Jordan Ian D, Park Il Memming
Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA.
Institute for Advanced Computing Science, Stony Brook University, Stony Brook, NY 11794, USA.
Entropy (Basel). 2020 May 11;22(5):537. doi: 10.3390/e22050537.
Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesized that some symptoms originate from the inability to spontaneously transition from one attractor to another. Using external perturbations, such as electrical pulses delivered by deep brain stimulation devices, it may be possible to induce such transition out of the pathological attractors. However, the induction of transition may be non-trivial, rendering the current open-loop stimulation strategies insufficient. In order to develop next-generation neural stimulators that can intelligently learn to induce attractor transitions, we require a platform to test the efficacy of such systems. To this end, we designed an analog circuit as a model for the multistable brain dynamics. The circuit spontaneously oscillates stably on two periods as an instantiation of a 3-dimensional continuous-time gated recurrent neural network. To discourage simple perturbation strategies, such as constant or random stimulation patterns from easily inducing transition between the stable limit cycles, we designed a state-dependent nonlinear circuit interface for external perturbation. We demonstrate the existence of nontrivial solutions to the transition problem in our circuit implementation.
脑动力学可表现出窄带非线性振荡和多稳定性。对于意识和运动控制障碍的一个子集，我们假设一些症状源于无法自发地从一个吸引子转变为另一个吸引子。利用外部扰动，如深部脑刺激装置传递的电脉冲，有可能诱导从病理吸引子中发生这种转变。然而，转变的诱导可能并非易事，使得当前的开环刺激策略并不充分。为了开发能够智能学习诱导吸引子转变的下一代神经刺激器，我们需要一个平台来测试此类系统的功效。为此，我们设计了一个模拟电路作为多稳态脑动力学的模型。该电路作为三维连续时间门控递归神经网络的一个实例，在两个周期上稳定地自发振荡。为了防止简单的扰动策略，如恒定或随机刺激模式轻易地诱导稳定极限环之间的转变，我们为外部扰动设计了一个状态依赖的非线性电路接口。我们在电路实现中证明了转变问题存在非平凡解。
