Phase Transition Models of Oculomotor Control

描述（由申请人提供）：许多物理系统表现出 以相变为代表的行为：随着“控制参数”的变化， 行为在两个（或更多个）不同的稳定状态或模式之间变化。 最近，这种相变的例子已经在 生理系统。例如，当受试者敲击每个人的食指时， 有两种稳定的模式：一种是手指同相敲击， 其中它们以反相方式敲击。这两种模式是鲁棒的（稳定的）， 行为从一个到另一个的变化， 各种各样。 这种行为表现出相变的一些共同特征： 模式对扰动是鲁棒的，当控制 参数（频率）接近过渡点，并且存在滞后， 从上方接近与从下方接近时，过渡点是不同的 （降低或增加频率）。 我们将研究类似类型相变的眼动行为。 眼科领域的数学建模是相当复杂的，但 还没有尝试分析相变行为。拟议工作 因此，这是一种尝试，旨在对尚未被研究过的动眼行为的一个方面进行建模 已解决。这里提出的建模将有价值，在改善现有的 模型，理解观察到的行为，并预测新的行为。 研究计划包括三个主要方面。首先是分析 周期性扫视的证据，多个稳定状态，在类比 手指敲击工作如上所述。初步数据显示， 在该系统中确实可能发生跃迁：作为目标跳跃频率 增加时，扫视从滞后于目标（正潜伏期）变为 预期目标（负延迟），并且存在增加的可变性 接近跃迁频率。关于这一系统的工作将进一步涉及 验证这种效应，检查滞后和响应， 扰动，并制定数学模型（和分析现有的 模型）以再现相变。第二项工作是研究 扫视和VOR（前庭眼反射）的相互作用，寻找模式 作为一个协调的结果，平滑和快速的眼球运动之间的协调， 频率的函数。最后，我们将对其他前庭进行调查， 以及那些可能表现出阶段性的行为和模型 过渡行为。 这个项目是高风险的，因为眼科系统可以避免这样的阶段 过渡，而是表现出平滑分级的行为变化，使阶段 转型模式不合适。这项工作代表了PI的新方向 因为他过去的工作没有涉及到独特的数学公式， 这项研究所需的。

DESCRIPTION (provided by applicant): Many physical systems exhibit patterns of behavior typified by phase transitions: as a "control parameter" varies, the behavior changes between two (or more) distinct stable states or modes. Recently, examples of such phase transitions have been demonstrated in physiological systems. For example, when subjects tap the index fingers of each hand, there are two stable modes: one in which the fingers tap in phase and one in which they tap in counter-phase. These two modes are robust (stable), and the behavior changes from one to the other as tapping frequency is systematically varied. This behavior exhibits a number of features common to phase transitions: each mode is robust to perturbations, there is increased variability when the control parameter (frequency) is near the transition point, and there is hysteresis such that the transition point is different when approached from above versus below (decreasing or increasing frequency). We will investigate oculomotor behavior for similar types of phase transitions. Mathematical modeling in the oculomotor field is quite sophisticated, yet analysis of phase-transition behaviors has not been attempted. The proposed work is thus an attempt to model an aspect of oculomotor behavior that has not been addressed. The modeling proposed here will have value in improving existing models, understanding observed behaviors, and predicting new ones. The research plan consists of three main efforts. First is the analysis of periodic saccades for evidence of multiple stable states, in analogy to the finger tapping work referred to above. Preliminary data suggests that phase transitions may indeed occur in this system: as target jumping frequency increases, saccades change from lagging the target (positive latency) to anticipating the target (negative latency), and there is increased variability near the transition frequency. Work on this system will involve further verification of this effect, examination of hysteresis and the response to perturbations, and formulation of mathematical models (and analysis of existing models) to reproduce the phase transitions. The second effort is a study of the interaction of saccades and the VOR (vestibulo-ocular reflex), looking for modes of coordination between the resulting smooth and fast eye movements as a function of frequency. Finally, we will carry out a survey of other vestibular and oculomotor behaviors and models for those which might exhibit phase transition behaviors. This project is high risk because the oculomotor system may avoid such phase transitions but rather exhibit smoothly graded behavioral changes, making phase transition models inappropriate. The work represents a new direction for the PI because his past work has not dealt with the unique mathematical formulations required for this study.