Optimal Control of Models of Neural Population Dynamics

神经群体动力学模型的最优控制

• 批准号: 523380209
• 负责人: Professor Dr. Klaus Obermayer
• 金额: --
• 依托单位: Institut für Softwaretechnik und Theoretische Informatik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/523380209?language=en
• 关键词: Optimal; Control; Models; Neural; Population

Neural systems are described mathematically as controlled dynamical systems. They are affected by external stimulating inputs ("control"), which can be natural - via synaptic connections - or artificial - via external electric or magnetic stimulation. The mathematical approach can help to understand the underlying mechanisms responsible for the reaction of neural systems to stimulation. Here we will study the design of efficient control signals using methods from nonlinear optimal control theory (OCT) and investigate their properties, with applications being twofold: In "synthetic" scenarios, one can study how to manipulate neural systems efficiently (e.g. modulate brain activity). In "analytic" scenarios, one can study the natural design of neural dynamical systems in terms of optimization principles (e.g. enforced by evolution). The efficiency of a control signal is measured in terms of a cost functional that trades the strength of the input against the closeness to a target state. In this project, we use Pontryagin’s Principle to numerically compute a cost gradient. We then approach the optimal control iteratively. The conventional optimal control approach is limited to settings where an exact time-dependent target state can be defined. By contrast, any scenario where one would try to enforce oscillations, synchrony of the network dynamics, or locking, irrespective of the phases at control onset or of the exact shape of the oscillations, requires an extension of the standard approach. Here we want to study how to adapt the OCT approach to such settings. To this end, we suggest novel cost functionals and study their applicability and usefulness in models of single neural populations, network motifs, and large whole-brain models. We will focus on two neural mass models of different levels of complexity: the comparatively simple Wilson-Cowan model, which describes the time-evolution of the activation of recurrently coupled excitatory and inhibitory populations of neurons, and a mean-field model that is derived from a network of randomly connected excitatory and inhibitory adaptive exponential integrate-and-fire neurons (“mean-field AdEx model”). The computation of optimal control signals requires numerical simulations of the state evolution of these models, for which we use Neurolib, an open-source Python software framework for modeling neural dynamics. We will provide additional algorithms as an open-source extension to Neurolib, which will enable us to compute optimal control signals or the aforementioned (and other) models, for deterministic and noisy systems, and for models of single neural populations and networks thereof. The software will be implemented in a modular fashion, such that it can easily be adjusted to the requirements of specific scenarios to facilitate future studies of stimulation of neural systems.

神经系统在数学上被描述为受控动力系统。它们受到外部刺激输入(“控制”)的影响，这可以是自然的-通过突触连接-也可以是人工的-通过外部电或磁刺激。数学方法可以帮助理解神经系统对刺激反应的潜在机制。在这里，我们将使用非线性最优控制理论(OCT)的方法来研究有效控制信号的设计，并研究它们的性质，应用有两个方面：在“合成”场景中，人们可以研究如何有效地操纵神经系统(例如，调节大脑活动)。在“分析”场景中，人们可以根据最优化原理(例如，由进化强制实施)来研究神经动力系统的自然设计。控制信号的效率是根据成本泛函来衡量的，该成本泛函将输入的强度与与目标状态的接近程度进行交易。在这个项目中，我们使用庞特里亚金原理来数值计算成本梯度。然后，我们迭代逼近最优控制。传统的最优控制方法限于可以定义精确的依赖于时间的目标状态的设置。相比之下，任何试图强制实施振荡、网络动态的同步或锁定的场景，无论控制开始时的阶段或振荡的确切形状，都需要标准方法的扩展。在这里，我们想研究如何使OCT方法适应这样的环境。为此，我们提出了新的代价函数，并研究了它们在单神经种群模型、网络主题模型和大型全脑模型中的适用性和有用性。我们将集中讨论两个不同复杂程度的神经质量模型：相对简单的Wilson-Cowan模型，它描述了兴奋和抑制神经元群体的激活的时间演化；以及从随机连接的兴奋和抑制自适应指数积分与点火神经元网络派生的平均场模型(“平均场ADEX模型”)。最优控制信号的计算需要对这些模型的状态演化进行数值模拟，为此，我们使用了Neurolib，这是一个用于建模神经动力学的开源Python软件框架。我们将提供额外的算法作为Neurolib的开源扩展，它将使我们能够计算确定性和噪声系统的最优控制信号或前述(和其他)模型，以及单个神经种群及其网络的模型。该软件将以模块化方式实施，这样就可以很容易地根据特定场景的要求进行调整，以促进未来对神经系统刺激的研究。