Chouzouris Teresa, Roth Nicolas, Cakan Caglar, Obermayer Klaus
Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Marchstraße 23, 10587 Berlin, Germany.
Bernstein Center for Computational Neuroscience Berlin, Philippstraße 13, 10115 Berlin, Germany.
Phys Rev E. 2021 Aug;104(2-1):024213. doi: 10.1103/PhysRevE.104.024213.
We apply the framework of optimal nonlinear control to steer the dynamics of a whole-brain network of FitzHugh-Nagumo oscillators. Its nodes correspond to the cortical areas of an atlas-based segmentation of the human cerebral cortex, and the internode coupling strengths are derived from diffusion tensor imaging data of the connectome of the human brain. Nodes are coupled using an additive scheme without delays and are driven by background inputs with fixed mean and additive Gaussian noise. Optimal control inputs to nodes are determined by minimizing a cost functional that penalizes the deviations from a desired network dynamic, the control energy, and spatially nonsparse control inputs. Using the strength of the background input and the overall coupling strength as order parameters, the network's state-space decomposes into regions of low- and high-activity fixed points separated by a high-amplitude limit cycle, all of which qualitatively correspond to the states of an isolated network node. Along the borders, however, additional limit cycles, asynchronous states, and multistability can be observed. Optimal control is applied to several state-switching and network synchronization tasks, and the results are compared to controllability measures from linear control theory for the same connectome. We find that intuitions from the latter about the roles of nodes in steering the network dynamics, which are solely based on connectome features, do not generally carry over to nonlinear systems, as had been previously implied. Instead, the role of nodes under optimal nonlinear control critically depends on the specified task and the system's location in state space. Our results shed new light on the controllability of brain network states and may serve as an inspiration for the design of new paradigms for noninvasive brain stimulation.
我们应用最优非线性控制框架来引导由菲茨休 - 纳古莫振荡器组成的全脑网络的动力学。其节点对应于基于图谱的人类大脑皮层分割的皮质区域，节点间耦合强度源自人类大脑连接组的扩散张量成像数据。节点采用无延迟的加法方案进行耦合，并由具有固定均值和加性高斯噪声的背景输入驱动。通过最小化一个成本函数来确定节点的最优控制输入，该成本函数对与期望网络动态的偏差、控制能量以及空间非稀疏控制输入进行惩罚。以背景输入强度和整体耦合强度作为序参量，网络的状态空间分解为由高振幅极限环分隔的低活动和高活动不动点区域，所有这些在定性上都对应于孤立网络节点的状态。然而，在边界处，可以观察到额外的极限环、异步状态和多稳定性。将最优控制应用于多个状态切换和网络同步任务，并将结果与针对相同连接组的线性控制理论的可控性度量进行比较。我们发现，如先前所暗示的那样，仅基于连接组特征的线性控制理论关于节点在引导网络动力学中作用的直觉，通常并不适用于非线性系统。相反，在最优非线性控制下节点的作用关键取决于指定任务以及系统在状态空间中的位置。我们的结果为脑网络状态的可控性提供了新的见解，并可能为无创脑刺激新范式的设计提供灵感。
