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Two-phase strategy of neural control for planar reaching movements: I. XY coordination variability and its relation to end-point variability

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Abstract

A quantitative model of optimal transport–aperture coordination (TAC) during reach-to-grasp movements has been developed in our previous studies. The utilization of that model for data analysis allowed, for the first time, to examine the phase dependence of the precision demand specified by the CNS for neurocomputational information processing during an ongoing movement. It was shown that the CNS utilizes a two-phase strategy for movement control. That strategy consists of reducing the precision demand for neural computations during the initial phase, which decreases the cost of information processing at the expense of lower extent of control optimality. To successfully grasp the target object, the CNS increases precision demand during the final phase, resulting in higher extent of control optimality. In the present study, we generalized the model of optimal TAC to a model of optimal coordination between X and Y components of point-to-point planar movements (XYC). We investigated whether the CNS uses the two-phase control strategy for controlling those movements, and how the strategy parameters depend on the prescribed movement speed, movement amplitude and the size of the target area. The results indeed revealed a substantial similarity between the CNS’s regulation of TAC and XYC. First, the variability of XYC within individual trials was minimal, meaning that execution noise during the movement was insignificant. Second, the inter-trial variability of XYC was considerable during the majority of the movement time, meaning that the precision demand for information processing was lowered, which is characteristic for the initial phase. That variability significantly decreased, indicating higher extent of control optimality, during the shorter final movement phase. The final phase was the longest (shortest) under the most (least) challenging combination of speed and accuracy requirements, fully consistent with the concept of the two-phase control strategy. This paper further discussed the relationship between motor variability and XYC variability.

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Notes

  1. Initial movement direction is often measured at a certain time after the movement onset, such as 100 ms (Bernier et al. 2005; Hinder et al. 2010) and 200 ms (Heuer and Hegele 2008), or at a certain kinematic landmark, such as peak velocity (Hinder et al. 2010; Wang and Sainburg 2005). The average distance of hand position at 180 ms into movements from the movement onset was 3.3 mm for the small-target, short-distance, slow-speed condition and 56.0 mm for the large-target, short-distance, maximum-speed condition. This wide range of the distance from the movement onset across different conditions prevented us from using a certain time from the movement onset or peak velocity for this measurement. It is because the initial direction measurement is unstable at a very short distance from the starting position (i.e., 3.3 mm) and because the angle of initial movement direction significantly varies depending on the distance from the starting position that is used for the measurement. Therefore, we employed a fix distance (3 cm), which was close to the average distance across the conditions at 180 ms into the movement.

  2. To someone who is used to thinking about motor control in terms of kinematic parameters as continuous sequences of values within a specific time interval, it might seem that, since, for instance, acceleration as a function of time can be computed as a time derivative of velocity, it must be sufficient to include only one such parameter in equations. In the case of the equation describing XY coordination, however, instantaneous values of such parameters are involved, and therefore, a different logic applies. Knowledge of hand velocity at a certain time point t in general does not allow one to calculate hand acceleration and vice versa. For this reason, these kinematic variables are viewed in theoretical mechanics as state coordinates independent of each other.

  3. It is important to acknowledge that the correlation matrix should not be, in general, used for this purpose. This is so because the variance of one or more movement parameters in general can be very small. For example, in the case of XY reaching movement, the stylus tip trajectory can be arranged along the x axis with negligible variation along the Y axis. In this example, the XYC model k y y − y 0 = 0, where k y  = 1 and y 0 is the average Y coordinate, accurately describes the movement, since the variation of y around y 0 is very small. On the first sight, it may seem incorrect to state that an optimal XYC is observed in this example. However, simply by rotating the XY coordinate system 45 degrees (clockwise or counterclockwise), one can obtain a trajectory where any displacement along the x axis is almost exactly equal (in its absolute value) to the corresponding displacement along the Y axis, thus showing a near-perfect XYC. The method of determining the XYC model’s precision obviously should not depend on the choice of the XY coordinate system.

  4. To see that, note that the total variance is equal to the sum of the diagonal elements (i.e., trace) of the covariance matrix, and the sum of the eigenvalues is equal to the above sum.

  5. This component does not reflect any significant nonoptimality of movement control if it is determined by the variability of the end-point within the boundaries of the target area. This is so because as long as the end-point is within the target area, its deviation from the area’s center does not increase the cost of a target acquisition error.

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Acknowledgments

We thank Dr. Herbert Heuer for his helpful comments on an earlier version of the manuscript. We also thank Eva Hanisch, Maia Iobidze, Jennifer Stube and Sarah Jacob for their help in data collection.

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Authors and Affiliations

  1. IfADo-Leibniz Research Centre for Working Environment and Human Factors, Ardeystraβe 67, 44139, Dortmund, Germany

    Miya K. Rand

  2. School of Biological and Health Systems Engineering, Arizona State University, Tempe, AZ, 85287-9709, USA

    Yury P. Shimansky

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Correspondence to Miya K. Rand.

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Rand, M.K., Shimansky, Y.P. Two-phase strategy of neural control for planar reaching movements: I. XY coordination variability and its relation to end-point variability. Exp Brain Res 225, 55–73 (2013). https://doi.org/10.1007/s00221-012-3348-5

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