MODELING 3-DIMENSIONAL VELOCITY-TO-POSITION TRANSFORMATION IN OCULOMOTOR CONTROL
MODELING 3-DIMENSIONAL VELOCITY-TO-POSITION TRANSFORMATION IN OCULOMOTOR CONTROL
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DOI：
10.1152/jn.1994.71.2.623
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发表时间：
1994-02-01
影响因子：
2.5
通讯作者：
RAPHAN, T
中科院分区：
文献类型：
--
作者：
SCHNABOLK, C;RAPHAN, T
1.人们对三维眼动控制中的速度-位置转换进行了大量的研究。许多工作都集中在这样的观点上，即三维旋转不能互换，速度-位置积分的“乘法四元数模型”对于解释三维眼球运动是必要的。我们的研究表明，这种方法与旋转眼睛所需的信号类型的生理学不一致。2.建立了眼球在眼眶周围组织内运动的三维动力学系统模型。该模型的主要观点是眼部肌肉产生扭矩来旋转眼睛。当眼睛到达一个方向，眼眶组织的恢复扭矩抵消了肌肉施加的扭矩时，就达到了一个独特的平衡点。达到平衡的眼球轨迹可以遵循任何路径，这取决于起始眼球方向和眼球速度。然而，根据欧拉定理，所达到的平衡等同于绕固定的轴从主方向绕某个角度旋转。这代表了眼睛在达到平衡时从主方位所能走的最短路径。因此，它也是使眼睛返回到主要方向的最短路径。因此，眼球周围组织产生的恢复力矩近似为该角度与沿该轴的单位向量的乘积成正比。定位和恢复扭矩之间的关系提供了独特的扭矩定位关系。3.一旦建立了合适的眼球旋转力矩-方位关系，速度-位置积分器就可以被建模为一个动力系统，它是一维速度-位置积分器的直接扩展。积分器状态和直接路径信号的线性组合被转换为扭矩信号，该扭矩信号激活肌肉来旋转眼睛。因此，积分器的输出与定位眼睛的扭矩信号有关。这不是眼睛朝向的信号。施加的扭矩信号将眼睛驱动到平衡方向，使得恢复扭矩等于施加的扭矩，但方向相反。平衡时达到的视线方向由独特的力矩-方向关系决定。因为扭矩信号是矢量，所以它们是换向的。因此，我们的模型表明，中枢神经系统中的信号可以被视为向量，并且眼球的非向量定向属性是与眼球及其下面的组织相关的动力学系统所固有的。4.列表定律被我们的模型简单地解释为驱动眼睛的CNS中的信号的矢量性质的属性，并且它的实现不局限于CNS中的任何特定位置。如果驱动眼睛的神经矢量信号被限制在列表平面，即在我们的模型中的俯仰-偏航平面，那么眼睛的方向将服从列表定律。5.仿真结果表明，无论是眼跳运动还是平稳追踪眼球运动，我们的模型在稳态下都符合Listing定律。模拟还表明，在稳态眼球方向方面，存在可换性。我们进行了模拟，将模型输出与其他人的数据进行了比较。与罗列定律的偏差与生理发现一致。
1. A considerable amount of attention has been devoted to understanding the velocity-position transformation that takes place in the control of eye movements in three dimensions. Much of the work has focused on the idea that rotations in three dimensions do not commute and that a ''multiplicative quaternion model'' of velocity-position integration is necessary to explain eye movements in three dimensions. Our study has indicated that this approach is not consistent with the physiology of the types of signals necessary to rotate the eyes. 2. We developed a three-dimensional dynamical system model for movement of the eye within its surrounding orbital tissue. The main point of the model is that the eye muscles generate torque to rotate the eye. When the eye reaches an orientation such that the restoring torque of the orbital tissue counterbalances the torque applied by the muscles, a unique equilibrium point is reached. The trajectory of the eye to reach equilibrium may follow any path, depending on the starting eye orientation and eye velocity. However, according to Euler's theorem, the equilibrium reached is equivalent to a rotation about a fixed axis through some angle from a primary orientation. This represents the shortest path that the eye could take from the primary orientation in reaching equilibrium. Consequently, it is also the shortest path for returning the eye to the primary orientation. Thus the restoring torque developed by the tissue surrounding the eye was approximated as proportional to the product of this angle and a unit vector along this axis. The relationship between orientation and restoring torque gives a unique torque-orientation relationship. 3. Once the appropriate torque-orientation relationship for eye rotation is established the velocity-position integrator can be modeled as a dynamical system that is a direct extension of the one-dimensional velocity-position integrator. The linear combination of the integrator state and a direct pathway signal is converted to a torque signal that activates the muscles to rotate the eyes. Therefore the output of the integrator is related to a torque signal that positions the eyes. It is not an eye orientation signal. The applied torque signal drives the eye to an equilibrium orientation such that the restoring torque equals the applied torque but in the opposite direction. The eye orientation reached at equilibrium is determined by the unique torque-orientation relation. Because torque signals are vectors, they commute. Thus our model indicates that the signals in the CNS can be treated as vectors and that the nonvector orientation properties of the eye globe are inherent in the dynamical system associated with the globe and its underlying tissue. 4. Listing's law is explained very simply by our model as being a property of the vector nature of the signals in the CNS driving the eyes, and its implementation is not localized to any specific locality within the CNS. If the neural vector signal driving the eye is confined to Listing's plane, i.e., the pitch-yaw plane in our model, then eye orientation will obey Listing's law. 5. We performed simulations to show that Listing's law is obeyed by our model for both saccades and smooth pursuit eye movements in the steady state. The simulations also showed that there is commutativity in terms of steady-state eye orientation. We performed simulations that compared the model output with data of others. Deviations from Listing's law were consistent with the physiological findings.