MULTISCALE MODELS OF NEURAL POPULATION CONTROL IN SPINAL CORD

越来越复杂的大脑记录技术还没有被类似的 复杂的数学方法，允许建模和预测之间的关系， 行为和神经系统深处细胞群的活动。尤其如此 对于运动系统，其主要目标是控制环境的动态。我们的目标是 创建脊髓运动组件的多尺度模型，其可以链接至少四个尺度：（1） 单个神经元放电，（2）局部神经群体活动，（3）整个神经元活动的地形图， 脊髓;（4）行为。我们建议使用棘蛙作为我们的试验平台，因为 生物力学被很好地理解，本体感受反馈被简化，脊髓可以被研究， 与皮层控制隔离，并且在没有 皮层控制 我们将使用和进一步发展一个新的数学框架的基础上叠加随机 动态算子认为神经活动引起系统的改变是恰当的 动力学，因此产生的动力学（包括运动，顺应性和振荡行为） 达到预期的结果。新的框架使我们能够模拟动态响应 环境，顺应性控制，反射行为，单一尖峰的影响，以及 在一个群体中的多个神经元。我们可以检查振荡活动（如在中央 用于运动的模式发生器（CPG））和本体感受反馈的作用。因为这个理论 在单个尖峰水平上操作，所有神经表示都是本地的，可以使用本地学习 规则，它提供了一个更密切的联系，以实际的生物计算，并可以提供洞察 脊髓用来产生复杂多样运动的机制。 为了测试我们对脊髓中层神经元群体行为的理解， 我们将（1）读出正在进行的运动的动态，包括扰动响应， 遵守，（2）修改正在进行的运动的动态，（3）创建地形图，显示 控制功能在线缆上的分布。 这些实验将使我们能够理解神经群体对神经元动力学的控制。 运动在一个详细的方式，连接神经规模的人口规模的运动行为 规模该数学框架为理解细胞的功能提供了一个新的模型。 神经元群体并预测它们对行为的影响。它还提供了一个定量模型 这使得可以预测射击或伤害对行为的影响。最后将 通过了解脊髓损伤的功能，为脊髓损伤的新治疗提供基础。 电刺激不仅可以用于在目标肌肉中产生力量，还可以用于 以身体自然使用的方式产生对动力学的平滑顺应控制。

Increasing sophistication of brain recording technology has not been matched by a similarly sophisticated mathematical approach that permits modeling and prediction of the relation between behavior and the activity of populations of cells deep within the nervous system. This is particularly true for motor systems, where the primary goal is control of the dynamics of the environment. Our goal is to create multiscale models of motor components of the spinal cord that can link at least four scales: (1) individual neuron firing, (2) local neural population activity, (3) topographic maps of activity across the spinal cord, and (4) behavior. We propose to use the spinalized frog as our testbed, because the biomechanics are well understood, proprioceptive feedback is simplified, the cord can be studied in isolation from cortical control, and repeatable complex movements can be generated in the absence of cortical control. We will use and further develop a new mathematical framework based upon superposition of stochastic dynamic operators. It is appropriate to consider neural activity as causing a modification of the system dynamics, so that the resulting dynamics (including movement, compliance, and oscillatory behavior) achieve a desired result. The new framework allows us to model the response to dynamic environments, compliant control, reflex behavior, the effect of single spikes, and the combined effect of multiple neurons in a population. We can examine oscillatory activity (such as found in the central pattern generator (CPG) for locomotion) and the role of proprioceptive feedback. Because this theory operates at the level of single spikes and all neural representations are local and can use local learning rules, it provides a much closer link to the actual biological computations and could provide insight into the mechanisms used by the spinal cord to generate complex and varied movement. To test our understanding of the behavior of populations of neurons in the intermediate layers of spinal cord, we will (1) read out the dynamics of ongoing movement including perturbation responses and compliance, (2) modify the dynamics of ongoing movement, (3) create topographic maps showing the distribution of control functions across the cord. These experiments will allow us to understand control by neural populations of the dynamics of movement in a detailed way that links the neural scale to the population scale to the motor behavioral scale. The mathematical framework provides a new model for understanding the function of populations of neurons and predicting their effect on behavior. It also provides a quantitative model that allows the prediction of the effect of modification of firing or injury on behavior. Finally, it will provide the basis for new treatments for spinal cord injury by giving an understanding of functional electrical stimulation that can be used not just to generate forces in target muscles, but can be used to generate smooth compliant control of dynamics in the way naturally used by the body.