Ly Cheng, Shew Woodrow L, Barreiro Andrea K
Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, USA.
Department of Physics, University of Arkansas, Fayetteville, USA.
J Math Neurosci. 2019 May 9;9(1):2. doi: 10.1186/s13408-019-0070-7.
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.
理解神经系统功能需要仔细研究神经元对来自外部世界快速变化的噪声输入的瞬态（非平衡）神经反应。这种神经反应源于多个异质脑区之间的动态相互作用。对这些大型网络进行逼真的建模需要巨大的计算资源，尤其是在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态；然而，在许多情况下，准稳态假设并不成立。在这里，我们为一个接收背景相关噪声输入的一般异质发放率模型开发了一种新的简化方法，该方法能够准确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高效的非线性常微分方程，而不是耗时的蒙特卡罗模拟或高维偏微分方程，并且它能够捕捉整个一阶和二阶统计集，同时允许所有模型参数存在显著的异质性。
