Dynamical systems for non-invasive control of neural activity

许多神经系统疾病，包括帕金森病（PD），其特征在于大脑活动异常强烈的振荡。在细胞水平上，这些振荡导致同步活动：神经元彼此步调一致，因此它们无法在控制运动、解释感官输入和规划未来行为方面发挥正常作用。这些病理性振荡的普遍存在促使人们寻找可以控制它们的干预措施。在神经科学领域之外，人们在许多其他系统中观察到了振荡，其规模从亚原子粒子到电网。在研究这些系统的过程中，数学家们发现了一种被称为“异步淬火”的现象。当振荡系统受到外部输入的扰动时，会出现这种情况，该外部输入以略微不同的频率和略微不同的振幅振荡。这种简单的干预可以大大降低不必要的振荡的强度。从数学上讲，异步淬火是包括大脑在内的某类振荡系统的普遍行为。然而，据我们所知，它还没有被用于任何以前的神经科学研究。这可能是由于相互作用的振荡器的令人生畏的复杂性，它可以产生广泛的不可预测的行为。因此，我们提出了一个紧密结合的实验和数学方法来测试异步淬火的有效性作为一种手段控制brain oscillations.Our的总体目标将是减少PD中看到的病理性振荡，使用非侵入性脑刺激。在目标1中，我们将模拟产生正常振荡的大脑功能模型，并寻找减少它们的刺激参数。然后，我们将在动物实验中验证这些数学结果，包括神经元群体的电生理记录。在目标2中，我们将使用药理学方法来产生类似于PD中的脑振荡。我们将更新模型以捕获这些振荡，然后确定恢复正常功能的刺激参数。在目标3中，我们将根据经验确定这些干预措施是否可以恢复PD中丢失的行为功能。总之，这些目标将导致对脑振荡的新理解，这将改善大量不适合标准手术治疗的PD患者的结局。

Many neurological disorders, including Parkinson's disease (PD), are characterized by abnormally strong oscillations in brain activity. At a cellular level, these oscillations lead to synchronous activity: Neurons fire in lockstep with each other, so that they are unable to perform their normal roles in controlling movements, interpreting sensory input, and planning future behaviours. The prevalence of these pathological oscillations has led to a search for interventions that can control them.Outside the field of neuroscience, oscillations have been observed in many other systems, at scales ranging from subatomic particles to power grids. In studying these systems, mathematicians have identified a phenomenon known as "asynchronous quenching". This results when an oscillating system is perturbed by an external input that oscillates at a slightly different frequency and with a slightly different amplitude. This simple intervention can drastically reduce the strength of the unwanted oscillation.Mathematically, asynchronous quenching is a universal behaviour of a certain class of oscillating systems that includes the brain. Nevertheless, it has not to our knowledge been used in any previous neuroscience study. This is likely due to the daunting complexity of interacting oscillators, which can produce a wide range of unpredictable behaviours. We therefore propose a tightly integrated experimental and mathematical approach to test the validity of asynchronous quenching as a means of controlling brain oscillations.Our overarching goal will be to reduce the pathological oscillations seen in PD, using non-invasive brain stimulation. In Aim 1, we will simulate models of brain function that produce normal oscillations and search for stimulation parameters that reduce them. We will then validate these mathematical results in animal experiments, involving electrophysiological recordings from populations of neurons. In Aim 2, we will use pharmacological methods to generate brain oscillations that resemble those in PD. We will update the model to capture these oscillations and then identify stimulation parameters that restore normal function. In Aim 3, we will determine empirically whether these interventions can restore behavioural functions that are lost in PD. Together, these Aims will lead to a new understanding of brain oscillations, which will improve outcomes for the large number of PD patients who are ineligible for standard surgical treatments.