Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models.

IF 2.3 4区 医学 Q1 Neuroscience Journal of Mathematical Neuroscience Pub Date : 2019-05-09 DOI:10.1186/s13408-019-0070-7
Cheng Ly, Woodrow L Shew, Andrea K Barreiro
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引用次数: 3

Abstract

Understanding nervous system function requires careful study of transient (non-equilibrium) neural response to rapidly changing, noisy input from the outside world. Such neural response results from dynamic interactions among multiple, heterogeneous brain regions. Realistic modeling of these large networks requires enormous computational resources, especially when high-dimensional parameter spaces are considered. By assuming quasi-steady-state activity, one can neglect the complex temporal dynamics; however, in many cases the quasi-steady-state assumption fails. Here, we develop a new reduction method for a general heterogeneous firing-rate model receiving background correlated noisy inputs that accurately handles highly non-equilibrium statistics and interactions of heterogeneous cells. Our method involves solving an efficient set of nonlinear ODEs, rather than time-consuming Monte Carlo simulations or high-dimensional PDEs, and it captures the entire set of first and second order statistics while allowing significant heterogeneity in all model parameters.

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耦合燃烧速率模型中非平衡统计量的高效计算。
理解神经系统的功能需要仔细研究瞬时(非平衡)神经对外界快速变化的嘈杂输入的反应。这种神经反应是由多个异质脑区之间的动态相互作用产生的。这些大型网络的真实建模需要大量的计算资源,特别是当考虑高维参数空间时。通过假设准稳态活动,可以忽略复杂的时间动力学;然而,在许多情况下,准稳态假设是不成立的。在这里,我们开发了一种新的简化方法,用于接收背景相关噪声输入的一般异质发射率模型,该模型可以准确地处理高度非平衡统计和异质细胞的相互作用。我们的方法涉及求解一组有效的非线性ode,而不是耗时的蒙特卡罗模拟或高维pde,并且它捕获了整个一阶和二阶统计数据集,同时允许所有模型参数中的显着异质性。
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Journal of Mathematical Neuroscience
Journal of Mathematical Neuroscience Neuroscience-Neuroscience (miscellaneous)
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审稿时长
13 weeks
期刊介绍: The Journal of Mathematical Neuroscience (JMN) publishes research articles on the mathematical modeling and analysis of all areas of neuroscience, i.e., the study of the nervous system and its dysfunctions. The focus is on using mathematics as the primary tool for elucidating the fundamental mechanisms responsible for experimentally observed behaviours in neuroscience at all relevant scales, from the molecular world to that of cognition. The aim is to publish work that uses advanced mathematical techniques to illuminate these questions. It publishes full length original papers, rapid communications and review articles. Papers that combine theoretical results supported by convincing numerical experiments are especially encouraged. Papers that introduce and help develop those new pieces of mathematical theory which are likely to be relevant to future studies of the nervous system in general and the human brain in particular are also welcome.
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