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Upper and Lower Eyelid Saccades Describe a Harmonic Oscillator Function

¹From the Institute of Physics, Federal University of Bahia, Bahia, Brazil; and the ²Department of Ophthalmology, Otorhinolaryngology, and Head and Neck Surgery, School of Medicine of Ribeirão Preto, University of São Paulo, São Paulo, Brazil.

PURPOSE. To determine whether experimentally measured upper and lower eyelid saccades can be fitted to a mathematical function.

METHODS. A charge-coupled device video camera connected to a personal computer was used to record upper and lower eyelid saccades accompanying 20° and 40° of vertical eye rotation in 19 normal adult subjects. Movement analysis was performed with software that calculated the center of a blue spot in each frame. The damped harmonic oscillator model was used to fit all saccadic functions obtained.

RESULTS. All downward and upward saccades of both upper and lower eyelids were fitted with the underdamped solution of the model with correlation coefficients ranging from 0.980 to 0.999 (mean = 0.995). It was possible to measure maximum velocity at any time, amplitude, and duration of the saccade movements. For the upper eyelid, downward saccades were faster than upward saccades, a difference that was not observed for the lower eyelid. For both the upper and lower eyelids, the velocity of upward and downward movements reached a peak at approximately 0.05/0.06 second and then decreased. For both the upper and lower eyelid saccades, there was good linear correlation between amplitude and velocity. Overshoots were detected in the downward saccades of both lids.

CONCLUSIONS. Normal upper and lower saccades are described by functions that are extremely well fitted by the underdamped solution of the harmonic oscillator model. Overshooting is a typical feature of normal downward saccades and can be explained by the elastic properties of the tissues.

This article has been cited by other articles:

				M. F. Falcao, J. M. C. Malbouisson, A. A. V. Cruz, and A. Messias The Relationship between Two Types of Upper Eyelid Movements: Saccades and Pursuit Invest. Ophthalmol. Vis. Sci., June 1, 2008; 49(6): 2444 - 2448. [Abstract] [Full Text] [PDF]