Perceptual Networks Group, University of Fribourg, Fribourg, Switzerland.
Laboratory of Psychophysics, Brain Mind Institute, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland.
PLoS Comput Biol. 2020 Aug 17;16(8):e1007566. doi: 10.1371/journal.pcbi.1007566. eCollection 2020 Aug.
Brain networks are complex dynamical systems in which directed interactions between different areas evolve at the sub-second scale of sensory, cognitive and motor processes. Due to the highly non-stationary nature of neural signals and their unknown noise components, however, modeling dynamic brain networks has remained one of the major challenges in contemporary neuroscience. Here, we present a new algorithm based on an innovative formulation of the Kalman filter that is optimized for tracking rapidly evolving patterns of directed functional connectivity under unknown noise conditions. The Self-Tuning Optimized Kalman filter (STOK) is a novel adaptive filter that embeds a self-tuning memory decay and a recursive regularization to guarantee high network tracking accuracy, temporal precision and robustness to noise. To validate the proposed algorithm, we performed an extensive comparison against the classical Kalman filter, in both realistic surrogate networks and real electroencephalography (EEG) data. In both simulations and real data, we show that the STOK filter estimates time-frequency patterns of directed connectivity with significantly superior performance. The advantages of the STOK filter were even clearer in real EEG data, where the algorithm recovered latent structures of dynamic connectivity from epicranial EEG recordings in rats and human visual evoked potentials, in excellent agreement with known physiology. These results establish the STOK filter as a powerful tool for modeling dynamic network structures in biological systems, with the potential to yield new insights into the rapid evolution of network states from which brain functions emerge.
大脑网络是复杂的动力系统，其中不同区域之间的定向相互作用在感觉、认知和运动过程的亚秒级尺度上演变。然而，由于神经信号的高度非平稳性质及其未知的噪声分量，对动态大脑网络进行建模一直是当代神经科学的主要挑战之一。在这里，我们提出了一种新的算法，该算法基于卡尔曼滤波器的创新公式，针对在未知噪声条件下跟踪快速演变的定向功能连接模式进行了优化。自调谐优化卡尔曼滤波器（STOK）是一种新颖的自适应滤波器，它嵌入了自调谐记忆衰减和递归正则化，以保证高网络跟踪精度、时间精度和对噪声的鲁棒性。为了验证所提出的算法，我们在真实的替代网络和真实的脑电图（EEG）数据中对其与经典卡尔曼滤波器进行了广泛的比较。在模拟和真实数据中，我们表明 STOK 滤波器以显著优越的性能估计了定向连通性的时频模式。在真实的 EEG 数据中，STOK 滤波器的优势更为明显，该算法从大鼠和人类视觉诱发电位的头皮 EEG 记录中恢复了动态连通性的潜在结构，与已知的生理学结果非常吻合。这些结果确立了 STOK 滤波器作为建模生物系统中动态网络结构的有力工具，有望为大脑功能出现的网络状态的快速演变提供新的见解。
