Rand Miya K, Shimansky Y P, Hossain Abul B M I, Stelmach George E
Motor Control Laboratory, Department of Kinesiology, Arizona State University, Box 870404, Tempe, AZ 85287-0404, USA.
Exp Brain Res. 2008 Jun;188(2):263-74. doi: 10.1007/s00221-008-1361-5. Epub 2008 Apr 26.
It has been found in our previous studies that the initiation of aperture closure during reach-to-grasp movements occurs when the hand distance to target crosses a threshold that is a function of peak aperture amplitude, hand velocity, and hand acceleration. Thus, a stable relationship between those four movement parameters is observed at the moment of aperture closure initiation. Based on the concept of optimal control of movements (Naslin 1969) and its application for reach-to-grasp movement regulation (Hoff and Arbib 1993), it was hypothesized that the mathematical equation expressing that relationship can be generalized to describe coordination between hand transport and finger aperture during the entire reach-to-grasp movement by adding aperture velocity and acceleration to the above four movement parameters. The present study examines whether this hypothesis is supported by the data obtained in experiments in which young adults performed reach-to-grasp movements in eight combinations of two reach-amplitude conditions and four movement-speed conditions. It was found that linear approximation of the mathematical model described the relationship among the six movement parameters for the entire aperture-closure phase with very high precision for each condition, thus supporting the hypothesis for that phase. Testing whether one mathematical model could approximate the data across all the experimental conditions revealed that it was possible to achieve the same high level of data-fitting precision only by including in the model two additional, condition-encoding parameters and using a nonlinear, artificial neural network-based approximator with two hidden layers comprising three and two neurons, respectively. This result indicates that transport-aperture coordination, as a specific relationship between the parameters of hand transport and finger aperture, significantly depends on the condition-encoding variables. The data from the aperture-opening phase also fit a linear model, whose coefficients were substantially different from those identified for the aperture-closure phase. This result supports the above hypothesis for the aperture-opening phase, and consequently, for the entire reach-to-grasp movement. However, the fitting precision was considerably lower than that for the aperture-closure phase, indicating significant trial-to-trial variability of transport-aperture coordination during the aperture-opening phase. Implications for understanding the neural mechanisms employed by the CNS for controlling reach-to-grasp movements and utilization of the mathematical model of transport-aperture coordination for data analysis are discussed.
我们之前的研究发现，在伸手抓握动作中，当手部与目标的距离越过一个阈值时，孔径闭合开始，该阈值是峰值孔径幅度、手部速度和手部加速度的函数。因此，在孔径闭合开始时，观察到这四个运动参数之间存在稳定的关系。基于运动最优控制的概念（纳斯林，1969年）及其在伸手抓握动作调节中的应用（霍夫和阿比比，1993年），我们假设，通过在上述四个运动参数中加入孔径速度和加速度，表达这种关系的数学方程可以推广，以描述整个伸手抓握动作中手部运输与手指孔径之间的协调。本研究考察了这一假设是否得到实验数据的支持，在这些实验中，年轻人在两种伸手幅度条件和四种运动速度条件的八种组合下进行伸手抓握动作。研究发现，数学模型的线性近似以非常高的精度描述了每个条件下整个孔径闭合阶段六个运动参数之间的关系，从而支持了该阶段的假设。测试一个数学模型是否能近似所有实验条件下的数据表明，只有在模型中加入另外两个条件编码参数，并使用一个基于人工神经网络的非线性近似器，该近似器有两个分别包含三个和两个神经元的隐藏层，才有可能达到同样高的数据拟合精度。这一结果表明，作为手部运输参数和手指孔径之间的一种特定关系，运输 - 孔径协调显著依赖于条件编码变量。孔径张开阶段的数据也符合一个线性模型，其系数与孔径闭合阶段确定的系数有很大不同。这一结果支持了上述关于孔径张开阶段的假设，因此也支持了整个伸手抓握动作的假设。然而，拟合精度明显低于孔径闭合阶段，这表明在孔径张开阶段运输 - 孔径协调存在显著的试验间变异性。文中讨论了这一结果对于理解中枢神经系统用于控制伸手抓握动作的神经机制以及运输 - 孔径协调数学模型在数据分析中的应用的意义。
