Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks
Fast numerical methods for simulating large-scale integrate-and-fire neuronal networks
复制标题
DOI：
10.1007/s10827-006-8526-7
复制
发表时间：
2007-02-01
影响因子：
1.2
通讯作者：
Cai, David
中科院分区：
文献类型：
--
作者：
Rangan, Aaditya V.;Cai, David
我们讨论了模拟大规模，集成和射击（I&F）神经元网络的数值方法。我们的数值方法中的重要元素是：(i)一个受神经生理学启发的积分因子，它将解作为一个数值上易于处理的积分方程，并允许我们获得稳定和准确的单个神经元轨迹（即电压和电导时间过程），即使在I&F神经元方程是僵硬的情况下，例如在强烈波动，高电导状态下；（ii）在强耦合神经元组内进行峰-峰校正的迭代过程，以解释单个大数值时间步长的峰-峰相互作用；（iii）网络中触发事件的聚类过程，以利用局部架构，例如强局部相互作用的空间尺度，这通常存在于大规模计算模型中，例如初级视觉皮层。（我们注意到，在我们的方法中，尖峰校正比在模拟I&F神经网络中常用的改进龙格-库塔方法中通过多项式插值对单个神经元尖峰时间的校正更复杂。）我们的方法可以以渐近最优的方式进化具有相对强的局部相互作用的网络，使得每个神经元在O(N)次操作中大约触发一次，其中N是系统中神经元的数量。我们注意到，在计算建模中使用的量化通常是统计的，因为在真实实验中表征生理系统的测量通常是统计的，例如放电率、尖峰间隔分布和尖峰触发电压分布。我们强调，解决某些I&F神经网络的统计特性比完全解决系统中每个神经元的轨迹需要更少的计算努力。对于运行在现实动态状态下的网络，如强波动、高电导状态，我们的方法被设计为在使用非常大的时间步长时实现统计精度。此外，当使用小时间步长时，我们的方法也可以实现轨迹智能精度。
We discuss numerical methods for simulating large-scale, integrate-and-fire (I&F) neuronal networks. Important elements in our numerical methods are (i) a neurophysiologically inspired integrating factor which casts the solution as a numerically tractable integral equation, and allows us to obtain stable and accurate individual neuronal trajectories (i.e., voltage and conductance time-courses) even when the I&F neuronal equations are stiff, such as in strongly fluctuating, high-conductance states; (ii) an iterated process of spike-spike corrections within groups of strongly coupled neurons to account for spike-spike interactions within a single large numerical time-step; and (iii) a clustering procedure of firing events in the network to take advantage of localized architectures, such as spatial scales of strong local interactions, which are often present in large-scale computational models-for example, those of the primary visual cortex. (We note that the spike-spike corrections in our methods are more involved than the correction of single neuron spike-time via a polynomial interpolation as in the modified Runge-Kutta methods commonly used in simulations of I&F neuronal networks.) Our methods can evolve networks with relatively strong local interactions in an asymptotically optimal way such that each neuron fires approximately once in O(N) operations, where N is the number of neurons in the system. We note that quantifications used in computational modeling are often statistical, since measurements in a real experiment to characterize physiological systems are typically statistical, such as firing rate, interspike interval distributions, and spike-triggered voltage distributions. We emphasize that it takes much less computational effort to resolve statistical properties of certain I&F neuronal networks than to fully resolve trajectories of each and every neuron within the system. For networks operating in realistic dynamical regimes, such as strongly fluctuating, high-conductance states, our methods are designed to achieve statistical accuracy when very large time-steps are used. Moreover, our methods can also achieve trajectory-wise accuracy when small time-steps are used.