Control of Dynamic Patterns in Neuronal Networks

在过去的十年中，神经刺激技术的开发和使用在操纵大脑中的神经活动方面取得了显着的增长。 这种技术的应用范围从科学目标，例如，研究大脑的不同部分如何相互作用，以达到临床目的，例如，使用刺激来缓解神经系统疾病的症状，如帕金森氏病。尽管有许多与这种刺激相关的技术进步，但其使用仍然在很大程度上限于微扰范式，其中刻板的输入（波形）用于激活或去激活整个神经元网络。换句话说，刺激用于创建统一的电路响应，打开或关闭整个脑细胞（神经元）群体，而不考虑特异性（即，群体中的哪些细胞响应）或定时（即，当它们打开或关闭时）。在工程学中，控制不被理解为简单的均匀刺激，而是在每一时刻精确地创建或阻止某些系统动作。这个项目将调查有关使用神经刺激来控制神经网络在这个时间上精确的意义上的基本问题。也就是说，这项研究的目标不是简单地刺激大脑，而是开发新的工程理论和方法，使从业者能够控制神经回路中的活动，从而创造复杂的活动模式或神经尖峰。因此，这个高度跨学科的项目将阐明使理论的神经刺激的使用，并将导致新的和基本的贡献，系统理论和控制工程。该项目还将支持新的举措，以促进跨学科教育的学生从传统上服务不足的人口，通过创建夏季讲习班，从当地的高中学生在圣路易斯市，MO。通过桥接合奏系统理论与计算神经科学，一般和通用的框架神经元控制将制定。具体来说，振荡器和电导为基础的神经模型将被用来数学建模的振荡和非振荡制度的大脑网络。使用这些模型，所提出的工作将确定基本限制的可控性神经元尖峰或同步的应用程序的外部输入。集成可达性的概念也被提出，并将通过熵增益分析和动态优化检查。振荡和非振荡的神经动力学制度的基本控制特性的这些特征，然后将促进控制设计范例的发展，以合成最佳控制，用于在神经元群体中创建复杂的模式，如发射或夹带模式。合奏控制和正式平均的方法将被用来获得最佳的序列和模式控制，这些问题的随机版本也将被视为使用随机控制技术，以确保容忍噪声和不确定性，这是普遍的神经电路。 因此，拟议的研究结果将包括一个统一的系统理论框架，用于分析生理相关的大脑网络的控制;此外，将包括一组正式的神经控制设计方法，可以很容易地转换为一系列的神经刺激实现。

The past decade has seen significant growth in the development and use of neurostimulation technology to manipulate neural activity in the brain. The applications of such technology range from scientific objectives, e.g., studying how different parts of the brain interact with each other, to clinical objectives, e.g., using stimulation to alleviate the symptoms of neurological disorders such as Parkinson's disease. Despite many technological advances associated with such stimulation, its use is still largely limited to perturbative paradigms, in which stereotyped inputs (waveforms) are used to activate or deactivate a neuronal network in its entirety. In other words, the stimulation is used to create a uniform circuit response, turning an entire population of brain cells (neurons) on or off, without regard for specificity (i.e., which cells in the population respond) or timing (i.e., when they turn on or off). In engineering, control is understood as not simply uniform stimulation, but as the precise creation or prevention of certain system maneuvers at each moment in time. This project will investigate fundamental questions regarding the use of neurostimulation to control neuronal networks in this temporally precise sense. That is, rather than simply stimulating the brain, the goal of this research is to develop new engineering theory and methods to allow practitioners to steer the activity in neural circuits so as to create complex patterns of activity, or neural spiking. Thus, this highly transdisciplinary project will elucidate enabling theory for the use of neurostimulation and will lead to new and fundamental contributions to systems theory and control engineering. The project will also support new initiatives to promote interdisciplinary education for students from traditionally underserved populations through the creation of summer workshops for students from local high schools in the city of St. Louis, MO.By bridging ensemble systems theory with computational neuroscience, general and versatile frameworks for neuronal control will be formulated. Specifically, oscillator and conductance-based neural models will be used to mathematically model both oscillatory and non-oscillatory regimes in brain networks. Using these models, the proposed work will determine fundamental limits on the controllability of neuronal spiking or synchronization by the application of external inputs. The notion of ensemble reachability is also proposed and will be examined via entropic gain analysis and dynamic optimization. These characterizations of fundamental control properties in both oscillatory and non-oscillatory neural dynamic regimes will then facilitate the development of control design paradigms to synthesize optimal controls for the creation of complex patterns in neuronal populations, such as firing or entrainment patterns. Methods of ensemble control and formal averaging will be employed to derive optimal sequence and pattern controls, and stochastic versions of these problems will also be treated using stochastic control techniques to ensure tolerance to noise and uncertainty, which are pervasive in neural circuits. Thus, the results of the proposed research will include a unified systems-theoretic framework for analyzing the control of physiologically relevant brain networks; and further, will include a set of formal neural control design methods that may be readily translated to a range of neurostimulation implementations.