Sotero Roberto C, Shmuel Amir
Montreal Neurological Institute, Departments of Neurology and Neurosurgery and Biomedical Engineering, McGill University, Montreal, Quebec, Canada.
J Comput Neurosci. 2012 Jun;32(3):563-76. doi: 10.1007/s10827-011-0370-8. Epub 2011 Nov 1.
Several studies posit energy as a constraint on the coding and processing of information in the brain due to the high cost of resting and evoked cortical activity. This suggestion has been addressed theoretically with models of a single neuron and two coupled neurons. Neural mass models (NMMs) address mean-field based modeling of the activity and interactions between populations of neurons rather than a few neurons. NMMs have been widely employed for studying the generation of EEG rhythms, and more recently as frameworks for integrated models of neurophysiology and functional MRI (fMRI) responses. To date, the consequences of energy constraints on the activity and interactions of ensembles of neurons have not been addressed. Here we aim to study the impact of constraining energy consumption during the resting-state on NMM parameters. To this end, we first linearized the model, then used stochastic control theory by introducing a quadratic cost function, which transforms the NMM into a stochastic linear quadratic regulator (LQR). Solving the LQR problem introduces a regime in which the NMM parameters, specifically the effective connectivities between neuronal populations, must vary with time. This is in contrast to current NMMs, which assume a constant parameter set for a given condition or task. We further simulated energy-constrained stochastic control of a specific NMM, the Wilson and Cowan model of two coupled neuronal populations, one of which is excitatory and the other inhibitory. These simulations demonstrate that with varying weights of the energy-cost function, the NMM parameters show different time-varying behavior. We conclude that constraining NMMs according to energy consumption may create more realistic models. We further propose to employ linear NMMs with time-varying parameters as an alternative to traditional nonlinear NMMs with constant parameters.
由于静息和诱发皮质活动的高成本，多项研究认为能量是大脑中信息编码和处理的一个限制因素。这一观点已通过单个神经元和两个耦合神经元的模型从理论上进行了探讨。神经群体模型（NMMs）处理基于平均场的神经元群体活动及其相互作用的建模，而非少数神经元的建模。NMMs已被广泛用于研究脑电图节律的产生，最近还作为神经生理学和功能磁共振成像（fMRI）反应综合模型的框架。迄今为止，能量限制对神经元集合活动及其相互作用的影响尚未得到探讨。在此，我们旨在研究静息状态下限制能量消耗对NMM参数的影响。为此，我们首先将模型线性化，然后通过引入二次代价函数使用随机控制理论，这将NMM转化为随机线性二次调节器（LQR）。求解LQR问题引入了一种机制，其中NMM参数，特别是神经元群体之间的有效连接性，必须随时间变化。这与当前的NMMs形成对比，后者在给定条件或任务下假设参数集是恒定的。我们进一步模拟了特定NMM（两个耦合神经元群体的威尔逊和考恩模型，其中一个是兴奋性的，另一个是抑制性的）的能量受限随机控制。这些模拟表明，随着能量代价函数权重的变化，NMM参数呈现出不同的时变行为。我们得出结论，根据能量消耗对NMMs进行限制可能会创建更现实的模型。我们还进一步建议采用具有时变参数的线性NMMs作为具有恒定参数的传统非线性NMMs的替代方案。
