In this paper, phase space reconstruction from stereo-electroencephalography data of ten patients with focal epilepsy forms a series of graphs. Those obtained graphs reflect the transition characteristics of brain dynamical system from pre-seizure to seizure of epilepsy. Interestingly, it is found that the rank of Laplacian matrix of these graphs has a sharp decrease when a seizure is close to happen, which thus might be viewed as a new potential biomarker in epilepsy. In addition, the reliability of this method is numerically verified with a coupled mass neural model. In particular, our simulation suggests that this potential biomarker can play the roles of predictive effect or delayed awareness, depending on the bias current of the Gaussian noise. These results may give new insights into the seizure detection.

在本文中，从 10 名局灶性癫痫患者的立体脑电图数据中重建相空间形成了一系列图形。获得的图表反映了脑动力系统从癫痫发作前到癫痫发作的转变特征。有趣的是，发现这些图的拉普拉斯矩阵的秩在癫痫发作即将发生时急剧下降，因此可能被视为癫痫的新潜在生物标志物。此外，该方法的可靠性通过耦合质量神经模型进行了数值验证。特别是，我们的模拟表明，这种潜在的生物标志物可以发挥预测效应或延迟感知的作用，这取决于高斯噪声的偏置电流。这些结果可能为癫痫检测提供新的见解。