Zhang J
Department of Psychology, The University of Michigan, Ann Arbor 48109-1109, USA.
J Neurosci Methods. 1998 Mar 13;80(1):49-63. doi: 10.1016/s0165-0270(97)00194-5.
Event-related potentials (ERPs) are evoked brain potentials that are averaged across many trial repetitions with individual trials aligned (i.e. time-locked) to a specific behavioral event, typically the onset of the stimulus (s-lock) or the onset of the behavioral response (r-lock). These evoked potential averages may reflect brain activities during the stimulus encoding/analyzing stage (stimulus component waveform, or 'S-component'), during the response preparation/production stage (response component waveform, or 'R-component'), or a combination thereof. In the stimulus-locked average of the ensemble of the recorded waveforms (i.e. in the s-locked ERP), the contribution of an R-component will be convoluted, due to the trial-by-trial variance in reaction time (RT): so will an S-component in the r-locked ERP. It is shown here that the knowledge of (1) the s-locked and r-locked ERP waveforms constructed from the same ensemble of trials and (2) the RT distribution of this ensemble allows us to determine whether the recorded potential results from a single S-component, a single R-component, or a single intermediate ('decisional' or D-) component related to the transition of the two stochastically independent stages. If it can be assumed that the evoked potential is the result of a linear summation of an S-component and an R-component, then there is a unique recovery into these two components, such that the reconstructed waveform on an individual trial is a superposition of the two components with their relative offset determined by the RT of that trial and the ensemble average is the experimentally obtained s-locked and r-locked ERP waveforms. Two independent methods can be used to recover those components, one based on Fourier transform techniques which was first proposed by Hansen (1983) in the context of ERP component isolation and the other based on a recursive iteration approach through which the contamination of the R or S-component is successively removed from the s-locked or r-locked ERP waveforms, respectively. The iterative procedure is analytically proven to converge to the Fourier-based solution, demonstrating the equivalence of the two approaches. Finally, if the condition of a single intermediate D-component is satisfied, then one can recover this component waveform along with the probability distributions of the relative durations of the two underlying linear stages; however, there is always an equivalent pair of S- and R-component which also satisfy the same data set (s-locked and r-locked ERP waveforms and the overall RT distribution). In this case, the S/R-component assumption and the D-component assumption cannot be distinguished solely on the ground of the available data set. The technique developed here outlines the assumptions and the boundary conditions upon which ensemble ERP waveforms are to be analyzed and interpreted in terms of processing mechanisms related to stimulus, to response, or to the transition between the two.
事件相关电位（ERP）是通过多次试验重复进行平均得到的诱发电位，其中各个试验与特定行为事件对齐（即时间锁定），通常是刺激的开始（s锁定）或行为反应的开始（r锁定）。这些诱发电位平均值可能反映刺激编码/分析阶段（刺激成分波形，或“S成分”）、反应准备/产生阶段（反应成分波形，或“R成分”）或两者的组合期间的大脑活动。在记录波形集合的刺激锁定平均值中（即s锁定ERP中），由于反应时间（RT）的逐次试验变化，R成分的贡献会被卷积；r锁定ERP中的S成分也是如此。本文表明，（1）由同一试验集合构建的s锁定和r锁定ERP波形以及（2）该集合的RT分布的知识使我们能够确定记录的电位是来自单个S成分、单个R成分还是与两个随机独立阶段的转换相关的单个中间（“决策”或D-）成分。如果可以假设诱发电位是S成分和R成分线性叠加的结果，那么可以唯一地恢复为这两个成分，使得单个试验上重建的波形是这两个成分的叠加，它们的相对偏移由该试验的RT确定，并且总体平均值是实验获得的s锁定和r锁定ERP波形。可以使用两种独立的方法来恢复这些成分，一种基于傅里叶变换技术，该技术由汉森（1983年）在ERP成分分离的背景下首次提出，另一种基于递归迭代方法，通过该方法分别从s锁定或r锁定ERP波形中相继去除R或S成分的污染。迭代过程经过分析证明收敛于基于傅里叶的解，证明了两种方法的等效性。最后，如果满足单个中间D成分的条件，那么可以恢复该成分波形以及两个基础线性阶段相对持续时间的概率分布；然而，总是存在一对等效的S和R成分，它们也满足相同的数据集（s锁定和r锁定ERP波形以及总体RT分布）。在这种情况下，仅根据可用数据集无法区分S/R成分假设和D成分假设。本文开发的技术概述了在根据与刺激、反应或两者之间的转换相关的处理机制分析和解释总体ERP波形时所依据的假设和边界条件。
