Department of Non-linear Dynamics, Max Planck Institute for Dynamics and Self-Organization Göttingen, Germany ; Bernstein Center for Computational Neuroscience Göttingen, Germany ; Frankfurt Institute for Advanced Studies Frankfurt, Germany ; Department of Neurophysiology, Max Planck Institute for Brain Research Frankfurt, Germany.
Magnetoencephalography Unit, Brain Imaging Center, Johann Wolfgang Goethe University Frankfurt, Germany ; Ernst Strüngmann Institute for Neuroscience in Cooperation with Max Planck Society Frankfurt, Germany.
Front Syst Neurosci. 2014 Jun 24;8:108. doi: 10.3389/fnsys.2014.00108. eCollection 2014.
In self-organized critical (SOC) systems avalanche size distributions follow power-laws. Power-laws have also been observed for neural activity, and so it has been proposed that SOC underlies brain organization as well. Surprisingly, for spiking activity in vivo, evidence for SOC is still lacking. Therefore, we analyzed highly parallel spike recordings from awake rats and monkeys, anesthetized cats, and also local field potentials from humans. We compared these to spiking activity from two established critical models: the Bak-Tang-Wiesenfeld model, and a stochastic branching model. We found fundamental differences between the neural and the model activity. These differences could be overcome for both models through a combination of three modifications: (1) subsampling, (2) increasing the input to the model (this way eliminating the separation of time scales, which is fundamental to SOC and its avalanche definition), and (3) making the model slightly sub-critical. The match between the neural activity and the modified models held not only for the classical avalanche size distributions and estimated branching parameters, but also for two novel measures (mean avalanche size, and frequency of single spikes), and for the dependence of all these measures on the temporal bin size. Our results suggest that neural activity in vivo shows a mélange of avalanches, and not temporally separated ones, and that their global activity propagation can be approximated by the principle that one spike on average triggers a little less than one spike in the next step. This implies that neural activity does not reflect a SOC state but a slightly sub-critical regime without a separation of time scales. Potential advantages of this regime may be faster information processing, and a safety margin from super-criticality, which has been linked to epilepsy.
在自组织临界（SOC）系统中，雪崩大小分布遵循幂律。神经活动也观察到了幂律，因此有人提出 SOC 是大脑组织的基础。令人惊讶的是，对于体内尖峰活动，SOC 的证据仍然缺乏。因此，我们分析了清醒大鼠和猴子、麻醉猫的高度并行尖峰记录，以及人类的局部场电位。我们将这些与两种已建立的临界模型的尖峰活动进行了比较：Bak-Tang-Wiesenfeld 模型和随机分支模型。我们发现神经活动和模型活动之间存在根本差异。通过三种修改可以克服这两种模型之间的差异：（1）子采样，（2）增加模型的输入（这样可以消除时间尺度的分离，这是 SOC 和其雪崩定义的基础），以及（3）使模型稍微亚临界。神经活动与修改后的模型之间的匹配不仅适用于经典的雪崩大小分布和估计的分支参数，还适用于两个新的措施（平均雪崩大小和单个尖峰的频率），以及所有这些措施对时间-bin 大小的依赖性。我们的结果表明，体内神经活动表现为一种混合的雪崩，而不是时间上分离的雪崩，并且它们的全局活动传播可以通过以下原理来近似：平均一个尖峰在下一个步骤中触发不到一个尖峰。这意味着神经活动不反映 SOC 状态，而是反映没有时间尺度分离的稍微亚临界状态。这种状态的潜在优势可能是更快的信息处理，以及免受超临界状态的安全裕度，超临界状态与癫痫有关。
