Dynamical Model Based Brain Network Control

大脑是一个复杂的神经网络，由数以百亿计的神经元和数万亿的突触连接构成。这些神经元网络形成多个大脑区域，每个区域都承担特定的功能，涵盖基本的感知和运动控制到高级的思维和情感处理。近年来，随着神经影像技术（如功能磁共振成像和弥散张量成像）以及神经电生理信号采集技术（头皮脑电图和立体脑电图等）的快速发展，我们可以更容易地获得大脑结构和功能的各种数据，覆盖不同的尺度。深入研究不同脑区之间的连接模式、了解这些区域之间的相互作用和信息传递方式对于理解大脑功能至关重要。这些研究也有助于进一步探索如何操控大脑的神经活动。

脑网络动力学建模为深入研究大脑神经活动机制提供了理论框架。利用复杂系统和机器学习理论，我们可以通过数学建模和仿真来还原大脑的神经活动。这些计算模型不仅能够解释大脑内部的计算过程，还能揭示大脑如何处理信息、执行认知任务以及展现复杂行为。此外，大脑的控制干预问题也备受瞩目。网络控制理论为我们提供了理论框架，特别是关于神经调控输入如何影响大脑神经响应输出的问题。通过不同的控制干预方法，我们能够实现情绪调节、操控神经活动模式等目标。然而，与传统的经验性设计控制干预策略不同，精确的脑网络动力学建模和优化控制理论等计算方法的引入为我们提供了技术思路，帮助我们更好地理解如何控制大脑神经活动。

本文围绕常见的体外培养的神经元群体网络、癫痫传播网络和大尺度大脑结构网络开展脑网络动力学建模与控制研究。然而，针对大脑网络动力学建模与控制需要考虑以下关键问题：(1)基于数据驱动的传统机器学习方法在重构刺激输入和神经响应输出关系时缺乏生物信息先验；(2)重构刺激输入和神经响应输出的动力学模型需要考虑模型的复杂度和预测准确度的权衡问题；(3)大尺度大脑结构网络约束下实现大脑认知功能的神经环路调控机制不明确。鉴于这三种不同类型的大脑网络和上述关键问题，本文提出了相应的技术解决方案，其创新点和主要贡献包括以下几个方面：

(1)针对数据驱动的机器学习方法重构刺激输入和神经响应输出的动力学模型缺乏生物信息先验的问题，我们以体外培养的神经元群体网络的刺激输入神经响应输出为研究对象，提出了一种结合大脑生物信息先验的循环神经网络，用于重构体外培养的神经元群体网络的神经活动。并在此基础上，我们借助动力学模型的分析方法分析体外培养的神经元群体网络的动态特性，并基于辨识的动力学模型实现体外培养的神经元群体网络的动态调控。实验结果表明，我们提出的方法具有较高的预测准确度（可解释方差大于0.85），且兼顾生物可解释性。同时，我们也验证了优化控制理论在指导调控神经元群体网络到达目标的神经响应状态的可行性。

(2)针对刺激输入神经响应输出动力学模型需要考虑模型复杂度与预测准确度的权衡问题，我们以抑制癫痫传播网络的异常神经活动为研究对象，提出了一种基于库普曼算子的模型预测控制框架，用于重构并控制癫痫传播网络的神经活动。我们借助库普曼算子的思想（即非线性动力系统能够在无限维的空间变换为线性系统），将高度非线性的癫痫传播动力学通过编码器升维到有限维状态空间使之近似为线性动力学方程，并在此基础上构建模型预测控制器。实验结果表明，我们提出的方法相比于循环神经网络、高阶自回归模型、核方法等，具有更优的预测准确度，并且在求解最优刺激输入时具有更高的计算效率。我们提出的框架对于实现临床神经系统癫痫网络的闭环神经调控具有理论支撑。

(3)针对大脑结构网络约束下实现大脑认知功能的神经环路调控机制不明的问题，我们提出了一种基于大脑网络控制理论架构的推断大脑调控节点与控制输入的方法，用于重构大脑执行复杂认知任务的神经活动。我们借助大脑网络控制理论架构，充分考虑大脑网络的可控性问题，以推断大脑调控节点与控制策略为优化变量，构建最小化重构神经活动误差的联合优化问题，并采取增广拉格朗日乘子法进行优化问题求解。实验结果表明，我们提出的方法能推断出与认知任务相关的控制节点，具有一定的神经科学解释性，且从能量代价与网络可控性的角度解释了不同工作记忆任务的神经机理。我们提出的方法为我们理解大脑结构网络约束下，大脑如何组织任务相关的神经环路实现复杂认知功能提供调控机制的解释。

大脑网络动力学建模与控制在神经科学探索和应用领域有着广泛的前景。本文的研究成果借助数学建模思想（动力学建模、控制理论、优化理论等）和神经科学理论，提升了数据驱动模型在还原大脑神经活动的生物可解释性。同时，我们也在权衡刺激输入神经响应输出模型的复杂度与计算效率取得进展。此外，我们也揭示了大脑结构约束下实现复杂认知功能的调控机制等关键问题。这些研究为解析大脑认知功能以及实现认知障碍脑疾病的控制干预提供了重要的理论基础。

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