Cognitive and Systems Neuroscience Group, Center for Neuroscience, University of Amsterdam, Amsterdam, the Netherlands.
Neuroimage. 2010 May 15;51(1):112-22. doi: 10.1016/j.neuroimage.2010.01.073. Epub 2010 Jan 28.
Oscillatory activity is a widespread phenomenon in nervous systems and has been implicated in numerous functions. Signals that are generated by two separate neuronal sources often demonstrate a consistent phase-relationship in a particular frequency-band, i.e., they demonstrate rhythmic neuronal synchronization. This consistency is conventionally measured by the PLV (phase-locking value) or the spectral coherence measure. Both statistical measures suffer from significant bias, in that their sample estimates overestimate the population statistics for finite sample sizes. This is a significant problem in the neurosciences where statistical comparisons are often made between conditions with a different number of trials or between neurons with a different number of spikes. We introduce a new circular statistic, the PPC (pairwise phase consistency). We demonstrate that the sample estimate of the PPC is a bias-free and consistent estimator of its corresponding population parameter. We show, both analytically and by means of numerical simulations, that the population statistic of the PPC is equivalent to the population statistic of the squared PLV. The variance and mean squared error of the PPC and PLV are compared. Finally, we demonstrate the practical relevance of the method in actual neuronal data recorded from the orbitofrontal cortex of rats that engage in a two-odour discrimination task. We find a strong increase in rhythmic synchronization of spikes relative to the local field potential (as measured by the PPC) for a wide range of low frequencies (including the theta-band) during the anticipation of sucrose delivery in comparison to the anticipation of quinine delivery.
振荡活动是神经系统中广泛存在的现象，与许多功能有关。来自两个独立神经元源的信号通常在特定频带中表现出一致的相位关系，即表现出节律性神经元同步。这种一致性通常通过 PLV（锁相值）或谱相干性测量来衡量。这两种统计测量都存在显著的偏差，因为它们的样本估计值过高，无法反映有限样本大小的群体统计数据。这在神经科学中是一个重大问题，因为在不同试验次数的条件之间或不同脉冲数的神经元之间，经常进行统计比较。我们引入了一种新的循环统计量，即 PPC（成对相位一致性）。我们证明了 PPC 的样本估计是其相应群体参数的无偏一致估计量。我们通过解析和数值模拟表明，PPC 的群体统计量等同于平方 PLV 的群体统计量。比较了 PPC 和 PLV 的方差和均方误差。最后，我们在大鼠眶额皮质记录的实际神经元数据中证明了该方法的实际相关性，这些数据是在大鼠进行两种气味辨别任务时记录的。与奎宁相比，在预期蔗糖输送期间，与局部场电位（如 PPC 测量）相比，在广泛的低频范围内（包括 theta 波段），发现尖峰的节律性同步性显著增强。
