Tripathi Richa, Gluckman Bruce J
Center for Neural Engineering, The Pennsylvania State University, University Park, PA, United States.
Indian Institute of Technology Gandhinagar, Gandhinagar, India.
Front Netw Physiol. 2022 Sep;2. doi: 10.3389/fnetp.2022.911090. Epub 2022 Sep 28.
Brain rhythms emerge from the mean-field activity of networks of neurons. There have been many efforts to build mathematical and computational embodiments in the form of discrete cell-group activities-termed neural masses-to understand in particular the origins of evoked potentials, intrinsic patterns of activities such as theta, regulation of sleep, Parkinson's disease related dynamics, and mimic seizure dynamics. As originally utilized, standard neural masses convert input through a sigmoidal function to a firing rate, and firing rate through a synaptic alpha function to other masses. Here we define a process to build mechanistic neural masses (mNMs) as mean-field models of microscopic membrane-type (Hodgkin Huxley type) models of different neuron types that duplicate the stability, firing rate, and associated bifurcations as function of relevant slow variables - such as extracellular potassium - and synaptic current; and whose output is both firing rate and impact on the slow variables - such as transmembrane potassium flux. Small networks composed of just excitatory and inhibitory mNMs demonstrate expected dynamical states including firing, runaway excitation and depolarization block, and these transitions change in biologically observed ways with changes in extracellular potassium and excitatory-inhibitory balance.
脑节律源自神经元网络的平均场活动。人们已做出诸多努力，以离散细胞群活动（即神经团）的形式构建数学和计算模型，尤其用于理解诱发电位的起源、诸如θ波等内在活动模式、睡眠调节、帕金森病相关动力学以及模拟癫痫发作动力学。最初使用时，标准神经团通过一个Sigmoid函数将输入转换为发放率，并通过一个突触α函数将发放率转换为其他神经团的发放率。在此，我们定义了一个构建机制性神经团（mNMs）的过程，将其作为不同神经元类型的微观膜型（霍奇金-赫胥黎型）模型的平均场模型，该模型复制了稳定性、发放率以及作为相关慢变量（如细胞外钾离子）和突触电流函数的相关分岔；并且其输出既是发放率，也是对慢变量（如跨膜钾离子通量）的影响。仅由兴奋性和抑制性mNMs组成的小型网络展示出包括发放、失控兴奋和去极化阻滞等预期的动力学状态，并且这些转变会随着细胞外钾离子和兴奋-抑制平衡的变化以生物学上可观察到的方式发生改变。
