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John Porrill, Paul A. Warren, Paul Dean; The role of torsional viscosity in saccadic listing's law. Journal of Vision 2003;3(9):430. doi: 10.1167/3.9.430.
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PURPOSE: During saccadic eye movements the torsional state of the eye satisfies Listing's law to good accuracy (e.g. Tweed & Vilis, 1990). Although various models have been proposed to account for this behaviour (e.g. Tweed & Vilis, 1987; Raphan, 1997) they rely on several simplifying assumptions, in particular isotropy of ocular viscosity. We show here that elevated torsional viscosity can ensure Listing's saccades in a model with fixed muscle pulleys. This result has implications for the interpretation of recent findings on muscle pulley movement (Kono, Poukens & Demer, 2002). METHODS: We use the Eyelab model of ocular mechanics (Porrill, Warren & Dean, 2000). EyeLab closely emulates Orbit (Miller & Shamaeva, 1995) and currently implements fixed muscle pulleys. EyeLab saccades between the vertices of a 60 x 60 degree square centred on primary position were generated by sending matched pulse-step commands to agonist muscles while temporarily de-innervating antagonist muscles. RESULTS: Under the assumption of isotropic viscosity, saccades in eccentric positions showed large torsional deviations from Listing's law. However approximately doubling torsional viscosity produced saccades consistent with empirical data in all positions. CONCLUSIONS: The hypothesis that there may be substantial anisotropy in effective ocular viscosity is not unreasonable since (i) the environment of the globe is anisotropic and (ii) an important component of viscosity during saccades comes from the extraocular muscles which are themselves anisotropic. Since a fixed pulley model can produce Listing's saccades with an appropriate value for torsional viscosity, we argue that quantitative interpretation of pulley movement is premature in the absence of firm viscosity data.
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