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