Deep brain stimulation (DBS) is an increasingly used medical treatment for various neurological disorders. While its mechanisms are not fully understood, experimental evidence suggests that through application of periodic electrical stimulation DBS may act to desynchronize pathologically synchronized populations of neurons resulting desirable changes to a larger brain circuit. However, the underlying mathematical mechanisms by which periodic stimulation can engender desynchronization in a coupled population of neurons is not well understood. In this work, a reduced phase-amplitude reduction framework is used to characterize the desynchronizing influence of periodic stimulation on a population of coupled oscillators. Subsequently, optimal control theory allows for the design of periodic, open-loop stimuli with the capacity to destabilize completely synchronized solutions while simultaneously stabilizing rotating block solutions. This framework exploits system nonlinearities in order to strategically modify unstable Floquet exponents. In the limit of weak neural coupling, it is shown that this method only requires information about the phase response curves of the individual neurons. The effects of noise and heterogeneity are also considered and numerical results are presented. This framework could ultimately be used to inform the design of more efficient deep brain stimulation waveforms for the treatment of neurological disease.

中文翻译：

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神经振荡器种群的最佳开环去同步。

深部脑刺激（DBS）是用于各种神经系统疾病的越来越多的药物。尽管尚未完全了解其机制，但实验证据表明，通过应用周期性的电刺激，DBS可能会使神经元的病理同步种群不同步，从而导致较大的大脑回路发生所需的变化。但是，对于周期性刺激可以在耦合的神经元群体中引起失步的基本数学机制还没有很好的理解。在这项工作中，使用减小的相位幅度减小框架来表征周期性激励对耦合振荡器群的去同步影响。随后，最优控制理论可以进行周期性的设计，开环刺激，具有使完全同步的解决方案不稳定的能力，同时又使旋转块解决方案稳定。该框架利用系统非线性来从策略上修改不稳定的Floquet指数。在弱神经耦合的极限中，表明该方法仅需要有关单个神经元的相位响应曲线的信息。还考虑了噪声和异质性的影响，并给出了数值结果。该框架最终可用于告知设计更有效的深部神经刺激波形，以治疗神经系统疾病。在弱神经耦合的极限中，表明该方法仅需要有关单个神经元的相位响应曲线的信息。还考虑了噪声和异质性的影响，并给出了数值结果。该框架最终可用于告知设计更有效的深部神经刺激波形，以治疗神经系统疾病。在弱神经耦合的极限中，表明该方法仅需要有关单个神经元的相位响应曲线的信息。还考虑了噪声和异质性的影响，并给出了数值结果。该框架最终可用于告知设计更有效的深部神经刺激波形，以治疗神经系统疾病。