括解剖学、电生理学、生物物理学、成像和分子生物学在内的各种方法中的任何一种来报告结果。研究神经系统病理生理机制的论文，或报告计算神经科学研究人员感兴趣的新技术的论文，包括神经数据分析方法的进展，从而深入了解神经系统的功能，也受到欢迎（在这种情况下，方法论论文应包括新方法的应用，举例说明它产生的见解）。预计从认知到细胞的所有分析水平都将在计算神经科学杂志上发表。

The Journal of Computational Neuroscience provides a platform for the exchange of ideas between computational and experimental neuroscience. This journal publishes original research articles, brief communications, and review papers that describe theoretical and experimental work related to the computation of the brain and nervous system. Papers that integrate theory and experiment are particularly encouraged. Major theoretical papers should address issues that are clearly relevant to biological neural systems, while experimental papers should impact the computational functions of the nervous system and may report results using a variety of methods, including anatomy, electrophysiology, biophysics, imaging, and molecular biology. Papers investigating the pathophysiological mechanisms of the nervous system, or reporting on new techniques of interest to computational neuroscientists, including advancements in neural data analysis methods that provide insights into the functioning of the nervous system, are also welcome (in such cases, methodological papers should include applications of new methods with examples illustrating the insights they generate). We expect to publish research at all levels of analysis, from cognition to cellular.

《Journal of Computational Neuroscience》为神经科学的计算与实验研究提供了一个交流平台。该期刊发表原创研究论文、快速通讯和评论文章，涵盖与大脑及神经系统计算相关的理论与实验工作。特别鼓励理论与实验相结合的研究。主要的理论论文应关注与生物神经系统密切相关的问题，而实验论文则需对神经系统的计算功能产生影响，研究方法可以包括解剖学、电生理学、生物物理学、成像技术和分子生物学等多种手段。关于神经系统病理生理机制的研究，或是介绍计算神经科学领域新技术的论文（尤其是那些展示新方法应用及其所带来的新见解的论文）也受到欢迎。我们期待涵盖从认知到细胞的各个分析层面的研究成果在《Journal of Computational Neuroscience》上发表。

Category	Quartile
医学	4
医学, 数学与计算生物学	4
医学, 神经科学	4

A cortical field theory – dynamics and symmetries

ivySCI AI Smartly Parses PDF, Answers Researchers' Questions, and Helps You Understand Papers in Seconds

Journal Info