Abstract
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.
Highlights
Multistability is a widespread phenomenon in the field of dynamical systems where a system exhibits multiple stable states or more generally attractors [1]
In previous work [34], we have shown that, for d = 2, the ct-gated recurrent unit (GRU) is capable of expressing a single limit cycle in phase space under the following set of parameters:
An electronic testbed for intelligent neurostimulation methods was developed from a physical realization of the dynamical system underlying the architecture of an artificial gated recurrent neural network
Summary
Multistability is a widespread phenomenon in the field of dynamical systems where a system exhibits multiple stable states or more generally attractors [1]. We hypothesized that multistability underlie some dynamical neurological diseases such that manifested symptoms are fundamentally due to the inability to naturally transition from one basin of attraction to another Under this hypothesis, neurostimulation techniques provide a means to perturb neural systems to assist transition between attractors as a treatment option. Given that the state of the system is sufficiently close to one of the two attractors, an intelligent stimulation algorithm can be tested by trying to perturb the system into the other basin of attraction While this may seem like a substantial simplification of global brain dynamics for typical neurological function, when viewing brain activity at different spatiotemporal scales under specific conditions far fewer attracting states may be present. The addition of this nonlinear stimulator circuit will ensure random or periodic stimulation patterns will be ineffective in inducing transitions between the two attractor states
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