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1 Centre for Vision Research and Departments of Psychology and Biology, York University, Toronto, Ontario M3J 1P3; and 2 Montreal Neurological Institute and Department of Neurology and Neurosurgery, McGill University, Montreal, Quebec H3A 2B4, Canada
Crawford, J. Douglas and Daniel Guitton. Visual-motor transformations required for accurate and kinematically correct saccades. J. Neurophysiol. 78: 1447-1467, 1997. The goal of this study was to identify and model the three-dimensional (3-D) geometric transformations required for accurate saccades to distant visual targets from arbitrary initial eye positions. In abstract 2-D models, target displacement in space, retinal error (RE), and saccade vectors are trivially interchangeable. However, in real 3-D space, RE is a nontrivial function of objective target displacement and 3-D eye position. To determine the physiological implications of this, a visuomotor "lookup table" was modeled by mapping the horizontal/vertical components of RE onto the corresponding vector components of eye displacement in Listing's plane. This provided the motor error (ME) command for a 3-D displacement-feedback loop. The output of this loop controlled an oculomotor plant that mechanically implemented the position-dependent saccade axis tilts required for Listing's law. This model correctly maintained Listing's law but was unable to correct torsional position deviations from Listing's plane. Moreover, the model also generated systematic errors in saccade direction (as a function of eye position components orthogonal to RE), predicting errors in final gaze direction of up to 25° in the oculomotor range. Plant modifications could not solve these problems, because the intrisic oculomotor input-output geometry forced a fixed visuomotor mapping to choose between either accuracy or Listing's law. This was reflected internally by a sensorimotor divergence between input-defined visual displacement signals (inherently 2-D and defined in reference to the eye) and output-defined motor displacement signals (inherently 3-D and defined in reference to the head). These problems were solved by rotating RE by estimated 3-D eye position (i.e., a reference frame transformation), inputting the result into a 2-D-to-3-D "Listing's law operator," and then finally subtracting initial 3-D eye position to yield the correct ME. This model was accurate and upheld Listing's law from all initial positions. Moreover, it suggested specific experiments to invasively distinguish visual and motor displacement codes, predicting a systematic position dependence in the directional tuning of RE versus a fixed-vector tuning in ME. We conclude that visual and motor displacement spaces are geometrically distinct such that a fixed visual-motor mapping will produce systematic and measurable behavioral errors. To avoid these errors, the brain would need to implement both a 3-D position-dependent reference frame transformation and nontrivial 2-D-to-3-D transformation. Furthermore, our simulations provide new experimental paradigms to invasively identify the physiological progression of these spatial transformations by reexamining the position-dependent geometry of displacement code directions in the superior colliculus, cerebellum, and various cortical visuomotor areas.
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 C. R. Cassanello and V. P. Ferrera Visual remapping by vector subtraction: analysis of multiplicative gain field models. Neural Comput., September 1, 2007; 19(9): 2353 - 2386. [Abstract] [Full Text] [PDF]
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A. G. Constantin, H. Wang, J. C. Martinez-Trujillo, and J. D. Crawford Frames of Reference for Gaze Saccades Evoked During Stimulation of Lateral Intraparietal Cortex J Neurophysiol, August 1, 2007; 98(2): 696 - 709. [Abstract] [Full Text] [PDF]
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E. M. Klier, D. E. Angelaki, and B. J. M. Hess Human Visuospatial Updating After Noncommutative Rotations J Neurophysiol, July 1, 2007; 98(1): 537 - 541. [Abstract] [Full Text] [PDF]
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 B. T. Crane, J.-R. Tian, and J. L. Demer Shifts in Listing's Plane Produced by Vertical Axis Rotation: Sustained Ocular Torsion Due to Semicircular Canal Stimulation Invest. Ophthalmol. Vis. Sci., May 1, 2007; 48(5): 2076 - 2083. [Abstract] [Full Text] [PDF]
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F. Farshadmanesh, E. M. Klier, P. Chang, H. Wang, and J. D. Crawford Three-Dimensional Eye-Head Coordination After Injection of Muscimol Into the Interstitial Nucleus of Cajal (INC) J Neurophysiol, March 1, 2007; 97(3): 2322 - 2338. [Abstract] [Full Text] [PDF]
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L. Ren, A. Z. Khan, G. Blohm, D.Y.P. Henriques, L. E. Sergio, and J. D. Crawford Proprioceptive Guidance of Saccades in Eye-Hand Coordination J Neurophysiol, September 1, 2006; 96(3): 1464 - 1477. [Abstract] [Full Text] [PDF]
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J. Park, M. Schlag-Rey, and J. Schlag Frames of Reference for Saccadic Command Tested By Saccade Collision in the Supplementary Eye Field J Neurophysiol, January 1, 2006; 95(1): 159 - 170. [Abstract] [Full Text] [PDF]
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J. L. Demer and R. A. Clark Magnetic Resonance Imaging of Human Extraocular Muscles During Static Ocular Counter-Rolling J Neurophysiol, November 1, 2005; 94(5): 3292 - 3302. [Abstract] [Full Text] [PDF]
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B. T. Crane, J. Tian, and J. L. Demer Kinematics of Vertical Saccades during the Yaw Vestibulo-ocular Reflex in Humans Invest. Ophthalmol. Vis. Sci., August 1, 2005; 46(8): 2800 - 2809. [Abstract] [Full Text] [PDF]
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 L. M. OPTICAN Sensorimotor Transformation for Visually Guided Saccades Ann. N.Y. Acad. Sci., April 1, 2005; 1039(1): 132 - 148. [Abstract] [Full Text] [PDF]
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M. A. Smith and J. D. Crawford Distributed Population Mechanism for the 3-D Oculomotor Reference Frame Transformation J Neurophysiol, March 1, 2005; 93(3): 1742 - 1761. [Abstract] [Full Text] [PDF]
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J. D. Crawford, D. B. Tweed, and T. Vilis Static Ocular Counterroll Is Implemented Through the 3-D Neural Integrator J Neurophysiol, October 1, 2003; 90(4): 2777 - 2784. [Abstract] [Full Text] [PDF]
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E. M. Klier, H. Wang, and J. D. Crawford Three-Dimensional Eye-Head Coordination Is Implemented Downstream From the Superior Colliculus J Neurophysiol, May 1, 2003; 89(5): 2839 - 2853. [Abstract] [Full Text] [PDF]
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L. M. OPTICAN and C. QUAIA Distributed Model of Collicular and Cerebellar Function during Saccades Ann. N.Y. Acad. Sci., April 1, 2002; 956(1): 164 - 177. [Abstract] [Full Text] [PDF]
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D.Y. P. Henriques, J. D. Crawford, and T. Vilis The Visuomotor Transformation for Arm Movement Accounts for 3-D Eye Orientation and Retinal Geometry Ann. N.Y. Acad. Sci., April 1, 2002; 956(1): 515 - 519. [Full Text] [PDF]
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S. Glasauer, M. Dieterich, and Th. Brandt Central Positional Nystagmus Simulated by a Mathematical Ocular Motor Model of Otolith-Dependent Modification of Listing's Plane J Neurophysiol, October 1, 2001; 86(4): 1546 - 1554. [Abstract] [Full Text] [PDF]
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M. A. Smith and J. D. Crawford Implications of Ocular Kinematics for the Internal Updating of Visual Space J Neurophysiol, October 1, 2001; 86(4): 2112 - 2117. [Abstract] [Full Text] [PDF]
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H. Scherberger, J.-H. Cabungcal, K. Hepp, Y. Suzuki, D. Straumann, and V. Henn Ocular Counterroll Modulates the Preferred Direction of Saccade-Related Pontine Burst Neurons in the Monkey J Neurophysiol, August 1, 2001; 86(2): 935 - 949. [Abstract] [Full Text] [PDF]
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C. Lee, D. S. Zee, and D. Straumann Saccades From Torsional Offset Positions Back to Listing's Plane J Neurophysiol, June 1, 2000; 83(6): 3241 - 3253. [Abstract] [Full Text] [PDF]
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 J. D. Crawford, D. Y. P. Henriques, and T. Vilis Curvature of Visual Space Under Vertical Eye Rotation: Implications for Spatial Vision and Visuomotor Control J. Neurosci., March 15, 2000; 20(6): 2360 - 2368. [Abstract] [Full Text] [PDF]
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J. D. Crawford, M. Z. Ceylan, E. M. Klier, and D. Guitton Three-Dimensional Eye-Head Coordination During Gaze Saccades in the Primate J Neurophysiol, April 1, 1999; 81(4): 1760 - 1782. [Abstract] [Full Text] [PDF]
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E. M. Klier and J. D. Crawford Human Oculomotor System Accounts for 3-D Eye Orientation in the Visual-Motor Transformation for Saccades J Neurophysiol, November 1, 1998; 80(5): 2274 - 2294. [Abstract] [Full Text] [PDF]
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M. A. Smith and J. D. Crawford Neural Control of Rotational Kinematics Within Realistic Vestibuloocular Coordinate Systems J Neurophysiol, November 1, 1998; 80(5): 2295 - 2315. [Abstract] [Full Text] [PDF]
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C. Quaia and L. M. Optican Commutative Saccadic Generator Is Sufficient to Control a 3-D Ocular Plant With Pulleys J Neurophysiol, June 1, 1998; 79(6): 3197 - 3215. [Abstract] [Full Text] [PDF]
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D. Y. P. Henriques, E. M. Klier, M. A. Smith, D. Lowy, and J. D. Crawford Gaze-Centered Remapping of Remembered Visual Space in an Open-Loop Pointing Task J. Neurosci., February 15, 1998; 18(4): 1583 - 1594. [Abstract] [Full Text] [PDF]
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J. D. Crawford and D. Guitton Primate Head-Free Saccade Generator Implements a Desired (Post-VOR) Eye Position Command by Anticipating Intended Head Motion J Neurophysiol, November 1, 1997; 78(5): 2811 - 2816. [Abstract] [Full Text] [PDF]
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