Abstract- The physiological motor response to double vision, vergence eye movements, shows a strong directional asymmetry: inward turning movements are ...
Proceedings of the Second Joint EMBS/BMES Conference Houston, TX, USA • October 23-26, 2002
Dynamic Asymmetry in Vergence Eye Movements: The Underlying Mechanism Revealed by Independent Component Analysis John Semmlow,1,2 Weihong Yuan,1 Tara Alvarez3 1 Department of Biomedical Engineering; Rutgers University, Piscataway 2 Department of Surgery (Bioengineering) Robert Wood Johnson Medical School - UMDNJ 3 Department of Biomedical Engineering, NJIT, Newark, NJ Abstract- The physiological motor response to double vision, vergence eye movements, shows a strong directional asymmetry: inward turning movements are faster than outward movements. Isolated neural components underlying these signals were identified using a new application of Independent Component Analysis. These components show that the direction-dependent nonlinearity is due primarily to a difference in only one of the major components that drive the vergence response: the transient component associated with neural burst cells. Keywords - Vergence, Independent component analysis, physiological motor control. I. INTRODUCTION Vergence movements, the inward or outward turning of the eyes, are evoked by several visual and psychological clues associated with depth. The strongest of these is disparity and the associated double vision drives the eyes inward or outward until a single image is perceived. The static and dynamic behavior of this physiological motor response have been extensively studied under laboratory and natural viewing conditions. A typical vergence response appears smooth and exponential, and this behavior led to theories that the response was mediated by continuous in feedback control. As with all physiological responses, nonlinear behavior has been observed. The most significant nonlinearity is direction-dependent response dynamics: convergence (i.e., inward) movements are significantly faster than divergence (i.e. outward) movements, Figure 1A. Movements in the same direction exhibit fairly linear behavior for amplitudes ranging between 1.0 and approximately 6.0 degrees. Larger responses sometimes exhibit double-step behavior in which the final position is attained through two, or more, step-like responses.[1] Although originally believed to be guided by continuous feedback control process, considerable experimental evidence amassed in our laboratory indicates that vergence step responses are mediated by at least two control processes: a “transient” component giving rise to a fast initial motor response; and a “sustained” component which more slowly brings the eyes to the final, highly accurate vergence position [1,2,3]. Indirect evidence and modeling studies suggest that the direction dependent nonlinearity may be the result of differences in convergent and divergent transient components. Based on a model that incorporated the two components,
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Horng et al.[5] predicted that the amplitude of the divergence transient component was much less than that of the convergence transient component, and could even be absent in divergence response. A new technique developed in our laboratory, allows us to isolate the two components from experimental data. This technique applies Independent Component Analysis [6] to multiple, or ensemble, response data to identify underlying components. While we use this technique to dissect vergence motor responses, it is applicable to any response that is controlled by multiple components, provided multiple observations can be obtained for that behavior. ICA analysis requires several different measurements of the signals, usually taken at different physical locations. In our application, each of a number of vergence responses produced by the same stimulus is treated as a separate signal source. A correction algorithm is required to compensate for small errors induced by the loss of independence between the neural sources due to stimulusinduced synchronization of their signals. This corrective algorithm is described elsewhere [7]. Simulations of a twocomponent model of disparity vergence [8] were used to evaluate the corrective algorithm and verify the ability of ICA to identify the underlying components.[7] II. METHODOLOGY The Independent Component Analysis technique used here requires a number of repetitive responses (observations) for the behavior being analyzed (approximately 15 to 20 based on simulation analyses). These responses were acquired using a commercially available infrared eye movement monitor (Skalor Model 6500) in a laboratory setting that has been described elsewhere [1-5,7]. The ICA model is a generative model: it attempts to explain how the sources (in this case the components) are mixed to generate the observed signals based on a linear mixing model [6]: x = As where x and s are vectors representing the signals and sources respectively. In this application, the signals, x, are the recorded eye movements, the sources, s, are the underlying transient and sustained components, and the mixing matrix, A, accounts for their mixture and movement-to-movement variability. Several popular ICA algorithms are available from the Web as MATLAB files. We selected the “FastICA”
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algorithm developed by the ICA Group at the Helsinki University [9]. Implemented under Windows-based MATLAB, the analysis required only a few seconds on a 500 MHz PC. III. RESULTS
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Figure 1B & C shows the transient and sustained components obtained by applying our analysis to an ensemble of convergence and divergence responses. Note that while the sustained components are similar for the two directions, the transient component is substantially reduced in divergence, Figure 1C. This result, obtained directly from the data, verifies the speculation that a reduced divergence transient component produces the direction asymmetry. Note that while much reduced, the transient component still exists in divergence.
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The transient and sustained components are likely mediated by burst and tonic cells first described for vergence by Mays’ group. [11,12,13]. Mays found that divergent burst cells (i.e., those generating the transient component) required more activity to achieve the same movement velocity as convergence burst cells. This finding implies that divergence burst cells are less effective in producing activity at the motor neuron level. A reduced level of pulse-like activity measured at the medial rectus nucleus during divergence responses [11] suggests that the some process between the divergent burst cells and the medial rectus nucleus interferes with the burst cell signal. This provides an underlying neurophysiological bases for our finding that the transient component is significantly reduced in divergence movements. It is this reduction that accounts for the reduced dynamics of divergent responses and the direction-dependent nonlinearity seen in vergence eye movements. 1 T. L. Alvarez, J. L. Semmlow JL, and W. Yuan W, J. Neurophysiol., vol. 79, pp. 37-44, 1998. 2 J. L. Semmlow, G. K. Hung and K. J. Ciuffreda, Invest. Ophthalmol. Vis. Sci., vol. 27, pp. 558-564, 1986. 3 J. L. Semmlow, et al. Ciuffreda, Ophthalmic and Physiol. Opt., vol. 13, pp. 48-55, 1993. 4 J. L. Semmlow, G. K. Hung, J.-L. Horng and K. J. Ciuffreda, Vis. Res., vol. 34, pp. 1335-1343, 1994. 5 J.-L. Horng, J. L. Semmlow, G. K. Hung and K. J. Ciuffreda, IEEE Trans. Biomed Engr., vol. 45, pp. 249-257, 1998. 6 A. Hyvarinen, Karhunen and E. Oja, Independent Component Analysis, John Wiley and Sons, NY 2001. 7 J. L. Semmlow and W. Yuan IEEE Trans. Biomed. Engr. (In press). 8 W. Yuan, J. L. Semmlow. T. L. Alverez, and P.Munoz, IEEE Trans. Biomed. Engr. vol 46, pp. 1191-1198, 1999. 9 http://www.cis.hut.fi/projects/ica/fastica/fp.html 10 F.Hsu, T. Bahill and L. Stark Comput. Programs Biomed. vol 6, pp 108-116, 1976. 11 P. D. R. Gamlin and L. E. Mays J. Neurophysiol. vol 67, pp. 64-67, 1992. 12 L.E.Mays J Neurophysiol. vol. 51, pp. 1091-1108, 1984. 13 L.E. Mays, J.D.Porter, D.R. Gamlin and C.A. Tello “J. Neurophysiol. vol 56, pp. 1007-1021, 1986.
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0.17 for the same amplitude divergence movement. These numbers compare favorably with estimates obtained using a model-based analysis [5].
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Figure 1 Convergent (upward going) and divergent (downward) vergence responses and components. A) Averaged responses. B) Sustained components found by ICA. C) Transient components.
IV. DISCUSSION AND CONCLUSION The ratio of pulse-to-step amplitude is quite small in vergence eye movements as compared to the more rapid saccadic eye movements. Hsu et al. [10] estimated a ratio of approximately 9.5 for a 5 deg. saccadic movement. Figure 1C shows a ratio of approximately 0.55 for a 4 deg. convergence movement and
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