May 2008
Volume 49, Issue 13
Free
ARVO Annual Meeting Abstract  |   May 2008
A Mathematical Model of Upper Eyelid Motion During Spontanoeous and Reflex Blinks
Author Affiliations & Notes
  • S. A. De Paula
    Ophthalmology, HCFMRP-USP, Ribeirão Preto, Brazil
  • A. A. V. Cruz
    Ophthalmology, HCFMRP-USP, Ribeirão Preto, Brazil
  • D. M. Garcia
    Ophthalmology, HCFMRP-USP, Ribeirão Preto, Brazil
  • A. Messias
    Ophthalmology, HCFMRP-USP, Ribeirão Preto, Brazil
  • J. M. Malbouisson
    Physic, UFBA, Salvador, Brazil
  • Footnotes
    Commercial Relationships  S.A. De Paula, None; A.A.V. Cruz, None; D.M. Garcia, None; A. Messias, None; J.M. Malbouisson, None.
  • Footnotes
    Support  None.
Investigative Ophthalmology & Visual Science May 2008, Vol.49, 5262. doi:
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      S. A. De Paula, A. A. V. Cruz, D. M. Garcia, A. Messias, J. M. Malbouisson; A Mathematical Model of Upper Eyelid Motion During Spontanoeous and Reflex Blinks. Invest. Ophthalmol. Vis. Sci. 2008;49(13):5262.

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Abstract
 
Purpose:
 

To provide a mathematical description of upper eyelid motion in normal human subjects during spontaneous (SB) and reflex (RB) blinks.

 
Methods:
 

Upper eyelid motion during SB and RB of 21 normal subjects was registered with a video camera connected to a personal computer. The sample comprised 7 men and 14 women (age range, 25-62 years; mean = 35.1 ± 11.2 sd). SB were recorded for 1 minute. Reflex blinks were obtained with electrical stimulation (1.5 to 4mA) of the supraorbital nerve. A mathematical model based on the assumption that the down phase of the blinks is an accelerated movement and the up phase describes a critically damped harmonic oscillator function was used to fit 5 SB and 5 RB of each subject (total n = 210). The association of the two phases was possible by a parameter (τ) which characterizes the instant of time of the transition between the two regimes. (Figure)

 
Results:
 

All SB and RB were extremely well fitted by the model (the mean coefficient of determination was 0.98 ± 0,01 SD for SB and 0.99 ± 0,01 SD for RB). For both SB and RB occurred at 70-75% of the amplitude of the down phase.

 
Conclusions:
 

Normal SB and RB are described by functions that are well fitted by a model that includes an accelerated and critically damped harmonic oscillator phase. This mathematical model allows a fine analysis of the eyelid motion during blinks and may be clinically relevant for the detection of subtle abnormalities of the orbicularis and levator muscle function in a variety of diseases such as in Graves’ upper eyelid retraction and facial palsy. Figure - A blink fitted by the model: A is the amplitude of the down phase, indicates the transition of the two regimes and t (min) is the time of A.  

 
Keywords: eyelid • eye movements • computational modeling 
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