Department of Neurology, The University of Kansas Medical Center, Kansas City, KS, USA.
Eur J Neurosci. 2009 Oct;30(8):1554-8. doi: 10.1111/j.1460-9568.2009.06923.x. Epub 2009 Oct 12.
Relevant and timely questions such as regarding the predictability of seizures and their capacity to trigger more seizures remain the subject of debate in epileptology. The present study endeavors to gain insight into these dynamic issues by adopting a non-reductionist approach and via the use of mathematical tools. Probability distribution functions of seizure energies and inter-seizure intervals and the probability of seizure occurrence conditional upon the time elapsed from the previous seizure were estimated from prolonged recordings from subjects with pharmaco-resistant seizures, undergoing surgical evaluation, on reduced doses of or on no medications. The energy and inter-seizure interval distributions for pharmaco-resistant seizures, under the prevailing study conditions, are governed by power laws ('scale-free' behavior). Pharmaco-resistant seizures tend to occur in clusters and the time to the next seizure increases with the duration of the seizure-free interval since the last one. However, characteristic size energy probability density functions were found in a few subjects. These findings suggests that: (i) pharmaco-resistant seizures have an inherent self-triggering capacity; (ii) their time of occurrence and intensity may be predictable in light of the existence of power law distributions and of their self-triggering capacity; and (iii) their lack of typical size and duration (scale-free), features upon which their classification into ictal or interictal is largely based, may be inadequate/insufficient classifiers.
在癫痫学领域,关于发作的可预测性及其引发更多发作的能力等相关且及时的问题仍然存在争议。本研究通过采用非还原论方法和数学工具,努力深入了解这些动态问题。从接受手术评估的、药物剂量减少或无药物治疗的耐药性癫痫患者的长时间记录中,我们估计了发作能量和发作间期的概率分布函数,以及在前一次发作后经过的时间条件下发生发作的概率。在当前研究条件下,耐药性癫痫的能量和发作间期分布受幂律(“无标度”行为)控制。耐药性癫痫往往呈簇状发生,下一次发作的时间随着从上一次发作以来的无发作间隔时间的增加而增加。然而,在少数患者中发现了特征性大小能量概率密度函数。这些发现表明:(i) 耐药性癫痫具有内在的自触发能力;(ii) 鉴于幂律分布及其自触发能力的存在,它们的发生时间和强度可能是可预测的;(iii) 它们缺乏典型的大小和持续时间(无标度),这是其分类为发作期或发作间期的主要依据,可能不足以作为分类器。