Cerf Roger, El Ouasdad El Hassan, Kahane Philippe
FORENAP, Centre Hospitalier, 68250, Rouffach, France.
Biol Cybern. 2004 Apr;90(4):239-55. doi: 10.1007/s00422-004-0463-9. Epub 2004 Mar 30.
In extending our previous results demonstrating critical fluctuations in electropathophysiological brain activity prior to onset of partial epileptic seizures, we used once again Haken's approach to self-organized complex systems, which resorts to identifying an order parameter. A renormalized density in phase space and a renormalized differential density were defined and substituted for the Lerner density, which we used previously. Fluctuations in electropathophysiological activity, consisting of periods of high activity recorded from both depth and scalp electrodes in six presurgical patients, were characterized on different time scales. Extension in space of the fluctuations was characterized by observing their synchronous occurrence in different areas of the brain. By simultaneously establishing the fluctuations' criticality, we were observing "synchronous instabilities". Criticality followed from characterizing the time course of the synchronously arising fluctuations, when approaching seizure onset (i). by their slowing, for the longer-lasting ones (up to about 2 min), and (ii). by their increase in rate of production, for those of shorter duration (up to 20-30 s). Critical behavior may be displayed in favorable cases over more than 1 h prior to seizure onset. Other effects are also described that in some cases may interfere with the simple time course of fluctuations and must be given further consideration, particularly with a view to application to seizure anticipation. Because periods of high activity are involved, any marker of increased electropathophysiological activity in the brain may, in principle, play the role of an order parameter or of an approximate order parameter, e.g., a signal's root-mean-square amplitude, or its excess energy content. Such markers may be put to use for the fluctuations they display or merely for their average time evolution prior to seizure onset. We compared the time evolution, prior to onset, of the excess production rate of synchronies and of the signals' excess energy content, both averaged over signal sections of a chosen duration. In view of potential noninvasive applications, those scalp electrodes showing effects similar to the observations we made at the epileptogenic focus were identified, and the time course of their order parameters prior to seizure onset was analyzed.
在扩展我们之前的研究结果时，我们再次使用了哈肯（Haken）关于自组织复杂系统的方法，该方法通过识别一个序参量来证明部分癫痫发作前脑电生理活动中的临界波动。定义了相空间中的重整化密度和重整化微分密度，并将其替代我们之前使用的勒纳（Lerner）密度。对六名手术前患者深部和头皮电极记录的高活动期组成的电生理活动波动在不同时间尺度上进行了表征。波动在空间上的扩展通过观察其在大脑不同区域的同步出现来表征。通过同时确定波动的临界性，我们观察到了“同步不稳定性”。临界性源于表征接近癫痫发作开始时同步出现的波动的时间进程：（i）对于持续时间较长（长达约2分钟）的波动，通过其变慢；（ii）对于持续时间较短（长达20 - 30秒）的波动，通过其产生速率的增加。在有利情况下，临界行为可能在癫痫发作开始前超过1小时出现。还描述了其他一些效应，在某些情况下这些效应可能会干扰波动的简单时间进程，必须进一步加以考虑，特别是考虑到其在癫痫发作预测中的应用。由于涉及高活动期，大脑中任何电生理活动增加的标志物原则上都可能起到序参量或近似序参量的作用，例如信号的均方根振幅或其多余能量含量。此类标志物可用于它们所显示的波动，或仅用于癫痫发作开始前它们的平均时间演变。我们比较了同步的多余产生速率和信号多余能量含量在发作前的时间演变，两者均在选定持续时间的信号段上进行平均。鉴于潜在的非侵入性应用，识别出那些显示出与我们在癫痫病灶处观察到的效应相似的头皮电极，并分析了它们在癫痫发作开始前序参量的时间进程。
