Controlling Populations of Neurons

拟议的研究将使用工程技术、数学原理和计算机模拟来了解与帕金森病相关的病理性神经同步如何通过注射电流刺激而被破坏。这包括确定控制输入，通过将神经元状态驱动到对噪声非常敏感的无相状态来最佳地重置神经元的相位。当一个群体中的神经元接受这样一个共同的刺激时，噪声会使神经元的阶段随机化，从而使群体非同步化。在这种控制方案中，这些输入将通过检测种群水平的同步来触发，从而给出一种基于事件的反馈控制算法，该算法只在必要时刺激生物组织，从而减少电刺激负面副作用的总体积累，也减少了所需的电量。在另一种方法中，非线性混合控制，包括应用一系列不同的控制律，将被用于通过稳定耦合神经元系统的张开状态来打破神经同步，这是神经元相位均匀分布的状态。这样的控制也将被推广到一个基于事件的框架，并进行优化，使其最小化总输入能量或达到伸展状态所需的总时间。控制算法的鲁棒性将根据神经元模型的不确定性、放电事件测量的不确定性、不同类型的耦合、输入刺激的变化、由于靠近电极而导致的刺激的异质性以及噪声的特性进行探讨。有证据表明，与帕金森病相关的震颤与患者大脑运动控制区神经元的病理同步有关。美国食品和药物管理局（fda）批准的一种治疗此类震颤的方法，称为深部脑刺激，包括在该区域植入电极，用于向脑组织注入电流。根据目前的实现，电流通常是频率约为100赫兹的周期性脉冲序列，经验表明这对某些患者是有效的治疗方法。这项研究将使用工程技术、数学原理和最先进的计算机模拟来为深部脑刺激的替代电流刺激发展理论基础，这可能会导致更好的治疗帕金森病。特别是，将开发控制算法，以最大限度地减少注入的电流，这将最大限度地减少组织损伤和能量消耗，后者减少了手术更换用于深部脑刺激的电池的需要。这也将包括使用反馈控制，其中神经群的状态由电极监测，电流刺激只在需要时注入。

The proposed research will use engineering techniques, mathematical principles, and computer simulations to understand how pathological neural synchronization associated with Parkinson's disease can be disrupted through the injection of current stimuli. This includes determining control inputs which optimally reset a neuron's phase by driving the state of the neuron to a phaseless set at which it is very sensitive to noise. When neurons in a population receive such a common stimulus, the noise serves to randomize the neurons' phases, thereby desychronizing the population. In this control scheme, such inputs will be triggered by the detection of population-level synchrony, giving an event-based feedback control algorithm for which the biological tissue is only stimulated when necessary, thereby reducing the overall accumulation of negative side effects of electrical stimulation, and also the amount of power used. In an alternative approach, nonlinear hybrid control, involving the application of a series of different control laws, will be used to break neural synchrony by stabilizing the splay state for the coupled neuron system, which is the state for which the neurons' phases are evenly distributed. Such control will also be generalized to an event-based framework, and optimized so that it minimizes the total input energy or the total time needed to reach the splay state. The robustness of the control algorithms will be explored with respect to uncertainties in the neuron model, uncertainties in the measurements of the firing events, different types of coupling, changes to the input stimulus, heterogeneity of the stimulus due to proximity to the electrode, and properties of the noise.There is evidence that the tremors associated with Parkinson's disease are associated with the pathological synchronization of neurons in the motor control region of the patient's brain. An FDA-approved treatment for such tremors, called deep brain stimulation, involves the implantation of an electrode into this region, which is used to inject electrical current into the brain tissue. As presently implemented, the electrical current is typically a periodic sequence of pulses with a frequency around 100 Hertz, which has been shown empirically to be an effective treatment for some patients. This research will use engineering techniques, mathematical principles, and state-of-the-art computer simulations to develop the theoretical foundation for alternative electrical current stimuli for deep brain stimulation, which could lead to better treatments for Parkinson's disease. In particular, control algorithms will be developed which minimize the amount of current injected, which will minimize tissue damage and energy consumption, the latter reducing the need for surgery to replace the battery which is used for deep brain stimulation. This will also include the use of feedback control, in which the state of the neural population is monitored by an electrode and the electrical current stimulus is only injected as needed.