Lewis C D, Gebber G L, Larsen P D, Barman S M
Department of Pharmacology and Toxicology, Michigan State University, East Lansing, Michigan 48824-1317, USA.
J Neurophysiol. 2001 Apr;85(4):1614-22. doi: 10.1152/jn.2001.85.4.1614.
Fano factor analysis was used to characterize the spike trains of single medullary neurons with sympathetic nerve-related activity in cats that were decerebrate or anesthetized with Dial-urethan or urethan. For this purpose, values (Fano factor) of the variance of the number of extracellularly recorded spikes divided by the mean number of spikes were calculated for window sizes of systematically varied length. For window sizes < or =10 ms, the Fano factor was close to one, as expected for a Bernoulli process with a low probability of success. The Fano factor dipped below one as the window size approached the shortest interspike interval (ISI) and reached its nadir at window sizes near the modal ISI. The extent of the dip reflected the shape (skewness) of the ISI histogram with the dip being smallest for the most asymmetric distributions. Most importantly, for a wide range of window sizes exceeding the modal ISI, the Fano factor curve took the form of a power law function. This was the case independent of the component (cardiac related, 10 Hz, or 2--6 Hz) of inferior cardiac sympathetic nerve discharge to which unit activity was correlated or the medullary region (lateral tegmental field, raphe, caudal and rostral ventrolateral medulla) in which the neuron was located. The power law relationship in the Fano factor curves was eliminated by randomly shuffling the ISIs even though the distribution of the intervals was unchanged. Thus the power law relationship arose from long-term correlations among ISIs that were disrupted by shuffling the data. The presence of long-term correlations across different time scales reflects the property of statistical self-similarity that is characteristic of fractal processes. In most cases, we found that mean ISI and variance for individual spike trains increased as a function of the number of intervals counted. This can be attributed to the clustering of long and short ISIs, which also is an inherent property of fractal time series. We conclude that the spike trains of brain stem sympathetic neurons have fractal properties.
采用Fano因子分析来表征猫的单个延髓神经元的放电序列，这些猫处于去大脑状态，或用Dial-乌拉坦或乌拉坦麻醉，且具有与交感神经相关的活动。为此，针对系统变化长度的窗口大小，计算细胞外记录的尖峰数量的方差值（Fano因子）除以尖峰的平均数量。对于窗口大小小于或等于10毫秒的情况，Fano因子接近1，这对于成功概率较低的伯努利过程来说是预期的。随着窗口大小接近最短峰峰间期（ISI），Fano因子降至1以下，并在接近模式ISI的窗口大小处达到最低点。下降的程度反映了ISI直方图的形状（偏度），对于最不对称的分布，下降最小。最重要的是，对于超过模式ISI的广泛窗口大小范围，Fano因子曲线呈幂律函数形式。无论单位活动与之相关的下心交感神经放电的成分（心脏相关、10赫兹或2 - 6赫兹）如何，也无论神经元所在的延髓区域（外侧被盖区、中缝、尾侧和嘴侧腹外侧延髓）如何，都是如此。即使间隔的分布不变，通过随机打乱ISI，Fano因子曲线中的幂律关系也会消除。因此，幂律关系源于ISI之间的长期相关性，而这种相关性会因数据打乱而被破坏。不同时间尺度上长期相关性的存在反映了分形过程所特有的统计自相似性属性。在大多数情况下，我们发现单个放电序列的平均ISI和方差随着计数间隔数量的增加而增加。这可归因于长ISI和短ISI的聚类，这也是分形时间序列的固有属性。我们得出结论，脑干交感神经元的放电序列具有分形特性。
